The sum of the expression in simplest form is 8( x + 2y)
What are algebraic expressions?Algebraic expressions are expressions made up of variables, terms, factors, constants and coefficients.
They are also made up of mathematical operations such as addition, subtraction, multiplication, division, etc
Given the expressions;
(3x+9y) and (5x+7y)
Let's find the sum
3x + 9y + 5x + 7y
collect like terms
3x + 5x + 9y + 7y
8x + 16y
Find common factor
8( x + 2y)
Thus, the sum of the expression in simplest form is 8( x + 2y)
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One lap around a track is 1/4 mile. It takes Parker 1/20 hour to sprint
one lap. What is Parker's unit rate, in miles, around the track
Answer:
Parker's unit rate is 5 miles per hour or 5mph.
Step-by-step explanation:
1 hour = 60 minutes
60/20 = 3 minutes
3 minutes for 1 lap
1 lap = 1/4 mile
1/4 mile (1 lap) x 4 laps = 1 mile
4 laps = 12 minutes
12 minutes per mile
60/12 = 5
5 miles per hour
A Web music store offers two versions of a popular song. The size of the standard version is 2.9 megabytes (MB). The size of the high-quality version is 4.1 MB. Yesterday, there were 1360 downloads of the song, for a total download size of 4532 MB. How many downloads of the high-quality version were there?
The number of standard version download and high-quality download is 870 and 490 respectively.
Number of downloads of the high-quality versionlet
Number of high-quality download = yNumber of standard version = xx + y = 1360
2.9x + 4.1y = 4532
From (1)
x = 1360 - y
Substitute x = 1360 - y into (2)
2.9x + 4.1y = 4532
2.9(1360 - y) + 4.1y = 4532
3944 - 2.9y + 4.1y = 4532
- 2.9y + 4.1y = 4532 - 3944
1.2y = 588
y = 588/1.2
y = 490
Substitute y = 490 into (1)
x + y = 1360
x + 490 = 1360
x = 1360 - 490
x = 870
So therefore, number of standard version download and high-quality download is 870 and 490 respectively.
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Can somebody help me if you know what this is
Answer:-2,2.5,-7/3
Step-by-step explanation:
Which equation represents a line which is parallel to the line
y = −3/5x − 7?
-
3x + 5y = 15
5x + 3y = 12
3y - 5x = 6
3x - 5y = -30
Submit Answer
Answer:
3x+5y=15
Step-by-step explanation:
3x+5y=15
5y=-3x-15
y=-3/5x-3
Because it has the same slope and a different y-intercept, it is parallel because the lines won't ever touch.
1. Consider the following propositions
• P: 2+5=3
. Q: Warsaw is the capital of Poland.
. R: The US has the largest population in the world.
R= is incorrect
the answer is china :)
The sum of two numbers is 14. Using x to represent the smaller of the two numbers , translate "the sum of twice the smaller number and two more than the larger number" into a variable expression. Then simplify
The smaller number is 4 and the larger number is 10.
Given that, the sum of the two numbers is 14.
What is an equation?In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, x represents the smaller of the two numbers.
Then the larger number is
The sum of twice the smaller number and two more than the larger number = 2x+2
Now, x+2x+2=14
⇒3x+2=14
⇒3x=12
⇒x=4
So, 2x+2=10
Therefore, the smaller number is 4 and the larger number is 10.
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Lena has to make 20 gallons of punch for a potluck. The punch is made of soda and fruit drink. The cost of the soda is $1.90 per gallon and the cost of the fruit drink is $2.10 per gallon. Lena’s budget requires that the punch cost $2 per gallon. How many gallons of soda and how many gallons of fruit drink does she need?
Answer:
10 for each
Step-by-step explanation:
1.90 x 10 = 19
2.10 x 10 = 21
so 19 + 21 = 30
Charmaine invested her savings in two investment funds. The amount she invested in Fund A was 3 times as much as the amount she invested in Fund B. Fund A returned a 6% profit and Fund B returned a 15% profit. How much did she invest in Fund B, if the total profit from the two funds together was 1380?
Using a system of equations, it is found that she invested 318.71 into Fund B.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: Amount invested in Fund A.Variable y: Amount invested in Fund B.The amount she invested in Fund A was 3 times as much as the amount she invested in Fund B, hence:
x = 3y.
Fund A returned a 6% profit and Fund B returned a 15% profit, and the total profit was of 1380, hence:
1.06x + 1.15y = 1380.
We have that x = 3y, hence:
1.06(3y) + 1.15y = 1380.
4.33y = 1380
y = 1380/4.33
y = 318.71.
She invested 318.71 into Fund B.
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Find the y-intercept, x- intercept and slope of the line with equation 8x +12y = 16.
(PLEASE EXPLAIN IN STEPS)
Answer juvhfVO"zohgvjozi nandish pro nbhvmno
if LK=MK, LK=7x-10, KN=x+3, MN=9x-11, and KJ=28, find LJ
Congruent segments are LK=MK, LK=7x-10, KN=x+3, MN=9x-11, and KJ=28, the LJ will be-
LJ = 18 + 28 = 46
LJ = 18 + 28 = 46
These are Congruent segments
Let J, K, L, M, N are points on the same line.
MK = MN + (-KN) = MN - KN = 9x - 11 - x - 3 = 8x - 14
As LK = MK and LK = 7x - 10, then
7x - 10 = 8x - 14
8x - 7x = -10 + 14
x = 4
LJ = MK + KJ
MK = LK = 7x - 10 = 7(4) - 10 = 28 - 10 = 18
LJ = 18 + 28 = 46
Congruent segments are segments which have the equal length. ≅ points that lie at the equal line are called collinear.
A theorem is a mathematical assertion that can be proved. The midpoint of a phase is a point that divides the phase into two congruent segments
If three or more points lie on a single straight line, they are said to be collinear. An axis is a term used to describe a line on which points are located, particularly if that line is connected to a triangle or other geometric shape. Since two points determine a line, two points are trivially collinear.
Two line segments are congruent if they have the same length. They do not need to have the same position or orientation
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Hi
The following set of four ordered pairs below defines the vertices, in counterclockwise order, of a quadrilateral (four-sided figure).
((-4, 1), (1, 2), (-1,6).(-6,5)}
Step 1 of 3: Find the slopes of the indicated sides of the quadrilateral. Simplify your answer.
Side connecting (-4,1) and (-6,5)
Side connecting (1, 2) and (-1,6)
G
7
a
Suba
The slope of the side connecting (-4,1) and (-6,5) = -2
The slope of the side connecting (1,2) and (-1,6) = -2
The slope of the segment joining two points (x₁, y₁) and (x₂, y₂) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
We have to find the slope of the side joining the points (x₁, y₁) = (-4,1) and (x₂, y₂) = (-6,5)
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{5-1}{-6--4}[/tex]
= 4/ -2
= -2
We have to find the slope of the side joining the points (x₁, y₁) = (1, 2) and (x₂, y₂) = (-1,6)
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{6-2}{-1-1}[/tex]
= 4/-2
= -2
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Simplify negative 3 and 4 over 5 minus 5 and 2 over 3.
Answer:
-9 7/15
Step-by-step explanation:
I took the test lol. Also if your in advanced you should know this!
-3y+7y+4y^3-2y^2+6y^3-7y^3-5y
What is the length of a rectangular holding pond with an area of 5 1/10 square miles and a width of 1/6 mile?
what is 0.25x 2.6 pls help me this is hw
Answer:
0.65
Step-by-step explanation:
Ethan got his first job and is making $8.50 an hour. He really wants to buy a couple of video games, so he is trying to estimate how much his paycheck will be. The first week Ethan works, he gets 18 hours. The second week Ethan works, he gets 25 hours. If Ethan pays 10% federal income tax and 2% state income tax, what can he expect to bring home in his first paycheck?
If Ethan got his first job and is making $8.50 an hour. He really wants to buy a couple of video games, so he is trying to estimate how much his paycheck will be. The amount he can expect to bring home in his first paycheck is: $321.64.
PaycheckTotal hours=18 hours+25 hours
Total hours=43 hours
Income tax=Federal income tax+ State income tax
Income tax=10%+2%
Income tax=12%
Hence,
First paycheck:
First paycheck=$8.50×43 hours×(1-12%)
First paycheck=$8.50×43 hours×0.88
First paycheck=$321.64
Therefore if Ethan got his first job and is making $8.50 an hour. He really wants to buy a couple of video games, so he is trying to estimate how much his paycheck will be. The amount he can expect to bring home in his first paycheck is: $321.64.
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Thomas bought 12 glass and plastic cups from
the store. Glass cups cost $3.25 and plastic
cups cost $2.75. Thomas spent a total of
$36.00. How many glass cups (g) and how
many plastic cups (p) did he buy?
g+p=12
3.25g +2.75p = 36
[?] glass cups [] plastic cups
Thomas bought 6 glass cups and 6 plastic cups
How to calculate the number of glass and plastic cups ?
Thomas bought 12 glass and plastic cups from the store
Glass cups costs $3.25
Plastic cups cost $2.75
He spent a total of $36
Let g represent the number of glass cups and p represent the number of plastic cups
g + p= 12.........equation 1
3.25g + 2.75p= 36..........equation 2
From equation 1
g+p= 12
g= 12-p2
Substitute 12-p for g in equation 2
3.25(12-p)+2.75p = 36
39-3.25p+2.75p= 36
39-0.5p= 36
-0.5p= 36-39
-0.5p= -3
p= -3/-0.5
p= 6
Substitute 6 for p in equation 1
g + 6= 12
g= 12-6
g= 6
Hence there are 6 glass cups and 6 plastic cups
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Calculate the perimeter of the rectangle in centimeters.
Lenght= 14cm
Width= 8cm
Shawn has 2 3/4 cups of berries. He uses 5/8 cups of berries to make a smoothie. He then uses 1/2 cup for a fruit salad.
Part A: How many cups of berries did he use?
Michael is trying to show that ABC to congruent to A'B'C
To find the reflection of ΔABC in the x-axis, the points would move as follows:
Point A would move 8 units Points B would remain at same point hence move 0 unitsPoint C would move 8 unitsUsing the original coordinates, Δ A'B'C' is a reflection of Δ ABC in the line?
line x = 4The triangles are?
The two triangles are congruentThe line of reflection Michael used is?
Michael used line x = 4What is reflection?
Reflection as used in geometry is the representation of an image in the mirror image copy. Reflection is done with respect to a line called line of reflection. Images formed are of equal distant to the line of reflection and the images are usually congruent.
Reflection as represented on a graph is most times in x axis or y axis. This axis shows the location of the line of reflection and it is very important when determining the position of the reflected image.
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if AC=38 3/4,AB=6x, BC=8x+1/4
what’s the value of x?
Applying the segment addition postulate:
x = 2.75
AB = 6x = 6(2.75) = 16.5 units
BC = 8x + 1/4 = 8(2.75) + 1/4 = 22.25 units.
What is the Segment Addition Postulate?Based on the segment addition postulate, since B lies between points A and C on a line segment, then:
AB + BC = AC
AC = 38 3/4
AB = 6x
BC = 8x + 1/4
Substitute
6x + 8x + 1/4 = 38 3/4 [segment addition postulate]
14x + 1/4 = 155/4
14x = 155/4 - 1/4
14x = (155 - 1)/4
14x = 154/4
14x × 4 = 154
56x = 154
x = 154/56
x = 2.75
AB = 6x = 6(2.75) = 16.5 units
BC = 8x + 1/4 = 8(2.75) + 1/4 = 22.25 units.
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Lisa, Bree, and Caleb are meeting at an amusement park. They each enter at a different gate. On this diagram of the park, explain how the friends could calcuate the point that is equistant from all three gates
By joining the entry point of all three friends to form a triangle and then finding the centroid of this triangle , they can calculate the required point.
If Lisa, Bree, and Caleb are meeting at an amusement park and each enter at a different gate as shown in reference picture attached hereby, the friends could calculate the point that is equidistant from all three gates by the equation [(Distance between gate 1 and gate 2) = (Distance between gate 2 and gate 3) = (Distance between gate 1 and gate 3)]
As per question statement, Lisa, Bree, and Caleb are meeting at an amusement park and each enter at a different gate as shown in reference picture attached hereby.
We are required to determine to calculate the point that is equidistant from all three gates.
The required equation goes as [(Distance between gate 1 and gate 2) = (Distance between gate 2 and gate 3) = (Distance between gate 1 and gate 3)],
Where, they will have to use the distance formula to find the distances in between which goes as [tex]D=\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2} }[/tex], in the above mentioned equation.
Equation: In mathematics, an equation is a formula or a mathematical statement, that expresses the equality of two expressions, by connecting them with the "Equal To" sign.Complete question: Lisa, Bree, and Caleb are meeting at an amusement park. They each enter at a different gate. On this diagram of the park, explain how the friends could calculate the point that is equidistant from all three gates.
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Frame three equations with solution x=-5
The three equations with solution x=-5 Are as follows:
25 + x = 15 ............... equation 1.
7x = -35 .......................equation 2.
15 + x = 10 ..................equation 3
In mathematics, what is linear equation?There is not more then one or two variables in a linear equation. In a linear equation, no variable is raised to a power larger than one or utilized as the denominator of a fraction. When you locate two values that satisfy a linear equation and display them on a coordinate grid, every one of the points falls on the same line.
What is a linear equation with one variable?A linear equation in one variable seems to be an equation that has just one solution and is stated in the form ax+b = 0, where a but instead b are two integers and x is a variable. 2x+3=8, for example, is a mathematical expression with a single variable.
According to the given information:x=-5 Given
This also can be written as :
25 + x = 15 ............... equation 1.
7x = -35 .......................equation 2.
15 + x = 10 ..................equation 3
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b)
73cm
92cm
56 cm
What is the
the
area and perimeter
Answer:
Area=2044..... perimeter=221
Step-by-step explanation:
Step1:- Area =1/2×breath×height
1/2×73×56
1/2×4088
= 2044
Area =2044cm^2
Step2:- Perimeter= a+b+c
=73+56+92
=221
Perimeter=221cm
Does 8÷10+7÷100 equal to 0.87
Answer:
Yes
Step-by-step explanation:
8÷10+7÷100=
8/10 + 7/100=
80/100 + 7/100= ==> make the denominators equal to each other
(80+7)/100=
87/100=0.87 √
Answer:
yes it does
Step-by-step explanation:
8÷10=0.8
7÷100=0.07
0.8+0.07=0.87
or the easy way ig
8÷10+7÷100=0.87
What’s the volume of a 9ft rectangular prism
The volume of the prism with length as 9 feet will be 9 w h where w is the width and h is the height of the prism.
We are given a prism.
It is a rectangular prism.
We are also given that it if 9 feet.
We need to find the volume of this rectangular prism.
V = w × h × l
where
w = width of the prism
h = height of the prism
l = length of the prism
Now, we are given that l = 9 feet
So, V = w × h × l
V = 9 w h
Therefore, we get that the volume of the prism with length as 9 feet will be 9 w h where w is the width and h is the height of the prism.
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Find the distance between the points A and B given below. (That is, find the length of the segment connecting A and B.) Round your answer to the nearest hundredth. 1 unit B
Answer:
theres no picture
Pentagon FGHJK is similar to pentagon MPQST. K What is the value of x? A 16 cm B Not here C) 12.5 cm 18 cm G S 12 cm M P
Answer:
I think it's a (16cm) ....
In Smithville, there were 234 teachers in 1990 and 318 teachers in 2000. Find the percent of increase in the number of teachers in Smithville during this time period.
Answer:
35.90%
Step-by-step explanation:
First, subtract the new no with that of 1990
318-234= 84
percentage of increase will be given by;
84/234×100= 35.8974%
Which of the following correctly explains how the Product of Powers and Quotient of Powers Properties helps you to multiply and divide numbers
in scientific notation?
OA) Each number has a factor that is a power of 10. Because the bases are the same, these properties can be applied to multiply or di-
vide the powers of 10.
OB) Because numbers written in scientific notation have exponents, you can use the Laws of Exponents to multiply or divide the
numbers.
OC) The Product of Powers Property and the Quotient of Powers Property can be used to multiply and divide any numbers.
OD) Each number has a factor that is a power of 10. Because the bases are different, these properties can be applied to multiply or di-
vide the powers of 10.
The correct option regarding the operations with scientific notation is given as follows:
B) Because numbers written in scientific notation have exponents, you can use the Laws of Exponents to multiply or divide the numbers.
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
An example of a multiplication in scientific notation is:
[tex]2 \times 10^3 \times 3 \times 10^5 = 6 \times 10^{3 + 5} = 6 \times 10^8[/tex]
That is, we multiply the factors, and for the bases of 10, we keep the bases and add the exponents. In a division, we would divide the factors, and for the base of 10, we keep the base and subtract the exponents.
That is, since the numbers have exponents, rules of exponents are used for both multiplication and division, and option b is correct.
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