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3 years ago

Is this all correct?

Mathematics

2 answers:

Bond [772]3 years ago

7 0

They look correct but I can't see the problems fully

antoniya [11.8K]3 years ago

7 0

They seem to be all correct, though the last one is kinda blurry, I checked them all, and they seem accurate

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Two friends are collecting cards. Frank has 7 more than half the number of cards as his friend. Together they have 42 cards. How

Naddika [18.5K]

Answer:

The number of cards Frank has is 18 and the number of cards his friend has is 24.

Step-by-step explanation:

The correct question is

Two friends are collecting cards. Frank has 6 more than half the number of cards as his friend. Together they have 42 cards. How many cards does each friend have?

Let

x ----> the number of cards that Frank has

y ----> the number of cards that his friend has

we know that

Together they have 42 cards

$x+y=42$ ----> equation A

Frank has 6 more than half the number of cards as his friend

$x=\frac{y}{2} +6$ ---> equation B

Solve the system by substitution

Substitute equation B in equation A

$\frac{y}{2} +6+y=42$

solve for y

$\frac{3}{2}y=42-6\\\\\frac{3}{2}y=36\\\\y=36(2)/3=24$

Find the value of x

$x=\frac{24}{2} +6=18$

therefore

The number of cards Frank has is 18 and the number of cards his friend has is 24.

7 0

3 years ago

The graph shows how many calories are in different amounts of popcorn. Which of these statements is true?

wlad13 [49]

Answer:

50 calories per cup of popcorn

Step-by-step explanation:

just subtract 25

5 0

3 years ago

Read 2 more answers

National credit union pays 5.5% intrest compounded quarterly on special notice savings accounts. Marco deposits $5698.80 in a sp

Reptile [31]

Answer: 6187.24

Step-by-step explanation: 5698.80(1+.0138)^6

6 0

3 years ago

The table shows values for functions f(x) and g(x). x f(x)=2x−3 g(x)=73x−2 −1 −52 −133 0 −2 −2 1 −1 13 2 1 83 3 5 5 4 13 223 5 2

Verizon [17]

0 and 2

f(x) = g(x) will be the input or x value at which f and g have the same output or y value. Look in the table where two numbers repeat right next to each other.

−1 −7/2 −9/2

0 −3 −3

1 −2 −3/2

2 0 0

3 4 3/2

4 12 3

5 28 9/2

There are two solutions to f(x) = g(x) which are x=0 and x=2.

6 0

3 years ago

Evaluate the triple integral ∭EzdV where E is the solid bounded by the cylinder y2+z2=81 and the planes x=0,y=9x and z=0 in the

dem82 [27]

Answer:

I = 91.125

Step-by-step explanation:

Given that:

$I = \int \int_E \int zdV$ where E is bounded by the cylinder $y^2 + z^2 = 81$ and the planes x = 0 , y = 9x and z = 0 in the first octant.

The initial activity to carry out is to determine the limits of the region

since curve z = 0 and $y^2 + z^2 = 81$

∴ $z^2 = 81 - y^2$

$z = \sqrt{81 - y^2}$

Thus, z lies between 0 to $\sqrt{81 - y^2}$

GIven curve x = 0 and y = 9x

$x =\dfrac{y}{9}$

As such,x lies between 0 to $\dfrac{y}{9}$

Given curve x = 0 , $x =\dfrac{y}{9}$ and z = 0, $y^2 + z^2 = 81$

y = 0 and

$y^2 = 81 \\ \\ y = \sqrt{81} \\ \\ y = 9$

∴ y lies between 0 and 9

Then $I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \int^{\sqrt{81-y^2}}_{z=0} \ zdzdxdy$

$I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{z^2}{2} \end {bmatrix} ^ {\sqrt {{81-y^2}}}_{0} \ dxdy$

$I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{(\sqrt{81 -y^2})^2 }{2}-0 \end {bmatrix} \ dxdy$

$I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{{81 -y^2} }{2} \end {bmatrix} \ dxdy$

$I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81x -xy^2} }{2} \end {bmatrix} ^{\dfrac{y}{9}}_{0} \ dy$

$I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81(\dfrac{y}{9}) -(\dfrac{y}{9})y^2} }{2}-0 \end {bmatrix} \ dy$

$I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81 \ y -y^3} }{18} \end {bmatrix} \ dy$

$I = \dfrac{1}{18} \int^9_{y=0} \begin {bmatrix} {81 \ y -y^3} \end {bmatrix} \ dy$

$I = \dfrac{1}{18} \begin {bmatrix} {81 \ \dfrac{y^2}{2} - \dfrac{y^4}{4}} \end {bmatrix}^9_0$

$I = \dfrac{1}{18} \begin {bmatrix} {40.5 \ (9^2) - \dfrac{9^4}{4}} \end {bmatrix}$

$I = \dfrac{1}{18} \begin {bmatrix} 3280.5 - 1640.25 \end {bmatrix}$

$I = \dfrac{1}{18} \begin {bmatrix} 1640.25 \end {bmatrix}$

I = 91.125

4 0

3 years ago