In the coordinate plane, line p has slope 13 and y-intercept (0, 2). Line r is the result of dilating line p by a factor of 3 centered at the origin.
Line P
Slope (m) = 13
y intercept is (0,2)
Equation is
y = mx+y
y= 13x+2
Dilated by scale factor of 3 with center at (0,3)
First make the centre at origin (0,0) by shifting the line 3 units downwards.
y = (13x+2)-3
y = 13x-1
In case of dilation, slope remains same only the y-intercept gets multiplied.
New equation is y = 13x-(1x3)
y = 13x-3
Now again take this line 3 units upwards
y = (13x-3)+3
y = 13x+0
Hence line r has slope of 13, y intercept is (0,0)
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Five lights, A, B, C, D, and E, are aligned in a row. The middle light is the midpoint of the segment between the second and fourth lights and also the midpoint of the segment between the first and last lights. Given: C is the midpoint of BD and AE. Prove: AB = DE
I need help writing the reason part of a two-column proof on this
Since C is mid - point of both BD and AE , therefore AB = DE .
Given : A , B , C , D and E are aligned in a row .
C is the mid - point of BD and AE .
To prove : AB = DE .
Since , C is the mid - point of BD ,
⇒ BC = CD ( 1 )
And since C is the mid - point of AE as well ,
⇒ AC = CE ( 2 )
Subtracting ( 1 ) from ( 2 ) ,
AC - BC = CE - CD
AB = DE
Hence , proved AB = DE .
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hii help pls n thanks
Answer:
(1,8.5)
Step-by-step explanation:
find the midpoint of x and yx=(-1+3)÷2
=1
y=(9+8)÷2
=8.6
(1 , 8.5)
Select each relation that has a range of {-5, 0, 4, 7}?
Responses
A{(4, 2), (0, 6), (-5, 12), (7, 6), (4, -3)}
B{(18, 4), (-1, 0), (-3, -5), (6, 7), (2, 4)}
C{(6, -5), (-11, 0), (6, 4), (-3, 7), (2, 9)}
D{(0, 6), (-5, 12), (7, 6), (4, -3)}
E{(6, -5), (-2, 4), (4, 7), (1, 0)}
F{(-5, 4), (-2, 4), (4, 7), (1, 0)}
Answer: E and B
I did the quiz
A relation that has a range of {-5, 0, 4, 7} is:{(6, -5), (-2, 4), (4, 7), (1, 0)}
The correct answer is an option (E)
In this question, we have been given some relations.
We need to find a relation that has a range of {-5, 0, 4, 7}
We know that in a relation is a set of ordered pairs (x, y)
where x is input and y is output.
We know that range is collection of all output values.
Therefore, a relation that has a range of {-5, 0, 4, 7} is:
E {(6, -5), (-2, 4), (4, 7), (1, 0)}
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3 1 0 -2
7 7 7 7
linear or not linear
I will give a star for the right one
The relationship given in the table is linear, as the rate of change of the output relative to the input is of zero.
How to identify linear relationships?Linear relationships are relationships in which the rate of change of the output relative to the input is constant, and called slope.
The points from the table in this problem are listed as follows:
Input of 3 with an output of 7.Input of 1 with an output of 7.Input of 0 with an output of 7.Input of -2 with an output of 7.The rate of change is given by the change in the output divided by the change in the input. Since the output remains constant, the rate of change remains constant at zero, and thus, this is a linear relationship.
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Shay is painting a fence. The fence has 7 sections that are each 4 feet long and one 18 foot long section. What is the total length of the fence shay is painting?
Answer:
You would have to add all of them up, which is (7*4) + 18 = 46.
Therefore the answer is 46 feet for the length of the fence.
what is the major difference between the two sample t-test and paired t-test? when should we use one versus the other? g
Two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs
The two-sample t-test defined as the method used to test whether the unknown population means of two groups are equal. The two sample t-test is also called independent samples t-test. Because the two samples of the data are statistically independent.
A paired t-test is used to find the difference between two variables usually separated by time for the same subject. By using the paired t-test we can find the mean difference between pairs of measurements is zero or not. So paired t-test is used, when data is in the form of matched pairs
Hence, two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs
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The graph shows the distance traveled by an Olympic-level sprinter over time during a race.
Find the slope of the line, and complete the sentences below.
100 meter race graph of a diagonal line on a coordinate plane going up and to the right with Time in seconds on the x axis and Distance in meters on the y axis. The line begins at the origin and passes through the point 2 comma 20.
Answer: Simplify your answer and write it as a proper fraction, improper fraction, or whole number
Step-by-step explanation:
enter two pairs of values for x and y that make the equation x + 2y = 10 true.
Which is the equation of a line that has a slope of 1/2
and passes through point (2, -3)?
Answer: A. : y=1/2x-4
Step-by-step explanation:
Use the equation y=mx+b: -3=1/2(2)+b
Simplify: -3=1+b
Simplify: -4=b
Final equation: y=1/2x-4
Please help, I'm having trouble
Answer:
Step-by-step explanation:
Okay, I can help. Please specify your question further so I can actually help you.
Rewrite the product using the distributive Property then simplifly to find the answer.
!8(26)
The answer to the question 18(26) is 18 * (20 + 6) = 468
What is the distributive property of multiplication?This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.
According to the distributive property, you can multiply a component by each addend separately before adding the total when multiplying it by two addends.
Based on this property, in order to solve a problem of this type, you have to expand the multiplication.
Hence 18(20 * 6)
is written as (18 * 20) + (18 * 6)
= 468
The answer is 468
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A line passes through the points (–14, 1) and (–4, 11). What is its equation in slope-intercept form?
Answer:
slope: (11-1)/(-4+14)
m: 10/10
M: 1
11 = -4 + b
b = 15
y = x + 15
For questions 7-10, determine the slope between the two points.
7. (-14, -10) and (12, 18) 8. (-3, 12) and (1, 2)
9. (25, -14) and (-3, 7) 10. (4, 14) and (16, 20)
The slope between the two points:
7. (-14, -10) and (12, 18) => m = 1.077
8. (-3, 12) and (1, 2) => m = -2.5
9. (25, -14) and (-3, 7) => m = -0.75
10. (4, 14) and (16, 20) => m = 0.5
In this question, we need to determine the slope between the two points.
We know that the formula of slope between the two points (x1, y1), (x2, y2)
m = (y2 - y1)/(x2 - x1)
7. (-14, -10) and (12, 18)
m1 = (18 + 10)/(12 + 14)
m1 = 1.077
8. (-3, 12) and (1, 2)
m2 = (2 - 12)/(1 + 3)
m2 = -2.5
9. (25, -14) and (-3, 7)
m3 = (7 + 14)/(-3 - 25)
m3 = -0.75
10. (4, 14) and (16, 20)
m4 = (20 - 14)/(16 - 4)
m4 = 0.5
Therefore, the slope between the two points:
7. (-14, -10) and (12, 18) => m = 1.077
8. (-3, 12) and (1, 2) => m = -2.5
9. (25, -14) and (-3, 7) => m = -0.75
10. (4, 14) and (16, 20) => m = 0.5
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please help with part (b) of this question!! thank you!!!
Answer:
p = 0, q = - 0.5-------------------------------
Part (b)Simplify first:
2p = q√76 + √192p = q(√4×√19) + √192p = 2q√19 + √192p = √19(2q + 1)We need both p and q be rational numbers and we know √19 is irrational.
It is only possible if both side are equal to zero:
2p = 0 ⇒ p = 0,2q + 1 = 0 ⇒ 2q = - 1 ⇒ q = - 0.5Answer:
[tex]\textsf{(a)} \quad h=3, \quad k=-2[/tex]
[tex]\textsf{(b)} \quad p=0, \quad q=-\dfrac{1}{2}[/tex]
Step-by-step explanation:
Part (a)Rearrange the given equation so that both sides are in the same form:
[tex]\begin{aligned}2-h\sqrt{11}&=-3\sqrt{11}-k\\2-h\sqrt{11}+k&=-3\sqrt{11}-k+k\\k+2-h\sqrt{11}&=-3\sqrt{11}\\k+2-h\sqrt{11}-2&=-3\sqrt{11}-2\\k-h\sqrt{11}&=-2-3\sqrt{11}\\\\\implies h&=3\\\implies k&=-2\end{aligned}[/tex]
Part (b)Rewrite and factor the right side of the equation.
As p and q are rationals, both sides of the equation have to equal zero.
[tex]\begin{aligned}2p&=q\sqrt{76}+\sqrt{19}\\2p&=q\sqrt{4 \cdot 19}+\sqrt{19}\\2p&=q\sqrt{4} \sqrt{19}+\sqrt{19}\\2p&=2q\sqrt{19}+\sqrt{19}\\2p&=\sqrt{19}(2q+1)\\\\\implies 2p&=0 \implies p=0\\\implies 2q+1&=0 \implies q=-\dfrac{1}{2}\end{aligned}[/tex]
Why is it 4 and 1/2? Where did you get the 1/2 and shouldn’t it be 5/10?
The reason for 1/2 and not 5/10 is it is a norm in math to reduce fractions to the least terms
What is equivalent form of fractions?This is a term used to refer to fractions that are equal even though they have different values in both he numerator and the denominator
Fractions are class of numbers that are of two parts the upper part is the numerator while the lower part is called the denominator.
In the given problem, 1/2
1 is the numerator2 is the denominator5/10 is an equivalent form of 1/2, this means that they are equal.
5/10 is shown to be equal to 1/2 by dividing by 5, this reduces the fraction to the least term which is 1/2. Using calculator can still show it that both numbers equal 0.5
In mathematics, it is preferred to reduce fractions to it's least form except it was stated.
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Andrea mixes 2 cups of water with 2/3 of lemonade concentrate. Nicholas mixes 1.5 cups of water with 1/3 cup of lemonade concentrate. whose lemonade mixture tastes stronger. (bonus points to the first person to show there work!)
HELP ASAP !!!!
Write and graph linear equations
Answer:
first graph the y-intercept start at 0 and go up 2 plot that. Then, go up 7 from 2 and to the right 1
Step-by-step explanation:
Kimberly's school is having a spring carnival. When Kimberly carries a bin of water balloons outside for the balloon toss, she trips and breaks 11 balloons. She counts the remaining water balloons, and there are 13 left.
Which equation can you use to find the number of water balloons w in the bin before Kimberly trips?
Equation can use to find the number of water balloons w in the bin before Kimberly trips is w-11=13.
Given that, Kimberly carries a bin of water balloons outside for the balloon toss, she trips and breaks 11 balloons.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The number of water balloons w in the bin before Kimberly trips.
She counts the remaining water balloons, and there are 13 left.
According to the question, the equation is
w-11=13
⇒ w=13+11
⇒ w=24
Hence, equation can use to find the number of water balloons w in the bin before Kimberly trips is w-11=13.
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For a project in his Geometry class, Levi uses a mirror on the ground to measure the height of his school’s football goalpost. He walks a distance of 12.05 meters from the goalpost, then places a mirror flat on the ground, marked with an X at the center. He then walks 2 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the goalpost clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.15 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
The measured distance of 1.15 meters from Levi's eyes to to the ground indicates that the height of the goalpost located 12.05 meters from the mirror when Levi is 2 meters from the mirror, found using similar triangles is approximately 6.93 meters.
What are similar triangles?Two triangles are similar if two angles in one triangle are congruent to two angles in the other triangle.
According the laws of reflection, the angle made by the incident ray with the normal is the same as the angle made by the reflected ray and the normal
Both the angle made by Levi and the angle made by the goalpost with the ground are perpendicular or 90°.
Therefore, the triangle formed by the line of site to the mirror and the reflected ray to the top of the goal post are similar triangles by Angle-Angle similarity postulate.
The ratio of corresponding sides is the same in similar triangles, therefore;
[tex]\dfrac{Levi's \, distance \, from \, the \, mirror}{Goalpost \, distance \, from \ the \ mirror }=\dfrac{Levi's \,height}{Height\, of \, the \, goalpost, H}[/tex]
[tex]\dfrac{2}{12.05} =\dfrac{1.15}{H}[/tex]
[tex]H =\dfrac{1.15\times 12.05}{2} \approx 6.93[/tex]
The height of the goalpost is approximately 6.93 meters
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Paula has 3 1/3 cups of sugar. Her apple pie recipe calls for 1 1/2 cups of sugar.
After she makes her pie, how much sugar will she have left?
please help me asap!!!!
From the total of 3 1/3 cups of sugar Paula used 1 1/2 cups of sugar to make apple pie recipe then amount of sugar left with Paula is given by
1 5/6 cups of sugar.
As given in the question,
Total amount of sugar Paula ha = 3 1/3 cups of sugar.
Amount of sugar used to make apple pie recipe is = 1 1/2 cups of sugar
Let x be the amount of sugar left with Paula after making apple pie
Required equation is :
x + 1 1/2 = 3 1/3
⇒x + 3/2 = 10/3
⇒ x = (10/3) - (3/2)
⇒x = ( 20 -9) /6
⇒ x= 11/6
⇒ x= 1 5/6 cups of sugar
Therefore, from the total of 3 1/3 cups of sugar Paula used 1 1/2 cups of sugar to make apple pie recipe then amount of sugar left with Paula is given by 1 5/6 cups of sugar.
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Identify the horizontal asymptote of f(x) = 3 over 5 x. y = 3 over 5 y = 0 y = 5 over 3 no horizontal asymptote
y = 0 is the horizontal asymptote for the given equation f(x)
To find : Horizontal Asymptote of function f(x)
Horizontal Asymptote
A horizontal line that a function's graph appears to coincide with but does not actually do so is said to be its horizontal asymptote. The end behavior of the function is determined using the horizontal asymptote.
Given that,
A function is provided as
f(x) = 3/5x
x serving as the denominator
By setting the denominator equal to 0, we can easily determine the vertical asymptote i.e,
Make x=0,
Specifically, the vertical asymptote is at y=0 or x=0
Identifying the horizontal asymptote
Write x in terms of y, then look for any instances where y differs.
We are able to write the given function
x=3/5
Here, y=0 renders x undefinable.
Thus y=0 is the horizontal asymptote.
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Answer:
B
Step-by-step explanation:
Got it right.
When collecting data, what is a sample?
Thank you for helping.
According to the given graph, the type of sample is continuous.
Sampling:
Basically, sampling refers the a statistical methodology that uses a portion of a total population to represent the full population.
Given,
Here we have the graph and that represents the data collection.
Now, we need to find the type sample used.
In order to find the type of sample used in the given data, we have to carefully looking into the point representation of the graph.
While we looking into the graph, we have identified that the point one the graph continuous and it will gradually moving upwards.
Therefore, the type of sample use here is continuous.
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24. Evaluate the expression for the values of b.
b
b(3) + 20.4
8.9
5.1
0.2
The expression for the values of b, when b = 8.9 is 47.1, when b = 5.1 is 35.7 and when x = 0.2 is 21
What is an expression?An expression in maths, a sentence with a minimum of two numbers or variables and at least one math operation.
Given an expression b(3) + 20.4
When b = 8.9
8.9*3 + 20.4 = 47.1
When b = 5.1
5.1*3 + 20.4 = 35.7
When b = 0.2
0.2*3 + 20.4 = 21
Hence, The expression for the values of b, when b = 8.9 is 47.1, when b = 5.1 is 35.7 and when x = 0.2 is 21
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In a particular city, taxi charge an initial fee of $3. 30 plu $2. 10 per mile. How far can a paenger travel for $49. 50
Answer: 22 miles
Step-by-step explanation: 49.50 - 3.30 = 46.20
46.20 ÷ 2.10 = 22
Complete an equation in slope-intercept form for the line that passes through (6, 5) and is parallel to the line x + 3y = 9.
The slope-intercept form is y = -1/3x +7 .
What is an explanation of the slope-intercept form?
A line's equation can be written in the slope-intercept form so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are immediately visible. This form is frequently known as the y = mx + b form.The standard form equation can be found by using the given point values in the given equation to find the new constant.
x +3y = (6) +3(5) = 21
Solving for y puts this equation into slope-intercept form.
3y = -x +21 . . . . . . . subtract x
y = -1/3x +7 . . . . . . divide by 3.
This is slope-intercept form.
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what is the quotient (3x² + 8x − 3) ÷ (x + 3)?
a. 3x + 5, r = 1
b. 3x - 5
c. 3x + 1
3x - 1
Answer:
d. 3x - 1
Step-by-step explanation:
(3x² + 8x − 3) ÷ (x + 3)
= ((3x - 1)(x + 3) ÷ (x + 3)
= 3x - 1
Answer:
D
Step-by-step explanation:
3x. 9x 3
x. -x -1
(3x-1)(x+3) /(x+3)
3x - 1
the sin of angle N in fig. is (leave answer as a frac)
In the given right-angled triangle sin(N) = 3/5.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjacent/hypotenuse and
tan = opposite/adjacent.
Given,, we have to obtain sin(theta) in the right-angled triangle with opposite = 3 units, hypotenuse = 5 units, and adjacent = 4 units.
We know sin = opposite/hypotenuse.
∴ Sin(N) = 3/5.
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Help mee someoneeeeee
Solve the system of inequalities by graphing.
y < -2x - 5
y > 6x + 5
Answer:
Take a look at the attachment...
Hope this helps! :)
What are the domain and range?
The domain of the given function f(x) is (−∞,∞) and the range is (-∞, 4].
What is the domain and range of a quadratic function?
The set of all real values of x that will result in real values for y is known as the domain of a function. A function's range is the set of all real values of y that may be obtained by substituting real numbers into x.
Given function is [tex]f(x)=-x^{2} +4[/tex]
The domain of [tex]f(x)[/tex] = Any real value of x i.e. (−∞,∞)
Range of [tex]f(x)[/tex] = (-∞, 4] i.e. y ≤ 4
Hence, the domain of f(x) is (−∞,∞) and range is (-∞, 4].
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