Answers
This is a right triangle and to solve this you must use Pythagorean theorem:
[tex]a^{2} +b^{2} =c^{2}[/tex]
a and b are the legs (the sides that form a perpendicular/right angle)
c is the hypotenuse (the side opposite the right angle)
In this case...
a = 60
b = x
c = 65
^^^Plug these numbers into the theorem
[tex]60^{2} +x^{2} =65^{2}[/tex]
simplify
3600 + [tex]x^{2}[/tex] = 4225
Now bring 3600 to the right side by subtracting 3600 to both sides (what you do on one side you must do to the other). Since 3600 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.
3600 - 3600 + [tex]x^{2}[/tex] = 4225 - 3600
0 + [tex]x^{2}[/tex] = 625
[tex]x^{2}[/tex] = 625
To remove the square from x take the square root of both sides to get you...
x = √625
x = 25
(option C)
Hope this helped!
Just a girl in love with Shawn Mendes
Related Questions
Need help in number 9. Thanks for helping
Answers
Answer:
A 6/7
Step-by-step explanation:
3/4 ÷ 7/8
Copy dot flip
3/4 * 8/7
The numerator is 3*8 = 24
The denominator is 4*7 = 28
24/28
Divide the top and botto by 4
6/7
Solve the system using Elimination
2x +6y=-12
5x-5y=10
A) 2,1
B) 0,-2
C) -2,0
D) 1,2
Answers
Answer:
B) 0,-2 (x = 0 , y = -2)
Step-by-step explanation by elimination:
Solve the following system:
{2 x + 6 y = -12 | (equation 1)
{5 x - 5 y = 10 | (equation 2)
Swap equation 1 with equation 2:
{5 x - 5 y = 10 | (equation 1)
{2 x + 6 y = -12 | (equation 2)
Subtract 2/5 × (equation 1) from equation 2:
{5 x - 5 y = 10 | (equation 1)
{0 x+8 y = -16 | (equation 2)
Divide equation 1 by 5:
{x - y = 2 | (equation 1)
{0 x+8 y = -16 | (equation 2)
Divide equation 2 by 8:
{x - y = 2 | (equation 1)
{0 x+y = -2 | (equation 2)
Add equation 2 to equation 1:
{x+0 y = 0 | (equation 1)
{0 x+y = -2 | (equation 2)
Collect results:
Answer: {x = 0 , y = -2
In 2015,in buffalo,new York there were 8.625 arrest,2.678 robberies,865 assaults and 20 murders.The population of Buffalo is 258.959.What is the ratio of number of assaults to the number of robberies in simplest form
Answers
Answer:
[tex] \frac { 8 6 5 } { 2 6 7 8 } [/tex]
Step-by-step explanation:
We are given the following information for year 2015:
Number of arrests = 8625
Number of robberies = 2678
Number of assaults = 865
Number of murders = 20
Population of Buffalo = 258959
We are to find the ratio of number of assaults to the number of robberies in simplest form.
Ratio of number of assaults to number of robberies = [tex]\frac{865}{2678}[/tex]
What is the solution to the system of equations below? y = -3X+5 and y=4x-2 (1, 2) (1, –18) (–1, 8) (–1, –6)
Answers
Answer:
(1, 2 )
Step-by-step explanation:
Given the 2 equations
y = - 3x + 5 → (1)
y = 4x - 2 → (2)
Substitute y = 4x - 2 into (1)
4x - 2 = - 3x + 5 ( add 3x to both sides )
7x - 2 = 5 ( add 2 to both sides )
7x = 7 ( divide both sides by 7 )
x = 1
Substitute x = 1 into (2) for corresponding value of y
y = (4 × 1) - 2 = 4 - 2 = 2
Solution is (1, 2 )
$6000 is invested for 15 years with an APR of 3% and monthly compounding.
Answers
Answer:
$2700.00
Step-by-step explanation:
6000 x 3% =180.00
180.00 x 15= 2700.00
choose the graph that represents the equation y=-|x+4|+1
Answers
The graph that represents y = -|x + 4| + 1 is graph (a)
The equation is given as:
y = -|x + 4| + 1
The above equation is a transformation from the parent function, which is represented as:
y = |x|
First the function is reflected across the x-axis, then translated 4 units left, and lastly 1 unit up.
The graph that represents this transformation is graph (a)
Hence, the graph that represents y = -|x + 4| + 1 is graph (a)
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Which formula would be used to find the measure of
angle 1?
1/2 (aº + bº).
1/2(a-cº).
1/2 (b° +cº).
1/2(aº – bº).
Answers
Check the picture below.
The formula that would be used to find the measure of angle 1 will be
m<1 =12(a - b)
To get the measure of angle 1, the circle theorem below will be used as shown:
The angle at the vertex of the circle is equal to half of the difference of the intercepted arc.
Angle at the vertex = m<1 Angles at the intercepted arc ar m<a and m<bThe formula that would be used to find the measure of angle 1 will be
m<1 =12(a - b)
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Which best describes bias, if any, from the sample surveyed? survey: favorite sports sample: randomly selected fans at a baseball game A. Since the sample is randomly selected, there is unlikely to be any bias. B. Since baseball fans are also likely to be fans of other sports, there is unlikely to be any bias. C. Since baseball is played in the summer, there is likely to be bias against sports played in the winter. D. Since the sample is taken at a baseball game, it is likely to be biased in favor of baseball.
Answers
Answer: B
Step-by-step explanation:
This is because it is just a statement, and may be true for some people, but not others.
If tan0=-3/4 and 0 is in quadrant IV, cos20= (33/25, -17/25, 32/25, 7/25, 24/25?) and tan20= (24/7, -24/7, 7/25, -7/25, 13/7, -13/7?) PLEASE HELP. More information in the picture
Answers
Answer:
cos(2θ) = 7/25tan(2θ) = -24/7Step-by-step explanation:
Sometimes, it is easiest to let a calculator do the work. (See below)
__
The magnitude of the tangent is less than 1, so the reference angle will be less than 45°. Then double the angle will be less than 90°, so will remain in the 4th quadrant, where the cosine is positive and the tangent is negative.
You can also use the identities ...
cos(2θ) = (1 -tan(θ)²)/(1 +tan(θ)²)
cos(2θ) = (1 -(-3/4)²)/(1 +(-3/4)²) = ((16-9)/16)/((16+9)/16)
cos(2θ) = 7/25
__
tan(2θ) = 2tan(θ)/(1 -tan(θ)²) = 2(-3/4)/((16-9/16) = (-6/4)(16/7)
tan(2θ) = -24/7
Answer: tan(2θ) = -24/7
Step-by-step explanation: N/A
pleaseeeee helppppppp
Answers
Answer:
[tex]\large\boxed{A.\ \sqrt{-4}}[/tex]
Step-by-step explanation:
[tex]A.\ \sqrt{-4}=\sqrt{(4)(-1)}=\sqrt4\cdot\sqrt{-1}=2i\ -\ \text{complex number}\\\\i-\text{imaginary unit}[/tex]
[tex]B.\ \sqrt{13}\approx3.61\ -\ \text{real number}\\\\C.\ \sqrt{16}=4\ -\ \text{real number}\\\\D.\ \sqrt1=1\ -\ \text{real number}[/tex]
One angle of a right triangle measures 19∘. What is the measure of the other angle?
Answers
Answer:
71°
Step-by-step explanation:
The equation should be 19+90+x=180
Step 1: Add 19+90=109
Step 2: Subtract 180-109=71
So, you're answer is 71°
Final answer:
To find the measure of the other angle in a right triangle when one angle is given, subtract the given angle and the right angle from 180 degrees to get the third angle, which is the measure of the other angle.
Explanation:
One angle of a right triangle measures 19∘. In a right triangle, one angle is always 90 degrees. Therefore, to find the measure of the third angle, you need to subtract the sum of the given angle and the right angle from 180 degrees.
Third angle = 180° - 90° - 19° = 71°. So, the measure of the other angle in the right triangle is 71 degrees.
Calculate 1.7 x 106 times 5.3 x 10^9 by using scientific notation and the product rule.
Express your answer in scientific notation with the proper number of significant figures.
Answers
The pH of a solution is a measure of how acidic it is. The greater the acidity, the lower the pH. The function f(x) = −log x gives the pH of a solution, where x is the concentration of hydrogen ions, in moles per liter.
The graph of f(x) = −log x is________________of the graph of g(x)=log x
answer options:
a: vertical translation (not correct answer)
b: horizontal translation
c: reflection in the x-axis
d: reflection in the y-axis
Answers
Answer:
c. a reflection in the x-axis.
Step-by-step explanation:
All values of log x are made negative by the transformation so it is a reflection in the x axis.
The graph of [tex]f(x) =-log x[/tex] is the reflection in the x-axis of the graph of [tex]g(x)=log x[/tex].
What is a graph?" Graph is defined as a pictorial representation of the relation between the variables in the coordinate plane along x-axis and y-axis."
According to the question,
Given function on the graph,
[tex]f(x) =-log x[/tex]
[tex]g(x)=log x[/tex]
[tex]'x'[/tex] represents the concentration of hydrogen ions, in moles per liter.
value of [tex]'x'[/tex] remain the same in both cases.
[tex]f(x)[/tex] value is negative.
[tex]g(x)[/tex] value is positive.
The graph of [tex]f(x)[/tex] lying in the first quadrant and the graph of [tex]g(x)[/tex] lying in the fourth quadrant.
Therefore, the graph of [tex]f(x)[/tex] is the reflection in the x-axis of the graph of [tex]g(x)[/tex].
Hence, Option(C) is the correct answer.
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Of the 425 tickets sold, 275 were adult tickets. What percent of the tickets were adult tickets? Round to the nearest tenth of a percent.
Answers
Answer:
64.7%
Step-by-step explanation:
Write a proportion:
275 / 425 = x / 100
x = 64.7
64.7% of the tickets were adult tickets.
What is the sum of the angle measures of 24 - gon
Answers
[tex]\bf \textit{sum of all \underline{interior angles} in a polygon}\\\\ S=180(n-2)~~ \begin{cases} n=\textit{number of sides}\\ \cline{1-1} n=24 \end{cases}\implies \begin{array}{llll} S=180(24-2)\\\\ S=3960 \end{array}[/tex]
The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new function? (x – 11)2 + 58 (x + 22)2 – 121 (x + 7)2 – 47 (x – 15)2 + 94
Answers
Answer:
Option C is correct.
Step-by-step explanation:
The given function f(x) is:
f(x) = x^2 + 22x + 58
To find the vertex find [tex](\frac{-b}{2a} )^2[/tex] and add and subtract it from both sides of the given function
b= 22, a= 1
Putting values:
[tex](\frac{-b}{2a} )^2 = (\frac{-22}{2(1)})^2\\=(\frac{-22}{2})^2\\= (-11)^2\\=11^2[/tex]
Adding (11)^2 on both sides
f(x) = x^2 + 22x + 58 +(11)^2 -(11)^2
f(x) = x^2+22x+(11)^2 +58-(11)^2
a^2 +2ab+b^2 = (a+b)^2 Using this formula:
f(x)=(x+11)^2+58-121
f(x)=(x+11)^2-63
The vertex of the given function is (-11,-63)
The function is translated 4 units to right and 16 units up
The vertex of new function will be:
(x+4,y+16) => (-11+4,-63+16)
=> (-7,-47)
So, the vertex of new function is (-7,-47)
The function will be
(x+7)^2 -47
So, Option C is correct.
Answer:
C
Step-by-step explanation:
How do you solve the following equation:
[tex]\int_2^a (3x^2+x-1) dx=52[/tex] for [tex]a[/tex]?
Answers
[tex]\displaystyle\\\int \limits_2^a(3x^2+x-1)\, dx=52\\\left|x^3+\dfrac{x^2}{2}-x\right|_2^a=52\\a^3+\dfrac{a^2}{2}-a-(2^3+\dfrac{2^2}{2}-2)=52\\a^3+\dfrac{a^2}{2}-a-(8+2-2)=52\\a^3+\dfrac{a^2}{2}-a-8=52\\a^3+\dfrac{a^2}{2}-a=60\\2a^3+a^2-2a=120\\2a^3+a^2-2a-120=0[/tex]
Now you need to solve the resulting equation, but it's not easy. The approx. solution is [tex]a\approx 3.8[/tex]
The exact solution is
[tex]a=\dfrac{1}{6}\left(-1+\sqrt[3]{6461-78\sqrt{6861}}+\sqrt[3]{6461+78\sqrt{6861}}\right)[/tex]
Answer:
a = 3.84
Step-by-step explanation:
Let's integrate the function
3x^2 becomes 3x^3/3 =x^3
x becomes x^2/2
-1 becomes -x
The intergral is x^3 +x^2/2 -x
We take the upper limit minus the lower limit
a^3 +a^2/2 -a - (2^3 + 2^2/2 -2) and that is equal to 52
Simplify
a^3 + a^2/2 -a - (8+2-2) = 52
a^3 +a^2/2 -a -(8) = 52
Subtract 52 from each side
a^3 +a^2/2 -a -8-52 = 52-52
a^3 +a^2/2 -a -60 =0
Multiply by 2
2a^3 +a^2 -2a -120 = 0
Using a graphing system, we see it only has 1 real root
This is at approximately
3.84
ABCD is a rectangle. What is the value of x?
Answers
Explanation
We can use pythagorean theorem to solve for the value of x:
45^2 + x^2 = 53^2
2025 + x^2 = 2809
We now subtract 2025 from both sides:
2809 - 2025 = 784
x^2 = 784
Square both sides
[tex]\sqrt{784}[/tex] = 28
x = 28
Answer
The value of x is 28
In a conference room, the number of chairs,c, is equal to 6 times the number of tables,t. Which equation matches the information
Answers
Answer:
t x 6=c or c divided by 6= t
Step-by-step explanation:
Answer: [tex]c=6t[/tex]
Step-by-step explanation:
You need to analize the information provided in the exercise:
- "c" represents the number of chairs in the conference room.
- "t" represents the number of tables in the conference room.
- "6 times the number of tables" indicates a multiplication. This is:
[tex]6t[/tex]
Therefore if the number of chairs in the conference room is equal to 6 times the number of tables, you can write this equation that matches the information provided:
[tex]c=6t[/tex]
What is the cube root of 512m12n15
Could anyone plz help me?
Answers
Answer:
[tex]8m^4n^5[/tex]
Step-by-step explanation:
cube root is basically taking to the power of [tex]\frac{1}{3}[/tex]
Also, there is a property that is [tex](x^m)^n=x^{mn}[/tex]
We can use these and find the cube root of the expression:
[tex](512m^{12}n^{15})^{\frac{1}{3}}\\=(512)^{\frac{1}{3}}*(m^{12})^{\frac{1}{3}}*(n^{15})^{\frac{1}{3}}\\=8*m^{\frac{12}{3}}*n^{\frac{15}{3}}\\=8*m^4 * n^5[/tex]
Thus, third answer chioce is right.
Answer:
C. 8m^4n^5[/tex]
Step-by-step explanation:
We are given [tex]\sqrt[3]{512m^{12}n^{15} }[/tex]
The cube root is nothing but the power of [tex]\frac{1}{3}[/tex]
Now we have to write 512 as the power 3.
512 = 8.8.8 = [tex]8^{3}[/tex]
So, [tex]\sqrt[3]{512m^{12}n^{15} }[/tex] = [tex](8^{3}.m^{12}.n^{15}) ^{\frac{1}{3}}[/tex]
We know that the exponent property: [tex](a^{m} )^n= a^{mn}[/tex]
Using this property, we can simplify the exponents.
= [tex]8.m^{4} .n^5 = 8m^4n^5[/tex]
If the measure of arc XY plus the measure of arc YZX equals 360°, and the
arcs do not overlap, then the arcs form a _
A. square
B. polygon
C. circle
D. parallelogram
Answers
Answer:
The arcs form a circle ⇒ answer C
Step-by-step explanation:
* Lets explain some facts in the circle
- The chord in a circle is a segment whose endpoints lie on the circle
- Any chord of a circle intersects it into 2 arcs
- The minor arc which its measure lies between 0° and 180°
-The major arc which its measure lies between 180° and 360°
- The sum of the measures of the minor arc and the major arc is equal
to the measure of the circle
- The measure of the circle is 360°
* Lets solve the problem
∵ The measure of arc XY + the measure of arc YZX = 360°
∵ The arcs do not overlap
- That means the endpoints of the arcs are X and y
∵ The measure of the circle is 180°
∴ The arcs form a circle
Answer:circle
Step-by-step explanation:
im lookin it on a question rn
The sum of two numbers is 58. The first number is 8 less than half the second number. Let c represent the first number. Let d represent the second number. Which statements about solving for the two numbers are true? Check all that apply.
Answers
Answer : The true statements are:
The equation [tex]c+d=58[/tex] represents the sum of two numbers.
The equation [tex]c=\frac{d}{2}-8[/tex] represents the relationship between the two numbers.
The number c is, 14
The number d is, 44
Step-by-step explanation :
Given:
Let 'c' represent the first number. Let 'd' represent the second number.
The sum of two numbers is 58. The equation will be:
[tex]c+d=58[/tex] .........(1)
The first number is 8 less than half the second number. The equation will be:
[tex]c=\frac{d}{2}-8[/tex] .........(2)
Now by solving the two equations, we get the value of c and d.
As, [tex]c+d=58[/tex]
or, [tex]c=58-d[/tex] ..........(3)
Now put equation 3 in 2, we get the value of d.
[tex]58-d=\frac{d}{2}-8[/tex]
[tex]58-d=\frac{d-16}{2}[/tex]
[tex]2(58-d)=d-16[/tex]
[tex]116-2d=d-16[/tex]
[tex]3d=132[/tex]
[tex]d=44[/tex]
Now put the value of 'd' in equation 3, we get the value of 'c'.
[tex]c=58-d[/tex]
[tex]c=58-44[/tex]
[tex]c=14[/tex]
Thus, the value of c and d is, 14 and 44 respectively.
Answer:
ABGH
Step-by-step explanation:
How do I do rate of change???
Answers
Answer:
12
Step-by-step explanation:
For our problem since we only in 10 am:
I'm going to let x=4 represent the time 10:04 am
which means I'm going to let x=17 represent 10:17am.
So when x=4, y=23 miles and when x=17,y=179 miles.
You have two points.
You can use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
Or just line the points up vertically and subtract them vertically, then put 2nd difference over first difference. Like this:
( 17 , 179)
-( 4 , 23)
-----------------------
13 156
So the slope is 156/13=12 miles/hour.
the area of a circle is 113.04in^2. what is the radius of the circle
Answers
[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} A=113.04 \end{cases}\implies 113.04=\pi r^2\implies \cfrac{113.04}{\pi }=r^2 \\\\\\ \stackrel{using~\pi =3.14}{36}=r^2\implies \sqrt{36}=r\implies 6=r[/tex]
What is the cube root of -729a^9b^6?
A. -9a^3b^2
B. -9a^2b^3
C. -8a^3b^2
D. -8a^2b^3
Answers
Answer:
[tex]\large\boxed{A.\ -9a^3b^2}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{-729a^9b^6}\qquad\text{use}\ \sqrt[n]{xy}=\sqrt[n]{x}\cdot\sqrt[n]{y}\\\\=\sqrt[3]{-729}\cdot\sqrt[3]{a^9}\cdot\sqrt[3]{b^6}\\\\=-9\cdot\sqrt[3]{a^{(3)(3)}}\cdot\sqrt[3]{b^{(2)(3)}}\qquad\text{use}\ (x^n)^m=x^{nm}\\\\=-9\cdot\sqrt[3]{(a^3)^3}\cdot\sqrt[3]{(b^2)^3}\qquad\text{use}\ \sqrt[3]{x^3}=x\\\\=-9a^3b^2[/tex]
Answer: A
Step-by-step explanation:
-9•9•9= -729a 9/3= 3
6/3=b^ 2
a landscaping company needs 160 gallons of 40% fertilize the shrubs in an office park. They have in stock 50% fertilizer and 30% fertilizer. how much of each type should they mix together?
Answers
Let
x--------> volume of 50% fertilizer
y--------> volume of 30% fertilizer
we know that
x+y=160-----> x=160-y-----> equation 1
x*0.5+y*0.3=160*0.4-----> equation 2
substitute equation 1 in equation 2
[160-y]*0.5+0.3*y=63.8----> 77-0.35*y+0.25*y=63.8
0.10*y=13.2------> y=13.2/0.10----> y=132 gal
x=220-y----> x=220-132----> x=88 gal
the answer is
88 gal of 50% fertilizer
132 gal 30% fertilizer
To obtain a 40% fertilizer mixture, the landscaping company should mix 80 gallons of 50% fertilizer with 80 gallons of 30% fertilizer.
Explanation:To solve this problem, we can set up an equation based on the amount of fertilizer needed and the percentage of fertilizer in each type. Let's call the amount of 50% fertilizer x and the amount of 30% fertilizer y. We know that the total amount of fertilizer needed is 160 gallons, so we can write the equation x + y = 160. We also know that the amount of fertilizer in the 50% type is 0.5x and the amount of fertilizer in the 30% type is 0.3y. Since we want a total of 40% fertilizer, we can write the equation 0.5x + 0.3y = 0.4 * 160. Solving this system of equations will give us the amounts of each type of fertilizer needed.
First, let's rearrange the first equation to solve for x: x = 160 - y. Substituting this into the second equation, we get 0.5(160 - y) + 0.3y = 0.4 * 160. Simplifying the equation, we get 80 - 0.5y + 0.3y = 64. Combining like terms, we have 80 - 0.2y = 64. Subtracting 80 from both sides, we get -0.2y = -16. Dividing both sides by -0.2, we get y = 80. Now we can substitute this value back into the first equation to solve for x: x = 160 - 80 = 80. Therefore, they should mix 80 gallons of the 50% fertilizer with 80 gallons of the 30% fertilizer to obtain the desired 40% mixture.
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what is the rise of ramp if slope is 2% and run is 4 feet
Answers
Answer:
.08 feet
Step-by-step explanation:
So slope=rise/run.
You are given slope is 2% or .02.
You are also given run is 4 ft.
Plug these into the formula
.02=rise/4
To solve this for rise multiply both sides by 4:
4(.02)=rise
.08=rise
The rise is .08 feet.
Luisa and Connor had $360 altogether . After Connor gave Luisa 2/5 of his money, she had the same amount of money has he did. How much money did Connor have in the beginning?
Answers
Answer:
$300
Step-by-step explanation:
Let's say that L is the amount of money Luisa had in the beginning, and C is the amount of money Connor had in the beginning.
C + L = 360
C - 2/5 C = L + 2/5 C
Simplifying the second equation:
3/5 C = L + 2/5 C
1/5 C = L
Substituting into the first equation:
C + 1/5 C = 360
6/5 C = 360
C = 300
Connor originally had $300, and Luisa $60. Connor gave Luisa $120, and they both had $180.
The variable z is inversely proportional to x. When x is 12, z has the value 1.5833333333333. What is the value of z when x= 18?
Answers
Answer:
Z=1.055
Step-by-step explanation:
Z is inversely proportional to X: [tex]Z=\frac{K}{X}[/tex] Where K is a constant
X=18, Z=1.583333333333 we can find K value
K=Z*X =1.58333333333*12= 19
So, Using X=18 We have the following
[tex]Z=\frac{19}{18}[/tex]= 1.055
Before any dinner service, the manager confirms when the number of reservations at a restaurant is subtracted from
Nice the number of loaves of bread on hand must be greater than 5. Which graph represents this scenario?
Answers
Final answer:
To graph the scenario where the number of loaves of bread on hand (L) minus the number of reservations (R) must be greater than 5, one would represent this inequality on a two-dimensional graph with L on the horizontal axis and R on the vertical axis, shading the region above the line L - R = 5.
Explanation:
The subject of the question is Mathematics, with a focus on inequalities and graphical representation of constraints. The scenario describes the requirement that the number of loaves of bread on hand minus the number of reservations must be greater than 5. To represent this mathematically, let's define the variable L as the number of loaves of bread on hand and R as the number of reservations. The inequality can, therefore, be expressed as L - R > 5.
This inequality needs to be represented on a graph. To do this, one typically uses a two-dimensional coordinate system where the horizontal axis, often labeled as x, could represent the number of loaves of bread (L), and the vertical axis, often labeled as y, could represent the number of reservations (R). The region that satisfies the inequality L - R > 5, would be shaded above the line L - R = 5 (since we are looking for L being greater than R by more than 5 units). This line will have a slope of 1 and a y-intercept at R = -5.