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2 years ago

14

Regan's New Year's resolution is to exercise more. Today, she plans to run 1.5 miles on the track around her school's football f

ield. If each lap around the track is 0.25 miles, how many laps should she run?

1 answer:

Contact [7]2 years ago

7 0

Answer:

6 laps

Step-by-step explanation:

According to the scenario, calculation of the data are as follows:

Each lap = 0.25 miles

Regan's plan to run= 1.5 miles

So, we can calculate number of laps by using following formula,

Number of laps = Total miles to run ÷ each lap miles

By putting the value, we get

Number of laps = 1.5 miles ÷ 0.25 miles

= 6 laps

So, she should run 6 laps.

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Graph the inequality y> 2x +3

adelina 88 [10]

Graph the inequality y> 2x +3

Solution

<u>Step 1: </u>To graph the inequality, we need to find a few coordinates and form the table.

<u>Step 2:</u> Forming the table.

Let's take x = -1 and find the value of y.

Plug in x = -1 and find the value of y.

y = 2(-1) + 3 = -2 + 3 = 1

When x = -1, the value of y is 1.

So the coordinates are (-1, 1)

Plug in x = 0 and find the value of y.

y = 2(0) + 3 = 3

The coordinates are (0, 3)

Plug in x =1 and find the value of y.

y = 2(1) + 3 = 2 + 3 = 5

The coordinates are (1, 5)

<u>Steo 3: </u>Now let's plot the points and draw the graph.

Since the graph is greater than, we have to draw the dotted lines and shade the region above.

Note: You can find the graph in the attachment.

Thank you :)

7 0

3 years ago

Plz help me with this

Cloud [144]

$\bold{\text{Answer:\qquad }b)\quad \bigg(\dfrac{1}{2},-2\bigg)}$

<u>Step-by-step explanation:</u>

The vertex form of an absolute value equation is: $f(x)=|x-h|+k$ where

(h, k) is the vertex. In the given equation, $f(x)=\bigg|x-\dfrac{1}{2}\bigg|-2$ , the h-value is 1/2 and the k-value is -2.

So, the vertex (h, k) = (1/2, -2)

8 0

2 years ago

MULTIPLE CHOICE<br> What is LM?<br> 3x + 5<br> 4x + 7<br> LN = 33 cm

FromTheMoon [43]

Answer:

C. 14

Step-by-step explanation:

Add LM and MN

(3x + 5) + (4x + 7)

(4x + 3x) + (5 + 7)

7x + 12

As we know the total is 33

So,

7x + 12 = 33

Subtract 12 from 33, which gives me 21

Now,

7x = 21

To make x alone, divide both sides by 7, and then we will get x = 3

If x = 3

LM = 3x + 5

= (3*3) + 5

= 9 + 5

= 14

7 0

3 years ago

Find the solutions to x⁴-5x²-36=0 and the x-intercepts of the graph of y=x⁴-5x²-36.

disa [49]

Answer:

The solutions $x^4-5x^2-36=0$ are $x=3,\:x=-3,\:x=2i,\:x=-2i$ and the x-intercepts of $y=x^4-5x^2-36$ are $x=3,\:x=-3$

Step-by-step explanation:

Finding the solutions to $x^4-5x^2-36$ means finding the roots, a root is where the function is equal to zero.

The x-intercept is the point at which the graph crosses the x-axis. At this point, the y-coordinate is zero.

To find the roots you need to:

Rewrite the equation with $u=x^2$ and $u^2=x^4$

$u^2-5u-36=0$

Solve by factoring

$\mathrm{Break\:the\:expression\:into\:groups}\\u^2-5u-36=\left(u^2+4u\right)+\left(-9u-36\right)$

$\mathrm{Factor\:out\:}u\mathrm{\:from\:}u^2+4u=u\left(u+4\right)$

$\mathrm{Factor\:out\:}-9\mathrm{\:from\:}-9u-36=-9\left(u+4\right)$

$u^2-5u-36=u\left(u+4\right)-9\left(u+4\right)$

$\mathrm{Factor\:out\:common\:term\:}u+4\\\left(u+4\right)\left(u-9\right)$

$u^2-5u-36=\left(u+4\right)\left(u-9\right)=0$

Using the Zero factor Theorem: if ab = 0 then a = 0 or b = 0 (or both a = 0 and b = 0)

The solutions to the quadratic equation are:

$\:u=-4,\:u=9$

Substitute back $u=x^2$ , solve for x

$x^4-5x^2-36=(u-9)(u+4)=(x^2-9)(x^2+4)$

Apply the difference of squares formula

$x^4-5x^2-36=(x^2-9)(x^2+4)=(x-3)(x+3)(x^2+4)$

$(x-3)(x+3)(x^2+4)=0$

Using the Zero factor Theorem: if ab = 0 then a = 0 or b = 0 (or both a = 0 and b = 0)

The solutions are:

$\:x=3,\:x=-3,\:x=2i,\:x=-2i$

Because two of the solutions are complex roots the only x-intercepts are $x=3,\:x=-3$

3 0

3 years ago

The price of a radio is marked as rs 7500 if shopkeeper allows 20 % Discount and adds 13 % VAT . how much customer pay for radio

Lisa [10]

Answer:

a) A shopkeeper marked the price of an article a certain percentage above the cost price and he allowed 16% discount to make 5% profit. If a customer paid Rs 9.492 with 13% VAT to buy the article, by what percent is the marked price above the cost of the price article? (I hope this helps)

3 0

2 years ago