Answer:
1. a. Greatest common factor: 4
b. Greatest common factor: x2
c. Greatest common factor: p2
d. Greatest common factor: x
2. a. (a2 + 1)(4a + 28)
b. (x + 3)(x2− 2)
c. (4x+ 1)(2x−y)
3. a. u2 – 100 = (u + 10)(u − 10)
b. 4a2 − 49 = (2a + 7)(2a − 7)
c. 81 − y2= (9 + y)(9 − y)
d. 16q4− 16 = 16(q4 − 1) 16 (q4 −1) = 16(q2 + 1) (q2− 1) = 16(q2 + 1) (q + 1) (q − 1)
e. 9c3− 9c = 9c (c2− 1) = 9c(c + 1)(c − 1)
f. 48a2b − 12b = 12b (4a2− 1) = 12b(2a + 1)(2a − 1)
Step-by-step explanation:
I got it at PennFoster
Just need help
the equations are above
Answer:
6×4p=24p
15a÷3=5a
3t×8y=24ty
24ef÷12e=2f
-4fx-5px-3 =-x(4f+5p)-3
-9abc÷3a=-3bc
Examine the table of input (x) and output (y) values below. What is the relationship between the input and output values? Write an equation for this relationship. input (x) –1 0 1 2 3 4 5 output (y) –4 –1 2 5 8 11 14 What do you notice about the relationship between the x and y values?
Answer:
Relationship: As the input increases by 1, the output increases by 3.
Equation: y=3x-1
~Hope this helps~
can someone please please help me :/ I have to get this right. please help
Work Shown:
Solve for y. Then replace y with f(x).
[tex]680x + 10y - 1000 = 0\\\\10y - 1000 = -680x\\\\10y = -680x + 1000\\\\y = \frac{-680x + 1000}{10}\\\\y = \frac{-680x}{10} + \frac{1000}{10}\\\\y = -68x + 100\\\\y = 100 - 68x\\\\f(x) = 100 - 68x\\\\[/tex]
Effectively this involves adding 1000 to both sides and subtracting 680x from both sides, afterward we divide both sides by 10 to isolate y.
Answer:
choice B
Step-by-step explanation:
I did this problem like 6 months ago......
Esmereldas family went out to dinner paying 20% tip at the end of the meal. Their credit card was charged $51.00. What was the amount on the bill without the tip
Answer:
42.50
Step-by-step explanation:
bill + tip = total bill
The tip is based on the bill
tip = bill * 20%
tip = bill * .20
Replace in the original equation
bill + .20 bill = total bill
Combine like terms
1.20 bill = total bill
The total bill was 51 dollars
1.20 bill = 51
Divide each side by 1.20
1.20 bill / 1.2 = 51/ 1.2
bill =42.50
Answer:
$42.50
Step-by-step explanation:
If the total was $51 with the tip, and you know the tip was 20%, you can set up an equation and solve:
0.2x+x=51
1.2x=51
x=42.5
Therefore, the bill (w/o tip) was $42.50
p.s.Please give me brainliest. Thank you! :)
please help, not so good with this subject
Answer:
I believe the answer is d
Step-by-step explanation:
A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers.
In this case, since [tex]\sqrt{81}[/tex] can be simplified to 9 and 9 can be written as a fraction (9/1) it is a rational number.
The graph of f(x)=sin(x) is transformed into a new function, g(x) , by stretching it vertically by a factor of 4 and shifting it 3 units down. What is the equation of the new function g(x) ?
Answer:
f(x) = 4sin(x) - 3
Step-by-step explanation:
WILL MARK BRAINLIEST Decide whether the triangles are similar. If so, determine the appropriate expression to solve for x.
Answer:
third option
Step-by-step explanation:
∠ E = 180° - (65 + 53)° = 180° - 118° = 62°, then
∠ A = ∠ F = 53° and ∠ C = ∠ E = 62° , thus
Δ ABC ~ Δ FDE by the AA postulate
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{BC}{DE}[/tex] = [tex]\frac{AB}{FD}[/tex] , substitute values
[tex]\frac{x}{z}[/tex] = [tex]\frac{w}{r}[/tex] ( multiply both sides by z )
x = z × [tex]\frac{w}{r}[/tex]
The expression to solve for x would be x = r × w/z Therefore, the correct option is 3.
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
Since,
∠ E = 180° - (65 + 53)°
= 180° - 118° = 62°,
then
∠ A = ∠ F = 53° and ∠ C = ∠ E = 62° ,
Thus, Δ ABC ~ Δ FDE are congruent by the AA postulate.
Since the triangles are similar then the ratios of corresponding sides are equal so,
BC / DF = AB / ED
Substitute;
x / r = w/ z ( multiply both sides by z )
x = r × w/z
Therefore, the correct option is 3.
Learn more about congruent triangles;
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What are the opposites of 3,7,5, and -2 2
Answer:
-3, -7, -5, 2, and -2
Step-by-step explanation:
When you are looking for opposites just think about a number line.
You are on the positive side
What is the opposite of a positive... negative
The same for the other way around
What is the opposite of a negative... positive
Answer:
Step-by-step explanation: The opposites are what you would imagine them to be, positive and negative.
the answer is -3, -7, -5 and 22
Round 2.1 to the nearest whole number.
When you round 2.1 to the nearest whole number, the answer will be 2.
Answer:
2 is the answer
Step-by-step explanation:
to round 2.1 to the nearest whole number consider the tents value of 2.1 which is 1 end less than five therefore we have to round down the ones place value of 2.1 . 2 remains 2 and the decimal point is removed.
2.1 to the nearest whole number is 2
One angle of a triangle has a measure of 66 degrees. The measure of the third angle is 57 degrees more than 1/2 the measure of the second angle. The sum of the angle measures of a triangle is 180 degrees. What is the Measure of the second angle? What is the measure of the third angle?
Answer:
76 degrees
Step-by-step explanation:
Let the angles be x, y and z
As per given:
x= 66z = 57 + 1/2yx+y+z = 180Considering the first 2 equations in the third one:
66 + y + 57 + 1/2y = 1801.5y = 180 - (66+57)1.5y = 57y = 57/1.5y = 38So the third angle is:
z = 57 + 38/2 = 76 degreesHELP ME PLEASE ASAP! Zoe is making a quilt. The ratio of red squares to green squares is 2 to 3. She uses a total of 55 squares. How many green squares does she use?
Answer:
33
Step-by-step explanation:
For every 5 squares, two are red and three are green. So 3/5 of the squares are green.
3/5x55=33
CAN SOMEONE HELP ME ASAP? The density of a certain material is such that it weighs 7 ounces for every 2.5 gallons of volume. Express this density in tons per cubic meter. Round your answer to the nearest hundredth.
Answer: Density = 0.23 tons per cubic meter.
Step-by-step explanation:
Formula : [tex]Density=\dfrac{Mass(in \ ton)}{Volume (in\ m^3)}[/tex]
1 ton = 32000 ounces
⇒ 1 ounce = 0.00003125 ton
⇒ 7 ounces = 7(0.00003125)= 0.00021875 ton
1 gallon = 0.00378541 cubic meter
2.5 gallons = 0.009475 cubic meter
Density= [tex]\dfrac{0.00021875}{0.009475}\text{ tons per cubic meter}[/tex]
[tex]\dfrac{21875}{94750}\text{ tons per cubic meter}\approx0.23\text{ tons per cubic meter}[/tex]
Hence, Density = 0.23 tons per cubic meter.
Answer:
0.02 tons per cubic meter
Step-by-step explanation:
Use the formula for the volume of a cylinder to find the volume of a water tank (in ft with a radius of 15 feet and a height of 35 feet. Round to two decimal places.
Answer:
24,740.04 ft³
Step-by-step explanation:
Use the cylinder volume formula, V = [tex]\pi[/tex]r²h, where r is the radius and h is the height.
Plug in the values and solve for V:
V = [tex]\pi[/tex](15²)(35)
V = 24740.04215
Round:
V = 24,740.04 ft³
The volume of a water tank will be; 24,740.04 ft³.
What is the volume of a cylinder?The volume of the cylinder is the product of the height, pie, and square of the radius.
The volume of the cylinder = πr²h
where r is the radius and h is the height.
We have been given a cylinder that has a radius of 15 feet and a height of 35 feet.
We need to find the volume of a water tank.
Now Plug in the values and solve for V:
V = π(15²)(35)
V = 24740.04215
Round: V = 24,740.04 ft³
Hence, the volume of a water tank will be; 24,740.04 ft³.
Learn more about volume;
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Becky's ship is 43 miles west all the harbor.
Clyde's yacht is a5 miles north from Beery. How
far is Clyde from the Harbor? Show your work.
С
x= Harbor
25
B.
43
Answer:
Clyde is 49.74 away from the harbor
Step-by-step explanation:
Here in this question, we are interested in knowing the distance of Clyde from the harbor.
The key to answering this question is having a correct diagrammatic representation. Please check attachment for this.
We can see we have the formation of a right angled triangle with the distance between Clyde’s ship and the harbor the hypotenuse.
To calculate the distance between the two, we shall employ the use of Pythagoras’ theorem which states that the square of the hypotenuse is equal the sum of the squares of the two other sides.
Let’s call the distance we want to calculate h.
Mathematically;
h^2 = 25^2 + 43^2
h^2 = 625 + 1849
h^2 = 2474
h = √2474
h = 49.74 miles
Convert the following:
1 meter is equivalent to
ao feet (rounded to the nearest hundredth)
Answer:
1 meter = 3.28 feet
Step-by-step explanation:
The unit of conversion from meters to feet is given as follows;
By convention
1 yard = 09144 meters
1 yard = 3 feet
Therefore, we have;
1 foot = 0.9144/3 = 0.3048 m
Alternatively we can get;
1 inch = 0.0254 meters
1 foot = 12 inches
Therefore, we have;
1 foot = 12 × 0.0254 = 0.3048 meter
Which gives;
1 foot = 0.3048 meter
Given that 0.3048 meter = 1 foot, to find the measure of 1 meter, we proceed by dividing both sides of the equation by 0.3048 to get
0.3048/0.3048 meter = 1/0.3048 foot = 3.28084 feet
1 meter = 3.28084 feet. ≈ 3.28 feet to the nearest hundredth
If the length of a room is 18 feet, how long should it be on a scale drawing
where 1 in. = 2 ft.?
Answer:
9 in.
Step-by-step explanation:
Proportions:
1 in ⇔ 2 ft
R in ⇔ 18
R = 18*1/2
R = 9 in
Which of the following expressions represents the distance between -3.9, and -4.7?
Answer:
[tex]d = \sqrt{(x2 - x1) {}^{2} + (y2 - y1) {}^{2} }[/tex]
Step-by-step explanation:
[tex]d = \sqrt{( - 4 + 3) {}^{2} + (7 - 9) {}^{2} } [/tex]
[tex]d = \sqrt{(1 + 4)} = \sqrt{5} [/tex]
Find the area of each polygon
Answer:
1. 66 ft²
2. 102 cm²
3. 35 in.²
4. 7.36 in.²
5. 60 in.²
6. 91 m²
7. 48 m²
5. 567 mm²
9. 255 m²
10. The side length of the square is 9 cm
The area of the square is 81 cm²
Step-by-step explanation:
1. The area of the parallelogram = 11 × 6 = 66 ft²
2. The area of the triangle = 1/2×12×17 = 102 cm²
3. The area of the trapezium = 1/2×(5 + 9)×5 = 35 in.²
4. The area of the triangle = 1/2×4.6×3.2 = 7.36 in.²
5. The area of the parallelogram = 10 × 6 = 60 in.²
6. The area of the trapezium = 1/2×(15 + 11)×7 = 91 m²
7. The area of the parallelogram = 8 × 6 = 48 m²
5. The area of the trapezium = 1/2×(27 + 36)×18 = 567 mm²
9. The height of the wall = 17 m - 8 m = 15 m
The area = 17 × 15 = 255 m²
10. The dimensions of a square with perimeter = 36 cm are;
Side length = 36/4 = 9 cm
The area of the square = 9 × 9 = 81 cm².
Find the values of the apple, banana and lollypop below.
Pls help
Answer:
a= Apple = 3
b= Banana =5
v= Lollypop=1
Step-by-step explanation:
36 is divided into 2 giving us 18
Let apple=a
Banana=b
Lollypop=c
In the first half
An apple + 3 bananas=18
a+3b=18 (1)
Second half is further divided into 2
That is,
18÷2=9
First half of the second half
3apples=9
3a=9 (2)
Second half of the second half
1 apple + 1 banana + 1 lollypop=9
a+b+c=9 (3)
a+3b=18 (1)
3a=9 (2)
a+b+c=9 (3)
From (2)
3a=9
Divide both sides by 3
a=9/3
a=3
Substitute a=3 into 1
a+3b=18
3+3b=18
3b=18-3
3b=15
Divide both sides by 3
b=15/3
=5
b=5
Substitute the value of a and b into (3)
a+b+c=9
3+5+c=9
8+c=9
c=9-8
c=1
Therefore,
a= Apple = 3
b= Banana =5
v= Lollypop=1
©
Christine went shopping and bought each of her ten nephews a gift, either a video costing $14.95 or a CD costing $16.88. She spent $164.94 on the
gifts. How many videos and how many CDs did she buy
Answer:
She bought 2 videos and 8 CDs.
The Nguyen family and the Reed family each used their sprinklers last summer. The Nguyen family's sprinkler was used for 15 hours. The Reed family's sprinkler was used for 25 hours. There was a combined total output of 1175L of water. What was the water output rate for each sprinkler if the sum of the two rates was 55L per hour? Nguyenfamily'ssprinkler:Lperhour Reedfamily'ssprinkler:Lperhour
Answer:
Nguyen family's sprinkler: 20 L per hour Reed family's sprinkler: 35 L per hourStep-by-step explanation:
Let n and r represent the output in liters per hour of the Nguyen and Reed family sprinklers, respectively. Then we have ...
15n +25r = 1175 . . . . total sprinkler output
n + r = 55 . . . . . . . . . sum of two output rates
The second equation tells us we can substitute n = 55 -r into the first equation:
15(55 -r) +25r = 1175
10r = 1175 -825 . . . . . . subtract 825
r = 350/10 = 35 . . . . . . divide by 10
n - 55 -35 = 20 . . . . . . find n from r
Nguyen family's sprinkler: 20 L per hour
Reed family's sprinkler: 35 L per hour
Please answer it now
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▹ Answer
435.20 square cm
▹ Step-by-Step Explanation
Diameter = 12
Radius = 1/2d
Radius = 1/2 * 12
Radius = 6
A = πr(r +√h² + r²) =
A = π · 6·(6 + √16²+6²)
≈ 435.19869 → 435.20 square cm
Hope this helps!
CloutAnswers ❁
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a diagonal of rectangle forms a 30 degree angle with each of the longer sides of the rectangle. if the length of the shorter side is 3, what is the length of the diagonal
Answer:
Length of diagonal = 6
Step-by-step explanation:
Given that
Diagonal of a rectangle makes an angle of [tex]30^\circ[/tex] with the longer side.
Kindly refer to the attached diagram of the rectangle ABCD such that diagonal BD makes angles of [tex]30^\circ[/tex] with the longer side CD and BA.
[tex]\angle CDB =\angle DBA =30^\circ[/tex]
Side AD = BC = 3 units
To find:
Length of diagonal BD = ?
Solution:
We can use the trigonometric ratio to find the diagonal in the [tex]\triangle BCD[/tex] because [tex]\angle C =90^\circ[/tex]
Using the sine :
[tex]sin\theta = \dfrac{Perpendicular }{Hypotenuse }[/tex]
[tex]sin\angle CDB = \dfrac{BC}{BD}\\\Rightarrow sin30^\circ = \dfrac{3}{BD}\\\Rightarrow \dfrac{1}2 = \dfrac{3}{BD}\\\Rightarrow BD =2 \times 3 \\\Rightarrow BD = \bold{6 }[/tex]
So, the answer is:
Length of diagonal = 6
Pranav and Trevon each improved their yards by planting daylilies and ornamental grass. They bought their supplies from the same store. Pranav spent $74 on 1 daylily and 9 bunches of
ornamental grass. Trevon spent $114 on 1 daylily and 14 bunches of ornamental grass. What is the cost of one daylily and the cost of one bunch of ornamental grass?
Answer:
Day lilies and ornamental grass are $2, $8 respectively
Step-by-step explanation:
step one
we need to represent the scenario with a system of equation
let day lilies be represented with x
and ornamental grass be y
Hence we have
[tex]x+9y= 74--------1\\x+14y= 114------2[/tex]
Let us subtract 1 from 2 we have
[tex]x+14y= 114------2\\\\\\ -(x+9y= 74--------1\\=0+5y= 40[/tex]
Dividing both sides by 5 we have
y= 40/5
y= 8
step 2
Substitute y = 8 in equation 1 we have
x+9(8)= 74
x+72= 74
x=74-72
x= 2
Day lilies and ornamental grass are $2, $8 respectively
Mr. Lee is 32 years older than his son. Five years later, Mr. Lee’s age will be 5 times that of his son. How old is Mr. Lee now?
Answer: mr lee is 37 year .
Step-by-step explanation:32+5=37
Answer:
Mr. lee is 35 yrs old right now. his son 3
Step-by-step explanation:
after 5 yrs, his son will be 8 and lee 40, 8×5=40
Type the correct answer in the box. Simplify this expression: 4(1 – 3x) + 7x – 8.
Answer:
-4 -5x
Step-by-step explanation:
4(1 – 3x) + 7x – 8.
Distribute
4 -12x +7x -8
Combine like terms
-4 -5x
Answer:
The simplified answer of this expression is -5x - 4
Step-by-step explanation:
4(1 - 3x) + 7x - 8
Distribute 4 to (1 - 3x)
4 - 12x + 7x - 8
Rearrange the terms so it'll be easier to combine them.
4 - 8 - 12x + 7x
Combine like terms.
-4 - 5x
Put the equation in standard form.
-5x - 4
What is 100,000+4,000+800+5 in standard form
Answer: 104,805
Step-by-step explanation:
just add
Answer:
104,805
Step-by-step explanation:
add it in each placement form
The following shape is based only on squares, semicircles, and quarter circles. Find the area of the shaded part.
Answer:
The area of the shaded part is 36.53 cm²
Step-by-step explanation:
The dimension of the side of the square ABCD = 8 cm
The shaded part is seen to be the area of intersection of two quarter circles
The dimension of the radius of the quarter circles = The side length of the square
Therefore;
The dimension of the radius of the quarter circles = 8 cm
The figure can be taken as being formed by the two quarter circles with a square removed
The shaded area is the
Therefore, the area of the shaded part Sₐ, is given by the relation;
Sₐ = Area of first quarter circle + Area of second quarter circle - Area of the square
Given that the dimensions (radius) of the two quarter circles are the same, we have;
Area of first quarter circle = Area of second quarter circle = (π × 8²)/4 cm²
Area of the square = (Side length of the square)² = 8² = 64 cm²
Sₐ = (π × 8^2)/4 + (π × 8^2)/4 - 64 = 36.53 cm²
The area of the shaded part = 36.53 cm².
shannon is paid £1150 a month after deductions.what is her net annual salary?(a year=12 months )
Answer:
£13800
Step-by-step explanation:
1150*12=£13800
Candy is on sale for $0.75 each. You have a coupon for $0.25 off your total purchase. Write a function rule for the cost of n pieces of candy
Answer:
t = 0.75n - 0.25
t represents your total
Step-by-step explanation:
So lets start by writing our total variable.
t =
Now each candy is 0.75 so lets write that down too.
t = 0.75
Since we don't know how much candy we buy, lets multiply 0.75 by n.
t = 0.75n
Now we have a $0.25 coupon so now subtract the 0.25 from the cost.
t = 0.75n - 0.25
There you go.
