(02.06 LC)
The figure below shows parallel lines cut by a transversal:
Which statement is true about ∠1 and ∠2?
A. ∠1 and ∠2 are complementary because they are a pair of corresponding angles.
B. ∠1 and ∠2 are congruent because they are pair of corresponding angles
C.∠1 and ∠2 are complementary because they are a pair of alternate interior angles.
D.∠1 and ∠2 are congruent because they are pair of alternate interior angles.
Answers
25 characters
Related Questions
Suppose i pick a jelly bean at random from a box containing two red and ten blue ones. i record the color and put the jelly bean back in the box. if i do this three times, what is the probability of getting a blue jelly bean each time? (round your answer to three decimal places.)
Answers
Each time the probability of picking blue is the same, since put back in the box whatever jelly bean we pick
P(blue, blue, blue) = P(blue) × P(blue) × P(blue) = 0.833×0.833×0.833=0.579
Answer: 0.579
16% of what number is 17 ?
Answers
(16 / 100) x 17 =
(16 x 17) / 100 =
272 / 100 =
The answer : 2.72
Step-by-step explanation:
To find out what 16% of 17 is, we create a cross multiply equation
16/100=17/x
Cross multiply
(16 * x = 16x)
(100 * 17 = 1700)
16x = 1700
1700/16 = 106.25
The city of Lakeside has a population of 22,000 people and is decreasing at a rate of 1.5% The population in 3 years would be
A)Approximately 21,000 people
B)None of the choices are correct
C)Approximately 20,000 people
D)Approximately 25,000 people
E)Approximately 19,000 people
Answers
P=Ae^rt
P ?
A 22000
R -0.015
T 3years
P=22,000×e^(−0.015×3)
p=21,032
So the answer is
A) Approximately 21,000 people
Martin is asked to find the probability of getting one head and three tails on for coin tosses this is a simple event
Answers
HTTT
THTT
TTHT
TTTH
Assuming the coin is a fair coin, we have:
Probability of tossing head is 0.5
Probability of tossing tail is 0.5
Probability of tossing the coin four times for each outcome combination listed above is
HTTT = 0.5×0.5×0.5×0.5 = 0.0625
THTT = 0.5×0.5×0.5×0.5 = 0.0625
TTHT = 0.5×0.5×0.5×0.5 = 0.0625
TTTH = 0.5×0.5×0.5×0.5 = 0.0625
Hence, probability of getting three tails and one head from 4 tossing is
4×0.0625 = 0.25
Answer: False
Martin is asked to find the probability of getting one head and three tails on for coin tosses this is a simple event.
A. True
B. False
In how many ways can 2 singers be selected from 4 who came to an audition?
A. 6
B. 2
C. 12
D. 4
In a batch of 280 water purifiers, 12 were found to be defective. What is the probability that a water purifier chosen at random will be defective? Write the probability as a percent. Round to the nearest tenth of a percent if necessary.
A. 4.3%
B. 5.6%
C. 95.7%
D. 71.8%
Answers
Second part
12 * 100
---------- = 4.3 %
280
Answer: A. 6
A. 4.3%
Step-by-step explanation:
The total number of singers = 4
To choose singers = 2
The number of ways to choose 2 singers from 4= [tex]^4C_2=\frac{4!}{2!(4-2)!}=3\times2=6[/tex]
Hence, A is the right option.
The total number of water purifiers T= 280
The number of defective purifiers D= 12
The probability that a water purifier chosen at random will be defective (in percent)=[tex]\frac{\text{T}}{\text{D}}\times100[/tex]
[tex]=\frac{12}{280}\times100\\=0.042857\times100\\=4.2857\%\approx4.3\%[/tex]
Hence, A is the right option.
Which rate is the lowest price?
$6.30 for 9
$5.50 for 5
$4.20 for 7
$0.80 each
Answers
This problem can be solved by dividing the pay by the number of items.
$6.30 / 9 = $0.70
$5.50 / 5 = $1.10
$4.20 / 7 = $0.60
$0.80 / 1 = $0.80
This shows that for the third option, $4.20 for 7, the rate per item is the lowest.
Identify the value of y
Answers
24^2 = 18 * (18 +y)
576 = 324+18y
252 =18y
y = 252/18 =14
y = 14
The value of y is 14.
What is a circle?'A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant'
According to the given problem,
We know,
⇒ 18 ( 18 + y ) = 24²
⇒ 324 + 18y = 576
⇒ 18y = 576 - 324
⇒ 18y = 252
⇒ y = 252/18
⇒ y = 14
Hence, we can conclude, the value of y is 14.
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A new machine can make 10,000 aluminum cans three times faster than an older machine. with both machines working, 10,000 cans can be made in 9 hours. how long would it take the new machine, working alone, to make the 10,000 cans?
Answers
Since the new machine is three times faster, it takes (12 hours) / 3 = 4 hours for the new machine to make 10,000 cans alone.
Let's denote the time it takes the older machine to make 10,000 cans as "t" hours.
The new machine can make 10,000 cans three times faster than the older machine, which means it takes "t/3" hours for the new machine to make 10,000 cans.
When both machines are working together, they can make 10,000 cans in 9 hours.
Now, we can set up an equation based on the work rates of the two machines:
Work rate of the older machine + Work rate of the new machine = Combined work rate
The work rate is the amount of work (number of cans made) per unit of time (hours).
For the older machine:
Work rate of the older machine = 10,000 cans / t hours
For the new machine:
Work rate of the new machine = 10,000 cans / (t/3) hours
Combined work rate when both machines work together:
Combined work rate = 10,000 cans / 9 hours
Now, the equation becomes:
10,000 cans / t hours + 10,000 cans / (t/3) hours = 10,000 cans / 9 hours
To solve for "t," we can start by finding a common denominator for the fractions on the left side of the equation:
t/3 is the same as (1/3)t. So the equation becomes:
10,000 cans / t hours + 10,000 cans / (1/3)t hours = 10,000 cans / 9 hours
Now, to combine the fractions, we find the common denominator, which is 3t:
(3t * 10,000 cans) / (3t * t hours) + (t * 10,000 cans) / (3t * t hours) = 10,000 cans / 9 hours
(30,000t + 10,000t) / (3t^2 hours) = 10,000 cans / 9 hours
Combine the terms on the left side of the equation:
40,000t / (3t^2 hours) = 10,000 cans / 9 hours
Now, cross-multiply to solve for "t":
40,000t * 9 hours = 10,000 cans * 3t^2 hours
360,000t hours = 30,000t^2 hours
Now, rearrange the equation:
30,000t^2 - 360,000t hours = 0
Divide by 30,000t to simplify the equation:
t - 12 = 0
Now, solve for "t":
t = 12 hours
Therefore, it takes the older machine 12 hours to make 10,000 cans.
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Julio paid 1.3 times his normal hourly rate for each he works over 31 hours in a week. Last week he worked 35 hours and earned $448.88. What is julios normal hourly rate ?
Answers
All the time worked past 31 hours gets paid 1.3 times.
He worked 4 hours at such a rate.
31+4(1.3)
31+5.2
=36.2
Paid as if he worked 36.2 at a normal rate.
To find his normal wage, divide 448.88 by 36.2
448.88/36.2
=12.40
His normal wage is $12.40.
To check:
12.40*31=384.40
12.40*1.3=16.12
16.12*4=64.48
384.40+64.48
=$448.88
Hope this helps.
-Benjamin
Let his hourly rate is x
then:
31x + (35-31)*1.3x = 448.88
solve for x:
31 x + 5.2x = 448.88
36.2 x =448.88
x = 12.4$
not fair hourly rate by the way ;)
For a fixed amount of a gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. At a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 in.3. Which function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi?
Answers
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
Let
x-------> the pressure in PSI
y------> the volume of the gas in cubic inches
In this problem we have the point [tex](30,600)[/tex]
so
[tex]x=30\ psi\\y=600\ in^{3}[/tex]
Find the constant k
[tex]y*x=k[/tex]
substitute the values of x and y
[tex]600*30=k[/tex]
[tex]k=18,000\ lb*in[/tex]
the equation is
[tex]y=18,000/x[/tex]
therefore
the answer is
[tex]y=18,000/x[/tex]
Answer:
[tex]y=\frac{18000}{x}[/tex]
Step-by-step explanation:
Let the volume of gas be y
Let the pressure be x
Since we are given that the volume of the gas is inversely proportional to its pressure.
⇒[tex]y \propto \frac{1}{x}[/tex]
Let the proportionality be k
So, [tex]y=\frac{k}{x}[/tex] ---A
Now we are given that At a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 cubic inches
So, substitute x = 30
y = 600
[tex]600=\frac{k}{30}[/tex]
[tex]600 \times 30=k[/tex]
[tex]18000 =k[/tex]
Substitute the value of k in A
So, [tex]y=\frac{18000}{x}[/tex]
Hence function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi is [tex]y=\frac{18000}{x}[/tex]
A wire is first bent into the shape of a rectangle with width
4in and length 14in. Then the wire is unbent and reshaped into a square. What is the length of a side of the square?
Answers
Area of a rectangle=L*W= 14*4=56
Then divide that by 4 since a square has 4 equal sides
56/4=14
The length of a side of a square is 14 in
Meike earned $1565 in tips while working a summer job at a coffee shop. She wants to use this money to take a trip to Europe next summer. If she places the money in an account which pays 6.5% compounded continuously, how much money will she have in nine months?
Answers
HELPPP Plzzzzzzzzzz ASAP
Use Addition of Composite Figures to find the total shaded regions.
1) Find the shaded area. Round your answer to the nearest tenth, if necessary.
Answers
Determine the standard variation of the data below. (1, 2, 3, 4, 5)
Answers
μ = (1 + 2 + 3 + 4 + 5) / 5 = 3
Then, we calculate for the summation of the squares of differences of these numbers from the mean, S
S = (1 - 3)² + (2 - 3)² + (3 - 3)² + (4 - 3)² + (5 - 3)²
S = 10
Divide this summation by the number of items and take the square root of the result to get the standard deviation.
SD = sqrt (10 / 5) = sqrt 2
SD = 1.41
Thus, the standard deviation of the given is equal to 1.41.
Answer:
So basically sqrt of 2...
Step-by-step explanation:
(02.05 MC)
Triangle ABC is transformed to obtain triangle A′B′C′:
Which statement is correct for Triangle ABC. and Triangle A prime B prime C prime.?
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 6. and then rotating it about the origin by 90 degrees
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 180 degrees
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 90 degrees
Triangle ABC is similar to triangle A prime B prime C prime. because triangle A prime B prime C prime. is obtained by dilating Triangle ABC.by a scale factor of 1 over 4. and then rotating it about the origin by 180 degrees
Answers
A store's cost for a stereo was $27. The markup was 75%. A customer purchased it on sale at 40% off the markup price. What was the purchase price of the stereo
Answers
if we take 27 to be the 100%, what's 175% of that?
[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 27&100\\ x&175 \end{array}\implies \cfrac{27}{x}=\cfrac{100}{175}\implies \cfrac{27\cdot 175}{100}=x\implies \boxed{47.25=x}[/tex]
alrite, then a customer showed up and found it on sale, 40% off that price, so if you take out 40% from the 100%, the price the customer found it at is the 60%, 100-40, of the current price of 47.25
so, if 47.25 is the 100%, what's 60% of that?
[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 47.25&100\\ x&60 \end{array}\implies \cfrac{47.25}{x}=\cfrac{100}{60}[/tex]
solve for "x".
Three times the difference of a number x and seven is twenty-three minus the sum of three times a number x and two. what is the value of x?
Answers
3x - 21 = 23 - 3x - 2 =
3x - 21 = -3x + 21
3x + 3x = 21 + 21
6x = 42
x = 42/6
x = 7 <==
The required value of x is 7.
What are linear equation?A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.
Now the given statement is,
Three times the difference of a number x and seven is twenty-three minus the sum of three times a number x and two.
So converting them into numerical form,
the difference of a number x and seven = x - 7
∴ Three times the difference of a number x and seven = 3(x - 7)
Similarly,
the sum of three times a number x and two = 3x + 2
∴ Twenty-three minus the sum of three times a number x = 23 - (3x + 2)
Therefore, the required equation is,
3(x - 7) = 23 - (3x + 2)
Expanding the brackets we get,
3x - 21 = 23 - 3x - 2
or, 3x - 21 = 21 - 3x
Taking alike terms together,
3x + 3x = 21 + 21
or, 6x = 42
Dividing both side by 6 we get,
x = 7
which is the required value of x.
Thus, The required value of x is 7.
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The function f(x) = –x2 + 16x – 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles sold, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points
please help
Answers
f is a quadratic function, which means it's graph is a parabola.
Notice that the coefficient of [tex] x^{2} [/tex] is negative, so the parabola opens downwards.
the x-coordinate of a parabola is always determined by the formula: [tex] -\frac{b}{2a} [/tex]
where a is coefficient of the [tex] x^{2} [/tex] term, and b is the coefficient of the x term.
Thus, x-coordinate of the vertex of the graph of f is :
[tex]-\frac{b}{2a}=-\frac{16}{2(-1)}=8[/tex]
the y-coordinate of the vertex is f(8)=-8*8+16*8-60=4.
The vertex is (8, 4).
This means that the maximum daily profit is when exactly 8 candles are sold.
B.
The x-intercepts are the values of x such that f(x)=0,
so to find these values we solve:
[tex]- x^{2} +16x-60=0[/tex]
[tex]x^{2}-16x+60=0[/tex]
complete the square:
[tex]x^{2}-2*8x+64-64+60=0[/tex]
[tex](x-8)^{2}-4=0[/tex]
[tex](x-8)^{2}= 2^{2} [/tex]
so x-8=2 or x-8=-2
the roots are x=10 and x=6, are the roots.
This means that when the shop sells exactly 6 or 10 candles, it makes no profit.
Final answer:
The vertex of the profit function f(x) = -x^2 + 16x - 60 is (8, 4), meaning the maximum profit is $4 when 8 candles are sold. The x-intercepts are (6,0) and (10,0), indicating zero profit when either 6 or 10 candles are sold.
Explanation:
The function given is a quadratic equation of the form f(x) = ax2 + bx + c, where the constants are a = -1, b = 16, and c = -60. To find the vertex of the parabola, we can use the formula -b/(2a) for the x-coordinate of the vertex.
Calculate the x-coordinate of the vertex: x = -b/(2a) = -16/(2 * -1) = 8.
Substitute x = 8 into the original function to find the y-coordinate: f(8) = -(8)2 + 16(8) - 60 = -64 + 128 - 60 = 4.
The vertex is at the point (8, 4). In the context of the problem, this point represents the maximum daily profit of $4, which occurs when 8 candles are sold.
To determine the x-intercepts, we set f(x) to zero and solve for x, which represents the number of candles sold when the profit is zero.
Set the function equal to zero and solve for x: 0 = -x2 + 16x - 60.
Apply the quadratic formula x = [-b ± sqrt(b2 - 4ac)]/(2a) to find the x-intercepts. In this case, a = -1, b = 16, and c = -60.
Calculate the discriminant, sqrt(162 - 4(-1)(-60)) = sqrt(256 - 240) = sqrt(16) = 4.
Find the two x-intercepts: x = [16 ± 4]/(2 * -1) which yields x = 6 and x = 10.
The x-intercepts (6,0) and (10,0) indicate the number of candles sold at which the profit would be zero, specifically at 6 and at 10 candles sold.
A school director must randomly select 6 teachers to participate in a training session. There are 34 teachers at the school. In how many different ways can these teachers be selected, if the order of selection does not matter?
Answers
where [tex]C(n, r)= \frac{n!}{r!(n-r!)} [/tex]
n! meaning 1*2*3*....*(n-1)*n
According to this, the selection of 6 teachers out of 34, can be carried out in C(34, 6) many different ways.
[tex]C(34, 6)= \frac{34!}{6!(34-6!)}=\frac{34!}{6!(28!)}= \frac{34*33*32*31*30*29*28!}{6!28!}= \frac{34*33*32*31*30*29}{6!}[/tex]
[tex]=\frac{34*33*32*31*30*29}{6*5*4*3*2*1}= 34*11*4*31*29=1,344,904[/tex]
The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Check all that apply.
0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x – 24 = 0
x2 + 2x – 48 = 0
x2 + (x + 2)2 = 24
x2 + (x + 2)2 = 100
Please help me quickly, I really need the help. I'll even mark brainiest if you do it correctly. I really need this and I need whoever does this to pay attention to the whole "Check all that apply". I'm adding the picture below.
Answers
A = 0.5 base x height
base = x , height = x+2
A = 0.5 x(x+2) = 24 sq feet
1) 0.5 x(x+2) = 24 (A)
2) x^2 + 2x - 48 = 0 (D)
To check the rest un-wrap the bracket:
x^2 + (x+2)^2 = 24
x^2 + x^2 + 4 + 4x = 24
2x^2 + 4x - 20 = 0
x^2 + 2x - 10= 0 (NO)
Likewise:
x^2 + (x+2)^2 = 100
x^2 + x^2 +4 + 4x = 100
2x^2 + 4x + 4 = 100
2x^2 + 4x - 96 = 0
3) x^2 + 2x - 48 = 0 (F)
To sum up: that's what apply:
1) 0.5 x(x+2) = 24 (A)
2) x^2 + 2x - 48 = 0 (D)
3) x^2 + 2x - 48 = 0 (F)
The equation that can be used to find the lengths of the legs of the triangle is [tex]\rm 0.5(x)(x + 2) = 24[/tex]
Given thatThe area of the right triangle shown is 24 square feet.
We have to determine
Which equations can be used to find the lengths of the legs of the triangle?
According to the question
From the given figure the base of the triangle is x.
And the height of the triangle is (x+2).
What is the area of a triangle?The area of the triangle is given by half the product of the height and base.
[tex]\rm Area = \dfrac{1}{2} \times base \times height\\ [/tex]
Substitute all the values in the formula;
[tex]\rm Area \ of \ right \ triangle= \dfrac{1}{2} \times base \times height\\ \\ \rm 24= \dfrac{1}{2} \times x \times (x+2)\\\\ \rm 0.5(x)(x + 2) = 24[/tex]
The equation can be used to find the lengths of the legs of the triangle is [tex]\rm 0.5(x)(x + 2) = 24[/tex].
Hence, the equation can be used to find the lengths of the legs of the triangle is [tex]\rm 0.5(x)(x + 2) = 24[/tex].
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(02.03 MC)
The figure shows two triangles on a coordinate grid:
What set of transformations is performed on triangle ABC to form triangle A'B'C'?
A.. A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units down
B. A translation 5 units down followed by a 180-degree counterclockwise rotation about the origin
C. A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units to the right
D. A translation 5 units to the right, followed by a 270-degree counterclockwise rotation about the origin
Answers
i know for sure it isnt C or D
I don't understand this and would appreciate an explanation as well :)
Solve for the variable in the equations below.
Round your answers to the nearest hundredth.
Do not round any intermediate computations.
e^x = 6
4^(y+3) = 3
[tex]e^x = 6[/tex]
[tex]4^y^+^3 = 3 [/tex]
Answers
[tex]e^{x}=6[/tex]
and
[tex]4^{y+3}=3[/tex]
First equation.
Take natural log of each side.
[tex]ln(e^{x})=ln(6)\\xln(e)=ln(6)\\ x=ln(6)=1.7918[/tex]
Note that ln(e) = 1 by definition.
Answer: x = 1.79 (nearest hundredth)
Second equation.
Take natural log of each side.
[tex]ln(4^{y+3})=ln(3)\\ (y+3)ln(4)=ln(3)\\ y+3= \frac{ln(3)}{ln(4)} =0.7925\\y=0.7925-3=-2.2075[/tex]
Answer: y = -2.21 (nearest hundredth)
5v + 7f =28.70 if f is 2.85
Answers
5v+7(2.85)=28.70
5v+19.95 = 28.70
5v = 8.75
v = 1.75
First, let's write the problem.
[tex]5v+7\left(2.85\right)=28.7[/tex]
Multiply [tex]7[/tex] with [tex]2.85[/tex].
[tex]5v+19.95=28.7[/tex]
Subtract [tex]19.95[/tex] from both sides.
[tex]5v+19.95-19.95=28.7-19.95[/tex]
[tex]5v=8.75[/tex]
Divide both sides by [tex]5[/tex].
[tex]\frac{5v}{5}=\frac{8.75}{5}[/tex]
[tex]v=1.75[/tex]
Let me know if you have any questions regarding this problem!
Thanks!
-TetraFish
Solve the equation: 2.6 = -0.2t
Answers
2.6 / -0.2 = t
-13 = t <==
T=2.6/-0.2=-13
T= -13
Hope this helps!
I need to find the answer to these questions in about 10 minutes or I'm screwed. please help me out.
Answers
For the second figure, the construction of the above figure in the circle represents how to find the intersection of the perpendicular bisectors of triangle ABC.
For the third figure, the statement that is demonstrated in the in line P intersecting line m perpendicularly is the set of points equidistant from the endpoints of a line segment is the perpendicular bisector of the segment.
State the Midpoint formula?
How are the midpoint formula and the Distance formula alike? How are they different?
Give a real-world example that could be addressed using the distance formula.
Give a real-world example that could be addressed using the midpoint formula.
Answers
Mid-point formula is given by: [tex][ \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}] [/tex]
The distance formula is given by: [tex] \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} [/tex]
The two formula are alike because they both need the information of two coordinate points
They are different because the mid point formula is adding up then divide by two, whereas the distance formula is subtracting then square the answer.
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Real life problem involving distance formula:
Plane A is spotted on a radar with cartesian coordinate (450, 640).
Plane B is spotted on the same radar with cartesian coordinate (350, 540)
Work out the distance between plane A and plane B.
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Real life problem involving mid point formula
Ms. Holland arranges a treasure hunt for a group of scouts. She marks two points, C and D, with cartesian coordinate (-5, 6) and (7, 10) respectively. The clue is that the treasure is buried in the middle point between C and D. Work out the coordinate where the treasure is buried.
Find the length of the diameter of a sphere with a surface area of 452.39^2 ft.
Answers
surface area = 4*pi*r^2
using 3.14 for pi
452.39 = 4*3.14*r^2=
452.39=12.56* r^2
r^2 = 452.39/12.56 = 36.0
sqrt(36) = 6= r
diameter = 2r = 6*2= 12
diameter = 12 feet
What is 5 plus 5 minus 5 divided by 5 and then multiplied by 5?
Answers
So you have 5+5-5/5(5)
We will divide first:
5+5-1(5)
Then multiply:
5+5-5
Then add and subtract from left to right:
10-5=5
Hope that helps.
Answer:
45Step-by-step explanation:
[tex](5+5-5:5)\cdot5\\\\\text{Use PEMDAS}\\\\\text{P Parentheses first}\\\text{E Exponents}\\\text{MD Multiplication and Division (left-to-right)}\\\text{AS Addition and Subtraction (left-to-right)}\\\\=(5+5-1)\cdot5\\\\=(10-1)\cdot5\\\\=9\cdot5\\\\=45[/tex]
Which is a sum of cubes? a3 + 18 a6 + 9 a9 + 16 a12 + 8
a3 + 18
a6 + 9
a9 + 16
a12 + 8
Answers
Answer: [tex]a^{12}+8[/tex]
Step-by-step explanation:
let's check all the expressions
1. [tex]a^3+18[/tex]
here 18 is not a perfect cube.
2. [tex]a^6+9[/tex]
here 9 is not a perfect cube.
3.[tex]a^9+16[/tex]
here 16 is not a perfect cube.
4.[tex]a^{12}+8[/tex]
here 8 is a perfect cube, thus we can write above expression by using laws of exponents as
[tex](a^4)^3+2^3[/tex]
Thus, [tex]a^{12}+8[/tex] is a sum of cubes.
Apply the distributive property to factor out the greatest common factor. 45+75=
Answers
15 * 5 = 75
15( 3 + 5)