Which expression uses the greatest common factor and the distributive property to rewrite the sum 75 + 45?
A. 45(30 + 1)
B. 15(5 + 3)
C. 15(3 + 7)
D. 5(70 + 40)
The expression that uses the greatest common factor and the distributive property to rewrite the sum 75 + 45 is B. 15(5 + 3)
What is distributive property?The distributive property states that an expression of the form A(B + C) can be solved by a multiplication over addition operation that is
A(B + C) = AB + AC
This property is known by distributive law and applies to subtraction also.
Given; the distributive property to rewrite the sum 75 + 45
First find the greatest common factor.
75: 1, 3, 5, 15, 25, 75
45: 1, 3, 5, 9, 15, 45
Their GCF is 15.
To get 75, we will multiply 15 by 5.
To get 45, we will multiply 15 by 3.
Therefore, 15(5 + 3) = 75 + 45.
The expression that uses the greatest common factor and the distributive property to rewrite the sum 75 + 45 is B. 15(5 + 3)
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Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 7 liters of natural oil for every 5 liters of synthetic oil. If 355 liters of synthetic oil are used, how many liters of petrolyn oil will be made?
The difference between three-fifths of a number and 7 is -36
The value of a number such that The difference between three-fifths of that number and 7 is -36 is -145/3.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
Subtraction = Minus of any two or more numbers with each other called subtraction.
Let's say that number is x.
Three-fifth of x ⇒ (3/5)x
The difference of (3/5)x and 7 will be,
(3/5)x - 7 = -36
Add 7 on both sides
(3/5)x = -29
Multiply 5/3 on both sides
x = -29(5/3)
x = -145/3
Hence "The value of a number such that The difference between three-fifths of that number and 7 is -36 is -145/3".
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Bruno's hourly salary is 6.75. Last Week he worked a 20 hour week. How Much did he earn
Julia plays volleyball and finished the regular season with 25 digs. The graph relates her total number of digs for the season to the number of games played in the post-season tournament. Graph in the coordinate plane with title Julia’s volleyball digs. Vertical axis goes from 0 to 60 in increments of 5 and is labeled number of digs. Horizontal axis goes from 0 to 10 in increments of 1 and is labeled games played. A ray on the graph starts at point begin ordered pair 0 comma 25 end ordered pair and goes through points begin ordered pair 4 comma 37 end ordered pair and begin ordered pair 8 comma 49 end ordered pair. What is the equation in standard form that represents the relationship shown in the graph? y=3x+25 y−37=3(x−4) 3x+y=25 −3x+y=25 y=−3x+25
Answer:
As given : Graph in the coordinate plane with title Julia’s volleyball digs. Vertical axis goes from 0 to 60 in increments of 5 and is labeled number of digs. Horizontal axis goes from 0 to 10 in increments of 1 and is labeled games played. A ray on the graph starts at point begin ordered pair 0 comma 25 end ordered pair and goes through points begin ordered pair 4 comma 37 end ordered pair and begin ordered pair 8 comma 49 end ordered pair.
As the ray passes through (0,25) and (4,37) and (8,49).
Equation of line passing through (a, b) and (p,q) is given by:
→ [tex]\frac{y-b}{x-a}=\frac{q-b}{p-a}[/tex]
→Equation of line passing through (0,25) and (4,37) is :
[tex]\frac{y-25}{x-0}=\frac{37-25}{4-0}=3\\\\y -25=3x\\y =3x + 25[/tex]
As , y= 3 x + 25, also passes through (8,49) also.
Equation of line is : y = 3 x + 25 or in Standard form : - 3 x + y = 25
Option (D) is the standard form of line which is : - 3 x + y = 25
every day, mike gets paid from his job. on monday, he gets 19 cents; on tuesday, he gets 14 cents; on wednesday, he gets 20 cents; on thursday, he gets 15 cents; and so on. how much money will he have by the 4th day?
Simplify:
4p + 12 – 3q – 4p – 18 + 6q
A. 8p + 3q – 6
B. 8p – 3q + 6
C. 3q + 6
D. 3q – 6
The simplifying value of the expression is,
⇒ 3q - 6
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 4p + 12 - 3q - 4p - 18 + 6q
Now,
Simplify the expression as;
⇒ 4p + 12 - 3q - 4p - 18 + 6q
⇒ 4p - 4p - 3q + 6q + 12 - 18
⇒ 0 + 3q - 6
⇒ 3q - 6
Thus, The simplifying value of the expression is,
⇒ 3q - 6
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If the equatorial diameter of the sun is 1.39 million km how many kilometers is the sun's radius
What is the best way to 7x7 in expanded form?
Answer: Add 7 7 times
Step-by-step explanation: if you add 7 7 times like this 7+7+7+7+7+7+7 then that is your answer easy way too.
list these number from greatest to least: 0.386, 0.3, 0.6833, 0.836
the correct order from greatest to least is:
0.863, 0.6833, 0.386, 0.3
Carly can ride her bicycle 6000 meters in 15 minutes how far can she ride her bicycle in two minutes
find the rate of change for 2x+4y=10
rate of change for 2x+4y=10
here rate of change can be found by finding slope
the general form for slope is y=mx+b
isolating y on the left side:
2x+4y=10
4y=[tex] y=\frac{-2x+10}{4}
[/tex]-2x+10
from here slope is -1/2
Rate of change =-1/2
what is -5x + 2 equals negative 48
The area of a rectangle is 201.5 square inches. The length of the rectangle is 13 inches. What is the width of the rectangle?
The amount of money Kelly earns is proportional to the number of hours she works. Kelly earns $32.40 working 4 hours. Create an equation that models the relationship between the amount of money Kelly earns, in dollars, and h, the number of hours she works.
Use the sequence below to answer parts a and b (8,17,26,35,44,53,...) Create an explicit formula to determine the 12th term of the sequence Create a recursive formula to prove the 7th term is 62.
The explicit formula for the sequence (8, 17, 26, 35, 44, 53, ...) is 8 + (n-1) * 9, and the 12th term can be found by substituting n = 12. The recursive formula for the sequence is a1 = 8 and an = an-1 + 9. Using this recursive formula, we can verify that the 7th term is indeed 62.
Explanation:To create an explicit formula for the sequence (8, 17, 26, 35, 44, 53, ...), we notice that the difference between each term is 9. So, the explicit formula for the sequence is 8 + (n-1) * 9, where n represents the position of the term in the sequence. Using this formula, we can find the 12th term by substituting n = 12: 8 + (12-1) * 9 = 89.
To create a recursive formula to prove that the 7th term is 62, we observe that each term is the previous term plus 9. So, the recursive formula for the sequence is:
a1 = 8an = an-1 + 9Using this recursive formula and starting with a1 = 8, we can find the 7th term as follows:
a1 = 8a2 = a1 + 9 = 8 + 9 = 17a3 = a2 + 9 = 17 + 9 = 26a4 = a3 + 9 = 26 + 9 = 35a5 = a4 + 9 = 35 + 9 = 44a6 = a5 + 9 = 44 + 9 = 53a7 = a6 + 9 = 53 + 9 = 62Therefore, the 7th term in the sequence is indeed 62.
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does it matter whether you remove x tiles or 1 tiles first
Answer This Problem,Please! :D
Type the integer that makes the following subtraction sentence true:
*blank*– 5 = -6
the exact radius of a circle with circumference 36 meters
What is the slope of this graph?
Answer: The slope (m) of the line using two points where the line goes through is:
m = - 4 (negative 4).
Solution:
m=(y2-y1) / (x2-x1)
Taking two points in the graph where the line goes through:
P1=(0,2)=(x1,y1)→x1=0, y1=2
P2=(1,-2)=(x2,y2)→x2=1, y2=-2
Replacing in the formula of the slope:
m=(-2-2) / (1-0)
m=(-4) / (1)
m=-4
Fill in the missing reasons in the Two-column proof below.
Given: m∠2 + m∠3 + m∠4 = 180°
Prove: m∠1= m∠3 + m∠4
Statement Reasons
a. m∠2 + m∠3 + m∠4 = 180° a.
b. m∠1 + m∠2 = 180° b.
c. m∠1 + m∠2 = m∠2 + m∠3 + m∠4 c.
d. m∠1 + m∠2 - m∠2 = m∠2 + m∠3 + m∠4 -m∠2 d.
e. m∠1 = m∠3 + m∠4 e.
Thomas earns $2100 per month and then got a 15 raise .how much will Thomas make per month after his raise
Final answer:
Thomas will earn $2415 per month after a 15% raise on his current salary of $2100, which results in a raise amount of $315.
Explanation:
Thomas currently earns $2100, and with a 15% raise, we need to calculate the increase in his monthly pay. To find the amount of the raise, we calculate 15% of his current earnings. That is, we multiply his earnings by the raise percentage expressed in decimal form: $2100 × 0.15 = $315.
After finding the raise amount, we add it to his current salary to find his new monthly earnings. $2100 + $315 = $2415 per month. Therefore, after a 15% raise, Thomas will make $2415 per month.
the temperature at 6:00AM was 0.8F. BY. 3:00pm the temperature had increased to 2.4 F find the differnce between the two temperatures. Draw models to find the difference
Rewrite the expression with parentheses to equal the given value 12+6÷2+4 value 13
Rebecca had 9/10 of a yard of ribbon. Then she gave 7/20 of a yard to a friend. How much does she have left? Explain your work
A yard is a unit of length. Hence, the Rebeccas have [tex]\frac{11}{20}[/tex] a yard of ribbon.
What is the yard?
A yard is a unit of length in both US Customary and British Imperial Systems of Measurement.
Here, Rebecca had [tex]\frac{9}{10}[/tex] a yard of ribbon, and Rebecca gives [tex]\frac{7}{20}[/tex] of a yard of a friend.
Now, we have to subtract [tex]\frac{7}{20}[/tex] from the original [tex]\frac{9}{10}[/tex].
Since the denominator is the same as the rules of fractions.
Now, we multiply [tex]\frac{9}{10}[/tex] by [tex]\frac{2}{2}[/tex] so that the denominator [tex]10[/tex] and [tex]20[/tex] would be the same.
Therefore,
[tex]\frac{9}{10}[/tex]×[tex]\frac{2}{2}[/tex]=[tex]\frac{18}{20}[/tex].
Here, both the denominator are the same, we can subtract [tex]\frac{7}{20}[/tex] from the [tex]\frac{18}{20}[/tex].
[tex]\frac{18}{20}-\frac{7}{20}\\=\frac{11}{20}[/tex]
Hence, the Rebeccas have [tex]\frac{11}{20}[/tex] a yard of ribbon.
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Final answer:
Rebecca has 11/20 of a yard of ribbon left after subtracting the 7/20 yard she gave to a friend from her initial 9/10 yard of ribbon by converting both fractions to have a common denominator.
Explanation:
Rebecca started with 9/10 of a yard of ribbon and gave away 7/20 of a yard. To find out how much ribbon she has left, we need to subtract the amount she gave away from the amount she started with. This can be done following these steps:
Ensure that both fractions have a common denominator. The least common multiple of 10 and 20 is 20, so multiply the numerator and the denominator of the first fraction (9/10) by 2 to get the equivalent fraction with a denominator of 20, which gives us 18/20.
Now subtract the second fraction (7/20) from the first fraction (18/20) since they now have a common denominator. This gives us 18/20 - 7/20 = 11/20.
Therefore, Rebecca has 11/20 of a yard of ribbon left.
The Hamptons family has a fish tank holding 10,450 ml of water.The water is leaking at a rate of 270 ml per minute.
Part A: Define the input and output in the given scenario.
Part B: Write a function to model this situation.
Part C: How many liters of water will be left in the tank after 10 minutes.?
A trough is 12 ft long and its ends have the shape of isosceles triangles that are 5 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 13 ft3/min, how fast is the water level rising when the water is 8 inches deep?
I have been getting 13/30, but apparently, that is wrong?
V=.5 * h * l * b
Because of similar triangles:
b = 5h (b/h = 5/1)
l = 12
V = .5 * h * 5h * 12
V = 30h^2
(dV/dt) = 60 h (dh/dt)
dV/dt = 13
h = .5 (because this is in feet)
13 = 60*.5(dh/dt)
13/30 = dh/dt
The rate at which the water level is rising when the water is 8 inches deep in the trough is 13/30 ft/min.
Explanation:To find how fast the water level rises when the water is 8 inches deep, we need to use the equation V = 30h^2, which represents the volume of the trough as a function of its height h. We are given that the trough is being filled at a rate of 13 ft^3/min, so we can set dV/dt (the rate of change of volume) equal to 13.
Substituting the given values into the equation dV/dt = 60h * dh/dt, we get 13 = 60 * h * dh/dt. Since h = 0.5 (in feet), we can solve for dh/dt which turns out to be 13/30 ft/min.
Therefore, the water level is rising at a rate of 13/30 ft/min when the water is 8 inches deep.
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What is 3x-6+1=-2x-5+5x
What is 24 divided by 1272
Which is an equation in point-slope form of the line that passes through the points (4, 5) and (−3, −1) ?
A linear equation or function is always a representation of a straight line in the coordinate plane. The equation of the line that passes through points (4, 5) and (−3, −1) is y = (6/7)x + 9/7.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
The equation of a straight line is given by, y = mx + c
Where m is the slope while c is the y-intercept.
The slope of line passing by two points (x₁, y₁) and (x₂, y₂)
Slope(m) = (y₂ - y₁)/(x₂ - x₁)
The slope of the line that passes through (4, 5) and (−3, −1) will be,
m = (-1 -5)/(-3-4)
m = -6/-7 = 6/7
So equation converts as, y = (6/7)x + c
Substitute, (4,5)
5 = (6/7)4 + c
c = 9/7
So, y = (6/7)x + 9/7 will be the equation.
Hence "The equation of the line that passes through points (4, 5) and (−3, −1) is y = (6/7)x + 9/7".
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