The lines x= 1/4y + a and y=1/4x +b intersect at the point (1,2). What is a+b?

The line through the points p(-3,-2) and Q(2,3) is perpendicular to the line through points R(10,-1) and S(15,-6) because the product of their slopes is -1

C: Yes, their slope have product -1

Two lines are perpendicular if the products of their slope equals -1

The slope(m) of a line passing through the points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given as:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

For the line PQ:

P(-3, -2) and Q(2, 3)

[tex]m_1 = \frac{3-(-2)}{2-(-3)} \\\\m_1 = \frac{3+2}{2+3} \\\\m_1 = \frac{5}{5} \\\\m_1 = 1[/tex]

For the line RS:

R(10,-1) and S(15,-6)

[tex]m_2 = \frac{-6-(-1)}{15-10} \\\\m_2 = \frac{-6+1}{5} \\\\m_2 = \frac{-5}{5} \\\\m_2 = -1[/tex]

[tex]m_1m_2 = -1(1) \\\\m_1m_2 = -1[/tex]

Since the products of the slopes of line PQ and RS is -1, the line PQ is perpendicular to the line RS

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After dividing the total number of eggs (175) by the number of eggs per box (8), the grocer will have 7 eggs left over once 21 boxes are filled.

To solve how many eggs the grocer will have left over, we need to divide the total number of eggs (175) by the number of eggs in a box (8).

This calculation involves basic division and understanding remainders, which are common math skills taught in middle school.

The grocer starts with 175 eggs and sells them in boxes of 8. To find the number of boxes he can fill, we divide the total number of eggs by the number of eggs per box: 175 / 8 = 21.875. Since the grocer can only sell whole boxes, he can fill 21 boxes. To find the number of eggs left over, we subtract the number of filled boxes from the total number of eggs: 175 - (21 * 8) = 175 - 168 = 7 eggs left over.

Answer:

Rock A had a weight of 0.33Kg

Step-by-step explanation:

Let X: the weight of rock A and Y: the weight of rock B. The information available suggests that:

X + Y = 3.3 [Eq. one]

X = 0.1 (X + Y) [Eq. two]

Considering equation 2, we have that X = 0.1X + 0.1Y, which produces:

0.9X = 0.1Y ------------> 9X = Y. Substituting this last result in equation 1, you have:

X + 9X = 3.3, that is,

10X = 3.3 --------> X = 3.3 / 10 = 0.33Kg. As Y = 9X, then, Y = 9 (0.33) = 2.97Kg

Answer:

D. The distance from Earth to Proxima Centauri is approximately two million times the distance from Earth to Venus.

Step-by-step explanation:

Sophie is not correct in her statement. The total number of stars is the same in both scenarios, which is 18.

Sophie is not correct in her statement. Let's calculate the total number of stars in each scenario:

Scenario 1: Sophie drew 6 circles, and in each circle, she drew 3 stars. So the total number of stars is 6 × 3 = 18 stars.

Scenario 2: Sophie drew 3 circles, and in each circle, she drew 6 stars. So the total number of stars is 3 × 6 = 18 stars.

As we can see, both scenarios result in the same total number of stars, which is 18. Therefore, Sophie's statement is correct, and she did get the same total number of stars both times.

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The factor of the expression is [tex]6 \div 7[/tex], c, and d.

Given that,

Based on the above information, the factors are as follows:

[tex]6 \div 7[/tex], c, and d.

Therefore we can conclude that the factor of the expression is [tex]6 \div 7[/tex], c, and d.

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Aaaay the answer is -8.8

[tex]

{\text{Here, we have the algebraic expression}} \hfill \\
8w \times {2^2} - 18w \hfill \\
{\text{For simplifying the expression, first we solve the exponent part,}} \hfill \\
{\text{and then the resultant will be multiply with the monomial }}18w \hfill \\
8w \times {2^2} - 18w \hfill \\
= 8 \times w \times {2^2} - 18w \hfill \\

= \left( {8 \times {2^2}} \right) \times w - 18w\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ {\because \,{\text{By associative law }}a \times \left( {b \times c} \right) = \left( {a \times b} \right) \times c} \right] \hfill \\

= \left( {8 \times 4} \right) \times w - 18w \hfill \\

= 32 \times w - 18w \hfill \\

= 32w - 18w \hfill \\

= 14w \hfill \\

[/tex]

product is multiplication so find the square root of 182

sqrt(182) = 13.49

 so use the whole number above and below that

13 * 14 = 182

 the page numbers are 13 & 14

Final answer:

Acelynn will pay back a total of $748.72 in interest over the 14 years of her loan for the four-wheeler. This was calculated using the simple interest formula.

Explanation:

To calculate how much interest Acelynn will pay back on the money borrowed for the four-wheeler, we use the simple interest formula: Interest (I) = Principal (P) × Rate (R) × Time (T).

Here, the principal P is $1337, the rate R is 4% (or 0.04 as a decimal), and the time T is 14 years.

Plugging these values into the formula, we get:

I = $1337 × 0.04 × 14

I = $53.48 × 14

I = $748.72

Therefore, as per the above explaination,Acelynn will pay back $748.72 in interest over the 14 years of the loan.

The inequality for the given statement is n+3<12.

The given statement is twelve is no less than the sum of a number n and 3.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Now, the sum of a number n and 3 = n+3

Twelve is no less than the sum of a number n and 3 = n+3<12

Therefore, the inequality for the given statement is n+3<12.

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Answer:

Step-by-step explanation:

A. (4 + 12) + 18 = 16 + 18 = 34; 4 + (12 + 18) = 4 + 30 = 34

Answer: The y-intercept of the exponential function is approximately 2000 less than the y-intercept of the linear function.

Step-by-step explanation:

Given: The exponential function in the table represents the student population of the county that Greenville is in, in years since 2010.

The standard exponential function is given by :-

[tex]y=Ab^x[/tex], where A is the initial population and x is the number of years.

From table , the multiplicative rate of change b=[tex]\frac{y_3}{y_2}=\frac{4400}{2200}=2[/tex]

Put x=2 and b=2 in the equation, we get

[tex]2200=A(2)^2\\\Rightarrow\ A=\frac{2200}{4}=1950[/tex]

We know that the value of y intercept occurs when x=0,

From the given table , the y intercept of exponential function (Initial population)= 550

The linear function in the graph shows the population of Greenville in the years since 2010.

From the given graph, the y intercept of linear function  (x=0 for year 2010)= 2500

The difference in y intercepts = [tex]2500-550=1950\approx2000....\text{{Rounded nearest thousand}}[/tex]

Hence, The y-intercept of the exponential function is approximately 2000 less than the y-intercept of the linear function.

Answer:the answer is C 804 hope this helps

Step-by-step explanation:

Answer:  Option 'C' is correct.

Step-by-step explanation:

Since we have given that

Scores of her experian, her Equifax and her TransUnion are as follow:

[tex]804, 810, 784[/tex]

We first write in ascending order:

[tex]784, 804, 814[/tex]

Since there are odd numbers of scores.

So, n = 3,

As we know the formula for "Median " :

[tex]Me=(\frac{n+1}{2})^{th}\\\\Me=\frac{3+1}{2}^{th}\\\\Me=\frac{4}{2}^{th}\\\\Me=2^{nd}\ term\\\\Me=804[/tex]

Hence, the Violet's Median Score is 804.

Therefore, Option 'C' is correct.