When solving a system by addition, our goal is to cancel out one of the variables by adding the two equations together.
Notice that if we add these two equations together,
neither one of our variables will cancel out.
In this situation, we need to set things up so that when we do add
our two equations together, one of our variables will cancel out.
Notice that we have a 2x in our first equation.
If we had a -2 in our second equation,
then the x's would cancel out.
In order to create a -2x in the second equation,
we simply multiply both sides of the second equation by -2.
So we have (-2)(x - 2y) = (10)(-2).
Rewriting both equations, we have 2x + 4y = 28 and for
our second equation we have -2x + 4y = -20.
Now when we add our two equations together,
our x terms will cancel out and were left with 8y = 8.
Dividing both sides by 8, y = 1.
To solve for x, substitute a 1 in for y
in either one of the two equations.
So let's go with our first equation.
If we substitute a 1 in for y, we have 2x + 4(1) = 28.
4(1) is 1 according to the identity property of multiplication.
So we have 2x + 4 = 28.
Now subtract 4 from both sides to get 2x = 24.
Now divide both sides by 2 and x = 12.
Now put your answer in the form of the ordered pair {12, 1}.
what is the multiplicative inverse of 1 ½
Answer:
-2/3
Step-by-step explanation:
Well, multiplicative inverse means the opposite of a answer in this case 1 1/2 has to be made into an improper fraction.
3/2.
Hence, the multiplicative inverse of 3/2 is -2/3.
Please answer this question fast in two minutes
Answer:
(7, 8)
Step-by-step explanation:
Midpoint Formula: [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex]
Simply set our midpoint and given point equal into a formula to find the other endpoint:
4 = (1 + x)/2
8 = 1 + x
x = 7
6 = (4 + y)/2
12 = 4 + y
y = 8
Jeanine is selecting various albums to be displayed in the front of her music coffee house. She will be choosing 4 albums for
one part of the display. This part of the display is very prominent and she is really trying to promote jazz. There are five albums
from Diana Kroll, seven albums from Harry Connick Jr. and four albums from Michael Bublé. In how many ways can she choose
four albums for display and at least two albums are from Diana Kroll? Evaluate using both the direct and indirect method.
Gt11.2014
Answer:
The number of ways she can choose four albums for display with at least two from Diana Kroll is from the sixteen albums is 665 ways
Step-by-step explanation:
1) The number of ways she can choose 2 albums of Diana from the 5 Diana Kroll albums is 5!/(2!(5 - 2)!) = 10 ways
Choosing the other 2 albums from the remaining 11 albums gives;
11!/(2!(11 - 2)!) = 55 ways
Total number of ways is then 10 × 55 = 550 ways
Choosing 3 from the 5 Diana Kroll albums is 5!/(3!(5 - 3)!) = 10 ways
Choosing the other 1 album from the remaining 11 albums gives;
11!/(1!(11 - 1)!) = 11 ways
Total number of ways is then 10 × 11 = 110 ways
Choosing 4 from the 5 Diana Kroll albums is 5!/(4!(5 - 4)!) = 5 ways
Choosing the other 0 album from the remaining 11 albums gives;
11!/(0!(11 - 0)!) = 1 way
Total number of ways is then 5 × 1 = 5 ways
Total number of ways = 550 + 110 + 5 = 665 ways
2) In the indirect method, we first find the number of ways to choose 4 albums out of the 16 albums, then we subtract the number of cases where there are 1 and 0 Diana Kroll albums as follows;
16!/(4!(16 - 4)!) = 1820 ways
With 1 Diana Kroll album gives
5!/(1!(5 - 1)!)×11!(3!(11 - 3)!) = 825 ways
With 0 Diana Kroll album gives
5!/(0!(5 - 0)!)×11!(4!(11 - 4)!) = 330 ways
Total number of ways with at least 2 Diana Kroll albums = 1820 - 825 - 330
Total number of ways with at least 2 Diana Kroll albums = 665 ways.
Which one of the following is the graph of:
Answer:
B
Step-by-step explanation:
Correct if wrong
WHAT IS THE LENGTH OF B QUICK HELP
Answer:
2 cm.
Step-by-step explanation:
The entire base is 10 cm and the top is 8 cm, so b is 10 - 8 = 2 cm.
Hope this helps!
I hope this helps you
b+8=10
b=2
Please answer this question in two minutes
Answer:
(7.5 , 5.5)
Step-by-step explanation:
The midpoint is halfway between the two end points:
Its x value is halfway between the two x values
Its y value is halfway between the two y values
To calculate it:
Add both "x" coordinates, divide by 2
Add both "y" coordinates, divide by 2
functions.
Which values are within the domain of the function?
Check all that apply.
st
x= -6
x=-4
2
1 x= -2
LED x = 0
-4
-2
2
4
I x = 2
0 x = 4
-2.
-4
Answer:
2,5 and 6
Step-by-step explanation:
The answer is going to be option 2, 5 and 6 because the line touches -4,2 and 4 on the x axis. And these are the x values so that's why this is going to be the answer.
Hope this information helps you!
x=-2, x=-4, x=2 and x=4 values are within the domain of the function
What is a function?A relation is a function if it has only One y-value for each x-value.
The domain of a function is the set of all possible inputs for the function.
If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that chosen x-value is said to belong to the domain of f.
x=2, x=4, x=5, x=-2, x=-4 are the values in domain
Hence, x=-2, x=-4, x=2 and x=4 values are within the domain of the function
To learn more on Functions click:
https://brainly.com/question/30721594
#SPJ7
The points A (-3, b), and B (1, 3) are 5 units apart. Find the value of b.
Answer:
b = 0
Step-by-step explanation:
To find the value of b, we will follow the steps below;
Using the distance formula:
D = √(x₂-x₁)² + (y₂-y₁)²
from the question given,
A (-3, b), this implies
(-3, b) = (x₁ ,y₁)
x₁=-3 and y₁ = b
similarly
B (1, 3)
(1, 3) = (x₂,y₂)
this implies
x₂ = 1 and y₂=3
D= 5
we can now proceed to insert the values into the formula and then solve for b
D = √(x₂-x₁)² + (y₂-y₁)²
5 = √(1+3)² + (3-b)²
5 = √4² + (3-b)²
5=√16 + (3-b)²
take the squares of both-side of the equation
5² = 16 + (3-b)²
25 = 16 + (3-b)²
subtract 16 from both-side of the equation
25 - 16 = (3-b)²
9 = (3-b)²
Take the square root of both-side
√9 = 3-b
3 = 3-b
add b to both-side of the equation
3 + b = 3 - b+ b
3 + b = 3
subtract 3 from both-side of the equation
3+b-3 = 3-3
b = 0
Therefore, the value of b is 0
What is the measure of XYZ?
Help plz
Answer:
The measure of angle XYZ will be 120° because the included arc of an inscribed angle will always be twice the measure of the inscribed angle
Answer:wrong. Its 249 degrees
Step-by-step explanation:
Just got it right on the quiz
Simplify the following expression (62)4
Answer:
[tex]3^{0} =1[/tex]
Step-by-step explanation:
What is the scale factor of ABC to DEF?
Answer:
answer is 1
Step-by-step explanation:
The scale factor of triangle ABC to triangle DEF is 1. Therefore, the correct answer is option D.
In the given triangle ABC, AB=5 units, BC=5 units and AC=5 units and in triangle DEF, DE=5 units, DF=5 units and EF=5 units.
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
So, the scale factor of ABC to DEF is
AB/DE = BC/EF = AC/DF = 5/5 = 1
Therefore, the correct answer is option D.
To learn more about the scale factor visit:
https://brainly.com/question/22312172.
#SPJ4
Can someone please help me I really need help
Answer:
-721 is greater than -723.
Step-by-step explanation:
Answer:
x < - 721
Step-by-step explanation:
x < - 721 is the one according to the pictured line
Use the general solution to solve 5 - 6x = 8x + 17
[tex]
5-6x=8x+17 \\
-14x=12\implies x=-\frac{6}{7}
[/tex]
Hope this helps.
Answer: -6/7
Step-by-step explanation: 5 - 6x = 8x + 17
5 + - 6x = 8x + 17
-6x + 5 = 8x + 17
-6x + 5 - 8x = 8x + 17 - 8x
-14x + 5 = 17
-14x + 5 - 5 = 17 - 5
-14x = 12
-14x/-14 = 12/-14
x = -6/7
Anita purchased apples priced at $1.79 per pound at the grocery store. Her receipt shows that she spent $5.37 on apples.
Answer:
She bought 3 pounds of apples.
Step-by-step explanation:
First we look at our given steps:
1 pound of apples=$1.79
total=$5.37
We need to divide her total by the cost per pounds of apples. So 5.37/1.79=3.
The number of pounds Anita purchased is 3.
How many pounds did Anita purchase?Given: $1.79 per pound, spent $5.37 on apples
We must divide her aggregate by the cost per pound of apples.
Number of pounds = Total Spent / Amount per pound
Number of pounds = 5.37/1.79
Number of pounds = 3.
The number of pounds Anita purchased is 3.
Therefore, the number of pounds is 3.
The completed question is,
Anita purchased apples priced at $1.79 per pound at the grocery store. Her receipt shows that she spent $5.37 on apples. Type the correct answer in the box.
To learn more about the algebraic expression
https://brainly.com/question/19864285
#SPJ2
Stacey wishes to make a hamburger which is lower in fat without having to give up the great taste. She purchases 5 pounds of ground beef which is 15% fat and combines it with 7 pounds of ground turkey which is only 3% fat. What is the percentage of fat in the mixture?
Answer:
%P = 8%
the percentage of fat in the mixture is 8%
Step-by-step explanation:
Given;
The percentage of fat in the mixture is;
%P = total mass of fat in mixture/total mass of mixture × 100%
%P = F/T × 100% ….....1
Mass of fat in mixture is;
She purchases 5 pounds of ground beef which is 15% fat
F1 = 15% of 5 pounds = 0.15×5 pounds
F1 = 0.75 pound
and combines it with 7 pounds of ground turkey which is only 3% fat
F2 = 3% of 7 pounds = 0.03 × 7
F2 = 0.21 pound
Total mass F = F1 + F2
F = 0.75+0.21
F = 0.96 pound
Total mass of mixture T = 5 + 7 pounds
T = 12 pounds.
From equation 1,
%P = F/T × 100%
%P = 0.96/12 × 100%
%P = 0.08×100%
%P = 8%
the percentage of fat in the mixture is 8%
please help me I really need this
Answer:
1. A. No
2. A. Yes
Step-by-step explanation:
1. B. Because the numbers to the left of 7 are smaller than the numbers to the right of 7 on the number line.
2. B. Because to the right side has more numbers than the left side so amber is correct
Which one of the following statements expresses a true proportion?
O A. 7:9 = 8:9
OB. 3:4 = 9:12
O C.54:9 = 6:3
OD. 2:1 1:2
Answer:
The answer is B.
Step-by-step explanation:
A true proportion is a set of ratios that equal each other.
For example, 1:2=2:4 is a proportion.
As we look through the list, we observe only B equals each other. Imagine 3:4 and 9:12 as a fraction. (¾ and 9/12). If we reduce 9/12, we get ¾. Thus, 3:4 = 9:12:)
I hope this helps!
Matthew wants to estimate the mean height of students attending his collage. He records the heigjts of 100 randomly selected students attending the college. What is the population?
Answer:
ned more info
Step-by-step explanation:
The correct option that shows the population of the research carried out by Matthew is Option D; all the students attending the college.
What is the mean?Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.
We are told that Matthew wants to estimate the mean height of students attending his college.
Now, let us say the total number of students in his college is x.
If he decides to select 100 students randomly to record their height, it means this 100 student is a sample out of the total number of students which is x that is the population.
In conclusion, we can say that the population of this research by Matthew is the total number of students that attend the college.
Hence, The correct option that shows the population of the research carried out by Matthew is Option D; all the students attending the college.
Read more about mean here at;
brainly.com/question/6028584
#SPJ2
Find the solutions to the equation below.
16x2 - 64 = 0
A. X=-4
B. X= 4
C. X = -2
D. X=-8
E. X= 2
F. X=-64
Answer:
C. X = -2
E. X = 2
Step-by-step explanation:
16(-4)² = 64
16(16) = 64
256 = 64 (false)
16(4)² = 64
16(16) = 64
256 = 64 (false)
16(-2)² = 64
16(4) = 64
64 = 64 (true)
16(-8)² = 64
16(64) = 64
1024 = 64 (false)
16(2)² = 64
16(4) = 64
64 = 64 (true)
16(-64)² = 64
16(4096) = 64
65356 = 64 (false)
Solve algebraically for x: -23(x + 12) + 23x = −54x + 2
Answer:
[tex]x=\frac{139}{27}[/tex]
Step-by-step explanation:
-23(x+12)+23x=-54x+2
-23x-276+26x=-54+2
-276=-54x+2
54x=2+276
54x=278
[tex]x=\frac{139}{27}[/tex]
Answer:
Use mathaway <3
Step-by-step explanation:
What is the slope and y-intercept of the equation 3(y − 2) + 6(x + 1) − 2 = 0
Which rule describes the composition of transformations
that maps ABC to A'B'C"?
Answer:
Step-by-step explanation:
To get from ABC to A'B'C', ABC is reflected across line m.
To get from ABC to A"B"C", ABC need to first be reflected across line m. Then, it needs to be rotated 90° clockwise to get to A"B"C".
I'm not exactly sure which one you were trying to get (so I just added both), because you said A'B'C", instead of A'B'C' or A"B"C", but I really hope this answers your question!
The rule which describes the composition of transformations that maps ABC to A'B'C' is,
⇒ reflect across the line m.
We have to given that,
To find the rule which describes the composition of transformations that maps ABC to A'B'C'.
Here, The triangle ABC and it's image A'B'C' is shown in image.
Clearly, Image of triangle ABC is reflect across the line m.
Thus, the rule which describes the composition of transformations that maps ABC to A'B'C' is,
⇒ reflect across the line m.
Learn more about the transformation visit:
https://brainly.com/question/30097107
#SPJ2
If α and β are the zeros of the quadratic polynomial f(x) = 3x2–4x + 5, find a polynomialwhose zeros are 2α + 3β and 3α + 2β.
Answer:
[tex]\boxed{\sf \ \ \ 3x^2-20x+37\ \ \ }[/tex]
Step-by-step explanation:
Hello,
a and b are the zeros, we can say that
[tex]f(x)=3(x^2-\dfrac{4}{3}x+\dfrac{5}{3}) = 3(x-a)(x-b)=3(x-(a+b)x+ab)[/tex]
So we can say that
[tex]a+b=\dfrac{4}{3}\\ab=\dfrac{5}{3}[/tex]
Now, we are looking for a polynomial where zeros are 2a+3b and 3a+2b
for instance we can write
[tex](x-2a-3b)(x-3a-2b)=x^2-(2a+3b+3a+2b)x+(2a+3b)(3a+2b)\\= x^2-5(a+b)x+6a^2+6b^2+9ab+4ab[/tex]
and we can notice that
[tex]a^2+b^2=(a+b)^2-2ab[/tex] so
[tex](x-2a-3b)(x-3a-2b)=x^2-5(a+b)x+6[(a+b)2-2ab]+13ab\\= x^2-5(a+b)x+6(a+b)^2+ab[/tex]
it comes
[tex]x^2-5*\dfrac{4}{3}x+6(\dfrac{4}{3})^2+\dfrac{5}{3}[/tex]
multiply by 3
[tex]3x^2-20x+2*16+5=3x^2-20x+37[/tex]
3/4t=2/3
What the answer
Answer:
[tex]t = \frac{8}{9} [/tex]Step-by-step explanation:
3/4 t = 2/3
Multiply both sides of the equation by 4/3
4/3 * 3/4 t = 4/3 * 2/3
Reduce the numbers with G.C.F 4
1/3 * 3t = 4/3 * 2/3
Reduce the numbers with G.C.F 3
t = 4/3 * 2/3
Multiply the fractions
t = 8/9
Hope this helps...
Good luck on your assignment...
Answer:
[tex]t= \frac{8}{9} \\ [/tex]
Step-by-step explanation:
[tex]3/4t=2/3 \\ \frac{3}{4} t = \frac{2}{3} \\ cross - multiply \\ 3t \times 3 = 4 \times 2[/tex]
[tex]9t = 8 \\ divide \: both \: sides \\ of \: the \: equation \: by \: 9 \\ \frac{9t}{9} = \frac{8}{9} [/tex]
[tex]t = \frac{8}{9} [/tex]
What does Cos mean in geometry
Answer:
cosine
Step-by-step explanation:
"Cos" is the abbreviation usually applied to the name of the cosine function. That function gives the x-coordinate of the point on a unit circle that is at some angle measured counterclockwise from the x-axis. A unit circle is a circle with a radius of 1 unit, centered at the origin.
help.. Me plssssssss
1)
2, 5, 8, 11, 14
2)
0, 2, 8, 18, 32
3)
-6, -1, 2, 3, 10, 29
substitute the given values for x and do as the function says.
What is the inequality shown?
Answer:
-4<n≤5
If you are using another variable just replace it in.
The information in the number line is an interval (-4,5]
What is Interval Notation?Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities. We know an interval expressed as 1 < x < 5 denotes a set of numbers lying between 1 and 5 and it is represented as (1,5)
Given here, the line extends to -4 and ends at 5 but the it is open on the LHS and closed on the RHS and thus the interval notation is (-4,5]
Hence the interval represented in the number line is (-4,5]
Learn more about interval notation here:
https://brainly.com/question/14264237
#SPJ2
Please help with atleast some❤️❤️❤️
Which of the following is the correct factored form of the given equation?
Answer: 3
Step-by-step explanation:
What is the nth term rule of the quadratic sequence below? 7, 14, 23, 34, 47, 62, 79
Answer:
Tn = Tn-1 + 2(n-1) + 5
Kindly note that Tn-1 means T subscript n-1
Step-by-step explanation:
Here, we want an expression for the nth term.
First term is 7
Then first common difference is 7
second common difference is 7 + 2
Third common difference is 9 + 2
So within the common differences, the nth term is 7 + (n-1) 2
Now, the nth term of the series would be;
Tn = Tn-1 + 7 + 2(n-1)
Tn = Tn-1 + 7 + 2n -2
Tn = Tn-1 + 2n + 5
Now there is a fix to this,
n for the term is not the same n for the common difference.
the 7th term works with the 6th common. difference, while the 8th term work for the 7th common difference.
So we might need to rewrite the final expression as follows;
Tn = Tn-1 + 2(n-1) + 5