Express the function graphed on the axes below as a piecewise function.

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

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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Solving a system of equations we will see that they sold 184 adult tickets.

We know that the theater sells two types of tickets:

adult tickets for $8 and child tickets for $4.

The variables that we will use are:

x = number of adult tickets sold.

y = number of child tickets sold.

Then we can write the cost revenue equation as:

8x + 4y = 1900

And the total number of tickets sold is 291, then:

x + y = 291

Then we have a system of equations:

8x + 4y = 1900

x + y = 291

We can isolate y on the second equation to get:

y = 291 - x

Replacing that on the other equation we will get:

8x + 4*(291 - x) =1900

4x + 1164 = 1900

4x = 1900 - 1164 =736

x = 736/4 = 184

They sold 184 adult tickets.

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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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Answer:

b = 10

Step-by-step explanation:

substitute x = 10 into the equation

b = [tex]\frac{2(10)^2(10-5)}{10(10)}[/tex]

  = [tex]\frac{2(100)(5)}{100}[/tex] ← cancel 100 on numerator/ denominator

 = 2(5)

 = 10

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

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:

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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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

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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The expression equivalent to given expression is -1/(4x²+9x+5).

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is 4/(4x+5) -1/(x+1)

Here, 4(x+1)-(4x+5)/(4x+5)(x+1)

= (4x+4-4x-5)/(4x²+5x+4x+5)

= -1/(4x²+9x+5)

Therefore, the expression equivalent to given expression is -1/(4x²+9x+5).

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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:

degree is 2

standard form is

-x^2+2x-8

classification is trinomial

leading coeff is -1

hope i helped

Step-by-step explanation:

Lastly, the 7 does not need to be multiplied so it remains at 7. After expanding and grouping like terms, we are left with 8h^3 - 32h^2 + 73h - 27.To solve the given equation, we first need to expand the terms in the parentheses and group like terms together.

= 8h^3 - 32h^2 + 73h - 27

To solve the given equation, we first need to expand the terms in the parentheses and group like terms together. We start by expanding the first term (8h - 4) which gives us 8h + -4. Then, we move on to the second term (4h^3 - 8h^2 + 9h + 7). We start by multiplying the 4h to the third power, which gives us 4h^3. Then, we multiply the 8h squared, which gives us -8h^2. Then, we multiply the 9h, which gives us 9h. Lastly, the 7 does not need to be multiplied so it remains at 7. After expanding and grouping like terms, we are left with 8h^3 - 32h^2 + 73h - 27.

The complete question is :

Simplify the expression : 8h - 4 + (4h to the third power - 8h squared + 9h + 7)

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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

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

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]

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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Lee estimated he would need a total number of ten bags of sand, which is 25% more than the eight bags he actually used.

Lee estimated he would need 10 bags of sand.

To calculate how many number of bags of sand Lee estimated he would need, we must first find 25% of 8 bags.

25% of 8 is 2, so Lee estimated he would need 8 + 2 = 10 bags of sand.

Lee estimated he would need a total of ten bags of sand, which is 25% more than the eight bags he actually used.

Lee was filling a new sandbox and he used his best judgement to estimate how many bags of sand he would need. He thought that he would need 25% more than the amount of sand he actually used, which was 8 bags. To calculate the amount of sand he estimated he would need, we must first find 25% of 8 bags. 25% of 8 is 2, so Lee estimated he would need 8 + 2 = 10 bags of sand to fill the sandbox. Thus, Lee estimated he would need a total of ten bags of sand, which is 25% more than the eight bags he actually used.

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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.

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

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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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

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.

Answer:

Below

Step-by-step explanation:

Equivalent interest rate in decimal form will be   ( 1+i)^n - 1    

   where i = periodic interest in decimal = .05/4     n = periods = 4  per year  

(1+ .05/4)^4 -1 = 5.09 % equivalent interest per year

.05 / 4 = .0125    or    1.25%   16 times   ( 4 times per year x 4 years)  

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

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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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)

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

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: