which equations has a solution for - 2/3 for x
A 3x=2
B x-1 =- 1/3
C x - 1/3 = 1
D 12x = -8

Answer:

10.8 units or [tex]2\sqrt{29}[/tex] units

Step-by-step explanation:

The line drawn connecting two points on a graph is known as a line segment.

The formula used to calculate the length of a line segment is derived from the Pythagorean Theorem

Length of a line segment: [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} -y_{1})^{2}}[/tex]

                                         = [tex]\sqrt{[2-(-2)]^{2} + (2-12)^{2} }[/tex]

                                         = [tex]\sqrt{(2+2)^{2} +(-10)^{2} }[/tex]

                                         = [tex]\sqrt{4^{2} + 100}[/tex]

                                         = [tex]\sqrt{16 +100}[/tex]

                                         = [tex]\sqrt{116}[/tex]

                                         = [tex]\sqrt{4}[/tex]×[tex]\sqrt{29}[/tex]

                                        = [tex]2\sqrt{29}[/tex] units

       Diagonal distance = 10.8 units (Rounded to 3 significant figures)

The factored form of the polynomial is x³( x + 2 ) - 1 ( 2x + 1 ).

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

Given that the polynomial is (x⁴)+(2x³)-2x-1. The expression will be factorized as below:-

E =  (x⁴)+(2x³)-2x-1.

E = x² ( x² + 2 ) -1 ( 2x + 1 )

Hence, the factorized form of the polynomial is x² ( x² + 2 ) -1 ( 2x + 1 ).

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he value of the expression cosB, sinB, sinA, tanB, tan A 4√15/17, 7/17, 4√15/17, 7/4√15 and 4√15/7

According to the trigonometry identity

tan Ф = opposite/adjacent

sin Ф = opposite/hypotenuse

cos Ф = adjacent/hypotenuse

From the given triangle;

AC = 7

AB = 17

BC = 4√15

Determine the following trigonometry given

cos B = BC/AB

cos B = 4√15/17

sinB = AC/AB

sin B = 7/17

sinA = cos B = 4√15/17

tan B = AC/BC

tan B = 7/4√15

tan A = BC/AC

tan A = 4√15/7

The value of the expression cosB, sinB, sinA, tanB, tan A 4√15/17, 7/17, 4√15/17, 7/4√15 and 4√15/7

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Answer:

Below

Step-by-step explanation:

51÷6= 51/6 = 8 3/6 = 8 1/2  = 8.5

6

Answer:

16

Step-by-step explanation:

we need to find how many servings can be made out of 12cups of lemonade if each serving is 3/4th of a cup . For that you just need to divide the total quantity of lemonade with each serving as ,

= 12 ÷ 3/4

= 12 * 4/3

= 4*4

= 16

And we are done!

The solution to the logarithmic equation is; x = 81/4

We want to solve the logarithmic equation;

log₃x + log₃4 - 2log3 = 2

From property of logarithms, we know that;

logₐ4 = log 4/log a

Similarly we know that;

log a + log b = log (ab)

log a - log b = log (a/b)

Thus;

log₃x + log₃4 - 2log₃3 = 2 is;

(log₃4x) - 2log₃3 = 2

(log₃4x) - log₃3² = 2

log₃(4x/3² ) = 2

3² = 4x/9

4x = 9 * 9

4x = 81

x = 81/4

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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, 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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Step-by-step explanation:

The given figure consists of some rectangles and square making up a bigger square.

As we know that,

area of rectangle= length*breadth, so

Area of rectangle A :-

A = lb

A = (6x+1)(x+2)

A = 6x(x+2)+1(x+2)

A = 6x² + 12x + x + 2

A = 6x² + 13x + 2

Area of rectangle B :-

A = (2x+2)(3x+1)

A = 2x(3x+1)+2(3x+1)

A = 6x² + 2x + 6x + 2

A = 6x² + 8x + 2

Area of rectangle C :-

A = (x+1)(x+2+2x+2)

A = (x+1)(3x+4)

A = 3x² + 4x + 3x + 4

A = 3x² + 7x + 4

Area of rectangle D :-

A = (3x+1)(3x+1)

A = 9x² + 3x + 3x + 1

A = 9x² + 6x + 1

Area of rectangle E :-

A = (6x+1-3x-1 )(2x+2+3x+1)

A = 3x(5x+3)

A = 15x² + 9x

Hence these are the simplified expressions making up the area of the whole square .

And we are done!

The asymptotes for the function are:

x = 5 and x = -1.

Option A is the correct answer.

A 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:

Step-by-step explanation:

After divide, the solution of the expression is,

⇒ x (x + 2y) / 5

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

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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Answer:

[tex]x=\dfrac{40}{11}, \quad y=-\dfrac{17}{11}[/tex]

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}-6x+4y=-28\\6x+7y=11\end{cases}[/tex]

To solve by the method of elimination, add the equations together to eliminate the terms in x.

[tex]\begin{array}{crcccl}&-6x & + & 4y & = & -28\\+&(6x & +&7y&=&\;\;\:11)\\\cline{2-6}\vphantom{\dfrac12}&&&11y&=&-17\\\cline{2-6}\end{array}[/tex]

Solve the equation for y:

[tex]\implies y=-\dfrac{17}{11}[/tex]

Substitute the found value of y into one of the equations and solve for x:

[tex]\implies 6x+7\left(-\dfrac{17}{11}\right)=11[/tex]

[tex]\implies 6x-\dfrac{119}{11}=11[/tex]

[tex]\implies 6x=\dfrac{240}{11}[/tex]

[tex]\implies x=\dfrac{240}{11\cdot 6}[/tex]

[tex]\implies x=\dfrac{40 \cdot \diagup\!\!\!\!\!6}{11\cdot \diagup\!\!\!\!\!6}[/tex]

[tex]\implies x=\dfrac{40}{11}[/tex]

Therefore, the solution is:

[tex]x=\dfrac{40}{11}, \quad y=-\dfrac{17}{11}[/tex]

An increasing exponential function is defined as follows:

y = a(1 + r)^x.

In which:

For this problem, the function is given as follows:

y = 20000(1.14)^t.

In which the parameters are given as follows:

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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.

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.

Now, we know the fractions would look like this:

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

Now, the fractions look like this:

Adding them together:

Now, we can convert this into a mixed number.

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

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

The part 6 kobo as required in the task content represents 1% of the whole, 6 naira.

It follows from the task content that the percentage of 6 naira which 6 kobo represents is to be determined.

On this note, it follows from currency conversion that 1 naira is equivalent to 100 kobo.

Hence , 6 naira = 600 kobo

The percent as required to be determined can be evaluated as follows;

6 / 600 = percent / 100.

Percent = 1%.

Ultimately, the fraction of 6 naira which 6 kobo represents is; 1%.

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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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Answer: 11 1/2 cm or 11.5 cm

Step-by-step explanation:

       To see how much taller the woman is than her son, we will subtract the son's height from the woman's height. We can convert these fractions into decimals to make it easier to subtract.

159 1/4 - 147 6/8 = 159.25 - 147.75 = 11.5 = 11 1/2 cm

When the value of c is 13 and d = 2, then the value of the expression

0. 5c -2. 7d is 1.1

It is given that the expression for the given value of the variables is

0. 5c -2. 7d

If the value  of c is 13 and the value of d is 2, then the value of expression is

0. 5c -2. 7d

putting the value of 'c' and 'd'

0. 5c -2. 7d = 0.5(13) - 2.7(2)

0. 5c -2. 7d = 6.5 - 5.4

0. 5c -2. 7d = 1.1

so, the value of the expressions for the given value of the variables  i.e., c = 13 and d = 2 is 1.1

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

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

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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Step 1: Solve the equation V(t) = 4 for t. To solve the equation V(t) = 4 for t, divide both sides of the equation by 11, which gives us t = 4/11.

Step 2: Interpret the result. The value of t = 4/11 tells us that when the temperature of the water in the cooler is 4/11, the volume of the water is 4.

Therefore, the value of t = 4/11 tells us that when the temperature of the water in the cooler is 4/11, the volume of the water is 4.

Since there are more molecules in larger volumes than smaller ones, the pace of cooling will be slower if the water's volume is increased. Losing the heat energy from all the molecules will therefore take longer.

The question is incomplete and requires further explanation. For the mentioned part, the information is not significant to determine volume of water in the cooler.

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The equation of the graphed line is expressed as: A. y + 5 = -3/2(x - 4).

The equation that represents a line can be written in point-slope form as y - b = m(x - a), where a point on the line is (a, b) and the slope is m.

Slope (m) = rise/run = -3/2

Substitute a point on the line (a, b) = (4, -5) and m = -3/2 into y - b = m(x - a):

y + 5 = -3/2(x - 4)

The equation is: A. y + 5 = -3/2(x - 4).

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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.

Answer:

Step-by-step explanation: the answer would be 60.

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

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

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

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

⇒ f ' (- 10) = 0.035

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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increase=(30/100)*50

=15

so,

value after increase

=50+15

=65

Answer:

x=5

Step-by-step explanation:

distribute: 6x-12=4x-2

subtract 4x and add 12 on both sides: 2x=10