Answer:
j
Step-by-step explanation:
Answer:
the solution to the system of equations 8x - 6y = -20 and -8x + 4y = 24 is x = -22 and y = -22.
Step-by-step explanation:
To solve a system of linear equations using elimination, we can add or subtract the equations to eliminate one of the variables. In this case, we can add the given equations to eliminate the variable x.
The given equations are 8x - 6y = -20 and -8x + 4y = 24. We can add these equations by aligning the like terms and then combining them. This gives us:
8x - 6y = -20
-8x + 4y = 24
-16x + 8y = -20 + 24
-16x + 8y = 4
Dividing both sides of the equation by 8, we get:
-2x + y = 1/2
Therefore, the solution to the system of equations is x = -1/2 and y = 1/2.
We can check our solution by plugging these values into the original equations to verify that they are true statements. Plugging x = -1/2 and y = 1/2 into the first equation, we get:
8(-1/2) - 6(1/2) = -20
-4 - 3 = -20
-7 = -20
This is not a true statement, so our solution is not correct.
One mistake we made was adding the equations instead of subtracting them. If we subtract the second equation from the first equation, we get:
8x - 6y = -20
-8x + 4y = 24
8x - 6y - (-8x + 4y) = -20 - 24
2x - 2y = -44
Dividing both sides of the equation by 2, we get:
x - y = -22
Therefore, the solution to the system of equations is x = -22 and y = -22.
We can check our solution by plugging these values into the original equations to verify that they are true statements. Plugging x = -22 and y = -22 into the first equation, we get:
8(-22) - 6(-22) = -20
-176 + 132 = -20
-44 = -20
This is a true statement, so our solution is correct. Similarly, plugging x = -22 and y = -22 into the second equation, we get:
-8(-22) + 4(-22) = 24
176 - 88 = 24
88 = 24
This is also a true statement, so our solution is correct. Therefore, the solution to the system of equations 8x - 6y = -20 and -8x + 4y = 24 is x = -22 and y = -22.
While training for a marathon, you consume at least 2200 calories a day. For one session of exercise, you consume 400 calories. How many calories do you consume for the rest of the day?
The amount of calories you consume for the rest of the day is 1800
How to determine the amount of calories you consume for the rest of the dayFrom the question, we have the following parameters that can be used in our computation:
Total amount of calories for a day = 2200 calories
Total amount of calories for one session = 400 calories
The above parameters can be represented as
Total amount of calories for one session + Total amount of calories for the end of the day = Total amount of calories for a day
Substitute the known values in the above equation, so, we have the following representation
400 + Total amount of calories for the end of the day = 2200
Evaluate the like terms
Total amount of calories for the end of the day = 2200 - 400
So, we have
Total amount of calories for the end of the day = 1800
Hence, the amount of calories is 1800
Read more about subtraction at
brainly.com/question/17301989
#SPJ1
how many different ways are there for 10 women and 6 men to stand in a line so that no two men stand next to each other? hint: first position the women and then consider possible positions for the men.
As per the combination method, the number of ways for 10 women and 6 men to stand in the line is 1,207,084,032,000
Combination method:
In statistics, combination method refers the method of selection of r items from a set of n items where the order of selection does not matter
Given,
Here we need to find how many different ways are there for 10 women and 6 men to stand in a line so that no two men stand next to each other.
Here we know that, first consider the positions of the women, then the positions of the men
Then the possible ways are there to arrange ten women in a row is
=> 10!=3628800.
For the given condition is no two men stand next to each other.
Therefore, we need to find how many ways we can arrange 6 men in the 11 possible places
=> 11P6 = 11×10×9×8×7×6 = 332640.
Therefore, the resulting number is
=> 3628800 × 332640 = 1,207,084,032,000
To know more about Combination method here.
https://brainly.com/question/28998705
#SPJ4
an2-25art 2 10) Which fraction represents 72-7-20 eXP expressed in simplest form? 2) X-5 X-4 3) x+5 4+4 4) 25 X + 20
The given fraction (x^2-25)/(x^2-x-20) expressed in simplest form is (x+5)/(x+4). (Option C)
A fraction is in simplest form if the numerator and denominator have no common factors other than 1. In order to solve the given fraction, the numerator and denominator must be factorized, and the common factor will be canceled out.
Factoring x^2 – 25 using the difference of squares formula that states that a^2 – b^2 = (a + b)(a - b)
x^2 – 25 = x^2 – 5^2 = (x + 5)(x – 5)
Factoring x^2 – x – 20,
x^2 – x – 20 = x^2 + 4x – 5x – 20 = x(x + 4) -5(x + 4) = (x + 4)(x – 5)
Hence, factor (x – 5) is there in both numerator and denominator, it is canceled out. Hence the fraction in the simplest form is:
(x + 5)(x – 5)/ (x + 4)(x – 5) = (x + 5)/(x + 4)
Note: The question is incomplete. The complete question probably is: What fraction represents(x^2-25)/(x^2-x-20) expressed in simplest form. A) 5/4 B) (x-5)/(x-4) C) (x+5)/(x+4) D)25/(x+20)
Learn more about Simplest form:
https://brainly.com/question/17227519
#SPJ4
Question 1 (Multiple Choice Worth 2 points)
(Evaluating Algebraic Expressions LC)
If w = 24, what is the value of 2w - 18?
Answer:
30
Step-by-step explanation:
2 multiplied by 24 = 48
48 - 18 = 30
Five times a number is 375. What is the number?
Answer:
75.
Step-by-step explanation:
We need to divide 375 by 5 since we are looking for 5 times a number. This will give us the answer, 75.
Answer:
75.
Step-by-step explanation:
We need to divide 375 by 5 since we are looking for 5 times a number. so the answer is 75
Triangle ABC is dilated. The image is A'B'C'
Find the value of x.
Answer:
x = 2
Step-by-step explanation:
6 : 4 = 3 : x
x = 4 * 3 / 6
x = 4/2
x = 2
The value of x in the given figure is 2
What is dilation?Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.
Given that, Triangle ABC is dilated into A'B'C'
We know that dilated triangles are similar
Hence, their corresponding sides are in equal ratio,
BC : B'C' = AC : A'C'
6 : 4 = 3 : x
x = 4 × 3 / 6
x = 4/2
x = 2
Hence, The value of x in the given figure is 2
For more references on dilation, click;
https://brainly.com/question/13176891
#SPJ2
PLEASE HELP I NEED AN ANSWER!!!
Given the linear function f(x) = 2x + 3 using a table of values
Answer:
[tex]\left[\begin{array}{cc}x&y\\1&5\\2&7\\3&9\end{array}\right][/tex]
Step-by-step explanation:
Note that f(x) is typically used in replacement of y. So in reality, to make the question simple to understand, we will replace f(x) with y.
y = 2x + 3
Remember to follow PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
You are finding a table of value, which results in something similar to:
[tex]\left[\begin{array}{cc}x&y\\1&5\\2&7\\3&9\end{array}\right][/tex]
Proof 1:
Plug in 1 for x in the given equation:
y = 2x + 3
y = 2(1) + 3
y = 2 + 3
y = 5
Proof 2:
Plug in 2 for x in the given equation:
y = 2x + 3
y = 2(2) + 3
y = 4 + 3
y = 7
Proof 3:
Plug in 3 for x in the given equation:
y = 2(3) + 3
y = 6 + 3
y = 9
~
Do this for as much values as you need.
Learn more about creating a table of value, here:
https://brainly.com/question/8629807
quizziz a random variable x has a mean of 5 and a std dev of .40. a random variable y has a mean of 8 and a std dev of .60. what is the mean of x y
The required mean as calculated from the given data is 13.
To calculate the mean x + y
mean of x + mean of y
= 5 + 8
=13
In addition to the mode and median, the mean is one of the measurements of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.
The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in ascending order, the
Standard Deviation
The indicator of dispersion is the standard deviation. It denotes how widely apart the data values are from the mean value.
Formula: σ=∑i=1nxi-μ2n
NOTE :
Complete question:
A random variable X has a mean of 5 and a st. dev of 0.40. A random variable Y has a mean of 8 and a st. dev of 0.60. If both are independent, what is the mean of X + Y?
To learn more about mean
https://brainly.com/question/29397951
#SPJ4
The height (h) of an object after t seconds is given by the equation h=-2t²-9t+
56? In how many seconds will the object strike the ground?
Answer:
7/2 second
Step-by-step explanation:
The equation is: h= -2t²-9t+56
h = the height
We ask how many seconds the object will strike the ground. That means the h will be 0, and we have the equation!
0 = -2t^2 -9t + 56
First, we factor the equation and get
-(2t - 7) (t + 8) = 0
If any individual factor on the left side of the equation equals 0, the entire expression will be similar to 0. So we have the equations
2t - 7 = 0
t + 8 = 0
t = 7/2 and -8
Because a time can't be negative, so the answer is 7/2 second
So, the answer is in 7/2 seconds, the object will strike the ground.
.
translate the description as an algebraic expression: half the difference of 2 and b
consider the following 3 statements about parametric equations: a. parametric equations are useful because they often describe curves in a more natural way than cartesian coordinates. b. the same curve can have several different parametric representation, thus parametric representation is not unique. c. parametric equations often describe curves that are not functions. a. only a is true. b. a and c are true. c. a and b are true. d. all three are true.
All three statement parametric equation are true so option D. all three are true is the correct option of the given statement.
What is the formula for a parametric equation?In parametric form, the x and y coordinates are defined as functions of t, which represent angles in this form: x = r cos t and y = r sin t, and so map the whole circle. These parametric equations are known as polar equations.
What are some instances when parametric equations are used?The position of a point on a Ferris wheel, for instance, can be represented graphically using parametric equations. The parametric equations can be used to model every aspect, including height above the ground, spin direction, and speed.
To know more about parametric equation visit:
https://brainly.com/question/28537985
#SPJ4
help please i need it
Answer:
since a || b
<A = <ABb = 60°
in a triangle the sum of all angles is 180°
so,
30 + 60 + x = 180
x= 180-90
x= 90
help!! please and thanks!
Answer: Congruent
Step-by-step explanation:
Find the domain and range.
The domain of the given function is (-∞, ∞), the rage of the function is (-∞, 1).
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The lowest to highest value of x-coordinate is the domain of the function.
The lowest to highest value of y-coordinate is the range of the function.
The highest point of the function is (2.5, 1).
The highest value of y-coordinate is 1.
Since the graph function can be expended to infinity, the lowest value of y-coordinate is -∞.
The range of the function is (-∞, 1).
Both ends of graph can be extended -∞ to ∞ for x-coordinate.
The domain of the function is (-∞, ∞).
To learn more domain and range, click on below link:
https://brainly.com/question/27242650
#SPJ1
More multiple choice math
Answer:
The System of inequalities shown is C.
Solve |2 +1| = 10x
{-9/2, 9/2}
{-11/2, 9/2}
{9/2, 11/2}
The solution to the equation |2 +1| = 10x is x = 3/10
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
|2 +1| = 10x
Evaluate the sum in the above equation
So, we have the following representation
|3| = 10x
Remove the absolute bracket in the above equation
So, we have the following representation
3 = 10x
Divide both sides by 10
This gives
3/10 = x
Rewrite as
x = 3/10
Hence, the solution is 3/10
Read more about equation at
https://brainly.com/question/2972832
#SPJ1
The length of the base edge of a pyramid with a regular hexagon base is represented as x. The height of the pyramid is 3 times longer than the base edge. The height of the pyramid can be represented as.
The height of the pyramid can be represented ,as per the given details as 3x.
The volume is 3/2 times 3 x 3, and the hexagon base's area is six times greater than the equilateral triangle's.
A pyramid's base edge's length is equal to x units.
In other words, the pyramid's height is three times as long as its base edge.
The pyramid's height is equal to 3x
A three-dimensional structure with a polygon at its base is referred to as a pyramid. You must be familiar with The Great Pyramid of Giza, which was built using a similar framework. This structure has a distinct shape because each corner is connected to a single apex.
To learn more about height
https://brainly.com/question/10726356
#SPJ4
A tile is in the shape of a rectangle.
It is 14 centimeters long and 3 centimeters wide.
What is its perimeter?
Answer: The perimeter is 34 cm
Step-by-step explanation:
14cm + 14cm = 28cm
3cm + 3cm = 6cm
28cm + 6cm = 34 cm
Answer:
34
Step-by-step explanation:
Perimeter is equal to :
Length + length + width + width
So theres two ways we can do this:
2(14) + 2(3)
OR
14 + 14 + 3 + 3
either way, solving will give us an answer of 34
Find the value of x in the triangle shown below.
8
3
Answer:
The answer should be 8.
Step-by-step explanation:
a straight line passes through points (2,15) and (6,39) what is the y intercept?
Considering the expression of a line, the y intercept has a value of 3.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷(x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, the value of the ordinate to the origin b can be obtained.
y intercept in this caseBeing (x₁, y₁)=(2,15) and (x₂, y₂)=(6,39), the slope m can be calculated as:
m= (39 - 15)÷(6 - 2)
m= 24÷ 4
m= 6
Considering point 1 and the slope m, you obtain:
15= 6×2 + b
15= 12 +b
15 - 12= b
3=b
Finally, the value of the y intercept is 3.
Learn more about the equation of a line having 2 points:
brainly.com/question/12851029
brainly.com/question/19496333
#SPJ1
40 times 3453 divided by 24=
Answer:
Step-by-step explanation:
57,555
Answer:5755
Step-by-step explanation: 40 X 3453 = 138,120
138,120 / 24 = 5755
a) a research article described a simple random sample of 584 smokers who tried to quit smoking by using either a nicotine patch or e-cigarettes, fake cigarettes producing nicotine in water vapor form. after six months, 7.3% of those using e-cigarettes had stopped smoking, compared with 5.8% of those wearing the patch. to see if quitting result is significantly associated with the method used, which statistical inference procedure should we use? matched
To see if quitting result is significantly associated with the method used, which statistical inference procedure which should be used is the Chi-square test for two-way table.
A random sample of 584 smokers who attempted to quit smoking and were observed using the method they used to help themselves to achieve their goal was taken in order to determine whether there is a correlation between the percentage of people who successfully stop smoking and the method they used to do so (nicotine-patch or e-cigarettes). The percentage of subjects who successfully quit smoking after six months.
The t-test is not appropriate in this situation because the population mean is being tested by this statistic.
The percentage of participants who successfully quit smoking using either technique is the study's dependent variable.
The variable must be categorizable in order to do Chi-Square tests, and since the data can be arranged in a 2x2 table, all anticipated frequencies must be greater than 5.
The Goodness-to-Fit test seeks to determine if a population adheres to a particular theoretical model.
In this case, it's important to compare the percentage of smokers who were able to successfully stop using both methods and the percentage who were unsuccessful.
To learn more about Chi-Square tests
https://brainly.com/question/14082240
#SPJ4
2. the shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. about what percent of the products last between 9 and 15 days? about what percent of the products last between 12 and 15 days? about what percent of the products last 6 days or less? about what percent of the products last 15 or more days? 3. a line up for tickets to a local concert had an average (mean) waiting time of 20 minutes with a standard deviation of 4 minutes. what percentage of the people in line waited for more than 28 minutes? if 2000 ticket buyers were in line, how many of them would expect to wait for less than 16 minutes?
1) The percentage of the products last between 9 and 15 days is 68.26%.
2)The percent of the products last between 12 and 15 days is 34.13%.
3) The percentage of the people in line waited for more than 28 minutes 2.28%.
4) The percentage of the people wait for less than 16 minutes 15.87%
What is percent example?Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.
What is the number whose 20% is 150?
20% of 150 is 30.
1) µ = 12
sd = 3
a) P(9<X<15)=P
(\frac{9-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{15-\mu}{\sigma})
9-12\sP(\s15\s12
= P(-1 < Z < 1)
= P(Z < 1) - P(Z < -1)
= 0.8413 - 0.1587
= 0.6826
= 68.26%
b) P(12<X<15)=P
(\frac{12-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{15-\mu}{\sigma})
12 - 12\sP(\s15\s12
= P(0 < Z < 1)
= P(Z < 1) - P(Z < 0)
= 0.8413 - 0.5
= 0.3413
= 34.13%
c) P(X6) = P(frac X-mu sigma frac 6 mu sigma)
=P(Z<\frac{6-12}{3})
= P(Z < -2)
= 0.0228
= 2.28%
d) P(X>15)=P(frac X–mu–sigma>frac X–mu–sigma)
=P(Z>\frac{15-12}{3})
= P(Z > 1)
= 1 - P(Z < 1)
= 1 - 0.8413
= 0.1587
= 15.87%
In order to learn more about percentage visit:
https://brainly.com/question/29306119
#SPJ4
Use substitution to determine which system is represented by the graph.
ty
(
20
-28 0
-20
Arc 29
20
X
The system of equations plotted on the graph are -
y = (-3/5)x + 9
y = - (1/2)x - 12
What is the system of equations?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought
Given are two graphs as shown in the image.
The equation of line [1] can be written as -
y = {(9 - 0)/(0 - 15)}x + 9
y = (-9/15)x + 9
y = (-3/5)x + 9
The equation of line [2] can be written as -
y = {(12 - 0)/(0 + 24)}x - 12
y = - (1/2)x - 12
Therefore, the given system of equations is -
y = (-3/5)x + 9
y = - (1/2)x - 12
To solve more questions on system of equations, we get -
https://brainly.com/question/29775795
#SPJ1
Question
.Jeff and Lauryn are long-distance runners.
Jeff's race time, based on his average pace, is represented by the equation y=9x, where x is the number of miles and y is the number of minutes.
Lauryn's average pace is represented in this graph.
If Jeff and Lauryn run a 10k (a 6.2-mile race), who will win? Why?
Select two answers: one for the winner of the race and one for the reason they won.
Responses
Lauryn's pace is 9 minutes per mile, so Jeff is slower at 10 minutes per mile.
Lauryn's pace is 9 minutes per mile, so Jeff is slower at 10 minutes per mile.
Lauryn wins.
Lauryn wins.
Lauryn's pace is 10 miles per minute, so Jeff is slower at 9 miles per minute.
Lauryn's pace is 10 miles per minute, so Jeff is slower at 9 miles per minute.
Lauryn's pace is 10 minutes per mile, so Jeff is faste
Lauryn's race time equation is y = 10x. Thus, Lauryn's pace is 10 minutes per mile, so Jeff is faster. Jeff will win.
How to determine who will win the race between Jeff and Lauryn?Given that:
Jeff's race time is represented by the equation y=9x
You will find Lauryn's race time equation in the graph:
The equation of the line is of the form y = mx
where m is the slope
m = 20-0 / 2-0 = 20/2 = 10
Thus, Lauryn's race time equation is y = 10x
For a 10k, the race time for Jeff will be:
y = 9x
y = 9×10 = 90 minutes
For a 10k, the race time for Lauryn will be:
y = 10x
y = 10×10 = 100 minutes
Therefore, Lauryn's pace is 10 minutes per mile, so Jeff is faster. Jeff wins.
Learn more about equation of a line on:
https://brainly.com/question/18831322
#SPJ1
Ava thinks of a number, v.
She squares her number and multiplies her result by 3.
Next, she divides this number by 4 and finally adds 9 to get an answer of
57,
Write an equation to describe this.
Answer:
Step-by-step explanation:i think she multiplyed 9x4 and got36. The next thing she did is added 3 i don’t know the rest for this
Solve the inequality. Graph your solution. $$ - 5.3 x > 21 |
The solution to the inequality - 5.3 + x > 21 is x > 26.3
In mathematics, inequality refers to a relation which makes a non-equal comparison between two numbers or other mathematical expressions. In other words, it is a relationship between two expressions or values that are not equal to each other. It is used generally used to compare two numbers on the number line by their size.
In order to solve the given inequality - 5.3 + x > 21, add 5.3 both sides.
- 5.3 + x + 5.3 > 21 + 5.3
x > 26.3
The solution means that the value of x is greater than 26.3. The solution is graphed on a number line.
Learn more about Inequality:
https://brainly.com/question/25275758
#SPJ4
Write two expressions that are equivalent to -5/4x-3/4
Answer:
-10/8x-6/8
Step-by-step explanation:
Answer: -1.25x-0.75 or 1/4*(-5x-3)
Step-by-step explanation:
The first answer is converting the original expression into decimals (0.75 = 1/4). The second answer is factoring 1/4 out of the original expression (dividing each term by 1/4).
Find two different sets of parametric equations for the rectangular equation. (Enter your answer in a list as [x = f(t), y = f(t)], [x = f(t), y = f(t)].) y = 6x - 1
The parametric equations of y = 6x -1 are [x = t, y = 6t - 1].
What are parametric equations?Parametric equations divide an equation into two or more equations, depending upon the variables in the original equation, both dependent and independent.
What does the variable t mean?In parametric equations we mostly use t as an independent variable and write all equations in terms of t.
To convert a rectangular equation in its parametric representation, the easiest way to do is to equate x with the variable t in the original equation. Now, our x is equal to t. Hence, the final answer is [x = t, y = 6t - 1].
To learn more about parametric equations visit the link below:
https://brainly.com/question/28537985
#SBJ4
4. Car dealer Lisa Kovach paid 82% of a car's options totaling $3,098. She paid 85% on a base price of $15,480.
The destination charge was $890. What is the dealer's cost?
a. $13,158.00
b. $16,588.36
c. $18,020.36
d. $19.001.20
Part (c) is the correct option i.e. The total dealer's cost is $16588.36.
What is Percentage ?
Percentage, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolised as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
Given, Cost paid for car's options = 82 % $3,098 = $2540.36
Cost paid for base price = 85 % $15,480 = $13158.
Destination charge = $890
∴ The total dealer's cost will be :
= Cost paid for car's options + Cost paid for base price + Destination charge
= $2540.36 + $13158 + $890
= $16588.36.
To learn more about Percentage, visit the link given below:
https://brainly.com/question/24877689
#SPJ1
