plzz tell me answer of 8 (b) question I can't get the right answer!!!​

The surface area of the pyramid is 113 cm².

A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.

The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.

To find the surface area of the pyramid, we need to find the area of each face and then add them up.

Area of the base:

The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:

Area of base = length × width = 7 cm × 5 cm = 35 cm²

Area of the four triangular faces:

Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:

Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²

Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²

There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:

Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face

= 2 × 19 cm² + 2 × 20 cm²

= 78 cm²

Total surface area:

Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:

Total surface area = area of base + total area of four triangular faces

= 35 cm² + 78 cm²

= 113 cm²

Therefore, the surface area of the pyramid is 113 cm²

.

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Answer:

65.83

Step-by-step explanation:

9514 1404 393

Answer:

  44.66 in

Step-by-step explanation:

The side opposite the marked angle is given, and the side adjacent to it is the one wanted. The relevant trig relation is ...

  Tan = Opposite/Adjacent

Solving for the Adjacent side, we find ...

  Adjacent = Opposite/Tan

  PQ = (29 in)/tan(33°) ≈ 44.66 in

Using the future value formula, the future value of periodic deposits or payments of $105 for 42 periods at 2% is $6,810.53.

The future value formula for a present value investment is as follows:

FV = PV(1+r)^n

FV = future value

PV = present value

r = annual interest rate

n = number of periods interest held

However, if there is periodic investments or payments, the future value can be determined using the following formula:

FV = PMT [((1 + r)^n - 1) / r]

FV = 105 [((1 + 0.02)^42 - 1) / 0.02]

= $6,810.53

We can also use an online finance calculator to determine the future value as follows:

N (# of periods) = 42

I/Y (Interest per year) = 2% (0.02)

PV (Present Value) = $0

PMT (Periodic Payment) = $105

Results:

FV = $-6,810.53

Sum of all periodic payments = $4,410.00

Total Interest = $2,400.53

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Answer: (1, 2)

Concept:

There are three general ways to solve systems of equations:

Since the question has specific requirements, we are going to use elimination

Solve:

Given expressions

x + 5y = 11

-x + 4y = 7

Add both equations together to elimination [x] variable

(x + 5y) + (-x + 4y) = 11 + 7

x - x + 5y + 4y = 18

9y = 18

Divide 9 on both sides

9y / 9 = 18 / 9

\(\boxed{y=2}\)

Find the x value

x + 5y = 11 ⇔ Given equation

x + 5(2) = 11 ⇔ Substitute values of y

x + 10 = 11 ⇔ Simplify by multiplication

x + 10 - 10 = 11 - 10 ⇔ Subtract 10 on both sides

\(\boxed{x=1}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Stack the two equations and add them together as if they were multi-digit numbers. That will eliminate the x and then you can solve for the y. Knowing y you can then go back and solve for x.

Step-by-step explanation:

x + 5y = 11

-x + 4y = 7

---------------- "Add" the equations above to get the equation below.

9y = 18

Now you can divide both sides by 9 to see that y is equal to 2.

Now that you know that y = 2 you can substitute y in either of the two original equations. I'll use the first.

x + 5(2)= 11

x + 10 = 11

x = 1

Answer:

2.4 hours to run 12 miles.

Step-by-step explanation:

\(\frac{7.5}{1.5} = \frac{12}{t} = 2.4\)

the proportion is 5:1

for every hour, jose runs 5 miles

Answer:

$47.48

Step-by-step explanation:

Let x = the amount owed Sept.

x + x - 2.23 = 292.43  Combine like terms

2x -2.23 = 292.43  Add 2.23 to both sides

2x - 2.23 + 2.23 = 292.43 + 2.23

2x = 294.66  Divide both sides by 2

\(\frac{2x}{2}\) = \(\frac{294.66}{2}\)

x = 147.33 this is the bill for September

Oct. 147.33 -2.23 = 145.10 This is the Bill for Oct.

Total:

147.33 + 145.10 = 292.43

292.43 ÷ 3 = 97.48  This is what each will owe rounded to the nearest penny.

Step-by-step explanation:

B. not a rational number

Answer:

Center - (1/2 , 1)

Radius - 2

Step-by-step explanation:

Answer: (1/2, 1) 2 units

Step-by-step explanation: Got it right

Answer:

7x + 2y = - 6

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

given

y = - \(\frac{7}{2}\) x - 3 ( multiply through by 2 to clear the fraction )

2y = - 7x - 6 ( add 7x to both sides )

7x + 2y = - 6 ← in standard form

Answer:

\( s = 7t \)

Step-by-step explanation:

The table given shows that both variables are directly proportional to each other. That is, as s variable increases, y variable also increases.

Equation to represent this direct proportion would be:

\( s = kt \),

where, k = constant of proportionality.

Let's find k from the table given.

Let's use any pair values of of s and t given in the table. Say, s = 21, t = 3

\( s = kt \)

\( 21 = k3 \)

Divide both sides by 3

\( \frac{21}{3} = \frac{k3}{3} \)

\( 7 = k \)

\( k = 7 \)

Plug in k = 3 into \( s = kt \):

\( s = 7t \)

Answer:

B

Step-by-step explanation:

Divide 7

Answer: 16) Shifted LEFT 1 unit and DOWN 3 units

               17) Shifted LEFT 1 unit and DOWN 3 units

               18) Vertical stretch by a factor of 2

               19) Reflected over x-axis, shifted RIGHT 1 unit and UP 7 units

Step-by-step explanation:

The vertex form of a quadratic equation is: y = a(x - h)² + k    where

f(x) = x²

16)  f(x) = (x - 1)² + 3

                    ↓      ↓

                  h= 1    k= 3

           Shifted RIGHT 1 unit and UP 3 units

17) f(x) = (x + 1)² - 3

                    ↓      ↓

                 h= -1   k= -3

           Shifted LEFT 1 unit and DOWN 3 units

18) f(x) = 2(x)²

              ↓    

             a= 2

           Vertical stretch by a factor of 2

19) f(x) = -(x - 1)² + 7

             ↓    ↓      ↓

           a= -1 h= 1  k= 7

           Reflected over x-axis, shifted RIGHT 1 unit and UP 7 units

Rules for the transformations of a parent function are given as,

 If the parent function f(x) = x² is transformed as,

        g(x) = (x + 1)²

        g(x) = (x - 1)²

        g(x) = x² + 1

        g(x) = x² - 1

        g(x) = kx²

        g(x) = -x²

With the help of these transformations, following transformed functions will be defined as,

 16). f(x) = (x - 1)² + 3

        Parent function is shifted 1 unit right and 3 units upwards.

  17). y = (x + 1)² - 3

        Parent function is shifted 1 unit left and 3 units left.

  18). g(x) = 2x²

        Parent function is vertically stretched by a factor of 2.

  19). f(x) = - (x - 1)² + 7

        Parent function is inverted about the x-axis, followed by 1 unit shift on the right and 7 units upwards.      

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The expression will be;

⇒ (x- 4)² - 11

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ x² - 8x + 5

Now,

Solve the expression as;

⇒ x² - 8x + 5

⇒ x² - 8x + 16 - 16 + 5

⇒ (x- 4)² - 11

Thus, The value of the expression = (x- 4)² - 11

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The line parallel to the x-axis passing through the points (5,5) and (-5,5) has a slope of 0, indicating a horizontal line with a constant y-coordinate value of 5.

To determine the slope of the line that represents this relationship, we can use the formula for slope, which is given by:

slope = (change in y-coordinates) / (change in x-coordinates)

In this case, we are given two points on the line: (5,5) and (-5,5).

The change in y-coordinates is 5 - 5 = 0, as the y-coordinate remains constant.

The change in x-coordinates is -5 - 5 = -10.

Substituting these values into the slope formula, we get:

slope = 0 / -10 = 0

Therefore, the slope of the line that represents this relationship is 0.

A slope of 0 indicates that the line is parallel to the x-axis. This means that the line has a constant y-coordinate value for all x-coordinate values. In this case, the line passes through the point (5,5) and (-5,5), and it remains at y = 5 for all x-values.

Visually, a line with a slope of 0 would be a horizontal line on the coordinate plane. It does not have an upward or downward slope but remains parallel to the x-axis.

It's important to note that the slope of 0 indicates a relationship where the dependent variable (y) does not change with respect to the independent variable (x). In this case, no matter the value of x, the corresponding y-value remains constant at 5.

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Answer:

a-25

b-243

5^3 = 125/3 = 25

3^6 = 729/3 = 243

The data set's environment variable(s) are quantified on a nominal scale.

Describe data sets?

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Answer:

how are we ment to know

Answer:

m > 1

Step-by-step explanation:

m+6 > 7

m > 7-6

m > 1

Answer:

d

Step-by-step explanation:

Answer:

0.62 grams

Step-by-step explanation:

Bernie initially added 0.61 grams of salt into the pot, and then added 0.01 grams before serving. To find the total grams of salt added to the pot, simply add 0.61 grams and 0.01 grams.

0.61+0.01=0.62 grams

Answer:

\(:\implies\) 64 = 4³

\(:\implies\) 81 = 3⁴

\(:\implies\) 512 = 8³

Step-by-step explanation:

Given :-

We know that

Therefore :-

\(:\implies\) 64 = 4³

\(:\implies\) 81 = 3⁴

\(:\implies\) 512 = 8³

In order for Kane to maximize profit, He should produce 60 of model A and 204 of model B to maximize profit

Let

model A = x

model B = y

x y Available

Pounds 3 5 1200

Labor 8 5 1500

Profit $2.00 $1.50

Maximum profit = 2x + 1.5y from the equation

3x + 5y ≤ 1200

8x + 5y ≤ 1500

x, y ≥ 0

By plotting the constraints we have the following feasible points

(x,y) = (0,300) (60,204) and (400,0)

Substitute these values in the function

P(x, y) = 2x + 1.5y

P(0,300) = 2(0) + 1.5(300) = 450

P(60,204) = 2(60) + 1.5(204) = 906

P(400,0) = 2(400) + 1.5(0) = 800

The maximum profit is at (60,204)

In conclusion, Kane should produce 60 of model A and 204 of model B to maximize profit

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The value of the equation f ( x ) is

f ( x ) = x³ + x² - 8x - 12

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

f ( x ) = ( x + 2 )²( x -3 )   be equation (1)

Now , on simplifying the equation , we get

f ( x ) = ( x + 2 )²( x -3 )

f ( x ) = ( x² + 4x + 4 ) ( x - 3 )

Now , multiplying each term with ( x - 3 ) , we get

f ( x ) = ( x - 3 ) x² + ( x - 3 ) 4x + ( x - 3 ) 4

f ( x ) = x³ - 3x² + 4x² - 12x + 4x - 12

On simplifying the equation ,we get

f ( x ) = x³ + x² - 8x - 12

Now , the value of the equation f ( x ) = x³ + x² - 8x - 12

On graphing the equation , we get

The graph of the equation f ( x ) = x³ + x² - 8x - 12 is shown below

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Answer:

The discount is 5.82

Step-by-step explanation:

To find the amount of the discount

48.50 * 12%

Change to decimal form

48.50 * .12

5.82

The discount is 5.82

Answer:

4 x \(10^{8}\)

Step-by-step explanation:

Round the number to

400,000,000

4 x \(10^{8}\)

We moved the decimal 8 places.

Answer:

4 x 10^8 (four times ten to the power of eight) is the best approximation of the number 399,867,231 written in scientific notation.

Step-by-step explanation:

The final answer for the surface area of the prism is 32 m^2 + 16h m^2.

To find the surface area of the prism, we need to calculate the area of each face and sum them up.

The prism has two identical square faces and four rectangular faces. The square face has a side length of 4 m. The area of one square face is given by:

Area of square face = side length^2 = 4^2 = 16 m^2

Since there are two square faces, the total area of the square faces is:

Total area of square faces = \(2 * 16 = 32 m^2\)

The rectangular faces have a length equal to the side length of the square face (4 m) and a width equal to the height of the prism. Let's assume the height of the prism is h. The area of one rectangular face is given by:

Area of rectangular face = length * width = \(4 * h = 4h m^2\)

Since there are four rectangular faces, the total area of the rectangular faces is:

Total area of rectangular faces = \(4 * 4h = 16h m^2\)

Therefore, the surface area of the prism is the sum of the areas of the square and rectangular faces:

Surface area of prism = Total area of square faces + Total area of rectangular faces

                          = \(32 m^2 + 16h m^2\)

                          = \(32 m^2 + 16h m^2\)

The answer for the surface area of the prism is 32 m^2 + 16h m^2.

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