For this case we must multiply the following expression:
[tex](6a ^ 3-5) (4a ^ 3-11a) =[/tex]
We apply distributive property considering that:
[tex]+ * + = +\\+ * - = -\\- * - = +[/tex]
So:
[tex]6a ^ 3 * 4a ^ 3-6a ^ 3 * 11a-5 * 4a ^ 3 + 5 * 11a =[/tex]
To multiply powers of the same base, we place the same base and add the exponents.
[tex]24a^ {3 + 3} -66a^ {3 + 1} -20a ^ 3 + 55a =\\24a ^ 6-66a ^ 4-20a ^ 3 + 55a[/tex]
Answer:
[tex]24a ^ 6-66a ^ 4-20a ^ 3 + 55a[/tex]
A number increased by negative eight is equal to fourteen. Which equation could be used to find the number? n + 8 = 14 n - (-8) = 14 n + (-8) = 14 8 - n = 14
im confused?
Answer:
n +(-8)=14
Step-by-step explanation:
a number is 'n'
is adding negative of 8
i. e. -8
is eaual to 14
then n=14+8
or; n =22
therefore the number is 22.
4
-5a+b=8
7a +9b = -32
I need to use substitution for this one. Help?
Answer:
a = -2, b = -2Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}-5a+b=8&\text{add}\ 5a\ \text{to both sides}\\7a+9b=-32\end{array}\right\\\\\left\{\begin{array}{ccc}b=5a+8&(1)\\7a+9b=-32&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\7a+9(5a+8)=-32\qquad\text{use the distributive property}\\\\7a+(9)(5a)+(9)(8)=-32\\\\7a+45a+72=-32\qquad\text{subtract 72 from both sides}\\\\52a=-104\qquad\text{divide both sides by 52}\\\\\boxed{a=-2}\\\\\text{Put the value of}\ a\ \text{to (1):}\\\\b=5(-2)+8\\\\b=-10+8\\\\\boxed{b=-2}[/tex]
Draw the image of the figure with the given vertices under a dilation with the given scale factor centered at the origin j(-2,2), K(4,2), L(4,-2), M(-2,-2); Scale factor: 1/2
To create the image of a figure under a dilation with a scale factor of 1/2 centered at the origin, multiply each vertex coordinate by 1/2. The new coordinates for vertices j, k, l, and m would be j'(-1, 1), k'(2, 1), l'(2, -1), and m'(-1, -1), respectively.
Explanation:The student is asking for the image of a figure after performing a dilation with a scale factor centered at the origin. To perform this dilation, you need to multiply the coordinates of each vertex by the scale factor. For a scale factor of 1/2, each coordinate of the vertices is halved. Therefore, the new vertices after the dilation will be:
j'(-2 \\times 1/2, 2 \\times 1/2) = j'(-1, 1)k'(4 \\times 1/2, 2 \\times 1/2) = k'(2, 1)l'(4 \\times 1/2, -2 \\times 1/2) = l'(2, -1)m'(-2 \\times 1/2, -2 \\times 1/2) = m'(-1, -1)These new vertices j', k', l', and m' will give you the dilated figure.
You earn $72 for every 8 hours you spend shoveling snow. You earn $60 for every 5 hours you spend babysitting. For every 3 hours you spend babysitting, you spend 2 hours shoveling snow. You babysit for 15 hours in January. How much money do you earn in January?
Answer:
$270.00
Step-by-step explanation:
The ratio of house of babysitting and house is 3:2. If you change the 3 into a 15, you would have to change the 2 into a 10 because 3 x 5 = 15, so 2 x 5 = 10.
After you do those calculations you divide 15 by 5 and that is 3. You then multiply 60 by 3 = 180.
After that you have to divide 10 by 8 and you get 1.25. You then multiply 72 by 1.25 = 90.
Then you add 180 and 90 together to get $270.00
kiaria is 7 years alder tham jay . martha is twice as old as kiaria , the sum of their three ares is 7u , find the ratio of jay,s age to kiatias age to marhas age
Answer:
The ratio of Jay's age to Kiaria's age to Martha's age is 1: 2 : 4.
Step-by-step explanation:
Here, let us assume the age of jay = u years
So, the age of Kiaria = Age of Jay + 7 = u + 7
And, the age of Martha = 2 x ( age of Kiaria) = 2 ( u + 7)
Now, the sum of the ages = 7 u
⇒ (u) + (u + 7) + 2 ( u + 7) = 7 u
or, u + u + 7 + 2 u + 14 = 7 u
or, 4 u + 21 = 7 u
⇒ 3 u = 21 or u = 21/3 = 7
⇒ u = 7 years
Hence, the age of Jay = m = 7 years
Age of Kiaria = m + 7 = 7 + 7 = 14 years
Age of Martha =2 ( m+7) = 2 ( 7 +7) = 28 years
So, the ratio of Jay's age to Kiaria's age to Martha's age
is 7: 14: 28 = 1: 2 : 4
Hence, the final ratio of the ages is 1: 2 : 4.
Which describes the combined variation shown in the equation F= kxy/z ?
Answer:
First question is D: F varies directly with x and y, and inversely with z.
Second Question is B Y=kx^3/sq root z
Edge Verified
Answer:
part 1 = d
part 2= b
Step-by-step explanation:
I just got it right on edg
Order the following least to greatest
-4, -5.1, and -14/3
Answer:
-5.1, -14/3, -4
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A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 30 books. There were 4 times as many large boxes sent as small boxes, which altogether can hold 280 books. Write a system of equations that could be used to determine the number of small boxes sent and the number of large boxes sent. Define the variables that you use to write the system.
Answer:
20*s+30*l = 280
4*s=l
Step-by-step explanation:
Let's say that the number of small boxes is s and the number of large boxes is l. Then, 20*s equals the amount of books in small boxes (as there are 20 books per small box), and 30*l for the amount of books in large boxes. Then, we know that 4 times the amount of small boxes, s, equals l, so 4*s=l. Then, as we know that the amount of books that can be held is 280, we can add the amount of books for each type of box, or 20*s+30*l, to get 280. Our equations are as follows:
20*s+30*l = 280
4*s=l
As we can define l in terms of s, making it so that we can limit the top equation to 1 variable, we can use this to determine the number of each type of box
Dylan opened a credit card account with $750.00 of available credit. Now that he has made some purchases, Dylan's account only has $412.50 of available credit. What is the percentage decrease of the amount of available credit in Dylan's account?
Answer:
45%
Step-by-step explanation:
The formula to work out the decrease is:
Percentage Decrease= actual decrease / original amount X 100%
1) So firstly, we have to work out the decrease, to do this we have to do is do $750-$412.50= $337.50
2) We can now substitute this into our formula which will now be. (We will also add the original amount, which is $750.00)
Percentage Decrease= 337.50 / 750.00 X 100% = 45
The percentage decrease is 45%
Calculate:
(−16)3 ÷ (4−2)−3
Need explanation!
Answer:
Factor the numerator and denominator and cancel the common factors.
−1
Answer:
it is -1 when all calculated
Step-by-step explanation:
Enter the unknown value that makes this statement true.
20% of _______ is 120
Answer:
600
Step-by-step explanation:
20%=0.2
120/0.2=600
Write a question to finish the word problem then solve the problem. The art teacher has 9 boxes of crayons there are 8 crayons in each box
A new singer is building a fan base. The table shows the number of people who attended her first,
second, third, and fourth month of her career. Graph the data shown in the table.
What you want to do is plot each point on the graph according to both the x and y coordinate. Then, when you've drawn all four points in their appropriate place, draw a relatively straight line through all of them. You might need to use a ruler for that part.
The table shows the month and the the total number of people
The graph for the given table is attached below.
Given :
The table shows the number of people who attended her first, second, third, and fourth month of her career.
From the given table the month represents x and number of people represents y
Lets make 4 coordinates from the given table
Plot all the 4 points on the graph
(1, 124), (2,201) (3,390)
(4,700)
For (1,124) , we take x=1 and y = 124 on graph
Look at the point where x=1 and y=125 intersects. That point is (1,124)
All the data are shown in the graph attached below
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Some friends made $48 selling
lemonade. If each friend
makes $12, how many friends
divided the money?
Melanie took out a 20-year loan for $50,000 at an APR of 3.3%, compounded
monthly. Approximately how much would she save if she paid it off 6 years
early?
To calculate Melanie's savings from paying off a 20-year loan early, we compare total payments over 20 years to total payments made if the loan is finished 6 years early, focusing on the saved interest.
Without the monthly payment, we can't provide the exact savings figure, but it certainly would be less interest paid over 14 years versus 20 years.
Explanation:To calculate the savings from paying off a loan early, we need to compare the total amount paid under the original loan terms with the total amount paid if the loan is paid off early.
For Melanie's 20-year loan of $50,000 at an APR of 3.3% compounded monthly, we can use financial formulas or a calculator to determine the monthly payment and the total amount paid over the terms of the loan.
If the loan is paid off 6 years early, we would compare the interest paid over 14 years with the interest paid over 20 years.
However, without the exact formula being used or the provided calculator, we can't give an exact figure for the amount saved.
You will typically find that by paying off a loan early, you save money on interest that would have accrued over the remaining term of the loan.
To answer the question, Melanie would need to calculate or look up the monthly payment, multiply by the number of payments she would make in the two scenarios, and then subtract the smaller total from the larger one to determine her savings.
Brainliest + thank you + 5 Stars + 18 points
Pam goes skydiving and falls at a constant rate toward the ground. The equation y = -32x + 13,500 represents the situation where y is the height of Pam in feet above the ground and x is the seconds since she jumped.
Which statement describes the situation?
From a starting position of 13,500 feet above the ground, she is ascending at 32 feet per second.
From a starting position of 32 feet above the ground, she is descending at 13,500 feet per second.
From a starting position of 32 feet above the ground, she is ascending at 13,500 feet per second.
From a starting position of 13,500 feet above the ground, she is descending at 32 feet per second.
Answer:
From a starting position of 13,500 feet above the ground, she is descending at 32 feet per second.
Step-by-step explanation:
The equation is in slope intercept form. [tex]y=mx+b[/tex]
The slope (m) is -32. This can be used as a unit rate: -32 ft per second.
The y-intercept (b) is 13,500. It would make most sense if she started at 13,500 ft in height.
From a starting position of 13,500 feet above the ground, Pam is descending at 32 feet per second.
Answer:
The answer is B) From a starting position of 13,500 feet above the ground, she is descending at 32 feet per second.
Step-by-step explanation:
D does not make since because if you start at 32ft you can't fall 13,500ft. There is nowhere for you to go.
A and C don't make since because you can't fall upward.
the area of a rectangle wall of a barn is 320 square feet. it's length is12 feet longer than twice it's width. find the length and width of the wall of the barn.
Answer:
Length = 32 feet
Width = 10 feet
Step-by-step explanation:
The area of a rectangle = length (L) x width (W)
The relationship between the length and width is that
L = 12 + 2W -------------- (i)
therefore
Area = L x W can be rewritten as (12 + 2W) x W
320 = (12 + 2W) x W
320 = 12W + 2W^2
this can then be turned into a quadratic equation:
2W^2 + 12W - 320 = 0
Divide through by 2
W^2 + 6W - 160 = 0
W^2 - 10W + 16W - 160 = 0
W(W- 10) + 16(W- 10) = 0
(W- 10)(W + 16) = 0
hence W = -16 and 10
since width cannot be a negative value,
Width = 10
hence substituting for width = 10 into equation (i)
L = 12 + 2(10)
L = 12 +20 = 32
A car travels 126 miles in 3 hours. At this rate, how many miles can the car travel in 4 hours?
A
168
B
94.5
C
42
D
10.5
Answer:
A. 168Step-by-step explanation:
[tex]\bold{METHOD\ 1:}\\\\\begin{array}{ccc}126\ mi&-&3h\\\\x\ mi&-&4h\end{array}\qquad\text{cross multiply}\\\\3x=(126)(4)\\3x=504\qquad\text{divide both sides by 3}\\x=168\ mi[/tex]
[tex]\bold{METHOD\ 2:}\\\\126\ mi\ \text{in}\ 3\ h,\ \text{then}\ \dfrac{126\ mi}{3}=42\ mi\ \text{in}\ 1\ h.\\\\\text{If}\ 42\ mi\ \text{in}\ 1\ h,\ \text{then}\ (42\ mi)(4)=168\ mi\ \text{in}\ 4h.[/tex]
Logan and Sarah work at a dry cleaners ironing shirts. Logan can iron 40 shirts per hour, and Sarah can iron 35 shirts per hour. Logan and Sarah worked a combined 13 hours and ironed 490 shirts. Determine the number of hours Logan worked and the number of hours Sarah worked.
In isosceles triangle RST shown below, RS = RT,
Mand N are midpoints of RS and RT , respectively,
and MN is drawn. If MN = 3.5 and the perimeter
of RST is 25, determine and state the length of
NT.
The length of NT in isosceles triangle RST is 7.
Explanation:In an isosceles triangle, the base angles are congruent, and the sides opposite those angles are also congruent. Let's denote the length of RS (and RT) as r, and the length of MN as m Since M and N are midpoints, MN is parallel to the base, and its length is half the length of the base. Therefore, [tex]\( m = \frac{r}{2} \).[/tex]
The perimeter of the triangle is the sum of the three sides, so [tex]\( 2r + r = 25 \) (as RS = RT).[/tex] Solving for r, we get [tex]\( r = \frac{25}{3} \).[/tex]
Now, we know that [tex]\( m = \frac{r}{2} \),[/tex] so [tex]\( m = \frac{25}{6} \)[/tex]. Finally, the length of NT is the difference between RT and MN, which is [tex]\( \frac{25}{3} - \frac{25}{6} = 7 \).[/tex]Therefore, the length of NT is 7 units.
QUESTION:Consider isosceles triangle RST, where RS = RT. Let M and N be the midpoints of sides RS and RT, respectively. A segment MN is drawn with a length of 3.5 units. The perimeter of triangle RST is given as 25 units. Determine and state the length of NT.
Please provide a comprehensive solution to this problem, including step-by-step calculations and explanations.
Final answer:
By applying properties of isosceles triangles and the given conditions, we calculate that the length of segment NT is 4.5 units.
Explanation:
The subject matter is a geometrical problem involving an isosceles triangle with given conditions. In isosceles triangle RST, RS and RT are equal in length, M and N are the midpoints of RS and RT respectively, and MN is drawn with a length of 3.5 units. Given that the perimeter of the triangle is 25 units, we need to find the length of segment NT.
To solve this, we first understand that in an isosceles triangle, the perpendicular from the vertex to the base bisects the base. Therefore, segment MN cuts the base ST equally in two, making each half 3.5 units, since MN = 3.5 units. Furthermore, because M and N are midpoints, segments MS and NT are equal. Finally, by knowing the perimeter, we can deduce that RS + ST + RT equals 25 units.
Thus, we can derive the lengths of RS and RT (which are equal) and then use that information to calculate the length of NT. If RS = RT and we call that length x, then 2x + 2(3.5) = 25. Solving for x gives us x = (25 - 7)/2 = 9. Thus, segment NT as the half of either RS or RT is 9/2 = 4.5 units.
ANSWER THIS AND GET BRAINLIEST AND 30 POINTS
A school basketball team has an expense account and a fundraising account. After t weeks, the balance of the expense account is (400−40t) dollars and the balance of the fundraising account is (150+32t) dollars.
a. Write an expression in simplest form that represents the total amount (in dollars) in both accounts after t weeks.
An expression is ( ) dollars.
b. What is the total amount (in dollars) in both accounts after 12 weeks?
Amount after 12 weeks: $___
Answer:
After t weeks, the balance in the expense account and fundraising account is
f(t)= 400 -40t +150+32t
f(t)= 550 -8t
After 12 weeks,
f(12) = 550- 8(12) = 454
Answer:
Step-by-step explanation:
After t weeks, the balance in the expense account and fundraising account is
f(t)= 400 -40t +150+32t
f(t)= 550 -8t
After 12 weeks,
f(12) = 550- 8(12) = 454
Each day Julian gives his dog, Banjo, 3 liters of water and 500 grams of food. Julian wants to track the total amount of the food and water he gives Banjo for 1 week. Julian plots a point at (3, 500) to represent the first day on a coordinate grid.
Then Julian uses a pattern to plot 6 more points. What are the coordinates and significance of the fifth point Julian plots?
A coordinate plane has a x-axis labeled
A.
(12, 2,500); In 5 days, Julian gave Banjo a total of 12 liters of water and 2,500 grams of food.
B.
(15, 2,500); In 5 days, Julian gave Banjo a total of 15 liters of water and 2,500 grams of food.
C.
(15, 2,500); On the fifth day, Julian gave Banjo 15 liters of water and 2,500 grams of food.
D.
(18, 3,000); In 5 days, Julian gave Banjo a total of 18 liters of water and 3,000 grams of food.
Answer:
The correct answer would be option C.
Step-by-step explanation:
Since he gives the dog 3 liters of water and 500 grams of food a day we know that on the fifth day the dog will have gotten 15 liters of water and 2,500 grams of food.
The required coordinate will be (15, 2,500)
Given that the coordinates of the point at (3,500) represent the first day on a coordinate grid if Julie uses a pattern to plot 6 more points, the pattern used can be geometric in nature.We can scale the coordinate point up by five units since we need to get the significance of the fifth point Julie plots.Hence the required coordinate will be (15, 2,500) which is interpreted as the fifth day, Julie gave Banjo 15 liters of water and 2,500 grams of food.
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Which of the following tables represents a function?
x 3 3 4 4
y 2 −2 3 −3
x 5 −5 5 −5
y 2 2 8 8
x 3 3 5 5
y 4 5 6 7
x 4 −4 5 −5
y 2 2 3 3
Answer:
x 4 −4 5 −5
y 2 2 3 3
Step-by-step explanation:
This is the obvious answer, since there are no repetitive x-coordinates.
I am joyous to assist you anytime.
The table which represents the function is:
x 4 −4 5 −5
y 2 2 3 3
A function is a mathematical relationship where each input (x-value) corresponds to exactly one output (y-value).
To determine which table represents a function, we need to check if there are any repeated x-values with different y-values.
x 4 −4 5 −5
y 2 2 3 3
This table represent a function.
Each x-value corresponds to a unique y-value, and there are no repeated x-values with different y-values.
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Find the product of (x − 7)^2. Basically Simplify It
Answer:
(x - 7)² = x² - 14x + 49Step-by-step explanation:
[tex]\bold{METHOD\ 1:}\\\\\text{Use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-7)^2=x^2-2(x)(7)+7^2=x^2-14x+49\\\\\bold{METHOD\ 2:}\\\\\text{We know:}\ a^2=a\cdot a\\\\(x-7)^2=(x-7)(x-7)\\\\\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(x)(x)+(x)(-7)+(-7)(x)+(-7)(-7)\\\\=x^2-7x-7x+49\qquad\text{combine like terms}\\\\=x^2-14x+49[/tex]
Which description best fits the distribution of
the data shown in the histogram?
A)skewed left
B)skewed right
C)uniform
D)approximately bell-shaped
Answer:
D) approximately bell-shaped
Step-by-step explanation:
a bell-shaped histogram is where you can draw a vertical line to the top of the histogram (in this case to the blue line at frequency 12) and a "mirror" line going back down (1 (200-249) ) where the bell-shape can make the shape going through all the lines of the histogram.
I hope I explained that well, and I hope that helps!
Given that n is an integer and that n>1, prove algebraically that n²-(n-2)²-2 is always an even number
Answer:
see explanation
Step-by-step explanation:
Any integer n > 1 multiplied by 2 will be even, that is
2n ← is even
Given
n² - (n - 2)² - 2 ← expand parenthesis
= n² - (n² - 4n + 4) - 2
= n² - n² + 4n - 4 - 2 ← collect like terms
= 4n - 6 ← factor out 2 from each term
= 2(2n - 3)
Hence 2(2n - 3) ← will always be even for n > 1
The statement can be proved by parenthesis that the expression [tex]n^{2} - (n - 2)^{2} - 2[/tex] is always an even number.
What is the process of expanding the polynomial and check whether it is a even number ?= [tex]n^{2} - (n - 2)^{2} - 2[/tex]
= [tex]n^{2} - (n^{2} - 4n + 4) - 2[/tex]
= [tex]4n - 4 - 2[/tex]
= [tex]4n - 6[/tex]
= [tex]2(2n - 3)[/tex]
As the expression 2(2n - 3) is always a multiple of 2 and also it is given that n>1 therefore by the parenthesis, the expression [tex]n^{2} - (n - 2)^{2} - 2[/tex] is always an even number.
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HELP QUICK PLEASEE
round your answer to the nearest hundredth and find
Answer:
45 degrees
Step-by-step explanation:
As all of the angles in a triangle add up to 180 and we already know that one angle is 90, that means that the sum of the other two angles is 90. So, you can do 90/2=45.
solve the following equation for x 7x-15=1
Answer:
x= 16/7
Step-by-step explanation:
7) CJ was painting his apartment. In 15 minutes,
CJ had used 3 gallon of paint. Write an equation
that represents the gallons of paint used, y, in x
hours.
re
y = 12x represents the gallons of paint used in x hours.
Step-by-step explanation:
CJ uses 3 gallons of paint in 15 minutes,
15 minutes = 3 gallons
1 minutes = [tex]\frac{3}{15} = \frac{1}{5} \ gallons\\[/tex]
1 hour = 60 minutes
Gallons of paint used in 1 hour;
1 hour = [tex]\frac{1}{5}*60=12\ gallons[/tex]
CJ uses 12 gallons of paint in 1 hour.
For x hours = 12*x = 12x
Gallons of paints used = y
y = 12x represents the gallons of paint used in x hours.
Keywords: linear equation, multiplication
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Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is
worth either 5 points or 2 points. Write a system of equations that can be used to find how many problems of each
point value are on the test.
Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points.
O x + y = 29, 5x + 2y = 100
O x + y = 100, 5x + 2y = 29
5x + y = 29, 2y + x = 100
2x + y = 100, 5y + x = 29
1) Intro
Done
Answer:
The two equations would be
x+y=29 5x+2y=100
Step-by-step explanation:
Looking at the points, x and y add up to be 100
x is worth 5 hence 5x and y are worth 2, hence 2y.
there are 29 problems in total. meaning the x + the y add up to 29 problems