Answer:
"vertical angles"
Step-by-step explanation:
Those are "vertical angles."
If tan Θ=3/4, then evaluate 3sin Θ +2cos Θ
Answer:
[tex]3\sin\theta+2\cos\theta=\dfrac{17}{5}[/tex]
Step-by-step explanation:
Given that,
The value of [tex]\tan\theta=\dfrac{3}{4}[/tex]
We know that, [tex]\tan\theta=\dfrac{\text{perpendicular}}{\text{base}}[/tex]
[tex]H^2=B^2+P^2[/tex]
H is hypotenuse
[tex]H^2=3^2+4^2\\\\H=5[/tex]
[tex]\sin\theta=\dfrac{P}{H}\\\\=\dfrac{3}{5}[/tex]
And, [tex]\cos\theta=\dfrac{B}{H}=\dfrac{4}{5}[/tex]
So,
[tex]3\sin\theta+2\cos\theta=3\times \dfrac{3}{5}+2\times \dfrac{4}{5}\\\\=\dfrac{9}{5}+\dfrac{8}{5}\\\\=\dfrac{17}{5}[/tex]
So, the value is 17/5.
Order these from least to greatest. -13/8, -2.1, -26/13, -9/4 I know how to do this I'm just to lazy too and I want to chat.
Answer:
-9/4, 2.1, -26/13, -13/8
Step-by-step explanation:
g 3.23 Marbles in an urn. Imagine you have an urn containing 5 red, 3 blue, and 2 orange marbles in it. (a) What is the probability that the first marble you draw is blue
Answer:
[tex]P(Blue) = 0.3[/tex]
Step-by-step explanation:
Given
Red = 5
Blue = 3
Orange = 2
Required
Probability that the first marble is Blue
First, the total number of marble has to be calculated;
[tex]Total = Red\ Marble + Blue\ Marble + Orange\ Marble[/tex]
[tex]Total = 5 + 3 + 2[/tex]
[tex]Total = 10[/tex]
The probability of Blue being the first is calculated as thus;
[tex]P(Blue) = \frac{n(Blue)}{Total}[/tex]
[tex]P(Blue) = \frac{3}{10}[/tex]
[tex]P(Blue) = 0.3[/tex]
Hence, the required probability is 0.3
Complete the following sentence. The coefficient of determination between the dependent variable, TEST SCORE, and the independent variable, HOURS SPENT STUDYING, equals 043. This means that:_________.
a. variation in the variable, HOURS SPENT STUDYING explains 43% of the variation in the variable. TEST SCORE
b. variation in the variable, TEST SCORE, explains 43% of the variation in the variable, HOURS SPENT STUDYING
c. the correlation between HOURS SPENT STUDYING and TEST SCORE equals 0.43
d. the correlation between HOURS SPENT STUDYING and TEST SCORE equals 0.57,
Answer: a. variation in the variable, HOURS SPENT STUDYING explains 43% of the variation in the variable. TEST SCORE
Step-by-step explanation:
The coefficient of determination is denoted by R square is the proportion of the variance in the dependent variable that is predictable from the independent variable.
Given: dependent variable = TEST SCORE
independent variable = HOURS SPENT STUDYING
coefficient of determination = 0.43
That means variation in the variable, HOURS SPENT STUDYING explains 43% of the variation in the variable. TEST SCORE.
Hence, the correct option is a.
Write the rule that transforms p(x) into q(x), where q(x)=2p(x+3)−6
Answer: - A horizontal shift of 3 units to the left.
- A vertical dilation of factor 2.
- A vertical shift of 6 units down.
Step-by-step explanation:
Here we have 3 transformations:
I will start giving general cases for each transformation:
Horizontal shift.
When we have a function f(x), an horizontal shift to the right of N units (N positive) is written as:
g(x) = f(x - N)
So in our case, we have a shift to the LEFT of 3 units.
Vertical dilation/contraction.
A vertical dilation/contraction of factor A, is written as:
g(x) = A*f(x)
if A > 1, this is a dilation, if A < 1, this is a contraction.
In the case of our problem, we have A = 2.
Vertical shift:
A vertical shift is written as:
g(x) = f(x) + N.
If N is positive, we have a shift of N units up, if N is negative, we have a shift of N units down.
in this case, N = -6.
Then the transformations are:
q(x) = 2*p(x -(-3)) - 6
- A horizontal shift of 3 units to the left.
- A vertical dilation of factor 2.
- A vertical shift of 6 units down.
An account earned interest of 5% per year. The beginning balance was $250. The equation t=log1.05E250 represents the situation, where t is the time in years and E is the ending balance.
Answer:
t=3 years
Step-by-step explanation:
t=log1.05E250
t= time in years
E= ending balance.
Interest=5% per year
Ending balance=$289.41
Note: write Log 1.05 as written in the question
t= log1.05 E/250
=log1.05 (289.41 / 250)
=Log 1.05 (1.15764)
=Log (1.15764) / log (1.05)
= 0.0636 / 0.0212
=3
Therefore,
t=3 years
X+y+z=1
X-2y+3z=2
X+z-5=0
x+y+z=1
x=1/(y+z)
1/(y+z)-2y+3z=2
1-2y²-2yz+3yz+3z²=2(y+z)
(1-2y²+yz+3z²)/2=y+z
z=(1-2y²+yz+3z²)/2 -y/1
z=(1-2y²+yz+3z²-2y)/2
24a + 72b - 40c what’s the answer can somebody help me I’m confused
Answer:
8⋅(3a+9b−5c)
Step-by-step explanation:
The equation in a simple form by using the greatest common factor is
8 ( 3a + 9b -5c ).
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The greatest common factor is the largest positive number which can be divided into given numbers evenly.
The expression will be simplified as below:-
E = 24a + 72b - 40c
Take the number 8 common from the expression.
E = 8 ( 3a + 9b -5c ).
Therefore, the equation in a simple form by using the greatest common factor is 8 ( 3a + 9b -5c ).
To know more about an expression follow
https://brainly.com/question/219464
#SPJ5
Hello. There is 2 questions in the links below if you could solve them that would be awesome!
Evaluate the expression shown below and write your answer as a fraction in simplest form. 3 (-20 8 Answer: Submit Answer attempt 1 out of 2 O
Answer:
[tex] -\frac{1}{40} [/tex]
Step-by-step explanation:
To evaluate [tex] -\frac{3}{8} - (-\frac{7}{20}) [/tex], start by opening the bracket.
When opening the bracket, we would be multiplying negative sign by negative sign, which equal positive sign.
Thus,
[tex] -\frac{3}{8} + \frac{7}{20} [/tex]
Solve further by performing addition operation to make both fractions one
The common denominator of 8 and 20 is 40,
[tex] \frac{5(-3) +2(7)}{40} [/tex]
[tex] \frac{-15 + 14}{40} [/tex]
[tex] \frac{-1}{40} = -\frac{1}{40} [/tex]
The answer of given expression in simplest form is: [tex]\dfrac{-1}{40}\\[/tex]
The given expression is:
[tex]-\dfrac{3}{8} - (-\dfrac{7}{20})[/tex]
Multiplying negative sign with negative sign will result in positive sign of the latter term.
The simplification will be done as follows:
[tex]\\-\dfrac{3}{8} - (-\dfrac{7}{20})\\\\= -\dfrac{3}{8} + \dfrac{7}{20}\\\\=\dfrac{-3 \times 5 + 7 \times 2}{40}\\\\= -\dfrac{1}{40}\\[/tex]
In the above process, we the lcm of 8 and 20 was taken which is equal to 40.
Thus, the simplest form of the given expression is [tex]\dfrac{-1}{40}\\[/tex].
Learn more here:
https://brainly.com/question/24161414
The deepest ocean depth is 35 , 840 feet, found in the Pacific Ocean's Mariana Trench. The tallest mountain is Mount Everest, with a height of 29 , 028 . What is the difference between the highest point on Earth and the lowest point on Earth?
Answer:
64868 feet
Step-by-step explanation:
The deepest point as a negative 35,840 feet mark
The tallest point has a positive 29,028 feet mark
The difference between them:
29,028 - (-35,840) = 64,868 feetAnswer is 64,868 feet
Call: Im(formula = Repair.Costs ~ Miles.Driven, data = Dataset) Residuals: Min 1Q Median 3Q Max -247.81 -144.68 29.07 64.89 343.86 Coefficients: Estimate (Intercept) 72.807562 Miles.Driven 0.009792 Std. Error 89.456108 0.001601 t value 0.814 6.117 Pr>It) 0.432 5.2e-05 *** Signif. codes: 0) ****' 0.001 '**'0.01 '*' 0.05'.'0.1''1 Residual standard error: 180.3 on 12 degrees of freedom Multiple R-squared: 0.7572, Adjusted R-squared: 0.7369 F-statistic: 37.42 on 1 and 12 DF, p-value: 5.2e-05
Using these regression results, what is the estimated repair cost on a car that has 74,000 miles on it?
Answer:
797.42
Step-by-step explanation:
Given the Output of a linear regression data using R;
From the result table;
Intercept = 72.807562
Gradient or slope = 0.009792
General form of a linear equation:
y = mx + c
Where y = response variable ; x = explanatory variable ; c = intercept and m = gradient / slope
Hence, the regression equation becomes :
y = 0.009792x + 72.807562
Using these regression results, what is the estimated repair cost on a car that has 74,000 miles on it?
x = 74,000
y = 0.009792(74000) + 72.807562
y = 724.608 + 72.807562
y = 797.42
Answer:
The estimated repair cost on a car that has 74,000 miles on it is $797.42.
Step-by-step explanation:
The statement: Im(formula = Repair.Costs ~ Miles.Driven, data = Dataset) implies that the variable "Repair.Costs" is the dependent variable and the variable "Miles.Driven" is the independent variable.
From the provided data the regression equation formed is:
[tex]\text{Repair.Costs}=72.807562+0.009792\cdot \text{Miles.Driven}[/tex]
Compute the estimated repair cost on a car that has 74,000 miles on it as follows:
[tex]\text{Repair.Costs}=72.807562+0.009792\cdot \text{Miles.Driven}[/tex]
[tex]=72.807562+0.009792\cdot 74000\\\\=72.807562+724.608\\\\=797.415562\\\\\approx 797.42[/tex]
Thus, the estimated repair cost on a car that has 74,000 miles on it is $797.42.
Simplify (5ab4c)(-abc2)
Answer: -5a²b⁵c³
Step-by-step explanation: 5ab⁴c can be thought of as 5a¹b⁴c¹ and in the second part of the problem, since there is no coefficient on -a¹b¹c², we can give it a coefficient of 1.
Now simply multiply the coefficients
and add the exponents to get -5a²b⁵c³.
10y-3(y+5) what’s the answer
Answer:
7y-15
Step-by-step explanation:
10y-3(y+5)
=10y-3y-15
=7y-15
Hope it helped :)
Bank A charges $30 monthly fee for a check account bank B charges $15 a month How much would Keiko pay at each bank each month
Answer:
Keiko would pay $30 a month at bank A.
Keiko would pay $15 a month at bank B.
Both bank A and bank B combined would be $45 a month.
Step-by-step explanation:
Show that the curve x = 7 cos(t), y = 5 sin(t) cos(t) has two tangents at (0, 0) and find their equations.
y = __________ (smaller slope)
y = __________ (larger slope)
The equations of the two tangents are; Larger slope; y = (5/7)x Smaller slope; y = (-5/7)x
What is the slope?Slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.
To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.
This is because the more the height of the line to thee amount we walk or run on the horizontal axis, the more the slope is. Thats why we took difference of horizontal axis in denominator and difference of vertical axis on numerator.
The curve x = 7 cos(t), y = 5 sin(t) cos(t) has two tangents at (0, 0) and we need to find their equations.
We can write
cos(t) = x/7
so
y = 5(±√(1 -(x/7)^2)*x/7
Then
y' = (±5/7)*(√(1 -(x/7)^2) + x/(2√(1 -(x/7)^2)*(-2(x/7))
The limit as x → 0 is ±5/7
The equations of the two tangents are;
Larger slope; y = (5/7)x
Smaller slope; y = (-5/7)x
Learn more about slope here:
https://brainly.com/question/2503591
#SPJ2
What percent of 175 is 7?
Answer:
12.25
7 percent of 175 = 12.25
(example attached below)
make h the subject A=1/2(a+c)h
Answer:
h = [tex]\frac{2A}{a+c}[/tex]
Step-by-step explanation:
Given
A = [tex]\frac{1}{2}[/tex](a + c)h
Multiply both sides by 2 to clear the fraction
2A = (a + c)h ( divide both sides by (a + c) )
[tex]\frac{2A}{a+c}[/tex] = h
Answer:
[see below]
Step-by-step explanation:
[tex]a = 1/2(a+c)h\\\\1/2(a+c)h = a\\\\2 * 1/2(a+c)h = a * 2\\\\h(a+c)=2a\\\\\frac{h(a+c)}{a+c}=\frac{2a}{a+c}; a \neq -c\\\\\boxed{h=\frac{2a}{a+c}; a \neq -c}[/tex]
Hope this helps.
How do i write 2.200 (in decimals) into word form. Explain pls
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Two Thousand Two Hundred
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
Answer:
Two and Two Tenths.
Step-by-step explanation:
The whole number if you were to just say it is two, so you have that part, but then for the decimals, the zeros don't really matter you can take them off and you have the same number ( but only if there is nothing after the zeros) so now you are left with 2.2 and the first decimal spot is the tenths so the wording for this would Two and Two Tenths.
Pleasee help multiple choice whoever gets it correct gets brainlest
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{j = 6}}}}[/tex]Option D is the correct option
Step-by-step explanation:
[tex] \sf{(5 + 3)j = 48}[/tex]
Distribute j through the parentheses
⇒[tex] \sf{5j + 3j = 48}[/tex]
Collect like terms
⇒[tex] \sf{8j = 48}[/tex]
Divide both sides of the equation by 8
⇒[tex] \sf{ \frac{8j}{8} = \frac{48}{8} }[/tex]
Calculate
⇒[tex] \sf{j = 6}[/tex]
Hope I helped!
Best regards!!
can someone help me with this
if xy=4 then what is d²y/dx² × d²x/dy²
please read carefully there not the same so they don't equal one
Answer:
Actually, this is equal to 1.
Step-by-step explanation:
Hello, please consider the following.
First of all, we assume x and y different from 0.
[tex]xy=4\\\\y=\dfrac{4}{x}\\\\x=\dfrac{4}{x}\\\\\text{So}\\\\y'(x)=\dfrac{-4}{x^2}\\\\y''(x)=\dfrac{-4*(-2)}{x^3}=\dfrac{8}{x^3}\\\\x''(y)=\dfrac{8}{y^2}\\\\\text{So, we can conclude}[/tex]
[tex]\dfrac{d^2y}{dx^2}\cdot \dfrac{d^2x}{dy^2}=\dfrac{8}{x^3}\cdot\dfrac{8}{y^3}\\\\=\dfrac{64}{(xy)^3}\\\\\text{We replace xy by 4}\\\\=\dfrac{64}{4^3}\\\\=\dfrac{64}{64}\\\\=\large \boxed{\sf \bf \ 1 \ }[/tex]
Thank you
I have a rectangular garden. I usually grow
carrots in 2/5 of my garden but I want to
take 1/4 of the carrots section to grow
strawberries. After I make this change, how
much of my whole garden will be
strawberries?
Answer:
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
If you originally have [tex]\frac{2}{5}[/tex] of your garden reserved for carrots, are taking [tex]\frac{1}{4}[/tex] of the carrot space ( [tex]\frac{2}{5}[/tex] ) for strawberries, then the total amount of your garden left for strawberries will be [tex]\frac{2}{5}\cdot\frac{1}{4}[/tex]
[tex]\frac{2}{5}\cdot\frac{1}{4} = \frac{2}{20}[/tex]
[tex]\frac{2}{20}[/tex] simplifies down to [tex]\frac{1}{10}[/tex].
Hope this helped!
Sixty percent of the cost of the dining set is the same as one half the cost of the dining set decreased by $180. What is the cost of the dining set?
Answer:
The cost of the dining set = $200
Step-by-step explanation:
Let
Cost of the dining set=x
Sixty percent of the cost of the dining set
= 60% of x
=60/100 * x
= 0.6x
One half the cost of the dining set decreased by $180.
=1 1/2 of x - 180
= 1.5 * x - 180
= 1.5x - 180
Sixty percent of the cost of the dining set is the same as one half the cost of the dining set decreased by $180
0.6x = 1.5x - 180
Collect like terms
0.6x - 1.5x = -180
-0.9x = -180
Divide both sides by -0.9
x= -180 / -0.9
=200
x= $200
Check:
0.6x
= 0.6(200)
=120
1.5x - 180
=1.5(200) - 180
= 300 - 180
=120
Find x. Assume that segments that appear tangent are tangent.
Answer:
27
Step-by-step explanation:
FE is tangent to the circle with center D at point E and DE is radius.
[tex] \therefore FE \perp DE \implies m\angle FED = 90\degree [/tex]
DE = x
DF = x + 18
FE = 36
By Pythagoras theorem:
[tex] DF^2 = DE^2 + FE^2 [/tex]
[tex] (x+18)^2 = x^2 + 36^2 [/tex]
[tex] x^2 + 36x + 324= x^2 + 1296[/tex]
[tex] 36x + 324= 1296[/tex]
[tex] 36x = 1296-324[/tex]
[tex] 36x = 972[/tex]
[tex] x = \frac{972}{36}[/tex]
[tex] x =27[/tex]
The value of x from the given figure, which is radius of a circle is 27 units.
From the given figure, FE=36 units, DE=x units and FD=x+18 units.
What is the angle formed with tangent and radius?Tangent and radius of a circle meet at 90°. If we draw a radius that meets the circumference at the same point, the angle between the radius and the tangent will always be exactly 90°.
Using Pythagoras theorem, we have
FD²=FE²+DE²
⇒ (x+18)²=36²+x²
⇒ x²+36x+324=1296+x²
⇒ 36x=1296-324
⇒ 36x=972
⇒ x=972/36
⇒ x=27 units
Hence, the value of x from the given figure, which is radius of a circle is 27 units.
To learn more about the tangents to a circle visit:
https://brainly.com/question/23265136.
#SPJ2
For parts a through f., A denotes an mxn matrix. Determine whether each statement is true or false. Justify each answer. a. A null space is a vector space. Is this statement true or false?
A. True because the null space of an mx n matrix A is a subspace of Rm
B. False, a column space is a vector space, but a null space is not a vector space
C. False, a vector space is a null space, but a null space is not necessarily a vector space
D. True because the null space of an mxn matrix A is a subspace of Rn
Answer:
D. True because the null space of an m x n matrix A is a subspace of [tex]$R^n$[/tex]
Step-by-step explanation:
A null space is also the vector space.
We know that a null set satisfies the following properties of a vector space.
Now let [tex]$x,y \in Null (A), \alpha \in IR$[/tex] , then
[tex]A[\alpha x+y] = \alpha A(x)+ A(y) = \alpha . 0 + 0 = 0$[/tex]
Thus, [tex]$ \alpha x+y \in Null (A)$[/tex]
Hence, option (d) is true.
A researcher performs an experiment to test a hypothesis that involves the nutrients niacin and retinol. She feeds one group of laboratory rats a daily diet of precisely 41.59 units of niacin and 17,995 units of retinol. She uses two types of commercial pellet foods. Food A contains 0.22 unit of niacin and 100 units of retinol per gram. Food B contains 0.23 unit of niacin and 65 units of retinol per gram. How many grams of each food does she feed this group of rats each day
Answer:
Food A = 165 grams
Food B = 23 grams
Step-by-step explanation:
Daily precise diet fed to the group:
Niacin = 41.59 units
Retinol = 17,995 units
Two food types :
Food A :
Niacin = 0.22 units per gram
Retinol = 100 units per gram
Food B:
Niacin = 0.23 units per gram
Retinol = 65 units per gram
Let:
a = gram of food A fed per day
b = gram of food B fed per day
Hence in 'a' grams of food A:
0.22a of Niacin + 100a of Retinol
In 'b' grams of food B:
0.23b of Niacin + 65b of retinol
Recall :
Total Niacin = 41.59 ; total Retinol = 17995
Then,
0.22a + 0.23b = 41.59 - - - (1)
100a + 65b = 17995 - - - (2)
From (2) ; 100a + 65b = 17995
100a = 17995 - 65b
a = 179.95 - 0.65b - - - (3)
Substitute (3) into (1)
0.22(179.95 - 0.65b) + 0.23b = 41.59
39.589 - 0.143b + 0.23b = 41.59
0.087b = 2.001
b = 2.001 / 0.087
b = 23
Put b = 23 in (3)
a = 179.95 - 0.65(23)
a = 179.95 - 14.95
a = 165
Find the z-scores (two of them) that separate the middle 48% of the distribution from the area in the tails of the standard normal distribution.
Answer:
The z-scores are [tex]Z_{\frac{\alpha }{2} } = 0643[/tex] and [tex]Z_{\frac{\alpha }{2} } = - 0643[/tex]
Step-by-step explanation:
From the question we are told that
The middle of the distribution area considered is 48%
Now the rest of the area under the standard normal distribution area is mathematically evaluated
[tex]\alpha = 100- 48[/tex]
[tex]\alpha = 52 \%[/tex]
[tex]\alpha = 0.52[/tex]
Now to obtain the area occupied by this proportion at the two tails we divide by 2 i.e
[tex]\frac{\alpha }{2} = \frac{0.52}{2} =0.26[/tex]
Now the z-score is obtained from the normal distribution table and the value is
[tex]Z_{\frac{\alpha }{2} } \pm 0.643[/tex]
The [tex]\pm[/tex] shows that we are considering the two-talil
The length of the longer leg of a right triangle is 19 cm more than five times the length of the shorter leg. The length of the hypotenuse is 20 cm more than five times the length of the shorter leg. Find the side lengths of the triangle
Answer:
13 cm, 84 cm, 85 cm
Step-by-step explanation:
Let the sides of triangle are be a, b, c
a = x, b = 5x + 19, c = 5x + 20As per Pythagorean theorem:
c² = a² + b²(5x+20)² = (5x +19)² + x²25x² + 200x + 400 = 25x² + 190x + 361 + x²x² - 10x - 39 = 0Solving the quadratic equation we get:
x= 13Then:
a= 13 cmb = 5*13 +19 = 84 cmc= 5*13 + 20 = 85 cmFor a 7 1/2 hour day, Ed makes $90. How much does he make in 1 hour?
Answer:
he makes $12 an hour
Step-by-step explanation:
Ed makes $6 in one hour.
To find out how much Ed makes in one hour, we can divide the total amount he makes in a 7 1/2 hour day by the number of hours in a day.
First, let's convert 7 1/2 hours to a mixed fraction.
7 1/2 hours = 7 + 1/2 = 14/2 + 1/2 = 15/2 hours.
Now, we can calculate how much Ed makes per hour by dividing the total amount he makes ($90) by the number of hours (15/2):
Amount per hour = $90 ÷ (15/2) = $90 × (2/15) = $6.
Therefore, Ed makes $6 in one hour.
Learn more about divide here
https://brainly.com/question/2492834
#SPJ2
Write an equation parallel to the line y=3/2x-2 that goes through (5,1) in point slope form.
Answer: y=3/2x-13/2
Step-by-step explanation:
concept to know: two parallel lines have the same slope
y=3/2x+b
in order to find b or the y-intercept, we plug the point in
y=3/2x+b
1=3/2(5)+b
1=15/2+b
b=-13/2
----------------------------
y=3/2x-13/2
Hope this helps!! :)