The expression (128 + 32) when rewritten using factoring is 4 * (32 + 8)
How to rewrite the expression using factoring?The expression in the question s given as
(128 + 32)
Express the numbers 128 and 32 as the product of their factors
i.e. we factor out 4 from the expression
So, we have
(128 + 32) = (4 * 32 + 4 * 8)
Next, we factor out the common factor (i.e. 4) from the expression
So, we have
(128 + 32) = 4 * (32 + 8)
Rewrite the above expression as follows
(128 + 32) = 4(32 + 8)
Hence, the expression (128 + 32) when rewritten using factoring is 4 * (32 + 8)
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In this problem, you will explore changing dimensions in circles.
d. Make a conjecture about the ratio between the circumferences of two circles, when the ratio between their radii is 2 .
A ratio shows us the number of times a number contains another number. If the ratio between their radii of two circles is 2, then the ratio of their circumference will also be equal to 2.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Given that the ratio of the radius of two circles is 2. Therefore, we can write the ratio as,
The radius of circle A = kThe radius of circle B = 2kNow, a conjecture that can be made regarding the ratio of the circumference of the circle is that the ratio of the circumference of circle A and circle B will also be 2.
Further, let's check the ratio of the circumference of the circle.
Circumference of the circle A = 2πkCircumference of the circle B = 2π(2k) = 4πkThe ratio of the circumferences can be written as,
Circumference of the circle A/Circumference of the circle B = 2πk / 4πk
Circumference of the circle A/Circumference of the circle B = 1/2
Hence, If the ratio between their radii of two circles is 2, then the ratio of their circumference will also be equal to 2.
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Solve each system by elimination.
5x - y = 4 , 2x - y = 1
By elimination, the solution of the system of equations, 5x - y = 4 and 2x - y = 1, is (1 , 1).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
Subtracting the two equations will eliminate the variable y.
5x - y = 4 (equation 1)
2x - y = 1 (equation 2)
3x = 3
x = 1
Substitute the value of x to any of the two equations and solve for y.
5x - y = 4 (equation 1)
5(1) - y = 4
-y = 4 - 5
-y = -1
y = 1
Hence, the solution of the system of equations is (1 , 1).
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Consider √23, an irrational number.
4. Between which two perfect squares does 23 lie?
5. Between which two integers is the value of √23?
23 lies between the two perfect squares 16 and 25 which are the squares of 4 and 5 respectively.
The value of √23 lies between 4 and 5.
What in mathematics is a perfect square?
Informally: A square number, perfect square, or simply "a square" is the result of multiplying an integer (a "whole" number), positive, negative, or zero, times itself. Therefore, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on are all square numbers.
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Salma got a prepaid debit card with $20 on it. For her first purchase with the card, she bought some bulk ribbon at a craft
store. The price of the ribbon was 7 cents per yard. If after that purchase there was $18.46 left on the card, how many yards of
ribbon did Salma buy?
Answer:
22 yards
Step-by-step explanation:
Let x equal the number of yards of ribbon at $.07 per yard:
$18.46 + 0.07x = $20.00
Solve for x
Subtract $18.46 from both sides
0.07x = $1.54
Divide both sides by .07
x = 22
Jayden correctly solved the equation below.
Which of the following is a valid first step in the solution process?
The value of x is 27/4
Given that [tex]\frac{x}{3}-2=\frac{1}{4}[/tex]
So, we will start by
Finding common denominator and combining them
[tex]\frac{x}{3}-2=\frac{1}{4} \\\frac{x}{3}+\frac{3(-2)}{3}=\frac{1}{4}[/tex]
[tex]\frac{x+3(-2)}{3}=\frac{1}{4}[/tex]
[tex]\frac{x-6}{3}=\frac{1}{4}[/tex]
then cross multiplying them
[tex]4(x-6)=1(3)\\4x - 24 = 3[/tex]
Add 24 to both sides
4x-24=3
4x - 24 + 24 = 3 + 24
Simplify Add the numbers
4x=27
Divide both sides by the same factor
4x=27
[tex]\frac{4x}{4}}=\frac{27}{4}}[/tex]
Simplify and Cancel terms that are in both the numerator and denominator
[tex]x=\frac{27}{4}[/tex]
So, the value of x for the given is x = 27/4.
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The value of x for the equation [tex]\frac{x}{3}-2 =\frac{1}{4}[/tex] is 27/4
Given that [tex]\frac{x}{3}-2 =\frac{1}{4}[/tex]
So, we will start by
Finding common denominator and combining them
[tex]\frac{x}{3}-2 =\frac{1}{4}\\\frac{x-6}{3} =\frac{1}{4}\\[/tex]
[tex]4({x-6}) =3({1})\\\\4x - 24 = 3\\[/tex]
Divide both sides by the same factor
[tex]4x - 24 + 24 = 3 +24\\x = \frac{27}{4}\\\\Simplify \ Add \ the \ numbers\\4x=27\\x=\frac{27}{4}[/tex]
So, the value of x for the given is x = 27/4.
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Beth knows the perimeter, P, and width, w, of a
rectangular window in her living room. Which
formula can she use to find the length, 1, of the
window?
Beth knows the perimeter, P, and width, w, of a
rectangular window in her living room. Which
formula can she use to find the length, 1, of the
window?
First we know about How to Find the perimeter?
Rectangles have four sides, congruent opposite sides, and four right angles and we find the perimeter of a rectangle with the equation P=2l+2w. Explore this formula, rectangles, and examples of finding rectangle perimeters.
so ,
The formula for the perimeter of a rectangle is given below: Perimeter = length + length + width + width P = l + l + w + w Or, P = 2 ( l + w) Hence, the formula for the perimeter of a rectangle, P = 2 × (length + width) = 2 × (sum of adjacent sides) .
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E is the midpoint of DF, DE=6x+1 and EF = 7x-4. Find DE, EF, and DF
The value for the given line DF are-
DE = 31 units.EF = 31 units.DF = 62 unit.What is meant by the mid point of the line?A midpoint is a point in the middle of a line connecting two points. The 2 points of reference are the line's endpoints, and also the midpoint is located between the two.For the points on the coordinate axes, the midpoint formula is defined. Let the endpoints of the a line segment be (x)1, (y)1, and (x)2, (y)2. The midpoint is equal to one-half of the sum of the two points' x-coordinates and half of a sum of the two points' y-coordinates.For the given values in question,
DE = 6x + 1 and EF = 7x - 4.
As, E is the midpoint of DF.
Thus,
DE = EF
Pu the values.
6x + 1 = 7x - 4
On solving.
x = 5
Put the values in the lines.
DE = 6x + 1
DE = 6×5 + 1
DE = 31 units.
EF = 7x - 4
EF = 7×5 - 4
EF = 31 units.
DF = DE + EF
DF = 31+ 31
DF = 62 units.
Thus, the values for the line segment are obtained.
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Xio is rolling marbles down a ramp. Every second that passes, she
measures how far the marbles travel. She records the information in the table
shown below.
eau marit
Second
1st
2nd 3rd 4th
Distance (cm) 20 60 100 140
Make a conjecture about how far the marble will roll in the fifth second
The marble will roll 180cm distance in fifth second.
Distance travelled by an object in rectilinear motion is always in arithmetic Progression. Arithmetic Progression is collection of number in increasing or decreasing order with a common difference.
The marble rolls 20cm, 60cm, 100cm, 140cm in 1st, 2nd, 3rd, 4rth second respectively
As the ball travels in rectilinear motion on floor, so the distance covered by it in successive seconds will be in Arithmetic Progression
so, 5th term of the AP 20,60,100,140..... will be the distance travelled by it 5th second
Since A=20 and common difference(d)=40
then, 5th term= A + (5-1)d
or, 20+ (4×40) = 180cm
Final answer, the marble will roll 180cm in 5th second.
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A 320 meter long tightrope is suspended between two poles. Assume that the line has an equal chance of breaking anywhere along its length.
a. Determine the probability that a break will occur in the first 50 meters of the tightrope.
The probability that a break will occur in the first 50 meters of the tightrope is about 15.625%.
Probability:
The term probability refers the possibility occurring the particular event.
Given,
A 320 meter long tightrope is suspended between two poles.
Here we assume that the line has an equal chance of breaking anywhere along its length.
Now, we need to determine the probability that the break will occur within 20 meters of a pole.
From the given question,
The line has an equal chance of breaking anywhere along its length.
The first 50 meters form ,
=> [ 50 / 320 ] x 100
=> [ 5 / 32 ] x 100
=> [ 0.15625] x 100
=> 15.625 %.
Therefore, the probability that a break will occur in the first 50
meters of the tightrope is about 15.625%.
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show your work
v= pi(3.14)r^2h
Answer: 2000.18 unit^3
Step-by-step explanation:
radius = 14 / 2 = 7
V of cylinder = π x r^2 x h
= 3.14 x 7^2 x 13
= 3.14 x 49 x 13
= 2000.18 unit^3
the difference between the areas of the figures is less than 2
Answer:
x < 1
Step-by-step explanation:
The temperature at the beginning of the day was 4°C. The temperature dropped 7°C by the end of the day. What was the temperature at the end of the day? Use the number line model to find 4 - 7
Based on the temperature at the beginning of the day, and the change in temperature by the end of the day, the temperature at day's end was -3°C.
What is the ending temperature?The temperature started at 4°C and then dropped during the day by a temperature of 7°C.
The temperature at day's end will therefore be:
= Beginning temperature - Change in temperature
Solving gives:
= 4 - 7
= -3 °C
In conclusion, the change in temperature would lead to an ending temperature of -3°C.
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If A y) = 4 y2 - 3 y+ 2, find A-5).
Answer:
Step-by-step explanation:
[tex]A(-5)=4(-5)^{2} -3(-5)+2\\A(-5)=100+15+2\\A(-5)=117[/tex]
Combining functions to write a new function that models a real-world situation
The function C that represents how much more it costs to rent a luxury car than an economy car is; C = 8.45 + 0.45M
How to combine functions?We are given the function that represents the charge E(in dollars) to rent an economy car as;
E = 12.95 + 0.60M
The function that represents the charge L (in dollars) to rent a luxury car is given by; L = 21.40 + 1.05M
Now, we are told that the function C represents how much more it costs to rent a luxury car than an economy car. This is expressed as;
C = L - E
Thus;
C = 21.40 + 1.05M - (12.95 + 0.60M)
C = 21.40 + 1.05M - 12.95 - 0.60M
C = 8.45 + 0.45M
Thus, the function C that represents how much more it costs to rent a luxury car than an economy car is; C = 8.45 + 0.45M
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HELP ME WITH THIS PROBLEM
x=5 that's my final answer because 2(8)=4x-4
The formula below is often used by project managers to compute EEE, the estimated time to complete a job, where OOO is the shortest completion time, PPP is the longest completion time, and MMM is the most likely completion time.
E=\dfrac{O+4M+P}{6}E=
6
O+4M+P
E, equals, start fraction, O, plus, 4, M, plus, P, divided by, 6, end fraction
Which of the following correctly gives PPP in terms of EEE, OOO, and MMM
The equation which correctly gives P in terms of E, O and M as required is; P = 6E - 4M - O.
Change of formula subjectIt follows from the task content that the expression which represents P in terms of E, O and M be determined.
On this note, since the initial formula is;
E = (O + 4M + P)/6
Multiply both sides by 6;
6E = O + 4M + P
Subtract O and 4M from both sides;
P = 6E - 4M - O.
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Find the distance between the pair of points: (-9, -5) and (6, -5)
Answer:15
Step-by-step explanation: if your at -9,-5 you would be on the 3rd quadrant, and in order to get to 6,-5 (4th quadrant) you would just move to the right. you would only move right because the y-axis stays the same but the x-axis changes.
Answer: 15
Step-by-step explanation:
the equation to find the length of a line using the points given:
[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
therefore you should understand which is y2, x2,y1 and x1
so you should always check which y value is bigger (the y value is the number in the right side of the point) so if the y value is bigger (y2) then eventually the value next to it which is x will always become x2 if the y value is big (y2)
so the other two values of the other point should become x1 and y1 since you already figured out the lager y value.
so now as for this question y2= -5, y1= -5, x2= 6 and x1= -9
now substitute these values to the equation I mentioned before ( you should make sure to remember the equation for sure as it is required when doing these types of questions)
[tex]\sqrt{[6-(-9)]^{2} +[-5-(-5)]^2} \\\sqrt{(6+9)^2 + (-5+5)^2[/tex]
[tex]\sqrt{15^2+0^2} \\\sqrt{225} \\15[/tex](therefore 15 is the answer you have been looking for!)
I hope you understood and don't forget the equation which is the main help!
Finding the initial amount and rate of change given a table for a linear function
Answer:Omg JUST use slope intercept form like I said: Pick a point in this case I have picked, but you can any: (15, 560) (20, 480). Remember
Y2 - Y1 /X2-X1 = M (Your slope). In this case 480-560/20-15 = -80/5 = -16
Now you have your slope. Y - Y2=M(x - x1). In this case Y - 560 = -16(x-15)
Distrubute: Y - 560 = -16x +240. Add 560 on both side. Y= -16x +800
And yes it water decreases as time increases.
Step-by-step explanation:
does someone mind helping me with this? Thank you!
Answer:
50.27
Step-by-step explanation:
A panel of judges must be chosen to judge the upcoming dance competition. There are 5 men and 8 women to pick from. How many ways can you pick a panel of 2 men and 2 women?
The number of ways of picking a panel of judges comprising of 2 men and 2 women is 280 ways
How to find the number of ways to pick a panel of 2 men and 2 women
Given data
number on men = 5
number of women = 8
The number of ways of picking a panel of 2 men and 2 women
= 5 combination 2 * 8 combination 2
= 5 C 2 * 8 C 2
= 5! / ( 2! ( 5 - 2 )! * 8! / ( 2! ( 8 - 2 )!
= 5! / ( 2! 3! ) * 8! / ( 2! 6! )
= 5 * 4 * 3! / ( 2! * 3! ) * 8 * 7 * 6! / ( 2! * 6! )
= 20 / 2 * 56 / 2
= 10 * 28
= 280 ways
The number of ways of picking a panel of judges comprising of 2 men and 2 women is 280 ways
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Given: BD ⊥ BC ; ∠ABD ≅ ∠DBE
Prove: ∠ABD and ∠EBC are complementary
Statement in step 8 is the proof that <ABD and <EBC are complementary angles.
What are a complementary angles?An angle in mathematics refers to an arc that joins two points. For angles to be formed there should be two points, the starting point and the ending point. In some cases the starting point coincides with the ending point, in this case the angle formed is 360 degrees which is equivalent to a circle. We can hence say that angle in a circle is 360 degrees
When angles are formed by two points in the same straight line or say two colinear points the angle formed here is 180 degree. Hence we say angles in a straight line is 180 degrees. In a case where a line intersects the straight line, the intersecting line bisects the the angle in a straight line. The sum of the two angles formed is 180 degrees. Such angles are said to be supplementary angles.
Assuming the bisector of the straight line in a perpendicular bisector, here the angle 180 is divided into two equal parts then each angle is 90 degrees.
When angle 90 degrees is bisected two different angles are formed. The sum of these two angles are known as complementary angles.
Hence angle <ABD and <EBC are complementary angles formed from bisecting angle <DBC which is 90 degrees or a right angle triangle
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two sides of a triangle are a=12,b=15 and the value of s(semi perimeter) used in heron's formula is 22 cm, then the length c of the third side is:
Answer:
how are you doing where you can do it for 5 Pts
Step-by-step explanation:
Aleena thinks of a number that has 2 decimal places.
Her number is 2.8 when rounded to 1 decimal place.
What is the smallest number that Aleena could be thinking of?
Answer:
The smallest number that Aleena could be thinking of is 2.75.
ive put 3 more of the same question gain lots of points! Rex and Samir participated in a walkathon. Rex walked for 1 2/3 hours, and Samir walked for 3 1/3 hours. complete the comparison. Samir walked _____ times ad many hours as Rex walked.
Answer:
2 times as much
Step-by-step explanation:
1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes
3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins
200 is twice as much as 100
Answer:
2 times as much
Step-by-step explanation:
1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes
3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins
200 is twice as much as 100
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WILL GIVE BRAINLIEST please help ! this is rly easy but I just want to clarify that I got everything right. tysm !
The subtraction equation to addition equation is as follows;
a = 6 + 9p = -30 + 20z + 12 = 15x + 7 = -20How to write subtraction equation to addition equation?By converting the subtraction equation to addition equation, we have to change the sign from subtraction to addition but the equation overall remain the same.
Therefore,
a - 9 = 6
add 9 to both sides
a - 9 + 9 = 6 + 9
a = 6 + 9
p - 20 = -30
add 20 to both sides
p = -30 + 20
z - (-12) = 15
open the bracket by multiplying the signs
Therefore,
z + 12 = 15
x - (-7) = -20
open the bracket by multiplying the signs
x + 7 = -20
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Simplify each complex fraction.
1 - 1/ 4 / 2 - 3/5
The simplification of the given complex fraction [tex]1- \frac{1}{\frac{4}{2-\frac{3}{5} } }[/tex] is equal to (23)/(28).
As given in the question,
Given complex fraction is [tex]1- \frac{1}{\frac{4}{2-\frac{3}{5} } }[/tex]
Simplify the given complex fraction by taking the least common multiple,
[tex]1- \frac{1}{\frac{4}{2-\frac{3}{5} } }\\\\\\= 1- \frac{1}{\frac{4}{\frac{10-3}{5} }}\\ \\= 1- \frac{(1)(5)}{(4)(7)}\\ \\= \frac{(28-5)}{28}\\ \\= \frac{23}{28}[/tex]
Therefore, the simplification of the given complex fraction [tex]1- \frac{1}{\frac{4}{2-\frac{3}{5} } }[/tex] is equal to (23)/(28).
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99. Cost, Revenue, and Profit A roofing contractor
purchases a shingle delivery truck with a shingle
elevator for $42,000. The vehicle requires an average
expenditure of $9.50 per hour for fuel and maintenance,
and the operator is paid $11.50 per hour.
(a) Write a linear equation giving the total cost C of
operating this equipment for t hours. (Include the
purchase cost of the equipment.)
(b) Assuming that customers are charged $45 per hour
of machine use, write an equation for the revenue R
obtained from t hours of use.
(c) Use the formula for profit P = R C to write
an equation for the profit obtained from t hours
of use.
(d) Use the result of part (c) to find the break-even
point that is, the number of hours this equipment
must be used to yield a profit of 0 dollars.
Total cost function is C=42000+21t
Revenue function is R=45t
Profit function is P=24t-42000
The breakeven number of hours is 1,750
What is the total variable cost per hour of operating the truck?
The total variable cost per hour of operating shingle delivery truck is the sum of the hourly fuel and maintenance cost and the hourly rate of the operator
total variable cost per hour=$9.50+$11.50
total variable cost per hour=$21.00
The liner equation formula for total cost is as shown below:
y=a+bx
y=total cost=C
a=fixed cost=cost of truck=42000
b=total variable cost per hour=21
x=number of hours the truck is operated=t
C=42000+21t
The total revenue is the customer charge per hour multiplied by number of hours
R=45t
P=R-C
P=45t-(42000+21t)
P=24t-42000
The breakeven number of hours is achieved at the point where the total cost is the same as revenue
45t=42000+21t
45t-21t=42000
24t=42000
t=42000/24
t=1,750 hours
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Find the arithmetic mean an of the given terms. a_{n-1}=7, a_{n+1}=1
The arithmetic mean an of the given terms a_{n-1}=7, a_{n+1}=1 is
a (n) = -3.
What is arithmetic mean?a_{n-1}=7, a_{n+1}=1
a(n) =(1-7)/2
a (n) = -3
The arithmetic mean is the most straightforward and widely used method of calculating a mean or average. It only requires adding up a group of figures, then dividing the result by the entire amount of figures in the series. Consider the numbers 34, 44, 56, and 78 as an example. It totals 212.
The mean or arithmetic average are other names for the arithmetic mean. It is determined by adding up each number in a particular data set, then dividing the result by the overall number of items in the data set. For uniformly distributed integers, the middle number serves as the arithmetic mean (AM).
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d-g=1/4a solve for a
Answer:
a = 4(d - g)
Step-by-step explanation:
d - g = [tex]\frac{1}{4}[/tex] a ( multiply both sides by 4 to clear the fraction )
4(d - g) = a
An equation of the line tangent to the graph of y=2x+33x−2
y
=
2
x
+
3
3
x
−
2
at the point (1, 5) is
The equation of line tangent is y-35x+30=0.
What is tangent of a line?
A tangent line to a circle is a line that touches the circle exactly one time in Euclidean plane geometry and never enters the interior of the circle. Tangent lines to circles are the focus of various theorems and are crucial to numerous geometric structures and mathematical arguments.
Given equation y=2x+33x-2
=>y=35x-2
General slope intercept form is y=mx+b
Comparing and we get m = 35
The equation of tangent is y-5=35 (x-1)
=> y-5=35x-35
=> y=35x-35+5
=>y-35x+30=0
Therefore, the equation of line tangent is y-35x+30=0.
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