Answers
(2p+7)(3p²+4p-3)=2p*[3p²+4p-3]+7*[3p²+4p-3]
resolving by parts
part 1
2p*[3p²+4p-3]=6p³+8p²-6p
and
part2
7*[3p²+4p-3]=21p²+28p-21
adding part 1 and part 2
[6p³+8p²-6p]+[21p²+28p-21]=6p³+29p²+22p-21
the answer is (6p³+29p²+22p-21)
Related Questions
Nancy builds a hollow wooden ramp for an obstacle course as part of an athletic event. The ramp and the net of the ramp are shown below. Units are in feet. The surface area of the ramp is square feet. Nancy wants to sell the wooden ramp at a price based on the surface area. If each square foot of wood of the ramp is sold for $3, the ramp would sell for $.
Answers
Nancy can sell the wooden ramp for $486 based on the surface area.
What is Area of Rectangle?The area of Rectangle is length times of width.
The area of each rectangular face is length times width, so the top and bottom faces have an area of:
2 x (8 feet x 3 feet) = 48 square feet
The side faces also have an area of:
2 x (8 feet x 6 feet) = 96 square feet
The area of each triangular face is one-half the product of the base and the height, so the front and back faces have an area of:
2 x (0.5 x 3 feet x 6 feet) = 18 square feet
The total surface area of the ramp is the sum of the areas of all the faces:
48 + 96 + 18 = 162 square feet
If each square foot of wood of the ramp is sold for $3, then the ramp would sell for:
162 square feet x $3/square foot = $486
Therefore, Nancy can sell the wooden ramp for $486 based on the surface area.
To learn more on Area of rectangle click:
https://brainly.com/question/20693059
#SPJ3
What does the expression 12f + 24 represent?
Answers:
Answers
Answer:
Option 1 : twenty four more than twelve times a number
Step-by-step explanation:
Given : 12f+24
To Find : What does the expression 12f+24 represents?
Solution:
The given expression : 12f+24
Option 1 : twenty four more than twelve times a number
The given expression 12f+24
This expression means 24 more than twelve times f
f is any number
So, we can say twenty four more than twelve times a number .
Thus Option 1 is correct
Option 2 :twenty four more than twelve plus a number
Let f be a number
So, (12+f)+24 is the obttained expression from option 2
Option 3 :twelve times the difference of number and twenty four.
Let f be a number
So, 12(24-f) is the obttained expression from option 3
Option 4 : twelve times the sum of a number plus twenty four
Let f be a number
So, 12(24+f) is the obttained expression from option 4
Thus option 1 represent the given expression 12f+24
Describe how to find the perimeter of an enlarged figure if you know the scale factor and the dimensions of the original figure.
Answers
Answer:
Perimeter of any figure is given by adding up all the side measurements.
So, when a figure is enlarged by a scale factor then we can multiply all the sides with the scale factor to get the new sides measurements and then we can find the perimeter.
Or simply we can find the perimeter of the original figure and then multiply by the scale factor.
In both the methods, the answer will be the same.
We can take an example:
Lets suppose the original figure to be a rectangle with length 5 cm and width 2 cm. The rectangle is enlarged by a scale factor of 6.
The original perimeter is = [tex]2(5+2)[/tex]
= [tex]2(7)=14[/tex] cm
1st method:
Multiply the length by 6 and width by 6 to get new dimensions.
Length becomes: [tex]5\times6=30[/tex]
Width becomes: [tex]2\times6=12[/tex]
Perimeter becomes: [tex]2(30+12)[/tex]
= [tex]2(42)=84[/tex] cm
2nd method:
Simply multiply 6 with the original perimeter.
[tex]14\times6=84[/tex] cm
We can see that in both methods, the perimeter is same.
Sample Response:
To find the perimeter of an enlarged figure, you can multiply the original figure’s perimeter by the scale factor. You could also multiply each dimension of the original figure by the scale factor to find the dimensions of the enlarged figure, and then add to find the perimeter.
Jalla's hourly wage is $11.791. Round her salary to the nearest cent
Answers
Which of the following is a solution to 3tan^3x=tanx?
PLEASE HELP
Answers
0, π, 2π, π/6, 5π/6, 7π/6 and 11π/6
Explanation:
3 tan³x = tan x
3 tan³x - tan x = 0
tan x (3 tan²x - 1) = 0
either tan x = 0
This means that:
x = 0 , π or 2π ...........> I
or 3 tan²x - 1 = 0
This means that:
3 tan²x = 1
tan²x = [tex] \frac{1}{3} [/tex]
tan x = ± [tex] \frac{1}{ \sqrt{3}} [/tex]
at tan x = [tex] \frac{1}{ \sqrt{3}} [/tex]
x = π/6 or 7π/6 ...................> II
at tan x = - [tex] \frac{1}{ \sqrt{3}} [/tex]
x = 5π/6 or 11π/6 ..............> III
From I, II and III, the solutions for x would be:
0, π, 2π, π/6, 5π/6, 7π/6 and 11π/6
Hope this helps :)
Answer:
its 150 degrees i think
Step-by-step explanation:
i could be wrong though but i'm like 80% sure im right
An open rectangular box having a volume of 108 in.3 is to be constructed from a tin sheet. find the dimensions of such a box if the amount of material used in its construction is to be minimal. hint: let the dimensions of the box be x in. by y in. by z in. then, xyz = 108 and the amount of material used is given by
Answers
That being the case, the height of the box is half the base edge length and the dimensions are
.. x = y = 6 in
.. z = 3 in
_____
If x and y are the base dimensions, the volume is
.. xyz = 108
and we want to minimize the area
.. area = xy +2(x+y)z
These equations are symmetrical in x and y, so the solution will require x=y. Making that substitution, we have
.. x^2*z = 108
.. x^2 +4xz = area = x^2 +4x(108/x^2)
That is, we want to minimize x^2 +432/x. A graphing calculator finds the minimum at x=y=6, (and z = 108/x^2 = 3).
Given that the volume of a rectangular box is a product of its length, breadth, and height, we define our problem using the given volume of 108 cubic inches and the formula for the surface area of an open box. To find the dimensions that will use minimal material requires the application of calculus and optimization techniques.
Explanation:In this problem, we know that the volume of the open rectangular box is 108 cubic inches. The volume of a rectangular box can be calculated with the formula V = xyz where x, y, and z are the length, width, and height. If we let the dimensions of the box be x, y, and z inches respectively, it means that the volume V = 108 = x*y*z.
The amount of material used or the surface area S of an open box (a rectangular box without a top) is given by the formula S = xy + 2xz + 2yz. Here, our task is to minimize this surface area.
To minimize the surface area, we need to employ calculus, specifically the concept of optimal control. However to apply calculus, we need to express S in terms of one variable. We can get this by expressing y in terms of x and z using the volume formula. This leads to a complex optimization problem that involves calculus.
Learn more about Optimization here:https://brainly.com/question/37742146
#SPJ2
A painting cost $225. If the sale price is $191.25, what is the percent discount
Answers
solve for x 3x−91>−87 OR 21x−17>25
Answers
Answer:
x > 4/3
Step-by-step explanation:
The first inequality can be solved this way ...
3x -91 > -87
3x > 4 . . . . . . . add 91
x > 4/3 . . . . . . divide by 3
__
The second inequality has solution ...
21x -17 > 25
21x > 42 . . . . . . add 17
x > 2 . . . . . . . . . divide by 21
__
The solution set is the union of these overlapping solutions, so will be equal to the first solution:
x > 4/3
Answer:
The solution is [tex]x>\frac{4}{3}[/tex]
Step-by-step explanation:
A compound inequality is an inequality that combines two simple inequalities.
We want to solve for x the following compound inequality
[tex]3x-91>-87 \:{OR} \:{21x-17>25}[/tex]
Solving the first inequality for x, we get:
[tex]3x-91+91>-87+91\\\\3x>4\\\\x>\frac{4}{3}[/tex]
Solving the second inequality for x, we get:
[tex]21x-17+17>25+17\\\\21x>42\\\\x>2[/tex]
So our compound inequality can be expressed as the simple inequality:
[tex]x>\frac{4}{3}[/tex]
The graph of a compound inequality with an "or" represents the union of the graphs of the inequalities. A number is a solution to the compound inequality if the number is a solution to at least one of the inequalities.
Graphically, we get
Find the inverse of the function. y = 2x2 –4
Answers
x=2y²-4
x+4=2y²
(x+4)/2=y²
√((x+4)/2)=y
Answer:
The inverse function is [tex]y=\sqrt{\frac{x+4}{2}}[/tex]
Step-by-step explanation:
The given function is [tex]y=2x^2-4[/tex].
This function is only invertible on the interval, [tex]x\ge 0[/tex].
To find the inverse on this interval, we interchange [tex]x[/tex] and [tex]y[/tex].
[tex]x=2y^2-4[/tex]
We now make [tex]y[/tex] the subject to get,
[tex]x+4=2y^2[/tex]
[tex]\Rightarrow \frac{x+4}{2}=y^2[/tex]
[tex]\Rightarrow \pm \sqrt{\frac{x+4}{2}}=y[/tex]
But the given interval is [tex]x\geq 0[/tex], This implies that, [tex]y\geq 0[/tex].
[tex]y=\sqrt{\frac{x+4}{2}}[/tex]
Solve. 3x2 − 6x = 24 A) x = 2, x = 4 B) x = 3, x = 4 C) x = −2, x = 4 D) x = −4, x = 3
Answers
3x^2 − 6x - 24 = 0
3(x^2 - 2x - 8) = 0
3(x - 4)(x + 2) = 0
x - 4 = 0; x = 4
x + 2 =0; x = -2
answer
C) x = −2, x = 4
Answer:
First Answer - C
Second Answer B
Step-by-step explanation:
How many MP3 players in the shipment would you predict to be damaged if 6 MP3s in the sample had been damaged
Answers
Substitute known values. Let x be the number of defective MP3 players in the population.
6 / 50 = x / 3500
50 x 70 = 3500, so multiply the numerator and denominator of the fraction 6/50 by 70.
(6x70) / (50x70) = x / 3500
420 / 3500 = x / 3500
420 = x
Based on the sample, we can predict that 420 MP3 players in the shipment would be defective.
Let v be the vector from initial point P1 to terminal point P2. Write v in terms of i and j. 2) P1 = (0, 0); P2 = (3, -4)
Answers
The vector [tex]\( \mathbf{v} = 6\mathbf{i} - 3\mathbf{j} \)[/tex].
Its magnitude is [tex]\( \sqrt{45} \)[/tex] in reduced radical form.
To find vector [tex]\( \mathbf{v} \)[/tex] from point [tex]\( P_1 \)[/tex] to point [tex]\( P_2 \)[/tex], we subtract the coordinates of [tex]\( P_1 \)[/tex] from the coordinates of [tex]\( P_2 \)[/tex]:
[tex]\[\mathbf{v} = \begin{pmatrix} x_2 - x_1 \\ y_2 - y_1 \end{pmatrix}\][/tex]
Given [tex]\( P_1 = (-2, 5) \) and \( P_2 = (4, 2) \), we can calculate \( \mathbf{v} \):[/tex]
[tex]\[\mathbf{v} = \begin{pmatrix} 4 - (-2) \\ 2 - 5 \end{pmatrix} = \begin{pmatrix} 6 \\ -3 \end{pmatrix}\][/tex]
So, [tex]\( \mathbf{v} = 6\mathbf{i} - 3\mathbf{j} \)[/tex].
To find the magnitude of [tex]\( \mathbf{v} \)[/tex], we use the formula:
[tex]\[|\mathbf{v}| = \sqrt{v_x^2 + v_y^2}\][/tex]
Where [tex]\( v_x \)[/tex] and [tex]\( v_y \)[/tex] are the components of [tex]\( \mathbf{v} \)[/tex]
For [tex]\( \mathbf{v} = 6\mathbf{i} - 3\mathbf{j} \), \( v_x = 6 \) and \( v_y = -3 \)[/tex]:
[tex]\[|\mathbf{v}| = \sqrt{(6)^2 + (-3)^2} = \sqrt{36 + 9} = \sqrt{45}\[/tex]
Thus, the magnitude of vector [tex]\( \mathbf{v} \) is \( \sqrt{45} \)[/tex] in reduced radical form.
Correct question is:
Let v be the vector from initial point P1 to terminal point P2.
Write v in terms of i and j, and find the magnitude of vector v.
Leave the magnitude in reduced radical form.
P1 = (-2,5) , P2 = (4,2)
Which equation could be used to find m∠J in △JKL? x = cos–1 x = cos–1 x = sin–1 x = sin–1
Answers
In in a random survey, 8 out of every 13 students were taking Pre-Algebra, how many students out of the larger population of 8,000 students would be taking Pre-Algebra?
Answers
how many degrees are In a 1/ 4 turn
Answers
the expression below is scientific notation for what number??
Answers
The answer is option A ".00000236".
Reason:
First write the equation:
2.36*10^-6
The exponent is negative so move to the left:
=.00000236
If you need anymore help feel free to ask me!
Hope this helps!
~Nonportrit
Prove or disprove: for all integers a, b, c, if a|bc, then a|b or a|c.
Answers
A building is in the shape of a square pyramid. Each side of the base is 54 meters long and the height is 260 meters.
I know is 1/3 b*h
is that correct... google failed me before
Answers
Help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
https://brainly.com/question/9281713
what is the equivalent fraction of each one. 3/4 and 9/15 and24/40 and 5/7
Answers
9/15 = 3/5
24/40 = 3/ 5
5/7 = 10/14
Helene bought 6 bottles of juice. The bottles were on sale at 10 bottles for $12. Which explanation correctly tells how to calculate the cost of 6 bottles? A. Step 1 Multiply $12 by 10 to figure out the cost of 1 bottle. Step 2 Divide that cost by 6. B. Step 1 Divide $12 by 10 to find out the cost of 1 bottle. Step 2 Multiply that cost by 6. C. Step 1 Multiply $12 by 10 to find out the cost of 1 bottle. Step 2 Multiply that cost by 6. D. Step 1 Divide $12 by 10 to find out the cost of 1 bottle. Step 2 Divide that cost by 6.
Answers
the cost of 10 bottles was $12.
therefore we need to find the cost of one bottle and then find the cost for 6 bottles.
if 10 bottles cost - $ 12
then 1 bottle costs - $ 12 / 10 bottles
here we divided 12 by 10 , cost of 1 bottle is 12/10 to find the cost of 6 bottles we have to multiply by 6 .12 / 10 x 6
correct answer is therefore B. divide 12 by 10 and then mulitply by 6
Option: B is the correct answer.
B. Step 1: Divide $12 by 10 to find out the cost of 1 bottle.
Step 2 : Multiply that cost by 6.
Step-by-step explanation:The cost of 10 bottles is: $ 12.
This means that the cost of 1 bottle is:$ (12/10)=$ 1.2
( Since the cost of 1 bottle will be less and hence the total cost must be divided by the number of items in order to obtain the cost of 1 item)
and similarly in order to find the cost of 6 items we need to multiply the cost of 1 item by 6.Hence, cost of 6 bottles of juice is: $ (1.2×6)=$ 7.2
Hence, the correct answer is:
B. Step 1: Divide $12 by 10 to find out the cost of 1 bottle.
Step 2: Multiply that cost by 6.
A large Pizza has a diameter of 18 inches. If each large pizza is cut into 10 equal slices, what is the approximate area of 3 slices of pizza?
Answers
Find Radius
--------------------------------------
Radius = Diameter ÷ 2
Radius = 18 ÷ 2
Radius = 9 inches
--------------------------------------
Area of the Pizza
--------------------------------------
Area = πr²
Area = π x (9)²
Area = 81π
Area = 254.47 in² (nearest hundredth)
--------------------------------------
find area of 1 slice of pizza
--------------------------------------
10 slices = 254.47 in²
1 slice = 254.47 ÷ 10
1 slice = 25.44 in²
--------------------------------------
Find area of 3 slices of pizza
--------------------------------------
1 slice = 25.44 in²
3 slices = 25.44 x 3
3 slices = 766.32 in²
--------------------------------------
Answer: 766.32 in²
--------------------------------------
a student found the volume of a rectangular pyramid with a base area of 92 square meters and a height of 54 Meters to be 4968 cubic meters explain and correct the error
Answers
The student found the volume by multiplying the base area with the height. He forgot to divide it by 3.
Formula to find the volume of the pyramid = 1/3 base area x height
volume = 1/3 x 92 x 54 = 1656 square meters
Answer:
1656
Step-by-step explanation:
1/3*92*54
Math question help please!
Answers
1) y = 3sin(x-π).
The function sine returns a value between -1 and 1, including those limits, so the range interal is [-1,1] no matter what the input be.
Multiplying the function by the factor 3, stretches the range by that factor.
So, the range of the given function is [-3,3].
2) y = 1 - sin(x)
Againt the range of sin(x) is [-1,1], then when you subtract that from 1, the limits of 1 - sin(x) are: 1 - (-1) = 2 and 1 - 1=0, and any other value wiill be in that range.
So, the answer is [0,2]
3) y = 3 + 4cos(x - π).
The range of the cosine function is also [-1,1], so the range of cos(x - π) is [-1,1].
By multiplying by 4 you stretch the range by that factor, so the new range is [-4,4].
By adding 3, the new borders are 3 - 4 = -1 and 3 + 4 = 7, so the range of the given function is: [-1, 7].
4) y = 2+cot(x)
The range of cot(x) is (-∞,∞), so adding 2 does not modify the range
So, the range for the given function is (-∞,∞).
Be sure to understand how this work. For both functions sine and cosine the range is [-1,1], when you mutiply by a constant factor you scale the range by that factor and when you add a constant you translate the range by that number of units.
an aviary places an order for 75 pounds of bird seeds. the order is filled by mixing different kinds of seeds from Bin A Bin B and Bin C Three times as much seed was added from Bin C as Bin A.Ifx respresents the amount of seed from Bin Cwhich expression represents the amount of bird seed mixed from Bin B
Answers
how to solve 5/8h = 1,1/2=5
Answers
Answer:
C
Step-by-step explanation:
Is this your question? I know that sometimes I accidentally put an equal sign instead of a plus.
what is the 5% of 300
Answers
300*5/100 =15
That's all
the best way to do it is see the % as a decimal in my opinion, then plug it into a calculator. just move the decimal over to the left 2 times, then multiply the number you're taking the percent out of. So, in this case it would be:
300x.05
which is 15
A science class is tracking the progress of plant growth. The class starts the experiment with a plant five centimeters high. The plant grows two centimeters each day. The model for plant growth "y" is given by: y = 2x + 5. What is the meaning of the y-intercept in this equation? A) the y-intercept is the starting date Eliminate B) the y-intercept is two times larger than five C) the y-intercept is the starting height of the plant D) the y-intercept is the largest height the plant can grow
Answers
In the equation of a straight line, there is a slope (2) and a y intercept (5). The y intercept is where the line crosses the y axis. It is the starting point for the y values. The science class starts the experiment with the plant being 5 centimeters high and since this is the starting point/height, this is also the y intercept.
check all that apply
Answers
You need to do the same steps I used for the other one.
x² < 81
Find the critical points of the inequality
x² = 81
Then take square root
x = [tex]\pm \sqrt{81} [/tex]
x = 9 or x = -9
Thus,
The answer is option B 9
Julia has to measure an object. She does not have a ruler. Tell what Julia could do to solve her problem.
Answers
so... say you can use a tie or something with length, and use that to measure whatever object you need it for.
for example, I can just grab a string, cut it, and measure something, and the measurement may just be that the object is my string 6 times, so I know the length of the object is 6 times the length of the string I cut.
it doesn't quite matter how long the string cut was, all that matters is that is relable or referenciable for reuse. Later on I could always just get the string measure and convert it to metric, once I found a ruler or imperial units.
but in the short run, it doesn't really matter the length of the string cut, all that matters is that is referenciable, the object will be 6 times my string cut, here, in France, in Pluto, in Andromeda, anywhere.
bear in mind that the measure units we use today, are only usable because they're referenciable, so if I tell you 15 inches of something, you know how much 15 inches is, so that's all that matters.