Use the diagram to find x and y

Answer:

Step-by-step explanation:

primero distrubuyas el cuatro a los dos numeros dentro del parentesis que lego se hace 12x+8-7x, combinas numeros similares para simplificar

"12x-7x=5x" haci que 4(3x+2)-7x= 5x+8

Answer:

Graph A

Step-by-step explanation:

As can be seen, the trend in graph A is increasing with each month but not seemingly by as much as graph B;

This is because the scale of the y-axis in graph B has smaller increments;

This creates the impression of a slow increase in sales even though the data in both graphs is actually the same.

Answer: graph A.

appear to increase less.

Step-by-step explanation:

\( {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } \)

\(9 \sqrt[4]{ {t}^{3} } \times 7 \sqrt[3]{ {t}^{2} } \\ 9( {t}^{ \frac{3}{4} } ) \times 7( {t}^{ \frac{2}{3} } )\)

\(63( {t}^{ \frac{3}{4} } \times {t}^{ \frac{2}{3} } ) = 63( {t}^{ \frac{3}{4}+\frac{2}{3} } ) \\ 63( {t}^{ \frac{9}{12} + \frac{8}{12} } ) \\ 63( {t}^{ \frac{17}{12} } )

\( \large \boxed {63 {t}^{ \frac{17}{12} } }\)

Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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The area of the shape = area of the 2 rectangles + area of the 2 trapeziums = 7 ft².

Area of a trapezium = 1/2(a + b) × h, where a and b are the lengths of the bases of the trapezium and h is the height of the trapezium.

Area of a rectangle = (length)(width).

The shape is composed of two identical rectangles and 2 identical trapeziums.

Area of the 2 identical trapeziums = 2(1/2(a + b) × h)

a = 1 ft

b = 2 ft

h = 1 ft

Substitute

Area of the 2 identical trapeziums = 2(1/2(1 + 2) × 1) = 3 ft²

Area of the 2 identical rectangles = 2(length)(width) = 2(2)(1)

Area of the 2 identical rectangles = 4 ft²

Area of the shape = area of the 2 rectangles + area of the 2 trapeziums = 3 + 4 = 7 ft².

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Answer:

A. -4

Step-by-step explanation:

Given the function f(x) = x + 3 for x ≤ -1 and 2x - c for x > -1, for the function to be continuous, the right hand limit of the function must be equal to its left hand limit.

For the left hand limit;

The function at the left hand occurs at x<-1

f-(x) = x+3

f-(-1) = -1+3

f-(-1) = 2

For the right hand limit, the function occurs at x>-1

f+(x) = 2x-c

f+(-1) = 2(-1)-c

f+(-1) = -2-c

For the function f(x) to be continuous on the entire real line at x = -1, then

f-(-1) = f+(-1)

On equating both sides:

2 = -2-c

Add 2 to both sides

2+2 = -2-c+2

4 =-c

Multiply both sides by minus.

-(-c) = -4

c = -4

Hence the value of c so that f(x) is continuous on the entire real line is -4

The value of 'c' is -4 and this can be determined by using the concept of continuous function and arithmetic operations.

Given :

f(x) is continuous on the entire real line when c f(x) = x + 3 for \(x \leq -1\), 2x - c for x > -1.

Remember for a continuous function, the left-hand limit is equal to the right-hand limit. So, determine the left-hand and right-hand limit.

The left-hand limit is calculated as:

f(-1) = (-1) + 3

f(-1) = 2    --- (1)

The right-hand limit is calculated as:

f(-1) = 2(-1) - c

f(-1) = -2 - c   --- (2)

Now, equate both the expression (1) and (2).

2 = -2 - c

c = -4

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Therefore, the correct response From these integral is option D   is.  

``` 10 + ∫₅¹  R(t) dt

An integral is a mathematical construct in mathematics that can be used to represent an area or a generalization of an area. It computes volumes, areas, and their generalizations. Computing an integral is the process of integration.

Integration can be used, for instance, to determine the area under a curve connecting two points on a graph. The integral of the rate function R(t) with respect to time t can be used to describe how much water is present in a tank.

The following equation can be used to determine how much water is in the tank at time t = 5 if there are 10 gallons of water in the tank at time t = 1.

``` 10 + ∫₅¹  R(t) dt

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The area covered by the signal is 181.37 m²

Here we can see that the area covered by the signal is the fourth of a circle of radius R = 15.2m

The area of a circle of radius R is given by:

A = 3.14*R²

Then the area of a fourth of a circle is:

A = (3.14/4)*R²

Replacing the value of the radius in the formula we will get:

A =  (3.14/4)*(15.2m)² = 181.37 m²

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The zeros of the polynomial function are x = -1 and x = 5

From the question, we have the following parameters that can be used in our computation:

y = x⁴ - 4x³ - 4x² - 4x - 5

To calculate the zeros of the polynomial function, we create a graph of the polynomial

The point where the graph intersect with the x-axis are the zeros of the polynomial function

using the above as a guide, we have the following:

Zeros: x = -1 and x = 5

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The condensed form of the expression is  log [(a⁵¹× c²⁵) / b²⁷

We can use the logarithmic identities:

log aˣ = x log a

to simplify the expression:

51 log a - 27 log b + 25 log c

= log a⁵¹- log b²⁷ + log c²⁵

using the identity log (a/b) = log a - log b

= log [(a⁵¹× c²⁵) / b²⁷

Therefore, the condensed form of the expression is  log [(a⁵¹× c²⁵) / b²⁷

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Answer:  $130 money did Brenda and Hazel have all together before buying decorations and snacks.

Here, we have,

You want to know Brenda and Hazel's combined money when the ratio of their remaining balances is 1 : 4 after Brenda spent $58 and Hazel spent $37. They had the same amount to start with.

Setup

Let x represent the total amount the two women started with. Then x/2 is the amount each began with, and their fnal balance ratio is ...

 (x/2 -58) : (x/2 -37) = 1 : 4

Solution

Cross-multiplying gives ...

 4(x/2 -58) = (x/2 -37)

 2x -232 = x/2 -37 . . . . . . eliminate parentheses

 3/2x = 195 . . . . . . . . . . . . add 232-x/2

 x = (2/3)(195) = 130 . . . . . multiply by 2/3

Brenda and Hazel had $130 altogether before their purchases.

Alternate solution

The difference in their spending is $58 -37 = $21.

This is the same as the difference in their final balances.

That difference is 4-1 = 3 "ratio units", so each of those ratio units is $21/3 = $7.

Their ending total is 1+4 = 5 ratio units, or $35.

The total they started with is $58 +37 +35 = $130.

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complete question:

Brenda and Hazel decide to throw a surprise party for their friend, Aerica. Brenda and Hazel each go to the store with the same amount of money. Brenda spends $58 on decorations, and Hazel spends $37 on snacks. When they leave the store, the ratio of Brenda’s money to Hazel’s money is 1 : 4. How much money did Brenda and Hazel have all together before buying decorations and snacks?

The lateral and total surface area of the prism are 1000 square feet and 1120 square feet.

In this problem we need to determine the lateral and total surface area of a prism with a triangular base. The lateral surface area is the sum of the areas of the three rectangles and the total surface area is the sum of the lateral surface area and the areas of the two triangles.

The area formulas for the triangle and the rectangle are, respectively:

Triangle:

A = s · √[s · (s - a) · (s - b) · (s - c)]

s = 0.5 · (a + b + c)

Where:

Rectangle:

A = w · h

Where:

Now we proceed to determine each surface area:

Lateral surface area:

A = 2 · (20 ft) · (17 ft) + (20 ft) · (16 ft)

A = 1000 ft²

Total surface area:

s = 0.5 · (17 ft + 17 ft + 16 ft)

s = 25 ft

A = √[(25 ft) · (25 ft - 17 ft)² · (25 ft - 16 ft)] + 1000 ft²

A = 1120 ft²

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The number of tiles is 96

From the question, we have

The width of the room is 16 feet, 8 inches and the client has chosen a square tile that measures 4 inches on each side.

16 feet = 192 inches

Number of tiles = (192*8)/(4*4)

= 96 tiles

The number of tiles is 96.

Multiplication:

The product of two or more numbers is computed by mathematicians using multiplication. In everyday life, it is a basic mathematical operation that is frequently used. We employ multiplication when we must combine groups of like sizes. The operation of multiplication serves as a representation of the fundamental idea of adding the same number repeatedly. The product of two or more numbers is what is obtained when those numbers are multiplied, and the factors are the quantities that are multiplied. Multiplying the numbers simplifies the process of adding the same number repeated.

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Answer:

See below

Step-by-step explanation:

Part A

\(f(g(x))=f(\frac{x}{3})=3(\frac{x}{3})=x\\g(f(x))=g(3x)=\frac{3x}{3}=x\)

Since BOTH \(f(g(x))=x\) and \(g(f(x))=x\), then \(f\) and \(g\) are inverses of each other

Part B

\(f(g(x))=f(\frac{x+1}{2})=2(\frac{x+1}{2})+1=x+1+1=x+2\\g(f(x))=g(2x+1)=\frac{(2x+1)+1}{2}=\frac{2x+2}{2}=x+1\)

Since BOTH \(f(g(x))\neq x\) and \(g(f(x))\neq x\), then \(f\) and \(g\) are NOT inverses of each other

Answer:

$98.00

Step-by-step explanation:

$245.00×.40 = $98.00

the ski boots are sold for $98.00

The area that Mr. Adams needs to paint is 34ft².

Given that the toy box measures 4 feet long, 1.5 feet wide, and 2 feet high. Since the area that mr Adams needs to paint is the outside area of this box, therefore, the area he needs to paint is the total surface area of the toy box.
Surface area of the box

= 2 [ (Length×Width) + (Height×Width) + (Length×height)]

= 2[ (4 ft ×1.5 ft) + (2ft × 1.5 ft) + (4 ft × 2 ft)]

= 2( 6 ft² + 3 ft² + 8 ft² )

= 34 ft²

Hence, the area is 34ft².

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The complete question must be:

Mr Adams is painting the outside of his son’s toy box, including the top and bottom. The toy box measures 4 feet long, 1.5 feet wide, and 2 feet high. What is the total area that Mr Adams needs to paint?

Answer:

Step-by-step explanation:

diameter= 22 mm

Radius is half of diameter

r = 22/2 = 11mm

Area of circle = πr²

                      = 3.14 * 11*11

                      = 379.94 mm²

Diameter (d) of circle = 22 mm

Area of circle.

Diameter (d) of circle = 22 mm (Given)

So, radius (r) of circle = \( \frac{d}{2} \) = \( \frac{22}{2} \) = 11 mm.

Now, we know,

Formula of Area of Circle is πr².

So, Area of Circle = \( \frac{22}{7} \) × (11)²

Area of Circle = \( \frac{22}{7} \) × 11 × 11

Area of Circle = \( \frac{22 \: × \: 11 \: × \: 11}{7} \)

Area of Circle = \( \frac{2662}{7} \)

Area of Circle = 380.29

Answer:

1:02

Step-by-step explanation:

There are 30 minutes in a half-hour, so add this to the time he left:

12:32 + 30 mins

= 1:02

He will need to be back at 1:02

Answer:

7200

Step-by-step explanation:

Step 1:

77 × 87    Round

Step 2:

80 × 90  Multiply

Answer:

7200

Hope This Helps :)

Answer:

7,200

Step-by-step explanation:

So you have 77 x 87

Round 77  ( look at the ones place, is it 5 and up? In this scenario it is. So you want to go up one in the tens place and replace the 7 with a 0 in the ones place) Which looks like this: 80

Do the same thing with the number 87

You should get 90

So now you have 80 x 90

If you want to solve without a calculator you should know your multiplication such as 4 x 5 which is obviously 20

In this scenario remove the zeros

  8

x 9

___

72

Now add the total number of zeros from both numbers which there are 2 zeros in total. Add the 2 zeros to the total of 8 x 9.

And you should get 7,200

Hope this makes sense!

The expression for the given word phrase is

46M + M² + 2 + 1/M²

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number = M

Reciprocal of M = 1/M

Now,

46 x (M + 1/M)²

Step 1:

46M + M² + 2 + 1/M²

Thus,

The expression is 46M + M² + 2 + 1/M²

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Answer:

B. 9x² - 25 = (3x - 5)(3x + 5)

Answer:

63%

Step-by-step explanation:

From the question, we aim to find the percent increase in the tuition

Given data

initial cost= $99 per credit hour

Final cost=  $268 per credit hour

% increase= (Final - initial )/initial *100

substitute

% increase= (268- 99 )/268 *100

% increase= 169 /268 *100

% increase= 0.630*100

% increase= 63%

Hence the increase in the tuition from 1990 to 2003 is 63%

The value of square root of x + y squared + z squared is 30

x = 2, y = 3 and z = -5

\(( \sqrt{x + y} )^{2} + z ^{2} \)

substitute the value of x, y and z

\( = ( \sqrt{2 + 3} )^{2} + - 5 ^{2} \)

simplify the square root and square

\( = (2 + 3) + 25\)

\( = 5 + 25\)

\( = 30\)

Ultimately, x + y squared + z squared is 30

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The maximum height reached by the ball is 908.5 feet.

Using the given values, we can substitute v0 = 152 and h0 = 6 into the equation:

\(h(t) = -16t^2 + 152t + 6\)

This quadratic function models the height of the ball at any time t after it is thrown.

To find the maximum height of the ball, we need to find the vertex of the parabolic curve described by the quadratic function. The vertex can be found using the formula:

t = -b / 2a

where a = -16 and b = 152 are the coefficients of the quadratic function.

t = -152 / 2(-16) = 4.75

So the maximum height is reached after 4.75 seconds. To find the maximum height, we can substitute this value back into the equation:

\(h(4.75) = -16(4.75)^2 + 152(4.75) + 6 = 908.5\)feet

Therefore, the maximum height reached by the ball is 908.5 feet.

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Question

A ball is thrown vertically upward from a height of 6 feet with an initial velocity of 152 feet per second. Write a quadratic function to model the vertical motion of the ball, given that the height of the ball at time t is given by: h(t) = -16t^2 + v0t + h0

Answer: A: It will cost $936.00 to carpet the floor.

B: It will cost $297.00 to wallpaper all four walls.

C: It will cost $33.25 to paint the ceiling.

D: The cost of the entire project will be $1266.25.

Step-by-step explanation:

To calculate the costs for carpeting, wallpapering, painting, and the overall cost of the project, we need to determine the areas that need to be covered and the corresponding prices for each material.

Given dimensions:

Room length: 26 feet

Room width: 18 feet

Room height: 9 feet

Door dimensions:

Height: 6 feet 6 inches

Width: 4 feet

Window dimensions (each):

Width: 2 feet

Height: 2 feet 6 inches

A: Carpeting the floor:

To find the area of the floor, we multiply the length and width of the room:

Floor area = Length × Width = 26 feet × 18 feet = 468 square feet.

To convert to square yards (since the carpet is sold per square yard), we divide by 9:

Floor area in square yards = 468 square feet / 9 = 52 square yards.

Cost to carpet the floor = Floor area in square yards × Cost per square yard = 52 square yards × $18.00 = $936.00.

B: Wallpapering the walls:

To find the area of the walls, we calculate the perimeter of the room (2 × (Length + Width)) and multiply it by the height of the room:

Wall area = Perimeter × Height = 2 × (26 feet + 18 feet) × 9 feet = 396 square feet.

Cost to wallpaper the walls = Wall area × Cost per square foot = 396 square feet × $0.75 = $297.00.

C: Painting the ceiling:

To find the area of the ceiling, we multiply the length and width of the room:

Ceiling area = Length × Width = 26 feet × 18 feet = 468 square feet.

Since a quart of paint covers 88 square feet, we need to determine the number of quarts required:

Number of quarts = Ceiling area / Coverage per quart = 468 square feet / 88 square feet = 5.32 quarts.

Since a gallon contains 4 quarts, the number of gallons required is 5.32 quarts / 4 quarts = 1.33 gallons.

Cost to paint the ceiling = Number of gallons × Cost per gallon = 1.33 gallons × $25.00 = $33.25.

D: Cost of the entire project:

Total cost = Cost to carpet the floor + Cost to wallpaper the walls + Cost to paint the ceiling

= $936.00 + $297.00 + $33.25 = $1266.25.

Therefore:

A: It will cost $936.00 to carpet the floor.

B: It will cost $297.00 to wallpaper all four walls.

C: It will cost $33.25 to paint the ceiling.

D: The cost of the entire project will be $1266.25.

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Answer:

Wheres the statements?

Step-by-step explanation:

Answer:

y=-4x-4

Step-by-step explanation:

y-y1=m(x-x1)

y-(-28)=-4(x-6)

y+28=-4(x-6)

y=-4x+24-28

y=-4x-4