The average reading score on a certain test is given by y=0.150x +255.34 where x is the number of years past 1970 . In what year would the average reading score be 259.24 if this model was accurate

Answers

Answer 1

Answer:

Answer:

The average was 259.24 in 1996.

Step-by-step explanation:

In order to find the year that the average, "y", is 259.24 we need to apply this value on the given expression, as done below:

$259.24 = 0.15*x + 255.34\n0.15*x = 259.24 - 255.34\n0.15*x =3.9\nx = (3.9)/(0.15)\nx = 26$

The average was 259.24 after 26 years, therefore it was in 1996.

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I can't figure this outthis question was on my exam and I got it completely wrong (I have a graphing calculator capble of matrices so yo don't have to solve the system of equations by hand, use rref (reduced row echelon form))values of a, b, and c and the equation of the graph of the parabola y=ax^2+bx+csuch that is passes through the points (2,-15) (-5,-29) (-3,5) rewrite it in the form (x-h)^2=4P(y-k) show all workif I were to sub the points in I would ge(2,-15): -15=4a+2b+c (-5,-29): -29=25a-5b+c (-3,5): 5=9a-3b+cthen solve for a, b and c I don't know how to solve, please help(if I don't undestand your answer, I will either report or ask you to explain more)
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A camera is placed in front of a hyperbolic mirror. The equation of the hyperbola that models the mirror is , where x and y are in inches. The camera is pointed toward the vertex of the hyperbolic mirror and is positioned such that the lens is at the nearest focus to that vertex.
What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?
How do you solve this? 18 " n=21

The function f(x) = −x2 − 7x + 30 shows the relationship between the vertical distance of a diver from a pool's surface f(x), in feet, and the horizontal distance x, in feet, of a diver from the diving board. What is a zero of f(x), and what does it represent?x = 10; the diver hits the water 10 feet away horizontally from the board
x = 3; the diver hits the water 3 feet away horizontally from the board
x = 10; the diver jumps in the pool at 10 feet per second
x = 3; the diver jumps in the pool at 3 feet per second

Answers

Setting f(x) = 0, we have:
-x2 -7x +30 =0

The roots of this quadratic equation are:
x = 3 and -10

Since the diver is on a diving board, the -10 is somewhere behind him. We use the root x = 3 since this distance is in front of the board.

Therefore, the answer is:
x = 3; the diver hits the water 3 feet away horizontally from the board

The diver hits the water 3 feet away horizontally from the board.

The correct option is (b)

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x, ax²+bx+c=0 with a ≠ 0 .

Given function: f(x)= -x² -7x +30

Factorising f(x), we get

-x² -7x +30 =0

x² +7x -30 =0

x² +10x - 3x -30 =0

x(x+10)-3(x+10)=

(x+10)(x-3)=0

The roots of this quadratic equation are x = 3 and -10.

As, the diver is on a diving board we will not use -10.

Hence, the diver hits the water 3 feet away horizontally from the board.

Learn more about quadratic equation here:

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You are building a rectangular deck. The area of the deck should be 250 ft.² . You want the lengths of the deck to be 5 feet longer than twice its width. What should the dimensions of the deck be?

Answers

et the width be x
"the length of the deck to be 5 ft longer than twice its width" --- >length = 2x+5

then
x(2x+5) = 250
2x^2 + 5x - 250 = 0
(x - 10)(2x + 25) = 0
x = 10 or x is a negative, which makes no sense

width = 10
length = 25

check:
is the length 5 more than twice the width ?? yes
is the area 250 ? yes

How to change numbers into decimals using common core standards?

Answers

Assuming you are talking about converting fractions to decimals, divide the numerator (top number) by the denominator (bottom number). If it isn't one you can solve in your head, use long division.

What is the greatest amount of money that rounds to $108.60 when rounded to the nearest dime? What is the least amount of money that rounds to $108.60? Explain your answers.

Answers

Answer:

$108.59

Step-by-step explanation:

The dime which is worth 0.10 U.S. dollar, is a ten-cent coin, one-tenth of a United States dollar

the value is 0.1

Now in rounding up of numbers the dime is located one decimal place away i.e 0.5 in the number given in the problem statement

to round up to the nearest dime we have to consider the next number to the dime if this number is greater than 5 we will round up if it is less than five we can not perform any rounding up operation

hence the greatest amount of money is

since the number next to 5 is 9 and 9 is greater than 5 we will round up from 5 to 6

This makes 108.59 the greatest amount of money that rounds to $108.60

Final answer:

The least amount of money that rounds to $108.60 is $108.60. The greatest amount that rounds to $108.60 is $108.64.

Explanation:

When rounding to the nearest dime, there is a range of values that can round to $108.60. The least amount of money that rounds to $108.60 is exactly $108.60 because when you are at the target, you don't need to round up or down. The greatest amount that rounds down to $108.60 would be any amount that is less than halfway to the next dime, which is $108.65. So, anything less than $108.65, but more than $108.60, would round to $108.60. As such, the greatest amount that would round to $108.60 when rounded to the nearest dime would be $108.64.

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Before embarking on a flight, the pilot of a private airplane plans the best route to the finaldestination. Suppose the pilot determines one route covers a distance of $\sqrt{500$ miles and another covers a distance of [tex] \sqrt{605} miles

a. a. Write an expression to represent the difference between the two distances of
each route. Then simplify the expression, keeping your answer in radical form.
Show all steps needed to write your answer in simplest form.

b.b. Use a calculator to change the answer to decimal form. Round the answer to the
nearest tenth. Using this decimal number, write a sentence to explain the
meaning of the answer in this situation.

Answers

Differ of these distances:

$√(605) - √(500)$

Simplify this distance:

$√(605) - √(500) = √(121 \cdot 5) - √(100 \cdot 5)= √(121) \cdot √(5)-√(100) \cdot √(5)= \n \n = 11√(5)-10√(5)=√(5)$

To a decimal form: $√(5) \approx 2.2$

Meaning of the answer? The answers 2.2 or $√(5)$ is just very clear to us

Find the area and the circumference of a circle with diameter 5 cm.Use the value 3.14 for it, and do not round your answers. Be sure to include the correct units in your answers.

Answers

The Circumference of the circle is
15.7

and Area is
19.625

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