9514 1404 393
Answer:
a^2·b^3
Step-by-step explanation:
Factors of both terms include 'a' to some power, and 'b' to some power. The greatest common factor will use the lowest power of each of these variables.
powers of 'a' are a^2, a^3. Greatest common power is a^2
powers of 'b' are b^5 and b^3. Greatest common power is b^3
The highest common factor of both terms is a^2·b^3.
__
Additional comment
When that is factored out of the sum, you have ...
a^2b^5 +a^3b^3 = a^2·b^3(b^2 +a)
The remaining two terms (b^2+a) have no common factors—as it should be.
-4x - 2 = -22
WILL MARK THE BRAINIEST
Answer:
x = 5
Step-by-step explanation:
-4x - 2 = -22
-4x = -22 + 2
-4x = -20
x = -20 / -4
x = 20 / 4
x = 5
Answer:
x = 5
Step-by-step explanation:
-4x - 2 = -22
add 2 to both of the sides
-4x -2 + 2 = -22 + 2
solve it
-4x = -20
then divide
-4x/4
-20/-4 = 5
x = 5
Sorry if my explanation was bad
1200$ invested at a rate of 3.5% compounded quarterly; 4 years
Step-by-step explanation:
1st year:
(1200 x 3.5 x 1) ÷ 100 = $42
2nd year:
(1242 x 3.5 x 1) ÷ 100= $43.47
3rd year:
(1285.47 x 3.5 x 1) ÷ 100= $44.99≈ $45
4th year:
(1330.47 x 3.5 x 1) ÷ 100= $46.56
Compound interest:
$(42 + 43.47 + 45 + 46.56)
=$ 177.03
Write an equation in standard form of the line that is
graphed. Then find the x- and y-intercepts.
The equation of the line in standard form is
1.) 4x - 5y = -1
2.) 4x - 5y = 9
3.) 5x - 4y = 9
4.) 5x - 4y = -1
The x-intercept is
1.) -9/5
2.) -5/4
3.) 1/5
4.) 9/4
The y-intercept is
1.) -9/5
2.) -5/4
3.) 1/5
4.) 9/4
Answer: equation= 4x-5y= 9
x intercept= 9/4
y intercept= -9/5
Step-by-step explanation: It was right on E2020
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Take points (1, -1) and (-4, -5)
so, slope of line
= -5 + 1 / (-4 -1)
= -4 /(-5)
= 4/5
So, the equation of line is
y+ 1= 4/5 ( x- 1)
y + 1 = 4/5x -4/5
y= 4/5x - 4/5 - 1
y= 4/5x - 9/5
4x - 5y = 9
So, the x- intercept is 9/4 and y- intercept is -9/5.
Learn more about slope here:
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Marcia biked 600 meters on friday. On saturday, she biked 3 kilometers. One sunday she biked 2 kilometers and 700 meters. How many kilometers did Marcia bike over the three days?
Answer:
6.3 km
Step-by-step explanation:
You want to know the total distance represented by segments of 600 m, 3 km, and 2km plus 700 m.
KilometerKilo- is a prefix meaning 1000. A kilometer is 1000 meters. That means we can write the distances as ...
600 m = 0.600 km3 km = 3.000 km2 km + 700 m = 2.700 kmTotalThe total of these distances is found by adding the decimal values in the usual way.
0.600 +3.000 +2.700 = 6.300
Marcia biked 6.3 km over the three days.
Un bidon de legoa contiene 4/5 de su capacidad,el dia de hoy se ha consumido 1/3 de la legia que contenia.Que fraccion de la capacidad del recipiente se ha consumido?
For this case we have the following question:
A disinfectant drum contains 4/5 of its capacity, today 1/3 of the disinfectant it contained has been consumed. What fraction of the capacity of the container has been consumed?
So, we have:
Initial disinfectant content: [tex]\frac {4} {5}[/tex] of its capacity
Consuming[tex]\frac {1} {3}[/tex]of disinfectant means: [tex]\frac {1} {3} * \frac {4} {5} = \frac {4} {15}[/tex]
Thus,[tex]\frac {4} {15}[/tex]of its capacity was consumed.
Answer:
[tex]\frac {4} {15}[/tex] of its capacity was consumed.
Betty sets up a lemonade stand and charges $1 per glass. It cost her $50 to set up the stand. Which function gives the profit, p, she makes by selling g glasses of lemonade?
The number of glasses of lemonade, g, that Betty needs to sell to make a profit, p, if the setup cost her $50 is given by the function
f(g) =
.
Answer:
The correct result would be f(g) = g * $1 - $50.
Step-by-step explanation:
If you would like to find the function that gives the profit Betty makes by selling a number of glasses of lemonade, you can find this using the following steps:
p ... profit
g ... glasses of lemonade
f(g) = p = g * $1 - $50
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Jon ate too many holiday cookies and gained 2.2, point, 2 kilograms in December. Then he went on a diet and lost 1.5, point, 5 kilograms in January. Then he lost another 3.7, point, 7 kilograms in February. Jon wants to know what the total change in his weight was over these three months.
Which of the following equations matches the situation above?
Choose 1 answer:
(Choice A)
2.2+(-1.5)+(-3.7) =
(Choice B)
2.2+1.5-3.7 =
(Choice C)
None of the above
Answer:
-2.9 kg. (loss)
Step-by-step explanation:
Total change in weight = 2.3 - 1.5 - 3.7
Total change in weight = -2.9 kg.
Step-by-step explanation:
The correct equation that represents the total change in Jon's weight over the three months is (Choice A) 2.2 + (-1.55) + (-3.77), which equals a total weight loss of 3.12 kilograms.
The total change in Jon's weight over the three months can be determined by adding his weight gain and subtracting his weight loss for each month. In December, Jon gained 2.2 kilograms, represented as "+2.2". Then he went on a diet and lost 1.55 kilograms in January, represented as "-1.55" and lost another 3.77 kilograms in February, represented as "-3.77".
The correct equation that matches this situation is (Choice A) 2.2 + (-1.55) + (-3.77). This equation takes into account the weight gain and losses, with losses represented by negative numbers. When we perform the calculation, we get:
2.2 - 1.55 - 3.77 = -3.12 kilograms
This means that Jon's total change in weight over the three months is a loss of 3.12 kilograms.
Jones figures that the total number of thousands of miles that an auto can be driven before it would need to be junked is an exponential random variable with parameter .fn. Smith has a used car that he claims has been driven only 10,000 miles. If Jones purchases the car, what is the probability that she would get at least 20,000 additional?
Answer:
0.3678
Step-by-step explanation:
Jones figures that the total number of thousands of miles that an auto can be driven before it would need to be junked is an exponential random variable with parameter 1/20. Smith has a used car that he claims has been driven only 10,000 miles. If Jones purchases the car, what is the probability that she would get at least 20,000 additional miles out of it?
Given that the total number of thousands of miles(X) that an auto can be driven
before it would need to be junked is an exponential random variable with parameter 1/20.
=> X ≅ Exponential(λ= 1/20)
=> f(x) = 1/20 * e^(-x/20) , 0 < x < ∞
=> F(X) = P{X < x} = 1 - e^(-x/20)
The probability that she would get at least 20,000 additional miles out of it.
P{X > 20} = 1-P{X < 20}
P{X > 20} = 1-(1 - e^(-20/20))
= e^(-1)
= 0.3678
can somebody explain how to do this ?
Answer:
-6
Step-by-step explanation:
12(5+2y) = 4y - (6-9y)
60+24y = 4y-6+9y
24y + 60 = 13y - 6
24y-13y = -6-60
11y = -66
y = -6
Answer:
[tex]y=-6[/tex] is the correct answer.
Step-by-step explanation:
The steps involved in solving an algebraic equation in one variable are as stated as:
Step 1: If necessary, simplify the expressions on each side of the equation. This would involve things like removing parentheses, adding like terms, removing fractions.
To remove fractions: Since fractions are another way to write division, and the inverse of divide is to multiply, you remove the fractions by multiplying both sides by the "Least Common Divisor" of all your fractions.
Step 2: Use Addition / Subtraction properties to move the variable term to one side and all other terms to the other side.
Step 3: Use Multiplication / Division properties to remove any values that in front of the variable.
Step 4: Check your answer.
Step-by-Step Solution:
[tex]12\left(5+2y\right)=4y-\left(6-9y\right)\\\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\\\\mathrm{Expand\:}12\left(5+2y\right)\:\:=\:\: 60+24y\\\\\mathrm{Expand\:}4y-\left(6-9y\right)\:\:=\:\: 13y-6\\\\60+24y=13y-6\\\\\mathrm{Subtract\:}60\mathrm{\:from\:both\:sides}\\\\60+24y-60=13y-6-60\\\\24y=13y-66\\\\\mathrm{Subtract\:}13y\mathrm{\:from\:both\:sides}\\\\24y-13y=13y-66-13y\\\\11y=-66\\\\\mathrm{Divide\:both\:sides\:by\:}11\\\\\frac{11y}{11}=\frac{-66}{11}\\\\y=-6[/tex]
Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 464 randomly selected adults showed that 64% of them would erase all of their personal information online if they could. Find the value of the test statistic.
Answer:
The value of the test statistic = 6.03
Step-by-step explanation:
The test statistics for a proportion of the population is the z calculated as follows;
[tex]z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}}[/tex]
Where:
[tex]\hat{p}[/tex] = 0.64
From the rule of large numbers we have, the proportion of adults who will erase their information online will tend towards 1/2 or 0.5 therefore, we have
p = 0.5 as the test
q = 1 - p = 1 - 0.5 = 0.5
n = Sample size = 464
Therefore, z is given by;
[tex]z=\frac{0.64-0.5}{\sqrt{\frac{0.5 \times 0.5}{464}}}[/tex]
= 6.03
The value of the test statistic = 6.03.
if angle y measures 65 degrees how much does x measure?
Answer:
supplementary angles add up to 180°
given y=65° thus...
x+y=180°
x + 65°=180°
x=180°- 65°
x=115°
Answer:
x = 115°
Step-by-step explanation:
x ; y = suplementary =>
=> x + y = 180° } => x = 180° - 65° = 115°
y = 65°
An _____
to a circle is a line, ray or segment in the plane of the circle that intersects
the circle in exactly one point.
Answer:
Tangent
Step-by-step explanation:
A TANGENT to a circle is a line, ray or segment in the plane of the circle that intersect the circle in exactly one point.
An tangent to a circle is a line, ray or segment in the plane of the circle that intersects the circle in exactly one point.
A circle is defined as a plane figure bounded by a single curved line, with every point on that line being equally distant from the center point. Tangents have a unique property where they touch the circle at precisely one point and are perpendicular to the radius drawn to the point of contact. This concept is fundamental to understanding circles and their geometric properties.
Kiara left out reasons from her proof. Which reason best supports the statement ∠3≅∠4 ∠ 3 ≅ ∠ 4 ?
Answer:
Corresponding angles postulate
Step-by-step explanation:
Answer:
coresponding angles postulate
Step-by-step explanation:
just did it on TTM
The points J(-1,-9) and K(5,1) are endpoints of a diameter of circle S. Which equation represents circle S?
Answer:
(x -2)² +(y +4)² = 34
Step-by-step explanation:
The center of the circle is the midpoint of the line segment:
S = (J +K)/2 = ((-1, -9) +(5, 1))/2 = (4, -8)/2 = (2, -4)
The radius of the circle is the distance between the center and either end point. We want the square of the radius for our formula.
r² = (5 -2)² +(1 -(-4))² = 9 +25 = 34
The equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
Using the numbers we have found, the equation for circle S is ...
(x -2)² +(y +4)² = 34
Answer:
(x-2)² + (y+4)²=34
Step-by-step explanation:
I got this answer right on my test :)
Four equivalent forms of a quadratic function are given. Which form displays the zeros of function h?
A.) h(x) = -4(x2 − 4)
B.) h(x) = -4x2 + 16
C.) h(x) = -4(x − 2)(x + 2)
D.) h(x) = -2(2x2 − 8)
The Answer is : C.) h(x) = -4(x − 2)(x + 2)
Final answer:
The quadratic function in form C displays the zeros of the function directly by being in factored form, showing x = 2 and x = -2 as the zeros.
Explanation:
Form C. h(x) = -4(x - 2)(x + 2) displays the zeros of function h because it is in factored form, making it easy to identify the zeros directly as x = 2 and x = -2.
By setting h(x) = 0 in form C, the solution can be seen as:
-4(x - 2)(x + 2) = 0
x = 2, x = -2
Therefore, form C, h(x) = -4(x - 2)(x + 2), directly shows the zeros of the function h to be x = 2 and x = -2.
if 2/3 = a/15, then a =
Step-by-step explanation:
Given
[tex] \frac{2}{3} = \frac{a}{15} [/tex]
Cross multiply ✖
3a = 2 * 15
3a = 30
a = 30/ 3
therefore a = 10
Hope it will help you. :)
Answer:
10
Step-by-step explanation:
because how many times does 3 enter into 15.
it is 5 as 5×3=15 so is that is our known knowledge then doing this to unknown knowledge we will get the answer. 5×2= 10 so we conclude 10/15 = a/15
10
20
30
40
50
60
Which of the following statements is not true?
The range of the two sets is the same.
The difference between the median of each set is 40.
Set B has a higher mean than set A
The mode of set A is 50 less than the mode of set B.
What is the Awnser
Answer:
The range of the two sets are the same
Step-by-step explanation:
A collection of 8 geodes has a mean weight of 14 ounces. A different collection of 12 geodes has a mean weight of 9 ounces. What is the mean weight of the 20 geodes? The mean weight is ounces.
Answer:
The mean weight of the 20 geodes is 11 ounce.
Step-by-step explanation:
Mean weight:
Mean weight is actually the average weight. Add up all weight, then divides by the number objects.
[tex]\textrm{Mean weight}=\frac{\textrm{Total weight}}{\textrm{Total number of objects}}[/tex]
Given that,
A collection of 8 geodes has mean weight of 14 ounce.
Then the total weight of 8 geodes is =(8×14) ounce
=112 ounce
A different collection of 12 geodes has a mean weight of 9 ounce.
Then the total weight of 8 geodes is =(12×9) ounce
=108 ounce
Therefore total weight of (12+8) =20 geodes is = (112+108) ounce
=220 ounce
The average mean of 20 geodes is
[tex]=\frac{220}{20}[/tex]
=11 ounce.
The mean weight of the 20 geodes is 11 ounce.
Answer: The mean weight of the 20 geodes is 11 ounce.
Mean weight means total weight divided by total number of objects.
Given that:
A collection of 8 geodes has mean weight of 14 ounce.
Then the total weight of 8 geodes is = (8×14) ounce = 112 ounce
A different collection of 12 geodes has a mean weight of 9 ounce.
Then the total weight of 8 geodes is = (12×9) ounce = 108 ounce
Therefore total weight of (12+8) =20 geodes is = (112+108) ounce =220 ounce
The average mean of 20 geodes is = [tex]\frac{220}{20}[/tex] =11 ounce.
Hence, the mean weight of the 20 geodes is 11 ounce.
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Use the information given in the diagram to prove that m∠JGI = One-half(b – a), where a and b represent the degree measures of arcs FH and JI.
A circle is shown. Secants G J and G I intersect at point G outside of the circle. Secant G J intersects the circle at point F. Secant G I intersects the circle at point H. The measure of arc F H is a. The measure of arc J I is b. A dotted line is drawn from point J to point H.
Angles JHI and GJH are inscribed angles. We have that m∠JHI = One-half b and m∠GJH = One-halfa by the . Angle JHI is an exterior angle of triangle . Because the measure of an exterior angle is equal to the sum of the measures of the remote interior angles, m∠JHI = m∠JGI + m∠GJH. By the , One-halfb = m∠JGI + One-halfa. Using the subtraction property, m∠JGI = One-halfb – One-halfa.
Answer:
See the attached figure which represents the problem.
Angles GJH and JHI are inscribed angles
Given: ∠GJH = 0.5a and ∠JHI = 0.5b ⇒ inscribed angle theorem
So, the angle JHI is an exterior angle of ΔGJH
AS, the measure of the exterior angle is equal to the sum of the sum of the remote interior angles
So, ∠JHI = ∠GJH + ∠JGI ⇒ by substitution property
∴ 0.5 b = 0.5a + ∠JGI
∴ ∠JGI = 0.5b - 0.5a ⇒ take 0.5 as a common
∠JGI = 0.5 ( b - a ) ⇒ by distributive property.
So, m∠JGI = One-half(b – a)
Answer:
see the explanation
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The measure of the exterior angle is the semi-difference of the arches it covers.
In this problem
m∠JGI is an exterior angle
so
[tex]m\angle JGI=\frac{1}{2}[arc\ JI-arc\ FH][/tex]
we have
[tex]arc\ JI=b^o\\arc\ FH=a^o[/tex]
substitute the given values
[tex]m\angle JGI=\frac{1}{2}(b-a)^o[/tex]
Prove
Remember that
In any triangle the measure of an exterior angle is equal to the sum of the measures of the remote interior angles
so
In the triangle GJH
[tex]m\angle JHI=m\angle JGI+m\ angle GJH[/tex] ----> equation A
Remember that
The inscribed angle is half that of the arc it comprises.
so
[tex]m\angle JHI=\frac{b}{2}[/tex]
[tex]m\angle GJH=\frac{a}{2}[/tex]
substitute in the equation A
[tex]\frac{b}{2}=m\angle JGI+\frac{a}{2}[/tex]
Using the subtraction property
[tex]m\angle JGI=\frac{b}{2}-\frac{a}{2}[/tex]
simplify
[tex]m\angle JGI=\frac{1}{2}(b-a)^o[/tex] ----> proved
In the survey of 891 US adults who follow baseball in a recent year, 184 said that the Boston red sox would win the world series. Construct a 90% confidence interval for the population proportion of US adults who follow baseball who in a recent year said the Boston red sox would win the world series
Answer:
90% confidence interval for the population proportion of US adults who follow baseball
( 0.1842 , 0.22880)
Step-by-step explanation:
Explanation:-
Given data the survey of 891 US adults who follow baseball in a recent year, 184 said that the Boston red sox would win the world series.
The sample proportion [tex]'p' = \frac{184}{891} = 0.20650[/tex]
q = 1-p = 1- 0.20650 =0.79350
Confidence intervals
90% confidence interval for the population proportion of US adults who follow baseball
[tex](p-Z_{\alpha } \sqrt{\frac{pq}{n} } , p + Z_{\alpha } \sqrt{\frac{pq}{n} } )[/tex]
The tabulated value Z₀.₉₀ = 1.645
[tex](0.20650-1.645\sqrt{\frac{0.20650X0.7935}{891} } , 0.20650 + 1.645\sqrt{\frac{0.20650X0.7935}{891} } )[/tex]
(0.20650 - 0.02230 , 0.20650+0.02230)
( 0.1842 , 0.22880)
Conclusion:-
90% confidence interval for the population proportion of US adults who follow baseball
( 0.1842 , 0.22880)
Valerie mixes 5 parts liquid fertilizer for every 9 parts water to make fertilizer for her garden. How many quarts of water and fertilizer does she need to make 20 quarts solution?
Answer:
7.14 Quarts of Liquid Fertilizer and
12.86 Quarts of Water
Step-by-step explanation:
Parts of Liquid Fertilizer Needed=5
Parts of Water Needed=9
Total=9+5=14
Therefore:
Proportion of Liquid Fertilizer Needed=5/14
Proportion of Water Needed=9/14
If she wants to make 20 Quarts of solution
Quarts of Liquid Fertilizer Needed=(5/14)*20=7.14 Quarts
Quarts of Water Needed=(9/14)*20=12.86 Quarts
A metal cube has sides of length 4.5 cm, correct to the nearest 0.5 cm.
The cube is melted down and the metal is used to make small spheres.
Each sphere has a radius of 3 mm, correct to the nearest millimetre.
Work out the greatest number of spheres that could be made from the metal.
828 small spheres can be made from the metal.
Step-by-step explanation:
Side of the cube = 4.5cm
Volume = (a x a x a)
= (4.5 x 4.5 x 4.5)
= 91.125 cubic cm
Radius of the sphere = 3mm = 0.3 cm
Volume of 1 sphere = (4/3) π(r x r x r)
= (4/3) (3.14) (0.3 x 0.3 x 0.3)
= (4/3) (3.14) (0.027)
= 0.34/3
= 0.11 cubic cm
No. of spheres = 91.125/0.11
= 828.4
So, 828 small spheres can be made from the metal.
Henrique drew and labeled the net shown. He also labeled the areas of the left and right triangular sides.
A net has a rectangle at the center and 4 triangles on the sides. The rectangle has a length of 10 inches and height of 4 inches. 2 triangles have a base of 10 inches and a height of 5 inches. The other 2 triangles have an area of 13.6 inches squared.
Use Henrique’s work and finish finding the areas of the faces.
What is the surface area of the rectangular pyramid?
in.2
Answer: [tex]SA=117.2\ in^2[/tex]
Step-by-step explanation:
You need to remember the following:
1. The area of a rectangle can be calculated with the following formula:
[tex]A_r=lw[/tex]
Where "l" is the length and "w" is the width.
2. The area of a triangle can be calculated with the following formula:
[tex]A_t=\frac{bh}{2}[/tex]
Where "b" is the base and "h" is the height.
Use those formulas to find the area of each face.
Area of the rectangle
[tex]A_r=(10\ in)(4\ in)=40\ in^2[/tex]
Area of two triangles
There are two equal triangles. Each one has a base of 10 inches and a height of 5 inches. Then, their areas are equal:
[tex]A_{t1}=A_{t2}=\frac{(10\ in)(5\ in)}{2}=25\ in^2[/tex]
The areas of the other two triangles (which are equal) are:
[tex]A_{t3}=A_{t4}=13.6\ in^2[/tex]
Adding the areas of the faces, you get that the surface area of the rectangular pyramid is:
[tex]SA=40\ in^2+25\ in^2+25\ in^2+13.6\ in^2+13.6\ in^2\\\\SA=117.2\ in^2[/tex]
Answer:
117.2 is the answer
Wesley read a total of 21 books with his book club over 7 months. After belonging to the book club for 22 months, how many books will Wesley have read in all? Solve using unit rates.
Answer:
45 cents
Step-by-step explanation:
A coin tosses 100 times 52 heads and 48 tail what is the probability of flipping a tail on the coin
Answer:
The answer is 48/100 or 12/25
Step-by-step explanation:
Since there is 48 tails and 100 times flipped the answer would be 48/100 and if you ask for the probability of flipping the heads that would be quite the same and its 52/100. So the ANSWER IS 12/25.
The experimental probability of flipping a tail on the coin is:
P = 0.48
How to get the probability?
When we do an experiment N times, the probability of a given outcome is equal to the quotient between the number of times that the outcome of the experiment was the desired one, and the total number of times that we performed the experiment.
In this case, we want to find the probability of flipping a tail.
The experiment is performed 100 times.
48 of these times, the outcome is "tails".
So the experimental probability is:
P = 48/100 = 0.48
If you want to learn more about probability, you can read:
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Find the input of the relation when the output is y= -1.
6x-3y = -15
X= ?
Answer:
2
Step-by-step explanation:
Robin and Evelyn are playing a target game. The object
of the game is to get an object as close to the center as
possible. Each player's score is the number of
centimeters away from the center. Robin's mean is 107,
and Evelyn's mean is 138. Compare the means. Explain
what this comparison indicates in the context of the data.
Who is winning the game? Why?
S
Answer:
Robin's mean score is lower than Evelyn's mean score. This means Robin is winning as you need to minimise your score in order to be as close to the target as possible.
Evelyn because she has a better mean then robins
Evelyn has the greater mean. It indicates that, on average, her objects landed farther away from the center than Robin’s. This difference means that Robin is winning the game.
i hope it helps :)
En el experimento Extraer una carta de una baraja española se consideran estos sucesos: A= 《Salir as 》 B= 《salir bastos 》 Calcula A U B y A interseccion B. ¿Son compatibles A y B ?
Answer:
They are compatible
Step-by-step explanation:
The first thing is to say that an "ace" and that it is a "coarse"
"ace" is card number 1. Group A
"coarse" is a type of the deck, found from number 1 to card 13. Group B
Thus:
Calculate A U B:
1 to 13 + 1 of the other types of cards in the deck.
At intersection B:
1 of "coarse"
Therefore, if group A is compatible with group B
A birthday cake is in the shape of 2 cylinders, one smaller one on top of another larger one. The radius of the bottom layer of cake is (3x 2) and the radius of the top layer of cake is (x 4) . The height for each layer is 6 cm. Determine a simplified expression for the difference in volume between the cake layers.
Answer: 6π(8x^2 + 4x - 12)
Step-by-step explanation:
Given that the radius of the bottom layer of cake is (3x + 2) and the radius of the top layer of cake is (x + 4) . The height for each layer is 6 cm
Volume of a cylinder = πr^2h
Small cylinder
Volume v = π( x + 4 )^2 × 6
v = 6π( x^2 + 8x + 16)
Big cylinder
Volume V = 6π( 3x + 2 )^2
V = 6π( 9x^2 + 12x + 4)
Expression for the difference in volume between the cake layers will be V - v
6π( 9x^2 +12x +4) - 6π( x^2 + 8x +16)
6π(8x^2 + 4x - 12)
A scale factor of 2 is used to enlarge a figure as shown below. A rectangle with an area of 18 inches squared. How many square inches is the area of the enlarged figure? 27 36 54 72
Answer:
36
Step-by-step explanation: All you have to do is multipy the area of the original figure by the scale factor. (18 times 2) which is 36.
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Answer:
Its D.72
Step-by-step explanation: