The GCF of the given expression is:
[tex]5x^2y[/tex]
Step-by-step explanation:The GCF ( greatest common factor ) is the greatest divisor which divides all the terms completely.
Here we have the expression as:
[tex]10x^4y^3-5x^3y^2+20x^2y[/tex]
Here we see that the factors of the first term are:
[tex]10x^4y^3=2\times 5\times x\times x\times x\times x\times y\times y\times y[/tex]
The factor of the second term is:
[tex]-5x^3y^2=-1\times 5\times x\times x\times x\times y\times y[/tex]
and the factor of the third term is:
[tex]20x^2y=2\times 2\times 5\times x\times x\times y[/tex]
i.e. the factor which is common to all the three terms are:
[tex]5\times x\times x\times y=5x^2y[/tex]
Hence, the GCF is: [tex]5x^2y[/tex]
The net of a square pyramid is shown:
What is the surface area of the figure?
A.0.5625 square inch
B.0.7625 square inch
C.1.5625 square inches
D.1.7625 square inches
Which statement describes the transformation of the graph of function f onto the graph of function g?
Lanas avarage step length is about 0.5 meters. How many steps will she need to finish the race? (5 KILMEMETER RACE)
find the slope of the line that passes through the points (2,1) and (-1,-1).
Answer:
all work is shown and pictured
Solve for x: -2.3(x - 1.2) = -9.66
Answer:
x = 5.4Step-by-step explanation:
[tex]-2.3(x-1.2)=-9.66[/tex] use the distributive property a(b + c) = ab + ac
[tex]-2.3x+2.76=-9.66[/tex] subtract 2.76 from both sides
[tex]-2.3x=-12.42[/tex] divide both sides by (-2.3)
[tex]x=5.4[/tex]
i dont understand please helpp asap
Which is the equation for AD?
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Based on the ideal gas law, what is the volume, in liters, of a sample that contains 1,200 moles?
A. 6,000
B. 24,000
C. 36,000
D. 60,000
Из листа картона длиной 35 см и шириной 20 см Маша вырезала четыре квадрата площадью 1 дм2 каждый.Найди площадь остатка картона.Ответ вырази в дм 2
The following tables each show the amount of money, in dollars, in four different bank accounts over time.
Which table best represents an exponential relationship?
Answer with explanation:
The general exponential relationship is
→[tex]y=a*b^x {\text{or}}, x=a*b^y[/tex]
The four tables which is given here, all of them represents exponential relationship because with increase in value of y ,x value increases or vice versa.
The exponential function can be either strictly increasing or strictly decreasing.
Table 1
[tex]\frac{1210}{1100}=\frac{1331}{1210}=\frac{1464.10}{1331}=\frac{1610.51}{1464.10}=1.1[/tex]
In Table 2, Table 3,and table 4, the rate of increase is not constant, it varies that is for different two consecutive y, values their ratio is not constant.
Table 1, best represents the exponential relationship, represented as
[tex]y=1100*(1.1)^x[/tex]
Where, x=1,2,3,4,5
Is 40% bigger than 2/5
What does (r−c)(5) mean about George's new store?
Which is the best estimate for the product of 123.519 × 311,982.21?
A.
372,000,000
B.
37,200,000
C.
3,720,000
D.
372,000
The function f(t)=-5t^2+15t+50 models the approximate height in feet of an object t seconds after it is launched. how many seconds does it take for the object to hit the ground?
PLEASE HELP ASAP!
You have been hired by a museum to make a scale drawing poster of a painting to sell at the gift shop. The painting is 65in high by 105in wide. You are asked to use a 1in = 5in scale. What will the dimensions of your poster be? (2 points)
PLEASE HELP ME ON THIS
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Since it is given that AB ≅ AC, it must also be true that AB = AC. Assume ∠B and ∠C are not congruent. Then the measure of one angle is greater than the other. If m∠B > m∠C, then AC > AB because of the triangle parts relationship theorem. For the same reason, if m∠B < m∠C, then AC < AB. This is a contradiction to what is given. Therefore, it can be concluded that ________.
Answer:
We are given that ΔABC is isosceles with AB ≅ AC. Using the definition of congruent line segments, we know that
✔ AB = AC
.
Let’s assume that angles B and C are not congruent. Then one angle measure must be greater than the other. If m∠B is greater than m∠C, then AC is greater than AB by the
✔ triangle parts relationship theorem
.
However, this contradicts the given information that
✔ side AB is congruent to side AC
. Therefore,
✔ angle B is congruent to angle C
, which is what we wished to prove.
Similarly, if m∠B is less than m∠C, we would reach the contradiction that AB > AC. Therefore, the angles must be congruent.
Step-by-step explanation:
edge 2020
A reflection of the pink triangle is shown. Which transformation makes this reflection?
A) (x', y') = (y, x)
B) (x', y') = (x, -y)
C) (x', y') = (-x, y)
D) (x', y') = (-x, -y)
Answer:
(x, y) → (-x, y).
Step-by-step explanation:
(x, y) → (-x, y). is correct. For example, the point (-3, 5) on triangle 1 goes to (3, 5) on triangle 2.
Suppose that 24% of people own dogs. if you pick two people at random, what is the probability that they both own a dog?
To find the probability that both people randomly picked own a dog, we multiply the probability of one person owning a dog (24%) by itself, resulting in a 5.76% chance that both own a dog.
The question is asking us to calculate the probability that two randomly selected people both own a dog, given that 24% of people own dogs. Since the events (each person owning a dog) are independent, the probability of both events happening is the product of their individual probabilities.
Let's denote the probability of one person owning a dog as P(dog) = 0.24. Then, for two independent people, the probability that both own a dog is [tex]P(dog) \times\ P(dog) = 0.24 \times\ 0.24 = 0.0576.[/tex]
So, the probability that both people picked at random own a dog is 5.76%.
So I've got a math problem I don't understand: simplify (3^ - 2 + 5^ - 2) ^ -1 I got 34 but apparently the answer's 225/34, shouldn't i just multiply -2 and -5 by 1 making it 3^2 + 5^2 which is 34 Pliz help, cramming for a test tmw
Which choice is the conjugate of the expression below when x -5?
4 - x+5
A. 4 + x - 5
B. 4 - x - 5
C. 4 - x + 5
D. 4 + x + 5
The option which is the conjugate of the expression 4 - (x + 5) will be D. 4 + (x + 5).
What is a conjugate?It should be noted that conjugate simply means changing the sign that is between two terms in a binomial.
In this case, the given expression is 4 - (x + 5). Therefore, one simply has to change the subtraction sign. This means one has to has to change the subtraction sign to addition. This will be 4 + (x + 5).
In conclusion, the correct option is 4 + (x + 5).
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The conjugate of the expression 4 - (x + 5) is formed by changing the minus sign to a plus sign, resulting in the expression 4 + x + 5, which corresponds to option D.
Explanation:The conjugate of a binomial expression like 4 - (x + 5) is obtained by changing the sign between the two terms. Hence, the conjugate of this expression would change the subtracted term (-x - 5) to its additive inverse, which is (+x + 5). Therefore, the correct choice is 4 + x + 5, which is option D.
You have 1500 and want to invest it for the future. Bank of westminster has a saving account with an interest rate of 3% compounded yearly, but a local credit union is offering 2% compounded continuously. Which account would give you more money if you leave the money in the account for 10 years? How much more? Show all calculation and label everything
19. A carpenter is putting a skylight in the roof. If the roof measures (10x + 9) by (7x + 7) and the skylight measures (x + 5) by (3x + 3), what is the area of the remaining roof after the skylight is built?
(A). 67x^2 + 115x + 48
(B). 73x^2 + 151x + 78
(C). 70x^2 + 133x + 63
(D). 3x^2 + 18x + 15
20. What is the factored form of the expression?
w^2 + 16w + 64
(A). (w + 8)(w - 8)
(B). (w + 64)(w - 1)
(C). (w + 8)^2
(D). (w - 8)^2
21. What is the factored form of the expression?
d^2 + 22d + 121
(A). (d + 11)^2
(B). (d - 11)^2
(C). (d - 11)(d + 11)
(D). (d - 121)(d - 1)
22. What is the factored form of the expression?
r^2 - 49
(A). (r - 7)(r + 7)
(B). (r + 7)(r + 7)
(C). (r - 7)(r - 7)
(D). (r - 7)(r + 9)
Hence, option (A) is correct.
Hence, option (C) is correct.
Hence, option (A) is correct.
Hence, option (A) is correct.
What is a factor?
A factor is a number that divides another number, leaving no remainder.
In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
There are two methods of finding factors: multiplication and division.
Here given that,
19)
The area of the ceiling is given by [tex](10x+9)(7x+7)[/tex].
[tex]10x(7x)+7(10x)+9(7x)+9(7)\\=70x^2+70x+63x+63\\=70x^2+133x+63\\[/tex]
The area of the skylight is of the form [tex](x+5)(3x+3)[/tex].
[tex]x(3x)+3(x)+5(3x)+5(3)\\=3x^2+3x+15x+15\\=3x^2+18x+15\\[/tex]
We subtract to find out the remaining ceiling:
[tex](70x^2+133x+63)-(3x^2+18x+15)\\=70x^2+133x+63-3x^2-18x-15\\=67x^2+115x+48[/tex]
Hence, option (A) is correct.
20)
For the factor, we find factors of
[tex]8(8)=64\\8+8=16[/tex]
Therefore we have:
[tex](w+8)(w+8)[/tex]
Hence, this is the same binomial twice, we write it as [tex](w+8)^2[/tex]
Hence, option (C) is correct.
21)
Again we look for the factors
[tex]11(11)=121\\11+11=22[/tex]
so it is of the form [tex](d+11)(d+11)[/tex].
Hence this is the same binomial twice, we have [tex](d+11)^2[/tex].
Hence, option (A) is correct.
22)
Factors [tex]-49[/tex] that sum to [tex]0[/tex]
As
[tex]-7(-7)=49\\-7-7=-14[/tex]
So:
[tex](r-7)(r+7)[/tex]
Hence, option (A) is correct.
To know more about the factors
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This graph compares shoe sizes for a group of 80 two-year-old boys and a group of 60 three-year-old boys. Two box and whisker plots showing shoes sizes on a number line from 2.5 to 13.
The upper plot represents the group of 2 year-old boys. For this upper plot, the minimum number is 3, the maximum number is 9.5, the right side of the box is 7.5, the left side of the box is 3.5, and the bar in the box is at 6. The lower plot represents the group of 3 year-old boys.
For this lower plot, the minimum number is 5, the maximum number is 11.5, the right side of the box is 9.5, the left side of the box is 6.5, and the bar in the box is at 8.
About how many more two-year-old boys have a shoe size of 6 or less, compared to the three-year-old boys?
About 25 more two-year-old boys have a shoe size of 6 or less, compared to the three-year-old boys.
How does a boxplot shows the data points?A box plot has 5 data description.
The leftmost whisker shows the minimum value in the data.The rightmost whisker shows the maximum value in the data.The leftmost line in the box shows the first quartile.The middle line shows the median, also called second quartile.The last line of the box shows the third quartile.We're specified that:
For two-years-old boys:
Total count = 80Minimum number = 3Maximum number is 9.5, the right side of the box is 7.5 (third quartile), the left side of the box is 3.5 (first quartile), and the bar in the box is at 6 (second quartile or median).For three-years-old boys:
Total count = 60Minimum number = 5Maximum number is 11.5, the right side of the box is 9.5 (third quartile), the left side of the box is 6.5 (first quartile), and the bar in the box is at 8 (second quartile or median).From data of 2-years-old boys, the size 6 is the median. That means, there are approx 50% boys on either of this 6 shoe size.
50% of 80 is 40.
So 40 two-years-old boys have shoe size 6 or less,
and another 40 two-years-old boys have shoe size 6 or more.
From data of 3-years-old boys, the size 6 is less than 6.5 which is first quartile. First quartile has approx 25% observation on its left, and 75% on right.
Left side is smaller or equal (the data is in ascending order, as visible that first quartile < third quartile) to 6.5, and right is bigger or equal to 6.5.
Now, we can take 6.5 approx 6, and therefore, 25% of three-years-old boys have a shoe size of 6 or less,.
25% of 60 is 60/4 = 15
Thus, approx 15 three-years-old boys have a shoe size of 6 or less.
The difference between both counts is: 40-15 = 25
Thus, about 25 more two-year-old boys have a shoe size of 6 or less, compared to the three-year-old boys.
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What is the length of the altitude drawn to the hypotenuse? The figure is not drawn to scale.
a) [tex] \sqrt{70} [/tex]
b) 70
c) [tex] \sqrt{19} [/tex]
d) 19
Answer:
The correct option is A) 70
Step-by-step explanation:
HELP PLS with this geometry problem
The nth term of the sequence
-2, 1, 4, 7, 10,...
is given by the formula
A) an = n - 3
B) an = 3n - 3
C) an = n - 5
D) an = 3n - 5
Aubrey says that the product 10x10x10x10 and 10x-10x-10
Answer:
Aubrey says that the product of 104 and 10–2 is 10–8. Is she correct? If not, explain why.
Yes, she is correct.
No, the exponent should be positive 8.
No, she multiplied the exponents instead of adding them.
No, she multiplied the exponents instead of subtracting them.
Step-by-step explanation:
C. No, she multiplied the exponents instead of adding them.
Answer this please and thank you
If DE=4x-1, EF=9, and DF=9x-22, find the value of x.
Question
If DE = 4x-1, EF = 9, and DF = 9x-22, find the value of x.Answer
x = 6
. A toy company is selling novelty soccer balls of all sizes. If one soccer ball, with a radius of 5 cm, is placed in a box with all equal dimensions, as shown below, and the ball is touching the sides of the box, approximately how much empty space is inside the box?
Answer:
The volume of the empty space is [tex]476.67\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the empty space inside the box is equal to the volume of the box minus the volume of the soccer ball
step 1
Find the volume of the box
The length side of the cube is equal to the diameter of the soccer ball
Let
b -----> the length side of the box
we have
[tex]b=2r=2(5)=10\ cm[/tex]
The volume of the box is equal to the volume of a cube
[tex]V=b^{3}[/tex]
substitute
[tex]V=10^{3}[/tex]
[tex]V=1,000\ cm^{3}[/tex]
step 2
Find the volume of the soccer ball
The volume of the sphere (soccer ball) is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=5\ cm[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]V=\frac{4}{3}(3.14)(5)^{3}[/tex]
[tex]V=523.33\ cm^{3}[/tex]
step 3
Find the volume of the empty space
[tex]V=1,000-523.33=476.67\ cm^{3}[/tex]
The sum of 19.3 and a number is 30.4. which eqation can be used to sole the problem?
Answer:
19.3+n+30.4 (B on edg)
Step-by-step explanation: