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3 years ago

9

Raj gets 1.5 mile head start and runs at a rate of 4.5 miles per hour.Jacinda's progress is represented by a graph that goes thr

ough the points (1,10), (2,20), (3,30). How long will Jacinda need to run to catch up with Raj?

1 answer:

Anuta_ua [19.1K]3 years ago

4 0

Jacinda: d = 10 * t ( a rate: 10 miles per hour )
Raj : d = 1.5 + 4.5 * t
Jacinda will catch up with Raj when:
10 t = 1.5 + 4.5 t
10 t - 4.5 t = 1.5
5.5 t = 1.5
t = 1.5 : 5.5 = 0.27 hours = 16.2 min = 16 min 12 seconds

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16 less than a number is 54.Write and solve an Algebraic Equation

vova2212 [387]

Step 1:

For a number, let us use n.

We know the equation equals 54, and we also know that 54 is sixteen less than n. Thus, we can make the equation:

$n - 16 = 54$

Step 2:

Now, to solve the equation, we simply have to get the integers to one side. To do this, add 16 to both sides of the equal sign. Our answer is:

$n = 70$

Hope this helps.

6 0

3 years ago

Read 2 more answers

A mixture of 12 liters of chemical A, 16 liters of chemical B, and 26 liters of chemical C is required to kill a destructive cro

VMariaS [17]

Answer:

From Commercial spray X: 4 liters from Chemical A, 8 liters from Chemical B and 8 liters from Chemical C.
From Commercial spray Y: 18 liters of Chemical C
From Commercial spray Z: 8 liters of Chemical A and 8 liters of Chemical B.

Step-by-step explanation:

Since we need a lot of chemical C, we are going to leave Commercial spray Y for last in case we lack in case we need more Chemical C, which is supplied by spray Y.

We need to cover the demand of both chemical A and B. For each liter of Chemical A we get 2 liters of Chemical B by using Commercial spray X. And for each liter of Chemical A we get 2 liters of Chemical B by using spray Z.

We will call X the number of units of Commercial spray X used, where each unit contains 1 liter of Chemical A, 2 liters of Chemical B and 2 iters of Chemical C. Y is the number of units of Commercial spray Y used, containing each of them 1 liter of Chemical C, and Z the number of units of commercial spray Z used, on units containing both 1 liter of Chemical A and Chemical B.

We can represent the amount of liters we have for each chemical on a vector of the form <em>(a,b,c)</em> where a reresents the amount of Chemical A, b the amount of chemical B, and c the amount of chemical C. We want<em> (a,b,c)</em> to be equal to (12,16,26), in other words, we want a to be 12, b to be 16 and c to b 26. Furthermore we can obtain <em>(a,b,c) </em>by using this equation

(a,b,c) = X * (1,2,2) + Y * (0,0,1) + Z * (1,1,0) = (1*X+0*Y+1*Z,2*X+0*Y+1*Z,2*X+1*Y+0*Z) = (X+Z,2*X+Z,2*X+Y)

Thus, we have

a = X+Z = 12
b = 2*X+Z = 16
c = 2*X+Y = 26

We can substract the second equation with the first one to obtain the value of X:

X = b-a = (2*X+Z)-(X+Z) = 16-12 = 4

Replacing X by 4, we obtain on the first expression that 4+Z = 12, hence, Z = 8. Since X is 4, 2*X+Y = 8+Y = 26. This gives us that Y must be 18.

We conclude that we need the following amount of Chemical A, B and C:

From Commercial spray X: 4, 4*2 = 8 and 4*2 = 8 liters respectively
From Commercial spray Y: 18 liters of Chemical C
From Commercial spray Z: 8 liters of Chemical A and 8 liters of Chemical B.

I hope i could help you!

6 0

3 years ago

Suppose you and three friends are equally sharing the total cost C of a mean, and you pay $7. Which equation represents this sit

Brrunno [24]

The equation would be c÷3=7 (haha i think thats the answer)

7 0

3 years ago

In 2005 the population of a district was 35.700 with a continuous annual growth rate of approximately 4%, what will the populati

denpristay [2]

Given:

Population is 2005 = 35,700

growth rate = 4% = 0.04

To find:

The population in 2030.

Solution:

The general exponential growth model is

$y=a(1+r)^t$

where, a is initial value, r is growth rate and t is time in years.

Let the initial year is 2005. So, number of years between 2005 to 2030 is

$2030-2005=25$

Putting a=35,700, r=0.04 and t=25 in the above model.

$y=35,700(1+0.04)^{25}$

$y=35,700(1.04)^{25}$

$y=35,700(2.665836)$

$y=95170.3452$

Approximate the value to the nearest whole number.

$y\approx 95,170$

Therefore, population of the district will be about 95,170.

8 0

3 years ago

What is the answer i really need help<br> 2x-7+-9x+81

jok3333 [9.3K]

<em>Your expression seems a little incomplete. It seems you mean to ask </em>

$2x-7+\left(-9x\right)+81=0$

<em>So, I am solving the question based on this, which anyways will solve your query.</em>

Answer:

Please check the explanation.

Step-by-step explanation:

Given the expression

$2x-7+\left(-9x\right)+81=0$

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a$

$2x-7-9x+81=0$

$\mathrm{Group\:like\:terms}$

$2x-9x-7+81=0$

$\mathrm{Add\:similar\:elements:}\:2x-9x=-7x$

$-7x-7+81=0$

$\mathrm{Add/Subtract\:the\:numbers:}\:-7+81=74$

$-7x+74=0$

$\mathrm{Subtract\:}74\mathrm{\:from\:both\:sides}$

$-7x+74-74=0-74$

$-7x=-74$

$\mathrm{Divide\:both\:sides\:by\:}-7$

$\frac{-7x}{-7}=\frac{-74}{-7}$

$x=\frac{74}{7}$

Therefore, the answer is:

$x=\frac{74}{7}$

3 0

3 years ago