Ask question

Ask question

All categories

4 years ago

15

1. Suzette ran and biked for a total of 110 mi in 7 h. Her average running speed was 5 mph and her average biking speed was 20 m

ph.
Let x = total hours Suzette ran.
Let y = total hours Suzette biked.

Use substitution to solve for x and y. Show your work. Check your solution.
(a) How many hours did Suzette run?
(b) How many hours did she bike?

1 answer:

timama [110]4 years ago

7 0

Answer:

Part a) Suzette ran 2 hours

Part b) Suzette biked 5 hours

Step-by-step explanation:

Let

x ------> total hours Suzette ran

y -----> total hours Suzette biked

we know that

x+y=7

x=7-y -----> equation A

5x+20y=110 -----> equation B

Solve the system by substitution

substitute equation A in equation B and solve for y

5(7-y)+20y=110

35-5y+20y=110

15y=110-35

15y=75

y=5 hours

Find the value of x

x=7-5=2 hours

therefore

Suzette ran 2 hours and biked 5 hours

<u><em>Check your solution</em></u>

Her average running speed was 5 mph

so

Find the distance

Multiply the speed by the number of hours

5(2)=10 miles

Her average biking speed was 20 mph

so

Find the distance

Multiply the speed by the number of hours

20(5)=100 miles

Adds the two distances

10 +100=110 miles ------> is correct

You might be interested in

Match the equations representing parabolas with their directrixes. y + 8 = 3(x + 2)2 y − 14 = -(x − 3)2 y + 7.5 = 2(x + 2.5)2 y

Shkiper50 [21]

Answer:

Part 1) $y+8=3(x+2)^{2}$ -----> $y=-8.08$

Part 2) $y-14=-(x-3)^{2}$ ----> $y=14.25$

Part 3) $y+7.5=2(x+2.5)^{2}$ ----> $y=-7.625$

Part 4) $y-17=-(x-3)^{2}$ -----> $y=17.25$

Part 5) $y+7=(x-4)^{2}$ ----> $y=-7.25$

Part 6) $y-6=-(x-1)^{2}$ ----> $y=6.25$

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

$y-k=\frac{1}{4p}(x-h)^{2}$

where

(h,k) is the vertex

The directrix is

$y=k-p$

case 1) we have

$y+8=3(x+2)^{2}$

the vertex is the point (-2,-8)

$\frac{1}{4p}=3$

$p=\frac{1}{12}$

The directrix is equal to

$y=-8-\frac{1}{12}=-8.08$

case 2) we have

$y-14=-(x-3)^{2}$

the vertex is the point (3,14)

$\frac{1}{4p}=-1$

$p=-\frac{1}{4}$

The directrix is equal to

$y=14+\frac{1}{4}=14.25$

case 3) we have

$y+7.5=2(x+2.5)^{2}$

the vertex is the point (-2.5,-7.5)

$\frac{1}{4p}=2$

$p=\frac{1}{8}$

The directrix is equal to

$y=-7.5-\frac{1}{8}=-7.625$

case 4) we have

$y-17=-(x-3)^{2}$

the vertex is the point (3,17)

$\frac{1}{4p}=-1$

$p=-\frac{1}{4}$

The directrix is equal to

$y=17+\frac{1}{4}=17.25$

case 5) we have

$y+7=(x-4)^{2}$

the vertex is the point (4,-7)

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

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

The directrix is equal to

$y=-7-\frac{1}{4}=-7.25$

case 6) we have

$y-6=-(x-1)^{2}$

the vertex is the point (1,6)

$\frac{1}{4p}=-1$

$p=-\frac{1}{4}$

The directrix is equal to

$y=6+\frac{1}{4}=6.25$

5 0

3 years ago

Find the quotient. 5 1/4 ÷ 1 3/4. *

weeeeeb [17]

Answer:

3

Step-by-step explanation:

私は怠惰なのでグーグルで調べました

5 0

3 years ago

Read 2 more answers

You need to move 45 boxes from the wearhouse to the loading dock. It takes 20 minutes to move 10 boxes. How long will it take fo

astraxan [27]

90 minutes because 20 + 20 + 20 + 20 + 10 = 90

7 0

3 years ago

What is the answer for 6r^2-10r-24

FrozenT [24]

$6r^2-10r-24 =0\\ \\a=6, \ b= -10, \ c= -24 \\ \\ \Delta =b^2-4ac = (-10)^2 -4\cdot6\cdot (-24) = 100+576 = 676 \\ \\ r_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{10-\sqrt{676}}{2\cdot 6 }=\frac{ 10-26}{12}= \frac{-16}{12}=- \frac{4}{3} \\ \\r_{2}=\frac{-b+\sqrt{\Delta }}{2a}= \frac{10+\sqrt{676}}{2\cdot 6 }=\frac{ 10+26}{12}= \frac{36}{12}=3\\ \\ 6r^2-10r-24 = 6(r+\frac{4}{3})(r-3)=(6r+8)(r-3)\\ \\ \\ Answer : \ 6r^2-10r-24 =(6r-8)(r-3)$

8 0

4 years ago

Pls help! Needing some info!

Neko [114]

Got two types of info here $ and #buttons
Line them accordingly and then cross multiply
a.
$18/12 dozen buttons =
$ x /4 dozen buttons
X= 4•18/12= $6
b.
$18/12 dozen buttons =
$ x/50 dozen buttons
X=18•50/12= $75
c.
$18/12 dozen buttons =
$27/x dozen buttons
X=27•12/18=18 dozen buttons

5 0

4 years ago