Answer:
x^3-12x^2+39x-28
Step-by-step explanation:
(x-4)(x-7)(x-1)
(x^2-4x-7x+28)(x-1)
(x^2-11x+28)(x-1)
x^3-11x^2+28x-x^2+11x-28
x^3-11x^2-x^2+28x+11x-28
x^3-12x^2+39x-28
Stewie wants to rent a moving truck.Suppose company a charges a rate of $40 per day band company b charges a $60 fee plus has a rate of $20 per day.For what number of days is the cost same?
Answer:
The indifference point is 3 days.
Step-by-step explanation:
Company A:
Total cost= 40*x
Company B:
Total cost= 60 + 20*x
x= number of days
To calculate the indifference point, we need to equal both formulas. and isolate x:
40x = 60 + 20x
20x= 60
x= 60/20
x= 3
The indifference point is 3 days.
Prove:
Company A:
Total cost= 40*3= $120
Company B:
Total cost= 60 + 20*3= $120
Find the slope of a line that goes through the points (-5,8) and (-7,-5)
Answer:
[tex]m=\frac{13}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-5, 8)
Point (-7, -5)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute [SF]: [tex]m=\frac{-5-8}{-7+5}[/tex]Subtract/Add: [tex]m=\frac{-13}{-2}[/tex]Simplify: [tex]m=\frac{13}{2}[/tex]Answer:
we will use the equation
(y2-y1)/ (x2-x1)
lets plug in our values
(-5-8)/(-7-(-5)
-13/-2
this answer is your slope value hope this helps
Step-by-step explanation:
At an electronic store, an air-conditioner marked $280 was on
sale at $259. What was the percentage of discount for the air-
conditioner?
986
Answer: maybe this will help
Step-by-step explanation:
Use the formula:
Discount = Marked Price – Selling Price
Percent Discount = Discount/Marked Price × 100%
Discount: 280 – 259 = 21
The marked price: 280
A theater seats 2,816 people. The first row has 26 seats while the last row has 150 seats. Assuming the number of seats per row follows an arithmetic sequence,
how many rows does the theater have?
Answer:
The theater has 32 rows
Step-by-step explanation:
The rule of the sum of n terms of an arithmetic sequence is S[tex]_{n}[/tex] = [tex]\frac{n}{2}[/tex] (a + l), where
a is the first terml is the last termn is the number of the terms∵ The number of seats per row follows an arithmetic sequence
∵ The first row has 26 seats
∴ a = 26
∵ The last row has 150 seats
∴ l = 150
∵ The theater seats are 2,816
∴ S[tex]_{n}[/tex] = 2,816
→ Substitute these values in the rule of the sum above to find n
∵ 2,816 = [tex]\frac{n}{2}[/tex](26 + 150)
∴ 2,816 = [tex]\frac{n}{2}[/tex](176)
∴ 2,816 = 88n
→ Divide both sides by 88
∴ 32 = n
∵ n represents the number of the rows
∴ The theater has 32 rows
Which expression results in a sum or difference of five and six fifty fourths? (3 points) a eight and seven ninths minus three and four sixths b six and eight ninths minus one and five sixths c four and one sixths plus one and one ninth d three and three sixths plus two and four ninths
Answer:
a) eight and seven ninths minus three and four sixths
Step-by-step explanation:
The required result is [tex]5\frac{6}{54}[/tex]
a)
[tex]8\frac{7}{9} -3\frac{4}{6}\\\\=\frac{79}{9} -\frac{22}{6} \\\\Simplifying\ the\ expression:\\\\=\frac{474-198}{54} \\\\=\frac{276}{54}\\\\=5\frac{6}{54}[/tex]
b)
[tex]6\frac{8}{9} -1\frac{5}{6}\\\\=\frac{62}{9} -\frac{11}{6} \\\\Simplifying\ the\ expression:\\\\=\frac{372-99}{54} \\\\=\frac{273}{54}\\\\=5\frac{3}{54}[/tex]
c)
[tex]4\frac{1}{6} +1\frac{1}{9}\\\\=\frac{10}{9} +\frac{25}{6} \\\\Simplifying\ the\ expression:\\\\=\frac{60+225}{54} \\\\=\frac{285}{54}\\\\=5\frac{15 }{54}[/tex]
d)
[tex]3\frac{3}{6} +2\frac{4}{9}\\\\=\frac{22}{9} +\frac{21}{6} \\\\Simplifying\ the\ expression:\\\\=\frac{132+189}{54} \\\\=\frac{321}{54}\\\\=5\frac{51 }{54}[/tex]
Answer: A
Step-by-step explanation: I did the assesment
What is
1/6
as a decimal?
Give your answer rounded to 3 decimal places.
Answer:
I think it is 0.167
Answer:
.167
Step-by-step explanation:
[tex]1 \div 6 = 0.16666666 \\ repeating \: so \: you \: round \: to \: the \: thousandths \: making \: it \: .167[/tex]
Tyra has 12 2/3 cups of sugar. If r is the amount of sugar called for in one batch of cookies, the expression 12 2/3 ÷ r can be used to find how many batches Tyra can make with the sugar she has. If r is 2/3 cup, how many batches of cookies can Tyra make? Enter your answer in the box. Quick I need help plz.
Answer:
19 batches
Step-by-step explanation:
Given that:
Total number of cups of sugar = [tex]12\frac{2}{3}[/tex]
Amount of sugar used in one batch = [tex]r[/tex]
Number of batches that can be made by Tyra with the amount of sugar that is available with Tyra can be calculated by dividing the total number of cups of sugar available with Tyra with the amount of sugar to be used in one batch.
i.e.
Number of batches = [tex]12\frac{2}{3} \div r[/tex]
Also, if we put the value:
[tex]r=\frac{2}{3}[/tex]
We have to find the number of batches of cookies that can be made by Tyra.
Solution:
First of all, let us have a look at the formula to convert the mixed fraction into fractional number.
[tex]a\dfrac{b}{c} = \dfrac{a\times c + b}{c}[/tex]
Therefore,
[tex]12\dfrac{2}{3} = \dfrac{12\times 3 + 2}{3} = \dfrac{38}{3}[/tex]
Number of batches:
[tex]\dfrac{38}{3} \div \dfrac{2}{3}\\\Rightarrow \dfrac{38}{3} \times \dfrac{3}{2}\\\Rightarrow \bold{19}[/tex]
Therefore, 19 batches can be completed.
Simplify 4a^2(a^3)/16b(b^2) edge
Answer: Above answer is correct
Step-by-step explanation:
I'LL MARK BRANLIST. A box contains 3 plain pencils and 3 pens. A second box contains 3 color pencils and 7 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected? Write your answer as a fraction in simplest form.
Answer:
First Box: 3/6 --- 1/2
Second Box: 3/10
Can someone show me the answer and maybe the work
Answer:
Solving the expression \frac{y^2z^{\frac{1}{4}} }{(z^{\frac{1}{2}}.xy^{\frac{3}{2}})^3} we get [tex]\mathbf{\frac{1}{y^{\frac{5}{2} }x^3z^{\frac{5}{4} }}}[/tex]
Step-by-step explanation:
We need to solve the expression:
[tex]\frac{y^2z^{\frac{1}{4}} }{(z^{\frac{1}{2}}.xy^{\frac{3}{2}})^3}[/tex]
We know the exponent rule: [tex](a^n)^m = a^{nm}[/tex]
[tex]\frac{y^2z^{\frac{1}{4}} }{(z^{\frac{1}{2}}.xy^{\frac{3}{2}})^3}\\\\=\frac{y^2z^{\frac{1}{4}} }{z^{\frac{3}{2}}.x^3y^{\frac{9}{2} }}[/tex]
Now, another exponent rule says that: [tex]\frac{a^m}{a^n}=a^{m-n}[/tex]
[tex]=\frac{y^{2-\frac{9}{2}} z^{\frac{1}{4}-\frac{3}{2} } }{x^3}\\=\frac{y^{\frac{4-9}{2}} z^{\frac{1-3*2}{4} } }{x^3}\\=\frac{y^{\frac{-5}{2}}z^{\frac{-5}{4} } }{x^3}[/tex]
We also know that: [tex]a^{-m}=\frac{1}{a^m}[/tex]
=[tex]\frac{1}{y^{\frac{5}{2} }x^3z^{\frac{5}{4} }}[/tex]
So, solving the expression \frac{y^2z^{\frac{1}{4}} }{(z^{\frac{1}{2}}.xy^{\frac{3}{2}})^3} we get [tex]\mathbf{\frac{1}{y^{\frac{5}{2} }x^3z^{\frac{5}{4} }}}[/tex]
If the polynomial shown below is to be a perfect square trinomial, what
must the value of k be? *
9a2 + ka + 16
Please help due in 20 mins
Answer:
1. -.005
2.-1/2
3. 0
4. 2
Step-by-step explanation:
if it is negative put positive and if it is positive put negative. for 0 it will always stay the same
b) through: (5, 5) and (0, -1)
Slope: m=
y-intercept: b =
Equation: y =
For the slope, we will use the slope formula*.
[tex]m = \frac{-1 - 5}{0 - 5} = \frac{-6}{-5}[/tex]
The y-intercept is already given. It is 1.
To create the equation of the line, we put what we got for m and b in slope-intercept form**.
[tex]y = -\frac{6}{5}x + 1[/tex]
Formulas:
Slope formula: y₂ - y₁/x₂ - x₁
Slope-intercept form: y = mx + b
Khalid and Jesse took different overnight trains. The graph shows the relationship between the total distance Khalid traveled and the time in hours. The distance Jesse traveled after x hours is given by the equation y = 150x. Who, if anyone, traveled at a faster speed? Use the drop-down menus to explain your answer.
Khalid’s rate is ____ miles per hour. Jesse’s rate is ____ miles per hour. So, ____ train traveled at a faster speed.
Answer:
Khalid’s rate is 140 mi/h. Jesse’s rate is 150 miles per hour
So, Jesse’s train traveled at a faster speed
Step-by-step explanation:
Here, we want to compare speeds
For Jesse’s train, the speed is 150 mi/h
we got this from the fact that the equation of a straight line is represented as;
y = mx + b
where m which is the slope represents the rate of change
m here is 150
For Khalid’s;
we can get his own rate from the graph
This can be obtained using the slope
We can simply have this as ;
m = (y2-y1)/(x2-x1)
Let us have two points
(4,560) and (0,0)
Thus;
m = 560/4 = 140 mi/h
Hence;
Khalid’s rate is 140 mi/h. Jesse’s rate is 150 miles per hour
So, Jesse’s train traveled at a faster speed
Cups are sold in packages of 8. Napkins are sold in packages of 12. What is the fewest number of packages of cups and the fewest number of packages of napkins that can be purchased so there will be the same number of cups as napkins? Hint**- What will you need to find GCF or LCM?
Answer:
24 packages
Step-by-step explanation:
Given
Represent Napkins with N and Cups with C
[tex]C = 8's[/tex]
[tex]N = 12's[/tex]
Required
Determine the smallest amount of N and C that will be equal
To do this, we simply calculate the LCM of N and C as follows:
List out the multiples of each..
[tex]C = 8,16,24,30....[/tex]
[tex]N = 12,24,36,48...[/tex]
The common multiple between both is 24.
Hence, 24 packages of N and C answers the question
Melissa works for a florist. She used her employee discount to purchase 10 roses at $1.00 each. If melissa saved $4.00 by using her employee discount, what is the regular price if one rose purchased from the florist?
Answer: $1.4
Step-by-step explanation:
Given that:
Discounted price roses = $1
Amount saved = $4
Regular price - discounted price = amount saved
x - 10(1) = 4
x - 10 = 4
x = 4 + 10
x = $14
Regular price of 10 roses = $14
Regular price per rose = $14 / 10 = $1.4
Suppose you want to go to the ice skating rink and it costs $8 to rent ice skates and $3.75 per hour to skate, write an equation that models this situation
Answer:
c=8+3.75x, where:
c is the cost to go to the ice skating ring
x is the number of hours
Step-by-step explanation:
From the information given, the cost to go to the ice skating ring is equal to the cost to rent ice skates plus the result of multiplying the cost to skate per hour for the number of hours and the equation would be:
c=8+3.75x, where:
c is the cost to go to the ice skating ring
x is the number of hours
If RT=6x+4 and SO =7x-6, what is the length of US
is y=30x a function?
Answer:no try y=Mx+b
Step-by-step explanation:
Answer:
y = 30x is a function.
Step-by-step explanation:
Given an equation, there should be only one corresponding (cor a sponding to pronounce) y value for any y value.
I need help with this pls anybody if u know these pls help
Answer: Please give me brainliest?
4: B
5: B
6: H (12)
8: C (3,-6)
7: 120
Step-by-step explanation:
6.
6x-6=3x+30
3x=36
x=12
7. 7x-6=5x+30
2x=36
x=18
5 x 18 = 90 +30 = 120
Solve the formula B=(R+M)/2 for R
Answer:
2B-M=R
Step-by-step explanation:
Determine the number of terms n in each geometric series.
13) a1 = 0.75, r = 4, Sn =1023.75
Answer:
Number of terms: n=6
Step-by-step explanation:
We are given:
a₁ = 0.75
r = 4
Sₙ = 1023.75
We need to find number of terms i.e n
The formula used will be:[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
Putting values and fining n
[tex]S_n=\frac{a(r^n-1)}{r-1}\\1023.75=\frac{0.75(4^n-1)}{4-1}\\ 1023.75=\frac{0.75(4^n-1)}{3}\\3\times 1023.75=0.75(4^n-1)\\3071.25=0.75(4^n-1)\\4^n-1=\frac{3071.25}{0.75}\\4^n-1=4095\\4^n=4095+1\\4^n=4096[/tex]
We know that [tex]4^6= 4096[/tex]
[tex]4^n=4^6[/tex]
Using Exponent rule: [tex]a^n=a^b => n=b[/tex]
[tex]n=6[/tex]
So, Number of terms: n=6
a local soccer team collected 2,385 this week and 2,805 last week by selling tickets. Tickets are 5 per person. How many tickets were sold
8x - 3 = 16x - 33 find x
Answer:
The answer is x=15/4
Step-by-step explanation:
8x - 3 = 16x - 33
8x−3−16x=16x−33−16x
−8x−3=−33
−8x−3+3=−33+3
−8x=−30
−8x/-8=−30/-8
x=15/4
The value of the x for the equation 8x-3=16x-33 is 3.75.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
8x-3=16x-33
Simplify the equation,
⇒33-3 = 16x-8x
⇒30 = 8x
⇒8x = 30
⇒x = 3.75
The value of x is 3.75.
To know more about Equation on:
https://brainly.com/question/187506
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A sign in front of a roller coaster says "You must be 40 inches tall to ride."
What percentage of this height is: 26 inches
Answer:
65%
Step-by-step explanation:
it is 65%
Answer:
10.4 Inches
Step-by-step explanation:
26% * 40 = 10.4
The number of peanuts in bags is normally distributed with a mean of 172.5 peanuts and a standard deviation of 1.9 peanuts. What is the z-score of a bag containing 168 peanuts
Answer:
- 2.368
Step-by-step explanation:
Given that :
Mean (m) = 172. 5
Standard deviation (s) = 1.9
Score (x) = 168
The Zscore can be obtained thus :
Zscore = (x - m) / s
Zscore = (168 - 172.5) / 1.9
Zscore = - 4.5 / 1.9
Zscore = −2.368421
Zscore = - 2.368
how to drawing a houses
Factor the expression using the GCF (Greatest Common Factor)
12x + 36
Answer:
12 ( x+3)
Step-by-step explanation:
We can factor a 12 out of each term
12 *x + 12*3
12 ( x+3)
Solve the equation
4n-9=2(5+2n)
Answer:
There is no values to make the equation true. Please check the equation.
Step-by-step explanation:
Answer:
19
Step-by-step explanation
A group of 24 people need transportation from a hotel to a concert. They will be picked up by Uber drivers that can fit 4 passengers in their compact car and 6 passengers in their SUV’s. You would like to determine how many compact cars and SUVs could be used to transport the entire group. Let x = the number of compact cars and let y = the number of SUV's.
Write and graph an equation that models the situation.
Answer:
Step-by-step explanation:
Compact cars:
24 divided by 4 = 6
6 cars for 24 people
SUV's:
24 divided by 6 = 4
4 SUV's for 24 people
Answer:
[tex]4x+6y=24[/tex]
See below for graph.
Step-by-step explanation:
A total of 24 people need to be transported.
Let x represent the number of Uber compact cars.
And let y represent the number of SUVs.
So, the number of people that can be picked up by x compact cars is 4x.
And the number of people that can be picked up by y SUVs is 6y.
And the total is 24 people. So, the two terms must total 24. So, we can write:
[tex]4x+6y=24[/tex]
We can convert this to slope-intercept form. First, we can divide everything by 2:
[tex]2x+3y=12[/tex]
Subtracting 2x from both sides yields:
[tex]3x=-2x+12[/tex]
Finally, dividing both sides by 3 yields our linear equation:
[tex]\displaystyle y=-\frac{2}{3}x+4[/tex]
Please refer to the below attachment for the graph.
*Note that we should restrain our graph to only QI. This is because we cannot use negative compact cars of SUVs. Also, only integer points on the line will work, as we cannot have, say, 2.5 compact cars.
**Also, the x- and y-intercepts tell us the maximum of each type needed. Either we need 6 compact cars and 0 SUVs, (6, 0); 4 SUVs and 0 compact cars (0, 4); or a combination of them.