Fill in the blanks to find x
Answers
The value of x is 42
According to the question,
Given that,
Line AB is a straight line
m<AOB = 180°
a straight line angle is 180 °
All these angles is equal to angle AOB
m<AOE +m <EOF+ m <FOB=m<AOB
Now put the value of all the angles
we get the value of x
x +2x +34 +20 = 180
add x variable
3x + 54 = 180
3x = 126
x = 42
The value of x is 42
The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation. In this way, a pair of the linear equation gets transformed into one linear equation with only one variable, which can then easily be solved. Before moving to solve the linear equations using the substitution method, get an idea on what the algebraic method and graphical method is.
Algebraic Method
An Algebraic method is a collection of several methods, which are used to solve a pair of the linear equations that includes two variables. Generally, the algebraic method can be sub-divided into three categories:
Substitution method
Elimination method
Cross-multiplication method
Graphical Method
The graphical method is also known as the geometric method and is used to solve the system of linear equations. In this method, the equations are designed based on the objective function and constraints. To solve the system of linear equations, this method has undergone different steps to obtain the solutions.
In this article, we will focus mainly on solving the linear equations using the first algebraic method called “Substitution Method” in detail.
Substitution Method Steps
For instance, the system of two equations with two unknown values, the solution can be obtained by using the below steps. Here, the list of steps is provided to solve the linear equation. They are
Simplify the given equation by expanding the parenthesis
Solve one of the equations for either x or y
Substitute the step 2 solution in the other equation
Now solve the new equation obtained using elementary arithmetic operations
Finally, solve the equation to find the value of the second variable
Graphing of Linear Equations
Solving Linear Equations
Linear Equations in Two Variables
Difference Between Linear and Non-Linear Equations
Elimination by Substitution Method
In this method, the elimination of the variable can be performed by substituting the value of another variable in an equation. Hence, this method is called the elimination by substitution method.
Let us assume the system of linear equations
2x+3y = 13 and x-2y = -4
Given:
2x+3y = 13 … (1)
x-2y = -4 …(2)
The equation (2) can be written as
x = 2y-4 … (3)
Now, in equation (1) eliminate the variable x by substituting the equation (3).
Hence, equation (1) becomes
2(2y-4) +3y = 13
Now, apply the distributive property for the above equation,
4y-8+3y = 13
Now, solve the above equation for the variable y
7y – 8 = 13
7y = 13+8
7y = 21
y= 21/7
y= 3
Hence, the value of y is 3.
Now, substituting y=3 in the equation (2), we get
x- 2(3) = -4
x – 6=-4
x = -4+6
x = 2
Therefore, the value of x is 2.
Hence, the solution for the system of linear equations is:
x = 2 and y=3
To check whether the obtained solution is correct or not, substitute the values of x and y in any of the given equations.
Verification:
Use Equation (2) to verify the solution
x-2y = -4
Now, substitute x= 2 and y=3
2-2(3) = -4
2-6= -4
-4=-4
Here, L.H.S = R.H.S
Hence, the obtained solution is correct
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Related Questions
x + 8 + 2x <= 2x + 13
Answers
Answer:
X = 15
Step-by-step explanation:
We move all terms to the left:
x+8+2x-(2x+13)=0
We add all the numbers together, and all the variables:
3x-(2x+13)+8=0
We get rid of parentheses:
3x-2x-13+8=0
We add all the numbers together, and all the variables:
x-5=0
We move all terms containing x to the left, all other terms to the right:
x=5
What is the equation of the line that passes through the point (-5,0) and has a
slope of 3/5
Quick please
Answers
This should be your answer
Equation: y=3/5x+3
Suppose that the functions q and r are defined as follows.
g(x)=x² +5
r(x)=√x+7
Find the following.
(roq)(2) = 0
&
X
(q or)(2) =
5
?
Answers
Answer:
(r o g)(2) = 4
(q o r)(2) = 14
Step-by-step explanation:
Given
[tex]g(x) = x^2 + 5[/tex]
[tex]r(x) = \sqrt{x + 7}[/tex]
Solving (a): (r o q)(2)
In function:
(r o g)(x) = r(g(x))
So, first we calculate g(2)
[tex]g(x) = x^2 + 5[/tex]
[tex]g(2) = 2^2 + 5[/tex]
[tex]g(2) = 4 + 5[/tex]
[tex]g(2) = 9[/tex]
Next, we calculate r(g(2))
Substitute 9 for g(2)in r(g(2))
r(q(2)) = r(9)
This gives:
[tex]r(x) = \sqrt{x + 7}[/tex]
[tex]r(9) = \sqrt{9 +7{[/tex]
[tex]r(9) = \sqrt{16}[/tex]{
[tex]r(9) = 4[/tex]
Hence:
(r o g)(2) = 4
Solving (b): (q o r)(2)
So, first we calculate r(2)
[tex]r(x) = \sqrt{x + 7}[/tex]
[tex]r(2) = \sqrt{2 + 7}[/tex]
[tex]r(2) = \sqrt{9}[/tex]
[tex]r(2) = 3[/tex]
Next, we calculate g(r(2))
Substitute 3 for r(2)in g(r(2))
g(r(2)) = g(3)
[tex]g(x) = x^2 + 5[/tex]
[tex]g(3) = 3^2 + 5[/tex]
[tex]g(3) = 9 + 5[/tex]
[tex]g(3) = 14[/tex]
Hence:
(q o r)(2) = 14
Help i don’t know if my answers are correct and I need the other ones I didn’t answer to be answered to please help I need the correct answer for 1-8 I need to bring my grade up
Answers
1) correct
2) correct
3) Not Congruent
4) Not Congruent
5) correct
6) Not Congruent
7) incorrect
8) SAS
Explanation:
7 is incorrect because the angle isn’t included in the sides
Hope this helps!
If a family has 6 children, in how many ways can the parents have 3 boys and 3 girls as children?
Answers
Answer:
one way?
Step-by-step explanation:
huh? what do you mean by this question?
Find the inequality represented by the graph
Answers
Answer:
y /< 5/2 x +5
Step-by-step explanation:
y is less than or equal to 5/2 x plus 5
since its a solid line and shaded below you would use less than or equal to
solve 7(82 - 60) + 3³
Answers
Answer:
181
Step-by-step explanation:
7× (82 - 60) + 3³
or. 7 × 22 + 27
or 154 + 27
or. 181
PLS HELP ASAP
Simplify 8 − (14). (1 point)
Question 5 options:
1)
−22
2)
−6
3)
6
4)
22
Answers
8 is positive and 14 negative. You can either draw a number line and help yourself with that or since the negative one is bigger you can do the subtraction 14 - 8 and then change the sign of the answer.
Question 5 Multiple Choice Worth 1 points) (04.05 MC) Determine if the ordered pair (-1 , -5) is a solution to the inequality y≤-3/4-1
No, because (-1. 5) is above the line
Yes, because (-1, -5) is below the line
No, because (-1, 5) is on the line
Yes, because 1-1, 5) is on the line
Answers
Answer:
(-1, -5) satisfies the inequality and will be the solution to the inequality.
From the attached figure, it is clear that (-1, -5) is below the line.
Therefore, the correct option is:
''Yes, because 1-1, 5) is on the line''.
Step-by-step explanation:
Given the inequality
[tex]y\le -\frac{3}{4}x-1[/tex]
substituting (-1, -5) to check whether it satisfies the inequality or not
[tex]-5\le \:-\frac{3}{4}\left(-1\right)-1[/tex]
[tex]-5\:\le \:\frac{3}{4}-1[/tex]
[tex]-5\:\le -\frac{1}{4}[/tex]
TRUE
Thus, (-1, -5) satisfies the inequality and will be the solution to the inequality.
From the attached figure, it is clear that (-1, -5) is below the line.
Therefore, the correct option is:
''Yes, because 1-1, 5) is on the line''.
The expression 9/2 = 3 is the same as
А
9/2 x3
B
9/2 x 3/2
с
9/2 x 1/3
D
2/9 = 3
Answers
Find the sample variance and standard deviation
19,12,6,7,11
Thank you
Answers
Answer:
Variance: 26.5
Standard Deviation: 5.1478150704935
Step-by-step explanation:
First, Add up all of the numbers: 6 + 7 + 11 + 12 + 19 = 55
Square the total, and then divided the number of items in the data set55 x 55 = 3025
3025 / 5 = 605
Take your set of original numbers from step 1, squared them individually this time, and added them all up:(6 x 6) + (7 x 7) + (11 x 11) + (12 x 12) + (19 x 19) = 711
Subtract the amount in step 2 from the amount in step 3:711 - 605 = 106
Subtract 1 from the number of items in my data set:5 - 1 = 4
Divide the number in step 4 by the number in step 5:106 / 4 = 26.5
Finally, take the square root of the number from step 6 (the variance),
√(26.5) = 5.1478150704935
is the relationship in this picture a function
if so why?
Answers
Answer:
PLEASE BE CAREFUL NightmareMech14 IS A PREDATOR HE ASKS FOR VIDEOS OF GIRLS AND TRYS TO GET THEM TO EMAIL HIM DONT GIVE HIM ANY INFORMATION STAY SAFE COPY AND PASTE THIS EVERYWHERE
Step-by-step explanation:
Help would be very much appreciated:)
Answers
Answer:
3 times x plus seven
Step-by-step explanation:
k
The pet shop had black birds, red birds, blue birds, and gray birds. What is the ratio of blue birds to the total number of birds?
Answers
Answer:
NUMBER PLEASE.
Step-by-step explanation:
Max's solar pool cover is 10 feet wide by 32 feet long. If it had a 1.5 ft overhang,
what would be the dimensions of the solar pool cover for the swimming pool?
Width
Feet
Length
Feet
का
Answers
Answer:
W=13 ft L=35 feet
Step-by-step explanation:
see detailed explanation below
Pls help 10pts which model shows 33 1/3?
Answers
The model that shows 33 1/3% is the first model that has one shaded box and two unshaded boxes.
What is percentage?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentage is a measure of frequency and the sign used to represent percentages is %.
33 1/3 % is expressed as a mixed fraction, that is it is made up of a whole number and a proper fraction. In order to convert 33 1/3 % to a fraction, divide 33 1/3 % by 100
33 1/3 % ÷ 100 = 1 / 3
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He company spent 32% of its annual budget developing a new machine what fraction of the company‘s budget was spent developing the new machine
Answers
The fraction of the company's annual budget which was spent on developing a new machine is; 8/25.
What fraction of the company budget was used to develop the new machine?It follows from the task content that the company in discuss spent 32% of its annual budget developing a new machine.
This insinuates that the percentage given can be as a fraction as follows;
= 32/100
When expressed in it's simplest form;
= 8/25
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HELP PLS FOR BRAINLIEST
The square of m reduced by 32.
2m - 32
m^2 - 32
32 - m^2
m^2 + 32
The product of 5 and r, and then increased by k.
5r - k
5r + k
k - 5r
5r/k
A number x is tripled and then decreased by 10.
3x - 10
3x + 10
x^3 - 10
x^3 + 10
8 reduced by the sum of x and y.
8(x - y)
(x + y) - 8
8 - (x + y)
8 + (x + y )
4 more than the product of 8 and n.
8n - 4
8n + 4
4(8 + n)
(8 + n) - 4
6 less than the sum of 9 and d.
6 - 9d
9d + 6
6 - (9 + d)
(9 + d) - 6
Eighty less than four times a number.
4x - 80
4x + 80
4x / 80
80 - 4x
Yvonne (y) runs three times as fast as Xavier (x). What is an algebraic translation of this?
y = 2x
y = 3x
y = 1/2x
y = 1/3x
n divided by 5
n/5
5n
n + 5
n - 5
a take away 19
a - 19
19 - a
a + 19
19a
Answers
Answer:
The square of m reduced by 32
m^2 - 32
The product of 5 and r, and then increased by k
5r + k
A number x in tripled and then decreased by 10
3x - 10
8 reduced by the sum of x and y
8 - (x + y)
4 more than the product of 8 and n
8n + 4
6 less than the sum of 9 and d
(9 + d) - 6
Eighty less than four times a number
4x - 80
Yvonne (y) runs three times as fast as Xavier (x). What is an algebraic translation of this?
y = 3x
n divided by 5
n/5
a takeaway 19
a - 19
5/8 and 3/4 I need an answer pleaseee
Answers
I'm not sure what you mean but I'll provide both.
5/8 + 3/4
11/8 or 1 3/8.
The common denominator of 5/8 and 3/4 is 8. 3/4 with a denominator of 8 would be 6/8.
5/8 + 6/8 = 11/8 or 1 3/8.
5/8 × 3/4
15/32.
Multiply the numerator by the numerator and the denominator by the denominator.
5 times 3 is 15 and 8 times 4 is 32.
So you get 15/32. This cannot be simplified.
Which of the following expressions represents 3 less than 5 times a number
A) 5n - 3
B) 5 - 35
C) 3n - 5
D) 3 - 5
Answers
Answer:
A)
Step-by-step explanation:
The correct expression which represents ''3 less than 5 times a number'' would be,
A) 5n - 3
Mathematical expression is defined as the collection of numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that,
A mathematical expression is,
''3 less than 5 times a number''
Let us assume that,
A number = x
Hence, the expression to represent ''3 less than 5 times a number'' is,
⇒ (5 × n) - 3
⇒ 5n - 3
So, the correct option is,
A) 5n - 3
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15 pts for this question :)
Answers
Answer:
it is not a function
What are the coordinates of point Q? HELPP QUICK !!!
Answers
Answer:
The coordinates of point Q are [tex]\mathbf{(4,2\frac{1}{2})}[/tex]
Step-by-step explanation:
The coordinates of point Q can be found looking at the graph
We need to find the value of x-coordinate and y-coordinate by looking at graph.
Check the value of x-coordinate that matches point Q similarly check the value of y-coordinate that matches point Q
Looking at the graph Point Q is at x=4 and y=2.5 or [tex]2\frac{1}{2}[/tex]
So, The coordinates of point Q are [tex]\mathbf{(4,2\frac{1}{2})}[/tex]
Someone please help me !
Find the slope of line then put the answer as a integer or as a reduced fraction in the form A/B
Answers
Answer:
-1/12
Step-by-step explanation:
The line passes through (0,10) and (-600,60)
So m = (60 - 10)/(-600 - 0) = 50/(-600) = -1/12
Factor completely
81x^12 - 1
Answers
Answer:
81x^(2)-1
Step-by-step explanation:
Rewrite 81^(2) as (9x)^(2)
Rewrite 1 as 1^(2)
Since they are perfect squares , factor using the perfect squares formula
(9x + 1) (9x - 1)
What is the wavelength measurement?
A. 2 m
B. 2 s
C. 0.4 m
D. 0.8 m
Answers
The wavelength measurement of the figure is,
⇒ 2 meter
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
We have to given that;
The figure is shown in image.
Since, We know that;
Wavelength is the distance between identical points in the adjacent cycles of a waveform signal propagated in space or along a wire.
Hence, We get;
The wavelength measurement of the figure is,
⇒ 3.5 - 0.5 meter
⇒ 2 meter
Thus, The wavelength measurement of the figure is,
⇒ 2 meter
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If connie pays $100 for 8 baskets, what is the unit rate for each Basket?
Answers
The unit rate is $12.50 per basket
Find the range of the function y=1/2x+3
When the domain is -2,0,2,4
Answers
Y=1/2(0)+3=3
Y=1/2(2)+3=4
Y=1/2(4)+3=5
help. please. I need help
Answers
8. Write the equation in Slope-Intercept Form with the following, information:
Remember, plug into point-slope, y - y, = m(x - x,), then solve down I
Passes through (7, 4) with a slope of -3
Answers
The slope-intercept equation of the given line is 3x + y = 25
Slope-intercept is one of the special forms of linear equations where we can find the slope-intercept of any point with its coordinates and its slope.
The line is passing through the point(x₁,y₁) = (7,4)
The slope of the line line(m) = -3
Slope-intercept equation
y-y₁ = m( x- x₁)
Where (x₁,y₁) is (7,4) and Slope,m is -3
Let us substitute these values in the slope-intercept equation, It becomes
y - 4 = -3(x - 7)
y - 4 = -3x + 21
3x + y = 21 + 4
3x + y = 25
which is the slope-intercept equation of the points (7,4) and slope -3
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directions - solve the liner system. enter your answer as an ordered pair. 2x + 3y = 31 y = x + 7
Answers
(1) 2x + 3y = 31 y
(2) 2x + 3y = x + 7
(3) 31y = x + 7
(3) x = 31y - 7
(2) 2(31y - 7) + 3y = 31y - 7 + 7 ; 62y - 14 + 3y = 31y ; 34y = 14 ; y = 14/34 ; y = 7/17
(3) x = 31y - 7 ; x = 31*(7/17) - 7 ; x = (217 - 119)/17 = 98/17
x = 98/17 ≈ 5.76
y = 7/17 ≈ 0.41