The equation that passes through (-12, 15 with a slope of -1 in point slope form is y - 15 = - 1(x + 12)
How to represent equation in point slope form?Linear equation can be represented in different form such as point slope form, slope intercept form and standard form.
Therefore, let's represent the line that passes through (-12, 15) with a slope of -1 in point slope form.
Hence,
y - y₁ = m(x - x₁)
where
m = slopey₁ and x₁ are the coordinates of the point.Therefore,
m = slope = -1
using (-12, 15)
Hence,
y - 15 = - 1(x - (-12))
Therefore,
y - 15 = - 1(x + 12)
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determine the equation of the line from the graph
Answer:
y = -x + 1
Step-by-step explanation:
y =mx + b
It is crossing the y axis at 1 that is the b
The slope (m) is -1. From one point on the line to another you go down 1 and left 1. That represents a negative slope of 1
Rewrite one fourteenth times x cubed times y plus three fourteenths times x times y squared using a common factor.
The expression which can be rewritten using a common factor is [tex]\frac{xy}{14} (x^{2} +3y)[/tex].
According to the question,
We have the following information:
One fourteenth times x cubed times y plus three fourteenths times x times y squared.
(We know that 'times' has to be replaced with multiplication.)
Now, we will change this into mathematical expression:
[tex]\frac{x^{3} y}{14} +\frac{3xy^{2} }{14}[/tex]
Now, from these two terms, the common factor can be [tex]\frac{xy}{14}[/tex].
(Common factor means that the number and the variables taken as a common factor should be able to completely divide the terms given any expression.)
Now, taking it as a common factor, we have the following expression:
[tex]\frac{xy}{14} (x^{2} +3y)[/tex]
Hence, the required expression is [tex]\frac{xy}{14} (x^{2} +3y)[/tex].
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What is the value of x+ y in the system of equations below?
8x + 9y = 4.92
9x + 14y = 6.93
The value of x + y in the system of equations is 0.82125.
Given system of equations:-
8x + 9y = 4.92 ...(1)
9x + 14y = 6.93 ...(2)
We have to find the value of x + y in the system of equations.
Multiplying (1) by 9 and (2) by 8, we get,
72x + 81y = 44.28 ...(3)
72x + 112y = 55.44 ...(4)
(4) - (3), we get,
0x + 31y = 11.16
31y = 11.16
y = 11.16/31
y = 0.36
Putting the value of y in (1), we get
8x + 9*(0.36) = 6.93
8x + 3.24 = 6.93
8x = 6.93 - 3.24
8x = 3.69
x = 0.46125
Hence,
x + y = 0.46125 + 0.36 = 0.82125
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pleas help quick
What is the value of the expression
PLUG IN THE VALUES IN THE RIGHT POSITIONS AND SIMPLIFY.
[tex] = 2( \frac{1}{2} + \frac{3}{4} ) + 6 \\ = 2( \frac{5}{4} ) + 6 \\ = \frac{10}{4} + 6 \\ = \frac{5}{2} + 6 \\ = \frac{17}{2} [/tex]
THE ANSWER IS OPTION C.
if the ratio of similarity of the figures above is 2/3, then what is the ratio of the perimeters of the two figures?
Perimeter = side 1 + side 2 ´+ side 3.
Triangle 1
Perimeter = 6 + 8 + 10
= 24
Triangle 2
Perimeter = 9 + 12 + 15
= 36
Ratio
24/36 = 2/3
The ratio of the perimeters is also 2/3
Sal elrove 3000 miles in 75 hours. At this rate how long will it take to drive 4000 miles
Answer:
Step-by-step explanation:
First, we need to find the rate. miles/hours. 3000/75 = 40mph (miles per hour). to find the answer we need to divide the rate by the distance they want us to find. to see a deeper explanation of why scroll past the answer. 4000/40 = 100 hours.
deeper explanation:
we can set the numbers given to us equal to what we are looking for.
miles/hour
3000/75 = 4000/x x being the time we are looking for
cross multiply 3000x=300000
divide by 3000 x=100 hours
Three t-shirts for $10. find the unit rate
Answer:
Step-by-step explanation:I don’t know
Traci planted a tree in her backyard.She made this graph to show the tree growth over 5 years. 100 POINTS IF YOU HELP!!!!
A. The slope of the function = 1.5.
a = 15; b = 3; c = 3; d = 1.5
B. y-intercept (b) = 7.5
C. The equation of the function is: y = 1.5x + 7.5.
The height in 10 years is approximately 17.5 feet.
How to Write the Equation of a Linear Function?The equation of a function can be expressed as y = mx + b, if we know the value of the slope, m, and the value of the y-intercept, b.
Part A:
Using the two points on the graph, we can find the slope of the function as shown below:
The two points are (3, 12) and (5, 15):
Slope of the function = (15 - 12)/(5 - 3)
= 3/2
Slope (m) = 1.5.
Thus, the values that represents each letters would be:
a = 15; b = 3; c = 3; d = 1.5
Part B: The y-intercept of the function
The y-intercept of the function can be defined as the initial tree height which is the point where the line intercepts the y-axis of the graph.
Substitute m = 1.5 and (x, y) = (3, 12) into y = mx + b to find the y-intercept (b) of the function:
12 = 1.5(3) + b
12 = 4.5 + b
12 - 4.5 = b
7.5 = b
b = 7.5
y-intercept (b) = 7.5
Part C: To write the equation of the function, substitute m = 1.5 and b = 7.5 into y = mx + b:
y = 1.5x + 7.5.
Therefore, the initiate tree height is 7.5 feet, and it increases at a rate of 1.5 feet per year.
To find the height in 10 years, substitute x = 10 into the equation of the function, y = 1.5x + 7.5:
y = 1.5(10) + 7.5
y = 10 + 7.5
y = 17.5 feet
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I have no clue what to do so pls include an explination
[tex]10=\frac{z}{2} +7[/tex]
The solution for the given linear equation is z = 6
How to solve the linear equation?
Here we have the following linear equation:
10 = z/2 + 7
To solve it, we need to isolate the variable in one of the sides of the equation.
First, we can subtract 7 in both sides:
10 - 7 = z/2 + 7 - 7
3 = z/2
Now we can multiply both sides by 2 to get:
2*3 = 2*(z/2)
6 = z
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Rajesh obtain 93 marks in English out of 100 marks but Sita obtained 82 marks.Convert their marks in a fraction and calculate who got more marks?How many parts more marks then other.Also write their grade by asking with your teacher
Answer:
Answer 1: Rajesh: 93/100 Sita: 82/100 (simplest form: 41/50) Rajesh earned more.
Answer 2: 11/100 more marks
Answer 3: Rajesh got an A, while Sita got a B-
Step-by-step explanation:
Put the 93 on top of 100, and do the same for 82.
Rajesh clearly earned more. Subtract 82 from 93 to find out Rajesh score 11 points more.
Find the value of x for which the lines p and q are parallel.
Question 17 options:
A) 6
B) 8
C) 9
D) 7
Answer:
D
Step-by-step explanation:
(14x + 18) and 116 are corresponding angles and are congruent, then
14x + 18 = 116 ( subtract 18 from both sides )
14x = 98 ( divide both sides by 14 )
x = 7
Identify the rule for fg when f(x) = –3x – 6 and g(x) = x2 – x – 6.
The rule for the given function f /g when the function f(x) = -3x -6 and
g(x) = x² -x - 6 is identified as f(x) / g(x) = -3 / (x -3).
As given in the question,
Given function are:
f(x) = -3x -6
g(x) = x² -x - 6
Rule to identify for the function f(x) / g(x) we get,
Substitute the value of f(x) and g(x) in the required rule we have,
f(x) / g(x) = (-3x -6 ) / ( x² -x - 6 )
Now simplify the function to get the rule:
f(x) / g(x) = -3(x+2) / (x² -3x +2x -6)
⇒ f(x) / g(x) = -3(x+2) /(x-3)(x+2)
⇒ f(x) / g(x) = -3 / (x-3)
Therefore, the rule for the given function f /g when the function f(x) = -3x -6 and g(x) = x² -x - 6 is identified as f(x) / g(x) = -3 / (x -3).
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What is the slope of the line that passes through the points (-2, 2) and (-4, -1)?
Write your answer in simplest form.
The slope of line through points (-2, 2) and (-4, -1) is 3/2 by using the slope-point formula that tells that change in y divided by change in x.
What is slope?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
What is point?A point is a basic concept in classical Euclidean geometry that represents an exact location in space and has no length, width, or thickness. In contemporary mathematics, a point more broadly refers to a component of a set known as a space.
Here,
The points are (-2, 2) and (-4, -1)
m=(y2-y1)/(x2-x1)
m=Δy/Δx
m=(-1-2)/(-4+2)
m=3/2
By dividing the change in y by the change in x, the slope of the line passing through the points (-2, 2) and (-4, -1) is 3/2.
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xThe number of hours of daylight in a city in the Northern hemisphere shows periodic behavior over time.• The average number of daylight hours is 12.• The maximum number of daylight hours is 14.4.• The period is 365 days.• The day with the least sunlight is December 20.Which equation models the number of hours of daylight on the day that comes t days after the shortest day of the previous year?
EXPLANATION
Since we know that the number of hours is represented by a periodic function, the appropriate model is the sine function.
As the average number of daylight hours is 12 with a maximum and minimum of 14.4 and 9.6 respectively.
Furthermore, the period is 365.
Thus, the period is as follows:
[tex]\frac{2\pi}{365}=0.017[/tex]The appropiate model is the following:
[tex]H(t)=a\sin(0.017t)+12[/tex]Now, we need to compute the value of a:
Since the sine function reaches its highest value at t=90° and is represented by 14.4, when t=90°, the value of the function is asin(0.017t) = 1
Therefore,
14.4 = a + 12
Subtracting -12 to both sides:
14.4 - 12 = a
Subtracting numbers:
2.4 = a
In conclusion, the final function is the following:
[tex]H(t)=2.4\sin(0.017t)+12[/tex]Since the minimum is at t=0, we want:
[tex]H\left(t\right)=-2.4cos\left(0.017t\right)+12[/tex]In conclusion, the solution is the OPTION C)
quick sell outlet sold a total of 40 televisions, each of which was either a model p television or a model q television. each model p television sold for $p and each model q television sold for $q. the average (arithmetic mean) selling price of the 40 televisions was $141. how many of the 40 televisions were model p televisions? (1) the model p televisions sold for $30 less than the model q televisions. (2) either p
Model P televisions made up 12 of the 40 televisions when Quick Sell outlet sold a total of 40 television, each of which was either a model P television or a model Q television.
Price plus quantity equals revenue.
Let x be the quantity of sold TVs of model p.
40 - x units of the model q TV would have been sold.
Profits from model p TV sales are
px
Sales of the type q TV bring in money.
(40 - x)q
Total income equals px plus (40 - x)q
The average price calculation formula is written as
Total revenue / total number of TVs sold equals average price.
The 40 televisions sold for an average (arithmetic mean) price of $141. It follows that
141 = (px + (40 - x)q)/40
141 × 40 = px + (40 - x)q
5640 = px + (40 - x)q
p = q - 30
5640 = x(q - 30) + (40 - x) (40 - x)
q
30x + 40q - xq = 5640
5640 = - 30x + 40q
Since q = 120,
5640 = - 30x + 40 × 120
5640 = - 30x + 4800
5640 - 4800 = - 30x
840 = - 30x
x = 840/- 30 = - 28
Q cannot equal 120 since x cannot be negative.
Again,
5640 = px + (40 - x)q
If q = 30 + p, then
5640 = px + (40 - x)(30 + p)
5640 = px + 1200 + 40p - 30x - px
5640 = 1200 + 40p - 30x
Therefore,
If p = 120, then
5640 = 1200 + 40 × 120 - 30x
5640 = 6000 - 30x
30x = 6000 - 5640
30x = 360
x = 360/30
x = 12
Therefore, out of 40 televisions 12 tv are of model p
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cuáles son las raíces de la ecuación x²-6x-7=0
Answer Las raíces de la ecuación x2 − 6x + 7 = 0 son α y β. Encuentra la ecuación con raíces α + 1 β y β + 1 α. Deduzco que α + β = − b a = 6 1 = 6 y que αβ = c a = 7 1 = 7.
Step-by-step explanation:
Y varies 1/x², when X=2, Y=1. Find the values of X when Y=4/9.
Answer:
x = ± 3
Step-by-step explanation:
given y varies as [tex]\frac{1}{x^2}[/tex] , then
y = k × [tex]\frac{1}{x^2}[/tex] = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
to find k use the condition x = 2 , y = 1
1 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
4 = k
y = [tex]\frac{4}{x^2}[/tex] ← equation of variation
when y = [tex]\frac{4}{9}[/tex] , then
[tex]\frac{4}{9}[/tex] = [tex]\frac{4}{x^2}[/tex] ( cross- multiply )
4x² = 36 ( divide both sides by 4 )
x² = 9 ( take square root of both sides )
x = ± [tex]\sqrt{9}[/tex] = ± 3
a container full of marbles has a ratio of orange marbles to black marbles of 5 : 12. a what does this ratio mean . b . if a container held 72 black marbles, how many oranges are in the container?
The ratio 5:12 means that we have 5 orange marbles for 12 black marbles (5 to 12) and the orange marbles will be 30 if the container has 72 black marbles.
According to the question,
We have the following information:
A container full of marbles has a ratio of orange marbles to black marbles of 5:12.
It means that we have 5 orange marbles when the number of black marbles is 12.
Now, let's take the number of orange marbles to be 5x and the number of black marbles to be 12x.
Now, we have the number of black marbles as 72.
So ,we have:
12x = 72
x = 72/12
x = 6
Now, we will put the value of x in 5x to find the number of orange marbles:
5x
5*6
30
Hence, the number of orange marbles in the container when it has 72 black marbles is 30.
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Find A (please help)
Answer:
a=1
Step-by-step explanation:
the question is the png
The slope of the line parallel to y = 4 / 7 x + 7 is 4 /7.
The slope of the line perpendicular to y = 4 / 7 x + 7 is - 7 / 4.
How to find lines that are parallel and perpendicular?The equation of a line can be described as follows:
y = mx + b
where
m = slopeb = y-interceptThe equation of the line given is y = 4 / 7 x + 7.
Parallel lines have the same slope.
Therefore, the slope of the line parallel to the given equation of the line is 4 / 7.
A line perpendicular to each other follows the rule below:
m₁ m₂ = -1
where
m₁ = first slopem₂ = second slopeTherefore, let's find the slope of the line perpendicular to the given equation.
4 / 7 m₂ = -1
cross multiply
4m₂ = -7
m₂ = - 7 / 4
Therefore, the slope of the line perpendicular to the equation is - 7/4
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Drag each label to the correct location on the table. Match each equation with its number of unique solutions. y = -52 – 41 +7 y = –202 + 91 - 11 y = 3.12 – 61 + 3 Two Real Solutions One Real Solution One Complex Solution Two Complex Solutions Reset Next reserved
When b²−4ac=0 there is one real root.
When b²−4ac>0 there are two real roots.
When b²−4ac<0 no real roots or two complex roots
First equation
-x²-4x+7
[tex]\begin{gathered} b^{2}-4ac \\ \mleft(-4\mright)^2-4\mleft(-1\mright)\cdot\: 7 \\ 16+28=44 \end{gathered}[/tex]b²−4ac>0, then equation -x²-4x+7 has two real roots.
Second equation
-2x²+9x-11
[tex]\begin{gathered} b^{2}-4ac \\ 9^2-4\mleft(-2\mright)\mleft(-11\mright) \\ 81-88=-7 \end{gathered}[/tex]b²−4ac<0, then equation -2x²+9x-11 has two complex roots.
[tex]x1=\frac{9}{4}-i\frac{\sqrt{7}}{4},\: x2=\frac{9}{4}+i\frac{\sqrt{7}}{4}[/tex]Third equation
3x²-6x+3
[tex]\begin{gathered} b^{2}-4ac \\ \mleft(-6\mright)^2-4\cdot\: \: 3\cdot\: \: 3 \\ 36-36=0 \end{gathered}[/tex]b²−4ac=0, then equation 3x²-6x+3 has one root.
In places where there are crickets, the outdoor temperature can be predicted by the rate at which crickets chirp. One equation that models the relationship between f = 1/4 * c + 40 , chirps and outdoor temperature is where c is the number of chirps per minute and ƒ is the temperature in degrees Fahrenheit. a. Suppose 110 chirps are heard in a minute. According to this model, what is the outdoor temperature? b. If it is 75 deg * F outside, about how many chirps can we expect to hear in one minute? c. The equation is only a good model of the relationship when the outdoor temperature is at least 55 deg * F (Below that temperature, crickets aren't around or inclined to chirp.) How many chirps can we expect to hear in a minute at that temperature?
HELPPPP ME PLEASEEEEEEE
a. Using the equation of the relationship, the temperature outdoor would be 67.5 °F.
b. 140 chirps in a minute.
c. 60 chirps at that temperature is expected.
d. The graph for the relationship is given below.
e. 1/4 is the unit rate or slope = in 1/4°F per chirp.
f. 40 represents the starting or initial temperature.
What is the Graph of a Linear Equation?The graph of a linear equation, y = mx + b, will have a slope value of m, and an initial value or y-intercept of b, which is the point on the y-axis that the line intercepts.
Given the equation, f = ¼c + 40, where:
f = temperature in degrees Fahrenheit
c = number of chirps
1/4 represents the temperature in °F per chirp
40 represents the initial temperature
a. Substitute c = 110 into the equation, f = ¼c + 40:
f = ¼(110) + 40
f = 67.5
The outdoor temperature is predicted to be 67.5 °F.
b. Substitute f = 75 into the equation, f = ¼c + 40:
75 = ¼c + 40
75 - 40 = ¼c
35 = 1/4c
4(35) = c
c = 140
140 chirps would be heard in a minute.
c. Substitute f = 55 into the equation, f = ¼c + 40:
55 = ¼c + 40
55 - 40 = ¼c
15 = c/4
4(15) = c
c = 60
Expect to hear 60 chirps at that temperature.
d. The graph for f = ¼c + 40 is in the attachment.
e. 1/4 is the unit rate or slope, which is the temperature in °F per chirp.
f. 40 tells us about the equation of the relationship that the initial temperature where we can start expecting the crickets to chirp starts from 40 °F.
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Valeria created a triangular pyramid as part of her science fair project. The triangular base has a height of 8 cm and a length of 6 cm. The height of the pyramid is 12 cm. Determine the volume of Valeria's pyramid.A. 192 cm B. 288 cmC. 96 cmD. 576 cm
Given:
Height of triangular base = 8 cm
Length of traingular base = 6cm
Height of pyramid = 12 cm
Let's determine the volume of Valeria's pyramid.
To find the volume of the triangular pyramid, apply the formula:
[tex]V=\frac{1}{3}(A\ast h)[/tex]Where A is the area of the triangular base and h is the height of the pyramid
To find the area of the triangular base, apply the area of a triangle formula:
[tex]\begin{gathered} A=\frac{b\ast h}{2} \\ \\ A=\frac{6\ast8^{}}{2}=\frac{48}{2}=24cm^2 \end{gathered}[/tex]To find the volume of the pyramid, substitute 24 for A and 12 for h in the formula above.
Thus, we have:
[tex]\begin{gathered} V=\frac{1}{3}(A\ast h) \\ \\ V=\frac{1}{3}(24\ast12) \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} V=\frac{1}{3}(288) \\ \\ V=\frac{288}{3} \\ \\ \text{ V = 96 cm}^3 \end{gathered}[/tex]Therefore, the volume of Valeria's pyramid is 96 cubic centimeters.
ANSWER:
[tex]\text{ C. 96 cm}^3[/tex]At the 6th grade school dance, there are 130 boys, 100 girls, and 20 adults. Write the ratio of the number of girls to the number of adults.
The ratio of the number of girls to the number of adults is 5 : 1.
What is the ratio?Ratio is used to compare two or more values together. Ratio shows the frequency of one number compared to the frequency of another number. The sign that is used to represent ratio is :.
The ratio of the number of girls to the number of adults = number of girls : number of adults
number of girls = 100
number of adults = 20
The ratio of the number of girls to the number of adults = 100 : 20
Express the ratio in its simplest form. To do this, divide both numbers by the greatest common factor of 100 and 20. The greatest common factor of 100 and 20 is 20.
The ratio of the number of girls to the number of adults = 5 : 1
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WRITE A SIMPLIFIED EXPRESSION FOR THE PERIMETER OF THE TRIANGLE.
The simplified expression of the perimeter of the triangle is 3.75x - 7.
How to find the perimeter of a triangle?A triangle is a a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The perimeter of a triangle is the sum of the whole three sides.
Therefore, the simplified expression that represents the perimeter of the triangle is as follows:
Hence, the three sides of the triangle are as follows;
1.5x - 31.5x - 30.75x - 1Hence,
perimeter of the triangle = 1.5x - 3 + 1.5x - 3 + 0.75x - 1
perimeter of the triangle = 1.5x + 1.5x + 0.75x - 3 - 3 - 1
perimeter of the triangle = 3.0x + 0.75x - 7
perimeter of the triangle = 3.75x - 7
Therefore, the simplified expression is 3.75x - 7
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When the internet first launched, it was slow, clogged up phone lines and was most certainly not cheap. In fact, most Internet service providers (ISP) charged a flat rate access fee that included 20 hours a month of internet time. After twenty-hours of use, the ISP’s charged an additional per-hour fee. Suppose in 1995, Charter charged a flat rate of $39.95 for the first twenty hours of service and an additional per-hour charge of $5.99.a. How much would a Charter bill for 18 hours of internet used be in 1995? b. How much would a Charter bill for 28 hours of internet used be in 1995?
from the question, we were told in 1995, Charter charged a flat rate of
$39.95 for the first twenty hours.
and an additional per hour charge of $5.99
if,
for 20 hours = 39.95
therefore for 1 hour = 39.95/20
so for 18 hours = 39.95/20 X 18.95/20
so for 18 hours = 9
so,
to get the amount Charter bill for 18 hours in 1995 is,
39.95 x 18/20
= 39.95 x 0.9
= $35.955
so Charter bill for 18 hours of internet used in 1995 is $35.955
ould bill for 28 hours is
so, what Charter would
(25)!!!!!
Two sidewalks in a park are represented by lines on a coordinate grid. Two points on each of the lines are shown in the tables.
Sidewalk 1
x y
2 7
0 3
Sidewalk 2
x y
1 5
3 3
(a)Write the equation for Sidewalk 1 in slope-intercept form.
(b)Write the equation for Sidewalk 2 in point-slope form and then in slope-intercept form.
(c)Is the system of equations consistent independent, coincident, or inconsistent? Explain.
(d)If the two sidewalks intersect, what are the coordinates of the point of intersection? Use the substitution method and show your work.
Helpppppp!! answer it who takes this test
Using linear functions, it is found that:
a) The equation is: y = 2x + 3.
b) The equations are:
Point - slope form: y - 5 = -(x - 1).Slope - intercept form: y = -x + 6.c) The systems are consistent independent.
d) The point of intersection is (1, 5).
Linear functionA linear function is defined in slope-intercept formula by the rule presented as follows:
y = mx + b.
In which:
m is the constant rate of change of the function, called slope.b is the value of y when x = 0, called intercept.For Sidewalk 1, it is found that:
When x increases by 2, y increases by 4, hence the slope is of m = 2.When x = 0, y = 3, hence the intercept is of b = 3.Then the rule is:
y = 2x + 3.
For Sidewalk 2, when x changes by 2, y decays by 2, hence the slope is:
m = -2/2 = -1.
The line goes through point (1,5), hence the equation in point-slope form is:
y - 5 = -(x - 1).
Combining the like terms, the slope-intercept form is:
y - 5 = -x + 1
y = -x + 6.
Since the two lines have different slopes, the system is consistent independent.
The x-coordinate of the intersection is:
-x + 6 = 3 + 2x.
3x = 3
x = 1.
The y-coordinate is:
-x + 6 = -1 + 6 = 5.
Hence the intersection point is:
(1, 5).
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Answer: I am I don't know man
Step-by-step explanation: answer is I don't know.
Trapezoid RSTU with vertices R(-13, 7), S(-1, 7), T(-1, -5),
and U(-13,-9); scale factor: k = 1/4,
center of dilation: (-5, 3)
The coordinates of the trapezoid RSTU with vertices R(-13, 7), S(-1, 7), T(-1, -5), and U(-13,-9) after dilation with scale factor of k= 1/4 are
R' (-7, -2) S' (-4, -2) T' (-4, -2.5)U' (-7, -6) How to determine the coordinates of the image after dilationData gotten from the question
Trapezoid RSTU with vertices R(-13, 7), S(-1, 7), T(-1, -5) U(-13,-9)scale factor: k = 1/4center of dilation: (-5, 3)Dilation refers to an increment or reduction in dimension and location of a preimage to get a new image
The coordinate of the image of dilation is gotten using the formula
x₂ = kx₁ - x₀(k - 1) for x coordinate
y₂ = ky₁ - y₀(k - 1) for y coordinate
definition of terms
terms with subscript 2 is corresponding to the image
terms with subscript 1 is corresponding to the preimage
terms with subscript 0 is corresponding to the center of dilation
\k = scale factor
R(-13, 7) ⇒ R'(-7, -2)
x₂ = 1/4 * -13 - -5(1/4 - 1) = -7
y₂ = 1/4 * 7 - -5(1/4 - 1) = -2
S(-1, 7) ⇒ S' (-4, -2)
x₂ = 1/4 * -1 - -5(1/4 - 1) = -4
y₂ = 1/4 * 7 - -5(1/4 - 1) = -2
T(-1, -5) ⇒ T' (-4, -2.5)
x₂ = 1/4 * -1 - -5(1/4 - 1) = -4
y₂ = 1/4 * -5 - -5(1/4 - 1) = -2.5
U(-13,-9) ⇒ U' (-7, -6)
x₂ = 1/4 * -13 - -5(1/4 - 1) = -7
y₂ = 1/4 * -9 - -5(1/4 - 1) = -6
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Given the 2 statements: "If you study for your test, then you will pass
your test," and "If you passed your test, then you studied for your
test." the biconditional is:
The biconditional statement is "You study for your test if and only if you passed".
What is biconditional statement?
A biconditional statement combines a conditional statement with its opposite expressed in the form of "if and only if."
The given statements are,
"If you study for your test, then you will pass your test" and "you passed your test then you studied for your test".
The biconditional statement is: "You study for your test if and only if you passed".
To know more about the biconditional statement, click on the link
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At his comic book store, Korey's Comics, Korey sells approximately $3,250 in comic books each month.
But as a comic book dealer, Korey only pays $1,285 for these comic books. Korey's monthly operating expenses, including labor, are $875. Calculate Korey's monthly net income.
Answer:
Korey's monthly net income is $1090Step-by-step explanation:
The spending is the cost plus expenses:
1285 + 875 = 2160Net income is the difference of money made and spent:
3250 - 2160 = 1090