Answer:
f(x)g(x) = 2x² - 6x
General Formulas and Concepts:
Algebra I
Expand by FOIL-ing (First, Outside, Inside, Last)Step-by-step explanation:
Step 1: Define
f(x) = 2x
g(x) = x - 3
Step 2: Find f(x)g(x)
Substitute: f(x)g(x) = 2x(x - 3)Distribute 2x: f(x)g(x) = 2x² - 6xWhich type of parent function does the equation f (x) = |x| represent?
Equation f (x) = |x| represent the Absolute Value Functions.
Parent Function :Parent functions are the simplest form of a given family of functions. A family of functions is a group of functions that share the same highest degree and, consequently, the same shape for their graphs.
Absolute Value Functions :
The parent function of absolute value functions is y = |x|. Absolute value functions are expected to return V-shaped graphs.
The vertex of y = |x| is found at the origin as well. Since it extends on both ends of the x-axis, y= |x| has a domain at (-∞, ∞). Absolute values can never be negative, so the parent function has a range of [0, ∞].
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Two figures are said to be SIMILAR if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor.
This pair of figures is similar. Find the value of the missing side (x).
Answer:
The ratio is 8:1 and it is a rectangle so x is 56
If on the similar image the sides are the same the other image will be aswell
Hope thie helps!
If you have any other question feel free to ask!
Points P, Q, R, and S are collinear. Point Q is between P and R, R is between Q and S, and PQ =RS. If PS= 23 and PR = 17, what is the value of QR?
QR=
(Simplify your answer.)
Answer:
QR = 11
Step-by-step explanation:
P-Q-R-S
PQ = RS
PS = 23
PR = 17
so RS = PS - PR = 23 - 17 = 6
RS = PQ = 6
QR = PS - (RS + PQ) = 23 - (6 + 6) = 23 - 12 = 11
What si the greatest multiple of 60 and 72
The greatest common multiple of 60 and 72 is 6.
The given numbers are 60 and 72.
What is the meaning of greatest common multiple?The greatest common factor (GCF) is a term used to describe the biggest number that can divide evenly into two or more numbers. Sometimes, this is also referred to as the greatest common divisor (GCD) or highest common factor (HCF). A factor is a smaller number that can divide evenly into that number.
Now, 60 = 2×2×3×5 and 72 = 2×2×2×3×3
The common factors are 2 and 3
So, the greatest common factor =2×3=6
Therefore, the greatest common multiple of 60 and 72 is 6.
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The Andersons are planning to take a 960-mile trip. They will travel 840 miles by car. What percent of the distance will they not travel by car?
The percent of distance that the Andersons will not travel by car is 12.5%, If they are planning to take a 960-mile trip and they will travel 840 miles by car.
Total distance the Andersons are planning to take is 960-mile
They will travel 840 miles by car
Distance they will not travel by car = total distance - distance travelled by car
= 960 - 840 miles
=120 miles
Percentage formula = (value/ total value) x 100
percent of the distance will they not travel by car =
(total distance - distance travelled by car) x 100/total distance
=((960 - 840)/ 960) x100
=(120/ 960) x 100
12.5
If the Andersons are planning to take a 960-mile trip and they will travel 840 miles by car then the percentage of distance they will not travel by car is 12.5%
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Write the expression (-7) x (-7) x 5 x 5 x 5 x 5 using exponents
Answer: [tex]-7^2 * 5^4[/tex]
Step-by-step explanation:
8 classes for
n = 75
measurements; minimum value = 40; maximum value = 195
40,60,80,100,120,140,160,180,200 are the class boundaries.
How to find the class boundaries?The lower class boundary (LCB) is the LCL minus one-half the tolerance, and the upper class boundary (UCB) is the UCL plus one-half the tolerance. Class borders are the end points of an open interval that contains the class interval.
given that
8 classes for n = 75measurements
minimum value = 40
maximum value = 195
from the question
smallest class boundary = (maximum - minimum value) / n classes
= (195 - 40) / 75 = 19.375 = 20
round off the value means 20
using minimum value and smallest class boundary.
Hence, the 40,60,80,100,120,140,160,180,200 are the class boundaries.
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Disclaimer: the question is incomplete on portal. Here is the complete question.
Question: Use the information given to find a convenient class width. Then list the class boundaries that can be used to create a relative frequency histogram. (Round your class width up to the nearest multiple of 5. Use the minimum value as the smallest class boundary. Enter your class boundaries as a comma separated list.)
8 classes for n = 75 measurements; minimum value = 40; maximum value = 195.
An article is marked at $30 but sold for $36.
(a) Is this a discount or a sale mark-up?
(b) What percentage difference does someone pay?
rectangle has a length of 35 yards less than 7 times its width. If the area of the rectangle is 6468 square yards, find the length of the rectangle.
Therefore the width of the rectangle is 33 yards
length of the rectangle is 196 yards.
Let the width of the rectangle be 'x'
Given the length of the rectangle = 35 yards less than 7 times the width
= 7x - 35
Given the area of rectangle = 6468 square yards
We know that area of rectangle = length * width
= (7x - 35 ) * x
By comparing both we get,
(7x - 35) * x = 6468
7x² - 35x - 6468 = 0
By dividing the equation by '7' we get
x² - 5x - 924 = 0
Factorize the above equation we get
x² - 33x + 28x - 924 = 0
x ( x - 33) +28 (x - 33 ) = 0
( x - 33 ) ( x + 28 ) = 0
∴ x = 33 , -28
Negative values are not consider
Therefore the width of the rectangle is 33 yards
length of the rectangle = 7(33) - 35
= 231 - 35
= 196 yards
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The circumference of a circle is 14 in. What is the area, in square inches?
Answer:
15.6 in² (nearest tenth)
Step-by-step explanation:
Circumference of a circle
[tex]\large\boxed{C=2\pi r}[/tex]
Where r is the radius of the circle.
Given:
C = 14 inSubstitute the given value into the equation for the circumference and solve for r:
[tex]\begin{aligned}\implies 14 & = 2 \pi r\\\\ r & = \dfrac{14}{2 \pi}\\\\ r & = \dfrac{7}{ \pi}\end{aligned}[/tex]
Area of a circle
[tex]\large\boxed{A=\pi r^2}[/tex]
Where r is the radius.
Substitute the found radius into the equation for area and solve for A:
[tex]\begin{aligned}\implies A&=\pi \left(\dfrac{7}{\pi}\right)^2\\\\ A&=\pi \cdot \dfrac{7^2}{\pi^2}\\\\ A&=\dfrac{49\pi}{\pi^2}\\\\ A&=\dfrac{49}{\pi}\\\\A & = 15.6\;\sf in^2\;(nearest\:tenth)\end{aligned}[/tex]
Therefore, the area of the circle with a circumference of 14 in is 15.6 in².
If-9(y-13) = 16, then y=
Hi there,
I hope you and your family are staying safe and healthy!
[tex]-9 (y-13) = 16[/tex]
This is called a linear equation. Let's distribute:
[tex]-9y + 117 = 16[/tex]
Now we need to subtract 117 from both sides
[tex]-9y +117-117=16-117[/tex]
[tex]-9y = -101[/tex]
Now divide both sides by -9
[tex]\frac{-9y}{-9} = \frac{-101}{-9}[/tex]
[tex]y = \frac{101}{9}[/tex]
Happy to help! All the best this semester!
Solve the equation for y. Then find the value of y for each value of x.
y + 2x = 5; x = - 2, 0, 3
The solution of the equation for y is y = 5 - 2x and the values of y are 9, 5 and -1
How to solve the equation for y?The equation is given as
y + 2x = 5
Subtract 2x from both sides of the equation
So, we have
y + 2x - 2x = 5 - 2x
Evaluate the like terms
y = 5 - 2x
Next, we solve the function for the values of x
When x = -2, we have:
y = 5 - 2 * -2
Evaluate
y = 9
When x = 0, we have:
y = 5 - 2 * 0
Evaluate
y = 5
When x = 3, we have:
y = 5 - 2 * 3
Evaluate
y = -1
Hence, the solution of the equation for y is y = 5 - 2x and the values of y are 9, 5 and -1
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The value of y when x = -2 , 0 , 3 are 9, 5 and -1 respectively.
How to determine the valueGiven the equation;
y + 2x = 5
Make 'y' the subject of formula
y = 5 - 2x (1)
When x = -2
Let's substitute the value of x as -2 in equation (1)
y = 5 - 2(-2)
expand the bracket
y = 5 + 4
y = 9
When x = 0
Substitute the value of x = 0
y = 5 -2(0)
y = 5 - 0
y = 5
When x = 3
Substitute the value of x = 3
y = 5 - 2(3)
y = 5 - 6
y = -1
Thus, the value of y when x = -2 , 0 , 3 are 9, 5 and -1 respectively.
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The lateral surface area of cone A is exactly the lateral surface area of
cylinder B.
A
h
57
B
A. True
B. False
SUBMIT
Answer:Cylinder B has the radius r and the height as h. The lateral surface area of cone is. The lateral surface area of cylinder is. 1/2 × lateral surface area of cylinder B, ⇒. ⇒ = lateral surface area of cone A. Hence we can conclude that the lateral surface area of cone A is exactly 1/2 the lateral surface area of cylinder B is option (A) true.
Hope this helped you :)
False, the statement that: The lateral surface area of cone A is equal to the lateral surface area of cylinder B. is not true.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Since, Lateral area of cone is given by: πrl
where r is the radius and l is the slant height
Here r = r and l = h
Hence, lateral area of cone A= π × r × h
= πrh
And, Lateral area of cylinder is given by:
= 2πrh
where r is the radius and h is the height
Hence, Lateral area of cylinder B=2πrh
Clearly, both the lateral areas are not equal.
Hence, the statement that: The lateral surface area of cone A is equal to the lateral surface area of cylinder B. is not true.
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Suppose that 23 of work is needed to stretch a spring from its natural length of 30 cm to a length of 44 cm.
(a) How much work is needed to stretch the spring from 34 cm to 36 cm? (Round your answer to two decimal places.)
(b) How far beyond its natural lehgth will a force of 45 N keep the spring stretched? (Round your answer one decimal place.)
cm
Need Help
a) The work done is 3.3 J
b) The new force would stretch it 1.9 cm beyond its natural length.
What is Hooke's law?Hooke's law states that, the force of elasticity that tends to stretch a spring is directly proportional to the extension that is caused by the force as long as we do not by any means exceed the elastic limit of the material. This implies that the Hooke's law can only be found to hold when the elastic limit of the material has not been exceeded and the material has not become plastic.
Now;
F = Ke
W =1/2 Fe
F = 2W/e
W = work done
F = force exerted
e = extension
F = 2 * 23 /(44 - 30) * 10^-2
F = 328.6 N
a) To stretch 34 cm to 36 cm;
W = 1/2 * 328.6 N * 2 * 10^-2
W = 3.3 J
The work done is 3.3 J
b) F = Ke
328.6 N/(44 - 30) * 10^-2 = K
K = 2347 N/m
Then;
45 N = 2347 N/m * e
e = 45 N/ 2347 N/m
e = 0.019 m or 1.9 cm
New length = 30 cm + 1.9 cm = 31.9 cm
The new force would stretch it to a distance of 31.9 cm or 1.9 cm beyond its natural length.
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The total cost after tax to repair Deborah's computer is represented by 0.06(50h) +50h,
where represents the number of hours it takes to repair Deborah's computer. What
part of the expression represents the amount of tax Deborah must pay?
Answer:
0.06(50h)
Step-by-step explanation:
Tax is usually computed by taking a percentage of the cost of a good or service. In the expression, we see that h represents the number of hours worked that are being paid for. Naturally, the cost of a service is the price times the hours worked. Therefore, 50 must represent the number of hours worked, and 50h represents the price Deborah must pay before tax. Knowing all this, we can deduce that the expression 0.06(50h) represents the tax that she must pay as it is a tax rate (6%) being multiplied by the cost before tax.
Problem
Tapiwa raked 5%, percent more leaves than Adam raked. Tapiwa raked 357liters of leaves.
How many liters of leaves did Adam rake?
Answer:
339.15
Step-by-step explanation:
5% is equal to 1/20, so we can use 1/20 in place of 5%. All that needs to be done is to determine 1/20 of 357 and subtract the result (we subtract because Tapiwa raked more than Adam)
357 x 1/20 = 17.85
357 - 17.85
339.15
(01.01 MC)
Which value of x would make the expression (75)* equal to 5?
a
b
3
12
C 4
5
d 5
4
Answer:
Step-by-step explanation:
Can somebody help me if you know what this is
Answer: i think it might be 72
Answer:72
Step-by-step explanation:
The least common multiple is the smallest common(of equal value) number. we get this number by multiplying the two numbers by a number value till we get a common number between the two.
The problem-solving plan identifies the letter W as "What do you need to do to solve the problem?" Which of the following answer choices are included in the problem solving plan for the letter W?
A. Solve the problem and change your strategy if necessary.
B. Did you check the answer and did you answer the question asked.
C. Read the problem carefully, find the question, understand the problem and find out what you know.
D. Organize the problem and find the question.
Answer:
d
Step-by-step explanation:
Answer:The answer would most likely be c Read the problem carefully,find the question,understand the problem and find out what you know.
George mixes 1/4  cup of sugar with 1/8 cup of honey. Give the ratio of sugar to one cup of honey as a unit rate.
What is f(3)?
-9
-1
1
9
Answer:
9
Step-by-step explanation:
Edge
Graph the image of rhombus TUVW after a reflection over the line x = 1.
104
-10 -8 -6
U
-4
T
V
W
22
8
6
4
CN
2
-2
-4
2
4
6
8
00
X
10
Answer:
its c
Step-by-step explanation:
Evaluate the algebraic expression for the given value of the variable.
2x² - 5x; x = -6
The value is 102.
Here the expression is 2x² - 5x.
We have to find the value of the algebraic expression for x = -6.
Expression = 2x² - 5x
Now put the value of x = -6 in the expression, we get
2x² - 5x = 2(-6)² - 5(-6)
= 2×36 + 30
= 72 + 30
= 102
Therefore the value of an algebraic expression is 102.
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If y=+3x-2 Complete the following
x=-2
y=
Answer:
-8
Step-by-step explanation:
If x = -2, then plug -2 into the equation where the x is:
y = 3(-2) - 2
Then solve:
3 * -2 = -6
-6 - 2 = -8
So, y = -8
The ball bearing have volumes of 1.6 cm cube and 5.4 cm cube. What is the ratio of their areas?
The ratio of area of the ball bearings will be equal to 4 / 9.
We are given the volume of the ball bearings as:
Volume 1 = 1.6 cm³
Volume 2 = 5.4 cm³
Now, the ratio of their volumes will be equal to:
r = 1.6 / 5.4
r = 16 / 54
r = 8 / 27
Now, we know that, the scale factor will be:
k = ∛8 / 27
k = 2 / 3
Also, we know that, the ratio of their areas is the square of their scale factor.
So, the ratio of area will be equal to:
R = (2 / 3)²
R = 4 / 9
Therefore, we get that, the ratio of area of the ball bearings will be equal to 4 / 9.
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The ratio of their areas is 4 / 9.
The scale factor for the linear dimensions of the ball bearings will be the cube root of the volume scale factor:
[tex]$$k=\sqrt[3]{(1.6 / 5.4)}=2 / 3$$[/tex]
Then the scale factor for the areas will be the square of this scale factor: ratio of surface area =(2 / 3)^2=4 / 9
The area is the product of two linear dimensions, so its scale factor is the product of the linear dimension scale factors. That is, the scale factor for area is the square of the linear dimension scale factor.
Similarly, volume is the product of three linear dimensions, so its scale factor is the cube of the linear dimension scale factor.
To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized. It is employed to change the size of an item.
If the original figure's dimensions and the dilated (increased or lowered) figure's dimensions are known, the scale factor can be determined. A rectangle, for instance, has dimensions of 5 units in length and 2 units in breadth.
The sides of this rectangle will change to 10 units and 4 units, respectively, if the size of the rectangle is increased by a scale factor of two. Therefore, we may use the scale factor to determine the modified figures' dimensions.
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Round 3.691 or the nearest hundredth
Answer:
3.69
Step-by-step explanation:
Answer:
3.69
Step-by-step explanation:
when the nearest number from the right side is lower than 5 it just disappears and all of the numbers after that will disappear as well.
The data represent the number of ounces of water that 26 students drank before donating blood: 8 8, 8, 16,16, 16, 32, 32, 32, 32, 32, 32 64 64, 64, 64, 64, 64, 64, 80 80, 80, 80, 88, 88, 88.
a. Create a dot plot for the data.
b. Create a box plot for the data.
c. What information about the data is provided by the box plot that is not provided by the dot plot?
d. What information about the data is provided by the dot plot that is not provided by the box plot?
e. It was recommended that students drink 48 or more ounces of water. How could you use a histogram to easily display the number of students who drank the recommended amount?
Answer: All the answers you need are attached in the file.
Step-by-step explanation: Hope it helps!
Calculus 1 Question.
Answer: B
Step-by-step explanation:
f(2) = 2, and is defined/exists. Holes (and asymptotes) like the hole at (2, -2) ruins continuity. The limit exists, but is not equal to f(2) which is why continuity is ruined at x=2
Answer: B
Step-by-step explanation:
f(2) = 2 and exists/is defined Holes (and asymptotes) such as the one at (2, -2) destroy continuity. The limit exists, but it is not equal to f(2), hence continuity is broken at x=2.
Help please
7/11 divided by 4/5
Answer: 35/4
Step-by-step explanation:
7/11 ÷ 4/5 》7/11 × 5/4 = 35/44
If 8 is 40% of N, then what does N equal?
Answer:20
Step-by-step explanation:
n x 40% =8
So n = 8 / 40%
n = 20