The manipulatives and paragraph forms are the two-column proof to prove that vertical angles are congruent.
Using manipulatives: Draw the same two intersecting lines on the paper. Then, fold the paper along the line via the joint. The fold bisects the other two borders, but only the lines of the folded border which are on top of each other are required. The edges check and lie straight on top of each separately. This folding procedure can be utilized with two vertical corners. As a result, the vertical angles are the same.
Paragraph Form: When ∠1 and ∠3 are connected to ∠2, they form a linear pair. This indicates that whether added dimension ∠2 to dimension ∠1 or dimension ∠2 to dimension ∠3, the total is 180°. That is, the measures of 1 and 3 are equal to the sum left before adding ∠2. As a result, the angles are the same. This argument applies to all pairs of vertical angles.
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the probability that it will rain is 0.42 what is the probability that it will not rain
Answer:
99.58
Step-by-step explanation:
Im not sure if its correct but the way I got the answer is 100-0.42
x - 2(x - 6) = -x + 12
The value of x in the equation given as x - 2(x - 6) = -x + 12 is 0
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the solution to the equation?A system of linear equations is a collection of at least two linear equations.
In this case, the equation is given as
x - 2(x - 6) = -x + 12
Open the bracket
So, we have
x - 2x + 12 = -x + 12
Evaluate the like terms
So, we have
x - 2x = -x
This gives
x = 0
Hence, the solution of x in the equation is 0
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Find the value of r so the line that passes through the pair of points has the given slope. ( − 2 , 8 ) , ( r , 4 ) , m = − 1 2
The line that passes through the pair of points has the given slope. ( − 2 , 8 ) , ( r , 4 ) , m = − 1 2, then the intersection with the domain is r = -5/3.
The line that passes through the pair of points has the given slope is,
( − 2 , 8 ) , ( r , 4 ) and m = -12
What is Slope :Slope, numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).
m = rise/run
[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
Where,
m = slope
[tex](x_{1} ,y_{1} )[/tex] = coordinates of first point in the line
[tex](x_{2} ,y_{2} )[/tex] = coordinates of second point in the line
Then, we can find the [tex]m_{1}[/tex]
We can use these two values, ( − 2 , 8 ) , ( r , 4 )
x1 = -2
y1 = 8
x2 = r
y2 = 4
m = [tex]\frac{4-8}{r-(-2)}[/tex]
[tex]m = \frac{-4}{r+2}[/tex]
We can substitute m= -12 value into m= -(4/r+2)
So,
We can write,
-12 = [tex]\frac{-4}{r+2}[/tex]
We can find the domain,
If the fraction is defined, the dominator can not be equal to zero.
2 + r ≠ 0
Rearrange variables to the left side of the inequality,
r ≠ -2
Append the inequality as the domain,
r ≠ -2
We can solve the equation,
-12 = [tex]\frac{-4}{r+2}[/tex]
Multiply both sides of equation by the common denominator,
-12 (r+2) = -4(r+2)/ (r+2)
Reduce the fractions,
-12 (r+2) = -4
Apply the distributive property,
-12r - 24 = -4
Rearrange variable to the left side of the equation,
-12r = -4 + 24
Calculate the sum or difference,
-12r = 20
Divide both sides of the equation by the coefficient of variables,
r = - 20/12
r = -5/3
Therefore,
The intersection with the domain is r = -5/3, so the line that passes through the pair of points has the given slope. ( − 2 , 8 ) , ( r , 4 ) , m = − 12.
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Ver en español
Cindy needs c cups of flour to make brownies. She has 5 cups of flour in her cupboard. Write an expression that shows how many cups of flour Cindy will have left after making the brownies.
The expression for the number of cups of flour Cindy has left in the cupboard is y = 5 - c.
A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
Let c be the number of cups of flour Cindy needs in her cupboard.
Let y be the number of cups of flour Cindy has left after making the brownies.
Now, the total number of cups in the cupboard is 5.
So, the expression for the total number of cups will be:
c + y = 5
Subtracting c from each side of the equation.
c + y - c = 5 - c
y = 5 - c
Therefore, the expression for the number of cups left is y = 5- c.
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Find the inverse function in slope-intercept form f(x)=x-5
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:f{}^{-1}(x) = x +5 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
We need to find the inverse of given function; f(x) = x - 5
[tex]\qquad \tt \rightarrow \: y = x - 5[/tex]
here, write x in terms of y.
[tex]\qquad \tt \rightarrow \: x = y + 5[/tex]
replace x with [tex]{\tt{{f}^{-1} (x)} } [/tex] and y with x, you will get your required inverse function.
[tex]\qquad \tt \rightarrow \: f {}^{ - 1} (x) = x + 5[/tex]
And it's already in slope intercept form
[tex]\qquad \tt \rightarrow \: y = mx + c[/tex]
where, slope (m) = 1 and y intercept (c) = 5
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Miguel can type 448 words in 8 minutes. Jaycee can type
700 words in 25 minutes. Who types faster?
Answer:
umm i will explain
Step-by-step explanation:
miguel = 448 in 8 min
jaycee = 700 in 25 min
in 1 min miguel can type=
448/8 = 56 words
in 1 min jaycee can type=
700/25 = 28 words
so miguel can type's faster than jaycee
Please answer the math question or help me on this.
The equation that represents the proportional relationship between the number of red paint and white paint is: y = 1/4x.
How to Write an Equation of a Proportional Relationship?A proportional relationship between two variables, x and y, where k represents the constant of proportionality or unit rate, can be expressed in slope-intercept form as: y = kx.
To find the value of k, which is the unit rate, the coordinates of any point on the line can be used and solved as: k = y/x.
Given the graph that represents the relationship between the number of red paint and white paint, we can use a point on the line, say (4, 1) to find k:
Unit rate/constant of proportionality, k = y/x = 1/4.
Substitute k = 1/4 into y = kx:
y = 1/4x.
The equation is: y = 1/4x.
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Solve the following inequality:
4c<14-3c
Answer: x < 2
Step-by-step explanation:
To solve this, we will isolate the variable c.
Given:
4c < 14 - 3c
Add 3c to both sides of the equation:
7x < 14
Divide both sides of the equation by 7:
x < 2
Maria and Jamal each have gardens. The area of Maria’s garden is represented by the expression 8x2 – 3x. Jamal’s garden is a rectangular plot with the width and length represented by the expressions 3x and 4x – 2.
Which expressions give how much bigger or smaller Jamal’s garden is compared to Jessica’s? Check all that apply.
4x2 – 9x
–4x2 + 3x
4x2 – 3x
12x2 – 6x – 8x2 – 3x
12x2 – 6x – 8x2 + 3x
The expression will be given as -4x² + 3x. Thus, option B is correct answer.
Area may be defined as the total amount of space which is covered by an entity. The area for a square will be given by the product of its sides and the area of the rectangle will be given as the product of its length and breadth. It is given that the area of Maria's garden is 8x² - 3x and the length and breadth of Jamal's garden are 4x - 2 and 3x respectively. The area of Jamal's garden is given by A = l×b = (4x - 2) × 3x = 12x² - 6x.
Now, difference between Maria's garden and Jamal's garden is given by
(8x² - 3x) - (12x² - 6x)
= 8x² - 3x - 12x² + 6x
=> -4x² + 3x which is the required answer.
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Is (x - 5) a factor of the following polynomial. Show your work. No work-no credit. 6) 5x³-28x + 13x³ + 5x² + 27x - 10 7) 2x² - 4x² - 10
(x-5) is not a factor of 6) 5x³-28x + 13x³ + 5x² + 27x - 10 and 7) 2x² - 4x² - 10.
What is the long division method?
You can divide huge numbers into numerous smaller groups or portions with the long division tool. The number of groups that can be formed when a dividend is divided by a divisor is given by the quotient, and the number of elements or integers that will remain ungrouped is given by the remainder.
6) we can simplify the equation 5x³-28x + 13x³ + 5x² + 27x - 10 further,
= 5x³+ 13x³+ 5x²-28x + 27x - 10
=[tex]18x^{3}+5x^{2} -x-10[/tex]
similarly, equation 2x² - 4x² - 10 can further be simplified
= [tex]-2x^{2} +0x-10\\[/tex]
now using the long-division method, in both cases (refer to the photo attached):
After referring to the picture we can conclude that (x-5) is not a factor of 6) 5x³-28x + 13x³ + 5x² + 27x - 10 or 7) 2x² - 4x² - 10.
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In the figure below, m
m
rjdjdjdufjfjfjfjfuuf
please help asap! i dont know what to do
rise over run to find the slope
y = mx+b
we rose 1 and went over by 2
which means the equation is 1/2 x or 0.5x
What is the answer to this question?
The perimeter of the square BCDE is 8√2 cm.
How to find perimeter of a square?A square is a quadrilateral that has all its sides equal to each other. All the angles in a square are also equal.
Therefore, the perimeter of a square is the sum of the whole sides of the square.
perimeter of the square BCDE = 4l
area of triangle ABC = 2cm²
area of triangle ABC = 1 / 2 bh
2 = 1 / 2 bh
The diagonal of square bisect each other.
The base and height of the triangle ABC are the same.
bh = 4
b² = 4
b = √4
b = 2 cm
Therefore,
BC = √2² + 2²
BC = √8
BC = 2√2 cm
Hence,
perimeter of the square BCDE = 4(2√2)
perimeter of the square BCDE = 8√2 cm
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HELP FOR 40 PTS AND BRAINLY :)
Answer:
A. 183Step-by-step explanation:
To solve this problem, use the order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAddSubtract112-38*14÷14+109
First thing you do is multiply.
[tex]\sf{38*14\div14}[/tex]
38*14=532
532÷14=38
112-38+109
Add and subtract the numbers from left to right.
[tex]\sf{112-38+109}[/tex]
[tex]\sf{112-38=74}[/tex]
[tex]\sf{74+109=\boxed{\sf{183}}[/tex]
[tex]\Rightarrow \boxed{\sf{183}}[/tex]
Therefore, the correct answer is A. 183.
I hope this helps, let me know if you have any questions.
Answer:
I’m believing it is A. 183
Step-by-step explanation:
is correct don’t you;)
A stack of recyclable newspaper 36 inches high will save one tree. The number of trees saved by recycling is directly proportional to the height of a stack of recyclable newspapers. How many trees would be saved from a stack of newspapers 24 feet high?
The number of trees that could be saved is 8 trees.
What is the number of trees?We know that papers are obtained from trees. The trees have to be cut down and then the Malina from the trees could be used in the production of paper.
It is also possible to save the trees by decreasing the number of trees that have to be cut by the recycling of the paper. The number of trees saved by recycling is directly proportional to the height of a stack of recyclable newspapers.
If stack of recyclable newspaper 36 inches high will save one tree;
Let the stack of recyclable newspaper = s
Number of trees = n
s α n
Introducing a constant of proportionality
s = kn
k = s/n
k = 36 inches/1
k = 36 inches
When the height is 24 feet high of 288 inches
n = s/k
n = 288 inches/36 inches
n = 8 trees
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1. The graph shows the height of a plant after a certain amount of time measured in days. Do you think that there may be a proportional relationship between the number of days and the height of the plant? Explain your reasoning. The graph shows how much snow fell after a certain amount of time measured in hours. 2. Do you think that there may be a proportional relationship between the number of hours and the amount of snow that fell? Explain your reasoning.
Due to different rates of change in each case, neither graph shows a proportional relationship.
When does a graph represents a proportional relationship?A graph represents a proportional relationship if the output variable y in the y-axis can be written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:
y = kx.
Item 1Between days 0 and 10, the plant grew by 4 centimeters.Between days 30 and 40, the plant grew by 8 centimeters.For the first case, the rate of change is of:
k = 4/10 = 0.4.
For the second case, the rate of change is of:
k = 8/10 = 0.8.
Different rates, hence cannot be written as proportional relationship.
Item 2Between hours 0 and 2, the amount of snow grew by 2 inches.Between days 2 and 4, the amount of snow remained constant at 2 inches.Hence the rates for each interval are given as follows:
Hours 0 - 2: 2/2 = 1 inch a hour.Hours 2 - 4: 0/2 = 0 inches a hour.Different rates, hence it is not a proportional relationship.
What is the missing information?The graphs are missing and are given by the image inserted at the end of the answer.
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hoang has worked as a nurse at springfield general hospital for 6 years longer than her friend bill. four years ago, she had been at the hospital for twice as long. how long has each been at the hospital?
By solving the equation we can conclude that Bill worked 4 years and Hoang worked 10 years in the hospital.
What do we mean by equations?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, Hoang worked for 6 years longer than her friend.
Let, the time Bill worked in the hospital be 'x'.So, Hoang worked in the hospital will be 'x + 6'.She spent twice as much time in the hospital two years ago. Then:
x + 6 - 2 = 2x4 = xx = 4Hence, Bill worked for 4 years and Hoang worked (4+6) for 10 years in the hospital.
Therefore, by solving the equation we can conclude that Bill worked for 4 years and Hoang worked for 10 years in the hospital.
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3/4 divided by 2/x simplified
Answer:3
Step-by-step explanation:
(-3/4)/(-2/8)=(-3/4)(-8/2)=(-3/4)(-4)=3
Two angles are supplementary if their sum is 180°. The larger angle measures three degrees more than twice the measure of a smaller
angle. If x represents the measure of the smaller angle and these two angles are supplementary, find the measure of each angle.
Does the function y equals 14 times the quantity 1 over 2 end quantity to the x power represent exponential growth or decay? what is the equation of the asymptote? decay; y = 0 growth; y = 0 decay; x = −3 growth; x = −3
The exponential function given in this problem represents an exponential decay, and it's asymptote is of y = 0.
What is an exponential function?An exponential function is modeled according to the rule given as follows:
[tex]y = ab^x + c[/tex]
The parameters of the function are defined as follows:
a + c is the y-intercept, which is the value of the function when x = 0.b is the rate of change of the function.c is the asymptote of the function.To verify if the function represents growth or decay, we have to check parameter b as follows:
If |b| > 1, the function represents exponential growth.If |b| < 1, the function represents exponential decay.In the context of this problem, the function is defined as follows:
[tex]y = 14\left(\frac{1}{2}\right)^x[/tex]
Hence the parameters of the given function are as follows:
a = 14, b = 0.5, c = 0.
Then:
Since |b| = 0.5 < 1, the function represents exponential decay.The asymptote of the function is of y = c = 0.More can be learned about exponential functions at https://brainly.com/question/25537936
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Answer:
Answer down bellow
Step-by-step explanation:
Q's asked: Does the function y equals 14 times the quantity 1 over 2 end quantity to the x power represent exponential growth or decay? What is the equation of the asymptote?
Answer: Decay; y = 0
hope this helps
~~Wdfads~~
24. How many dimensions does a line have?
a. No dimensions
b. One dimension
c. Two dimensions
d. Three dimensions
Answer:
b. one dimension
Step-by-step explanation:
0 dimensions would be a point.
1 dimension is a line
2 dimensions is an area
3 dimensions is a volume.
PLEASE I NEED ANSWER
Answer:
C and D. The x-axis is horizontal, the y-axis is vertical. Quadrant 3 is where you would find a point where the x is positive and the y is negative. Quadrant 3 is below the x-axis and is to the left of the y-axis.
Step-by-step explanation:
Hope it helps! =D
A line passes through the point (5,-2) and has a slope of -3
Answer: not sure
Step-by-step explanation: this: by this -
Equals this: ur mom
Which equation is equivalent to the equation 4x + 28 = 40?
a. 4 (x + 28) = 40
b. 4 (x + 7) = 40
c. 4x = 68
d. 32x = 40
Answer:
b
Step-by-step explanation:
4x + 28 = 40
4x + 4*7 = 40
4(x+7) = 40
In a small private school 3 students are randomly selected from 17 available students what is the probability that they are the three youngest students
Probability of three youngest student are selected is [tex]\frac{1}{816}[/tex]
What is probability?The field of mathematics known as probability concerns with numerical representations of the possibility that an event will occur or that a statement is accurate. An event's probability is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 represents certainty.
Given data
Total number of students available = 17
Number of students selected = 3
C₍₁₈₋₃₎ = [tex]\frac{18!}{3!(18-3)!}[/tex]
C₍₁₈₋₃₎ = [tex]\frac{18(17)(16)}{3(2)(1)}[/tex]
C₍₁₈₋₃₎ = [tex]\frac{4896}{6}[/tex]
C₍₁₈₋₃₎ = 816
Number of ways where students selected are youngest = 1
Probability of three youngest student are selected
= [tex]\frac{1}{C}[/tex]₍₁₈₋₃₎
= [tex]\frac{1}{816}[/tex]
Probability of three youngest student are selected is [tex]\frac{1}{816}[/tex].
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Lucy wants to drink 2L of water.
She has poured this amount into a jug. Between breakfast and lunch she pours 2 glasses of water each measuring 250ml.
Between lunch and her dinner she pours 3 glasses also measuring 250 ml.
How much water does she need to drink before going to bed?
The amount of water that Lucy should drink more is 750 ml.
How to calculate the value?From the information, Lucy between breakfast and lunch she pours 2 glasses of water each measuring 250ml. This will be:
= 250ml × 2
= 500ml
Between lunch and her dinner she pours 3 glasses also measuring 250 ml. This will be:
= 3 × 250ml
= 750 ml
Since Lucy wants to drink 2L of water, the amount needed to drink more will be:
= 2L - (750 + 500)
= 2000ml - 1250ml
= 750ml
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The number of students at Longview Middle School decreased by 0.75% from the number of students the previous year. To represent the percent, Don uses a 10 × 10 grid and divides one of the squares in the grid into 100 smaller squares. How many of the smaller squares will be shaded to represent 0.75%?
The area of Nevada is about 245% of the area of Ohio. How many squares would be shaded on 10 × 10 grids to represent 245%?
The number of the smaller squares which would be shaded to represent 0.75% as given in the task content is; 75.
The number of squares to correctly represent 245% on the grid is; 245.
What is the number of smaller squares which would be shaded to represent 0.75%?It follows from the task content that; To represent the percent, Don uses a 10 × 10 grid and divides one of the squares in the grid into 100 smaller squares.
Since each Square in the 10 × 10 grid represents 1%, it follows that on division of one of the squares in the grid into 100 smaller squares;
The percentage, 0.75% can be represented by shading 75 smaller squares.
Also, the number of squares to be shaded on 10 × 10 grids to represent 245% according to the task content is; 245. This follows from the fact that, all 100 squares on the on 10 × 10 grids represent 100%.
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need to show my work and find the surface area
4) The surface area of the square pyramid is; 145 ft²
5) The surface area of the rectangular prism is; 948 ft²
How to find the surface area of regular shapes?
4) For the square pyramid, we see that the faces have been broken down into 4 equal rectangles and one square base.
We know that;
Area of triangle = 1/2 * base * height
Thus
Area of 4 triangles = 4(1/2 * 5 * 12) = 120 ft²
Area of square = 5 * 5 = 25 ft²
Total surface area = 120 + 25 = 145 ft²
5) The surface area of a rectangular prism is;
A = 2(wl + hl + hw)
Thus, Area = 2((20 * 3) + (20 * 18) + (18 * 3))
Area = 2(474)
Surface area = 948 ft²
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on june 10, 2010 the boston globe reported that in the six years between 2006 and 2012 boston firefighters received raises of 2%, 2.5%, 3%, 3.5%, 2.5%, and 1.5%.
on june 10, 2010 the boston globe reported that in the six years between 2006 and 2012 boston firefighters received raises of 2%, 2.5%, 3%, 3.5%, 2.5%, and 1.5%. then overall raise is 16%
on june 10, 2010 the boston globe reported that in the six years between 2006 and 2012 boston firefighters received raises of 2%, 2.5%, 3%, 3.5%, 2.5%, and 1.5%.
let us assume the amount be 100
in 2007 it increase at 2% then it become 102
in 2008 at rate 2.5% then =102+2.55=104.55
in 2009 at rate 3% then it become =3.1365+104.55= 107.68
in 2010 at rate 3.5% = 3.7690+107.68=111.44
in 2011 at rate 2.5% = 2.786+111.44=114.22
in 2012 at rate 1.5%= 1.71+114.22=115.93
Hence, overall increase is 16%
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Show all work. Round all percentages to the nearest tenth of a percent. Mr. McCullough paid 80 people to say they were his friends. After he paid them, 26 of them still did not claim to be his friend. What percent of the people he paid claimed to be his friends?
The percent of the people he paid claimed to be his friends is 67.5%
Given,
Mr. McCullough paid 80 people to say they were his friends.
and, After he paid them, 26 of them still did not claim to be his friend.
To find the percent of the people he paid claimed to be his friends
Now, According to the question:
Based on the given condition,
Formulate :
(80- 26) ÷ 80
Calculate:
(80- 26) / 80
= 54/80
Simplify
= 27/40
=0.675
Convert to percentage;
Multiply a number to both the numerator and the denominator
0.675 × 100/100
Calculate
67.5 / 100
= 67.5%
Hence, The percent of the people he paid claimed to be his friends is 67.5%.
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