Final answer:
To find the formula for f(q), solve the equation 11q-4=3r-6 for r. The steps include adding 6 to both sides and then dividing by 3, resulting in f(q) = (11q + 2) / 3.
Explanation:
To write a formula for f(q) in terms of q, we need to solve the equation 11q - 4 = 3r - 6 for r, the output of the function f. First, we add 6 to both sides to isolate the terms with r on the right side of the equation:
11q - 4 + 6 = 3r - 6 + 6
11q + 2 = 3r
Next, we divide both sides by 3 to solve for r:
(11q + 2) / 3 = 3r / 3
(11q + 2) / 3 = r
Therefore, the formula for f(q) is:
f(q) = (11q + 2) / 3
A skydiver jumps out of an airplane. After 0.8 seconds, she has fallen 100 feet. After 3.1 seconds, she has fallen 500 feet. Emtiaz says that the skydiver should fall about 187.5 feet in 1.5 seconds. Is his answer reasonable? Explain.
whats 603X4 estimate go math
10 ways to divide 96 into equal groups
These are the ten ways to divide 96 into equal groups:
96 divided by 2 = 2 groups of 48
96 divided by 48 = 48 groups of 2
96 divided by 12 = 12 groups of 8
96 divided by 8 = 8 groups of 12
96 divided by 32 = 32 groups of 3
96 divided by 3 = 3 groups of 32
96 divided by 24 = 24 groups of 4
96 divided by 4 = 4 groups of 24
96 divided by 6 = 6 groups of 16
96 divided by 16 = 16 groups of 6
Solve for x. The triangles in each pair are similar.
A water desalination plant can produce 2*10^6 gallons of water in one day. How many gallons can it produce in 79 days?
Write your answer in scientific notation.
The water desalination plant can produce 1.58 x 10^8 gallons of water in 79 days, expressed in scientific notation.
To calculate how many gallons of water a desalination plant can produce in 79 days, we will multiply the daily production capacity by the number of days. The plant's daily production capacity is given as 2 x 106 gallons. So, for 79 days, the calculation would be:
(2 x 106 gallons/day) x 79 days = 1.58 x 108 gallons
Expressed in scientific notation, the plant can produce 1.58 x 108 gallons of water in 79 days.
Charlie made four out of 23 free-throw shots. What percentage of shots does he make? Round to the nearest whole number
Shawn has been hired as a sales associate Horizon Mobile Phone Company. He has two salary options. He can either receive a fixed salary of $750.00 per week or a salary of $400.00 per week plus an 8% commission of his weekly sales. Which solution set among the options below represents the dollar amount of sales that he must generate each week in order for the option with commission to be the better choice?
A polynomial expression is shown below.
(mx³ + 3)(2x² + 5x + 2) - (8x⁵ + 20x⁴)
The expression is simplified to 8x³ + 6x² + 15x + 6. What is the value of m?
The value of the m in the polynomial expression for which the simplified expression is 8x³ + 6x² + 15x + 6 is 4.
What is the simplified form of a equation?Simplified form of an equation is the simplest way of expression the equation, which is obtained by applying the required operations of mathematics.
A polynomial expression is shown below.
[tex](mx^3 + 3)(2x^2 + 5x + 2) - (8x^5 + 20x^4)[/tex]
The expression is simplified to the following expression,
[tex]8x^3 + 6x^2 + 15x + 6[/tex]
As the equation is a simplified expression of the given polynomial. Thus, both the equation are same.
[tex](mx^3 + 3)(2x^2 + 5x + 2) - (8x^5 + 20x^4)=8x^3 + 6x^2 + 15x + 6[/tex]
Open the brackets and simplify it further,
[tex]2mx^5+5mx^4+2mx^3+6x^2+15x+6-8x^5-20x^4=8x^3 + 6x^2 + 15x + 6\\2mx^5+5mx^4+2mx^3=8x^3+6x^2+15x+6-6x^2-15x-6+ 8x^5+20x^4\\m(2x^5+5x^4+2x^3)= 8x^5+20x^4+8x^3 \\m(2x^5+5x^4+2x^3)=4(2x^5+5x^4+2x^3)[/tex]
On comparing both side of the equation, the value of m we get is,
[tex]m=4[/tex]
Thus, the value of the m in the polynomial expression for which the simplified expression is 8x³ + 6x² + 15x + 6 is 4.
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Ivan has a piece of lumber 104 inches long. He is sawing it into 12-inch lengths to make fence posts. He says he can get about 9 fence posts out of the board.
the temperature on monday was -1.5°C. The temperature on Tuesday was 2.6°C less than the temperature on Monday.what was the temperature on Tuesday?
if 2/3 of the girls in class have brown eyes and 1/4 of the girls have blue eyes, what fraction of the girls in class have neither blue or brown eyes.
25=2y-5 solve the equation for y
What’s 36/1000 (fraction) Simplified
What’s 506/1000 simplified (fraction)
write the addition sentence illustrated by each figure
Classify -2x4 - x3 + 8x2= 12 by degree.
Question 12 options:
cubic
quadratic
quartic
quintic
The solution is Option C.
The equation A = -2x⁴ - x³ + 8x² = 12 is a quartic equation as the degree of the equation is 4
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
-2x⁴ - x³ + 8x² = 12 be equation (1)
On simplifying the equation , we get
Adding 2x⁴ + x³ on both sides of the equation , we get
2x⁴ + x³ + 12 = 8x²
Subtracting 8x² on both sides of the equation , we get
2x⁴ + x³ - 8x² + 12 = 0 be equation (2)
Now , the highest degree of the variable x in the equation is x⁴ which is 4
Therefore , the equation is quartic
Hence , the equation is 2x⁴ + x³ - 8x² + 12 = 0
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the local bakery uses 1.75 cups of flour in each batch of cookies. The bakery used 5.25 cups this morning. How many batches of cookies did the barkey make?
divide total by amount needed for each batch
5.25 / 1.75 = 3
they made 3 batches of cookies
At a car repair shop, the cost of repair depends on the time the mechanic works. Which of the following shows this idea in function notation?
Pleas show all work.
A. number of cars (time)
B. time(cost)
C. time(number of cars)
D. cost(time)
Jeff left 13% tip at a restaurant where the bill was $29.62. How much did Jeff leave as a tip?
Final answer:
To calculate Jeff's tip, multiply 13% as a decimal (0.13) by the bill amount of $29.62, which equals a tip of $3.85.
Explanation:
To calculate how much Jeff left as a tip at the restaurant, we need to find 13% of his bill total, which was $29.62. To do this, convert the percentage to a decimal by dividing by 100 (which makes 13% become 0.13) and multiply that by the bill amount.
So, the calculation will be:
0.13 * $29.62
When you perform this calculation:
$3.85 (rounded to the nearest cent)
Jeff left a $3.85 tip at the restaurant.
Karl participated in a two-day charity walk. His parents donated money for each mile he walked. Karl walked 3 1/4 miles on the first day and 5 1/2 miles on the second day. His parents donated $175. How much money did his parents pay for each mile
A motorcross rider is in the air for 2.5 seconds. Your camera can take a picture very 0.125 second. Your friend's camera can take a picture every 0.15 second.
a. How many times faster is your camera than your friend's camera?
b. How many more pictures cna you take while the rider is in air?
Two families are sharing the cost of vacation home for one week. The cost to rent the home is $3,513 plus a $351.30 deposit. What is each family’s fair share of the home plus deposit?
$1756.50
$1128.10
$1932.15
.
$1432.15
The answer is $1932.15
3,513+351.30=3864.30
3864.30÷2=1932.15
Hope this helps!
Write an expression that shows how to multiply 7 x 256 using the expanded form and the Distributive Property.
What is 15% higher than 60?
A.9
B.24
C.69
D.75
A used electronics store pays $30 for each cell phone, spends $20 refurbishing the phone, and sells the refurbished phone to a customer for $115.
a. Write an expression in simplest form that represents the company's earnings (in dollars) from buying, processing, and selling cell phones. Use x to represent the number of cell phones they sell.
An expression is ([answer]) dollars.
In the diagram shown, ∠2 measures 77 degrees. What is the measure of ∠4?
Jason works at least 5 hours but not more than 10. He earns $15.30 per hour. The function f (t) = 15.3t represents the money he earns for working t hours. What is the practical range? Show all your work.
1. Correctly determine the minimum and maximum money earned.
2. Correctly identify the practical range as inclusive or exclusive.
3. Correctly state the practical range.
1. The minimum number of hours is 5 hours, so the minimum money earned is:
minimum money = 15.30 * 5 = $76.50
The maximum number of hours is 10 hours, so the maximum money earned is:
maximum money = 15.30 * 10 = $153
2. Since the words “at least” and “not more than” are used, hence this is inclusive.
3. The practical range is:
$76.50 ≤ f(t) ≤ $153
Answer:
$76.50 ≤ f(t) ≤ $153
Step-by-step explanation:
Which point represents the fraction 3/6???
A
B
C
or
D
????
PLEASE HELP
The point that represents the fraction 3/6 is point B.
Explanation:The point that represents the fraction 3/6 is point B.
When we simplify the fraction 3/6, we obtain 1/2.
To represent a fraction on a number line, we divide the line segment between 0 and 1 into equal parts. Since the denominator is 2, we divide the segment into 2 equal parts. The numerator, 1, represents the number of parts we need to take from the line (starting from 0) to reach the fraction. Thus, we locate point B on the number line to represent the fraction 3/6.
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Jennifer has 3 1/2 cups of jelly beans to share with 7 friends how many cups does each person get
Each small square on the grid is 1 ft².
Which estimate best describes the area of this figure?
25 ft²
35 ft²
50 ft²
65 ft²
Answer:
50 ft²
Step-by-step explanation:
As you can see the polygon on the grid is not a regular polygon, so to calculate the area would be very complicated without having the right tools, what we can doo is to draw a squre that covers the whole height but not the total length, that way we can take a close estimate of the area, the closest square that can be formed would be a 6x9 square, and the estimated area would be 54, that would be the maximun area, so the answer would be 50 squared feet.
Alicia and Elena each earned $135 doing telephone surveys. Alicia did her surveys in 12 hours. It took Elena 75% as long to do her surveys. How much money did Elena earn per hour? A. $7 B. $11 C. $12 D. $15
Answer:
d 15
Easy. As that