solve the absolute value inequality and express the solution in interval and algebraic notation

Answer:

Question 3.

[tex]y = \frac{2}{7} x - 3[/tex]

question 4

[tex]y = - 4x - 1[/tex]

question 5

[tex]y = 5x + 3[/tex]

Step-by-step explanation:

Question 3

1.Write down what is given in equation form

[tex]y = \frac{2}{7} x + c[/tex]

2. Insert the given point to work out c

[tex] - 5 = \frac{2}{7} ( - 7) + c[/tex]

[tex]c = - 3[/tex]

3. answer

[tex]y = \frac{2}{7} x - 3[/tex]

Question 4

1 write what was given in an equation

[tex]y = - 4x + c[/tex]

2. insert given point (-1;3) to work out c

[tex]3 = - 4( - 1) + c[/tex]

[tex]c = - 1[/tex]

3. final answer

[tex]y = - 4x - 1[/tex]

question 5

1.with what was given write it in equation form

[tex]y = 5x + c[/tex]

2. substitute the given point (-2;-7) to work out c

[tex] - 7 = 5( - 2) + c[/tex]

[tex]c = 3[/tex]

3.final answer

[tex]y = 5x + 3[/tex]

Answer:

Your answer would be 4 over 1

Answer:

-8 + (-10)

Hope this help!

Step-by-step explanation:

it is a linear equation

Normally two if them are given together to solve

hope it helps

We solve as follows:

Answer:

237

Step-by-step explanation:

3×(9-4)³ - 46×3
subtract 4 from 9 to get 5
3x5³-46x3
calculate 5 to the power of 3 and get 125
3x125-46x3

multiply 3 and 125 to get 375.

375-46x3
Multiply 46 and 3 to get 138
375-138

subtract 138 from 375 to get 237.
And there's your answer

You can follow the rule of BODMAS.

BODMAS stands for Bracket, Of, Division, Multiplication, Addition, Subtraction

By following the rule of BODMAS, the solution will be like this:

3×(5)³ - 46×3

= 3×125 - 46×3

= 375 - 138

= 237

I hope my explanation has helped you.

You can do well to declare this answer as the Brainiest Answer.

Thanks so much

Answer:

Least to greatest: 1. International finance center

2. Petronas towers

3. Zifeng towers

4. Burj Khalifa

Answer:

0.4

Step-by-step explanation:

The absolute value is just the number in the line things but positive.

The absolute value is the distance between a number and zero. The distance between − 0.4 and 0 is 0.4

if |-0.4| is all that is in the question it is 0.4

Answer: 60 and 68/1000

Step-by-step explanation:

Not sure if you wanted it in fraction, decimal, or percentage form.

Answer:

60 and 68.000

Step-by-step explanation:

i not sure if that was what u were looking for

For the given functions , f(1) = -3 and f(-2) = -6 .

In the question

a graph is given

we have to find the value of the functions  f(1) and f(-2)

the value of f(1) means the value of y, when x=1 .

we see that ,

on the graph when x = 1 , the value of y = -3 .

so the value of [tex]f(1)[/tex] = -3 .

the value of f(-2) means the value of y, when x = -2 .

we see that ,

on the graph when x = -2 , the value of y = -6 .

so the value of [tex]f(-2)[/tex] = -6 .

Therefore , For the given functions , f(1) = -3  and f(-2) = -6 .

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[H+] = -1.7243

Explanation:

Since [H+] = 5.7 * 10 - 4, in the function -log[H+] representing pH, replace H+

pH = -log [5.7 *10 - 4]

pH = -log[53]

pH = -1.7243

NB:

This number is rounded up from -1.72427.....

Answer: 0.8 m

Step-by-step explanation:

1.  The perimeter P of the wooden frame is equal to:

P=2(0.8+0.5)

P=2(1.3)

P=2.6 m

2. The remaining length of wood is equal to:

3.4-2.6=

0.8 m

The value of y in each case are 18,8 and 4 respectively.

Given equation:-

y = -x + 9

Values of x = {-9, 1, 5}

We have to find the corresponding values of y for each value of x.

Putting x = -9 in the given equation, we get,

y = -(-9) + 9 = 9 + 9 = 18

Putting x = 1 in the given equation, we get,

y = -1 + 9 = 8

Putting x = 5 in the given equation, we get,

y = -5 + 9 = 4

Hence, the values of y are {18, 8,4}

The complete ordered pair of (x,y) is given by:-

(-9,18)

(1,8)

(5,4)

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Answer:

Step-by-step explanation:

A, B:  Define the Variables and Write Equations

Let T be the number of toppings.

Option 1:  $3 + $0.75*T

Option 2:  $4 + $0.50*T

C.  Graph the System

See the attached graph.  The intersection point is (4,6).  This means that 4 toppings will result in a cost of $6 for both yogurt options.

D.  Solution to the Problem

The solution is given above, but we can also solve using equations, instead of graphing.  We want the value of T that will make these expressions equal:

$3 + $0.75*T = $4 + $0.50*T

$0.25*T = $1

T = 4 toppings

=============

CHECK:

For 4 toppings:

Option 1:  $3 + $0.75*T

                  $3 + $0.75*(4)

                  $3 + $3 = $6

Option 2:  $4 + $0.50*T

                  $4 + $0.50*(4)

                  $4 + $2 = $6

Four toppings will make both options equal in cost.

E:  Is the solution reasonable?

Yes.  The cheaper option ($3) has a more expensive topping, so at some point (at 4 toppings) it will be the same price as the second option, with a higher initial price, but with cheaper toppings.

Answer: 1/12

Step-by-step explanation:

1) Set up the equation

1/3 / 4

2) Change 4 into a fraction

1/3 / 4/1

3) Change the divide into a multiply by flipping the 2nd fraction

1/3 * 1/4

4) Solve

1/12

Answer:

No

Step-by-step explanation:

The graph fails the vertical line test. More than one y-value is on one x-value.

Answer:

10× + 25y ≤ 25

Answer:

0.1x + 0.25y ≤ 25

Step-by-step explanation:

A call within the US is $0.10, a call to France is $0.25, and you have $25.00. Your total amount of money spent depends on how many calls you make. Now, turn this information into an inequality.

Answer:

How is this math?

Step-by-step explanation:

Answer:

Visiting the zoo on cold days limits the number of people there and it isn't too hot so you don't stand in the sweltering heat. Besides, on cold days, the animals may be in a better mood, but be cautioned, remember to bring a jacket just in case.

Step-by-step explanation:

The number of members that the club had last year was 85

The number of members that the club has this year is 120.

The number by which it increased is

120 - 85 = 35

Percentage is expressed in terms of 100. Thus, the percentage increase is

35/85 * 100

= 41.2%

The percentage isncrease is 41.2%

Considering exponential functions, it is found that:

6.

12. The number of hits 3 weeks from now will be of 27,348, hence option B is correct.

An exponential function is modeled according to the rule given next:

[tex]y = ab^x[/tex]

The parameters of the exponential function are defined as follows:

For item 6, considering the points (0,10) and (1,7.5), the parameters are given as follows:

For item 12, the initial amount and the rate of change are given as follows:

a = 34,000, b = 1 - 0.07 = 0.93.

Hence the number of hits x weeks from now is modeled according to the following function:

[tex]h(x) = 34000(0.93)^x[/tex]

After 3 weeks, x = 3, hence the number of hits will be of:

[tex]h(3) = 34000(0.93)^3 = 27348[/tex]

Meaning that option B is correct.

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Answer:

-12

Step-by-step explanation:

hope it helps

have a nice evening

If we call the middle number in the sequence [tex]x[/tex], the numerical values of the other terms will be [tex]x-1[/tex] and [tex]x+1[/tex], respectively, since they are consecutive.

We are told that [tex]4[/tex] times the smallest number is equal to [tex]3[/tex] times the largest number. Let us write our equality.

We found our number in the middle. Since it wants the value of our largest number, let's add 1 to the middle number.

The answer is B.

Answer:

a

Step-by-step explanation:

your a could be the same.

The side MD measures 10 cm and ∠D=72° for the given triangle.

What is triangle?

The perimeter of ΔMUD= 38cm

MU=DU=14cm

∠U=36°

⇒∠M=∠D=x

Applying Angle sum property,

36°+x+x=180°

2x=180°-36°

x=72°

∴∠D=72°

Perimeter of triangle=14+14+MD

38=28+MD

⇒MD=10cm.

The side MD measures 10 cm and ∠D=72° for the given triangle.

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The bacteria present at t=37 minutes is found to be 8.40, with no change in growth rate.

When a population's per capita growth rate remains constant, regardless of population size, exponential growth occurs, causing the population to grow exponentially as the population increases.

Given:

P = 340

It has been discovered that a specific bacterial population doubles in 20 minutes.

k = 2/20 = 0.1

t = 37 minutes

We know that,

P = P₀[tex]e^{kt}[/tex]

340   = P₀([tex]e^{0.1*37}[/tex])

340 =P₀(40.44)

P₀ = 8.40

As a result, the bacteria that will be present in t=37 minutes is found to be 8.40 with no change in growth rate.

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Answer:

See Explanation

Step-by-step explanation:

[tex]x+y=40\\2.25x+1.75y=83.5\\[/tex]

from the first you have

[tex]h=40-p[/tex] substitute into the second:

[tex]2.25(40-p)+ 1.75x= 83.5\\90-2.25y+1.75x= 83.5[/tex]remaining

[tex]0.5y=6.5\\p= \frac{6.5}{0.5} =13\\[/tex]

substitute back into [tex]h= 40 - y\\h = 40 - 13 = 27[/tex]

Hope this helped :)

Expressing y in terms of x gives y = x - 19/ 6

Subject of formula can be defined as the variable that is being expressed in terms of other variables in an equation, function or expression.

It is also described as the variable that is being worked out in an expression or equation.

It is made to stand alone on on side of the equality sign.

We have the equation;

6(x-y) = 19

To make 'y' the subject of formula, let's take the following steps;

Divide both sides by 6, we have;

x - y = 19/ 6

now, take the variable 'x' over the equality sign

-y = 19/ 6 - x

Divide both sides by -1

y = x - 19/ 6

Hence, the equation is y = x - 19/ 6

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If the amount deposited is a positive integer , so the amount withdrawn is represented by -3748  and the balance amount in the Manvita's account is Rs 1252 .

In the question ,

it is given that

Money deposited by Manvita =  Rs 5000 .

Money withdrawn by Manvita = Rs 3748 .

Since , amount deposited is a positive integer ,

So, the amount withdrawn will be a negative integer

Balance in Manvita's account = Money deposited + Money Withdrawn

Substituting the values , we get

Balance in Manvita's account = 5000 + (-3748)

= 5000 - 3748

= 1252

Therefore , if the amount deposited is a positive integer , so the amount withdrawn is represented by -3748  and the balance amount in the Manvita's account is Rs 1252 .

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