Two negative integers are 5 units apart on the number line, and their product is 126. What is the sum of the two integers?

A. –23
B. –5
C. 9
D. 14

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Answer:

  z = 6/13

Step-by-step explanation:

The new value of x is 13/3 times the old value. Since z is inversely proportional to x, it will be multiplied by the inverse of that, 3/13.

  2 × 3/13 = 6/13 . . . . value of z when x=13

Answer:

1 -> f

2 -> a

3 -> d

4 -> b

5 -> e

6 -> c

Step-by-step explanation:

We are given:

h(x) = 2 - 2x and g(x) = -2^x+2

a) k(x)= (g-h)(x) = g(x) - h(x)

              = -2^x+2 - (2 - 2x)

              = -2^x+2 - 2 + 2x

              = -2^x+2x or 2x-2^x

k(x) = 2x-2^x = (g-h)(x)

So, 2 matches with a

b) k(x)= (g+h)(x) = g(x) + h(x)

              = -2^x+2 + (2 - 2x)

              = -2^x+2 + 2 - 2x

              = -2^x+4-2x or 4 - 2^x -2x

So, k(x) = 4 - 2^x -2x = (g+h)(x)

So, 4 matches with b

c) k(x)= (2h - 2g)(x) = 2h(x) - 2g(x)

              =  2(2 - 2x)-2(-2^x+2)

              = 4 - 4x+2.2^x-4

              = -4x+2^x+1 or 2^x+1-4x

So, k(x) = 2^x+1-4x = (2h - 2g)(x)

So, 6 matches with c

d) k(x) = (h-2g)(x) = h(x) - 2g(x)

         = (2 - 2x)-2(-2^x+2)

         = 2 - 2x+2.2^x-4

         = -2-2x+2^x+1

         = 2^x+1-2x-2

So, k(x) = 2^x+1-2x-2 = (h-2g)(x)

So, 3 matches with d

e) k(x) = (h-g)(x) = h(x) - g(x)

          = (2 - 2x)-(-2^x+2)

              = 2 - 2x+2^x-2

              = -2x+2^x or 2^x-2x

So, k(x) =  2^x-2x = (h-g)(x)

So, 5 matches with e

f) k(x) = (2g+h)(x) = 2g(x)+h(x)

          = 2(-2^x+2) + (2 - 2x)

          = -2.2^x+4 + 2 - 2x

          = -2^x+1+6-2x or 6 - 2^x+1-2x

So, k(x) = 6 - 2^x+1-2x = (2g+h)(x)

So, 1 matches with f

Final answer:

The function formulas are h(x) = 2 - 2x and g(x) = -2x + 2.

Explanation:

h(x) = 2 - 2x

g(x) = -2x + 2

Even function times an even function produces an even function, Odd function times an odd function produces an even function.

Answer:

5/75 in my opinion. 75 is total of hot drink

Step-by-step explanation:

Answer:

23/14

Step-by-step explanation:

42x - 5 = 64

Add 5 to both sides in order to isolate 42x

42x = 64 + 5

42x = 69

Divide 42 from both sides in order to isolate x

x = 69/42

The answer gives an uneven decimal so it'd be best to leave it as a simplified fraction. The simplified fraction is 23/14.

Answer:

x = 1.64

Step-by-step explanation:

42x – 5 = 64

add 5 to both sides

42x - 5 + 5 = 64 + 5

42x = 69

divide via by 42

x = 69/42

x = 1.64

Hope this helps!

Answer:

Option C is correct.

Step-by-step explanation:

We need to multiply the following terms using vertical multiplication method

 3x^2-5x+1

x x^2+2x+4

The vertical multiplication is shown in the figure attached.

The result is: 3x^4+x^3+3x^2-18x+4

So, Option C is correct.

The vertical method of multiplication involves multiplying each digit of one number by each digit of another, one at a time, recording partial results and adding them together for the final result.

To perform multiplication using a vertical method, first write the numbers vertically aligning them properly. We will be multiplying like this:

Start from the rightmost digit of the second number (bottom number) and multiply it with each digit of the first number (top number), advancing from right to left. Record each result underneath, shifted appropriately (similar to 'carry digits' in addition). After fully multiplying by one digit, proceed to the next digit in the second number, remembering to shift your results accordingly. Finally, add all the results together to get the final answer. This is the vertical method of multiplication.

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Answer:

Option A. True

Step-by-step explanation:

we know that

The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

we have

4,3 and 6

Applying the triangle inequality theorem

case 1) 4+3 > 6 -----> is true

case 2) 3+6 > 4 ----> is true

therefore

The given segments could form a triangle

Is true

Answer: true

Step-by-step explanation:

Answer:

83.0 degrees to the nearest tenth.

Step-by-step explanation:

17^2 = 8^2 + 16^2 - 2*8*16 cos X

cos X =  (17^2 - 8^2 - 16^2)  / - 2*8* 16

cos X =  0.12109

X = 83.04 degrees

Answer:

Step 1: Factor left side of equation.

(5x−1)(3x−5)=0

Step 2: Set factors equal to 0.

5x−1=0 or 3x−5=0

x=

1 /5

or x=

5 /3

Answer:::::::::

x=5/3 or x=1/5

Answer:

  $2701.11

Step-by-step explanation:

The buyer owes for taxes for the remainder of the year, 11 days in May and 7 more months: 7 11/30 months out of 12.

  (7 11/30)(1/12)(4400) = (221/360)(4400) = 2701 1/9 ≈ 2701.11

The buyer will owe prorated taxes of $2701.11.

Answer:

(x+3)(3x-5)(3x+5)

Step-by-step explanation:

Let's consider the possible rational zeros:  factors of -75 over factors of 9

So one such possible 0 is -3

let's try it and see if it works:

-3   |    9          27          -25       -75

     |               -27             0         75

       ------------------------------------------

           9          0            -25         0

So x+3 is a factor and we have another there which is 9x^2+0x-25 or 9x^2-25

So far we have this as the factored form (x+3)(9x^2-25)

The second factor is a difference of squares so we can factored this more:

(x+3)(3x-5)(3x+5)

--------You could have also done factored by grouping here:

9x^3+27x^2-25x-75

(9x^3+27x^2)+(-25x-75)

9x^2(x+3)+-25(x+3)

(x+3)(9x^2-25)

(x+3)(3x-5)(3x+5)

Answer:

Step-by-step explanation:

9n^3 + 27n^2 – 25n – 75=9n²(n+3)-25(n+3)

                                         = (n+3)(9n²- 25)

but : 9n²- 25 = (3n)² - 5²

by identity : a²-b² =(a-b)(a+b)

now : a =3n  and b = 5 you have : 9n²- 25 = (3n)² - 5² = (3n-5)(3n+5)

Factor the polynomial :

9n^3 + 27n^2 – 25n – 75=(n+3)(3n-5)(3n+5)

Answer: Hiking was most prefered between ages 20-29

Answer:

Step-by-step explanation:

Given that a survey asked two age groups which summer sport they most preferred. the results are shown in the table below.

We have to find which sport was most preferred by people by ages 20-29 and what is the relative frequency within this age group

From the table we find that age group 20-29 prefers s

ski        15           [tex]\frac{15}{268}[/tex]

Swim    88          [tex]\frac{88}{268}[/tex]

Kayak   42          [tex]\frac{42}{268}[/tex]

Hike    123          [tex]\frac{123}{268}[/tex]

Total   268          1

We find that hike liking are more in this age group

Relative frequency calculated as frequency/268 is shown above.

Answer: c. 91,445,760 yd3

Step-by-step explanation:

571,536 x 48 = 27,433,728

27,433,728 ÷ 3 = 9,144,576

9,144,576 x 10 = 91,445,760

Answer:

Step-by-step explanation:

The formula for the perimeter of a rectangle is ...

  P = 2(L+W)

If the length is 30 yards more than the width, we can use L = W+30 and substitute known values into the above formula:

  300 = 2((W+30) +W)

  150 = 2W +30 . . . . . divide by 2 and collect terms

  120 = 2W . . . . . . . . . subtract 30

  60 = W . . . . . . . . . . . divide by 2

  60+30 = L = 90

The length is 90 yards; the width is 60 yards.

Answer:

[tex]d=\sqrt{26}\ m[/tex]  or  [tex]d=5.1\ m[/tex]

Step-by-step explanation:

The question in English is

Juan built a ramp that is 5 m long and 1 m high. How much is the distance (d) he travels when he climbs the ramp?

let

x -----> the length of the ramp

y ----> the height of the ramp

d ----> the distance Juan travels when he climbs the ramp

we know that

Applying the Pythagoras Theorem

[tex]d^{2}=x^{2}+y^{2}[/tex]

we have

[tex]x=5\ m[/tex]

[tex]y=1\ m[/tex]

substitute the given values

[tex]d^{2}=5^{2}+1^{2}[/tex]

[tex]d^{2}=26[/tex]

[tex]d=\sqrt{26}\ m[/tex] -----> exact value

[tex]d=5.1\ m[/tex] ----> approximate value

The polynomial remainer theorem says that a polynomial [tex]p(x)[/tex] leaves a remainder of [tex]p(c)[/tex] when divided by [tex]x-c[/tex]. When [tex]x=2[/tex], we have

[tex]2x^3+ax^2+3x-5=4a+17[/tex]

[tex]x^3+x^2-2x+a=a+8[/tex]

Both operations leave the same remainder, which means

[tex]4a+17=a+8\implies3a=-9\implies\boxed{a=-3}[/tex]

Then the remainders are both 5.

Answer:

y = sec(x) +2

i got you

Answer:

B: Exponential decay

Step-by-step explanation:

Answer:

exponential decay

Step-by-step explanation:

[tex]f(x)= 2(\frac{1}{2})^x[/tex]

[tex]f(x)= ab^x[/tex] is an exponential function, where 'a' is the initial value and 'b' is the exponential factor

When the value of 'b' is between 0 and 1 then it is exponential decay

when the value of 'b' is greater than 1 then it is an exponential growth

In the given exponential function , the value of b is 1/2 that is 0.5

The value of 'b' is between 0 and 1 so it is an exponential decay

Answer:

Step-by-step explanation:

A vertical line intersects the graph twice, so the relation is not a function. It is only allowed to intersect once if the relation is a function.

The domain is the horizontal extent, which is from -2 to +2.

The range is the vertical extent, which is -4 to +4.

The relation is indeed a function, and its domain is [-2, ∞), and its range is (-∞, ∞), as you assumed. The verification process aligns with your initial statements.

If the assumed domain is [-2, ∞) and the assumed range is (-∞, ∞), it suggests that you believe the relation is a function that is defined for all real numbers and can output any real number.

To determine whether the relation is indeed a function, we need to check whether each input (x-value) corresponds to a unique output (y-value) and ensure it satisfies the vertical line test. Let's proceed with the verification:

Function Test (Vertical Line Test):Trace a vertical line through the entire graph. If the vertical line intersects the graph at only one point for each x-value, then the relation is a function. If the vertical line intersects the graph at more than one point for any x-value, then the relation is not a function.

Based on the assumed domain and range, it appears that you are considering the relation to be a function defined for all real numbers. In such a case, the relation would be a function by definition, as it assigns a unique y-value to each x-value.

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Answer:

b. x + y = 4

Step-by-step explanation:

For to lines to have an infinite number of points that intersect, the lines have to have the exact same equation, so that every coordinate of H and K is the exact same.

Simplify the equation for H:

[tex]2x+2y=8\\2y=8-2x\\y=4-x[/tex]

Rearrange the equation:

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

Answer:

  Php 770.00

Step-by-step explanation:

The cost of labor is ...

  (hours) × (hourly rate)

  = (3 h) × (Php 150.00/h) = Php 450.00

The total cost is ...

  total cost = cost of labor + cost of parts

  = (Php 450.00) + (Php 320.00) = Php 770.00

Randolf owes Mr. Solidarios Php 770.00 for the repair.

Answer:

YOUR ANSWER IS C.(x-6)²=94

Step-by-step explanation:

HENCE PROVED

Answer:

Answer: The Answer Is B

Answer:

I think is D is the best answer

14 different outcomes.

3 blue + 4 red = 7 different marbles you could draw total.

since you have heads or tails possible with each of the 7, you multiply by 2(heads & tails)

7x3=14

Follow below steps:

When selecting a marble from a bag and flipping a coin, we are combining two separate actions that result in a compound event. The number of possible outcomes in the sample space can be calculated by multiplying the number of outcomes for each action. Since there are 3 blue marbles and 4 red marbles, there are 3 + 4 = 7 possible outcomes for drawing a marble. For flipping a coin, there are 2 possible outcomes: Heads (H) or Tails (T). To find the total number of possible outcomes for the combined actions, we multiply the outcomes for drawing a marble by the outcomes for flipping a coin: 7 (marble outcomes) times 2 (coin outcomes) = 14 possible outcomes in the sample space.

Janet = 1/3

Gary = 1/2

(1/3) + (1/2) = 5/6

Let x = time they both can do the job together

(1/2) + (5/6)x = 1

Solve for x to find your answer.

Answer:

16 shirts

Step-by-step explanation:

To determine the number of shirts that can be made, take the total amount of cloth and divide by the cloth needed per shirt

6 ÷ 3/8

Copy dot flip

6 * 8/3

48/3

16

We can make 16 shirts

Answer:

31 aces

Step-by-step explanation:

To find the number of aces you would expect, take the probability of an aces and multiply by the number of tries

1/13 * 400 =30.76923

Rounding up, approximately 31 aces

Answer:

30 times

Step-by-step explanation:

1/3 * 400

30.76923

31 times

Answer:

B.

Step-by-step explanation:

Basically, to draw a dot plot, what you do is place one circle above the corresponding value on the number line for each value in the data set, ie. if there is a 0 in the data set, then you would draw one 'dot' above 0 on the number line. If there was another 0, then you would draw another dot above the dot you drew for the first 0, and so on.

The data set given is:

0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8

If we count the number of each value, then we can say that:

a) there are three 0's

b) there are four 1's

c) there are three 2's

d) there are two 3's

e) there are two 4's

f) there is one 8

Now you could draw this up on a dot plot and compare this with the answers, or you could technically also just look at the dot plots in the multiple choice answers and count each of the values to see which one matches up with the values we defined above. So:

A. There are three 0's (correct), four 1's (correct), three 2's (correct), but there are no 3's - therefor this is not the correct dot plot.

B. There are three 0's (correct), four 1's (correct), three 2's (correct), two 3's (correct), two 4's (correct) and one 8 (correct) - therefor this is the correct dot plot.

We could use the same method to check if C and D were correct; then we would see that C only has two 0's and one 3 and is thus incorrect, and D only has one 3 and one 4, and has an extra value of 5, thus it is also incorrect.

Therefor, the answer is B.

Whilst this method may be used, a quick sketch of the dot plot may be a little easier to work with to compare visually with the answers, however everyone has their own way so try both methods and see what works for you.

''Option B'' shows the correct dot plot.

We have to given that,

A teacher asked her students how many pets they own.

Here are the results:

0,0,0,1,1,1,1,2,2,2,3,3,4,4,4,8

Now, From the data set,

0 is repeat 3 times.

1 is repeat 4 times.

2 is repeat 3 times

3 is repeat 2 times.

4 is repeat 3 times

8 is repeat only 1 times.

Hence, Option B shows the correct dot plot.

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Answer:

1. y=-5x+10

Step-by-step explanation:

if it reflect over the x it changes the y if it reflects over y it changes the x

The function y = f(x), when shifted down by 2 units and then reflected over the x-axis will become g(x) = 5x + 10.

        where : [m] → is slope of line and [c] → is the y - intercept

We have the some sub - questions given in question.

We will solve part [1].

We have -

y = - 5x - 8

Shifting down by 2 units, we get -

y = - 5x - 8 - 2

y = - 5x - 10

Reflection over the [x] axis, would be -

g(x) = - y

g(x) = - (- 5x - 10)

g(x) = 5x + 10

Therefore, the function y = f(x), when shifted down by 2 units and then reflected over the x-axis will become g(x) = 5x + 10.

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Answer:

P (−11, 13), Q (−17, −19), R (23, 27)

Step-by-step explanation:

we know that

The reflection of a figure across the x-axis has the following rule

(x,y) -----> (x,-y)

so

P(-11,-13) -----> P(-11,13)

Q(-17,19) -----> Q(-17,-19)

R(23,-27) ----> R(23,27)

Answer:

P (−11, 13), Q (−17, −19), R (23, 27)

Step-by-step explanation:

Got it right on my test :)