When a line has an undefined slope what will any two points on the line have in common

The range of possible scores for the third quiz that would yield an average score between 90 and 95 is 85 to 100, inclusive.

The objective is to find the range of possible scores for the third quiz that would give an average score between 90 and 95, inclusive. As per the question, the sum of the student's first two quizzes is 98+87=185. If we denote the third quiz score as 'x', then the equation could be written as (185+x)/3 = average score. Considering the lower and upper limit of the average, we form two inequalities. For the lower limit, it's (185+x)/3 >= 90, which simplifies to x >= 270 - 185, thus x >= 85. For the upper limit, it's (185+x)/3 <= 95, which simplifies to x <= 285 - 185, thus x <= 100. So, the range of scores for the third quiz that would give an average between 90 and 95 inclusive is 85 <= x <= 100.

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Answer:

a weak acid and its conjugate base    

Step-by-step explanation:

A Buffer solution is a solution that tends to keep the pH almost constant when small amounts of acids (H +) or  bases (OH-) are added, therefore, they are very useful to reduce the impact of drastic changes in (H+) and (OH-) in processes that require a specific pH. They can be prepared by dissolving in water adequate amounts of a weak acid and a salt of its conjugate base, or a weak base and a salt of its conjugate acid.

Answer:

27

Step-by-step explanation:

2(8 - 4)^2 - 10/2

Using the order PEMDAS, or parenthesis, exponents, multiplication, division, addition, subtraction, we will start with the parenthesis, or 8-4.

2(4)^2 - 10/2

Next is exponents.

2(16) - 10/2

And then multiplication.

32 - 10/2

Then division.

32 - 5

Finally, subtraction.

27

Therefore, the answer is 27.

Answer:

Option 1)  -7  

Step-by-step explanation:

Given : The equation shows the relationship between x and y : [tex]y=-7x+9[/tex]

To find : What is the slope of the equation?

Solution :

The general slope form of the equation is [tex]y=mx+b[/tex]

Where, m is the slope and b is the y-intercept.

Now, We compare the given equation with general form of the equation

[tex]y=-7x+9[/tex]

On comparing, m=-7 and b=9

So, The slope of the given equation is -7.

Therefore, Option 1 is correct.

Answer:  The required co-ordinates of the point 'P' are (-3.5, 2.3).

Step-by-step explanation:  We are to find the coordinates of point P on the directed line segment from R to Q such that P is 5/6 the length of the line segment from R to Q.

We are to find the co-ordinates of point 'P'.

The ratio in which the point 'P' dives the line segment RQ will be

[tex]m:n=5:1.[/tex]

The co-ordinates of the end-points of line segment RQ are

R(4, -1)  and  Q(-5, 3).

If a point 'H' divides a line segment with end points (p, q) and (s, t) in the ratio m : n, then the co-ordinates of the point 'H' are

[tex]H=\left(\dfrac{ms+np}{m+n},\dfrac{mt+nq}{m+n}\right).[/tex]

Therefore, the co-ordinates of point 'P' are

[tex]\left(\dfrac{5\times (-5)+1\times 4}{5+1},\dfrac{5\times 3+1\times (-1)}{5+1}\right)\\\\\\=\left(\dfrac{-25+4}{6},\dfrac{15-1}{6}\right)\\\\\\=\left(\dfrac{-21}{6},\dfrac{14}{6}\right)\\\\\\=(-3.5,2.3).[/tex]

Thus, the required co-ordinates of the point 'P' are (-3.5, 2.3).

To find point P's coordinates, calculate weights for points R and Q using the ratio 5/6 and apply these to R and Q's coordinates based on linear interpolation.

The question involves determining the coordinates of a point P located at a specific fraction of the distance from point R to point Q on a directed line segment. The fraction given is 5/6, meaning that point P is 5/6th the distance from R to Q. The process to find the coordinates of point P involves calculating the weights for R and Q in the form of (1 - 5/6) and (5/6) respectively and then applying these weights to the coordinates of R and Q. This method is based on the concept of linear interpolation or finding a point of division in a line segment.

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Answer:

[tex]x^{2}+y^{4}+2xy^{2}[/tex]

Step-by-step explanation:

The given expression is (x + y²)² and we have to simplify it to find the binomial expansion.

(x + y²)² is in the form of (a + b)².

When we expand (a + b)² we get the binomial expression

(a + b)² = a² + b² + 2ab

Now we put the value of a = x and b = y²

(x + y²)² = x² + (y²)² + 2(x)(y²)

            = [tex]x^{2}+y^{4}+2xy^{2}[/tex]

Therefore answer is [tex]x^{2}+y^{4}+2xy^{2}[/tex]

Answer:

He hit 552 home runs in 12 years

Step-by-step explanation:

To solve this problem, we will follow the steps below;

Using proportion;

Let x be the number of home runs he hits in 12 years

46 home runs = 1 year

    x                  = 12

cross -multiply

x × 1  = 46× 12

x =  552 home runs

Therefore, he hit 552 home runs in 12 years

Answer:

triangle.  

Step-by-step explanation:

given: a square pyramid

to find : shape of cross section made when a plane perpendicular

             to base and passes through top vertex.                                                                  

when a plane cuts the square pyramid perpendicular to base and passes through top vertex we get a cross section made by its two equal slant height and side of the square.

therefore, we get a triangle or more specifically isosceles triangle.

picture is attached.

Answer:

-3

Step-by-step explanation:

Its decresing by -3.

L * W = 300 sq ft
Length is 10 ft greater than twice the width.
L = 2W + 10
Substituting
(2W+10)*W = 300
2W^2 + 10W = 300
Divide both sides by 2
W^2 + 5W = 150
W^2 + 5W - 150 = 0
Factor
(W +15)(W -10) = 0

Roots are W=-15 and W=10.
A negative width is impossible, so W=10
L = 2W + 10
L = 2(10) + 10
L = 30

 length = 30 feet, width = 10 feet

 Check: 30*10 = 300

To find the dimensions of the barn wall, we first expressed the given information as an equation using the formula for area. After simplifying and factoring the quadratic equation, we determined the width to be 10 feet and the length to be 30 feet.

The question involves finding the length and width of a rectangular wall when given the area and a relationship between the length and width. We know the area of the wall is 300 square feet and that the length is 10 feet longer than twice the width. Let's denote the width as 'w' and the length as 'l'. The relationship between them can be expressed as l = 2w + 10. Using the formula for the area of a rectangle, which is A = l * w, we substitute the given area and the relationship between length and width to create an equation: 300 = (2w + 10) * w.

Solving this quadratic equation:

Therefore, the width of the wall is 10 feet, and the length is 30 feet.

The probability of drawing two gold ornaments in a row from a bag containing three green and four gold ornaments is 2/7. This is calculated by multiplying the probability of drawing a gold ornament on the first draw, 4/7, by the probability of drawing another gold ornament from the remaining ornaments, 1/2.

The subject matter of this problem is probability. Probability tells us how likely an event is to occur given certain conditions. In this case, we are interested in the probability of drawing two gold ornaments from a bag containing three green and four gold ornaments. To solve this problem, we have to calculate the probability of selecting a gold ornament on the first and second draw.

Start with the total amount of ornaments, which is seven (three green and four gold). The probability of drawing a gold ornament on the first pick is 4 out of 7, or 4/7. However, if you draw a gold ornament first, there will be 6 ornaments left with 3 being gold.

So, the probability of drawing another gold ornament becomes 3 out of 6, or 1/2. The probable event is happening two times in a row and we're not replacing the ornaments, so we multiply these probabilities together:

4/7 * 1/2 = 2/7

Therefore, the probability of drawing two gold ornaments in a row from this bag is 2/7, so the correct answer is B) 2/7.

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Answer:

C. identity property

Step-by-step explanation:

Using the formula for decrement, the resale value of a $28,000 car that depreciates at a 35% rate annually for three years would be roughly $10,012.

This question is about calculating the effects of percent decrease over a period of time. Specifically, the student is asked to calculate the value of a $28,000 car, after it undergoes a 35% percent decrease in value each year for three years. This type of problem is typically solved using the formula v = p * ((1 - r)^n), where v is the final value, p is the initial value, r is the rate of decrease, and n is the number of periods. In this case, the initial value (p) is $28,000, the rate of decrease (r) is 35% or 0.35, and the number of periods (n) is 3 years. Substituting these into the formula, we can find that the resale value after 3 years is v = 28000 * ((1 - 0.35)^3) = $10,011.75. Rounding this to the nearest dollar, we get an estimated resale value of $10,012.

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The limitations of determining a function's average rate of change by examining the function's graph include incomplete information, the need for tangent lines, and limited interval-specific data.

When determining a function's average rate of change by examining the function's graph, there are several limitations to consider.

These limitations highlight the importance of understanding the limitations of graph analysis and considering alternative methods, such as calculus, to accurately calculate the average rate of change of a function.

F(180) = x/30

= 180/30 = 6 gallons of gas is needed

Answer:

A.  

product being used by everyone  

B.  

the aesthetic value of nature  

C.  

identifying internal costs  

D.  

categorizing internal and external costs

Step-by-step explanation:

Answer:

More input results in less output.
The function is inversely proportional.

Step-by-step explanation:

those two. other answer is completely wrong

If you quadruple the input of a function and the resulting output is one-fourth the original output, what may be true of the function? The correct options are A. The function is inversely proportional and C. More input results in less output.

In mathematical terms, let's consider the function as f(x), where x is the input, and f(x) is the output.

1. Option A: The function is inversely proportional.

If quadrupling the input (4x) leads to the output being one-fourth of the original output (1/4 f(x)), it implies that f(4x) = 1/4 f(x). Inverse proportionality means that as the input increases, the output decreases, and vice versa. In this case, increasing the input by a factor of 4 (4x) causes the output to reduce to one-fourth of its original value (1/4 f(x)), indicating an inverse relationship.

2. Option C: More input results in less output.

As mentioned earlier, quadrupling the input (4x) and obtaining an output of one-fourth the original (1/4 f(x)) demonstrates that increasing the input leads to a decrease in the output. When x increases, 4x (quadruple of x) will also increase, and as a result, f(4x) will be less than f(x). This aligns with the statement that more input results in less output.

It is important to understand the relationship between the input and output of a function. In this case, the given conditions indicate inverse proportionality and that increasing the input leads to a decrease in the output. Keep in mind that mathematics often deals with relationships between variables, and understanding such relationships can help solve various problems and make predictions about how a system behaves.

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