if a triangle is other side is 7m and other side is 12m what is the other side going to be

Answers

Answer 1

If a triangle has one side of 7 meters and another side of 12 meters, the other side is approximately 13.928 meters long.

A triangle is a three-sided polygon that has three angles and three sides. The sides of a triangle are connected by its angles, and the sum of the angles of a triangle is always equal to 180 degrees. The length of the sides of a triangle affects the size of its angles, and the size of its angles affects the length of its sides.

Now, in the case of a triangle where one side is 7 meters and another side is 12 meters, the length of the third side can be calculated using the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, it can be written as

=> a² + b² = c²,

where a and b are the lengths of the two sides, and c is the length of the hypotenuse.

Using the Pythagorean theorem, we can find the length of the third side of the triangle. Let's call the length of the third side "x". So,

=> x² = 7² + 12² = 49 + 144 = 193.

Taking the square root of both sides, we get

x = √(193) = 13.928.

So, the third side of the triangle is approximately 13.928 meters long.

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Related Questions

What is 16.15549442 rounded to the nearest 10th

Answers

Answer:

Below

Step-by-step explanation:

16.15549442 rounded to the nearest 10th is 16.2

Answer:

16.2

Step-by-step explanation:

Find the number in the tenth place 1 and look one place to the right for the rounding digit 5. Round up if this number is greater than or equal to 5 and round down if it is less than 5



When Carmen leaves school at the end of the day, she walks to soccer practice at the park and then to the hobby shop before walking home. How many blocks does Carmen walk after school in all?

Answers

Since 1 unit on the map represents 1 block, Carmen walks 22 blocks after school.

To find the total distance Carmen walks, we need to find the distance between each of the four locations: school, park, hobby shop, and home.

The distance between two points (x1, y1) and (x2, y2) in a plane can be calculated using the Pythagorean theorem:

d = √((x2 - x1)² + (y2 - y1)²)

First, let's find the distance between the school and the park:

d = √((-5 - (-5))² + (4 - (-3))²) = √((0)² + (7)²) = √(49) = 7

Next, let's find the distance between the park and the hobby shop:

d = √((3 - (-5))² + (-3 - (-3))²) = √((8)² + (0)²) = √(64) = 8

Then, let's find the distance between the hobby shop and home:

d = √((3 - 3)² + (-3 - 4)²) = √((0)² + (7)²) = √(49) = 7

Finally, the total distance Carmen walks after school is the sum of the distances between the four locations:

d = 7 + 8 + 7 = 22

Since 1 unit on the map represents 1 block, Carmen walks 22 blocks after school.

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There is an antenna on the top of a building. From a location 319 feet from the base of the building, the angle of elevation to the top of the building is measured to be 7°. From the same location, the angle of elevation to the top of the antenna is measured to be 5° more than the angle of elevation to the building. Find the height of the antenna. Round the height to the nearest 10th of a foot. No units necessary.

Answers

Answer:

Step-by-step explanation:

Let's call the height of the building "h", and the height of the antenna "a". From the given information, we have:

Angle of elevation to the top of the building = 7°

Angle of elevation to the top of the antenna = 7° + 5° = 12°

We can use tangent to find the height of the building and the height of the antenna. The tangent of an angle is equal to the height divided by the distance, so we have:

tan(7°) = h / 319

And

tan(12°) = (a + h) / 319

We can use the first equation to solve for h:

h = 319 * tan(7°)

And use the second equation to solve for a:

a = 319 * tan(12°) - h

Now that we have expressions for h and a, we can use the tangent function to find the values for h and a. We can use a calculator or look up the values in a table of tangent values.

Rounding the height of the antenna to the nearest 10th of a foot, we find:

a = 319 * tan(12°) - h = approximately 69.9 feet.

PLEASE PLEASE PLEASE HELP ME!!!!

A plane, 50 miles away from its
destination, is flying toward the airport at
an altitude of 30,500 feet. Later, this same
plane is 20 miles from the airport and has
descended to an altitude of 18,000 ft.

How far has the plane flown?

Answers

Answer:

Below

Step-by-step explanation:

The plane's distance is the hypotenuse of a right triangle with legs of

(50 -20)mi = 30 miles     and     30500 - 18000 = 12500 ft

                             for consistent units  12500ft/5280ft/mile = 2.36742 miles

Now just use Pythagorean theorem

Hypotenuse^2 = leg1^2 + leg2^2

               h^2    = 30^2 + 2.36742^2

                   h = ~ miles 30.093 miles  ( note that the vertical descent distance does not matter much)

    (this is 158 892 feet)

question 10b. how many different ways can the combination of 5 heads and 5 tails occur? in other words, the coefficient for this term in the binomial equation is

Answers

There are 252 different ways that the combination of 5 heads and 5 tails can occur. The coefficient for this term in the binomial equation is [tex]\mathrm{10C_x}[/tex]

What do you mean Binomial Theorem?

The binomial theorem is a mathematical result that describes the expansion of the power of a binomial expression. A binomial expression is an expression that consists of two terms, such as (x + y) or (a + b). The binomial theorem states that for any positive integer n, the expansion of the expression (x + y)^n will contain exactly n+1 terms, each of which is a power of x multiplied by a coefficient.

If we want 5H and 5T,hence there are 10 trials.

Hence it is similar to choosing 5 out of 10 or choosing 2 similar sets of 5 each out of 10 in 10C5 ways:

[tex]$\mathrm{10C_5=\frac{10!}{5!(10-5)!}=252}[/tex]

The coefficient is actually the number of ways of choosing the 5 out of 10.

So similarly the coefficient of:

[tex]$\mathrm{coeff(p^xq^{10-x})=10C_x=\frac{10!}{x!(10-x)!}}[/tex]

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Help Help! Due in an hour!

Answers

Answer:

gradient= -1 1/5

Step-by-step explanation:

1st point : (3,-3)

2nd point : (-2,3)

gradient= rise/run

= -3-3/3-(-2)

=-6/5

=-1 1/5

5,8,11,14

What term comes next?

What formula can we use?

What is the 10th term?

What formula can we use to find the 10th term?

Answers

Answer:

(1) 17 (2) +3 every new term (5+3) or 8+3) or 5+x*3

we can use this as to find 2nd number (1) as its first one to be found 5+3(1) 5+3=8

(3) 5+9*3=5+27 , 32

(4) 5+9*3 ,

we can test this out by counting

starter: 5

1 -> 8

2-> 11

3-> 14

4 -> 17

5 -> 20

6 -> 23

7 -> 26

8 -> 29

9 -> 32 (realisticly it is still the 10th but it's the 9th after the 1st.)

Step-by-step explanation:

the last me Else ved Adventure Island, she rode her favorite roller coaster, Maximum Velocity, d times Maxmum Velocity has ride time of 145 seconds. Write on sixpression that shows how many seconds Elise spn riding Maximum city the last time she visited Adventure island.

Answers

The total time Elise spent riding Maximum Velocity on her last visit to Adventure Island can be expressed as: 145d seconds.

What is expression?

In mathematics, an expression is a combination of numbers, symbols, and/or variables that can be evaluated to produce a value. Expressions can also include functions, such as sin(x) or log(y), as well as operators like multiplication (*), division (/), and exponentiation (^). Expressions can be used to represent mathematical formulas, equations, and relationships in a concise and symbolic way, making them easier to work with and manipulate using mathematical tools and techniques.

Here,

If we know the value of d, we can calculate the total time Elise spent riding Maximum Velocity by simply multiplying the ride time by the number of rides.

For example, if Elise rode Maximum Velocity 3 times, the total time she spent on the ride would be:

145 seconds/ride x 3 rides = 435 seconds

So, using the expression from the previous answer, we can substitute the value of d to get the actual calculation:

Total time = 145d seconds

For instance, if Elise rode Maximum Velocity 5 times during her last visit, the total time spent on the ride would be:

Total time = 145 x 5 = 725 seconds

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This graph represents one of the following descriptions. Which one?

a. A phone loses 80% (20% left) of its value every year after purchase: the relationship​ between​ ​the​ ​number​ ​of​ ​years​ ​since purchasing​ ​the​ ​phone​ ​and​ ​the​ ​value​ ​of​ ​the​ ​phone.

b. The number of stores a company triples approximately every 5 years: the relationship ​between​ ​the number of years and the​ ​number​ ​of​ ​stores​.

c. A camera loses 40% (60% left) of its value every year after purchase: the relationship​ between​ ​the​ ​number​ ​of​ ​years​ ​since purchasing​ ​the​ ​camera​ ​and​ ​the​ ​value​ ​of​ ​the​ ​camera.

Answers

It is c because the value is decreasing by 40 percent each time

if you wanted to test, using a 5% significance level, whether or not a specific slope coefficient is equal to one, then you should

Answers

The significance level is an factor in hypothesis testing and helps us determine the likelihood of making a Type I error.

A significance level is a critical value in hypothesis testing that determines the probability of making a Type I error, which is rejecting a null hypothesis when it is actually true.

To test whether a specific slope coefficient is equal to one, we can perform a t-test to see if the estimated slope coefficient is significantly different from one at a certain significance level.

The null hypothesis for this test is that the slope coefficient is equal to one, and the alternative hypothesis is that it is not equal to one.

We can use the t-statistic to determine the level of significance for the estimated slope coefficient. The t-statistic is calculated by dividing the estimated slope coefficient minus one by the standard error of the slope coefficient.

The resulting t-value is then compared to the critical t-value from a t-distribution table with the appropriate degrees of freedom.

If the t-value is less than the critical t-value, we fail to reject the null hypothesis and conclude that the estimated slope coefficient is not significantly different from one at the 5% significance level.

On the other hand, if the t-value is greater than the critical t-value, we reject the null hypothesis and conclude that the estimated slope coefficient is significantly different from one at the 5% significance level.

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To solve for the lengths of the right triangle sides, which equation is correct?

Answers

According to the Pythagorean theorem [tex]c^{2} = a^{2} + b^{2},[/tex] Option D is accurate since[tex](2x-10)^{2} + x^{2} = (3x)^{2}.[/tex]

The Pythagorean Theorem: What is it?

The Pythagorean Theorem, also known as the Equation, is the fundamental Cartesian geometry relationship between a right triangle's three sides.

The Pythagorean Theorem states that the sum of the squares that thus span the angles of a right triangle is equal to the number that crosses the right triangle's rectangular prism opposite any right angle. Sometimes it is expressed using the general geometric notation [tex]a^{2} + b^{2} = c^{2}[/tex]

Given,

according to the diagram

in right triangle

[tex](base )^{2} + (perpendicular) ^{2} = (hypotenuse)^{2}[/tex]

[tex](2x-10 )^{2} + x^{2} = (3x)^{2}[/tex]

According to the Pythagorean theorem [tex]c^{2} = a^{2} + b^{2}[/tex],

Option D is accurate since [tex](2x-10)^{2} + x^{2} = (3x)^{2}.[/tex]

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Can you please find the perimeter of the blueprint room in feet? And could you find the area of the blueprint room in sqaure feet.

2 of the walls are 11 and 11, there's 3 more walls to find. Break thr room into rectangles and then do Base × height then add both rectangles together.

Answers

Based on the information in the graph, it can be inferred that the perimeter of the room is 44 feet.

How to find the perimeter of the room in the graph?

To find the perimeter of the room in the graph we must apply the following formula:

Perimeter = base + upper base + left side + right side

According to the above, if each of the sides is 11 feet long we have two alternatives

perimeter = 4 * 11perimeter = 11 + 11 + 11 + 11

In both operations the result would be 44.

Based on the above, the perimeter of the room would be 44 feet.

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Where are the asymptotes for the following function located?
f (x) = StartFraction 14 Over (x minus 5) (x + 1) EndFraction
x = –1 and x = 5
x = –1 and x = 14
x = 1 and x = –5
x = 14 and x = 5

Answers

The asymptotes for the function are:

x = 5 and x = -1.

Option A is the correct answer.

What is a function?

function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

There are three types of asymptotes.

1) Horizontal asymptotes

2) Vertical asymptotes

3) Oblique asymptotes

Now,

Horizontal asymptotes.

f(x) = 14 / (x - 5)(x + 1)

f(x) = 14/(x² + x - 5x - 5)

f(x) = 14 / (x² - 4x - 5)

The degree of the numerator is less than the denominator.

So,

Horizontal asymptotes.

y = 0

i.e

The x-axis.

Now,

Vertical asymptotes

f(x) = 14 / (x - 5)(x + 1)

Simplify in its lowest term.

Now,

Set the denominator to zero.

So,

(x - 5) ( x + 1) = 0

x - 5 = 0

x = 5

And,

x + 1 = 0

x = -1

Now,

Since there is a horizontal asymptote there are no oblique asymptotes.

Thus,

The asymptotes for the function are:

x = 5 and x = -1.

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Answer:

A. x = -1 and x = 5

Step-by-step explanation:

A punter for a football team is trying to determine the optimal angle for striking the football off his foot—this is called the launch angle. Using video, his coach records a number of punts kicked using different launch angles and the height in feet for each punt. Using computer software, the coach achieves a linear model by taking the log of each launch angle and plotting against the log of each height.

A graph titled log (height) versus log (launch angle) has log (launch angle) on the x-axis, and log (height) on the y-axis. The points increase in a line with positive slope.

A graph titled residuals versus log (launch angle) has log (launch angle) on the x-axis, and residual on the y-axis. The points curve down, and then up.

Based on the scatterplot and residual plot, which type of model would best summarize the relationship between launch angle and punt height?

A linear model is appropriate because the residual plot shows a random scatter.
A logarithmic model is appropriate because logarithms were used to transform the data sets.
A power model is appropriate because the scatterplot of log angle and log height is roughly linear.
An exponential model is appropriate because the scatterplot of log angle and log height is roughly linear.

Answers

Correct answer is: A power model is appropriate because the scatter plot of log angle and log height is roughly linear.

What is Scatter plot?

The graphs known as scatter plots show how two variables within a data collection relate to one another. Both a two-dimensional plane and the Cartesian system are used to represent the data points. The Y-axis is used to plot the dependent variable, while the X-axis is used to represent the independent variable or characteristic. Data points are shown on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another.

According to Scatter plot, the relation between log(height) and log(launch angle) is linear.

Let, us consider log(height) = m log(launch angle) + b

Height = [tex]10^{(log(launch angle))}[/tex] + b

Height = [tex](launch angle)^{m}[/tex] + 10ᵇ

Height = (10)ᵇ + [tex](launch angle)^{m}[/tex]

Thus, the relation of height and launch angle is in power mode.

Correct answer is: A power model is appropriate because the scatter plot of log angle and log height is roughly linear.

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Jara wants to select a negative integer that is closer to zero than -3 on the number line. How many possible choices does she have?

Answers

Jara has 2 alternatives: -2 and -1 A number line is a diagram that depicts numbers,

As we walk along the line from left to right, the numbers rise. Positive numbers are often to the right and negative numbers to the left of zero, which is typically in the middle of the line.

Jara wants to choose a negative number that, in this instance, is closer to zero than -3. This suggests that instead of choosing -3, she should choose a negative integer that is situated nearer to zero on the number line.

-2 and -1 are the two negative numbers that are nearer to zero than -3. On the number line, these values are to the right of -3 and are nearer to zero than -3.

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Find the approximate side lengths and perimeter of quadrilateral WXYZ. If necessary, round your answers to the nearest hundredth.


The approximate length of segment WX is
[tex]\left[\begin{array}{ccc}2\\4. 12\\4. 47\\5\end{array}\right][/tex]

The approximate length of segment XY is
[tex]\left[\begin{array}{ccc}2\\4. 12\\4. 47\\5\end{array}\right][/tex]

The approximate length of segment YZ is
[tex]\left[\begin{array}{ccc}2\\4. 12\\4. 47\\5\end{array}\right][/tex]

The approximate perimeter of quadrilateral WXYZ is [tex]\left[\begin{array}{ccc}14\\14. 47\\15\\15. 59\end{array}\right][/tex]

Answers

The side length of quadrilateral WXYZ are

|WX| = 4.47

|XY| = 2

|YZ| = 4

|ZW| = 4

The perimeter of quadrilateral WXYZ is 14.47 units.

The four points W, X, Y, and Z are located at ponts (3,1), (7,-1), (7,-3), and (3,-3) respectively.

To find the distance between two points, A and B, with coordinates (x1, y1) and (x2, y2) respectively, we use the formula:

|AB|=√(x2 – x1)² + (y2 – y1)²

The side lengths of the quadrilateral are calculated using this formula.

|WX| = √(– 1 – 1)² + (7 – 3)² = 4.47

|XY| = √(– 3 – (– 1))² + (7 – 7)² = 2

|YZ| = √(– 3 – (– 3))² + (3– 7)² = 4

|ZW| = √(– 3 – 1)² + (3 – 3)² = 4

Hence, the Perimeter of the quadrilateral = |WX| + |XY| + |YZ| + |ZX| = 4.47 + 2 + 4 + 4 = 14.47 units

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If 42 push ups can be done in 3 minutes how many push ups in 5 minutes

Answers

Answer:

Step-by-step explanation:

3 divided by 42 = 14 so 14 times 5 = 70

Answer: 70

Step-by-step explanation:

Since 42 push-ups can be done in 3 minutes, then you would divide

42 by 3 and get 14.

Once you get that, you would need to Multiply 14 by 5 and get as your final answer, 70

what are the excluded values?

Answers

After divide, the solution of the expression is,

⇒ x (x + 2y) / 5

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒ (x² - 4y²) ÷ (5x - 10y) / x

Now, We an simplify as;

⇒ (x² - 4y²) ÷ (5x - 10y) / x

⇒ (x² - (2y)²) ÷ (5x - 10y) / x

⇒ (x - 2y) (x + 2y) ÷ 5(x - 2y) / x

⇒ (x - 2y) (x + 2y) × x/ 5 (x - 2y)

⇒ x (x + 2y) / 5

Thus, The solution of the expression is,

⇒ x (x + 2y) / 5

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Determine the solution to the inequality. one fourth times the absolute value of the quantity x plus 1 end quantity is greater than or equal to 4 x ≥ −1 or x ≥ 17 x ≤ −17 or x ≥ 15 x ≤ −9 or x ≥ 7 x ≤ −2 or x ≥ 0

Answers

The solution of the inequality will be x ≥ -1/4.

What is inequality?

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that inequality is one-fourth time the absolute value of the quantity x plus 1 end quantity.

The given inequality can be solved as below:-

4x ≥ −1

4x ≥ −1

x ≥ -1 / 4

Therefore, the value of x for the inequality is - 1 / 4.

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Answer:

The answer Is B)  x ≤ −17 or x ≥ 15

Step-by-step explanation:

Find the ratios of the side lengths of ΔHIJ to the corresponding side lengths of ΔEFG. Then determine the ratio of the area of ΔHIJ to the area of ΔEFG.

Answers

The ratio of the sides are 1:2 and the ratio of the areas is 1:4

What is similarity?

Two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other, this is called similarity.

Since, the side lengths of the triangles are not given, let us consider,

Δ HIJ =

HI = 12, IJ = 14, HJ = 16

And,

Δ EFG =

EF = 24, FG = 28, EG = 32

Therefore, the ratios of the side lengths of Δ HIJ to the corresponding side lengths of Δ EFG are;

HI / EF = 12/24 = 1/2

IJ / FG = 14/28 = 1/2

HJ / EG = 16/32 = 1/2

Since, we get all the ratios equal, therefore, the Δ HIJ is similar to Δ EFG

With a scale factor of 1/2,

The ratio of area is found by squaring the scale factor for length.

Therefore,

ar(Δ HIJ) / ar(Δ EFG) = (1/2)² = 1/4

Hence, the ratio of the sides are 1:2 and the ratio of the areas is 1:4

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Please help, I’m not good at math

Answers

Step-by-step explanation:

a regular function finds the functional result y to a given x value.

the inverse function finds the original x to a given y value.

g^-1(1) is therefore the x-value, so that g(x) = 1.

so, we look through the value pairs. where do we find y = 1 ? ah, in the pair (9, 1).

x = 9 lead to the functional result y = 1.

therefore, g^-1(1) = 9

h(x) = y = -3x - 14

in other words, h(x) expresses y in terms of x.

h^-1(x) expresses x in terms of y.

so, we want to transform the functional equation, so that it says "x = ...." :

y = -3x - 14

y + 14 = -3x

x = (y + 14)/-3

and to turn it into regular function notation, we rename x to y and y to x :

y = h^-1(x) = (x + 14)/-3 = (-1/3)(x + 14)

(h○h^-1)(x) = x

always.

in that process we find first what original input value for h lead to the value of x. and then we use that as input value for h. and, of course, we have to get x as result.

to check here in our case

(h○h^-1)(-5) = -5

h^-1(-5) = (-5 + 14)/-3 = 9/-3 = -3

h(-3) = -3×-3 - 14 = 9 - 14 = -5

there you have it.

Find the distance between the points (3, 8, 2)and (3,8,2)

Answers

The solution is,  the distance between the points (3, 8, 2)and (3,8,2) is 0.

What is Distance Formula?

The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 3 dimensional plane, the distance between points (X1, Y1, Z1) and (X2, Y2, Z2) is given by:

d=√(x2−x1)2+(y2−y1)2+(z2−z1)2

here, we have,

the given points are,

(3, 8, 2)and (3,8,2)

so, distance = √(x2−x1)2+(y2−y1)2+(z2−z1)2

solving we get,

d= 0

as the points are same.

Hence, The solution is,  the distance between the points (3, 8, 2)and (3,8,2) is 0.

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Which of the following is the correct answer?

Answers

From the given data value of function f ' (- 10) is,

⇒ f ' (- 10) = 0.035

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable.

Given that;

Table for the given data is shown.

Now, We have to find the value of f ' (- 10).

Since, - 10 is in between - 11 and - 9.

Hence, The slope given the value of f ' (- 10) as;

⇒ f ' (- 10) = (1.12 - 1.05) / (- 9 - (- 11))

⇒ f ' (- 10) = (0.07/2)

⇒ f ' (- 10) = 0.035

Thus, From the given data value of f ' (- 10) is,

⇒ f ' (- 10) = 0.035

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Suppose that C and D are points on the number line.
If CD=6 and D lies at 4, where could C be located?
If there is more than one location, separate them with commas.

Answers

On the number line if CD = 6 then the point C lied either on -2 or 10.

What is a number line?

A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it. Just to refresh your memory, the whole number is a collection of numbers that contains both zero (0) and all counting numbers (1, 2, 3,4,5,6), whereas the natural number is a collection of all counting numbers (1, 2, 3,4, 5, 6).

Given that, CD = 6 and D lies at 4.

Then C would lie either on the left or right side of the point D.

On left the point C would be:

4 - 6 = -2

On right the point C would be at:

4 + 6 = 10

Hence, on the number line if CD = 6 then the point C lied either on -2 or 10.

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Write a function rule for "The output is one more than twice the input x ."

Answers

The function rule for "The output is one more than twice the input x ." is y= 2x+ 1.

What is Expression?

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.

given:

"The output is one more than twice the input x ."

let the output by y.

Then, the mathematical expression for the above statement is

= 1+ 2x

Thus, the output is, y= 2x+ 1.

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I need help with this question(Divide.
Express your answer as a decimal.
51
÷
6
=
51÷6) the first person answer get 10 points thanks for the help!

Answers

Answer:

Below

Step-by-step explanation:

51÷6= 51/6 = 8 3/6 = 8 1/2  = 8.5

6

the sum of three fractions is 6.if 18/7 and5/6 are two of the fractionsfind the third fraction

Answers

What is a fraction?

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

First, we need to solve for a common denominator.

What is a common denominator?

A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.

To get the common denominator between [tex]\frac{18}{7}[/tex] and [tex]\frac{5}{6}[/tex], we multiply their denominators.

7 × 6 = 42

Now, we know the fractions would look like this:

[tex]\frac{?}{42} \frac{?}{42}[/tex]

To solve for the numerators, we can use these equations:

18 × 6 = 1085 × 7 = 35

Now, the fractions look like this:

[tex]\frac{108}{42}[/tex] and [tex]\frac{35}{42}[/tex]

Adding them together:

[tex]\frac{108}{42} +\frac{35}{42} = \frac{143}{42}[/tex]

Now, we can convert this into a mixed number.

[tex]\frac{143}{42} = 3\frac{17}{42}[/tex]

Now that we have this, we can subtract that from 6 to get the missing value.

[tex]6 - 3\frac{17}{42}[/tex][tex]=2\frac{25}{42}[/tex]

Therefore, the third fraction is [tex]2\frac{25}{42}[/tex].

Find the first 5 terms of each sum and compute S5.

Answers

The total of all S5 terms, the first five terms, and the two different types of mathematical advancement equal 105.5.

what is arithmetic progression ?

An arithmetic progression whenever there is a steady difference amongst terms that follows to each other in a series. For instance, following new number 5, 7, 9, 11, 13, and 15 is an example of an exponential function with a limitation of two. A progress with a set tolerance among any two consecutive numbers generally referred to as a "arithmetic progression" (A.P.). Two types of mathematical progress are possible: series in arithmetic with a finite length A finite mathematical progression is a progression with a finite number of terms. The soon, late, allowance, and quantity of terms may all be calculated using the entries in the series.

given

The geometric sequence 8,12,18,27,81/2's 

first five partial sums, S1,S2,S3,S4, and S5, must be found in order.

S1=8

S2=8+12=20

S3=8+12+18=38

S4=8+12+18+27=65

S5=8+12+18+27+81/2=105.5 as a result.

The total of all S5 terms, the first five terms, and the two different types of mathematical advancement equal 105.5.

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The proportional relationship between the number of sweaters a clothing store buys and sells, s, and the profit, in dollars and cents, that it makes off those sweaters, can be represented by the equation p=23sp=23s. What is the profit in dollars and cents that the store makes per sweater?

Answers

The profit in dollars cent that the store makes per sweater is $23.

In general, the profit is defined as the amount gained by selling a product, which should be more than the cost price of the product. It is the gain amount from any kind of business activity. In short, if the selling price (SP) of the product is more than the cost price (CP) of a product, then it is considered as a gain or profit. It describes the financial benefit obtained if the revenue from the business activity exceeds the taxes, expenses, and so on, which are involved in sustaining business activities.

Through this information, we can calculate.

[tex]\because p=23 \mathrm{~s} \text {. }[/tex]

when S=1, we could get:

[tex]\therefore P=23 \times 1=23$ \{Operation\}.[/tex]

Therefore, the profit in dollars cent that the store makes per sweater is $23.

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Two variables, y and x, are inversely proportional.
When x = 12, y = 10.

(a) Find an equation that relates y and x.

(b) Given that x and y are positive integers, find the values of x and y when y=x+7.

I don’t understand this question at all!

Answers

Answer:

x = 8, y = 15

Step-by-step explanation:

Part (a)

If x and y are inversely proportional, the relationship can be expressed as
[tex]y \propto \dfrac{1}{x}\\\\\rm{(or \;alternatively\;x \propto \dfrac{1}{y})\\\\}\\\\[/tex]

The above relationship [tex]y \propto \dfrac{1}{x}[/tex] can be written as an equation:

[tex]y = \dfrac{k}{x} \codts\cdots(1)[/tex]

where the constant k is known as the constant of proportionality

Part (b)

We know that when x = 12, y = 10

Plugging this into equation (1):

10 = k/12

k/12 = 10

k = 12 x 10

k = 120

So the proportional equation (1) becomes
y = 120/x

We are now given the equation
y = x + 7

Substitute y = 120/x

120/x = x + 7

Subtract 120/x from both sides
0 = x + 7 - 120/x

Multiply by x both sides;
0 = x² + 7x - 120

Or,
x² + 7x - 120 = 0

This is a quadratic equation which we can solve by factoring. There are various techniques. One of them is to find two factors of 120 and see if their sum or difference can be made -7

Factors of 120 are:
[tex]1,\:2,\:3,\:4,\:5,\:6,\:8,\:10,\:12,\:15,\:20,\:24,\:30,\:40,\:60,\:120[/tex]

Take the two factors, a and b that will add or subtract to -7 and multiply to -120

We see that if we choose a = -15 and b = 8

a + b = -7

and

a x b = -120

The solution to the equation is x = 8 or x = -15

Since we are told that both x and y are positive, we can ignore x = -15 and just state that x = 8 is a solution

If x = 8, substitute this in y = x + 7 to get

y = 8 + 7 = 15

This checks with our original proportionality equation:
y = 120/x = 120/8 = 15

Answer
x = 8, y = 15

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