Select the GCF of these numbers. 2^5 · 5· 11 and 2^3· 5^2 · 7
Answers
The greatest common factor (GCF) of the expressions 2^5 · 5· 11 and 2^3· 5^2 · 7 is 2^3 · 5, or 40. This is determined by comparing the exponents of the common base terms in both expressions and selecting the lowest exponents.
Explanation:The student's question is about finding the greatest common factor (GCF) of two different mathematical expressions, namely: 2^5 · 5· 11 and 2^3· 5^2 · 7. In this context, 'GCF' refers to the greatest number that is a factor of two or more numbers. For these expressions, we will look at the shared factors of the two expressions.
Steps to find the GCF:
Compare the exponents of the common base terms in the two expressions. Here, the common base terms are '2' and '5'. In the first expression, '2' is raised to the power of '5' and '5' is raised to the power of '1'. In the second expression, '2' is raised to the power of '3' and '5' is raised to the power of '2'. For each base, select the lowest exponent. Therefore, for base '2', we select '3' as the exponent and for base '5', we select '1'. Therefore, the GCF of the two expressions is 2^3 · 5 or 40. Learn more about Greatest Common Factor here:
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Related Questions
Rate of Change , you are given the dollar value of a product in 2004 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value (v) of the product in terms of the year
(Let t=0 represent 2000.)
2004 value= $156 with $4.50 increase per year
...?
Answers
Linear equation:v = 4.5t +138this means the product had value of $138 in 2000
Answer:
The linear equation is v = 4.5t +138
The product had value of $138 in 2000.
Step-by-step explanation:
In 2004, dollar value(v) = $156 and rate of change (m) = $4.50
The linear equation is in the form of y = mx + b, where "m" is slope or rate of change, b is the y-intercept.
We can rewrite the equation as v = m(t) + b.
Now let's find the value of b, when t = 4, m = 4.5, v = 156
156 = 4.5(4) + b
b = 156 - 4.5(4)
b = 156 - 18
b = 138
So, the linear equation is v = 4.5t +138
When t=0, the dollar value (v) = 4.5(0) + 138
v = $138
So, the product had value of $138 in 2000
Identify the converse of the following conditional:
If a point is in the fourth quadrant, then its coordinates are negative.
A. If a point is in the fourth quadrant, then its coordinates are negative.
B. If the coordinates of a point are not negative, then the point is not in the fourth quadrant.
C. If a point is not in the fourth quadrant, then the coordinates of the point are not negative.
D. If the coordinates of a point are negative, then the point is in the fourth quadrant.
Answers
The converse of the conditional is "If the coordinates of a point are negative, then the point is in the fourth quadrant."
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Identify the slope and y-intercept.
y=2x−8
Enter your answers in the boxes in simplest form.
M=
B=
Answers
How many pounds does 64 ounces weigh?
Answers
Answer:
4 lbs
Step-by-step explanation:
There are 16 ounces in a pound, so divide 64 by 16 to get the number of pounds. 64 ÷ 16 = 4 lbs
11 less than the product of a number y and -2 is z
Answers
What are the zeros of the polynomial function: f(x) = x3 + x2 – 6x ? ...?
Answers
x³ + x² − 6x = 0
x (x² + x − 6) = 0
x (x − 2) (x + 3) = 0
x = 0, 2, −3
f(x) = 2x³ + 5x² + 6x − 4
f(−x) = −2x³ + 5x² − 6x − 4
Let's look at signs only and how many sign changes there are:
f(x) = + + + −
1 sign change ----> 1 positive root
f(−x) = − + − −
2 sign changes ----> 2 or 0 negative roots
Min. number of real roots = 1 ----> max. number of complex roots = 2
Max. number of real roots = 3 ----> min. number of complex roots = 0
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Find the measure of
Answers
Suppose you deposited $10 into your savings account each month, as indicated in the table. Your account pays 4%, compounded monthly. How much will you have in your account at the end of 15 years? a. $2,908 c. $3,668 b. $2,461 d. $1,800 Please select the best answer from the choices provided
Answers
Ahmed is taking orders for lunch. A slice of pizza cost $2 and a chicken sandwich costs $3. He collects $24 for the group of 10 people.How many people ordered a chicken sandwich?
Answers
p+c=10
solve for p: p= 10-c
Substitute for p: 20-2c+3c=24
add the Cs: 20+c=24
Subtract: c=4
So four people ordered a chicken sandwich.
1.5x+2.5y=21.50
x+y=9
8 people ordered chicken sandwich
Enter the slope-intercept equation of the line that has slope -6 and y-intercept (0, 2).
Answers
so ur equation in slope intercept form with a slope of -6 and a y int of 2 is :
y = -6x + 2
The slope-intercept form of equation of the line that has slope -6 and y-intercept (0, 2) is y=-6x+2.
What is the slope intercept form?The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.
The standard form of the slope intercept form is y=mx+c.
Given that, the line that has slope -6 and y-intercept (0, 2).
The y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x=0.
Here, m=-6 and c=2
Substitute m=-6 and c=2 in y=mx+c, we get
y=-6x+2
Therefore, the slope-intercept form of equation of the line that has slope -6 and y-intercept (0, 2) is y=-6x+2.
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A flower vase, in the form of a hexagonal prism, is to be filled with 512 cubic inches of water. Find the height of the water if the wet portion of the flower vase and its volume are numerically equal.
Answers
Height of water in hexagonal prism vase = 384 inches, given equal volume of water and wet portion.
Let's denote the height of the water in the vase as [tex]\( h \)[/tex] inches.
The volume of a hexagonal prism can be calculated using the formula:
[tex]\[ V = \frac{3\sqrt{3}}{2}a^2h \][/tex]
where [tex]\( a \)[/tex] is the length of one side of the hexagon (which represents the base of the prism), and [tex]\( h \)[/tex] is the height of the prism.
Since the base of the vase is a hexagon, we need to find the side length of this hexagon.
The area of a regular hexagon can be calculated using the formula:
[tex]\[ A = \frac{3\sqrt{3}}{2}a^2 \][/tex]
Given that the volume of water in the vase is 512 cubic inches, and the wet portion's volume and its height are equal, we have:
[tex]\[ 512 = \frac{3\sqrt{3}}{2}a^2h \][/tex]
We are also given that the wet portion's volume is numerically equal to its height, so:
[tex]\[ h = 512 \][/tex]
Substituting this value of [tex]\( h \)[/tex] into the volume equation, we have:
[tex]\[ 512 = \frac{3\sqrt{3}}{2}a^2(512) \][/tex]
Now, we can solve for [tex]\( a \).[/tex]
[tex]\[ a^2 = \frac{512}{\frac{3\sqrt{3}}{2} \times 512} \]\[ a^2 = \frac{512}{\frac{3\sqrt{3}}{2} \times 512} \]\[ a^2 = \frac{2}{3\sqrt{3}} \]\[ a^2 = \frac{2\sqrt{3}}{9} \]\[ a = \sqrt{\frac{2\sqrt{3}}{9}} \]\[ a = \frac{\sqrt{2\sqrt{3}}}{3} \][/tex]
Now, let's find the height of the water by substituting the value of [tex]\( a \)[/tex]into the volume equation:
[tex]\[ 512 = \frac{3\sqrt{3}}{2}\left(\frac{\sqrt{2\sqrt{3}}}{3}\right)^2h \]\[ 512 = \frac{3\sqrt{3}}{2}\left(\frac{2\sqrt{3}}{9}\right)h \]\[ 512 = \frac{3\sqrt{3}}{2}\left(\frac{2\sqrt{3}}{9}\right)h \]\[ 512 = \frac{4}{3}h \]\[ h = \frac{512 \times 3}{4} \]\[ h = 384 \][/tex]
So, the height of the water in the vase is 384 inches.
Solve the equation.
–2 3/7 + b = 6 1/7
A.
b = 3 5/7
B.
b = 4 2/7
C.
b = 8 2/7
D.
b = 8 4/7
Answers
Jarek buys jerseys for his team online. He pays a constant shipping price plus a special rate for each jersey. During the spring season, Jarek paid $151 for 24 jerseys. In the summer season, he paid $79 for 12 jerseys. What is the special rate Jarek pays for each jersey and how much does he pay for shipping?
Thanks to anyone who can help!
Answers
Six different written driving tests are administered by the Motor Vehicle Department. One of these six tests is selected at random for each applicant for a driver's license. A group consisting of two women and three men apply for a license. (Round your answers to three decimal places.)
(a) What is the probability that exactly two of the five will take the same test?
(b) What is the probability that the two women will take the same test?
Answers
To find the probability that exactly two of the five will take the same test, we use combinations. The probability is 2/3 or 0.667. To find the probability that the two women will take the same test, we use combinations. The probability is 1/2 or 0.500.
To find the probability that exactly two of the five will take the same test, we can use the concept of combinations. There are six different tests, and we need to choose two of them to be taken by two people. The total number of ways to select two tests out of six is given by the combination formula C(6,2) = 6!/(2!(6-2)!) = 15. Now, for each of these two selected tests, there are two people (either two men or two women) who can take the test, resulting in a total of two possibilities. Therefore, the number of favorable outcomes is 2 * 15 = 30. Finally, the probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes, which is 6!/(2!3!) = 15. So the probability is 30/15 = 2/3 or 0.667 (rounded to three decimal places).
To find the probability that the two women will take the same test, we can use similar reasoning. There are six different tests, and we need to choose one of them to be taken by both women. The total number of ways to choose one test out of six is given by the combination formula C(6,1) = 6!/1!(6-1)! = 6. Now, for the chosen test, there are three possible ways both women can take it, since they can be the first two applicants, the last two applicants, or the middle two applicants. Therefore, the number of favorable outcomes is 3. The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes, which is also 6. So the probability is 3/6 = 1/2 or 0.500 (rounded to three decimal places).
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Final answer:
The probability that exactly two of the five will take the same test is 0.00463. The probability that the two women will take the same test is 1.167.
Explanation:
To find the probability that exactly two of the five will take the same test, we can use combinations. There are 6 different tests and we want to select 2 of them for the same test. Since order doesn't matter, we can use combinations. The number of ways to choose 2 tests out of 6 is 6 choose 2 = 15.
Now, for each pair of tests, we have 5 people who can take those tests. The probability that exactly 2 of the five will take the same test is the probability that exactly 2 people are randomly assigned to the same test out of the 5 people. The total number of possible outcomes is 6^5 since each person has 6 choices for which test to take, and there are 5 people.
So, the probability that exactly two of the five will take the same test is 15/6^5, which is approximately 0.00463.
To find the probability that the two women will take the same test, we consider the different possibilities. The two women can take the same test out of the 6 tests, or they can take different tests.
If they take the same test, there are 5 possible tests for them to choose from. The probability of this happening is 5/6.
If they take different tests, there are 5 possible tests for each of them to choose from. The probability of this happening is (5/6) * (4/5) = 2/3.
Therefore, the probability that the two women will take the same test is (5/6) + (2/3) = 7/6, which is approximately 1.167.
Word Problem help please
1. The magician said "The average of seven numbers is 49. If 1 is added to the fisr number, 2 is added to the second number, 3 is added to the third number and so on up to seventh number". what is the new average ? ...?
Answers
Need help ASAP
Will upvote!
I think it's A but i'm not sure
Lines A and B are represented by the equations given below:
Line A: x + 2y = 3
Line B: x + y = 3
Which statement is true about the solution to the set of equations?
There are infinitely many solutions.
There are two solutions.
There is one solution.
There is no solution.
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Which input value produces the same output value for the two functions on the graph?
x = -3
x = -2
x = -1
x = 3
Answers
You estimate that a baby pig weighs 20 pounds. The actual weight of the baby pig is 16 pounds. Find the percent error.
Answers
16/4=4
1/4=.25
.25=25%
Answer:
It's mainly 25% as the percent error.
Step-by-step explanation:
How to simplify and expression by combining like terms?
Answers
what is the correct expansion of the binomial (x+y)^5
Answers
Answer: The correct expansion is,
[tex]x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5[/tex]
Step-by-step explanation:
Since, by the binomial expansion,
[tex](p+q)^n=\sum_{r=0}^{n} ^nC_r (p)^{n-r}(q)^r[/tex]
Where,
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Here, p = x and q = y and n = 5,
By substituting values,
[tex](x+y)^5=\sum_{r=0}^{5} ^5C_r (x)^{n-r}(y)^r[/tex]
[tex] =^5C_0(x)^{5-0}(y)^0+^5C_1 (x)^{5-1}(y)^1+^5C_2 (x)^{5-2}(y)^2+^5C_3 (x)^{5-3}(y)^3+^5C_4 (x)^{5-4}(y)^4+^5C_5(x)^{5-5}(y)^{5}[/tex]
[tex]=1(x)^5(y)^0+\frac{5!}{4!(5-4)!}x^4y^1+\frac{5!}{3!(5-3)!}x^3y^2+\frac{5!}{2!(5-2)!}x^2y^3+\frac{5!}{1!(5-1)!}xy^4+\frac{5!}{5!(5-5)!}x^0y^5[/tex]
[tex]=x^5+\frac{5!}{4!1!}x^4y^1+\frac{5!}{3!2!}x^3y^2+\frac{5!}{2!3!}x^2y^3+\frac{5!}{1!4!}x^1y^4+\frac{5!}{5!0!}x^0y^5[/tex]
[tex]=x^5+\frac{5\times 4!}{4!}x^4y^1+\frac{5\times 4\times 3!}{3!2!}x^3y^2+\frac{5\times 4\times 3!}{2!3!}x^2y^3+\frac{5\times 4!}{4!}x^1y^4+\frac{5!}{5!}y^5[/tex]
[tex]=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5[/tex]
Which is the required expansion.
Determine the coordinates of the vertices of the triangle to compute the area of the triangle using the distance formula (round to the nearest integer).
FIRST GRAPH
A) 20 units^2
B) 30 units^2
C) 40 units^2
D) 50 units^2
Answers
Now, consider a triangle that’s graphed in the coordinate plane. You can always use the distance formula, find the lengths of the three sides, and then apply Heron’s formula. But there’s an even better choice, based on the determinant of a matrix.
Here’s a formula to use, based on the counterclockwise entry of the coordinates of the vertices of the triangle
(x1, y1), (x2, y2), (x3, y3) or (2, 1), (8, 9), (1, 8): A = x1y2 + x2y3 + x3y1 – x1y3 – x2y1 – x3y2.
Find the solution to the equations.
3x - y = -4
x + y = 0
(0, 0)
(-1, 1)
(1, -1)
Answers
3x-y = -4
x+y = 0
------------
4x = -4
Since 4x = -4, this means x = -1 after we divide everything by 4. The only answer choice that has this is (-1,1) which is the final answer
Sara tells Michael she is 160 centimeters tall, while Michael says he is 60 inches tall. If there
are 2.54 centimeters in an inch, who is taller?
Answers
Sara: 160 cm
Michael: 60 in
1 in = 2.54 cm
60 in = 60 * 1 in = 60 * 2.54 cm = 152.4 cm
Sara: 160 cm
Michael: 152.4 cm
160 cm > 152.4 cm
Sara > Michael
mx+4y=3t, Solve for the value of x
Answers
mx + 4y = 3t
__________
Distract 4y from both sides of the equation:
mx = 3t - 4y
__________
Divide both sides of the equation by m:
x = (3t - 4y)/m
To solve mx+4y=3t for x, subtract 4y from both sides to isolate the x term, giving mx = 3t - 4y. Then, divide both sides by m to solve for x, resulting in x = (3t - 4y) / m.
Explanation:To solve the equation mx+4y=3t for the value of x, follow these steps:
First, isolate the x term by moving the 4y to the other side of the equation. This gives us:mx = 3t - 4yNext, divide both sides of the equation by m to solve for x:x = (3t - 4y) / mYou can now plug in the known values for y, t, and m to find the value of x.
x + 2 > -8
a. x > -6
b. x > -10
c. x <-10
d. x < -6
Answers
__________________________
Explanation:
___________
Given the inequality:
___________
→ x + 2 > - 8 ;
____________
→ Subtract "2" from EACH side; to isolate "x" on one side; and solve, or simplify, for "x" ;
_______________________
→ x + 2 − 2 > - 8 − 2 ; to get:
_______________________
→ x > -10 ; which is: 'Answer choice: [B]'.
_______________________
A homemade lip balm consists of coconut oil and beeswax. Coconut oil costs $0.50 per ounce and beeswax costs $2.00 per ounce. If 6 ounces of coconut oil and 5 ounces of beeswax are used to create the lip balm mixture, which values represent a and b in the table?
what does a and b equal
a = $
b = $
Answers
And B) represents the total cost of 5 beeswax at $10
Let
a--------> the total cost in dollars of [tex]6[/tex] ounces of coconut oil
b--------> the total cost in dollars of [tex]5[/tex] ounces of beeswax
we know that
[tex]a=0.50 \frac{\$}{ounce}*6=\$3[/tex]
[tex]b=2.00 \frac{\$}{ounce}*5=\$10[/tex]
therefore
the answer is
the total cost in dollars of [tex]6[/tex] ounces of coconut oil is [tex]a=\$3[/tex]
the total cost in dollars of [tex]5[/tex] ounces ofbeeswax is [tex]b=\$10[/tex]
simplify 8a+4b-3a+5b
Answers
Here, take a's together & b's together,
(8a-3a) +(4b+5b)
5a+9b
So, your answer is 5a+9b
The simplified form of the expression [tex]8a+4b-3a+5b[/tex] is [tex]\boxed{5a+9b}[/tex].
Further explanation:
The given expression is [tex]8a+4b-3a+5b[/tex].
The given expression consists of [tex]2[/tex] different variables [tex]a[/tex] and [tex]b[/tex]. These variables can take any values since, its value is not fixed.
An algebraic expressions are formed if different variables and are added, subtracted, multiplied and divided.
The given expression is obtained when the variable [tex]a[/tex] and variable [tex]b[/tex] is added and subtracted with multiplication with different integers.
In the given expression there are [tex]4[/tex] terms with each term having different coefficients.
Like terms in the given expression are those whose algebraic factors are same that is [tex]8a[/tex] and [tex]-3a[/tex] are like terms and [tex]4b[/tex] and [tex]5b[/tex] are like terms.
The given expression is a binomial since, it have two unlike terms.
To simplify the given expression first we have to identify the like and unlike terms.
The like terms are [tex]8a[/tex] and [tex]-3a[/tex] and other set of like terms are [tex]4b[/tex] and [tex]5b[/tex]
Since, [tex]a[/tex] and [tex]b[/tex] are variable and they are numbers they can be added or subtracted using distributive property.
[tex]8a[/tex] and [tex]-3a[/tex] are subtracted as follows:
[tex]\begin{aligned}8a-3b&=(8\cdot a)-(3\cdot a)\\&=(8-3)\cdot a\\&=5\cdot a\\&=5a\end{aligned}[/tex]
[tex]4b[/tex] and [tex]5b[/tex] are added as follows:
[tex]\begin{aligned}4b+5b&=(4\cdot b)+(5\cdot b)\\&=(4+5)\cdot b\\&=9\cdot b\\&=9b\end{aligned}[/tex]
Therefore, simplified form of the given expression is [tex]5a+9b[/tex] since both are positive terms.
Thus, the simplified form of the expression [tex]8a+4b-3a+5b[/tex] is [tex]\boxed{5a+9b}[/tex].
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Algebraic expressions
Keywords: Simplify, 8a+4b-3a+5b, expression, 5a+9b, terms, coefficients, like, unlike, addition, subtraction, variables, values, distributive property, like terms, unlike terms.
-2i over 1+i ... help :(
Answers
= -1 -i
The answer would be the same even if you divided...and or, wrote it in simplest form.
ABCD ~ WXYZ. AD=12, DC=3 AND WZ=35. FIND YZ.
THE FIGURES ARE NOT DRAWN TO SCALE.
Answers
The unknown length YZ can be found through the ratios of corresponding sides in similar figures ABCD and WXYZ. Given AD=12, DC=3, WZ=35, the equation 3/YZ = 12/35 is formed. Solving for YZ, we find that YZ is 8.75.
Explanation:In the given question, ABCD and WXYZ are similar figures which mean the ratio of corresponding sides are equal. So, the ratio AD/WZ equals to the ratio DC/YZ. Given, AD=12, DC=3 and WZ=35. The length of YZ can be found by cross multiplying these ratios.
So, DC/YZ = AD/WZ.
By substituting the given values:
3/YZ = 12/35.
To find YZ, we simply cross-multiply and solve for YZ:
3 × 35 = 12 × YZ,
Hence, YZ = (3 × 35) / 12, which is 8.75 units.
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A quadrilateral has angles that measure 74°, 93°, and 117°.
Answers
it would be: 360 - (74+93+117)
= 360 - 284
= 76 degrees
So, Your final answer is 76 degrees.
Hope this helps!