Solve 2(5x + 6) < x

Amber and Allen both leave there house to go to their grandmother's house 240 miles away. Amber travels at a speed 60 mph. If sh

Montano1993 [528]

If she leaves 15 minutes earlier than Allen, she would have to drive at 56.47 mph to arrive at the same time as Amber

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more number and variables.

Amber travels at a speed 60 mph, hence the time taken (t) is:

60 = 240/t

t = 4 hours

If he leaves 15 minutes earlier, the time would be 4 hr + 0.25 hr (15 min) = 4.25 hr, hence:

Speed = 240 miles / 4.25 hr = 56.47 mph

If she leaves 15 minutes earlier than Allen, she would have to drive at 56.47 mph to arrive at the same time as Amber

Find out more on equation at: brainly.com/question/2972832

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4 0

2 years ago

The triangle T has vertices at (-2, 1), (2, 1) and (0,-1). (It might be an idea to

Firdavs [7]

Rewrite the boundary lines y = -1 - x and y = x - 1 as functions of y :

y = -1 - x ==> x = -1 - y

y = x - 1 ==> x = 1 + y

So if we let x range between these two lines, we need to let y vary between the point where these lines intersect, and the line y = 1.

This means the area is given by the integral,

$\displaystyle\iint_T\mathrm dA=\int_{-1}^1\int_{-1-y}^{1+y}\mathrm dx\,\mathrm dy$

The integral with respect to x is trivial:

$\displaystyle\int_{-1}^1\int_{-1-y}^{1+y}\mathrm dx\,\mathrm dy=\int_{-1}^1x\bigg|_{-1-y}^{1+y}\,\mathrm dy=\int_{-1}^1(1+y)-(-1-y)\,\mathrm dy=2\int_{-1}^1(1+y)\,\mathrm dy$

For the remaining integral, integrate term-by-term to get

$\displaystyle2\int_{-1}^1(1+y)\,\mathrm dy=2\left(y+\frac{y^2}2\right)\bigg|_{-1}^1=2\left(1+\frac12\right)-2\left(-1+\frac12\right)=\boxed{4}$

Alternatively, the triangle can be said to have a base of length 4 (the distance from (-2, 1) to (2, 1)) and a height of length 2 (the distance from the line y = 1 and (0, -1)), so its area is 1/2*4*2 = 4.

6 0

3 years ago

Krista's mom has told her she needs to make the pen ½ the size that she had planned (5 feet long by 4 ½ feet wide). What will th

saw5 [17]

Answer:

1. area of new pen = 11 $\frac{1}{4}$ $ft^{2}$

2. i. 5 feet by 2 $\frac{1}{4}$ feet

ii. 2 ½ feet by 4 ½ feet

Step-by-step explanation:

The size of the pen as planned = 5 ft long by 4 ½ ft wide

Area of the pen = length x width

= 5 x 4 ½

= 5 x $\frac{9}{2}$

Area of the pen = $\frac{45}{2}$

= 22 ½ $ft^{2}$

But, Krista has to make the pen ½ the size of planned. So that;

area of new pen = ½ x 22 ½

= ½ x $\frac{45}{2}$

= $\frac{45}{4}$

= 11 $\frac{1}{4}$

area of new pen = 11 $\frac{1}{4}$ $ft^{2}$

The area of the new pen would be 11 $\frac{1}{4}$ $ft^{2}$ .

The possible values she could use are:

i. 5 feet by 2 $\frac{1}{4}$ feet

ii. 2 ½ feet by 4 ½ feet

6 0

3 years ago

Can someone PLEASE help meeeeee

Novay_Z [31]

#1

(4,8)
(6,12)

Slope:-

m=12-8/6-4=4/2=2

Equation

y-8=m(x-4)
y=2x

Y intercept 0

#2

y=12x-20

Slope=12

Y intercept=-20

#3

m=13t

Slope=14

y intercept=0

7 0

2 years ago

tickets for a harlem globetrotter show cost $28 general admission, $43 courtside, or $173 bench seats. Nine times as many genera

densk [106]

Answer:

general admission tickets 1170

courtside tickets 985

tickets bench seats. 130

Step-by-step explanation:

To solve the problem, it is necessary to generate a system of equations with the information provided by the statement.

First be

x = # general admission tickets

y = # courtside tickets

z = # tickets bench seats.

The first equation would be that they sold nine times more general admission tickets than bench seats tickets.

That is: x = 9 * z (1)

And the second equation is that the number of general admission tickets sold was 55 more than the sum of the number of courtside tickets and bench seats tickets.

That is: x = 55 + y + z (2)

Now the third equation would be the money raised.

28 * x + 43 * y + 173 * z = 97605 (3)

Now if I replace I rearrange (1):

z = x / 9 (4) and replacement in 2, I have:

x = 55 + y + x / 9, rearranging:

y = (8/9) * x - 55 (5)

Now replacing (4) and (5) in 3, we have:

28 * x + 43 * ((8/9) * x - 55) + 173 * (x / 9) = 97605

Solving the above:

x = 1170, therefore

y = (8/9) * 1170 55 = 985

z = 1170/9 = 130

We can confirm this with equation (3)

28 * x + 43 * y + 173 * z = 97605

28 * 1170 + 43 * 985 + 173 * 130 = 97605

5 0

3 years ago

Solve 2(5x + 6) < x - 15 + 9x.​

Solve 2(5x + 6) < x - 15 + 9x.