Use the elimination method to solve the system of equations.3x + 4y = 8x - y = 12
Answers
Answer:
We have to use to elimination method to solve the provided system of equations, this method essentially involves eliminating one of the variables in the first equation by adding or subtracting a multiple of the second equation:
[tex]\begin{gathered} 3x+4y=8\rightarrow(1) \\ \\ x-y=12\rightarrow(2) \end{gathered}[/tex]The elimination of the variable y in equation (1) is achieved by adding the 4 times the equation 2 into the equation (1), the steps of the process are as follows:
[tex]\begin{gathered} 3x+4y=8 \\ \\ + \\ \\ 4\times(x-y)=4\times12 \\ \\ ------------------------------- \\ \\ 3x+4x=8+48 \\ \\ \\ 7x=56 \\ \\ \\ x=8 \end{gathered}[/tex]We have found the x value, the last step is to plug in the variable x value in any of the (1) or (2) equations, and solve for the y variable, the steps are as follows:
[tex]\begin{gathered} x-y=12 \\ \\ x=8 \\ \\ \therefore\Rightarrow \\ \\ 8-y=12\rightarrow y=8-12=-4 \\ \\ y=-4 \end{gathered}[/tex]The final answer is as follows:
[tex](8,-4)\Rightarrow\text{ Option \lparen B\rparen}[/tex]Therefore the answer is Option(B).
Related Questions
For the point P(-24,-24) and Q(-19,-19), find the distance d(P,Q) and theof the midpoint M of the segment PQ,coordinates
Answers
Solution:
Given;
[tex]P(-24,-24),Q(-19,-19)[/tex]The distance d(P,Q) is;
[tex]\begin{gathered} d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\ \\ x_1=-24,y_1=-24,x_2=-19,y_2=-19 \\ \\ d=\sqrt{(-19-(-24))^2+(-19-(-24))^2} \\ \\ d=\sqrt{50} \\ \\ d=5\sqrt{2} \end{gathered}[/tex]Also, the midpoint, M, is;
[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \\ M=(\frac{-24+(-19)}{2},\frac{-24+(-19)}{2}) \\ \\ M=(-\frac{43}{2},-\frac{43}{2}) \end{gathered}[/tex]I need help with this problems please I need a huge explanation
Answers
In this case we must apply the properties of supplementary angles and opposite angles.
1 .
opposite angles
∠ 1 = 120 °
supplementary angles
∠ 1 + ∠ 2 = 180
120 + ∠ 2 = 180
∠ 2 = 180 - 120
∠ 2 = 60 °
The same properties can be applied in the other exercises to solve them.
The solution is:
∠ 1 = 120 °
∠ 2 = 60 °
The measures of two complementary angles are described by the expressions (11x−11)° and (16x−7)°. Find the measures of the angles.I know complementary when their measures add to 90 degrees. but I'm not to sure where to plug the numbers in
Answers
Given:
[tex](11x-11)^{\circ}and(16x-7)^{\circ}\text{ forms an complementary angles.}[/tex][tex]\begin{gathered} 11x-11+16x-7=90 \\ 27x-18=90 \\ 27x=90+18 \\ 27x=108 \\ x=\frac{108}{27} \\ x=4 \end{gathered}[/tex]what was the initial amount of water in a barrel, in liters, if x liters remain after y liters were spilled and 6 were added?
Answers
Let's call A the initial amount of water, in liters, in that barrel.
After y liters were spilled, the amount left was
A - y
Then, after 6 liters were added, the final remaining amount was given by:
A - y + 6
Now, since x liters remain, we have:
x = A - y + 6
Therefore, if we can find the expression for the initial amount of water, in liters, by isolating A in that equation:
x = A - y + 6
x + y = A + 6
x + y - 6 = A
A = x + y - 6
Thus, the initial amount of water was (x + y - 6) liters.
((x-j) ÷ k) + m =n what does x equal?
Answers
Explanation
[tex]\frac{x-j}{k}+m=n[/tex]
Step 1
subtract m in both sides
[tex]\begin{gathered} \frac{x-j}{k}+m=n \\ \frac{x-j}{k}+m-m=n-m \\ \frac{x-j}{k}=n-m \end{gathered}[/tex]Step 2
multiply each side by k
[tex]\begin{gathered} \frac{x-j}{k}=n-m \\ \frac{x-j}{k}\cdot k=(n-m)\cdot k \\ x-j=(n-m)\cdot k \end{gathered}[/tex]Step 3
finally, add j in both sides
[tex]\begin{gathered} x-j=(n-m)\cdot k \\ x-j=nk-mk \\ x-j+j=nk-mk+j \\ x=nk-mk+j \end{gathered}[/tex]I hope this helps you
Which segment is a reflection of segment AB over the line x=1? X CD O EF O GA O IJ
Answers
Since the line on which segment AB is reflected is x = 1 then the rule for this reflection will be
[tex](x,y)\rightarrow(-x+2\cdot1,y)=(-x+2,y)[/tex]Then, the coordinates of the segment that is reflections of segment AB with respect to the line x = 1 will be
[tex]\begin{gathered} A(-4,3)\rightarrow(-(-4)+2,3)=(4+2,3)=(6,3) \\ B(-1,1)\rightarrow(-(-1)+2,1)=(1+2,1)=(3,1) \end{gathered}[/tex]And the segment with these coordinates is EF
[tex]\begin{gathered} E(6,3) \\ F(3,1) \end{gathered}[/tex]Therefore, the correct answer is b. EF.
Voters in Arizona in 2020 passed Prop 207, legalizing the sale of recreational marijuana. At the time the industry estimated that the Arizona Department of Revenue would collect $135 million in taxes. In the first year, the state has generated approximately $200 million in tax revenue.State the absolute difference in the estimated amount of tax revenue generated and the actual amount received by the AZ Department of Revenue. Be sure to answer in a complete sentence.
Answers
The estimated amount of tax is 135 million
The actual amount received is 200 million
The difference means subtraction
Taking the absolution value means when we subtract, we find the positive value of the result
| estimated - actual |
| 135 million - 200 million |
| -65 million|
Taking the positive result
65 million
The absolute value of the difference in the estimate amount of the tax revenue generated and the actual amount received by the AZ department of Revenue is 65 million dollars.
-. Write an equation in slope-intercept form that
describes the line through the points (2,7) and
(-1,-5).
Answers
The slope-intercept form equation of the line is y=(-2/3)x-(17/3) when the line is passing through the points (2,7) and (-1,-5).
What is meant by slope?Finding the ratio of vertical change to horizontal change between any two distinct points on a line yields the slope. Occasionally, the ratio is written as a quotient, which produces the same number for every two distinct points on the same line. A negative rise refers to a diminishing line. The line could be functional, set by a road surveyor, or depicted in a diagram that represents a road or a roof as a description or a plan.
The absolute value of the slope is used to determine how steep, incline, or grade a line is. The steeper the line, the larger the absolute magnitude of the slope.
The slope-intercept form is y=mx+c
Given points are (2,7) and (-1,-5)
Slope m= (y₂-y₁)/(x₂-x₁)
m=(-5+7)/(-1-2)
m=-2/3
By substituting m value in the above equation we get,
y=(-2/3)x + c
Given that, the above equation is passing through the point (-1,-5)
-5=(-2/3)(-1)+c
c=-5-(2/3)
c=-17/3
y=(-2/3)x-(17/3)
Therefore, the equation of the slope-intercept form is y=(-2/3)x-(17/3)
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3. The equation 11a +8s = 4752 represents the ticket sales at last night's football game for a
adult tickets and s student tickets.
a. How much money was collected in total from all ticket sales?
b. What is the price of an adult ticket? What is the price of a student ticket?
c. If the ticket booth sold only adult tickets, how many would they have sold?
d. If the ticket booth sold only student tickets, how many would they have sold?
Answers
Step-by-step explanation:
The equation 11a +8s = 4752 represents the ticket sales at last night's football game for a adult tickets and s student tickets.
a. How much money was collected in total from all ticket sales? $4,752
________________________
b. What is the price of an adult ticket? $11 What is the price of a student ticket? $8
________________________
c. If the ticket booth sold only adult tickets, how many would they have sold?
if only adults:
11a = 4752
a = 432 tickets
________________________
d. If the ticket booth sold only student tickets, how many would they have sold?
if only students:
8a = 4752
a = 594 tickets
help please, do working outs too i don’t understand it
Answers
1.) The line with the greatest slope.
The greater the slope of the line, the more upright it is. Observing the given graph, the line with the greatest slope is line a.
2.) Lines that are parallel.
Two lines are parallel if they do not have an intersection with each other at any point in the graph. We can see that line b and line d, do not intersect at any point in the graph and are thus parallel lines.
3.) Line with a negative slope
A line with a negative slope is a line that goes downwards from left to right, in the graph we can see that line e and line f goes downwards from left to right.
4.) Line that is perpendicular to the y-axis.
A line that is perpendicular to the y-axis, is a line that is parallel to the x-axis. Looking at the graph, line c is perpendicular to the y-axis.
Leah is buying titles for her bathroom. Each tile is 3/8 foot wide and covers an area that is 7/3 square feet. The bathroom floor is in the shape of a rectangle. She is putting 8 tiles along the longer wall of the bathroom and 5 tiles along the shorter wall of the bathroom. What is the perimeter of the bathroom? The bathroom and one tile are pictured below.
Answers
The perimeter of the rectangular floor is 103 feet.
What are rectangles?With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel.Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's length is its longer side, while its width is its shorter side.So, the perimeter of the bathroom floor will be:
First, let the length of the tiles be 'x'.Now,
7/3 = x × 3/8x = 7/3 ÷ 3/8x = 7/3 × 8/3x = 56/9So, the length of the tile is 56/9.
Now, the l and b of the rectangular floor will be:
56/9 × 8 + 3/8 × 5448/9 + 15/88(448) + 9(15)/723584 + 135/723719/7251.65Formula is: 2(l+b)
Now,
2 × 51.65103.3Rounding off: 103 feet
Therefore, the perimeter of the rectangular floor is 103 feet.
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Determine if the expression -y^4 is a polynomial or not. If it is a polynomial, state the
type and degree of the polynomial.
Answers
This expression -y⁴ is a polynomial and it's a type of biquadratic polynomial.
What is a polynomial?
One-variable polynomials are algebraic expressions that have terms of the form axⁿ, where n is a non-negative (i.e., positive or zero) integer and an is a real number that is known as the term's coefficient. A polynomial with one variable has its biggest exponent at its degree.
We have,
-y⁴
It has a degree of 4 and a coefficient is -1 a real number.
It is called a biquadratic equation or quartic equation. Generally, any polynomial with a degree of 4, which means the largest exponent is 4 is called a fourth-degree equation.
Hence, this expression -y⁴ is a polynomial and it's a type of biquadratic polynomial.
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help please tyyyyyyyyy
Answers
Answer: 5 tadoples
Step-by-step explanation:
Please get me the Braniliest award, thanks!
Answer:
30
Step-by-step explanation:
If there are 18 swans in the ratio of 3
you divide 18 by 3 = 6
So you times 5 by 6 to get 30 as your answer
I'm having a problem with logarithms I will upload a photo
Answers
SOLUTION:
Step 1 :
In this question, we are asked to solve the equation:
[tex]In\text{ ( 4 x + 4 ) = 2}[/tex]Step 2 :
Now, taking the exponents of both sides, we have that:
[tex]\begin{gathered} e^{In\text{ ( 4 x + 4 ) }}=e^2 \\ 4x+4=e^2 \\ \text{But e}^2\text{ = 7.3891 ( to 4 decimal places )} \\ 4\text{ x + 4 = 7. 3891} \\ \text{ 4 x = 7. 3891 - 4} \\ \text{4 x = 3.3891} \\ \text{Divide both sides by 4 , we have that:} \\ x\text{ = }\frac{3.3891}{4} \\ x\text{ = 0.847275} \\ \text{x = 0.8473( to 4 decimal places)} \end{gathered}[/tex]1. If Rocco makes 18 out of 25 free throws and Graham makes 14 out of 20 free throws, who has the better free
throw record? Show why using comparable rates.
Answers
119° 100° 88° 116° 11. Determine the value of x. A. 117° B. 59° C. 63° D. 90°
Answers
We have that the shape is a pentagon of sorts, and we will have that the sum of the internal angles of a pentagon equals 540°.
Knowing this, we will find the missing interior angle in the shape:
100° + 119° + 88° + 116° + a = 540°
Then, we will have that the missing side we named a, will have a measure of 117°.
Now, by supplementary angles, we will have the following:
117° + x = 180°
When we solve for x, we will have that is has a measure of 63°
***
You can determine the total sum of interior angles by the function:
[tex](n-2)\cdot180[/tex]Where n is the number of sides the shape has.
This table gives a few (x,y) pairs of a line in the coordinate plane.
x y
40 -30
61 -45
74 -60
What is the x-intercept of the line?
( , )
its on khan academy
Answers
The x-intercept of the line is found to be -38 from the given table data using the slope-point form.
What exactly is the slope-point form?The equation of a straight line that is inclined at a specific angle to the x-axis and passes through a specific point may be found using the slope-point form. Only when the line's slope and a particular point are known can the point slope formula be applied. The slope-point form's equation is as follows: y - y₁ = m(x - x₁)Take a look at any two points, such as (40, -30), and (61, -45).
The line connecting them must have the following slope:
(y₂ - y₁)/(x₂ - x₁) = (-45 -(- 30))/(61 - 40) = -15/21.
Since they are on the same line, any combination of (48,30) and (74,60) will have the same answer.
The slope-point form is given as follows:
y - y₁ = m(x - x₁)
y -(- 30) = (-15/21) (x - 40)
21(y + 30) = -15(x - 40)
-15x + 21y = 570
Now, we can convert the above equation in intercept form to find x-intercept.
The intercept form is given as:
x/a + y/b = 1, where a and b are x and y intercepts.
-15x + 21y = 570
Dividing by 570 we get,
(-15x)/570 + (21y/570) = 1
x/-38 + y/27 = 1
Compare this to x/a + y/b = 1, where a and b are the x and y intercepts, respectively.
In this case, the x intercept is -38.
Therefore, the x-intercept of the line is found to be -38 from the given table data.
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PLS ANSWER THIS FOR ME ASAP!
Answers
Answer:
D,E,F
Step-by-step explanation:
dialation causes the sides to get smaller or bigger when it’s more or less than 1
Hopes this helps please mark brainliest
The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?A 4B. -2C -1D. 1
Answers
You need to know the following:
1. The "difference" is the result of a subtraction.
2. The word "times" indicates a multiplication.
3. The sum is the result of an addition.
Let be "n" the number mentioned in the exercise.
Knowing the explained above, you know that "the difference of a number and 6" can expressed as:
[tex]n-6[/tex]And "5 times the sum of the number and 2" can be expressed as:
[tex]5(n+2)[/tex]Therefore, "the difference of a number and 6 is the same as 5 times the sum of the number and 2" can be written as the following equation:
[tex]n-6=5(n+2)[/tex]Now, in order to find the number, you must solve for "n":
[tex]undefined[/tex]What is the value of x?
Answers
Answer:
75 degree
Step-by-step explanation:
We know that a straight angle is 180 degree
and in the picture we can see an angle of 105 degree
so we get 180-105= 75 degree
Find z_1 x z_2 for z_1 = 9(cos225° + isin225°) and z_2 = 3(cos45° + isin45°).The 'z' is all subscript.
Answers
Using Euler's Formula:
[tex]re^{i\theta}=r(\cos (\theta)+i\sin (\theta))[/tex]Since:
[tex]\begin{gathered} z1=9(\cos (225)+i\sin (225)) \\ z2=3(\cos (45)+i\sin (45)) \\ \end{gathered}[/tex]We can rewrite them as:
[tex]\begin{gathered} z1=9e^{225i} \\ z2=3e^{45i} \end{gathered}[/tex]So:
[tex]\begin{gathered} z1\times z2=(9e^{225i})(3e^{45i})=27e^{225i+45i}=27e^{270i} \\ so\colon \\ z1\times z2=27(\cos (270)+i\sin (270)) \end{gathered}[/tex][tex]\begin{gathered} a=r\cos (\theta) \\ b=r\sin (\theta) \\ where \\ r=27 \\ \theta=270 \end{gathered}[/tex]So:
[tex]undefined[/tex] 3.152 written as an improper fraction or a mixed number and explained how it was done.
Answers
Answer: 3.152 as an improper fraction would be: 394 / 125
Step-by-step explanation: You can take any number, such as 3.152, and write a 1 as the denominator to make it a fraction and keep the same value, like this:
3.152 / 1
To get rid of the decimal point in the numerator, we count the numbers after the decimal in 3.152, and multiply the numerator and denominator by 10 if it is 1 number, 100 if it is 2 numbers, 1000 if it is 3 numbers, and so on.
Therefore, in this case we multiply the numerator and denominator by 1000 to get the following fraction:
3152 / 1000
Then, we need to divide the numerator and denominator by the greatest common divisor (GCD) to simplify the fraction.
The GCD of 3152 and 1000 is 8. When we divide the numerator and denominator by 8, we get the following:
394 / 125
(have a nice day)
b. A family of four went to see a live concert in Vancouver. Each family member bought
a commemorative concert T-shirt, which cost 1/5 of the price of a ticket. The total bill
for 4 tickets and 4 T-shirts was $384. How much did each ticket and each T-shirt cost?
Answers
The cost of 1 ticket is $80 and the cost of 1 T-Shirt is $16 .
In the question ,
it is given that ,
a family of four people went to see a live concert in Vancouver ,
and the price of T-shirt is 1/5 of the price of the ticket .
let the price of 1 ticket be = x ,
so , the price of 1 T-Shirt be = x/5 .
also given that the bill for 4 tickets and 4 T-Shirts was $384 ,
that means
4x + 4x/5 = 384
taking LCM as 20 and solving further ,
we get,
20x/5 + 4x/5 = 384
24x/5 = 384
24x = 384*5
24x = 1920
x = 1920/24
x = 80
the cost for T-Shirt = 80/5 = 16
Therefore , The cost of 1 ticket is $80 and the cost of 1 T-Shirt is $16 .
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write an equation in slope intercept form for the lines that passes through (-2,-8) and is parallel to y=-9x-81
Answers
The general form of an equation in slope intercept form is ;
y= mx + c where m is the gradient and c is the y-intercept
The equation given is : y = -9x-81 ------this means the slope is -9
This is determined from the general equation ;
y = m x + c
y= -9 x - 81
where -9 is the gradient
Because the two lines are parallel, it means the other equation should have a slope of -9, thus apply the formula for slope give point {-2,-8}
m= change in y-coordinates value / change in x coordinate values
-9 = y --8/x--2
-9 = y+8 /x+2
-9 {x+2} = y+8
Can someone please explain to me why -4² = -16?
Answers
Answer:
-4 x -4 = -16
4 x 4 = 16
^2 or to the power of 2 basely means 4 times itself, because 2.
Geometry! Just the first question:)
Answers
Hi your answers would be
a) 30 degrees
b) 65 degrees
c) 115 degrees
d) 85 degrees
e) 150 degrees
f) 30 degrees
Hope these answers help.
Answer:
5 round table pizza and amen and amen and amen and amen
Step-by-step explanation:
the program I think the banner side effects
Find the volume of this object.Use 3 for a.Volume of a CylinderV=Tr2hVolume of a Sphere4 cmV=-Tr36 cm8 cmV ~ [?]cm3
Answers
The figure given in the question is a composite figure, meaning that it comprises two different figures
The volume of the composite figure can be found as follow
The two figures are:
Cylinder and sphere.
To solve this, we will first find the area of a cylinder
[tex]\begin{gathered} \text{Area of a cylinder is given by:} \\ V_{\text{cylinder}}=\pi r^2h \\ \text{where} \\ \pi=3 \\ r=4 \\ h=6 \end{gathered}[/tex]So, we will have
[tex]\begin{gathered} V_{\text{cylinder}}=3\times4^2\times6 \\ V_{\text{cylinder}}=288\operatorname{cm}^3 \end{gathered}[/tex]Then, we will find the volume of the sphere
[tex]\begin{gathered} V_{\text{sphere}}=\frac{4}{3}\pi r^3 \\ \text{where} \\ \pi=3 \\ r=4 \end{gathered}[/tex]Thus, the volume of the sphere will be
[tex]\begin{gathered} V_{\text{sphere}}=\frac{4}{3}\times3\times4^3 \\ V_{\text{sphere}}=256\operatorname{cm}^3 \end{gathered}[/tex]Thus, the total volume will be
[tex]288+256=544\operatorname{cm}^3[/tex]The volume is:
[tex]544\operatorname{cm}^3[/tex]The answer is 544cm³
Suppose a 95% confidence interval for the average amount of weight loss on a diet program for males is between 13. 4 and 18. 3 pounds. These results were based on a sample of 42 male participants who were deemed to be overweight at the start of the 4-month study. What is the standard error of the sample mean?.
Answers
The standard error of the sample mean is 1.213
How to calculate the standard error of the sample mean?
Given,
c = 95% = 0.95
n = 42
lower limit = 13.4
upper limit = 18.3
Since standard deviation population is unknown, we use this formula to calculate standard error.
standard error = margin of error / [tex]t_{\alpha/2,d.f.}[/tex]
First, we calculate the t distribution value
[tex]t_{\alpha/2,d.f.}[/tex] = [tex]t_{(1-c)/2,n-1}[/tex]
= [tex]t_{(1-0.95)/2,42-1}[/tex]
= [tex]t_{0.025,41}[/tex]
To find the value use t table. So, [tex]t_{0.025,41}[/tex] = 2.0195
Next, we calculate the margin of error
margin of error = (upper limit - lower limit)/2
= (18.3 - 13.4)/2
= 4.9/2
= 2.45
Now, we can calculate the standard error. So,
standard error = 2.45 / 2.0195
= 1.213
Thus, the standard error of the sample mean is 1.213
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QuestionSolve the inequality 37v < -18 and write the solution in interval notation, using improper fractions if necessary.
Answers
Solve for w4/6 = w/9Simplify your answer as much as possible.
Answers
We want to find the value of w, so the following equation is true:
[tex]\frac{4}{6}=\frac{w}{9}[/tex]Since both sides of the equation are equal, we must do the same on both sides, so they keep equal.
We want to leave w in only one side of the equation.
Then we want to bring 9 of the division to the left side so w can be alone in the right sides.
In order to do so we multiply both sides by 9:
[tex]\begin{gathered} 9\cdot\frac{4}{6}=9\cdot\frac{w}{9} \\ \downarrow\text{right side} \\ 9\cdot\frac{w}{9}=\frac{9w}{9}=w \\ \downarrow left\text{ side} \\ 9\cdot\frac{4}{6}=\frac{36}{6}=6 \end{gathered}[/tex]Then, we have that:
[tex]\begin{gathered} 9\cdot\frac{4}{6}=9\cdot\frac{w}{9} \\ \downarrow \\ 9\cdot\frac{4}{6}=w \\ \downarrow \\ 6=w \end{gathered}[/tex]Answer: w = 6