Which equation represents a direct linear variation?

Answer: {-10, +10}

Step-by-step explanation: A common mistake in this problem would be to say that if x² = 100, x must equal 10.

Remember however that before you do anything else you must set the equation equal to 0.

So our first step is to subtract 100 from both sides to get x² - 100 = 0. Next, factor the left side to get (x + 10)(x - 10) = 0.

So either x + 10 = 0 or x - 10 = 0.

Solving for x in each equation, we have x = -10 or x = +10.

So our answer is not just 10, it's -10 or +10.

I have also attached my work in the image provided.

Answer : C

A. (5 + 3) × 2 = 16

Here we have 5 +3 . there is a + sign in between.  so it does not comes under Associative property of multiplication

B. 5 × (3 + 2) = 25

We have 3 + 2 . there is a + sign in between.  so it does not comes under Associative property of multiplication

C. 5 × (3 × 2) = 30

we have 5 times 3 times 2.  so it comes under Associative property of multiplication

D. 2 + (4 × 7) = 30

We have  2 + . there is a + sign in between.  so it does not comes under Associative property of multiplication

The sum of the first four terms of the series would be c. -102

Why hello there

The correct answer is B

If my answer helped please mark me as brainliest thank you and have the best day ever!

[tex]A.\ (-2,\ 0)\\\\substitute\ to\ y=x+2\\\\0=-2+2\\0=0\ CORRECT\\\\substitute \ to\ (x+1)^2+(y-4)^2=9\\\\(-2+1)^2+(0-4)^2=9\\(-1)^2+(-4)^2=9\\1+16=9\\17=9\ \ FALSE[/tex]

[tex]B.\ (1,\ -1)\\\\substitute\ to\ y=x+2\\\\-1=1+2\\-1=3\ \ \ FALSE[/tex]

[tex]C.\ (2,\ 4)\\\\substitute\ to\ y=x+2\\\\4=2+2\\4=4\ \ \ CORRECT\\\\substitute\ to\ (x+1)^2+(y-4)^2=9\\\\(2+1)^2+(4-4)^2=9\\3^2+0^2=9\\9+0=9\\9=9\ \ \ CORRECT[/tex]

[tex]D.\ (-1,\ 4)\\\\substitute\ to\ y=x+2\\\\4=-1+2\\4=1\ \ \ \ FALSE[/tex]

there is a point discontinuity ( hole ) at (- 6, - 3 )

factor the numerator/denominator

f(x) = [tex]\frac{(x-6)(x+6)}{4(x+6)}[/tex]

the factor (x + 6) cancels leaving the simplified version of f(x)

f(x) = [tex]\frac{x-6}{4}[/tex]

the removal of the factor (x + 6) from the numerator/denominator means there is a discontinuity at x + 6 = 0 , that is x = - 6

f(- 6 ) = [tex]\frac{-6-6}{4}[/tex] = - 3

there is a point discontinuity ( hole ) at (- 6, - 3 )

P = 10 + x + 2x + 7

= (10 + 7) + (x + 2x)

= 17 + 3x

Therefore, the perimeter is 17 + 3x feet.

Answer:7x+12

Step-by-step explanation:

By setting up an equation with x as the cost of Tanya's items, we find that each of Tanya's items cost $9.00. Tony's items, being $2.25 cheaper, cost $6.75 each. The solution is checked by ensuring both Tanya's and Tony's total expenditure was equal.

The question asks us to find the individual cost of items purchased by Tanya and Tony at a store, given that Tony's items each cost $2.25 less than Tanya's but both spent the same amount overall.

Equation Setup

Let x represent the cost of one of Tanya's items. Since Tanya bought 3 items, she spent 3x dollars. Tony's items each cost $2.25 less, so they cost (x - $2.25) each. Tony bought 4 items, spending 4(x - $2.25). Since both spent the same amount:

3x = 4(x - $2.25)

Solving the Equation

To solve for x:

So, each of Tanya's items cost $9.00.

Checking the Solution

To verify:

Both totals match, confirming that the solution is correct.

Tanya's items each cost $9.00, while Tony's items, costing $2.25 less, each cost $6.75.

Answer: C. Weak Positive

Step-by-step explanation:

In a scatter plot , a positive correlation is a relationship between the two variables x and y  in which if value at x axis increases, then other value at y axis also increases.

In the given scatter plot the the association between variables x and y is a weak positive correlation because there is a lower likelihood in the relationship between variables.

Answer:

B. $1,449.54

Step-by-step explanation:

That's the answer

To solve this equation, distribute, combine like terms, and isolate the variable, x.

To solve this equation, we need to simplify both sides and isolate the variable, x.

Starting with the left side, distribute the 3 to the terms inside the parentheses: 3x - 15 - 5x = 25 + 6x.

Combine like terms on both sides of the equation: -2x - 15 = 25 + 6x.

Add 2x to both sides of the equation and add 15 to both sides: -15 - 25 = 6x + 2x.

Simplify the equation: -40 = 8x.

Finally, divide both sides by 8 to solve for x: x = -5.

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To round off to 10, the difference should range from 5 to 14. If the difference between two numbers is from 5 to 14, they all are rounded to 10.

Example:

[tex]18-9=9[/tex] (near to 10)

[tex]26-15=11[/tex]

[tex]46-39=7[/tex]

[tex]50-42=8[/tex]

If Julia rounded to the nearest ten to estimate the difference between two numbers. The estimated difference was 10. (18,9)(25,14), (36,22) and (45, 38) are few pairs of numbers she might have subtracted.

A number system is defined as a system of writing to express numbers.

The difference should range from 5 to 14.

Difference in math is the result of one of the important mathematical operations, which is obtained by subtracting two numbers

To round off to 10.

If the range of difference between two numbers is from 5 to 14. Then those numbers are rounded to ten.

Let us consider some pairs of numbers whose difference is rounded to ten.

18-9=9

25-14=11

36-22=14

45-38=7

Hence (18,9)(25,14), (36,22) and (45, 38) are few pairs of numbers she might have subtracted.

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Answer:

60

Step-by-step explanation:

Answer:

60 dollars.

Step-by-step explanation:

Markup is nothing but the difference between the selling price of a good or service and its cost. It is expressed as a percentage above the cost. In short, we can say that  it is the added price over the total cost of the good or service that provides the seller with a profit.

Original price = 50 dollars

ADD: 20% on original price = Markup price = 50(20/100) = 10 dollars

Hence Sales price = 50+10 = 60 dollars

You simply need to mulotiply those two numbers

Then u get 126!

Easy Peasy

A

to calculate the slope m , use the ' gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 3) and (x₂, y₂ ) = (5, 4)

m = [tex]\frac{4 - 3}{5 - 1}[/tex] = [tex]\frac{1}{4}[/tex] → A

Answer:

he missed 5 targets

Step-by-step explanation:

Since there are 4 people and they each spent 4 hours working, all we have to do is multiply the number of people (4) by the amount of hours each person spent (4)

4 x 4 = 16

Therefore, the total amount of hours is 16

Hope this helps you

-AaronWiseIsBae

Answer:

16 hours

Step-by-step explanation:

Given: There are 4 people in your crew.

Each spent 4 hours of laying sod.

To find the person hours, we have to multiply the number of people (4) by the amount of hours each person spent (4).

Total number of hours = Number of persons * Number of hours spent

Total number of hours = 4 x 4 = 16 hours

Therefore, the total amount of hours is 16.

Final answer:

To calculate the interest after 6 months with a principal of $750,000 and an annual interest rate of 5%, you need to convert the annual rate to a monthly rate and then use the formula Interest = Principal × Rate × Time. The interest after 6 months is $1,562.50.

Explanation:

To calculate the interest after 6 months, we can use the formula:

Interest = Principal × Rate × Time

Here, the principal is $750,000, the annual interest rate is 5%, and the time is 6 months.

First, we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 5% / 12 = 0.4167%

Now, we can calculate the interest:

Interest = $750,000 × 0.4167% × 6/12

Interest = $1,562.50

The remainder when dividing 23870 by 38 is 16.

To find the remainder when dividing 23870 by 38, you divide the larger number (the dividend) by the smaller number (the divisor). If the division operation does not produce a whole number, the 'left over' digits are considered the remainder. When you divide 23870 by 38, the quotient (or the answer) is 628, and the remainder is 16. Therefore, 16 is the remainder when 23870 is divided by 38.

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Answer:

Step-by-step explanation:

x2+3/x2-4x+3

Answer:

x^2+3/(x-1)(x-3)

Step-by-step explanation:

Answer:

336.49 calories.

Step-by-step explanation:

if;                      87.4 calories  = 1 serving of cherries

so;                  how much calories  =  3.85 serving of cherries

hence:

           3.85 seving * 87.4 calories / 1 serving

the answer is

               336.49 calories

Hey there!!

Let's take the first number an the smallest number as ' x '

Then, the second consecutive even integer would become ' x + 2 '

Third integer ' x + 4 '

Hence, adding them up, we get,

x + x + 2 + x + 4

... 3x + 6

This is equal to 4 times the smallest number.

We got the smallest number as ' x '

Hence, the final equation :

... 3x + 6 = 4x

Hope my answer helps!!

Answer:

A. 12

Step-by-step explanation:

i= use complicated conjugate to search out definite quantity of 8 + 12i

i = 12i

i= twelve × ei 90°

i = twelve × (cos 90° + i sin 90°)

r = |i| = twelve

The absolute value of the complex number 8 + 12i is found by squaring the real part, squaring the imaginary part, adding these two results, and then taking the square root. This results in the square root of 208.

The absolute value of a complex number a + bi is calculated through the formula sqrt(a² + b²). So, to find the absolute value of the complex number 8 + 12i, we substitute a with 8 and b with 12. We can perform the calculations as follows:

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Answer:

4256

Step-by-step explanation:

460 cm

note that 1m = 100 cm, thus

4.6m = 4.6 × 100 = 460 cm

Solution

Step 1: Isolate the variable x and plug in the values of x in the second and third equations.

Step 2: Isolate variable y and solve for y.

We get the value of y = 5/26

When we substitute the value of y , 1 = 0 which is not true.

Therefore, this system has No Solution.

Answer: No solution

y=20,000-.10x

with x being the number of years

Answer:

[tex]y=\$20,000\cdot (0.90)^x[/tex]

Step-by-step explanation:

We have been given that Kelly bought a new car for $20,000. The car depreciates at a rate of 10% per year. We are asked to write an equation to model the car's value.

Since car's value depreciates by 10% per year, so value of car is depreciating exponentially.

We know that an exponential decay function is in form [tex]y=a\cdot (1-r)^x[/tex], where

a = Initial value,

r = Decay rate in decimal form.

Let us convert 10% into decimal form as:

[tex]10\%=\frac{10}{100}=0.10[/tex]

Upon substituting our given values in decay formula, we will get:

[tex]y=\$20,000\cdot (1-0.10)^x[/tex]

[tex]y=\$20,000\cdot (0.90)^x[/tex]

Therefore, our required equation would be [tex]y=\$20,000\cdot (0.90)^x[/tex].

Answer:  y  ≤ 8

Solution:

Step 1: Rearrange the equation so that all the like terms are on one side

5y + 16 ≤ 56  

= 5y ≤ 56 - 16                      constants on one side and variable on the other

= 5y ≤ 40

= y  ≤ 8

Hope the solution helps to understand the question!

Tip: Remember that if the inequality is multiplied by a negative sign the inequality sign flips.