MATHEMATICS HIGH SCHOOL

Given the function f(x)=0.5|x-4|-3, for what values of x is f(x)=7?

A. x=-24, x=16
B. x=-16, x=24
C. x=-1, x=9
D. x=1, x=-9

Answers

Answer 1

Answer:

we have

$f(x)=0.5\left|x-4\right|-3$ -----> equation A

$f(x)=7$ -----> equation B

equate equation A and equation B

$0.5\left|x-4\right|-3=7$

Adds $3$ boths sides

$0.5\left|x-4\right|-3+3=7+3$

$0.5\left|x-4\right|=10$

Multiply by $2$ boths sides

$\left|x-4\right|=20$

we know that

The function absolute value has two solutions

Step 1

Find the first solution (positive case)

$+(x-4)=20$

Adds $4$ boths sides

$x-4+4=20+4$

$x=24$

Step 2

Find the second solution (negative case)

$-(x-4)=20$

Multiply by $-1$ boths sides

$(x-4)=-20$

Adds $4$ boths sides

$x-4+4=-20+4$

$x=-16$

therefore

the answer is the option B

$x=-16, x=24$

Answer 2

Answer: 7 = 0.5|x-4|- 3 add 3 to both sides: -
0.5|x-4| = 10 divide bs by 0,5:-
|x-4| = 20

either x - 4 = 20 or x - 4 = -20

this gives x = 24, x = -16

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So I need a little help here... I just learn this and I'm horrible at math :( Please state each steps clearly and explain them too (if you can, if not it's ok) Thanks!

Answers

$y = \sqrt{ (5x+3)/(x-5) }$
$y^(2) = (5x+3)/(x-5)$
Transpose the equation to eliminate any fractions:
$y^(2)(x-5) = 5x+3$
Expand the brackets:
$x y^(2) - 5 y^(2) = 5x+3$
Put x terms on one side and the others on the other side:
$xy^(2) - 5x = 5y^(2)+3$
Factorise to take x out of the terms:
$x(y^(2) - 5) = 5 y^(2) +3$
Transpose to leave only x on the left hand side of the equation:
∴ $x = (5 y^(2) + 3 )/( y^(2) -5 )$

A train can travel 1136 miles in 4 hours. what is the unit rate that this train is traveling per hour? _____ miles per hour

Answers

Good Morning

4hours .........1136 miles

1 hour ...........x

Cross-Multiply

4x= 1136*1

4x= 1136

x= 1136/4

x= 284

The train is traveling 284 miles per hour

I hope that's help !

Happy Sunday :)

Final answer:

To find the unit rate of the train's speed, divide the total distance traveled by the total time taken.

Explanation:

To calculate the unit rate at which the train is traveling per hour, you can apply a straightforward formula: divide the total distance covered by the total time taken. In this specific instance, the train covered a distance of 1136 miles within a time frame of 4 hours.

So, the unit rate for the train's speed is determined as follows:

Total distance traveled (1136 miles) divided by the total time taken (4 hours) equals 284 miles per hour.

This unit rate, expressed as 284 miles per hour, is a crucial metric for assessing the speed at which the train is moving. Understanding unit rates is valuable not only in transportation but also in various fields like economics, physics, and everyday calculations where quantities are compared with respect to time.

Learn more about Unit Rate here:

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A researcher wants to develop a product for families who have small children. He needs to determine if there is a nationwide interest in a toy that will help children describe their emotions. He asks only a sample of the population to complete his survey. What should be true of the sample so that the results of the survey can be used to predict the results of surveying the population?A) The size of the sample should be the same size as the population.
B)The families included in the sample should represent the families in the population.
C) The families included in the sample cannot be included in the population.
D)The size of the sample should be larger than the size of the population.

Answers

Here is the answer to the given question above. Given the scenario, that statement that is considered true of the sample so that the results of the survey can be used to predict the results of surveying the population is this: The families included in the sample should represent the families in the population. The answer would be option B.

Answer:

The answer is B.

Systems of equations word problem."Flying with the wind a plane went 183 km/h. Flying into the same wind the plane only went 141 km/hr. Find the speed of the plane in still air and the speed of the wind.

Answers

Well, the plane has speed p and the wind has speed w.
p+w=183, p-w=141. Add them up to get 2p=324 or p=162. The wind has speed 183-162=21 km/h, while the plane has the speed in still air 162 km/h.

A 1/2 gallon of paint covers 1/6 of a wall. How much paint is needed to cover the entire wall? Could u show me how to do this question?

Answers

"A 1/2 gallon of paint covers 1/6 of a wall."
So a gallon of paint covers 2/6 of a wall.

2/6 = 1/3

a gallon ⇒ 1/3 of a wall
3 gallons ⇒ 3/3 of a wall (entire wall)

Jordan takes 50% of the cherries from a bowl. then Mei takes 50%of the remaining cherries. Finally Greg takes 50 %of the remaining cherries. There are 3 cherries left. How many cherries were in the bowl before Jordan arrived

Answers

Answer:

Step-by-step explanation:

Let total cherries in a bowl=x

Jordan takes cherries=50% of x= $(50)/(100)x$

Remaining cherries= $x-(50)/(100)x=(50)/(100)x=(x)/(2)$

Mei takes cherries=50% of $(50x)/(100)=(x)/(4)$

Now, remaining cherries= $(x)/(2)-(x)/(4)=(x)/(4)$

Greg takes cherries=50% of $(x)/(4)=(x)/(8)$

Now, remaining cherries= $(x)/(4)-(x)/(8)=(x)/(8)$

Now,remaining cherries in a bowl=3

We have to find total cherries in a bowl before Jordan arrived.

According to question

$(x)/(8)=3$

$x=3* 8=24$

Hence, total cherries in a bowl=24

So in the final smallest bowl when half are removed there are 3 so the total amount was double 3 which is 6 before greg removed some.
Mei had removed half of the cherries which left 6 cherries so the total amount before Mei removed half was 12.
Jordan took half of the cherries which left 12. If you follow the same logic you double 12 which makes....
Good luck, hope this helped you understand the question more, feel free to comment and ask for help :)

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