Jackson gave Lena this expression to evaluate: 14(8 + 12). Lena said that to evaluate the expression was simple; just multiply the factors 14 and 20. Jackson told Lena she was wrong. He solved it by finding the product of 14 and 8 and then adding that to the product of 14 and 12.


a. Evaluate the expression using each student’s method.

b. Who was right in this discussion? Why?

Answer:

The answer is D 477 in.2

Step-by-step explanation:

The surface area of the composite figure is 333 sq. in.

The correct answer is an option (2) 333 in²

"It is a three-dimensional geometric shape with a polygon as its base and the lateral surfaces as triangles which meet at a common point."

"It is a three-dimensional geometric structure which has six faces that are rectangles."

"A figure that consists of two or more geometric shapes."

A = length × width

A = 1/2 × base × height

For given example,

A rectangular prism and a square pyramid were joined to form a composite figure.

The composite figure would have nine faces with four triangular faces and five rectangular faces.

Surface area of the composite figure would be the sum of surface area of  all nine faces.

The dimensions of the rectangular base the composite figure are length of 9 inches, width of 9 inches.

Using the formula for an area of the rectangle,

⇒ A1 = 9 × 9

⇒ A1 = 81 square inches

The surface area of the larger vertical rectangular faces is same.

So, A2 = 2 × (area of the larger vertical rectangular faces)

The dimensions of the larger vertical rectangular faces 9 inches × 5 inches.

⇒ A2 = 2 × (9 × 5)

⇒ A2 = 2 × 45

⇒ A2 = 90 square inches

Similarly, the surface area of the smaller vertical rectangular faces is same.

So, A3 = 2 × (area of the smaller vertical rectangular faces)

The dimensions of the smaller vertical rectangular faces 9 inches × 5 inches

⇒ A3 = 2 × (9 × 5)

⇒ A3 = 2 × 45

⇒ A3 = 90 square inches

The four triangular faces are identical.

Let A4 be the total surface area of four triangular faces.

⇒ A4 = 4 × (area of triangular face)

⇒ A4 = 4 × (1/2 × base × height)

⇒ A4 = 4 × (1/2 × 9 × 4)

⇒ A4 = 4 × 18

⇒ A4 = 72 square inches

So, the surface area of the composite figure is,

⇒ A = A1 + A2 + A3 + A4

⇒ A =  81 + 90 + 90 + 72

⇒ A = 333 sq. in.

Therefore, the surface area of the composite figure is 333 sq. in.

The correct answer is an option (2) 333 in²

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Answer

the answer is b. im not sure though

Step-by-step explanation:

1042 square inches is the total surface area of composite solids.

It is clear from the image that the resulting composite solid is a cuboid.

whose sides are as follows

Across the length, there are 3 blocks along the side of 7 inches each.

[tex]Length = 7 \times 3 = 21\ inch[/tex]

Width = 5 inch

Across the height, there are 4 blocks along the side of 4 inches each.

[tex]Height = 4 \times 4 = 16\ inch[/tex]

[tex]\text{Total Surface Area = } 2 (l\times w+ w \times h+ h \times l)[/tex]

We know that the total surface area of a cuboid is,

[tex]\text{Total Surface Area = } 2 (l\times w+ w \times h+ h \times l)\Rightarrow 2 (21 \times 5 + 16 \times 21 + 16 \times 5 )\\\Rightarrow 2 (105 + 336+80)\\\Rightarrow 2 \times 521\\\Rightarrow 1024[/tex]

Therefore, the total surface area = 1024 square inches.

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Answer:

y > 0 best describes the range of the function f(x) = 2(3)x. A function whose value is a constant raised to the power of the argument, especially the function where the constant is e

Step-by-step explanation:

Using exponential function concepts, it is found that the range of the function after it has been reflected over the x-axis is given by:

all real numbers less than 0.

It is modeled by:

[tex]y = ab^x + c[/tex]

In which:

In this problem, a reflection over the x-axis means that it was multiplied by -1, hence the range will be (-infinity, 0), hence the correct option is;

all real numbers less than 0.

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Answer:

Step-by-step explanation:

This graph is a circle. The general equation for a circle is x² + y² = r², where r is the radius. In this case, the radius is 3 because √9 = 3. Also, the center is (0,0) because the circle is not translated. Therefore, the graph is a circle with center (0,0) and radius 3. If you still need help, the y-intercepts are (0,±3) and the x-intercepts are (±3,0). Hope this makes sense!

Answer:

52 miles

Step-by-step explanation:

A to B:

sqrt( (3 - (-2))^2 + (-11 - 1)^2 )

sqrt( (5)^2 + (-12)^2 )

sqrt( 25 + 144 )

sqrt( 169 )

13

B to C:

sqrt( (-2 - 3)^2 + (-23 - (-11))^2 )

sqrt( (-5)^2 + (-12)^2 )

sqrt( 25 + 144 )

sqrt( 169 )

13

C to D:

sqrt( (-7 - (-2))^2 + (-11 - (-23))^2 )

sqrt( (-5)^2 + (12)^2 )

sqrt( 25 + 144 )

sqrt( 169 )

13

D to A:

sqrt( (-2 - (-7))^2 + (1 - (-11))^2 )

sqrt( (5)^2 + (12)^2 )

sqrt( 25 + 144 )

sqrt( 169 )

13

Adding:

13 + 13 + 13 + 13

52

Answer:

5 cubes

Step-by-step explanation:

15/3=5

Answer:

5

Step-by-step explanation:

5/3=15

Answer:

The answer is [9, 5, -4, 12]

Step-by-step explanation:

1) distribute the 3 within all the numbers on the right side. 3*2, 3*0, 3*-1, 3*4.

2) your right side should now have the numbers, 6, 0, -3, 12.

3) now add the numbers on the left with the numbers on the right, each should correspond with their place within the box. 3+6, 5+0 -1+-3 0+12

Hope this helps :)

Answer:

1/52

Step-by-step explanation:

There is only one 8 of diamonds in a deck of 52 cards.  The deck is properly shuffled, so every card has an equal probability of being selected.  So the probability is 1/52.

Missing Part of the Question

Answer:

Step-by-step explanation:

Given

y = 3

Required

Which pair of expression are equal

To get the pair of expression that are equal; we simply substitute 3 for y in each of the expressions

3 (4 - y) -7 and 5 + 3y

Substitute 3 for y in 3 (4 - y) -7

This gives 3(4 - 3) -7

= 3(1) - 7

= 3 - 7

= -4

Then Substitute 3 for y in 5 + 3y

This gives  5 + 3(3)

= 5 + 9

= 14

-4 and 14 are not equal

---------------------------------------------------------------------------------------

9 + y + 4y - 2 - 3y; -2y + 7

Substitute 3 for y in 9 + y + 4y - 2 - 3y

This gives 9 + 3 + 4(3) - 2 - 3(3)

= 9 + 3 + 12 - 2 - 9

= 13

Then Substitute 3 for y in -2y + 7

This gives  -2(3) + 7

= -6 + 7

= 1

13 and 1 are not equal

---------------------------------------------------------------------------------------

5 + y - 2 - 6y + y; 8y + 3

Substitute 3 for y in 5 + y - 2 - 6y + y

This gives 5 + 3 - 2 - 6(3) + 3

= 5 + 3 - 2 - 18 + 3

= -9

Then Substitute 3 for y in 8y + 3

This gives  8(3) + 3

= 24 + 3

= 27

-9 and 27 are not equal

---------------------------------------------------------------------------------------

2y + 7 + y - 2 + y; 4y + 5

Substitute 3 for y in 2y + 7 + y - 2 + y

This gives 2(3) + 7 + 3 - 2 + 3

= 6 + 7 + 3 - 2 + 3

= 17

Then Substitute 3 for y in 4y + 5

This gives  4(3) + 5

= 12 + 5

= 17

17 and 17 are equal

Hence, Option D is correct

Answer: 2y + 7 + y - 2 + y; 4y + 5

Step-by-step explanation: just did it

Answer:

32   (Answer D)

Step-by-step explanation:  

  -1

(4   )(2^3 / 16)

or:

  1            8*16

------- * ------------ = 32   (Answer D)

  4            1

Answer:

D

Step-by-step explanation:

Answer:

Mean of the distribution shown in picture:

M = sum of all elements/number of elements

M = (2 + 6 + 4 + 2 + 0 + 1 + 6 + 4 + 2 + 1)/10 = 2.8

=> Option D is correct

(3 is closest number to mean = 2.8)

Hope this helps!

:)

Answer:

it should be 1.5 inches.....

Answer:

b =-6

Step-by-step explanation:

[tex](y^{b})^4=\frac{1}{y^{24}} \\\\y^{4b}=y^{-24}\\4b = -24\\b=\frac{-24}{4}\\b =-6[/tex]

Answer:

B , -6

Step-by-step explanation: took the quiz

Answer:

0.39

Step-by-step explanation:

1 tenth: 1/10 = 0.1

1 hundredth = 1/100 = 0.01

3(0.1) + 9(0.01)

0.3 + 0.09

0.39

Answer:

5.16 mm; 10.31 mm

Step-by-step explanation:

Circumference: [tex]C = 2\pi r[/tex]

So all you do is:

[tex]32.4=2\pi r\\32.4/2\pi = r\\5.16 = r[/tex]

and then the radius is just half of the diameter so

[tex]5.16*2=10.31[/tex]

Answer:

3

Step-by-step explanation:

Answer: 246 laptops.

Step-by-step explanation: if they each each take 20 for insurance and 385 then its 405 title. hen you take 100,000 and divide it by 405 getting 246.91358. but you cant buy .91358 of a computer so you round down.

Answer:

66.04

Step-by-step explanation:

0.13 * 508 = 66.04

Answer:

Step-by-step explanation:

508/x=13/100

508*100=50800

50800/3=?

now do that and simplify

Answer:

its 1/2

Step-by-step explanation:

people stop putting answer if your not sure you just want points

Answer:

problem can't be solved

Step-by-step explanation:

Answer:

A?

Step-by-step explanation:

Answer:

1. Constant multiplicative.

2. 1.05.

Step-by-step explanation:

Their savings increase by 1.05x every year.

Answer:

(-4,7)

Explanation:

I graphed the two equations with a graphing tool.

The first equation forms a parabola.

The second equation is linear.

The graphed equations intercept at two points. Since the question asked for one, then one solution of the system is (-4,7).

Answer:

(- 4, 7 ) and (2, - 5 )

Step-by-step explanation:

Given the 2 equations

y = x² - 9 → (1)

y = - 2x - 1 → (2)

Substitute y = x² - 9 into (2)

x² - 9 = - 2x - 1 ( subtract - 2x - 1 from both sides )

x² + 2x - 8 = 0 ← in standard form

(x + 4)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 2 = 0 ⇒ x = 2

Substitute these values into (2) for corresponding values of y

x = - 4 → y = - 2(- 4) - 1 = 8 - 1 = 7 ⇒ (- 4, 7 )

x = 2 → y = - 2(2) - 1 = - 4 - 1 = - 5 ⇒ (2, - 5 )

Answer:

D

Step-by-step explanation:

parenthesis

exponents

multiply or divide from left to right

add or subtract from left to right

14 - 8 + 6 - 5

6 + 6 - 5

12 - 5

7

Answer:

D. 7

Step-by-step explanation:

PEMDAS

there arent parentheses, exponets or multiplication but the is division

so divide first

14-8+6-5

Next subtract

6+6-5

then subtract from left to right

12-5

7

Answer:r=16 ft , d =32 ft (a)

Step-by-step explanation:

c=2 pi r

32pi= 2 x pi x r

r=32 pi/2pi

r= 16

diameter = radius x 2

d= 16 x 2

d = 32

Answer:

D y= ax^2 + bx+c = 0

Step-by-step explanation:

The standard form of a quadratic equation is

ax^2 + bx+c = 0

x = -b/2a is the equation for the line of symmetry

a quadratic is a parabola, but that is not the standard form

vertex is the minimum or maximum of the parabola

Answer:

The rate of increase is 40%

14 - 10 = 4

4/10 = 40%

Answer: B

Step-by-step explanation:

38 height

-16 is the time

Answer:

Step-by-step explanation:

A

The factored equivalent of x² - 5x + 4 is option A: (x - 1)(x - 4).

To factor the quadratic expression x² - 5x + 4, we need to find two binomials that, when multiplied, will result in the given expression.

We can start by looking for two numbers whose product is 4 (the constant term) and whose sum is -5 (the coefficient of the x term).

The numbers that satisfy these conditions are -1 and -4, as (-1)(-4) = 4 and -1 + (-4) = -5.

Using these numbers, we can express the quadratic expression as:

x² - 5x + 4 = (x - 1)(x - 4)

Therefore, the factored equivalent of x² - 5x + 4 is option A: (x - 1)(x - 4).

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Answer:

x = 3

y = 8

Step-by-step explanation:

y = x + 5

y = 2x + 2

They both equal y, so:

x + 5 = 2x + 2

x + 3 = 2x

3 = x

Put the value of x into the equations:

y = 3 + 5 = 8

y = 2(3) + 2 = 8

x = 3

y = 8