If Hannah can drive 20 miles in 4 minutes, what is her unit rate in miles per minute?

Valerie runs track and field. At meets, Valerie lkes to buy protein bars, bananas and sports drinks Protein bars are $1. bananas

VladimirAG [237]

Complete Question

Valerie runs track and field. At meets, Valerie likes to buy protein bars, bananas, and sports drinks. Protein bars are $1, bananas are $0.50, and sports drinks are $2. Valerie has $10 to spend. She will spend no more than twice as much on sports drinks as bananas and at least three times as much on bananas as protein bars.

Let p represent the number of protein bars, b represent the number of bananas, and d represent the number of sports drinks that Valerie buys.

Which statements are true regarding Valerie's situation? Select all that apply A: p + 0.5b + 2d < 10 B: 0.5d + b + 3p < 10. C: d < 2b. D: b > 3p. E: 2d < b. F: 3b > p

Answer:

The statements that are true regarding Valerie's situation:

A: p + 0.5b + 2d < 10

C: d < 2b

D: b > 3p

Step-by-step explanation:

Lets represent

The number of protein bars as p.

The number of bananas as b.

The number of sports drinks that Valerie buys as d.

From the question:

We are told

Protein bars are $1

Bananas are $0.50

Sports drinks are $2.

She will spend no more than twice as much on sports drinks as bananas

d ≤ 2b = d < 2b

At least three times as much on bananas as protein bars.

b ≥ 3p = b > 3p

We are also told that:

Valerie has $10 to spend.

Hence:

$1 × p + $0.50 × b + $2 × d < $10

= p + 0.5b + 2d < 10

Therefore, the statements that are true regarding Valerie's situation:

A: p + 0.5b + 2d < 10

C: d < 2b

D: b > 3p

5 0

3 years ago

Consider h(x)=x^2+8+15. identify its vertex and y-intercept.

OleMash [197]

Answer:

Vertex: (-4, -1)

Y-intercept: (0, 15)

Step-by-step explanation:

Given the quaratic function, h(x) = x² + 8x + 15:

In order to determine the vertex of the given function, we can use the formula, $[x = \frac{-b}{2a}, h(\frac{-b}{2a})]$ .

<h3>Use the equation: $[x = \frac{-b}{2a}, h(\frac{-b}{2a})]$ </h3>

In the quadratic function, h(x) = x² + 8x + 15, where:

a = 1, b = 8, and c = 15:

Substitute the given values for <em>a</em> and <em>b</em> into the equation to solve for the x-coordinate of the vertex.

$x = \frac{-b}{2a}$

$x = \frac{-8}{2(1)}$

x = -4

Subsitute the value of the x-coordinate into the given function to solve for the <u>y-coordinate of the vertex</u>:

h(x) = x² + 8x + 15

h(-4) = (-4)² + 8(-4) + 15

h(-4) = 16 - 32 + 15

h(-4) = -1

Therefore, the vertex of the given function is (-4, -1).

<h3>Solve for the Y-intercept:</h3>

The <u>y-intercept</u> is the point on the graph where it crosse the y-axis. In order to find the y-intercept of the function, set x = 0, and solve for the y-intercept:

h(x) = x² + 8x + 15

h(0) = (0)² + 8(0) + 15

h(0) = 0 + 0 + 15

h(0) = 15

Therefore, the y-intercept of the quadratic function is (0, 15).

5 0

2 years ago

X = 4. 5x +23x^3 - 360.

Zinaida [17]

Missing: 360 ‎| ‎Must include: ‎360

look at

https://www.google.com/search?q=x+%3D+4.+5x+%2B23x%5E3+-+360&rlz=1CAJAIV_enUS838&oq=x+%3D+4.+5x+%2B23x%5E3+-+360&aqs=chrome..69i57&sourceid=chrome&ie=UTF-8&safe=active&ssui=on

4 0

3 years ago

Read 2 more answers

What times 17 -20 equals 180?

grigory [225]

Answer:

60

Step-by-step explanation:

17-20=3. 60times3 equals 180. So 60

7 0

3 years ago

David has a piece of wood that is 7.28 meters long. He needs 4 pieces of wood that are each 1.75 meters long. If he cuts the woo

Tema [17]

9514 1404 393

Answer:

yes

Step-by-step explanation:

You can go at this a couple of ways:

1. The total length David needs is (1.75 m) × 4 = 7.00 m. His 7.28 m piece is long enough to provide the pieces he needs.

__

2. The length of each piece when the wood is cut into quarters is ...

(7.28 m)/4 = 1.82 m

This is longer than the 1.75 m needed, so each piece is long enough.

5 0

2 years ago