Solve the equation. Check for extraneous solutions.

Answers

Answer 1

Answer: assume
if |a|=b
a=b and -a=b

so

9|9-8x|=2x+3
divide both sides by 9
|9-8x|=2/9x+1/3
assume
9-8x=2/9x+1/3 and
-9+8x=2/9x+1/3

9-8x=2/9x+1/3
times 9 both sides
81-72x=2x+3
add 72x both sides
81=74x+3
minus 3
78=74x
divide both sides by 74
39/37=x

other one
-9+8x=2/9x+1/3
multiply both sides by 9
-81+72x=2x+3
minus 2x both sides
-81+70x=3
add 81 to both sides
70x=84
divide boh sides by 70
x=6/5

x=39/37 and 6/5
check

9|9-8(39/37)|=2(39/37)+3
2646/37=189/37
false

9|9-8(6/5)|=2(6/5)+3
351/5=27/5
false

no soltion evidently, weird

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Dylan got his math test back and saw a -12 1/2 points on the top of his math test. The grade was 100% because he earned extra credit points. How much extra credit did Dylan receive on his math test?

Answers

Since he got 100 percent, that means he didn't lose any points overall on his test. Since it said he lost 12 1/2 points, Dylan got 12 1/2 points back.

Which is more?
1. Riding a bike 10 miles in 1 hour
2. Jogging 3 miles in 24 minutes

Answers

I say that number one is more reasonable but 10 miles in one hour, compared to 3 miles in 24 minuets
and 3*3 = 9
which is close to ten and
24 * 3 = 72 minuets
there are 60 minuets in an hour
so i would say the second option is correct :)

The line y= -3 is a reflection of the line y=5. What is the equation for the line of reflection?

Answers

Answer:

y = 1

Step-by-step explanation:

The line of reflection will be a parallel line midway between y = - 3 and y = 5

y = $(-3+5)/(2)$ = $(2)/(2)$ = 1

line of reflection is y = 1

Answer:

y=1

Step-by-step explanation:

the line of reflection will be a parallel line midway between y=-3and y=5

y=-3+5/2

=2/2=1

Decide whether the sequence 4,10,20,34,52 ....... is a linear model,Quadratic model or cubic model.

Answers

Answer:

Lineal.

Step-by-step explanation:

To determine if the sequence 4,10,20,34,52 ....... is a linear model, a quadratic model or a cubic model, the following mathematical logical reasoning must be carried out:

4 to 10 = +6

10 to 20 = +10

20 to 34 = +14

34 to 52 = +18

Thus, we can see at a glance that the sequence increases 4 numbers in each digit, adding first 6, then 10, then 14 and so on, with which the next numbers in that sequence should be 74 (+22), 100 ( +26), 130 (+30), 164 (+34), and so on.

Therefore, since there is no quadratic or cubic relationship, the sequence is linear.

Determine whether each number is a solution of the given inequality.
3y-8<22

Answers

y has to equal 9 or less

3y-8 < 22
3y < 30
y < 10

Hope this helps!!

Find the X-intercept of the line 4x+11y=20

Answers

Answer:

Step-by-step explanation:

To find the x-intercept of the line 4x+11y=20, we need to set y=0 and solve for x. This is because the x-intercept is the point where the line crosses the x-axis, which is the point where y=0.

First, substitute y=0 into the equation: 4x+11(0)=20

Simplify: 4x=20

Solve for x: x=5

Therefore, the x-intercept of the line 4x+11y=20 is 5.