Answers
4. Definition of complementary
5. Substitution
6. Subtraction property
7. Definition of Congruence
What are corresponding angles?
According to the equivalent angle postulate, if a transversal meets two parallel lines, the corresponding angles must be congruent. In other words, the corresponding angles will always be identical if a transversal intersects two parallel lines.The angles that use the same relative location at each intersection of two parallel lines with a third line are known as corresponding angles to one another.The matching angles are similar to one another in nature.The two lines are parallel in nature if the corresponding angles in the two regions of intersection are congruent.Based on their sum, corresponding angles can be:Supplementary Corresponding Angles (if their sum is 180 degree)Complementary Corresponding angles (if their sum is 90 degrees)To know more about Corresponding Angles check the below link:
https://brainly.com/question/2009183
#SPJ1
Related Questions
I need to solve this equation
Answers
The linear equation is y = x+25.
What is linear equation?
An equation for a straight line is called a linear equation. The general representation of the straight-line equation is y=mx+b, where m is the slope of the line and b is the y-intercept. Linear equations are those equations that are of the first order.
Let the linear equation shown in data be written as
y = mx+b
Here, the value of m
53-45 = 8
for y,
68-60 = 8
m = 8/8 = 1
Hence,
60 = 1(45)+c
c = 25
hence, y = x +25
To know more about linear equation, visit,
https://brainly.com/question/28307569
#SPJ9
Answer:
Below
Step-by-step explanation:
Since it is given this is a linear equation, we can find the slope, m, between any two points as (y1-y2)/(x1-x2)
using the first two points (45,60) and (53,68)
m = ( 60 - 68) / (45-53) = 1
so for the slope intercept form of a line ( y = mx + b ) we have
y = (1) x + b plug in any of the points to calculate 'b'
70 = (55) + b shows b = 15
so you line equation becomes y = x + 15
Help! I’m confused and need help finding the answer!
Answers
Answer:
y=11x
Step-by-step explanation:
we use formula y2-y1/x2-x1 with 2 of the order pairs
22-11/2-1
11/1
11 is the slope
We find y intercept by finding when x is equal to zero and we subtract 11 until we find the 0 x unit since it goes down 11 every time
When x is zero y is zero so we write it like this
Y=11x
Hopes this helps please mark brainliest
which graph represents the solutions of p+1 <-1 or p- 5 > 7?
Answers
A graph which represents the solutions of p + 1 < -1 or p - 5 > 7 is shown in the image attached below.
What is an interval notation?In Mathematics, an interval notation simply refers to a set of real numbers which consist of all the real numbers that represents a continuous function and lies between two set of numbers.
This ultimately implies that, an interval notation should be used for writing all of the subsets of a real number line (graph) as shown below:
For the first interval, we have:
p + 1 < -1
p < -1 - 1
p < -2
Therefore, in interval notation, we have:
p = {∞, -2}
For the second interval, we have:
p - 5 > 7
p < 7 + 5
p < 12
Therefore, in interval notation, we have:
p = {12, ∞}
Read more on interval notation here: brainly.com/question/27997656
#SPJ1
any help would be really appreciated :)
Answers
Answer:
D = 30/7; R =32/7
Step-by-step explanation:
First, we need to find the scale of the number line. We can see that there are 7 ticks between 4 and 5. Thus, we can use (5-4)/7 to find the scale which is 1/7.
Since D is two ticks away from 4, we can use the equation:
[tex]4+2(\frac{1}{7})=D\\ 4+\frac{2}{7}=D\\ 4\frac{2}{7}=D\\ 4*7=28+2=\frac{30}{7}=D[/tex]
Since R is two ticks away from D or 30/7, we can use a similar equation:
[tex]\frac{30}{7}+2(\frac{1}{7})=R\\ \frac{30}{7}+\frac{2}{7}=R\\ \frac{32}{7}=R\\ 4\frac{4}{7}=R[/tex]
Your problem doesn't tell us whether we need to we use improper or mixed fractions, but I've included both for you.
Solve the compound inequality y−1<2 and y+2≥1. Write the solution in set-builder notation.
Answers
The solution in set builder notation is given by = {y:3>y≥-1}
Given the inequalities are,
y-1<2 ............(i)
y+2 ≥ 1 ..............(ii)
Solving the first inequality we get,
y-1 < 2
y-1+1 < 2+1, adding 1 to both sides
y < 3
Solving second inequality we get,
y+2 ≥ 1
y+2-2 ≥ 1-2
y ≥ -1
So the range is 3>y≥-1
So the solution in set builder notation is = {y:3>y≥-1}
To know more about Inequality refer to:
https://brainly.com/question/24372553
#SPJ1
A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ______ second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ______feet.
(Simplify your answer.)
Answers
The rocket reaches its maximum height at 2.25 second(s) after launch
The maximum height reached by the object is 88 feet.
Time to reach the maximum heightThe function is given as
h(t) = -16t² + 72t + 7
Differentiate the above function
So, we have the following representation
h'(t) = -32t + 72
Set to 0
-32t + 72 = 0
So, we have
32t = 72
Divide by 32
t = 2.25
Hence, the time is 2.25 seconds
The maximum heightIn (a), we have
t = 2.25
Substitute t = 2.25 in h(t) = -16t² + 72t + 7
h(2.25) = -16(2.25)² + 72(2.25) + 7
Evaluate
h(2.25) = 88
Hence, the maximum height is 88 feet
Read more about height functions at
https://brainly.com/question/10837575
#SPJ1
In exercises 1 and 2, find m∠1 and m∠2
Answers
The measures of the angles formed by the common transversal to the parallel lines are;
1. Angle 1 = 87°
Angle 2 = 100°
2. Angle 1 = 78°
Angle 2 = 78°
What are parallel lines?Parallel lines are lines that have the same slope but pass throuh different points.
The diagram consists of parallel lines that have a common transversal, therefore;
The alternate interior angles are congruentThe same side interior angles are supplementaryThe alternate exterior angles are congruentThe corresponding angles are congruentVertical angles are congruent (vertical angle theorem)1. The 87° angle and the Angle 1 are alternate interior angles, therefore;
87° ≅ Angle 1
87° = Angle 1
The 87° angle and the Angle 2 are same side interior angles
Therefore;
87° + Angle 2 = 180°
Angle 2 = 180° - 80° = 100°
Angle 2 = 100°
2. The 78° angle and the Angle 1 are corresponding angles, therefore;
78° ≅ Angle 1
Angle 1 = 78° (by the definition of congruency)
Angle 1 and Angle 2 are vertical angles
Therefore, Angle 1 is congruent to Angle 2 by vertical angle theorem
Angle 1 = Angle 2 by definition of congruency
Angle 1 = 78° = Angle 2
Learn more about the angles formed by parallel lines that have a common transversal here:
https://brainly.com/question/27950732
#SPJ1
Which equation represents the transformation formed by horizontally stretching the graph of f(x)=x√ by a factor of 4 and then vertically shifting the graph 2 units down?
Responses
g(x)=4x√−2
g left parenthesis x right parenthesis equals 4 square root of x minus 2
g(x)=4x−2−−−−−√
g left parenthesis x right parenthesis equals square root of 4 x minus 2 end root
g(x)=14x−−−√−2
g left parenthesis x right parenthesis equals square root of 1 fourth x end root minus 2
g(x)=4x−−√−2
Answers
The equation, [tex]g(x) = \sqrt{\frac{1}{4}x }-2[/tex], represents the transformation formed by horizontally stretching the graph of [tex]f(x) = \sqrt{x}[/tex] by a factor of 4 and then vertically shifting the graph 2 units down.
What is transformation of graph?
The process of algorithmically producing a new graph from an original graph is known as graph transformation, sometimes known as graph rewriting. It has several uses, including software engineering, layout algorithms, and image.
Consider, the given function [tex]f(x) = \sqrt{x}[/tex].
If horizontally stretching the graph by 4 units then, the graph becomes,
[tex]f(x) = \sqrt{\frac{x}{4} }[/tex].
If vertically shifting the graph 2 units, then the graph becomes,
[tex]h(x) = \sqrt{\frac{x}{4} } - 2[/tex].
Hence, the transformed form of the graph is, [tex]h(x) = \sqrt{\frac{x}{4} } - 2[/tex].
So, the third option is correct.
To know more about the transformation of graph, click on the link
https://brainly.com/question/1548871
#SPJ1
The table defines the observed data values and the corresponding predicted values, based on a line of fit. Observed Predicted 9 7.77 12 12.87 12 11.17 15 14.57 17 16.27 24 24.77 28 26.47 33 31.57
How many negative residuals does the data set have? How many positive residuals does the data set have?
2 negative residuals and 6 positive residuals 3 negative residuals and 5 positive residuals 5 negative residuals and 3 positive residuals 6 negative residuals and 2 positive residuals
Answers
The correct option regarding the residuals are given as follows:
2 negative residuals and 6 positive residuals.
What are residuals?For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:
Residual = Observed - Predicted.
Then the residuals of this data-set in the table are given as follows:
As for each point, the actual value is given and then the predicted value.
Then the numbers of each positive and negative residuals are given as follows:
Positive residuals: 6.Negative residuals: 2.Hence the first option is the correct option.
More can be learned about residuals at https://brainly.com/question/1447173
#SPJ1
2. Sam is paid $14 per hour plus 6% of sales. If he worked 37.5 hours in one
week, what would his sales need to be for him to make $733.50 per week
before taxes?
Answers
The sales Sam need to make $733.50 per week before taxes is $3475.
Given, Sam is paid $14 per hour plus 6% of sales.
If he worked 37.5 hours in one week, what would his sales need to make
$733.50 per week before taxes = ?
Let the sales be represented by x
Amount made from no of hours worked :
= $14 × 37.5 hours
=$525
Sales made = 6% of x
=0.06x
Total = 0.06x+$525
=$733.50
0.06x=733.50-$525
=$208.5
x=$3,475
Hence we get the required answer.
Learn more about Percentage here:
https://brainly.com/question/843074
#SPJ9
Identity 74.1 and 74.2
Answers
Answer:
A decimal or consecutive tenths decimals. Also 0.1 away from each other.
Step-by-step explanation:
They have decimal endings: .1 and .2
And are 0.1 away.
Select the correct answer.
What is √-9 + √121 written as a complex number in the form a + bi?
3 - 11i
11 + 3i
3 + 1li
11 - 31
Answers
You swap it around to put it in the form and find the square roots of the numbers. Square root of -9 is 3i and square root of 121 is 11
On a coordinate plane, a line goes through (negative 6, 8) and (2, 6). A point is at (negative 2, negative 4). What is the slope of the line that is parallel to the given line and passes through the given point? 1/4 What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the given point? What is the y-intercept of the line that is parallel to the given line and passes through the given point?
Answers
Answer of the following questions:
Slope of the line which is parallel to the given line passes through the given point is -1/4.Equation of the line in point-slope form as per given condition is given by y = (-x/4) -(9/2).y-intercept of the line which is parallel to the given line and passes through the point (-2, -4) is -9/2.As given in the question,
For a coordinate plane,
Line passes through the points (-6, 8) and (2,6).
Slope of the line = ( y₂ - y₁)/ (x₂ - x₁)
= ( 6 - 8) / (2- (-6))
= -2 /8
= -1/4
Slopes of the parallel line are always equal.
Equation of the line parallel to the given line and passes through (-2, -4)
is given by:
y -(-4) = (-1/4)(x -(-2))
⇒y + 4 = -x/4-1/2
⇒ y = -x/4 -9/2
y-intercept of the line which is parallel to the given line and passes through (-2, -4) is given by:
x = 0
y = -9/2 is the y-intercept.
Therefore, answer of the questions for the given condition :
Slope of the line which is parallel to the given line passes through the given point is -1/4.Equation of the line in point-slope form as per given condition is given by y = (-x/4) -(9/2).y-intercept of the line which is parallel to the given line and passes through the point (-2, -4) is -9/2.Learn more about slope here
brainly.com/question/3605446
#SPJ1
{Question 17} Please help! Need this by tonight! Thanks so much :)
Answers
The slope is, 1/4.
And the y - intercept is (0, -1).
What is slope and y-intercept?
A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.
A y-intercept, also known as a vertical intercept, is a point in analytical geometry where the graph of a function or relation meets the y-axis of the coordinate system, employing the convention that the horizontal axis represents a variable x and the vertical axis represents a variable y. Thus,
x = 0 is satisfied at these sites.
Let the x - intercept is 4.
The x - intercept is the point on x - axis, when y = 0.
So, the x - intercept is (4, 0).
The y - intercept is -1.
y-intercept is the point on the y - axis, when x is zero.
So, the y - intercept is (0, -1).
Here we have two points (4, 0) and (0, -1).
By using these points we can find the slope.
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m = \frac{-1-0}{0-4}= \frac{-1}{-4} = \frac{1}{4}[/tex]
Hence, the slope is 1/4 and the y - intercept is (0, -1).
To know more about the slope and y - intercept, click on the link
https://brainly.com/question/25722412
#SPJ1
Answer the attached questions
Answers
Answer:
Step-by-step explanation:
89,83,91,92,93,x
n=6
average=91
total=91*6=546
89+83+91+92+93+x=546
448+x=546
x=546-448=98
Answer:
Step-by-step explanation:
1)
Let Andre's grade needs to be a x on his next test
Hence,
[tex]\displaystyle\\\frac{89+83+91+92+93+x}{6} =91\\\\\frac{448+x}{6} =91[/tex]
Multiply both parts of the equation by 6:
[tex]448+x=91(6)\\\\448+x=546\\\\448+x-448=546-448\\\\x=98[/tex]
2)
[tex]\displaystyle\\\frac{1000+1181+1191+1200+1268+1328+2584+x}{8} =1344\\\\\frac{9752+x}{8}=1344[/tex]
Multiply both parts of the equation by 8:
9752+x=1344(8)
9752+x=10752
9752+x-9752=10752-9752
x=$1000
3)
302, 293, 218, 330, 199, 253, 288
Arrange this series:
199, 218, 253, 288, 293, 302, 330
[tex]\displaystyle\\a)\ the \ median = \$288\\\\b) \ the\ mean =\frac{199+218+253+288+293+302+330}{7} \\\\=\frac{1883}{7} \\\\=\$269\\c)\\\\\frac{1883+x}{8} =269+5\\\\\frac{1883+x}{8} =274[/tex]
Multiply both parts of the equation by 8:
1883+x=274(8)
1883+x=2192
1883+x-1883=2192-1883
x=$309
write the following term as a cube 27z^3
Answers
Answer:
(3z)^3
Step-by-step explanation:
27 = 3 * 3 * 3 = 3^3
3^3 z^3 = (3z)^3
The table shows tickets in an envelope to different concerts.
Rock:6
Pop:8
Country:6
Hip-hop:4
You randomly select two tickets, without replacement. What is the probability that you select two rock
concert tickets?
The probability is
Answers
The probability that you select two rock concert tickets is 0.25.
What is the probability?
Probability is the branch of mathematics concerned with numerical descriptions of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, where 0 represents the event's impossibility and 1 represents certainty.
We have,
[tex]Probability =\frac{number \ of favorable outcomes}{total number \ of outcomes}[/tex]
Number of favorable outcomes = 6
Total number of outcomes = 24
Probability rock concert tickets = 6/24
= 1/4
Probability rock concert tickets = 0.25
Hence, the probability that you select two rock concert tickets is 0.25
To learn more about the probability visit,
https://brainly.com/question/25870256
#SPJ1
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C(t) = −2t2 + 8t, where the time, t, is hours after injection.
Part A: What are the domain and range of the function C(t) based on the context of the problem? Show all necessary calculations. (5 points)
Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body. (5 points)
Answers
The domain of the given function is the hours or time taken whereas the range will be the concentration and greatest concentration of the medication that a patient will have in their body is 8 mg/L.
What is Domain of a function?
Inputs are assigned outputs by functions. The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.
Therefore, The domain of the given function is the hours or time taken.
What is range of a function?
The collection of potential output values for a function is known as its range.
Therefore, the range of the function is concentration.
B) Graph of the function is attached and we can see from the graph that greatest concentration of the medication that a patient will have in their body is 8 mg/L.
To know more about range and domain, go to link
https://brainly.com/question/2264373
#SPJ1
"A farmer with 350 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed? What are the dimensions of the enclosed area?
The width, labeled x in the figure, is
(Type an integer or decimal rounded to the nearest tenth as needed.)
The length, labeled 350-2x in the figure, is
(Type an integer or decimal rounded to the nearest tenth as needed.)
The largest area that can be enclosed is"
Answers
The dimensions of the shape will be 175 meters and 87.5 meters
The largest area that can be enclosed is 15312.5m².
How to calculate the area?Based on the information given, the equation to illustrate this will be:
2x + y = 350
y = 350 - 2x
Note that area = length × width
= x × y
We'll substitute the value into the equation. This will be:
A = x × (350 - 2x)
A(x) = 350x - 2x²
Differentiating the area, x will be 87.5
Width = 87.5m
Since y = 350 - 2x
= 350 - 2(87.5)
= 350 - 175
= 175
Length = 175m
Area = Length * Width
= 175 × 87.5
= 15312.5m²
Learn more about area on:
brainly.com/question/15535920
#SPJ1
Rearrange the equation
a= 1/2 (b- c)
to make b the subject.
Answers
I hope this helps.
Determine the value of each variable.
x=______
y=______
z=______
Answers
The value of the variables x, y , z are 28.75° , 135.5°, and 44.5° respectively .
What are corresponding angles?Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal.
When two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.
Corresponding angles are equal to each other. This means that (6x/5 +10)°=z= (2x-13)°
therefore( 6x/5 +10)° =(2x-13)°
collect like terms
10+13= 6x/5-2x
23= (10x-6x)/5
multiply both sides by 5
115=4x
x= 115/4= 28.75°
z= (2x-13)°
z= 2×28.75-13
z= 57.5-13
z= 44.5
z+y= 180( sum of angles on a straight line)
y= 180-44.5
y= 135.5
therefore the values x, y , z are 28.75° , 135.5°, and 44.5° respectively .
learn more about corresponding angles from
https://brainly.com/question/11853802
#SPJ1
Changing each of the values in a data set in a different way is called transforming the data.
A. True
B. False
Answers
Answer:
The answer is B false
Step-by-step explanation:
Determine the monthly principal and interest payment for a 15 -year mortgage when the amount financed is $85,000 and the annual percentage rate (APR) is %.7.0
Answers
Monthly Mortgage Payment is $495.88
Mortgage is a long-term amortized loan where loan is provided to buy certain capital asset and pay back total sum due in small periodic annuities. In Mortgage title of asset lies with lender and passes to borrower after complete mortgage payment.
Hence,
Mortgage Amount is $77,000
Monthly Payment for each $1,000 is $6.44
Monthly Mortgage Payment is $495.88
To learn more about Mortgage visit: https://brainly.com/question/8845095
#SPJ1
3.75 ÷ 0.4 =
What is the quotient of Php 8,750.50 and 50?
Answers
The quotient for both the parts are 9.375 and 175.01.
What is quotient?
In arithmetic, a quotient may be a amount created by the division of 2 numbers. The quotient has widespread use throughout arithmetic, and is usually brought up because the number a part of a division, or as a fraction or a quantitative relation.
Main body:
A) 3.75/ 0.4
first removing the decimals,
= 375/ 40
= 9.375
B) 8750.50/50
same process of removing decimals,
= 8755050/ 5000
= 175.01
Hence the value of quotient for both the parts are 9.375 and 175.01.
To know more about quotient click on the link below
https://brainly.com/question/11418015
#SPJ1
An electrician charges $80 for a service call, and then $100/hr for labor. Find the linear equation that models the cost based on the number of labor hours. How much will it cost for 3 ½ hours of the electrician’s time?
Answers
round 345.867234 to the nearest ten thousandths.
Answers
Answer:
I believe this should be it,
Step-by-step explanation:
344.8572
345.8672
———— -|
ten thousandth
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!
Answers
1. G
2. B
3. E
Before gaining popularity in the music industry, a young artist had 500 social media followers. As her popularity grew, her social media following increased at a rate of 6% per month. Which function represents this situation?
Answers
The function that represents the 6% popularity growth per month is P(x) = 500 + 0.06x
Function:
Function also known as an expression, rule, or law that defines a relationship between one variable called independent variable and another variable called dependent variable.
Given,
Before gaining popularity in the music industry, a young artist had 500 social media followers. As her popularity grew, her social media following increased at a rate of 6% per month.
Here we need to find the function that represents the given situation.
Let us consider the number of months to be modeled as x.
Then P(x) is the function that represents the situation.
And from the given question we know that, the initial population was 500.
And the population growth per month is 6%.
When we convert this percentage value into decimal then we get the growth rate as, 0.06.
Through this details, the function is written as,
P(x) = 500 + 0.06x
To know more about Function here.
https://brainly.com/question/1415414
#SPJ1
please help me! (20pts)
Answers
Answer:
gpaph C.
Step-by-step explanation:
graph 'C' represents the provided function. Its equation is
[tex]y=-\frac{5}{2}x +4.[/tex]
5. Evaluate the expressions.
(-3)⁰ = -(4/9)⁰ =
Answers
Answer:
1
Step-by-step explanation:
anything to the power of 0 is equal to 1
Hopes this helps please mark brainliest
