Answer:
2[tex]x^{4}[/tex] + x³ - x² + 54x - 56
Step-by-step explanation:
Area (A) is calculated as
A = length × width
= (x² - 2x + 8)(2x² + 5x - 7)
Each term in the second factor is multiplied by each term in the first factor, that is
x²(2x² + 5x - 7) - 2x(2x² + 5x - 7) + 8(2x² + 5x - 7) ← distribute all parenthesis
= 2[tex]x^{4}[/tex] + 5x³ - 7x² - 4x³ - 10x² + 14x + 16x² + 40x - 56 ← collect like terms, thus
A = 2[tex]x^{4}[/tex] +x³ - x² + 54x - 56
The expression which represents the area of Dylan’s room will be 2x⁴ - 7x³ - 21x² + 82x - 56.
What is the area?
The area is the space occupied by any shape, find out by multiplying its length and breadth.
We have,
Lenght = (x² – 2x + 8)
and
Breadth = (2x² + 5x – 7)
Now, simplifying the above expressions,
(x² – 2x + 8)
It can be written as , Using middle term split method,
x² – 4x + 2x + 8
= x(x – 4) - 2(x - 4)
= (x – 4) (x - 2)
In the same way,
(2x² + 5x – 7)
= 2x² +7x - 2x – 7
= x(2x +7) - 1(2x + 7)
= (x - 1) (2x +7)
So,
So,
Using the area formula,
i.e.
Area = Length × Breadth
Area = (x² – 2x + 8) × (2x² + 5x – 7) = (x – 4) (x - 2) (x - 1) (2x +7)
Now,
Area = 2x⁴ - 7x³ - 21x² + 82x - 56
Hence we can say that the expression which represents the area of Dylan’s room will be 2x⁴ - 7x³ - 21x² + 82x - 56.
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PLEASE HELP ME The length of the one of the legs of a right triangle is 8m and the hypotenuse is 12m. Which of the following choices is the length of the other leg? 5 4 5 None of these choices are correct.
Answer:
The length of the other leg is 8.94 m.
Step-by-step explanation:
Given that,
Hypotenuse of a right triangle is 12 m
The length of the one of the legs of a right triangle is 8 m
We need to find the length of the other leg. It is based on the concept of Pythagoras theorem. Let the other leg is h. So, according to this theorem,
[tex]H^2=b^2+h^2[/tex]
H = hypotenuse = 12 m
b = base = 8 m
[tex]h^2=H^2-b^2\\\\h^2=12^2-8^2\\\\h=\sqrt{80}\\\\h=8.94\ m[/tex]
So, the length of the other leg is 8.94 m.
What is the height of the prism if there is 30 square centimeters and the volume is 90 cubic centimeters
Answer:
60
Step-by-step explanation:
when you use the distance formula you are building a right triangle whose _____ connects two given points a. right angle b. shorter leg c. hypotenuse d. longer leg
Answer:
hypotenuse
Step-by-step explanation:
hypotenuse. The length of the hypotenuse is the distance between the two given points.
Answer:
hypotenuse
Step-by-step explanation:
One airline ticket costs $412. for each additional airline ticket sold to a group, the price of all the tickets is reduced by $4. Write a quadratic function that gives the initial cost of buying x tickets.
Answer:
f(x)=104x-x^2
Step-by-step explanation:
Let
x = number of tickets sold.
example, 2 tickets cost 2 · 408 = $816
3 tickets cost 3 · 404 = $738.
The cost of buying x tickets= the number of tickets sold × the price of each ticket.
If x tickets are sold, then the price of each ticket is 412-4(x-1)
Then the quadratic function that gives the total cost of buying x tickets is given by
Cost =quantity sold*price
=412-4(x-1)*x
=(412-4x+4)*x
=412x-4x^2+4x
=416x-4x^2
Divide through by 4
=104x-x^2
Therefore, the required quadratic function is
f(x)=104x-x^2
A circle has an area of 30in². What is the area of a 60° sector of this circle?
Answer:
5 in^2
Step-by-step explanation:
The area of the sector will always be proportionate to the angle in the circle.
(The area of the sector / area of the circle) is equal to( the angle of the section divided by the angle of the circle)
The total degrees of a circle is 360
(area of the sector) = (60° / 360°) * 30 in^2
Suppose a firm in a competitive market earned $1,000 in total revenue and had a marginal revenue of $10 for the last unit produced and sold. What is the average revenue per unit, and how many units were sold?
Answer:
$5 and 50 units
Step-by-step explanation:
find the 10th term of the following sequences T(2)=20 and the term-to-term rule is subtract 6
==================================================
Work Shown:
T(2) = 20 means the second term is 20
T(1) = 26 because we go backwards from what the rule says (subtract 6) to step back one term. Going forward, 26-6 = 20.
Since a = 26 is the first term and d = -6 is the common difference, the nth term is
T(n) = a + d*(n-1)
T(n) = 26 + (-6)(n-1)
T(n) = 26 - 6n + 6
T(n) = -6n + 32
Plugging n = 1 into the equation above leads to T(1) = 26. Using n = 2 leads to T(2) = 20.
Plug in n = 10 to find the tenth term
T(n) = -6n + 32
T(10) = -6(10) + 32
T(10) = -60+32
T(10) = -28
Answer:
-28.
Step-by-step explanation:
T(1) = 20 + 6 = 26.
This is an arithmetic series with:
nth term T(n) = 26 - 6(n - 1).
So T(10) = 26 - 6(10-1)
= 26 -54
= -28.
You are graphing Rectangle ABCD in the coordinate plane. The following are three of the vertices of the
rectangle A(-7.-2), B(3.–2), and C(3,-5).
What are the coordinates of point D?
Answer:
D(-7, -5)
Step-by-step explanation:
There are a couple of ways to figure this.
1) When the rectangle is aligned with the axes, as this one is, each coordinate value shows up twice. In the given list, x-values of 3 are repeated, but -7 is not, so the x-coordinate is -7.
The y-values of -2 are repeated, but -5 is not, so the y-coordinate is -5.
The coordinates of point D are (-7, -5).
__
2) The midpoint of diagonal AC is the same as the midpoint of diagonal BD, so the sum of coordinates at the ends of the diagonals will be the same:
A+C = B+D
Subtracting the coordinates of B from the sum of A and C will give you the coordinates of D:
D = A +C -B = (-7, -2) +(3, -5) -(3, -2) = (-7+3-3, -2-5+2)
D = (-7, -5)
_____
Comment on the solution
The second approach works with any parallelogram, rhombus, rectangle, or square--any figure in which the diagonals bisect each other. The figure does not have to be aligned with the axes, as it does in the first approach.
please heellllpppp ....
Answer:
x ≈ 2.3 cm
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos55° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{4}[/tex] ( multiply both sides by 4 )
4 × cos55° = x , thus
x ≈ 2.3 cm ( to 1 dec. place )
Find the angle of rotation about the center of the regular pentagon that maps A to D.
Answer:
216
Step-by-step explanation:
Find each angle's value. This is a pentagon, so 360/5 = 72. Now, to get from A to D, you have to go 3 spaces counter-clockwise. This'll get you 72 x 3 = 216.
Answer:
216
Step-by-step explanation:
Find each angle's value. This is a pentagon, so 360/5 = 72. Now, to get from A to D, you have to go 3 spaces counter-clockwise. This'll get you 72 x 3 = 216.
There were some pieces of candy in a bowl. Shirley took half of them. Then Rose took half of the pieces left in the bowl. After that, Susan took half of the remaining pieces of candy. In the end there were 8 pieces of candy left in the bowl. How many candies were there in the bowl at the beginning?
Answer:
Number of pieces of candy in the bowl=64
Step-by-step explanation:
Let
x=number of pieces of candy in a bowl
Shirley took=1/2 of x
=1/2x
Remaining
x-1/2x
= 2x-x/2
=1/2x
Rose took half of the pieces left in the bowl=1/2 of 1/2x
=1/2*1/2x
=1/4x
Remaining
1/2x-1/4x
=2x-x/4
=1/4x
Susan took 1/2 of the remaining pieces of candy=1/2 of 1/4x
=1/2*1/4x
=1/8x
Remaining 8
1/8x=8
x=8÷1/8
=8*8/1
=64
x=64
PLEASE help me with this question! REALLY URGENT...
In the supermarket a loaf of bread costs 37p how many loaves can david buy with a 2 coin ? How much money will be left over?
Answer: He can buy 5 loaves of bread.
After buying 5 loaves 15 p will be left.
Step-by-step explanation:
Given, In the supermarket a loaf of bread costs 37p .
To find: How many loaves can David buy with a [tex]\pounds 2[/tex] coin?
Since [tex]\pounds 1=100\text{ pence}[/tex]
Then, [tex]\pounds 2=200\text{ pence}[/tex]
Number of loaves he can buy = (Amount he has) ÷ (Cost of a loaf of bread)
= 200 p ÷ 37 p
[tex]=5\dfrac{15}{37}[/tex]
i.e. he can buy 5 loaves of bread and 15 p will be left.
Hence, He can buy 5 loaves of bread.
After buying 5 loaves 15 p will be left.
The base of a regular pyramid is a hexagon.
Answer:
The base of the regular pyramid is a square.
Step-by-step explanation:
In △ABC, m∠A=15°, a=10, and b=11. Find c to the nearest tenth.
Answer:
There are two answers, c=20.2 or c=1.0
Step-by-step explanation:
The value of c is 20.2 units
What is cosine rule?The law of cosine states that the square of any one side of a triangle is equal to the difference between the sum of squares of the other two sides and double the product of other sides and cosine angle included between them.
Let a, b, and c be the lengths of the three sides of a triangle and A, B, and C be the three angles of the triangle. Then, the law of cosine states that: a2 = b2 + c2 − 2bc·cosA. As stated above, the law of cosines in trigonometry generalizes the Pythagorean theorem.
Law of Cosines FormulaThe law of cosines formula can be used to find the missing side of a triangle when its two sides and the included angle is given i.e., it is used in the case of a SAS triangle. We know that if A, B, and C are the vertices of a triangle, then their opposite sides are represented by the small letters a, b, and c respectively. The law of cosines formula is used to:
find a when b, c, and A are given (or)find b when a, c, and B are given (or)find c when a, b, and C are given (or)find any angle of the triangle when a, b, and c are given.
There are three laws of cosines and we choose one of them to solve our problems depending on the available data.
a2 = b2 + c2 - 2bc·cosAb2 = c2 + a2 - 2ca·cosBc2 = a2 + b2 - 2ab·cosCAs,
m∠A=15°, a=10, and b=11.
Now, using cosine rule
cos A = b² + c² - a²/ 2bc
cos 15 = 121+ c²-100/22c
0.96 = 121+ c²-100/22c
21.25 c = 21 + c²
21 + c² - 21.25 c=0
By solving the quadratic equation
c=20.2 units.
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Although mercury is a metal, it is a liquid at room temperature. Mercury melts at about -39°C. If the temperature of a block of mercury starts at -54°C and increases by 22°C, does the mercury melt?
Answer:
yes
Step-by-step explanation:
because mercy is a semi liquid metal that is mostly used in checking high temperature of a substance .
I need answer in degrees! Thank you to anyone who answers ;P.
Answer:
x = 84
Step-by-step explanation:
Sum of angles around a point = 360
Sum of given angles = 132+54+90 = 132+144 = 276
So, x must cover the angle remaining from 276 to form 360, which is
360-276 = 84degrees.
Hope this helps
Answer:
84 DEGREES
Step-by-step explanation:
SO WE KNOW THAT THER IS 132 +54 DEGREES AND THAT THE 3RD ONE IS A RIGHT ANGLE
SO
132+90+54=276
360-276=84
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
ANSWER ASAP
PLEASE AND THANK YOU
Answer:
(C) $111.83
Step-by-step explanation:
If Sonya buys four pairs of shoes, each on a buy one get one 50% off, that means that we can find the value if she bought ONE deal of buy one get 50% off one, then multiply that by 2 (as if you do the deal, you are paying for two.)
The shoe costs $35, and if we have a 50% discount on it:
[tex]35\cdot0.5=17.5[/tex]
So the cost of the shoe ON DISCOUNT is 17.50, however the first pair still stays the same.
So the cost of two pairs of shoes using the discount is [tex]35+17.5 = 52.5[/tex]
So four pairs cost [tex]52.5\cdot2 = 105[/tex]
However, there is a tax of 6.5%
So we can multiply 105 by 1.065 to get the cost after tax.
[tex]105\cdot1.065=111.825[/tex]
This simplifies down to 111.83.
Hope this helped!
08.03 MC) The ages of two groups of dance students are shown in the following dot plots: A dot plot shows Age in years on the horizontal axis. For Group X, there are 3 dots on 4, 1 dot on 5, 5 dots on 8, 2 dots on 10, 3 dots on 12, and 2 dots on 16. For Group Y, there are 2 dot on 5, 3 dots on 7, 1 dot on 9, 3 dots on 11, 1 dot on 13, 2 dots on 14, 1 dot on 15, 1 dot on 18, 3 dots on 20, 1 dot on 22, and 2 dots on 24. The mean absolute deviation (MAD) for group X is 3.07 and the MAD for group Y is 5.25. Which of the following observations can be made using these data?
Answer:
FLVS ANSWR!!!!!!
Step-by-step explanation:
Group X has less variablility
Answer:
What the guy above me said.
Step-by-step explanation:
Can someone pls help will mark u as brainliest
Answer:
9*((2-1)/9)
or
2 -1
9
2-9 =-7
9. 9
9× -7
9
=-7
2- 3
9. -3
=(1.22222222222)
or
11/9
or
1*(2/9)
Please help asap! I don’t really understand
Answer:
x² +3x -8x -24(x² +3x) +(-8x -24)x(x +3) -8(x +3)(x +3)(x -8)Step-by-step explanation:
This is trying to help you understand a method of factoring trinomials.
The first step is to look at the linear term (-5x) and the constant term (-24) and identify the coefficients and their signs: -5 and -24.
The next step is to identify factors of -24 (the constant) that have a sum equal to -5 (the linear term coefficient). We can look at the ways that -24 can be factored:
-24 = 1(-24) = 2(-12) = 3(-8) = 4(-6)
The sums of these factor pairs are 1-24=-23, 2-12=-10, 3-8=-5, 4-6=-2. Of course, the pair we're looking for is +3 and -8.
The next step from here is to rewrite the linear term using these factors. (-5x=3x-8x) This is the first step of the sequence shown in the figure:
x² +3x -8x -24
The next step is to group these terms in pairs:
(x² +3x) +(-8x -24)
And then, to factor each pair using the distributive property:
x(x +3) -8(x +3)
Finally, finish the factoring, again using the distributive property:
(x +3)(x -8)
Determine an expression for the perimeter of the following shape. I need a step by step solution pleaseeeee:)
Answer:
The perimeter of the figure is: 8x + 34.
Step-by-step explanation:
The perimeter of a shape is the sum of the length of all its sides. In this case there is one side missing, we need to find its length. To do that we will have to use Pythagora's theorem, because we will create a right triangle as shown in the attached picture. Where a, b and c are the sides of the right triangle. We can determine the lengths of a and c. If we pay close attention to the figure we will realize that a is:
[tex]a = 2x + 5 - 2x = 5[/tex]
While c is:
[tex]c = 2(x + 7) - (x + 5) - (x - 3)\\c = 2x + 14 -x - 5 -x + 3\\c = 2x - 2x + 12\\c = 12[/tex]
We can now apply Pythagora's theorem:
[tex]b^2 = a^2 + c^2\\b^2 = 5^2 + 12^2\\b^2 = 25 + 144\\b = 13[/tex]
With this we can sum all the sides and calculate the perimeter of the shape.
[tex]2x + 5 + x - 3 + 2x + x + 5 + 13 + 2(x + 7)\\2x + x + 2x + x + 2x + 5 - 3 + 5 + 13 + 14\\8x + 34[/tex]
Suppose that you and a friend are playing cards and decide to make a bet. If you draw two red cards in succession from a standard deck of 52 cards without replacing the first card, you win $50. Otherwise, you pay your friend $20. What is the expected value of your bet? Round your answer to the nearest cent, if necessary.
Answer:
E=$19.307
Step-by-step explanation:
Total number of cards = 52
If you win then you will get $50
If you lose then you will give him $20
Therefore the probability
[tex]P(first\ card\ is\ face\ card)=\dfrac{12}{52}[/tex]
[tex]P(Second\ card\ is\ face\ card)=\dfrac{11}{51}[/tex]
[tex]P(Third\ card\ is\ face\ card)=\dfrac{10}{50}[/tex]
Thus the probability for all the three cards are face card
[tex]P=\dfrac{12}{52}\times \dfrac{11}{51}\times \dfrac{10}{50}[/tex]
P=0.0099
Thus the probability for all the three cards are not face card
P=1-0.0099=0.9901
P=0.9901
Therefore , expected value
[tex]E=20\times 0.9901-50\times 0.0099[/tex]
E=$19.307
Therefore the answer will be $19.307.
Find the derivative of f(x) = negative 9 divided by x at x = -4. 4 divided by 9 16 divided by 9 9 divided by 16 9 divided by 4
Answer:
ﾠﾠﾠﾠﾠﾠﾠﾠ
Step-by-step explanation:
ﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠ
Answer:
9/16
Step-by-step explanation:
Help me please with kim!
Answer: Kim - Resp after 24 months = $4,416.00
Kim - Technology Fund after 24 months = $1,120.06
Kim's Technology Fund has enough money to buy a laptop.
Kim's Savings (Resp) will last less than 6 months
Step-by-step explanation for Kim:
January - June 2019
$14.50 + 30($0.25) = $22.00/hr
$22/hr x 15 hr x 4 wks x 6 months = $7920 Gross Income
Resp (15%): $7920(0.15) = $1188CPP(5%): $7920(0.05) = $396EI(2%): $7920(0.02) = $158.40Taxable Income is $7920 - $1188 = $6732 (Annual Income $13,464)
Income Tax (0% for 0-9,000 Annual): $4500(0) = $0Income Tax (8% for 9-25,000 Annual): ($6732-$4500)(0.08) = $178.56→ $7,920 -($1188 + $396 + $158.40 + $0 + $158.40) = $5,999.04 Net Income
Tech Fund (5%): $5999.04(0.05) = $299.95
Food Expense (30%): $5999.04(0.3) = $1,799.71
Clothing Expense (30%): $5999.04(0.3) = $1,799.71
Entertainment Expense (25%): $5999.04(0.25) = $1,499.76
Miscellaneous Expense (10%): $5999.04(0.1) = $599.90
Other Expenses: $5,699.08
July - December 2019 (excluding August)
$22/hr x 20 hr x 4 wks x 5 months + $200 = $6800 Gross Income
Resp (15%): $6800(0.15) = $1020CPP(5%): $6800(0.05) = $340EI(2%): $6800(0.02) = $136Taxable Income is $6800 - $1020 = $5780 (Annual Income $12,512)
Income Tax (0% for 0-9,000 Annual): $4500(0) = $0Income Tax (8% for 9-25,000 Annual): ($5780-$4500)(0.08) = $102.40→ $6,800 - ($1020 + $340 + $136 + $0 + $102.40) = $5,201.60 Net Income
Tech Fund (5%): $5201.60(0.05) = $260.08
Food Expense (30%): $5201.60(0.3) = $1,560.48
Clothing Expense (30%): $5201.60(0.3) = $1,560.48
Entertainment Expense (25%): $5201.60(0.25) = $1,300.40
Miscellaneous Expense (10%): $5201.60(0.1) = $520.16
Other Expenses: $4,941.52
January - June 2020
same as January - June 2019
July - December 2020 (excluding August)
same as July - December 2019
[tex]\boxed{\begin{array}{l|r|r|r|r||r}\underline{KIM}&\underline{Jan-Jun'19}&\underline{Jul-Dec'19}&\underline{Jan-Jun'20}&\underline{Jul-Dec'20}&\underline{Totals\quad }\\Gross&\$7920.00&\$6800.00&\$7920.00&\$6800.00&\$29440.00\\Resp&\$1188.00&\$1020.00&\$1188.00&\$1020.00&\$4416.00\\Net&\$5999.04&\$5201.60&\$5999.04&\$5201.60&\$22401.28\\Other&\$5699.08&\$4941.52&\$5699.08&\$4941.52&\$21281.20\\Tech&\$299.95&\$260.08&\$299.95&\$260.08&\$1120.06\end{array}}[/tex]
paid after the grace period, on average, more than 4 times in 2018, what are the null and alternative hypotheses? Select the correct answer below: H0: μ=4; Ha: μ>4 H0: μ>4; Ha: μ=4 H0: μ=4; Ha: μ<4 H0: μ=4; Ha: μ≠4
Answer:
H₀: μ = 4 vs. H ₐ: μ > 4
Step-by-step explanation:
A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.
It is a hypothesis of no difference.
It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.
Whereas, the alternate hypothesis is the contradicting statement to the null hypothesis.
The alternate hypothesis describes direction of the hypothesis test, i.e. if the test is left tailed, right tailed or two tailed.
It is also known as the research hypothesis and is denoted by H ₐ.
In this case we need to test whether the amount is paid after the grace period, on average, more than 4 times in 2018.
The hypothesis can be defined as follows:
H₀: μ = 4 vs. H ₐ: μ > 4
Which equation is modeled below?
4 x tiles and 2 negative 1 tiles = 2 x tiles and 4 1 tiles.
2 x + (negative 2) = negative 2 x + 6
4 x + (negative 2) = negative 2 x + 6
2 x + 4 = 6 x + 2
Negative 2 x + 4 = 6 x + (negative 2)
(Ignore the filled in bubble)
Answer:
B
Step-by-step explanation:
4 (x) + 2 (-1) = 2 (-x) + 6(1)
4x + -2 = -2x + 6
The equation for the given figure is 4x-2=-2x+6. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
From the given figure,
x+x+x+x+(-1-1)=(-x-x)+(1+1+1+1+1+1)
⇒ 4x-2=-2x+6
So, equation modeled as 4x-2=-2x+6
The equation for the given figure is 4x-2=-2x+6. Therefore, option B is the correct answer.
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Which of the following is equivalent to the following complex fraction? [1-(1/x)]/2
Answer:
Option 1
Step-by-step explanation:
=> [tex]\frac{1-\frac{1}{x} }{2}[/tex]
=> [tex]\frac{\frac{x-1}{x} }{2}[/tex]
=> [tex]\frac{x-1}{x} / 2[/tex]
=> [tex]\frac{x-1}{x} * \frac{1}{2}[/tex]
=> [tex]\frac{x-1}{2x}[/tex]
Can someone please help me please?
Answer:
Step-by-step explanation:
What is the total number of common tangents that can be drawn to the circles?
Answer:
The answer would be zero. This is due to the fact that the tangent is a line on a point around the circle. These two circles share no common tangents.
Step-by-step explanation:
The number of the common tangent to the concentric circles is zero. Option D is correct.
Two concentric circles are given in the figure, and common tangents to the circles are to be determined.
The circle is the locus of a point whose distance from a fixed point is constant i.e center ( h, k ). The equation of the circle is given by[tex](x-h)^2 + (y-k)^ = r^2[/tex]. where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.
Since the line passes through the circumference of the circle is known as a tangent to the circle and the common tangent of the concentric circle is not possible because the tangent to the inner circle results secant to the outer circle.
Thus, the number of the common tangent to the circles is zero. Option D is correct.
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