11) Solve the system by the addition method.
5x + 15y = -80
0.1x = -4.1 -0.3y
Answers
"5x + 15y = -80" + "0.1x = -4.1 -0.3y" using the addition method given equation "5.1x + 15.3y = -12.1".
What is the addition method of equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. Using the Addition Method to Solve Two-Variable Equation Systems The addition method, also known as the elimination method, is a third approach to solving systems of linear equations. In this method, the sum is zero by adding two terms with the same variable but opposite coefficients.So, "5x + 15y = -80" + "0.1x = -4.1 -0.3y" using addition method:
Change 0.1x = -4.1 -0.3y to: 0.1x + 0.3y = -4.1Now, "5x + 15y = -80" + "0.1x = -4.1 -0.3y" (refer to the image attached below for calculation)The resulting equation is: 5.1x + 15.3y = -12.1
Therefore, "5x + 15y = -80" + "0.1x = -4.1 -0.3y" using the addition method given equation "5.1x + 15.3y = -12.1".
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Related Questions
Solve each of these systems of equations. You may use either the substitution or elimination method.2x+y=15x+6y =4
Answers
Answer:
x=2/7 and y=3/7
Explanation:
Given the systems of equations:
[tex]\begin{gathered} 2x+y=1 \\ 5x+6y=4 \end{gathered}[/tex]We use the substitution method to solve.
Step 1: Make y the subject in the first equation.
[tex]\begin{gathered} 2x+y=1 \\ y=1-2x \end{gathered}[/tex]Step 2: Substitute y into the second equation.
[tex]\begin{gathered} 5x+6y=4 \\ 5x+6(1-2x)=4 \\ 5x+6-12x=4 \\ 5x-12x=4-6 \\ -7x=-2 \\ x=-\frac{2}{-7} \\ x=\frac{2}{7} \end{gathered}[/tex]Step 3: Solve for y
[tex]\begin{gathered} y=1-2x \\ =1-2(\frac{2}{7}) \\ =1-\frac{4}{7} \\ y=\frac{3}{7} \end{gathered}[/tex]Therefore, x=2/7 and y=3/7.
based on the graph what is the solution to the system of the equation?
Answers
The graph cross at (2, 1) . Therefore, the solution of the of the system of equation is (2, 1). x = 2 and y = 1.
Solve 2x2 + x - 4=0.X2+be += 0DONEIntro
Answers
Find the values of x that make mlln
Answers
Answer:
4x² = 100° (corresponding angles)
x² = 100÷4
= 25
x = √25
= 5°
The population of the city of Woodville is growing in a constant rate the expression 35,000+2400 X model would real population which three statements are correct
Answers
The expression is,
38000+2400x.
The x represents the number of year.
38,000 represents the current population.
2400 represents the yearly growth.
Thus, option (a), (c) and (d) are the correct solution.
For her 9th birthday, Cindy
wanted to buy her class
number nine donuts. If each
number donut costs $1.09 and
she has 22 students in
her class, how much will
she spend on donuts?
Answers
Answer:
23.98 dollars
Step-by-step explanation
Multiply 22 x 1.09
Answer:
$23.98
Step-by-step explanation:
If there's 22 students to serve, Cindy needs to take the price of one donut ($1.09) and multiply that by 22.
22 x 1.09 = 23.98
Eleni's landscaping company placed two orders. The first order was for 13 bushes and 4 trees and totaled $487. The second order was for 6 bushes and 2 trees and totaled $232. What is the price of one tree?
Answers
The required cost of the bushes is $23 and the cost of the tree is $45.
What is arithmetic?
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Let the prices of bushes are x and prices of tress are y,
According to the question,
13x + 4y = 487 - - - - - -(1)
6x +2y = 232 - - - - - - -(2)
From equation 2
y = 116 - 3x - - - - -(3)
Put this y in equation 1
13x + 4(116 - 3x) = 487
13x + 464 - 12x = 487
x = 487 - 464
x = 23
Now put this x in equation 3
y = 116 - 3(23)
y = 116 - 69
y = 45
Thus, the required cost of the bushes is $23 and the cost of the tree is $45.
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Nikki has rowing lessons every four days and tennis every 7 days. If she had both lessons on the last day of the previous month, when will she have both lessons on the same day of the current month?
Answers
we know that
Nikki has rowing lessons every four days
so
4 8 12 16 20 24 28
and
tennis every 7 days
7 14 21 28
therefore
She will have both lessons again the day 28 of the current month
Using factoring, what are the solutions to the polynomial below? 2x ^ 3 + 4x ^ 2 - 30x = 0
Answers
We can start solving the solution to the polynomial given by factoring out 2x, getting:
[tex]2x(x^2+2x-15)=0[/tex]The expression inside the parenthesis is a quadratic equation. By methods of factoring, we can rewrite this as:
[tex]\begin{gathered} 2x((x+5)(x-3))=0 \\ 2x(x+5)(x-3)=0 \end{gathered}[/tex]Solving for the value of x that satisfies the polynomial given, we have:
[tex]\begin{gathered} 2x=0,x+5=0,x-3=0 \\ x=0,x=-5,x=3 \end{gathered}[/tex]Hence, the solutions to the polynomial given are x = -5, 0, 3.
Answer: x = -5, 0, 3
Heather decorated her house for a birthday party. She had 30 balloons to hang in three different rooms?
Which expression represents the total number of balloons if each room had an equal number of balloons as shown in the image?
A. 10x3
B. 3x10
C. 5x6
D. 6x5
Answers
Option A, which is 10×3, represents the total number of balloons if each room had an equal number of balloons as shown in the image.
What is meant by expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.An expression is 3x - 2. On the other hand, an equation is when two independent expressions are linked together by an equal to sign. For instance, an equation is when 3x - 2 = 5 + x.To learn more about expression refer to:
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One afternoon you picked 6/8 of a pound of strawberries that night you ate 3/6 of what you picked
Answers
Given :
the amount of picked strawberries = 6/8 pounds
you ate 3/6 of what you picked.
so, the amount is eaten =
[tex]\frac{6}{8}\times\frac{3}{6}[/tex]cross out the number 6
so, the answer will be = 3/8 pounds
Marisa's hair grew 1 1/4 inches in 2 months. How many inches will her hair grow in 1 month?
Answers
Answer:
5/8 of an inch.
Step-by-step explanation:
do these pairs of values (x and y) represent two quantities that are proportional? x. y3. 125. 206. 249. 36
Answers
Info given
We have the following info given
x. y
3. 12
5. 20
6. 24
9. 36
Solution
In order to see if the two quantites are prportional we can check the following:
k=y/x
If we analyze the first pair of values we have:
k= 12/3=4
And for the next pairs we have:
k= 20/5=4
k= 24/6=4
k=36/9=4
So then as we can see the value of k is the same so then we can say that x and y are proportional since for each unit that x increase y increase 4 units
Is 8 a solution of the equation x+6=−2?
Answers
a box has the dimensions of 5, 2x, and 6x. Find a total area of all faces of this box
Answers
The total area of the box is 10
Total area
Total area means the area including the base(s) and the curved part. It is the total area covered by the surface of the object.
Given,
A box has the dimensions of 5, 2x, and 6x.
Here we need to find the total area of all faces of this box.
Basically, area is the total area occupied by the surface.
To find the total area of the box, we have to add the all the side values.
So, when we add the side value, then we get,
=> Total area = 5 + 2x + 6x
=> 8x + 5
=> 8x = 5
=> x = 5/8
Here we removed the negative sign because the area doesn't take the negative value.
So, the side values are
=> 2x = 2 (5/8) = 5/4
=> 6x = 6(5/8) = 15/4
Now, we have to find the total area as,
=> 5 + 5/4 + 15/4
=> 5 + 20/4
=> 5 + 5
=> 10
Therefore, the total area of the box is 10.
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Percent decrease of $16 to $4
Answers
Answer:
75% decrease
Step-by-step explanation:
x/100*12/16
x = percent decrease
subtract what you got in the end (4) from the original number (16) to get 12
(12*100) ÷ 16
1200 ÷ 16 = 75% decrease
x = 75%
I need help answering this please ! The calculator has to be In degree mode and the second picture is used to help you find the answer
Answers
A) AB is a side and not an angle. A side is a length, an angle is a junction of two lines.
B) You are given a side, AC and two angles, Angles B and C
C) Angles and lines are named according to their oppositeness. Angle A is opposite to side a.
[tex]\frac{\sin A}{BC}=\frac{\sin B}{AC}=\frac{\sin C}{AB}=\frac{\sin A}{BC}=\frac{\sin50}{12}=\frac{\sin 62}{AB}[/tex]D) To find AB, we crossmultiply with the expression in the middle of the equation. This gives:
[tex]AB\text{ = }\frac{\text{12 sin 62}}{\sin 50}=13.8313[/tex]Line AB is 13.83 to the nearest hundredth
The Empire State building in New York City is approximately 1250 ft tall. How many U.S. dimes would be in a stack of the same height? Each dime is 1.35 mm thick.
Answers
Answer:
It is necessary to stack 277778 dimes.
Step-by-step explanation:
The height of the Empire State building in meters is 1250 * 0,30 = 375 meters.
6. A poll was taken of 14,502 working adults aged 40-70 to determine their level of education. The participants were classified by sex and by level of education. The results are shown below. Education Level Male Female Total High School or Less 3618 3117 6735 Bachelor's Degree 2860 3762 6622 Master's Degree 574 476 1050 Ph.D. 41 54 95 Total 7093 7409 14,502 A person is selected at random. Compute the following probabilities. (a) What is the probability that the selected person does not have a Ph.D.? (b) What is the probability that the selected person does not have a Master's degree? (c) What is the probability that the selected person is female or has a Master's degree? (d) What is the probability that the selected person is male or has a Ph.D.?
Answers
Okay, here we have this:
We need to calculate the probability that the selected person is female or has a Master's degree, so according with this we obtain the following information:
The number of female is 7409, and the number of male with a master's degree is 574, so finally we obtain the following probability:
[tex]\begin{gathered} p=\frac{7409+574}{14502} \\ p=\frac{7983}{14502} \\ p\approx0.5505 \\ p=55.05\text{ percent} \end{gathered}[/tex]Finally we obtain that the percentage is %55.05.
Solve: 82 ÷ 3 Follow the steps for long division. Write the number that should appear in the letter blank to solve the problem. Write the remainder in the box represented as "R:" in the image. And i need it now please
Answers
Answer:27 R1
Step-by-step explanation:2 7
3 8 2
- 6
2 2
- 2 1
1
Rewrite the given standard form linear equation using function notation. Identify the slope, y-intercept, and z
-intercept. Sketch the graph of the linear equation.
-5x +9y = 45
Writing f as a function of z, the equivalent function notation form of the equation is:
Answers
Part 1
[tex]-5x+9y=45 \\ \\ 9y=5x+45 \\ \\ y=\frac{5}{9}x+5 \\ \\ \therefore f(x)=\frac{5}{9}x+5[/tex]
Part 2
Correct.
Part 3
Correct.
Part 4
Correct.
a groundskeeper needs grass seed to cover a circular field 290 ft in diameter. a store sell 50 lb bags of grass seed. 1 lb of grass seed covers about 400 square feet of field. what is the smallest number of bags the groundskeeper must buy to cover the circular field?
Answers
The diameter of circular field is 290ft .
The area of circular field is
[tex]A=\Pi(r^2)^{}[/tex][tex]A=\Pi(145)^2=66018.5ft^2[/tex]It is given that 1 lb of grass seed covers about 400 square feet of field.
The smallest number of bags he should buy is
[tex]\frac{66018.5}{400}=165\text{ bags}[/tex]Urgent!! Math work in image!! Urgent help!!
Answers
The TV would not fit as the TV is too tall option (C) is correct after applying the concept of the ratio.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
The aspect ratio is:
= 4:3
Multiply by 16 to the above ratio:
= 64: 48
The height in the area = 47"
But from the aspect ratio the height of the TV = 48"
Thus, the TV would not fit as the TV is a too tall option (C) is correct after applying the concept of the ratio.
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In the accompanying table, the random variable x represents the number of televisions in a household in a certain country. Determine whether or not the table is a probability distribution. If it is a probability distribution, find its mean and standard deviation.xP(x)00.0310.1220.2430.3140.1850.12
Answers
For the table to be a complete probability distribution we need to check that the addition of the probabilities (P(x)) is equal to 1.
[tex]0.03+0.12+0.24+0.31+0.18+0.12=1[/tex]As it is equal to one, we can be certain that no household has more than 6 TVs. The function P(x) is indeed a probability distribution
Now, we need to find its mean and standard deviation
[tex]\begin{gathered} \operatorname{mean}=\mu=\sum ^{}_{}xP(x) \\ \Rightarrow\mu=0\cdot0.03+1\cdot0.12+2\cdot0.24+3\cdot0.31+4\cdot0.18+5\cdot0.12 \\ \Rightarrow\mu=2.85 \end{gathered}[/tex]And the Standard Deviation is:
[tex]SD=\sigma=\sqrt[]{\sum^{}_{}}P(x)(x-\mu)^2[/tex]Then, in our case:
[tex]\begin{gathered} \sigma=\sqrt[]{0.03(-2.85)^2+0.12(-1.85)^2+0.24(-0.85)^2+0.31(0.15)^2+0.18(1.15)^2+0.12(2.15)^2} \\ \Rightarrow\sigma=1.2757\ldots \end{gathered}[/tex]PROBLEM: Equivalent Expressions Create three different expressions that are each equal to 20. Each expression should include only these three numbers: 4. -2. and 10.
Answers
Given the numbers: 4, -2, and 10.
We want to create three different expressions that are each equal to 20.
First Expression
[tex](4-2)\times10=20[/tex]Second Expression
[tex]\begin{gathered} (4\times10)+(-2\times10) \\ =40+(-20) \\ =40-20 \\ =20 \end{gathered}[/tex]Third Expression
[tex]\begin{gathered} 10\lbrack4+(-2)\rbrack \\ =10\lbrack4-2\rbrack \\ =10\times2 \\ =20 \end{gathered}[/tex]Find the perimeter of the triangle whose vertices are
(-2, 4), (-2, 1), (-4,-2).
Answers
The sum of the length of the sides is the perimeter of the triangle.
The perimeter of the triangle is 5[tex]\sqrt{10}[/tex] + [tex]\sqrt{13}[/tex].
How to find the perimeter of a triangle?The sum of the length of the sides is the perimeter of the triangle.
d = [tex]\sqrt{(x^2 - x^1)^2 + (y^2 - y^1)^2}[/tex]
Lets take (-2, 4) and (-2, 1).
[tex]d = \sqrt{(-2+2)^2 + (1 - 4)^2}\\\\d = \sqrt{0 + -3^2} \\\\d = \sqrt{9} \\[/tex]
d = 3
Now, let's take the points (-2, 1) and (-4,-2).
d = [tex]\sqrt{(x^2 - x^1)^2 + (y^2 - y^1)^2}[/tex]
[tex]d = \sqrt{(-4+2)^2 + (-2-1)^2}\\\\d = \sqrt{-2^2 + -3^2} \\\\d = \sqrt{4 + 9} \\[/tex]
d = [tex]\sqrt{13}[/tex]
Now, let's take the points (-2, 4) and (-4,-2).
d = [tex]\sqrt{(x^2 - x^1)^2 + (y^2 - y^1)^2}[/tex]
[tex]d = \sqrt{(-4+2)^2 + (-2-4)^2}\\\\d = \sqrt{-2^2 + -6^2} \\\\d = \sqrt{4 + 36} \\[/tex]
d = 40 = 2[tex]\sqrt{10}[/tex]
The sum of the length of the sides is the perimeter of the triangle d= 3 + [tex]\sqrt{13}[/tex] + 2[tex]\sqrt{10}[/tex]
The perimeter of the triangle is 5[tex]\sqrt{10}[/tex] + [tex]\sqrt{13}[/tex].
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What is the effect on the graph of f(x) = x2 when it is transformed toh(x) = 12 – 13?
Answers
downloading about 35%
Write the equation of the line, with the given properties, in slope-intercept form. Slope = -7, through (-5,7)
Answers
the general equation of a line is
[tex]y=mx+b[/tex]where m is the slope an b an initial point
we can replace m=-7 and (x,y)=(-5,7) to find b an creat the equation for this case
[tex]\begin{gathered} (7)=(-7)(-5)+b \\ 7=35+b \\ b=-28 \end{gathered}[/tex]and the equation is
[tex]y=-7x-28[/tex]The directions are with the pic below. I have to send an additional pic. All wouldn’t fit on the page.
Answers
Given:
We get the points A(-1,-2) , K(-2, 2) and M(0,2).
Aim:
We need to find the new figure which is obtained by rotating the given figure by 90-degree counterclockwise.
Explanation:
Recall that when we rotate the point (x,y) 90 degrees counterclockwise then the image of the point (x,y) can be written as follows.
[tex](x,y)^{\prime}\rightarrow(-y,x)[/tex]The image of point A(-1, -2).
[tex]A(-1,-2)\rightarrow A^{\prime}(-(-2),-1)[/tex][tex]A(-2,-2)\rightarrow A^{\prime}(2,-1)[/tex]The image of point K(-2,2)
[tex]K(-2,2)\rightarrow K^{\prime}(-(2),-2)[/tex][tex]K(-2,2)\rightarrow K^{\prime}(-2,-2)[/tex]The image of point M(0,2).
[tex]M(0,2)\rightarrow M^{\prime}(-(2),0)[/tex][tex]M(0,2)\rightarrow M^{\prime}(-2,0)[/tex]Mark points A'(2,-1), K'(-2,-2), and M'(-2,0) on the graph and join all points.
Final answer:
The new figure is
Help please
Stem: 6, 7, 8, 9
Leaf: 8, 579, 02, 2667
Questions: What score represents the median of this data? What score represents the mode of this data? What is the mean of this data? If you use the mean, median, or mode to describe this data, which one would be the most misleading?
Answers
1. The score that represents the median is 81.
2. The score that represents the mode is 96.
3. The score that represents the mean is 84.2.
4. The mode will be the most misleading since it's far away from the mean and median.
What is a mean?The stem and leaf plot data are 68, 75, 77, 79, 80, 82, 92, 96, 96, and 97.
A mean simply means the average of a set of numbers. The mean will be:
= Sum of all data values / Number of values
= 842 / 10
= 84.2
The mode is the number that occurs most and this will be 96.
The median is the number in the middle. This will be:
= (80 + 82)/2
= 162/2
= 81
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