Answer:
6x^3(x+2)(x-7)
Step-by-step explanation:
1st step: factor out common term, 6x^3(x^2 - 5x - 14)
2nd step: Factor x^2 - 5x - 14, (x + 2)(x - 7)
3rd step: simplify, 6x^3(x+2)(x-7)
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Troy and Lisa were shopping for school supplies. Each purchased different quantities of the same notebook and thumb drive. Troy bought 4 notebooks and 13 thumb drives for $254. Lisa bought 5 notebooks and 8 thumb drives for $169. Find the cost of each notebook and each thumb drive.
Answer:
The cost of each notebook is $5
The cost of each thumb drive is $18
Step-by-step explanation:
We solve this problem by the system of equations
Equation for Troy and equation for Lisa and then solve the two
equations simultaneous using the elimination method
Assume that the price of one notebook is $x and the price of one
thumb drive is $y
Troy bought 4 notebooks and 13 thumb drives for $254
∴ 4 x + 13 y = 254 ⇒ (1)
Lisa bought 5 notebooks and 8 thumb drives for $169
∴ 5 x + 8 y = 169 ⇒ (2)
To solve the equation multiply equation (1) by 5 and equation (2) by -4
to eliminate x
∵ 20 x + 65 y = 1270 ⇒ (3)
∵ -20 x - 32 y = -676 ⇒ (4)
Add equations (3) and (4)
∴ 33 y = 594
Divide both sides by 33
∴ y = 18
Substitute the value of y in equation (1) or (2) to find x
∴ 4 x + 13(18) = 254
∴ 4 x + 234 = 254
Subtract 234 from both sides
∴ 4 x = 20
Divide both sides by 4
∴ x = 5
x represents the cost per notebook and y represents the cost per
thumb drive
The cost of each notebook is $5
The cost of each thumb drive is $18
Answer: n=4, d=20
Step-by-step explanation:
Find the inverse function of y=9x
Answer:
Replace
F
(
x
)
with
y
.
y
=
9
x
Interchange the variables.
x
=
9
y
Solve for
y
.
Tap for more steps...
y
=
x
9
Solve for
y
and replace with
F
−
1
(
x
)
.
Tap for more steps...
F
−
1
(
x
)
=
x
9
Step-by-step explanation:
Answer is attached below.
Triangle J is shown below. James drew a scaled version of Triangle J using a scale factor of 4 and labeled it
Triangle K
Triangle J
What is the area of Triangle K?
Answer:
160 not 16
Step-by-step explanation:
The area of Triangle K is 4 times the area of Triangle J.
Explanation:The area of Triangle K can be determined by using the scale factor of 4. Since the scale factor determines how lengths are scaled, the area of a figure is scaled by the square of the scale factor. In this case, the scale factor is 4, so the area of Triangle K will be 4 times the area of Triangle J.
Let's say the area of Triangle J is A. Then, the area of Triangle K will be 4A.
Therefore, the area of Triangle K is 4 times the area of Triangle J.
Emma's final grade in her math class is the average (mean) of her 5 chapter tests she took throughout the year. If she received a 92%, 85%, 78%, 97%, and 88% on the five tests, what is her final grade?
Answer:
Step-by-step explanation:
The mean (or average) of a set of numbers can be found with the following formula:
[tex]Mean = \frac{A_{1} + A_{2} + ... + A_{N}}{N}[/tex]
For this problem, we have five numbers, so we add them together and divide by 5:
[tex]Mean = \frac{92 + 85 + 78 + 97 + 88}{5}[/tex]
[tex]Mean = \frac{440}{5}[/tex]
[tex]Mean = 88[/tex]
Answer:
88%
Step-by-step explanation:
Emma took tests of her 5 chapters throughout the year.
She received the score on the five tests
92%, 85%, 78%, 97% and 88%
We have to calculate the average (mean) of her final grade.
average = [tex]\frac{\text{addition of all grades}}{\text{total number of tests}}[/tex]
= [tex]\frac{92+85+78+97+88}{5}[/tex]
= [tex]\frac{440}{5}[/tex]
= 88%
Her final grade would be 88%.
PLEASE HELP
Part A: If (6^2)x = 1, what is the value of x? Explain your answer.
Part B: If (6^0)x = 1, what are the possible values of x? Explain your answer.
Answer:
A. 1/36 B. 1
Step-by-step explanation:
A. if (6^2)x=1; 6^2=36
36x=1
x=1/36
B. If (6^0)x=1; 6^0=1
(1)x=1
x=1
A triangle has vertices at (-3, 4), (-1,0), and (-4,0). What are the
coordinates of the vertices after it is rotated 180° about the origin?
Answer:
'(3, -4), '(1, 0), '(4, 0)
Step-by-step explanation:
According to the 180°-rotation rule, you take the OPPOSITE of both the x-coordinate and y-coordinate:
(-3, 4) → (3, -4)
(-1, 0) → (1, 0)
(-4, 0) → (4, 0)
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The coordinates of the vertices after rotated 180° about the origin are;
( 3, -4 ), ( 1, 0 ) and ( 4, 0 ).
Here,
Given that;
A triangle has vertices at (-3, 4), (-1,0), and (-4,0).
We have to find the value of the coordinates of the vertices after rotated 180° about the origin.
What is Rotation 180 degree about the origin?
The rule for a rotation by 180° about the origin is (x, y) → (−x,−y).
Now,
A triangle has vertices at (-3, 4), (-1,0), and (-4,0).
Hence the coordinates of the vertices after rotated 180° about the origin are,
(-3, 4) ⇒ (3, -4)
(-1, 0) ⇒ (1, 0)
(-4,0) ⇒ (4, 0)
So, The coordinates of the vertices after rotated 180° about the origin are;
( 3, -4 ), ( 1, 0 ) and ( 4, 0 ).
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The formula E= mgh, where E = gravitational potential energy, m = mass, g = gravity, and h = height, is used to calculate gravitational potential energy. Solve this formula for h.
h = E − mg
h equals E over m times g
h = E + mg
h equals m times g over E
Answer: [tex]h=\dfrac{E}{mg}[/tex], where E = gravitational potential energy, m = mass, g = gravity, and h = height.
Step-by-step explanation:
Given : The formula [tex]E= mgh[/tex] , where E = gravitational potential energy, m = mass, g = gravity, and h = height, is used to calculate gravitational potential energy.
To find the formula for h (height), we need to divide mg on both the sides , we get
[tex]h=\dfrac{E}{mg}[/tex]
Hence, the formula for h will be [tex]h=\dfrac{E}{mg}[/tex], where E = gravitational potential energy, m = mass, g = gravity, and h = height.
For the formula E= mgh, when we solve for h, we would get : Option B. h equals E over m times g
How to solve for the value of hTo solve the formula E = mgh for h,
we need to isolate the variable h on one side of the equation.
Here's the step-by-step process:
equation: E = mgh.
Divide both sides of the equation by mg to make h the formula of the equation
E/(mg) = h
Therefore, the formula E = mgh, when solved for h, becomes h = E/(mg). Option B is correct.
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mark spends $30.00 on 9 gallons of gasoline. At the same price per gallon, approximately how many gallons of gas can Mark buy for $54.00? Please answer quickly
Solve for y.
-38 = 7v+17 – 12v
Answer:
v = 11Step-by-step explanation:
[tex]-38=7v+17-12v\qquad\text{subtract 17 from both sides}\\\\-38-17=7v+17-17-12v\qquad\text{combine like terms}\\\\-55=-5v\qquad\text{divide both sides by (-5)}\\\\\dfrac{-55}{-5}=\dfrac{-5v}{-5}\\\\11=v\to v=11[/tex]
Identify the property demonstrated.
3 +4 = 4 +3
DONE
Answer:
communicative property of addition
Step-by-step explanation:
communicative property of addition: The order in which numbers are added doesn't change the sum of the numbers .
For any number a & b,
a + b = b + a
similarly,
3 +4 = 4 +3
The property demonstrated in statement 3 + 4 = 4 + 3 is known as the commutative property of addition.
What is the commutative property of addition?According to the commutative property of addition, altering the order of addends has no impact on the sum.
How to solve this problem?The given statement is 3 + 4 = 4 + 3.
The value of the R.H.S and L.H.S are the same i.e. 7. Clearly if we alter the addends 3 and 4, we can get the same result. So, it can be concluded that this property is the commutative property of addition.
Therefore the property demonstrated in statement 3 + 4 = 4 + 3 is known as the commutative property of addition.
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How can 4.17 be written as a whole number with a fraction?
Final answer:
4.17 can be written as 4 17/100.
Explanation:
The number 4.17 can be written as a whole number with a fraction by separating it into the whole number part and the fractional part.
To write 4.17 as a whole number with a fraction, we need to separate the whole number part and the fractional part. The whole number part is 4, and the fractional part is 0.17. Since 0.17 is already expressed as a decimal, we can convert it to a fraction by considering the place value of each digit. The 7 is in the hundredths place, so it can be expressed as a fraction with the denominator 100.Thus, 4.17 can be written as 4 17/100.
Sales tax on a $400 stereo is $16. What is the tax on a $650 tv?
Answer:
$2.6
Step-by-step explanation:
firstly we find percentage of tax .
(16/400) * 100
= 16/4
= 4 %
now ,
so 4% of 650
= (4*650)/ 100
=260/100
= $2.6
Answer:
the answer is 26 no decimal i got it right on my test.
X=tax on a $650 TV
16/400 = X/650
16*650=400*X
10,400=400*X
10,400/400=X
26=X
What is a reasonable height for a doorway? NEEDS TO BE ANSWERED ASAP
A. 2 cm
B. 2 m
C. 2 mm
D. 2 km
Answer:
B. 2 m
Step-by-step explanation:
cm are centimeters and mm means millimeters and these a both smaller than an inch, and km kilometers is a distance like miles. Whilst m stands for meters.
How do you solve -4.46•11
Answer:
Step-by-step explanation:
(−4.46)(11)=−49.06
How do i explain 5×23×2
Answer:
Step-by-step explanation:
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An old cell phone battery would last for 13 hours. The new battery lasts 29 percent longer. How long will the new battery last?
Answer:
16.77 hours
Step-by-step explanation:
the new battery lasts 29 percent longer so you multiply 13 × 1.29 and you get
16.77 hours
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What is the value of the 6 in 861
In the number 861, the value of the digit 6 is 60 because it falls in the tens place.
Explanation:The value of the 6 in 861 is in the tens place. This means that it's value is not simply 6, but 60. In other words, the value of a digit depends on its position or place value in the number. In this case, because 6 falls in the tens place, it represents 60 rather than 6.
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Order the numbers from least to greatest.
5/8, 60%, 0.64
Answer:
60%,5/8,0.64
Step-by-step explanation:
you covert 64 to 64% and 5/8 to 62.5%
A concession stand sold ice cream cones, salted pretzels, and tacos at a basketball game. Ice cream cones were sold for $3.00, salted pretzels were sold for $2.50, and tacos were sold for $2.00. The total number of ice cream cones, salted pretzels, and tacos sold was 140, and the total amount of money from these items was $359.50. If $70.00 was made just from selling tacos, how many salted pretzels were sold?
Answer:
51 salted pretzels were sold.
Step-by-step explanation:
Step 1: Write the data
Number of Ice cream cones sold: x
Cost of ice cream cones sold: 3x
Number of Salted pretzels sold: y
Cost of salted pretzels sold: 2.5y
Number of tacos sold: z
Cost of tacos sold: 2z
Step 1: Make equation 1
Total money made: $359.5
Money made from tacos: $70
Money made from ice cream cones and salted pretzels: 359.5-70 = $289.5
Equation 1:
3x + 2.5y = 289.5
Step 3: Make equation 2
Cost per tacos: $2
Total number of tacos sold: z
Money made from total tacos: $70
2z = 70
z = 35 tacos were sold
Total number of ice cream cones and salted pretzels sold: 140-35 = 105
Equation 2:
x + y = 105
Step 4: Find the unknown value by substitution
3x + 2.5y = 289.5
x + y = 105
Find x in terms of y from equation 2
x + y = 105
x = 105 - y
Substitute x in equation 1
3x + 2.5y = 289.5
3(105-y) + 2.5y = 289.5
315 - 3y + 2.5y = 289.5
0.5y = 25.5
y = 51
y represents the number of salted pretzels sold. Therefore, 51 salted pretzels were sold.
Solve this equation. Enter your answer in the box.
13(y+7)=3(y−1)
To solve the equation 13(y+7)=3(y−1), it's needed to expand the equation, isolate the variable, then solve for y. The solution to the given equation is y = -9.4.
Explanation:To solve the equation 13(y+7)=3(y−1), we first expand each side of the equation by multiplying: 13y + 91 = 3y - 3. Next, we need to isolate the variable y on one side of the equation. We can do this by subtracting 3y from both sides which gives us 10y + 91 = -3. Then, subtract 91 from both sides of the equation to get: 10y = -94. Finally, divide each side by 10 to solve for y. Therefore, the solution is y = -9.4.
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The equation 13(y+7)=3(y−1) simplifies to y = -9.4 after expanding both sides of the equation, bringing like terms together and dividing by 10.
Explanation:To solve the equation 13(y+7)=3(y−1), we start by expanding both sides of the equation:
13y + 91 = 3y - 3
We then bring like terms together:
13y - 3y = -3 - 91
This simplifies to:
10y = -94
Finally, we divide each side of the equation by 10 to isolate y:
y = -94/10
Hence, the solution to the equation is y = -9.4.
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I I need help on the ones that are not crossed out
Answer:
#4: 2/45 (0.044444...)
#11: 39/250 (0.156)
#12: 2/15 (0.133333)
5) If f(x)=x2-x, what is f(-5)?
A. -30
B. -20
C. 20
D. 30
Gabby’s goal is to save more than $400. She saves $20 per week plus $50 initially. Let we b the number of week.
1. Write an inequality that represents this situation.
2. What is the least number of weeks she must have?
Answer: 17
Step-by-step explanation:
Gabby's savings over 'b' weeks can be written as an inequality 50 + 20b > 400. Simplifying this, we find that Gabby has to save up for at least 18 weeks to save more than $400.
Explanation:Gabby's savings can be represented as 50 + 20b, with 'b' being the number of weeks. For her to save more than $400, we can write this inequality 50 + 20b > 400. Subtract 50 from both sides to simplify the inequality and we get 20b > 350. To find the least number of weeks, divide both sides by 20 to solve for b and we get b > 17.5. However, since 'b' must be a whole number (because you can't have half a week), the least number of weeks Gabby must save is 18 weeks.
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Find the slope of the line passing through the
points
(-9, 2) and (7, 2).
Answer:
0
Step-by-step explanation:
-y₁ + y₂\-x₁ + x₂ = m
[tex] \frac{ - 2 + 2}{9 + 7} = \frac{0}{16} = 0[/tex]
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7.4x + 5) = 32
Help me please
Answer:
x = 3.65
Step-by-step explanation:
7.4x + 5 = 32
-5 -5
7.4x = 27
----- -----
7.4 7.4
x = 3.64864865
This rounds to 3.65
x = 3.65
On Monday, the price of an online movie dropped $3 in the morning and then another $3 that afternoon. The following Monday morning, the price increased $6. What is the price of the online movie whne its changed from morning to the following Monday morning
Answer:
The change in price is $0
Step-by-step explanation:
dropped $3 means "-3", increased $6 means "+6"
the price dropped twice so 2(-3) and increased once by 6
so, 2(-3) + 6 = 0
The price of the online movie stayed the same from Monday morning to the following Monday morning. It dropped $6 on the first day and increased $6 on the next Monday, so the decrease and increase balanced each other out.
Explanation:This problem belongs to the field of basic mathematics, specifically, arithmetic operations. To solve this, we'll follow the changes day by day. On Monday morning, the price of the online movie dropped $3 and then another $3 in the afternoon. That's a total drop of $3 + $3 = $6. The following Monday morning, the price increased by $6. So overall, the movie price just returned to its original price because the total amount of decrease, which is $6, and the total amount of increase, which is also $6, balanced each other out. So, the price of the online movie when its changed from Monday morning to the following Monday morning remained the same.
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PLEASE HELP AND SHOW WORK FOR HOW TO DO THIS THANKYOU IN ADVANCE
Answer:
C
Step-by-step explanation:
There are six dots in total at and after 4 1/2, therefore your answer is C. 6
Answer:
[tex]C.[/tex] [tex]6[/tex]
Step-by-step explanation:
If we look on the line plot, we are asked how many students spent [tex]4\frac{1}{2}[/tex] more hours or more on homework.
So find [tex]4\frac{1}{2}[/tex] on the line plot
You need to count the ones over 4 and a half and after it.
Which would be 6.
How do you solve 4x−5=7+4y for y an easier way
Answer:
y=x-3
Step-by-step explanation:
4x − 5 = 7 + 4y
4y=4x-5-7
4y=4x-12
y=4x-12/4
y=x-3
The nail must be shorter than 1 3/8 inches in order to fit. Which number below is less than 1 3/8?
Final answer:
1 mm is less than 1 3/8 inches. An inch is 25.4 millimeters, therefore 1 mm is much smaller than 1.375 inches (equivalent to 1 3/8 inches). The correct answer is option (a).
Explanation:
To answer this question, we need to first understand that 1 3/8 inches is a mixed number, meaning it is made up of a whole number and a fraction. In this case, it is 1 plus 3/8 of an inch. We can convert it into a decimal to compare with other measurements easily, and 1 3/8 inches is equal to 1.375 inches. Now we will compare it with the provided options.
1 mm - 1 millimeter is less than 1 3/8 inches because there are 25.4 millimeters in one inch. Therefore, 1 mm is much smaller than 1.375 inches.
So in this scenario, option (a) 1 mm is less than 1 3/8 inches.
what is median, the mode, and the range of the leaf plot?
1/1112345 2/23447 3/2579
Answer:
Step-by-step explanation:
median- 23447
mode- 2579
range-1109766