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2 years ago

Solve the equation. −10x + 1 + 7x = 37

2 answers:

8 0

You combine like terms which are -10x and 7x and 1 and 37. Then it becomes -3x=36. x would equal to 36/-3, which is -12.

ycow [4]2 years ago

6 0

−10x+1+7x=37

Simplify both sides of the equation.

−10x+1+7x=37

Simplify:

−10x+1+7x=37

(−10x+7x)+(1)=37(Combine Like Terms)

−3x+1=37

−3x+1=37

Subtract 1 from both sides.

−3x+1−1=37−1

−3x=36

Divide both sides by -3.

−3x/−3 = 36/−3

x=−12

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You and a friend have a hula hoop competition. you win 3 out of every 7 trials. your friend wins 5 more trials than you. how man

Ivenika [448]

Answer:

Total number of trials is 35.

Step-by-step explanation:

Given : Me and my friend have a hula hoop competition. I win 3 out of every 7 trials. My friend wins 5 more trials than me.

To find : How many trials are in the competition?

Solution :

Probability of my winning is 3 out of 7 trials $=\frac{3}{7}$

and probability of my friend's winning is $=1-\frac{3}{7}=\frac{4}{7}$

Let there be n numbers of trials.

Therefore, my score after n trials $=\frac{3n}{7}$

and my friend's score after n trials $=\frac{4n}{7}$

Now, the number of trials my friend won more than me is

$\frac{4n}{7}-\frac{3n}{7}=\frac{n}{7}$

We know, that my friend won 5 more trials than me so comparing the actual and given we get,

$\frac{n}{7}=5\\n=7\times5=35$

Therefore, total number of trials is 35.

We can also verify our answer by placing value of n,

After 35 trials I will win $\frac{3\times 35}{7}=15$ trials

and my friend will win $\frac{4\times 35}{7}=20$ trials.

Hence, my friend won 5 more trials than me.

3 0

2 years ago

A motorboat takes 3 hours to travel 144 km going upstream. The trip takes 2 hours going downstream. What is the rate of the boat

allsm [11]

Let x be rate of boat in still water
let y be rate of current

we use this equation to relate quantities:
distance = speed · time

we have two unknowns so we might need to create a system of equationss

upstream:

speed (in km/h) = x - y
(we get speed of boat then subtract the current's speed from it since current is going against boat direction)

time = 3 hours

distance = 144 km

downstream:

speed (in hm/h) = x + y
(we get speed of boat then add the current's spd from it since current is going against boat direction)

time = 2 hours

distance = 144 km (same distance upstream and downstream)

using distance = speed times time

for upstream
144 = 3(x-y)
144 = 3x - 3y

for downstream
144 = 2(x+y)
72 = x + y

system of eqns:
144 = 3x - 3y
72 = x + y

solve by substitution: move 72 = x + y into x = 72 - y and subst into other equation for x

144 = 3(72 - y) - 3y
144 = 216 - 3y - 3y
144 = 216 - 6y
144 - 216 = -6y
-72 = -6y
y = 12 km/h

Use x = 72 - y to find x with y = 12: x = 72 - 12 = 60 km/h

rate of boat in still water is 60 km/h
rate of the current is 12 km/h

6 0

2 years ago

A one story home has a total square footage of 1,200. If 900sq ft of the home has a basement, and 300 sq ft has a slab foundatio

anastassius [24]

Answer:

it has 1200

Step-by-step explanation:

because 900+300=1200

8 0

1 year ago

Read 2 more answers

A father lifts a toddler 1.5 m up in the air. The child gains 187.5 J of energy in her gravitational potential energy store as a

bearhunter [10]

The mass of the toddler is 12.5 kg.

Step-by-step explanation:

The equation for gravitational potential energy is Ep=mgh where;

Ep=gravitational potential energy

m=mass of an object

g=gravitational field strength

h=height in meters

Given that ; h= 1.5m, Ep=187.5J , g=10 N/kg then finding m;

Ep=mgh

187.5=m*10*1.5

187.5=15m

187.5/15 =15m/15

12.5 kg=m

Learn More

Gravitation potential energy : brainly.com/question/939365

Keyword : Mass, gravitational potential energy

#LearnwithBrainly

5 0

2 years ago

Find the P-value in a test of the claim that the mean IQ score of acupuncturists is equal to 100, given that the test statisti

klemol [59]

Answer:

P-value = 0.0455

Step-by-step explanation:

In this question, we are concerned with calculating the P- value in a test.

Mathematically we know that;

P-value = 2 * P(Z > |z|)

Please check attachment for complete solution and by step explanation

7 0

2 years ago