Which pair shows equivalent expressions?
A.2(2/5x + 2)=2 2/5x + 1
B.2(2/5x + 2)=4/5x + 4
C.2(2/5x + 4)=4/5x + 2
D.2(2/5x + 4)=2 2/5x + 8
Answers
Which pair shows equivalent expressions?
A.2(2/5x + 2)=2 2/5x + 1
B.2(2/5x + 2)=4/5x + 4
C.2(2/5x + 4)=4/5x + 2
D.2(2/5x + 4)=2 2/5x + 8
Solution:
[tex] 2(\frac{2}{5}x + 2) [/tex]
Let us distribute 2 inside the parenthesis.
That is, we use distributive property:
a(b+c)=ab+ac
[tex] 2(\frac{2}{5}x + 2) =\frac{2*2}{5}x+2*2 [/tex]
So, [tex] 2(\frac{2}{5}x + 2) =\frac{4}{5}x+4 [/tex]
Answer:Option (b)
[tex] 2(\frac{2}{5}x+4) [/tex]
Applying distributive property, a(b+c)=ab+ac
[tex] 2(\frac{2}{5}x+4) =2*\frac{2}{5} x+2*4 [/tex]
[tex] 2(\frac{2}{5}x+4) =\frac{2*2}{5} x+2*4 [/tex]
[tex] 2(\frac{2}{5}x+4) =\frac{4}{5} x+8 [/tex]
So, Option (B) is correct.
Answer:
B.
Step-by-step explanation:
Related Questions
nelly bought a computer for $400. it was on sale for 20%. what was the original price?
Answers
x*.8=400
divide .8 from both sides
x=500
Jessica rented 1 video game and 3 movies for a total of $11.50. . The video game cost $4.75 to rent. . The movies cost the same amount each to rent. What amount did Jessica pay to rent each movie?
Answers
6.75 / 3 = $2.25 each
Using the distributive property, which of the following expressions is equivalent to 5(3 + 5y)?
Answers
Answer:
15+25y
Step-by-step explanation:
I did this test!
have a great day:D
Match the two numbers with their least common multiple (LCM). Match Term Definition 10 and 4 A) 40 10 and 6 B) 30 10 and 8 C) 20
Answers
B) 30
C) 20
a) 10 and 4
b) 10 and 6
c) 10 and 8
Answers:
C) 20 —-> a) 10 and 4
B) 30 —-> b) 10 and 6
A) 40 —-> c) 10 and 8
Explanation:
20: 10 x 2 = 20 ; 4 x 5 = 20
30: 10 x 3 = 30 ; 6 x 5 = 30
40: 10 x 4 = 40 ; 8 x 5 = 40
Which counterexample shows that the conjecture "All animals that can fly are birds" is false?
Answers
So A is the logical choice and according to what Jimthompson5910 said "bats are one animal where they can fly but they aren't birds."
What are the dimensions of the rectangle shown below? Remember to use the axes on the coordinate grid to help you. 6 units × 4 units 8 units × 6 units 12 units × 8 units 18 units × 12 units
Answers
Answer:
6 units
Step-by-step explanation:
What expression is equivalent to the expression given below?
3/8 - 1/2y-5/6
:) 20 p0ints
Answers
Answer:
[tex]-\frac{1}{2}y-\frac{11}{24}[/tex]
Step-by-step explanation:
[tex]\frac{3}{8}\:-\:\frac{1}{2}y-\frac{5}{6}\\\\ =-\frac{1}{2}y+\frac{3}{8}-\frac{5}{6}\\\\ =-\frac{1}{2}y-\frac{11}{24}[/tex]
Hello!
Your answer is -1/2y - 11/24
Rectangle ABCD is congruent to rectangle A"B"C"D" .
Which sequence of transformations could have been used to transform rectangle ABCD to produce rectangle A"B"C"D" ?
A) Rectangle ABCD was reflected across the y-axis and then across the x-axis.
B) Rectangle ABCD was translated 8 units left and then 7 units down.
C) Rectangle ABCD was rotated 180° around the origin and then translated 7 units down.
D) Rectangle ABCD was translated 2 units left and then 3 units down.
Answers
the best answer is
b
Answer:
B
Step-by-step explanation:
A package of hot dogs cost $2 and a package of hamburger cost $8. You bought a total of 11 packages of meat and you spent $52. How many packages of hotdogs did you buy? Use a system to solve. 6 packages 4 packages 7 packages 5 packages
Answers
To solve this, you have to write and solve a system of equations. Let B stand for hamburgers and H stand for hot dogs.
B + H = 11
8B + 2H = 52 If you multiply the top equation by -2, you can solve by eliminatoin.
-2B + -2H = -22
8B + 2H = 52 Add the equations
6B = 30
B = 5
If you bought 5 packages of hamburgers, then you bought 6 packages of hot doges. 11 - 5 = 6
carl wants to buy a television that costs $500, including taxes. To pay for the television, he will use a payment plan that requires him to make a down payment of $125, and then pay $72.50 each month for 6 months. What is the percent increase from the original costs of the television to cost of the television using the payment plan?
Answers
The percent increase from the original costs would be:
($560-$500) / $500 * 100%= 12%
Answer:
($560-$500) / $500 * 100%= 12%
Step-by-step explanation:
Hope it helps
shannon uses 30 inches of ribbon to make one bow how many feet of ribbon are needed to make 10 bows
Answers
Since 30 inches of ribbon is used in one bow, to make 10 bows, we need multiply:
30 x 10 = 300
Now, we need to convert the inches to feet.
300 in = 25 ft
Our answer is 25 ft of ribbon.
Hope this helped!
Two parallel lines are cut by a transversal. Which statements are true for all such cases? Select three that apply.
A. Each pair of vertical angles is congruent.
B. Each pair of corresponding angles is congruent.
C. Each pair of supplementary angles is congruent.
D. Each pair of alternate interior angles is congruent.
Answers
For c, if the pair of angles are supplementary and congruent, they can only be 90° because they are congruent ( meaning they are the same measurements) however this is not the case all the time
Hope this helps
A ramp has a rise of 10 feet and run of 50 feet find the slope
Answers
The slope with the given rise and run is 1/5.
Given that, a ramp has a rise of 10 feet and a run of 50 feet.
We need to find the slope.
What is the slope?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of a line in the coordinate plane. Calculating the slope of a line is similar to finding the slope between two different points. In general, to find the slope of a line, we need to have the values of any two different coordinates on the line.
Now, slope=rise/run
=10/50
=1/5
Therefore, the slope is 1/5.
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The length of a rectangle is 4 times its width. The area of the rectangle is 144 square inches. Find the dimensions of the rectangle
Answers
4w*w=144
4w^2=144
w^2=38
w=6.16
l=4*6.16=24.63
(*there might be small rounding errors)
and they are both in inches
The width is 6 inches and the length is 24 inches.
To find the dimensions of the rectangle when given the area and the relationship between length and width, we will use algebra. Let the width be w inches. The length is 4 times the width, so the length is 4w inches. The area of the rectangle is w times the length (4w), which gives us w * 4w = 144 square inches. Simplifying, this equation becomes 4w^2 = 144 inches2. To find w, we divide both sides by 4, getting w^2 = 36. Taking the square root of 36 gives us w = 6 inches. Since the length is four times the width, the length is 24 inches. Therefore, the dimensions of the rectangle are 6 inches by 24 inches.
Answer these for 22 points
Answers
8. ΔAEC = 3/12 = 1/4
.. ΔDFB = 2/8 = 1/4
9. The angles at E, G, and F are right angles. Lines CE and BF are parallel, so the alternate interior angles at B and C where the transversal AD crosses them are equal. The triangles of interest are similar by AA~.
10. See problem 7. The ratio is the same.
11. Hard to tell what rule they want you to state. Every axis-aligned right triangle with its hypotenuse on AD will have the same ratio of side lengths. (That's one of the features of the graph of a line. It has the same slope everywhere, measured over any distance.)
The johnson twins were born twelve years after their older sister.This year,the product of the three siblings' ages is exactly 1244 more than the sum of their ages.How old are the twins?
Answers
(s - 12)(s - 12)(s). The sum of their ages would be s + (s - 12) + (s - 12). Since the product of their ages is 1244 more than the sum, we have the equation
(s - 12)(s - 12)(s) = s + (s - 12) + (s - 12) + 1244
Multiplying the first two factors on the left (First, Outer, Inner, Last) we have
(s² - 12s - 12s + 144)(s) = s + (s - 12) + (s - 12) + 1244
Combining like terms on both sides we have:
(s² - 24s + 144)(s) = 3s + 1220
Using the distributive property on the left we have
s³ - 24s² + 144s = 3s + 1220
We don't want a variable on both sides, so subtract 3s:
s³ - 24s² + 144s - 3s = 1220
Subtract 1220 from both sides to get our cubic equation to solve:
s³ - 24s² + 144s - 3s - 1220 = 0
Combine like terms:
s³ - 24s² + 141s - 1220 = 0
We want to consider the factors of 1220. After using a factor tree, we get the factors are 2*2*5*61. This gives us possible ages for the sister of 2, 4 (2*2), 4, 10 (2*5), 20 (2*2*5), 61, or older. We can eliminate 2, 4, and 5, since the twins are born and they are 12 years younger than her. This leaves 20, 61 or the older ages (which are improbable; the next age from 61 would be 61*2 = 122).
We will use synthetic division to try 20. Set up the problem with the coefficients of our equation (first image). We bring the 1 down. Now we multiply this 1 by the 20 we're dividing by and put it under the second coefficient (second image). We add these two together now (third image). Continue by multiplying again by 20, then adding, etc. (remaining images; I can't add more than 5, but you keep the pattern going). Since we get 0 at the end, that means that 20 did indeed divide into the problem and is the sister's age. Since the twins are 12 years younger, they are 20-12 = 8.
A teacher asked the class to solve the equation 3(times+2)= 21 Robert wrote 3 times + 6=21 as his first step. Which property did he use.
1. Associative property
2. Commutative property
3. Distributive Property
4. Zero property of addition
Answers
Vincent uses 2 cups of flour for every 12 muffin that he makes. What is the total number of cups of flour Vincent will use to make 4 muffins.
Answers
Answer:
[tex]\frac{2}{3}\ cups\ of\ flour[/tex]
Step-by-step explanation:
we know that
Vincent uses 2 cups of flour for every 12 muffin that he make
so
Using proportion
Find out what is the total number of cups of flour Vincent will use to make 4 muffins
Let
x -----> the total number of cups of flour
[tex]\frac{2}{12}\frac{cups\ of\ flour}{muffins}=\frac{x}{4}\frac{cups\ of\ flour}{muffins}\\\\x=2*4/12\\\\x=\frac{2}{3}\ cups\ of\ flour[/tex]
May anyone HELP ME please
Answers
1b. 6.4*10^7 +0.54*10^7 = 6.94*10^7 . . . . square miles
.. yes, we can find the same answer this way
2. The ratio of areas is 6.4*10^7/(5.4*10^6) ≈ 11.85
The Pacific Ocean is about 12 times the size of the Arctic Ocean.
The difference of areas is 6.4*10^7 -0.54*10^7 = 5.86*10^7
The Pacific Ocean is 5.86*10^7 square miles larger than the Arctic Ocean.
In a geometric sequence, a7=14 and r= -1/2. What is the 10th term of the sequence?
• -3.50
• -1.75
• 1.75
• 3.50
Answers
in geometric sequence the formula is
an=a1*r^(n-1)
where
an---------> is the nth term
a1 --------> is the first term
n ----------> is the number of the term
r ----------> is the common ratio
a7=14
r=(-1/2)
Step 1
find the a1 term
a7=a1*r^(7-1)-------------> 14=a1*(-1/2)^(6)
a1=14/[(-1/2)^(6)]------------> a1=896
Step 2
find the a10 term
a10=a1*r^(10-1)--------> 896*(-1/2)^9=-1.75
the answer is a10=-1.75
1) a yes 2
2) c 405
3) b an=-4 (-2) -64
4) a triangle 4
5) b -1.75
The line plot shows the weight gain, in pounds, of several dogs seen on Monday by a veterinarian at the animal clinic. A number line with one x above .5, one x above 1.5, one x above 2, one x above 3, two xs above 3.5, two xs above 4, one x above 4.5, and one x above 8.5. How many dogs gained fewer than 3 lb? Enter your answer in the box.
Answers
Answer:
3 x's
Step-by-step explanation:
Write a problem that can be solved by comparing feet and inches using a model.Include a solution.Explain why you are changing from a larger unit to a smaller unit . ASAP
Answers
Ex. 5 feet= 60inches
See pic attached ... Urgent
Answers
Answer:
3) y = -1 + (1/2)x
This is a linear function.
4) y = 1.7(4^x)
This is an exponential function.
What’s bigger? 0.125 or 1/8?
Answers
1/8 IS BIGGER
A function has the rule y = -2x + 11. Which of the following ordered pairs represents an input of 4 and its output?
(4, 3.5)
(4, 3)
(3, 4)
(3.5, 4)
Answers
y=-2(4)+11
y=(-8)+11
y=3
(4,3)
A circle flower garden has a radius of 4.5 feet. What is the circumference of the flower garden
Answers
What is the volume of a right circular cylinder with a diameter at 46.25 cm and a height of 18.5 m?
Answers
V = pi * r ^ 2 * h
Where
r: radio
h: height
Also we have:
r = d / 2
Where
d: diameter.
Substituting values:
V = pi * ((d / 2) ^ 2) * h
V = (3.14) * ((46.25 / 2) ^ 2) * 18.5
V = 31064.5352
Answer:
The volume of a right circular cylinder is:
V = 31064.54 cm ^ 3
Answer:
Volume of right circular cylinder(V) is given by:
[tex]V = \pi r^2h[/tex] ......[1]
where,
r is the radius of the cylinder
h is the height of the cylinder.
As per the statement:
A right circular cylinder with a diameter at 46.25 cm and a height of 18.5 m
⇒diameter(d) = 46.25 cm and height(h) = 18.5 cm
We know that:
diameter(d) = 2r
then;
[tex]46.25 = 2r[/tex]
Divide both sides by 2 we have;
[tex]23.125 = r[/tex]
or
r = 23.125 cm
Substitute these given values in [1] we have;
Use [tex]\pi = 3.14[/tex]
[tex]V = 3.14 \cdot (23.125)^2 \cdot 18.5[/tex]
⇒[tex]V = 31,064.5351 cm^3[/tex]
Therefore, the volume of a right circular cylinder to the nearest hundredth is, 31,064.54 cubic centimeters.
The verticals of a parallelogram are G(-8,3), R(-7,6),A(-3,6), and M(-4,3). Graph GRAM and G’R’A’M’, it’s image after a translation 13 units right and 2 units up
Answers
The image of parallelogram GRAM, G'R'A'M', after a translation 13 units right and 2 units up is formed by the points G'(5, 5), R'(6, 8), A'(10, 8), and M'(9, 5).
To graph the parallelogram GRAM and its image G'R'A'M' after a translation 13 units right and 2 units up, follow these steps:
Plot the points G(-8,3), R(-7,6), A(-3,6), and M(-4,3) to form the parallelogram GRAM.
Calculate the new coordinates for G', R', A', and M' after the translation. You'll add 13 units to the x-coordinates (rightward) and 2 units to the y-coordinates (upward):
G'(-8 + 13, 3 + 2) = G'(5, 5)
R'(-7 + 13, 6 + 2) = R'(6, 8)
A'(-3 + 13, 6 + 2) = A'(10, 8)
M'(-4 + 13, 3 + 2) = M'(9, 5)
Plot the new points G'(5, 5), R'(6, 8), A'(10, 8), and M'(9, 5) to form the parallelogram G'R'A'M'. These points will be the image after the translation.
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The first step to solve the equation x/4 - 3/4 = 16 is shown below?
x/4 - 3/4 + 3/4 = 16 + 3/4
A.Addition Property of Equality
B.Subtraction Property of Equality
C.Multiplication Property of Equality
D.Division Property of Equality
Answers
Answer:
The first step to solve the equation Addition Property of Equality.
Step-by-step explanation:
Given the equation
[tex]\frac{x}{4}-\frac{3}{4}=16[/tex]
we have to find the first step to solve the above equation.
To solve the above equation we have to combine the like terms here we have to combine the constant terms.
[tex]\frac{x}{4}-\frac{3}{4}=16[/tex]
[tex]\text{Therefore, to solve the equation we have to add }\frac{3}{4}\text{ on both sides}[/tex]
[tex]\frac{x}{4}-\frac{3}{4}+\frac{3}{4}=16+\frac{3}{4}[/tex]
[tex]\frac{x}{4}=\frac{67}{4}[/tex]
[tex]x=67[/tex]
Hence, the first step to solve the equation is the
Addition Property of Equality
A real estate agent spends $79.95 each month for cell phone service. About how much money does the agent spend for 48 months
Answers
He would be spending $3,837.60
(Multiply 79.95 by 48)