Answer:
12
Step-by-step explanation:
This is an example of Addition property between two positive integers (i.e. whole value numbers), which means the result will be positive and larger than the two numbers.
The result of the addition would be:
[tex]5 + 7 = 12[/tex]
Another way to do it if you are struggling a bit you can write the value of [tex]7[/tex] as [tex]7 = 5 +2[/tex] so then you can say:
[tex]5 + (5 + 2) = 5 + 5 + 2 = 10 + 2 = 12[/tex]
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is twice the measure of the first angle. The third angle is 12 more than the second.
Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
x = first angle
y = second angle
z = third angle
x + y + z = 180
The sum of the measures of the second and third angles is twice the measure of the first angle. ----> y + z = 2x
The third angle is 12 more than the second. ----> z = y + 12
Use substitution to find each variable. Since z is already isolated/by itself, plug it into the other equation
y + z = 2x Plug in (y + 12) for z
y + (y + 12) = 2x Simplify
2y + 12 = 2x Divide 2 on both sides
y + 6 = x Isolate "y"
y = x - 6 Next you could plug this into z = y + 12, so that z has the x variable
z = y + 12
z = x - 6 + 12
z = x + 6
Now that you have y and z, you can do this:
x + y + z = 180
x + (x - 6) + (x + 6) = 180 Simplify
3x = 180 Divide 3 on both sides
x = 60 Now that you found x, plug it into the other equations to find y and z
y = x - 6
y = 60 - 6
y = 54
z = x + 6
z = 60 + 6
z = 66
x = 60°
y = 54°
z = 66° [sorry if this is confusing]
PROOF
x + y + z = 180
60 + 54 + 66 = 180
180 = 180
The problem can be solved by setting up and solving a system of equations based on the information given in the problem. Using these equations, we are able to establish a relationship between the angles and thus calculate their individual measures.
Explanation:To solve this problem, we need to set up and solve a system of equations based on the information provided. We know from the problem that:
The sum of the angles of a triangle is 180 degrees, so x + y + z = 180.The sum of the measures of the second and third angles is twice the measure of the first, so y + z = 2x.The third angle is 12 more than the second, so z = y + 12.First, let's substitute z = y + 12 into the other two equations:
In x + y + z = 180, replace z with y + 12 to get x + y + y + 12 = 180; or, simplifying further, x + 2y = 168.In y + z = 2x, replace z with y + 12 to get y + y + 12 = 2x or, simplifying further, 2x = 2y + 12 or x = y + 6.We now substitute x = y + 6 into the equation x + 2y = 168 to find the values of x and y and hence z.
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in general, f−1(f(x)) = f(f−1(x)) =
Answer:
f−1(f(x)) = f(f−1(x)) = x
Step-by-step explanation:
Follow this simple example using the function f(x) = x + 2
f(x) = x + 2
NOw we find the inverse function f^(1)(x).
y = x + 2
x = y + 2
y = x - 2
f^(-1)(x) = x - 2
The inverse function is f^(-1)(x) = x - 2
Now we do the two compositions of functions:
f^(-1)(f(x)) = x + 2 - 2 = x
f(f^(-1)(x)) = x - 2 + 2 = x
Both are equal to x.
Answer: f−1(f(x)) = f(f−1(x)) = x
The expression [tex]f^{-1}(f(x)) = f(f^{-1}(x)) = x[/tex]
We are to prove the relationship;
[tex]f^{-1}(f(x)) = f(f^{-1}(x)) = ?[/tex]
To get the unknown, let f(x) = x - 2
Find its inverse:
Let y = x - 2
Replace y with x;
x = y - 2
y = x+2
Hence [tex]f^{-1}x = x+2[/tex]
Next is to get [tex]f(f^{-1}(x))[/tex]
[tex]f(f^{-1}(x))=f(x+2) = (x+2) - 2\\f(f^{-1}(x))= x\\[/tex]
We can conclude that [tex]f^{-1}(f(x)) = f(f^{-1}(x)) = x[/tex]
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its was taylor's 8th birthday and there were 47 presents. Each kid brought 10 presents, except for three kids who brought five presents each and two kids who bought one present each. How many kids came to Taylor's party
Total of 8 kids came to Taylor's party.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.
Given is Taylor's 8th birthday and there were 47 presents. Each kid brought 10 presents, except for three kids who brought five presents each and two kids who bought one present each.
Assume that [n] students bought 10 presents. Then, we can write -
3 x 5 + 2 x 1 + 10n = 47
15 + 2 + 10n = 47
10n = 30
n = 3
Total kids = 3 + 3 + 2 = 8
Therefore, total of 8 kids came to Taylor's party.
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What is the equation of the line that is parallel to the line y - 1 = 4(x + 3) and passes through the point (4, 32)?
A: y=-1/4x +33
B: y=-1/4x + 36
C: y = 4x - 16
D: y = 4x + 16
Answer:
Option D: y = 4x + 16
Step-by-step explanation:
Given the line: y - 1 = 4(x + 3) ⇒ y = 4x + 13
The slope of the given line = m = 4
The required line is parallel to the given line
So, the slope of the required line = m = 4
So, the general equation of the required line: y = 4x + c
Where c is constant represents y-intercept
To find the value of c, substitute with the point (4,32)
At x = 4 y = 32
∴ 32 = 4 * 4 + c
∴ c = 32 - 16 = 16
∴ y = 4x + 16
The answer is option D: y = 4x + 16
1. Justin divided 403 by a number and got a quotient of 26 with a remainder of 13. What was the
number Justin divided by?
a. 13
b. 14
c. 15
d. 16
Answer:
15
Step-by-step explanation:
First subtract the remainder from 403 to get 390. then divide 390 by 26 to get 15.
The number used by Justin used to divide 403 to get a quotient of 26 with a remainder of 13 is 15.
What number was used to divide 403?
Division is theartimetic process used to divide a number into equal parts using another number. The sign used to denote division is ÷.
In order to detemine the number used to divide 403, take the following steps:
Subtract 13 from 403 = 403 - 13 = 390
Now divide 390 by 26: 390 / 26 = 15
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What is the inverse of f(x)=-x-1
Answer:
f^-1 (x)=-x-1
Step-by-step explanation:
y=-x-1
x=-y-1
-y=x+1
y=-x-1
Brian has reduced his cholesterol level by 20% after his last check up. If his original level was 240, what is his cholesterol level now?
Answer:
192
Step-by-step explanation:
20% of 240 is 48
240-48 = 192
Answer:
192
Step-by-step explanation:
20%/100% x 240 =48
His cholesterol level now will be 240 - 48 = 192
If 5/8 = x/16 , then x is equal to
Answer:
10/16
Step-by-step explanation:
what should be added to both sides of the equation to solve for the variables? 45=30+m
Answer: m = 15
Step-by-step explanation:
45 = 30 + m
subtract 30 , from both sides , that is , -30 should be added to both sides to find the variable
45 - 30 = 30 + m - 30
15 = m
Therefore : m = 15
What’s -3 + 6k + 11k - 10 (combining like terms)
Answer:
17k + -13
Step-by-step explanation:
6k + 11k take the + next to the 6k making it say 6k+11
-3 - 10 take the - next to the 10 making it say -3 - 10
Linda's start up cost for her online jewelery store was $250, as she has to pay an additional $60per month to keep it running. Write an expression or equation modeling the real world
Total Cost = 250 + 60x is the equation that models the given situation
Solution:
Given that, Linda's start up cost for her online jewelery store was $250
She has to pay an additional $60 per month to keep it running
To find: Equation that models this situation
From given,
Start up cost = $ 250
Let "x" be the number of months she keeps the store running
Additional pay per month = $ 60
Thus, the total cost Linda spend to keep the store running is given as:
Total Cost = Startup cost + (Additional pay per month)(number of months)
[tex]Total\ Cost = 250 + 60x[/tex]
Thus the equation that models the given situation is found
Find fifth roots of z⁵ + 32 = 0 and draw its graph?
Answer:
Step-by-step explanation:
Which of the following points is a solution of the inequality y < -|x|?
a) (1, -2)
b) (1, -1)
c) (1, 0)
Answer:
a) (1, -2)
Step-by-step explanation:
The given inequality is y < -|x|
We substitute the point to see which points satisfy the inequality.
For a) (1, -2), we substitute x=1 and y=-2 to get:
-2 < -|1|---------->-2<-1--------->True
For b) (1, -1), we substitute x=1 and y=-1 to get:
-1 < -|1|---------->-1<-1--------->False
For a) (1, 0), we substitute x=1 and y=0 to get:
0 < -|1|---------->0<-1--------->False
The first choice is correct.
Julian bought 8 books this year. He gets a free book every time he buys 1. How many books altogether did he get this year
Answer:16 books
Step-by-step explanation:
Final answer:
Julian bought 8 books and received a free book with each purchase, resulting in 16 books altogether by the end of the year.
Explanation:
The question is asking how many books Julian would have altogether if he bought 8 books and received a free book with each purchase this year. To solve this, we need to consider that for every book purchased, he gets an additional book without cost. Therefore, Julian gets 2 books each time he makes a purchase for one book. As he bought 8 books, we simply need to double that amount to account for the free books he received.
To calculate: 8 books purchased × 2 = 16 books altogether.
Julian would have a total of 16 books by the end of the year after his purchases and receiving the complementary books.
rectangle ABCD is graphed in the cordinate plane. The following are the verticies of the rectangle; A(-6,-4),B(-4,-4),C(-4,-2), and D (-6,-2). what is the perimiter
Answer:
Therefore Perimeter of Rectangle ABCD is 4 units
Step-by-step explanation:
Given:
ABCD is a Rectangle.
A(-6,-4),
B(-4,-4),
C(-4,-2), and
D (-6,-2).
To Find :
Perimeter of Rectangle = ?
Solution:
Perimeter of Rectangle is given as
[tex]\textrm{Perimeter of Rectangle}=2(Length+Width)[/tex]
Length = AB
Width = BC
Now By Distance Formula we have'
[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]
Substituting the values we get
[tex]l(AB) = \sqrt{((-4-(-6))^{2}+(-4-(-4))^{2} )}[/tex]
[tex]l(AB) = \sqrt{((2)^{2}+(0)^{2} )}=2\ unit[/tex]
Similarly
[tex]l(BC) = \sqrt{((-4-(-4))^{2}+(-2-(-4))^{2} )}[/tex]
[tex]l(BC) = \sqrt{((0)^{2}+(2)^{2} )}=2\ unit[/tex]
Therefore now
Length = AB = 2 unit
Width = BC = 2 unit
Substituting the values in Perimeter we get
[tex]\textrm{Perimeter of Rectangle}=2(2+2)=2(4)=8\ unit[/tex]
Therefore Perimeter of Rectangle ABCD is 4 units
Answer:
Therefore Perimeter of Rectangle ABCD is 4 units
Step-by-step explanation:
Given:
ABCD is a Rectangle.
A(-6,-4),
B(-4,-4),
C(-4,-2), and
D (-6,-2).
To Find :
Perimeter of Rectangle = ?
Solution:
The line passing through (11,y) and (2,0)is parallel to the line joining (7,5) and (-2,2). Find y.
Answer: y = 3
Step-by-step explanation:
Two lines are said to be parallel if they have the same slope. All we need to do is to find the slope of each line . The formula for finding slope is given as :
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
For the first line
[tex]x_{1}[/tex] = 11
[tex]x_{2}[/tex] = 2
[tex]y_{1}[/tex] = y
[tex]y_{2}[/tex] = 0
substituting into the formula , we have
m = [tex]\frac{0 - y}{2 - 11}[/tex]
m = [tex]\frac{-y}{-9}[/tex]
m = [tex]\frac{y}{9}[/tex]
Also Finding the slope of the second line we have
[tex]m_{2}[/tex] = [tex]\frac{2-5}{-2 - 7}[/tex]
[tex]m_{2}[/tex] = [tex]\frac{-3}{-9}[/tex]
[tex]m_{2}[/tex] = [tex]\frac{1}{3}[/tex]
Since the two lines are parallel , we will equate their slope , that is
[tex]\frac{y}{9}[/tex] = [tex]\frac{1}{3}[/tex]
3y = 9
y = 3
A piece of paper is 0.01 centimeters thick When you fold it once it becomes 0.02 cm thick. If you fold it again it doubles again to 0.04 cm thick each fold doubles thickness of the paper. how thick is the paper?
Answer: Should Be 0.01
Step-by-step explanation: It’s Asking How Thick it is and never asked when So it would automatically mean from the start therefore it’s 0.01 cm thick
Perform the indicated operation.(7 - 11/) + (-3 + 5/)
Answer:
The correct answer is C. 4 -6
Step-by-step explanation:
Let's solve the operation given, this way:
(7 - 11/) + (-3 + 5/)
7 - 11 - 3 + 5=
12 - 14 = - 2
After resolving the parenthesis, adding and subtracting the result of thhe operation is - 2
The correct answer is C. 4 -6
Ryder used front-end estimation to estimate the product of (–24.98)(–1.29). What was his estimate?
Answer:
20
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
why do banks pay interest on saving accounts
Answer: irs
Step-by-step explanation:
Banks give interest on savings accounts to encourage consumers to deposit and retain their money in the bank
The reason why banks pay interest
Banks give interest on savings accounts to encourage consumers to deposit and retain their money in the bank.
Banks can attract and maintain consumer cash by providing interest, which they can then use to lend to other people or invest in various financial operations.
Paying interest on savings accounts assists banks in maintaining liquidity, generating money, and developing a mutually beneficial relationship.
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Which equation represents the line shown
on the graph?
x = y + 2
y = x + 2
y = 2x
x = 2y
Answer: Third option:
Step-by-step explanation:
The equation in Slope Intercept form of a line that does not pass through the point (0,0), which is known as "Origin, is the following:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
The equation in Slope Intercept form of a line that passes through the Origin, is:
[tex]y=mx[/tex]
Where "m" is the slope of the line.
In this case you can observe in the picture attached that the line passes through the point (0,0).
You can also notice that "y" would be the Dependent variable and "x" the Independent variable.
Therefore, the equation of this must have this form:
[tex]y=mx[/tex]
The only equation that matches with that form, is the one given in the Third option. This is:
[tex]y=2x[/tex]
The linear equation shown in the graph can be written as.
y = 2x
Which equation represents the line shown on the graph?A general linear equation is written as:
y = ax + b
Where a is the slope and b is the y-intercept.
In this graph, we can see that the line intercepts the y-axis at y = 0, so we have:
y = ax
We also can see that the line passes through the point (1, 2), replacing these values in the equation we will get:
2 = a*1
2 = a
Then the linear equation is:
y = 2x
The third option.
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WILL MARK BRAINLIEST 25 POINTS
The graph shows f(x) and its transformation g(x) .
Enter the equation for g(x) in the box.
Answer:
g (x) = 2 ^ (x + 2)
Step-by-step explanation:
For this case the transformation of f (x) is given by
g (x) = 2 ^ (x + 2)
To prove it, we must verify that equality is met by replacing the ordered pairs shown in the function g (x)
For (-2,1)
g (-2) = 2 ^ ( -2 + 2)
g(-2)=1
For (-1,2)
g (-1) = 2 ^ ( -1+ 2)
g(-1)=2
For (0,4)
g (0) = 2 ^ ( 0+ 2)
g(0)=4
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find the value of m<1 m<2 and m<3
Answer:
i don't know
Step-by-step explanation:
Select True or False.
The expression 5x − 3(2x − 4) is equivalent to the expression 12 − x.
True
False
Answer:true
Step-by-step explanation:
5x-3(2x-4)=
1) solve the parentheses
5x-6x-12=0
2) we just can rest the X
5x-6x=X
3) X-12=0
4) The order of factors does not alter the product
12-X=0
Answer:
True
Step-by-step explanation:
5x − 3(2x − 4)
Expand
5x - 6x + 12
-x + 12
12 - x
( ) are called "parentheses" or "brackets "
Whatever is inside the ( ) needs to be treated as a "package".
So when multiplying: multiply by everything inside the "package".
Multiplying negatives has special rules: a negative times a positive gives a negative, but multiplying two negatives gives a positive:
In that case −3 · -5 = +15 (a positive answer)
jacob qnd jordan are training for track season. jacob did 39 sit-ups in 30 secs. jordan did 59 sit-ups in 50 secs. who will likely do more sit-ups in 2 1/2 mins
Jordan it a bigger number
Mark as BrainliestCan someone please help me :) !!!!
In the diagram, PCG and CGR are supplementary, the measure of AGK =10x° and the measure of PCG=(6x100)°
Based on this information , which equation can be used to the find the value of x?
A. 6x +100 + 10x =180
B. 6x+ 100 -10x =90
C. 6x+100+10x=90
D. 10x=6x+100
Answer:
A
Step-by-step explanation:
supplementary angles add up to 180
angle cgr and kga are vertical angles so they are equal
that makes the two angles in question add up to 180
Please help ASAP! Thanks! For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answer:
Part 1) [tex]A=36(\pi-2)\ cm^2[/tex]
Part 2) [tex]P=6(\pi+2\sqrt{2})\ cm[/tex]
Step-by-step explanation:
Part 1) Find the area
we know that
The area of the shape is equal to the area of a quarter of circle minus the area of an isosceles right triangle
so
[tex]A=\frac{1}{4}\pi r^{2}-\frac{1}{2}(b)(h)[/tex]
we have that the base and the height of triangle is equal to the radius of the circle
[tex]r=12\ cm\\b=12\ cm\\h=12\ cm[/tex]
substitute
[tex]A=\frac{1}{4}\pi (12)^{2}-\frac{1}{2}(12)(12)[/tex]
[tex]A=(36\pi-72)\ cm^2[/tex]
simplify
Factor 36
[tex]A=36(\pi-2)\ cm^2[/tex]
Part 2) Find the perimeter
The perimeter of the figure is equal to the circumference of a quarter of circle plus the hypotenuse of the right triangle
The circumference of a quarter of circle is equal to
[tex]C=\frac{1}{4}(2\pi r)=\frac{1}{2}\pi r[/tex]
substitute the given values
[tex]C=\frac{1}{2}\pi (12)[/tex]
[tex]C=6\pi\ cm[/tex]
The hypotenuse of right triangle is equal to (applying the Pythagorean Theorem)
[tex]AC=\sqrt{12^2+12^2}[/tex]
[tex]AC=\sqrt{288}\ cm[/tex]
simplify
[tex]AC=12\sqrt{2}\ cm[/tex]
Find the perimeter
[tex]P=(6\pi+12\sqrt{2})\ cm[/tex]
simplify
Factor 6
[tex]P=6(\pi+2\sqrt{2})\ cm[/tex]
Answer:
36(π-2)cm^2 is area
Perimeter is 6(π+2√2)
Step-by-step explanation:
Draw a model for a fraction1/6
Answer:
Step-by-step explanation:
picture to help
Answer: I can't draw it but i answered
Step-by-step explanation:
To draw a model for 1/6 you would have draw six shapes of any kind. Then you would only fill one of them.
What is the equation of the line that has a slope of -4 and goes through (-1,6)
Answer:
y = - 4x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 4, thus
y = - 4x + c ← is the partial equation
To find c substitute (- 1, 6) into the partial equation
6 = 4 + c ⇒ c = 6 - 4 = 2
y = - 4x + 2 ← equation of line
Round 5 9/17 to the nearest whole number
Answer:
6
Step-by-step explanation: