Explanation:
The outer term 2p is distributed among the three terms inside the parenthesis. We will multiply 2p by each term inside
2p times 4p^2 = 2*4*p*p^2 = 8p^3
2p times 5p = 2*5*p*p = 10p^2
2p times 7 = 2*7p = 14p
The results 8p^3, 10p^2 and 14p are added up to get the final answer shown above. We do not have any like terms to combine, so we leave it as is.
Please answer now correct answer fast
Answer:
[tex] Area = 112.1 m^2 [/tex]
Step-by-step Explanation:
Given:
∆WXY
m < X = 130°
WY = x = 31 mm
m < Y = 26°
Required:
Area of ∆WXY
Solution:
Find the length of XY using Law of Sines
[tex] \frac{w}{sin(W)} = \frac{x}{sin(X)} [/tex]
X = 130°
x = WY = 31 mm
W = 180 - (130 + 26) = 24°
w = XY = ?
[tex] \frac{w}{sin(24)} = \frac{31}{sin(130)} [/tex]
Multiply both sides by sin(24) to solve for x
[tex] \frac{w}{sin(24)}*sin(24) = \frac{31}{sin(130)}*sin(24) [/tex]
[tex] w = \frac{31*sin(24)}{sin(130)} [/tex]
[tex] w = 16.5 mm [/tex] (approximated)
[tex] XY = w = 16.5 mm [/tex]
Find the area of ∆WXY
[tex] area = \frac{1}{2}*w*x*sin(Y) [/tex]
[tex] = \frac{1}{2}*16.5*31*sin(26) [/tex]
[tex] = \frac{16.5*31*sin(26)}{2} [/tex]
[tex] Area = 112.1 m^2 [/tex] (to nearest tenth).
The figure shows the location of 3 points around a lake. The length of the lake, BC, is also shown. (Figure is not drawn to scale.) Which of the following options is closest to the distance (in miles) between points A and B?
6.71 miles
7.35 miles
8.66 miles
10.82 miles
Answer:
3rad5
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {a }^{2} + {6}^{2} = {9}^{2} \\ {a }^{2} + 36 = 81 \\ {a}^{2} + 81 - 36 \\ {a}^{2} = 45 \\ \sqrt{a} = \sqrt{45} \\ a = 3 \sqrt{5} [/tex]
Answer:
It's A.) 6.71 miles
Step-by-step explanation:
I just took the quiz. May I have Brainiest???
Which statements must be true about the reflection of
AXYZ across MN? Select three options.
A. m< X’ Z’ Y’= 90°
B. m< MCY= 90°
C. XX = YY
D. BZ = BZ
E. XY || X’ Y’
Answer:
abd
Step-by-step explanation:
The true statements about the reflection shown in picture attached are :
M∠X'Z'Y' = 90°
M∠X'Z'Y' = 90°m∠MCY = 90°
M∠X'Z'Y' = 90°m∠MCY = 90°BZ' ≅ BZ
What is reflection?Reflection is a type of transformation that flips a shape in a mirror line (also called a line of reflection) so that each point is the same distance from the mirror line as its reflected point.
here, we have,
When reflection of a preimage occurs, the image produced is congruent to the preimage because reflection produces isometric images. This means that both the preimage and image are similar in shape and size.
Since m∠XZY = 90°, will be congruent with the angle m∠X'Z'Y' ; Hence, m∠X'Z'Y' = 90°
The segment MN and YY' are perpendicular, hence forming a right angle. m∠MCY = 90°
B is the midpoint between ZZ'. Hence, the distance between BZ' and BZ will be the same. BZ' ≅ BZ
From the image produced, XY and X'Y are not parallel
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Complete question:
Which statements must be true about the reflection of ΔXYZ across Line M N? Select three options. M∠X'Z'Y' = 90° m∠MCY = 90° XX' ≅ YY' BZ' ≅ BZ XY || X'Y
in a certain town there are 30000 registered voters, of whom 12000 are Democrats. A survey organization is about to take a simple random sample of 1000 registered voters. a) the expected value for the percentage of Democrats in the sample is
Answer:
400.
Step-by-step explanation:
The following data were obtained from the question:
Total number of Registered voters = 30000
Total number of Democrats = 12000
Next, we shall determine the percentage of Democrats in the registered voters.
This can be obtained as follow:
Percentage of Democrats = number of Democrats / Total number of registered voters x 100
Percentage of Democrats = 12000/30000 x 100
Percentage of Democrats = 40%
Now, we can obtain the expected value of percentage of Democrats in the 1000 sample as follow:
Percentage of Democrats = 40%
Total number of Sample = 1000
Number of Democrats in the sampl=..?
Percentage of Democrats = number of Democrats in sample / Total number of sample x 100
40% = number of Democrats in sample/1000
Cross multiply
Number of Democrats in sample
= 40% x 1000
= 40/100 x 1000
= 400
Therefore, the expected number of Democrats in the sample is 400.
Aubrey has a new art box in the shape of a rectangular prism. The box is 12 cm by 20 cm by 5 cm. The
only thing in the art box is a new pink eraser with the dimensions shown below.
0.5 cm
2 cm
4 cm
What is the volume of the art box not taken up by the eraser?
Answer:
1196cm³
Step-by-step explanation:
Step 1
Find the volume of the Rectangular Prism = Length × Width × Height
Length = 12 cm
Width = 20 cm
Height = 5 cm
Volume of a Rectangular prism = 12 × 20 × 5
= 1200cm³
Step 2
Volume of the Eraser
The Eraser has the shape of a box.
Volume = Length × Width × Height
Length = 0.5 cm
Width = 2 cm
Height = 4 cm
Volume = 4cm³
Step 3
Find the volume of the art box not taken up by the eraser
Volume of the art box not taken up by the eraser = Volume of the Art box - Volume of the Eraser
= 1200cm³ - 4cm³
= 1196cm³
Therefore, volume of the art box not taken up by the eraser is 1196cm³
PLEASE HELP NOW WILL MARK BRAINLEST FOR CORRECT ANSWER A Brazilian town near the Amazon River has experienced 7% annual decrease in size of rainforest as trees are cut down and forest is converted to farmland. In the year 2009, there were about 28,000 acres of rainforest in town. a. Write an exponential model that relates the number of acres of rainforest y as a function of t years since 2009. b. How many acres of rainforest remained in 2013 (that is, in year 4)? Show work.
Answer:
a. y = 28,000×(1 - 0.07)^t
b. 20,945.46 acres
Step-by-step explanation:
a. The annual percentage decrease in in size of rainforest = 7%
The size of the rainforest in 2009 = 28,000 acres
The exponential decay formula is y = C×(1 - r)^t
Where:
y = Final Amount
C = Initial amount = 28,000 acres
r = Rate of Change = 0.07
t = Time
Which gives;
y = 28,000×(1 - 0.07)^t
b. In 2013 (year 4, t = 4), the amount of rainforest remaining is therefore;
y = 28,000×(1 - 0.07)^(4) = 28,000×0.93^4 = 20,945.46 acres
The size of the rainforest that remained in 2013 is 20,945.46 acres.
Answer:
20(-3)
Step-by-step explanation:
Examine the graph and the map.
On the left, a bar graph titled Deforestation Trend in the Amazon Rainforest. The x-axis is labeled Acres in kilometers squared of Rainforest Lost. The y-axis is labeled Year from 2004 to 2016. 2004 lost 27,772 acres. 2005 lost 19,014 acres. 2010 lost 7,000 acres. 2012 lost 4.571 acres. 2016 lost 7,989 acres. On the right, a map titled Deforestation of the Amazon Rainforest by 2016. The Amazon River is labeled. A key notes deforestation by 2016, amazon forest in 2016, and non-forest vegetation. Labeled clockwise are Roraima, Amapá, Maranhäo, Pará, Tocantins, Mato Grosso, Rondônia, Acre, and Amazonas. Acre, Amazonas, Roraima, Amapá, Maranhäo, Mato Grosso and Rondônia are deforested by 2016. Pará, Maranhäo, Tocantins, Mato Grosso, and Rondônia have the Amazon forest in 2016. Mato Grosso, Tocantins and Maranhäo have majority of non-forest vegetation.
Which is the best conclusion about the Amazon rainforest that can be drawn from these sources?
Deforestation in the Amazon has accelerated since 2004.
Deforestation in the Amazon is no longer an important issue.
Despite population growth, the Amazon rainforest is increasing in size.
Despite positive trends, the Amazon rainforest remains in danger of destruction.
Which is the best estimate of A.2 B.6 C.12 D.24
Answer:
24
Step-by-step explanation:
90/7 ÷ 1 3/4
Change to an improper fraction
90/7 ÷ ( 4*1 +3 ) /4
90/7 ÷ 7/4
Copy dot flip
90/7 * 7/4
90/4
22.5
Best estimate is 24
Answer:
A:2
Step-by-step explanation:
A is the answer because 90 divided by 7 is 12.8 which would be 13, and the 1 and 3/4 would be 7. 13 divided by 7 would equal 1.85. When rounded your answer would be 2.
If y varies directly with x and y is -6 when x is 2, what is x when y is -22?
Answer:
x = [tex]\frac{22}{3}[/tex]
Step-by-step explanation:
Given that y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = - 6 when x = 2, then
- 6 = 2k ( divide both sides by 2 )
- 3 = k
y = - 3x ← equation of variation
When y = - 22, then
- 22 = - 3x ( divide both sides by - 3 )
x = [tex]\frac{-22}{-3}[/tex] = [tex]\frac{22}{3}[/tex]
Movie tickets for 2 adults and 3 children cost $44.50. Tickets for the same movie cost $25.50 for 1 adult and 2 children. (a) Let a represent the cost of a ticket for an adult and c represent the cost of a ticket for a child. Write a system of equations that can be used to find a and c. (b) What is the total cost of tickets for 1 adult ticket and 1 child ticket?
Answer:
a) 2a + 3c = $44.50
a + 2c + $25.50
b) $19
Step-by-step explanation:
Simultaneous equations. A = adult. C = children
2a + 3c = $44.50 (EQUATION 1)
a + 2c = $25.50 (EQUATION 2)
Now solve this using the method of elimination:
2a + 3c = $44.50 (EQUATION 1)
a + 2c = $25.50 (EQUATION 2)
Multiply equation 2 by 2 so that both equations have the same a coefficient.
2a + 4c = $51 (NEW EQUATION 2)
Now subtract equation 1 from equation 2:
2a - 2a + 4c - 3c = $51 - $44.50 (2a cancels out)
c = $6.50
Now substitute c into one of the equation, in this case, I'm using original equation 2.
a + 2($6.50) = $25.50
a + $13 = $25.50
a = $12.50
Total cost of one adult and child = $6.50 + $12.50
= $19
Answer:
option d
Step-by-step explanation:
hope this helps
A circle has a radius of 21 inches. What is the length of the arc intercepted by a central angle that measures 4π/7 radians? Express the answer in terms of π .
Answer:
12π inches
Step-by-step explanation:
s = rθ
s = (21) (4π/7)
s = 12π
The length of the arc will be;
⇒ Arc = 37.68 inches
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The central angle = 4π/7
And, A circle has a radius of 21 inches.
Now,
We know that in circle;
⇒ Arc = Radius × Angle
Substitute all the values, we get;
⇒ Arc = 21 × 4π/7
⇒ Arc = 3 × 4 × 3.14
⇒ Arc = 37.68 inches
Thus, The length of the arc will be;
⇒ Arc = 37.68 inches
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Find the volume of the cuboid which length is 10cm, breadth is 8cm and height is 7cm. Who answers first gets brainliest answer
Answer:
560cm
Step-by-step explanation:
Volume = Length × Breadth × Height
= 10 × 8 × 7
= 560 cm³
Answer:
Step-by-step explanation:
Volume =length x breadth x height
10 x 8 x 7=560cm^3
asap help !!
How much additional interest is earned if $8000 is invested for 7 years at 6.5% when
interest is compounded annually, as compared with simple interest paid at the same
rate?
Answer:
put it in a calculator, 8,000 times whatever number u need
How do you solve a system of equations approximately using tables, without using graphs or equations ? Please I need to figure out how to do it with out graphing or equations
Answer:
Ok, a system of equations means that we have a given number of equations with the same solutions.
If we only have tables, this means that we need to have one table for each equation:
For example, if we are working only with two variables, x and y, in those tables we can see the pints (x, y) that belong to each equation.
Now, a point (x, y) will be a solution of the system of equations only if it belongs to the data table for each equation
This would mean that if we graph those data sets, the graphs will intersect at the point (x, y) that belongs to all the tables of data.
Other way may be using the data in the tables to construct the equations, but you said that you only want to use the tables, so this method can be discarded.
p(a)= .5, p(b)= .4, and p(a and b)= .15. what is p(a OR b)
Answer:
Step-by-step explanation:
Hello
p(A∪B) = p(A) + p(B) - p(A∩B) = 0.5 + 0.4 - 0.15 = 0.9 - 0.15 = 0.75
hope this helps
PLEASE HELP!
Line R is represented by the following equation: x + y = 2
Which equation completes the system that is satisfied by the solution (1, 1)?
2x + y = 2
4x − 2y = 2
2x − 2y = 2
x + y = 4
Answer:
4x - 2y = 2
Step-by-step explanation:
Given that (1, 1 ) is a solution then it must satisfy the equation
Consider the equations given
2x + y = 2 → 2(1) + 1 = 2 + 1 = 3 ≠ 2 ← not True
4x - 2y = 2 → 4(1) - 2(1) = 4 - 2 = 2 ← True
2x - 2y = 2 → 2(1) - 2(1) = 2 - 2 = 0 ≠ 2 ← not True
x + y = 4 → 1 + 1 = 2 ≠ 4 ← not True
Thus
4x - 2y = 2 completes the system.
A box contains 6 red, 3 white, 2 green, and 1 black (total 12) identical balls. What is the least number of balls necessary to take out randomly (without looking) to be sure of getting: at least three the same color?
Answer:
We shall need to pick at least 4 balls to be sure that we are getting balls with the same color
Step-by-step explanation:
Here, we want to know the least number of balls to be taken out of the box to be sure that we have all the three colors represented.
We know there are 12 identical balls, with the least numbers of balls being 1 and 2. Hence, to be able to know we have all the colors of balls represented, we will need to have taken all the less represented ones i.e the 1 and 2 , and this means that the next number of ball which would be taken will confidently confirm that we have taken all the colors since we would have exhausted picking other balls at this point.
So we shall be needing at least 4 balls picked to ensure that we have all the colors represented
What is the angle of rotation from figure A to figure A? Assume that the center of rotation is the origin.
A. 360° clockwise
B. 270° clockwise
C. 180° clockwise
D. 90° clockwise
Answer:
the answer is C. 180°clockwise
$i^5+i^{-25}+i^{45}$[tex]$i^5+i^{-25}+i^{45}$[/tex]
[tex]i^5+i^{-25}+i^{45}[/tex]
Rewrite the term [tex]i^{-25}[/tex]
[tex]=i^5+\dfrac{1}{i^{25}}+i^{45}[/tex]
Expand each term so we have
[tex]=i(i^2)^2+\dfrac{1}{i(i^2)^{12}}+i(i^2)^{22}[/tex]
Use the fact that [tex]i^2=-1[/tex]
[tex]=i(-1)^2+\dfrac{1}{i(-1)^{12}}+i(-1)^{22}[/tex]
Use the fact that [tex](-1)^{a}=1[/tex] when a is an even number
[tex]=i+\dfrac{1}{i}+i[/tex]
Simplify
[tex]=i-i+i[/tex]
[tex]=i[/tex]
Let me know if you need any clarifications, thanks!
Answer:
1/i +2i
Step-by-step explanation:
i^5+i^-25+i^45 i^2=-1
i^4*i +i^-24*i^-1 +i^44 *i
(i²)² i+ (i²)^-12*i^-1+(i²)^22 *i since i²=1
i+i^-1+i=
i+1/i +i=1/i +2i
Um empresário possui um espaço retangular de 100 m por 750 m para corrida. Determine quantos metros percorreu um atleta que deu apenas 6 voltas pelas extremidades do espaço: * (A) 300 (B) 1700 (C) 10200 (D) 75000 (E) 7500
Answer:
(C) 10200m
Step-by-step explanation:
Dizem-nos na pergunta que um homem de negócios tem um espaço retangular de 100 m por 750 m para correr.
O primeiro passo é calcular o perímetro do retângulo.
Perímetro de um rectângulo = 2 (Comprimento × Largura)
Da pergunta,
Comprimento = 100m
Largura = 750m
Perímetro do rectângulo = 2 ( 100 + 750)
= 2(850)
= 1700m
Perímetro do rectângulo = 1700m
Somos questionados na pergunta para determinar quantos metros (Distância) um atleta viajou que tem apenas 6 voltas ao redor das extremidades do espaço.
A distância total percorrida pelo atleta ao correr é calculada como:
6 × perímetro do rectângulo.
= 6 × 1700
= 10200m
Quantos metros percorreu um atleta que deu apenas 6 voltas pelas extremidades do espaço = 10200
I NEED HELP PRONTO PLZZZ HELP ME
Answer:
12 ÷ 4
Step-by-step explanation:
Let's try to solve the given expression to see if it matches with any of the options guven..
[tex] \frac{1}{4}*12 [/tex]
[tex] = \frac{1*12}{4} [/tex]
[tex] = \frac{12}{4} [/tex] (this is equivalent to 12 ÷ 4, which is given in the question)
Thus,
12 ÷ 4 equivalent to [tex] \frac{1}{4}*12 [/tex]
Please help me with this question!! TRIGONOMETRY
Work Shown:
sin(angle) = opposite/hypotenuse
sin(35) = 10/x
x*sin(35) = 10
x = 10/sin(35)
x = 17.434467956211 make sure your calculator is in degree mode
x = 17.4
Answer:
[tex]\boxed{17.4}[/tex]
Step-by-step explanation:
sin [tex]\theta[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
sin (35) = [tex]\frac{10}{x}[/tex]
x = [tex]\frac{10}{sin(35)}[/tex]
x = 17.4344679562...
x ≈ 17.4
HELP I WILL GIVE 50 POINTS AND BRAINLIEST TO WHOEVER ANSWERS FIRST Graph y>1−3x.
Answer:
The last graph
Step-by-step explanation:
This is because when there is a greater than sign, the line on the graph is dotted and the shaded area is facing upwards. I try to remember that when there is a greater than sign or a greater than or equal to sign, the shaded area faces up towards the sky.
Hope this helps. Please inform me if my answer is wrong.
Answer:
The last graph is correct
Step-by-step explanation:
Hello,
First of all, you need to identify the line y = -3x + 1
This is a line so two points are enough to identify it.
-3*0+1 = 1 so (0,1) is a point of this line and
-3*1 + 1 = -2 so (1,-2) is another point of this line.
I attached a graph of this line.
Now, the inequality is y > 1-3x
It means that we are looking for the part of the plan which is (strictly) above this line.
This is not ( [tex]\geq[/tex] ) inequality but a strict equality ( > ) so the points of the line are not included, so the last graph is the correct one.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Simplify.
a3 x a9 over a4
PLEASE HELP!!! ASAP!!!
Answer:
[tex]\frac{\left(a^3\right)\left(a^9\right)}{a^4}=a^8[/tex]
Step-by-step explanation:
[tex]\frac{\left(a^3\right)\left(a^9\right)}{a^4}\\\\= \frac{a^3a^9}{a^4}\\\\=a^3a^9\\\\=a^{3+9}\\\\=a^{12}\\\\=a^{12-4}\\=a^8[/tex]
Answer:
a⁸
Step-by-step explanation:
a³*a⁹/a⁴
Product law:Says that if the base of the number being multiplied is the same, then we can add the exponents
Therefore
a to the power of 3+9/a⁴
a¹²/a⁴
Quotient law:Says that when we divide two numbers with the same base,we can subtract the exponents
Therefore
a to the power of 12-4
a⁸
If f(x)= x/2 -2 and g(x) = 2x² + x - 3, find (f + g)(x).
O A. x²-6
O B. 2x²+ 3/2x +1
O C. 2x² - x/2 +1
O D. 2x² + 3/2 x-5
Answer:
Step-by-step explanation:
Its d
a) A and B are the subsets of a universal set U in which there are n (U) = 54,
n (A) = 32, n (B) = 22 and n (
AB) = 9.
(i) Draw a Venn-diagram to illustrate the above information.
(ii) Find the value of n (AUB).
Step-by-step explanation:
I DON'T KNOW WHICH ANSWER IS CORRECT .
BUT MY ANSWER CAME THIS .
I HOPE IT WILL HELP YOU.
HAVE A NICE DAY.....
Yo tenía $2.00
Mi mamá medio$100
Mi papá medio$100
Mi tío y mi tía me dieron $100
Y yo tenía otros $5.00
Cuanto tenía??
Answer:
$307
Step-by-step explanation:
$2.00 + $100 + $100 + $100 + $5.00 = $307
Marked price of a pen is Rs 20. It is sold at a discount of 15%. Find the selling price?
Answer:
Rs 17Step-by-step explanation:
Solution,
Marked price ( MP ) = Rs 20
Discount % = 15%
Selling price ( SP ) = ?
let's find the discount amount:
Discount amount = Discount % of MP
plug the values
= 15% of 20
Calculate
= Rs 3
Discount amount = Rs 3
Now, let's find the SP
Selling price ( SP ) = MP - discount amount
plug the values
= Rs 20 - Rs 3
Calculate the difference
= Rs 17
Hope this helps..
Best regards!!
Please answer the question in the image below ASAP
Evaluate the following: 3 to the power 2 ÷ (2 + 1). 2 3 4 5
Answer:
3
Step-by-step explanation:
plz help me x+y=7
x=3-y
Answer:
no solution
Step-by-step explanation:
x+y=7
x=3-y
Substitute the second equation into the first
(3-y) +y = 7
Combine like terms
3 = 7
This is never true so there is no solution
Answer:
[tex]\boxed{\mathrm{No \: solution}}[/tex]
Step-by-step explanation:
x + y = 7
Plug x = 3 - y
3 - y + y = 7
Combine like terms.
3 = 7
No solution.