[tex]Use\ (a^n)^m=a^{nm}\ and\ a^3-b^3=(a-b)(a^2+ab+b^2).\\\\m^{15}=m^{5\cdot3}=(m^5)^3\\\\m^{15}-1,000=(m^5)^3-10^3=(m^5-10)[(m^5)^2+(m^5)(10)+10^2]\\\\=(m^5-10)(m^{10}+10m^5+100)\\\\Answer:\ \boxed{m^5-10}[/tex]
Final answer:
The binomial factor in the factorization of [tex]m^{15}[/tex] - 1,000 is [tex]m^{5}[/tex] - 10
Explanation:
To find the binomial factor in the factorization of [tex]m^{15}[/tex] - 1,000, we should recognize this expression as a difference of two powers. Both [tex]m^{15}[/tex] and 1,000 (which is the cube of 10, or 103), can be written as a power of their respective bases. We can factor this expression using the difference of cubes formula, which states that [tex]a^{3}[/tex] - [tex]b^{3}[/tex] = (a - b)([tex]a^{2}[/tex] + ab + [tex]b^{2}[/tex]). Applying this formula, we look for a cube of m that matches one of the options provided. The closest match here is [tex](m^{5})^3[/tex] [tex]-10^{3}[/tex], which gives us the factor of ([tex]m^{5}[/tex] - 10). Therefore, the binomial factor is [tex]m^{5}[/tex] - 10.
Apply distributive property to factor out the GCF
27+18r=
Answer: 9(3 + 2r)
Step-by-step explanation:
27 18r
∧ ∧
3 9 2 9r
∧ ∧
3 3 3 3r
27: 3 * 3 * 3
18r: 2 * 3 * 3 * r
Common Factors are 3 * 3 = 9
27: 9 * 3
18: 9 * 2r
27 + 18r = 9(3 + 2r)
Joe borrowed $9,000 from the bank at a rate of 7% simple interest per year. How much interest did he pay in 2 years?
Joe paid $1,260 in interest over 2 years.
Explanation:To calculate the amount of interest Joe paid in 2 years, we can use the formula: Interest = Principal * Rate * Time. In this case, the principal is $9,000, the rate is 7% (which is equivalent to 0.07), and the time is 2 years. Plugging these values into the formula gives: Interest = $9,000 * 0.07 * 2 = $1,260. Therefore, Joe paid $1,260 in interest over 2 years.
One hot Saturday, Richard scooped 234 regular cones and 156 large cones. One scoop of ice cream is 3 ounces. A tub of ice cream weighs 10 pounds. How many tubs of ice cream did Richard use to make the cones?
Answer:
18
Step-by-step explanation:
The total number of scoops of ice cream that Richard got from the tub is,
(234 regular cones) x (2 scoops / 1 regular cone) + (156 large cones) x (2 scoops / 1 large cone) = 936 scoops
Given that each scoop weighs 3 ounces, the total weight of the ice cream is 2808 ounces. For the number of tubs,
(2808 ounces) x (1 lb / 16 ounces) x (1 tub /10 lb) = 17.55
Thus, the answer is 18.
Hope this helped!
Geometry//Arcs and chords//Find the value of x // please explain
Answer:
x=22
Step-by-step explanation:
In the top lines, it is given they are perpendicular, in the bottom case, you don't know that. However, it is given that the line from the center intersects halfway the chord (I looked that up). By definition that means that these lines are also perpendicular. Since the line from the center is 12 units in both cases, the top chord must be the same size as the bottom chord.
x seems to denote the total length, so that's twice 11, x=22
Answer:
11
Step-by-step explanation:
if you folded the circle in help the 12s would line us and so would x and 11 so x = 11
Which graph represents a non proportional relationship?
The graph of a proportional relationship passes through origin (0, 0).
Therefore your answer is B).
Answer:
The answer is B
Step-by-step explanation:
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you have a case of our mom's each one weighs 1.4 pounds and weight of 28 lb how many watermelons do you have
Answer:
20 watermelons
Step-by-step explanation:
28/1.4 = 20
Plz give me brainiest!!!!
List the first 5 multiples,and find ALL the factors of 13.
What is a positive number that equals 30 when added to it squared
Answer: 5
Step-by-step explanation:
Let x represent the number, then
x² + x = 30
x² + x - 30 = 0
(x + 6) (x - 5) = 0
x + 6 = 0 x - 5 = 0
x = -6 x = 5
↓
not valid since the restriction is that x > 0 (a positive number)
So, x = 5
Can you help me solve that
Answer:2.6
Step-by-step explanation:
Use your graphing calculator of you have one and if you don't you can find one online and plug in the equation and find the intersection . If you get 2.5571 round it to the nearest tenth and you should get 2.6
Answer:2.6
Step-by-step explanation:
Use your graphing calculator of you have one and if you don't you can find one online and plug in the equation and find the intersection . If you get 2.5571 round it to the nearest tenth and you should get 2.6
Find the slope of the line represented by the table of values.
A) −4
B) −1/4
C) 4
D) 1/4
Answer:
B) −1/4
Step-by-step explanation:
The slope represents the change in y values divided by the change in x values. We can use the formula
slope = (y2-y1)/(x2-x1)
(2,4) (-2,5)
slope = (5-4)/(-2-2)
= 1/-4
slope = -1/4
Answer:
B. -1/4
Step-by-step explanation:
To get the slope you have to use the formula: y2-y1/x2-x1
y2-y1/x2-x1 = 4.47-5/-1-(-2)
4.75-5 = -.25
-1 - (-2) = 1
-.25/1 = -.25 or -1/4
Father gave me some money. I could choose between 15% of 1,500$ or 25% of 1,000$. Which amount did I choose
Answer:
25% of 1000 > 15% of 1500
Step-by-step explanation:
Lets calculate how much money you could receive
15% of 1500
.15 * 1500 = 225
25% of 1000
.25*1000 = 250
250>225
Final answer:
After calculating 15% of $1,500 and 25% of $1,000, it is evident that choosing the latter provides more money, amounting to $250 compared to $225 from the former option.
Explanation:
Choosing between percentages of different amounts involves straightforward arithmetic. To determine which option gives you more money, calculate the numerical value of each percentage. Option one is 15% of $1,500, which can be calculated as follows:
Convert the percentage to a decimal: 15% = 0.15.
Multiply the decimal by the total amount: 0.15 x $1,500 = $225.
Option two is 25% of $1,000:
Convert the percentage to a decimal: 25% = 0.25.
Multiply the decimal by the total amount: 0.25 x $1,000 = $250.
Now, compare the two amounts: $225 from the first option and $250 from the second option. It is clear that you would receive more money by choosing the 25% of $1,000, as it gives you a total of $250 compared to the $225 from the first option.
Which statement shows the associative property of addition? 3⋅(5⋅x)=(3⋅5)⋅x 21 + 2y = 2y + 21 (u + 7) + 13 = u + (7 + 13) If m + 3 = 18, then 18 = m + 3.
Answer:
(u + 7) + 13 = u + (7 + 13)
Step-by-step explanation:
The associative property moves the parenthesis. We are doing addition , so we need to look for the problem that moves the parenthesis on addition.
Over time the value at property on 397 west lake street increased by 275. If the initial value of the property was p which expression represents the property current value? A) 375p B) 275p C) 3.75p D) 2.75p
Answer:
b
Step-by-step explanation:
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
Initial value of the property = P
Rate of growth = 275%
So, we need to find the property's current value:
We will use "compound interest ":
What is the equation of the line that passes through the points (−2, 3) and (2, 7)?
x − y = −1
x − y = −2
x − y = − 5
x − y = − 6
The point-slope form of line:
[tex]y-y_1=m(x-x_1)[/tex]
The fomula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the coordinates of the points:
[tex]m=\dfrac{7-3}{2-(-2)}=\dfrac{4}{2+2}=\dfrac{4}{4}=1\\\\y-7=1(x-2)[/tex]
[tex]y-7=x-2[/tex] subtract y from both sides
[tex]-7=x-y-2[/tex] add 2 to both sides
[tex]-5=x-y\to\boxed{x-y=-5}[/tex]
[30 POINTS] An automobile steering wheel is shown. The ideal mechanical advantage of this wheel and axle = _____ .
The mechanical advantage is found by dividing Rw by Ra:
Mechanical advantage = 18 / 2 = 9
Answer:
Step-by-step explanation:
so it is basically nine
determine two numbers that have a sum of 12 but a difference of 12
Answer:
0 And 12
Step-by-step explanation:
0 + 12 = 12
But 0 is 12 away from 12. hope i helped :)
Answer:
0 and 12
Step-by-step explanation:
0+12=12
12-0=12
A line passes through the point , ( − 6, 1) and has a slope of − 4/3 .
Final answer:
A line with a slope of -4/3 passes through the point (-6, 1) can be represented by the equation y = -4/3x - 7.
Explanation:
A line with a slope of -4/3 passes through the point (-6, 1).
To find the equation of the line, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the values into the equation, we get y - 1 = -4/3(x - (-6)).
Simplifying, we have y - 1 = -4/3(x + 6).
Expanding, y - 1 = -4/3x - 8.
Moving the constant term to the other side, we get y = -4/3x - 7.
what is the value of x in the diagram below ?
Answer:
x = 9
Step-by-step explanation:
12^2 + a^2 = 54^2
a^2 = 54^2 - 12^2
a = sqrt (54^2 - 12^2) = 6 * sqrt(77)
Then calculate it for another triangle, where each side is 6 times shorter (as 12/2 = 6):
2^2 + (sqrt(77))^2 = x^2
x^2 = 81
x = 9
Kyle has entered into a 5k marathon (5 kilometers). He wanted to figure out how many miles are in the marathon. If there are 1000 meters in 1 kilometer, and 1 mile equals approximately 1609.34 meters, how many miles will Kyle run in the marathon? Round your answer to the nearest hundredth place.
Answer:
3.10 miles
Step-by-step explanation:
1k = 0.62 miles
5x.62= 3.10
Kyle will run approximately 3.11 miles in a 5K marathon. This calculation is performed by first converting the 5K race distance into meters and then into miles, rounding the result to the nearest hundredth place.
Explanation:The subject of this question is conversions between different units of distance, specifically kilometers to miles. To help Kyle with this, first, we need to convert the kilometers into meters. Since 1 kilometer equals 1000 meters, therefore, 5 kilometers will be 5000 meters.
Then, remembering that 1 mile is approximately 1609.34 meters, we can divide the total meters by the conversion factor for meters to miles. Therefore, the conversion from meters to miles is as follows: 5000 meters / 1609.34 meters/mile = 3.11 miles.
So, if Kyle is running a 5K marathon, he will be running approximately 3.11 miles. This answer has been rounded to the nearest hundredth place as per your instructions.
Learn more about unit conversion here:https://brainly.com/question/19420601
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find the value of x and y
Answer:
2x+10 // 2 • (x + 5)
Step-by-step explanation:
Final Result :
y + 10
Processing ends successfully
find the next three term in the sequence-8, 24,-72,216
Answer:
- 648, 1944, - 5832
Step-by-step explanation:
the terms form a geometric sequence with
common ratio r = [tex]\frac{-72}{24}[/tex] = [tex]\frac{24}{-8}[/tex] = - 3
to obtain the next term in the sequence multiply the previous term by r
216 × - 3 = - 648
- 648 × - 3 = 1944
1944 × - 3 = - 5832
the next 3 terms are - 648, 1944, - 5832
Under the dilation, the point (-3, -4) is moved to (-15, -20)
what is the scale factor of the dilation?
Answer:
The scale factor of dilation is: 5
Step-by-step explanation:
" A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.
If the scale factor is greater than 1, the image is an enlargement (a stretch) " .
Whenever we multiply an coordinates or for some figure if all the coordinates get multiply by same factor 'a' then 'a' is called as scale factor in the dilation.
Here in this question:
(-3,-4) is moved to (-15,-20).
Here when (-3,-4) is multiplied by 5 we get the coordinate as: (-15,-20).
Hence, the scale factor is 5.
11/12− 1/6q+5/6q−1/3
Answer:
16/12 = 1 4/12 or 1 2/6
Step-by-step explanation:
find the circumstances of a circle with a diameter of 27 cm
Answer:
84.78 cm
Step-by-step explanation:
The circumference = pi * d
d = 27
The circumference = 27 * pi
p = 3.14
The circumference = 84.78
If that is not among your choices, list what is.
State the domain and range of the following function. {(2,3), (7,9), (4,-7), (6,2), (3,-5)}
Answer:
Domain: {2,3,4,6,7}
Range: { -7,-5,2,3,9}
Step-by-step explanation:
The domain is the input, or x, values.
The range is the output, or y, values.
They are normally written from least to greatest.
Answer:
Domain: 2,3,4,6,7
Range: -7,-5,2,3,9
Step-by-step explanation:
hope this helps :)
Eliza travels 6 times as many minutes to school as ricky does.Altogether,they travel 63 minutes each day.How many minutes does Eliza travel?
Answer:
Eliza travels 54 minutes.
Step-by-step explanation:
Let's use the variable r to represent the number of minutes Ricky travles to school.
Eliza travels 6 times as many minutes as Ricky, so Eliza travels 6r minutes.
Altogether, they travel r + 6r minutes, or 7r minutes.
We are told they travel 63 minutes altogether, so 7r must equal 63.
7r = 63
Divide both sides by 7.
7r/7 = 63/7
r = 9
Ricky travels 9 minutes.
Eliza travels 6r minutes.
6r = 6 * 9 minutes = 54 minutes
Eliza travels 54 minutes.
A flight from New York City to Chicago takes 3 1/2 hours
Answer:
8 HOURS PLEASE GIVE BRAINLIEST
Step-by-step explanation:
NY TO CHICAGO = 3.5 HOURS
CHICAGO TO LA = 4.5 HOURS
NY TO CHICAGO CHICAGO TO LA
3.5 + 4.5 = 8 HOURS
(x-2)(3x+4) destributive property
Answer:
FOIL IT:
First multiply the first terms in each parenthesis.
Outside is next. You multiply the terms on the outer edges of each parenthesis.
Inside is next. Multiply the terms on the inside edge of each parenthesis.
Last: Multiply last terms in each parenthesis.
YOU GET:
3x^2 - 2x - 8
You save $5,000.00 and invest 60% of it in stocks while leaving the rest in a savings account earning a 4.9% APR. The stock increases 9% in the first year and loses 4% of its value the second year. What would the gain have been if all of the investment had been left in the savings account?
Answer:
5,340
Step-by-step explanation:
Hi there:)
Amount invested in stock
=5000×0.6=3000
Amount invested in a saving account
5000-3000=2000
The stock increases 9% in the first year
3,000×(1+0.09)=3,270
and loses 4% of its value the second year
3,270×(1−0.04)=3,139.2
Amount of a saving account after two years
2,000×(1+0.049)^(2)=2,200.8
the total amount gained during the 2 years
3,139.2+2,200.8=5,340...answer
Hope it helps
Find an equivalent ratio for the ratio 4 : 5.
400/500
10 : 12
48 to 60
20/30
Answer:
400/500
48 to 60
both are correct
Step-by-step explanation:
4/ 5
Multiply top and bottom by 100
4*100/ 5* 100 =400/500
400:500
4/5
Multiply top and bottom by 12
4/5 * 12/12 = 48/60
we can rewrite as 48:60