The sum of a number and its additive inverse is equal to ?

Answer:

the numbers are 3 and 5

Step-by-step explanation:

x = first number

y = second number

a.        x+2 = y

b.        x^2 + y^2 = 34

Replace y from equation a into equation b:

x^2 + (x+2)^2 = 34

Expand it

x^2 + x^2 + 4x + 4 = 34

2*x^2 + 4x = 30

2x^2 + 4x - 30=0

solving x:

x = -5 and x =3 , it says it is a positive number, then it is x is 3

and the second number, y = x + 2

y = 5

Lets test it!

3^2 + 5^ 2 = 9 + 25 = 34

Final answer:

The volume of the earth is approximately 1.0839 x 10¹⁵ cubic miles.

Explanation:

To find the volume of the earth, we can use the formula for the volume of a sphere: V = (4/3)πr³. Since we are given the diameter of the earth, we can calculate the radius by dividing the diameter by 2. In this case, the diameter is 7917.5 miles, so the radius is 3958.75 miles. Now, we can substitute the radius into the formula to find the volume:

V = (4/3)π(3958.75 miles)³

V ≈ 1.0839 x 10¹⁵ cubic miles.

The inverse function of f(x) = -0.75x is [tex]\(f^{-1}(x) = -\frac{4}{3}x\)[/tex].

To find the inverse function [tex]\( f^{-1}(x) \)[/tex]for the given function f(x) = -0.75x , you can follow these steps:

1. Start with the original function:

   f(x) = -0.75x

2. Replace f(x)  with y:

   y = -0.75x

3. Swap x and y to solve for x:

x = -0.75y

4. Solve for y:

  Divide both sides by -0.75:

[tex]\( y = \frac{x}{-0.75} )\\ \( y = -\frac{4}{3}x \)[/tex]

5. Replace y with [tex]\( f^{-1}(x) \)[/tex]:

[tex]\( f^{-1}(x) = -\frac{4}{3}x \)[/tex]

So, the inverse function for f(x) = -0.75x  is [tex]\( f^{-1}(x) = -\frac{4}{3}x \)[/tex].

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Final answer:

The response provides the inverse function of f(x) = -0.75x step-by-step.

Explanation:

Given: f(x) = -0.75x

To find the inverse function f-1(x):

Replace f(x) with y: y = -0.75x

Swap x and y: x = -0.75y

Solve for y: y = x/-0.75 = -4/3x

Therefore, f-1(x) = -4/3x

Answer:

Step-by-step explanation:

Rarely does the payroll office want to get involved in minor in-office expenses, such as coffee, donuts, or cupcakes. Perhaps more rarely, will a municipality impose a payroll tax.

However, it is quite common to see health insurance costs and Social Security taxes deducted from gross pay.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula of an area of a triangle:

[tex]A=\dfrac{1}{2}bh=\dfrac{bh}{2}[/tex]

b - base

h - height

We have b = 15, A = 200.

Substitute:

[tex]200=\dfrac{15h}{2}[/tex]

[tex]200=7.5h[/tex]              divide both sides by 7.5

[tex]\dfrac{200}{7.5}=\dfrac{7.5h}{7.5}[/tex]

[tex]h\approx26.7[/tex]

Answer:

Step-by-step explanation:

The two temperatures that will be located as shown in the vertical number line representing a thermometer will be:

4°C  and -4°C

Given that the vertical number line is to be used to represent a thermometer.

If 0 represents 0°C on the vertical number line, therefore:

Therefore, the two temperatures that will be located as shown in the vertical number line representing a thermometer will be:

4°C  and -4°C

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Answer:

8x + 6 = 7x

x = -6

Step-by-step explanation:

this is the solution

Answer:

[tex]2t-t+4=0[/tex] gives me [tex]t=-4[/tex]

This is a linear equation.

Did you really mean [tex]2t-t+4=0[/tex]? I just want to make sure since you said something about a quadratic in your question.

Step-by-step explanation:

[tex]2t-t+4=0[/tex] can be simplified to [tex]t+4=0[/tex].

This is a linear equation since the exponent on all the variables we have is 1.

To solve [tex]t+4=0[/tex] for t we are going to subtract 4 on both sides:

[tex]t+4-4=0-4[/tex]

[tex]t=-4[/tex]

The speed of each planes are 375 mph and 415 mph.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now,

Let x be the speed of the slower plane, in mph.

Then, the speed of the other plane is x +40 mph.

Hence, The distance between two planes decreases at the rate;

⇒ x + (x+40)

⇒ 2x + 40 mph.

So, we can write equation as;

⇒ 3950 / (2x+40) =  5

⇒ 3950 = 10x + 200

⇒ 10x = 3750

⇒ x = 375

Thus, The speed of the slower plane = x

                                                         = 375  mph.

And, The speed of the other plane = x +40

                                                      = 375 + 40

                                                      = 415 mph.

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Final answer:

To solve the problem, we use the concept of relative speed and set up an equation with the combined distance traveled by both planes. Solving the equation reveals that the speed of the slower plane is 375 mph and the faster plane is 440 mph.

Explanation:

The problem of two planes flying toward each other with a speed difference and meeting after a certain amount of time is a typical algebra question in relative speed and motion. We can let the slower plane's speed be x mph and the faster plane's speed be x + 65 mph. Since they meet after 3 hours and are 2445 miles apart, the sum of their distances traveled will equal 2445 miles.

Using the equation d = rt, where d denotes distance, r the rate, and t the time, we set up two expressions for the distances each plane travels:

We then add these expressions and set the sum equal to the total distance:

3x + 3(x + 65) = 2445

Solving for x, we get:

6x + 195 = 2445

6x = 2445 - 195

6x = 2250

x = 375

Therefore, the speed of the slower plane is 375 mph and the speed of the faster plane is 375 + 65 = 440 mph.

Answer: look below

Step-by-step explanation:

Write: -7-(-3)=-4

Solve: -7-(-6)=-1

A function with direct variation is a linear function that passes through the origin (0, 0) and has a constant rate of change, the slope. Only the line passing through (negative 1, negative 4), (0, 0), and (1, 4) from the given options fulfills these conditions.

In Mathematics, a function with direct variation is a linear function that passes through the origin (0, 0).  It can be represented as the equation y = mx, where m is the slope of the line. The slope of the line determines if it is a direct variation. If it's a positive slope, y increases as x increases. If it's a negative slope, y decreases as x increases.

From the given options, only the coordinate plane with a line passing through (negative 1, negative 4), (0, 0), and (1, 4) represents a function with direct variation as it's a straight line passing through the origin.

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Answer:

The answer is 4.5

Step-by-step explanation:

In order to get this answer you will have to use PEMDAS and solve the expression step by step.

[tex]4(3-1)2[/tex]

Using PEMDAS:

[tex]3-1=2[/tex]

[tex]4\times2\times2[/tex]

[tex]2\times4=8[/tex]

[tex]8\times2[/tex]

[tex]8\times2=16[/tex]

[tex]=16[/tex]

Therefore your answer is option C "16."

Hope this helps.

Answer:

C. 16

Step-by-step explanation:

basically the order of operations states you deal with parentheses first then indices then either division/multiplication and then addition/subtraction

So when you deal with 3- 1=2

the only operation left is multiplication(something in parenthesis stuck on another mathematical term without any other operation attached to it signals multiplication and it is commutative so it can be done in any pair. so u have 4×2×2=16

Answer:

The answer is 6.875 inches.

Step-by-step explanation:

After a snow storm, Michael measured [tex]6\frac{7}{8}[/tex] inches of snow.

We will convert this to improper fraction and then solve.

[tex]6\frac{7}{8}=\frac{55}{8}[/tex]

Now we can divide 55 by 8 to get decimal value.

This becomes 6.875 inches.

Answer:

5 : 30

Step-by-step explanation:

Note that [tex]\frac{1}{2}[/tex] × 10 = 5

Thus 3 × 10 = 30

Hence

[tex]\frac{1}{2}[/tex] : 3 = 5 : 30

Ratios are used to relate quantities of different measurement

The ratio is given As

[tex]Ratio = \frac 12 : 3[/tex]

Represent the new numbers with  P1 and P2.

So, we have:

[tex]P1 : P2 = \frac 12 : 3[/tex]

The second number is 5 So, we have:

[tex]5 : P2 = \frac 12 : 3[/tex]

Multiply the ratio by 10

[tex]5 : P2 = \frac 12 \times 10: 3 \times 10[/tex]

[tex]5 : P2 = 5: 30[/tex]

By comparison

[tex]P2 = 30[/tex]

Hence, the ratio is equal to the ratio of 5 and

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Leonardo Da Vinci was a painter, sculptor, architect, engineer, scientist, philosopher, and a visionary. He was also commissioned to create a bronze statue nicknamed "Leonardo's Horse".

Solve for a:

3a +11 > 5

Subtract 11 from both sides:

3a >-6

Divide both sides by 3:

a > -6/3

a > -2

The Correct graph is the second one, because it has the dot on the -2 and the arrow points to the right

The 2 number line shows the solutions to the inequality 3a + 11 > 5 and the correct option is B.

The image shows two number lines, and asks which one shows the solutions to the inequality 3a + 11 > 5.

To solve this inequality, we can subtract 11 from both sides, and then divide both sides by 3. This gives us a simpler inequality: a > -2.

This means that all values of a that are greater than -2 are solutions to the inequality. On a number line, this can be represented by an open circle at -2, and an arrow pointing to the right.

The number line on the left of the image shows exactly this. Therefore, the number line on the left shows the solutions to the inequality 3a + 11 > 5.

The number line on the right of the image does not show the solutions to the inequality correctly. The open circle at -2 is missing, and the arrow points to the left, which is incorrect, since the solutions to the inequality are all values of a that are greater than -2, not less than -2.

Here is a more detailed explanation of the steps involved in solving the inequality:

1. Subtract 11 from both sides:

3a + 11 > 5

-11 - 11

3a > -6

2. Divide both sides by 3:

3a > -6

3 / 3

a > -6 / 3

3. Simplify:

a > -2

Therefore, the solution to the inequality is a > -2. On a number line, this can be represented by an open circle at -2, and an arrow pointing to the right.

The number line on the left of the image shows exactly this. Therefore, the 2 number line on the left shows the solutions to the inequality 3a + 11 > 5 and the correct option is B.

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Answer: b. Z+5

Step-by-step explanation:

B. Z+5

Let’s say z was 9

The only equation that would work to find 5 more that 9 is 9+5

Answer:

Step-by-step explanation:

4x - 48 = x there is the equation

Answer:

x = 48/5

Step-by-step explanation:

Let x = number, then:

[tex]48 - 4x = x[/tex]

By adding 4x on each side:

[tex] 48 - 4x + 4x = x + 4x[/tex], which is [tex] 48 = 5x [/tex]

Then, divide by 5 on both sides:

[tex]\frac{48}{5} = \frac{5x}{5}[/tex]

Simplifying x = 48 / 5

x + 8 = -7

move +8 to the other side

sign changes from +8 to -8

x+8-8= -7-8

x=-7-8

Answer:

x= -15

Answer:

x=-15

Step-by-step explanation:

Subtract 8

x-8+8=-7-8

x=-7-8

x=-15

The number of boys in class is 9.

Let the number of boy = b and girls = g

We can create the following equations from the parameters

b + g = 27 ____(1)

g - 3 = 3(b - 4) ___ (2)

From (1)

g = 27 - b ___(3)

Substitute (3) into (2)

27 - b - 3 = 3(b - 4)

24 - b = 3b - 12

collect like terms

-b - 3b = -12 - 24

-4b = -36

b = 9

Hence, the number of boys is 9

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Answer:

each book costs $13

Step-by-step explanation:

Let the cost of each book be $x

cost of buying 8 books = $8x

It is given that with an original amount of $116, after buying 8 books, he had $12 left over. Hence,

$8x + $12 = $116   (dropping the $ signs)

8x + 12 = 116

8x = 116 - 12

8x = 104

x = 13  (each book costs $13)

Answer:

he possibly spent $13 on order to end up with $12 left.

Step-by-step explanation:

1) look. at the number 116 you can use a calculator.

2) if 14 only leaves you with nothing you take it away

3) add 13 + 8X that should give you 104

4). substract 116-104 your total should be $12

I hope I helped you.

Final answer:

When Jonathan stops to tie his shoelaces four times, each adding 2 1/2 minutes, his jog takes an extra 10 minutes in total.

Explanation:

Jonathan stops to tie his shoelaces four times during his jog. Each time he stops, it adds 2 1/2 minutes to his total jog time. To find out how much longer his jog takes, we need to multiply the number of stops by the additional time per stop.

Let's calculate this step by step:

So, if Jonathan stops to tie his shoelaces four times, his jog will take an extra 10 minutes in total.

Answer:

C (-16, 3)

Step-by-step explanation:

[tex] 12 + 3 \leqslant - 3 \times - 16 \\ 15 \leqslant 48[/tex]

replace x and y

Answer:

c) (-16,3)

Step-by-step explanation:

Given: inequality [tex]12+\text{y}\leq -3\text{x}[/tex]

To Find: Which ordered pair is part of the solution set of the inequality

Solution:

Simplifying inequality,

[tex]12+\text{y}\leq -3\text{x}[/tex]

[tex]12}\leq -3\text{x}-\text{y[/tex]

now,

putting ordered pairs from options

a) [tex](3,-16)[/tex]

[tex]-3\times3-(-16)[/tex][tex]16-9=7[/tex]

as [tex]7<12[/tex], it does not satisfy inequality

b)  [tex](4,-1)[/tex]

[tex]-3\times4-(-1)[/tex][tex]1-12=-11[/tex]

as [tex]-11<12[/tex], it does not satisfy inequality

c)  [tex](-16,3)[/tex]

[tex]-3\times(-16)-(3)[/tex][tex]48-3=45[/tex]

as [tex]45>12[/tex], it satisfy inequality

d)  [tex](1,4)[/tex]

[tex]-3\times1-(4)[/tex][tex]-3-4=-7[/tex]

as [tex]-7<12[/tex], it does not satisfy inequality

So, from above only option c is part of the solution set of inequality.

Answer:

The area of the figure is 48 cm^2

Step-by-step explanation:

Break it into 3 different quadrilaterals and find the area of each one.

Answer:

Step-by-step explanation:

/ -1/3 / = 1/3

Answer:

Step-by-step explanation:50,897 is in standard form.

Expanded form is adding all your place values which is 50,000+800+90+7. There was a 0 in the thousand place so you do not add anything for that place value.

So (5×10,000) + (8×100) +(9×10)+(7×1) which is each number times it place value then add them all up.

Written form would be fifty thousand, eight hundred and ninety seven. So your answer is A, B, D