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3 years ago

Which situation represents a proportional relationship?

Mathematics

1 answer:

Natalka [10]3 years ago

7 0

Answer:

B) Jack biked 5 miles in 25 minutes and 8 miles in 40 minutes.

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y=kx$

The ratio between the two variables is a constant called constant of proportionality k

$k=y/x$

<u><em>Verify each case</em></u>

A) Julie sold 4 necklaces for $12 and 9 necklaces for $25.

$\frac{4}{12}=\frac{9}{25}$

Multiply in cross

$4(25)=9(12)\\100\neq108$

Is not true

therefore

The situation not represent a proportional relationship

B) Jack biked 5 miles in 25 minutes and 8 miles in 40 minutes.

$\frac{5}{25}=\frac{8}{40}$

Multiply in cross

$5(40)=8(25)\\200=200$

Is true

therefore

The situation represent a proportional relationship

C) Larry packed 24 apples in 6 boxes and 46 apples in 9 boxes

$\frac{24}{6}=\frac{46}{9}$

Multiply in cross

$24(9)=46(6)\\216\neq276$

Is not true

therefore

The situation not represent a proportional relationship

D) Allie put 14 pieces of candy in 2 bags and 30 pieces of candy in 4 bags

$\frac{14}{2}=\frac{30}{4}$

Multiply in cross

$14(4)=30(2)\\56\neq60$

Is not true

therefore

The situation not represent a proportional relationship

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Nesterboy [21]

Answer:

$b = \sqrt{65}$

Step-by-step explanation:

${b}^{2} + {4}^{2} = {9}^{2} \\ {b}^{2} + 16 = 81 \\ {b}^{2} = 81 - 16 \\ {b}^{2} = 65 \\ b = \sqrt{65}$

I hope I helped you^_^

8 0

3 years ago

Match the function with its graph.

Oxana [17]

Answer:

The answer is 1D , 2A , 3C , 4B ⇒ answer (c)

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

function g(x) = - f(x)

- If the function f(x) translated horizontally to the right

by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left

by h units, then the new function g(x) = f(x + h)

* Lets explain each function

∵ y = tan(x)

∵ y = -tan(x - π/2)

# (x - π/2) means the graph translated horizontally to

the right π/2 units

# -tan(x - π/2) means the graph reflected across the x-axis

∴ The graph is (D)

* 1) y = -tan(x - π/2) ⇒ (D)

∵ y = tan(x + π/2)

# (x + π/2) means the graph translated horizontally to

the left π/2 units

∴ The graph is (A)

* 2) y = -tan(x - π/2) ⇒ (A)

∵ y = -cot(x - π/2)

# (x - π/2) means the graph translated horizontally to

the right π/2 units

# -cot(x - π/2) means the graph reflected across the x-axis

∴ The graph is (C)

* 3) y = -cot(x - π/2) ⇒ (C)

∵ y = cot(x + π/2)

# (x + π/2) means the graph translated horizontally to

the left π/2 units

∴ The graph is (B)

* 4) y = -tan(x - π/2) ⇒ (B)

∴ The answer is 1D , 2A , 3C , 4B answer (c)

4 0

3 years ago

You deposit $500 into an account that pays 4.25% annual interest compounded continuously. What is the balance after 10 years?

scZoUnD [109]

$~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 4.25\%\to \frac{4.25}{100}\dotfill &0.0425\\ t=years\dotfill &10 \end{cases} \\\\\\ A=500e^{0.0425\cdot 10}\implies A=500e^{0.425}\implies A\approx 764.80$

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2 years ago

What are the x-intercepts of the equation y=4x^2-16

jenyasd209 [6]

Answer:

x = ± 2

Step-by-step explanation:

To find the x- intercepts let y = 0 , that is

4x² - 16 = 0 (add 16 to both sides )

4x² = 16 ( divide both sides by 4 )

x² = 4 ( take the square root of both sides )

x = ± $\sqrt{4}$ = ± 2

The x- intercepts are x = - 2 and x = 2

3 0

3 years ago

Read 2 more answers

What is the midpoint (-4,0) and (10,7)?

mestny [16]

We first use midpoint formula
X1+X2 divided by 2 we want x for midpoint.
Y1+Y2 divided by 2 we want Y for midpoint
10-4 divided by 2 =3
7-0 divided by 2 =7/2
therefore midpoint= (3;7/2)

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3 years ago