Answer:
p - 4
Step-by-step explanation:
Prime number is a number that only has 2 factors, 1 and the number itself. Therefore, multiplying p by 2 or 7 means giving the number more than 2 factors, which would make the number no longer prime. Squaring the prime number itself does the same.
Let p = 7.
2p = 2*7 = 14 14 = 1*2*7*14
7p = 7*7 = 49 49 = 1*7*49
p - 4 = 7 - 4 = 3 3 = 1*3
p^2 = 7^2 = 49 49 = 1*7*49
Can the sides of a triangle have lengths 6, 20, and 20?
Answer:
Yes.
Step-by-step explanation:
This would be an isosceles triangle - with 2 equal sides both 20 long with a base of length 6.
A triangle can be formed from 3 line segments as long as the sum of the length of any 2 sides exceeds the length of the third side.
I'm thinking of a number. If I add 4 to the number and then multiply the result by 3,the answer is the same as subtracting 5 from the number and then multiplying the result by 2.
(a) in terms of x?
(b) solve the equation n find the number what I'm thinking of
Answer:
x=-22
Step-by-step explanation:
Let's substitute the number you are thinking of with x
(x+4)*3=(x-5)*2
3x+12=2x-10
x+12=-10
x=-22
pls help i don’t know how to do this
Answer: [tex]\displaystyle\\\frac{2\pi }{3},\ \frac{5\pi }{3} .[/tex]
Step-by-step explanation:
[tex]\displaystyle\\tan\theta=-\sqrt{3}\ \ \ \ 0\leq \theta\leq 2\pi \\\theta =\frac{2\pi }{3}+\pi N\ \ \ (N=0,\ 1,\ 2,\ 3\ ...)\\ N=0\\\theta=\frac{2\pi }{3} +\pi *0\\\theta=\frac{2\pi }{3}\ \ \ \ ( 0\leq \theta\leq 2\pi)\\ N=1\\\theta=\frac{2\pi }{3}+\pi *1 \\\theta=\frac{2\pi }{3} +\pi \\\theta=\frac{2\pi +3\pi }{3} \\\theta=\frac{5\pi }{3} \ \ \ ( 0\leq \theta\leq 2\pi)\\[/tex]
[tex]N=2\\\theta=\frac{2\pi }{3}+2\pi \\ \theta=\frac{2\pi +3*2\pi }{3}\\ \theta=\frac{2\pi +6\pi }{3} \\\theta=\frac{8\pi }{3} \\\theta=2\frac{2}{3} \pi \ \ \ \ (\notin0\leq \theta\leq 2\pi).\\[/tex]
-6 - (2x + 7) = -2(x +6) -1
Answer:
Infinite solutions
Step-by-step explanation:
You can put in any number for x and the 2 sides of the equation will equal each other.
Answer:
The equation has not solution, both parts of the equation correspond to the same line.
Step-by-step explanation:
-6 -(2x+7) = -2(x+6) - 1
-6 -2x - 7 = (-2*x + (-2*6)) - 1
-6 - 2x - 7 = -2x - 12 - 1
-2x - 13 = -2x - 13
-2x = - 2x
NEED HELP SOLVING
has to be simplified
A hamster is 2 1/2 inches long a rabbit is 3 1/2 times as long as a hamster how long is the rabbit
Find two positive numbers whose product is 81 and whose sum is a minimum. (enter your answers as a comma-separated list. )
Answer: 18
Step-by-step explanation: the smallest two positive numbers whose product is 81 are 9 and 9. 9+9 is equal to 18.
Pick the correct answer
Please help thanks :)
Answer:
B
Step-by-step explanation:
First create the equation that has slope of -1 in the form of y=mx+b. Because the slope is -1, m=-1, so the equation is y=-x+b. Now we see that we are given the point (-3, 8) as an intersection point. Substitute x and y for -3 and 8 in our equation. With this information, our equation becomes 8=3+b. Solving, b=5. Our equation is now y=-x+5.
Simplifying all of the answer choices, we have
A. y=-x-5
B. y=-x+5
C. y=-x-5
D. and E. as what they already show
The only answer that matches is B.
Find a b, 6a 9b, |a|, and |a − b|. (simplify your vectors completely. ) a = −9, 12 , b = 6, 4
The values of a + b, 6a + 9b, |a|, and |a − b| are −3i + 16j, 0i + 108j, 15 and 17 respectively. This can be obtained by using vector addition, vector subtraction and formula to find magnitude of a vector.
Find the values of a + b, 6a + 9b, |a|, and |a − b|:Given that,
a = <−9, 12> , b = <6, 4>
These vectors can be rewritten as,
a = <−9, 12> = −9i + 12j
b = <6, 4> = 6i + 4j
To find a + b,we add both vectors a and b together,a + b = −9i + 12j + 6i + 4j
a + b = −9i + 6i + 12j + 4j
a + b = (−9 + 6)i + (12 + 4)j
a + b = −3i + 16j
To find 6a + 9b, we first find 6a and 9b then add them both together,
6a = 6 (−9i + 12j )
6a = −54i + 72j
9b = 9(6i + 4j)
9b = 54i + 36j
Now add 6a and 9b together,
6a + 9b = −54i + 72j + 54i + 36j
6a + 9b = −54i + 54i + 72j + 36j
6a + 9b = 0i + 108j
To find |a|, use the formula to find the magnitude of a vector,If a = a₁i + a₂j, |a| = √a₁² + a₂²
Here, a = −9i + 12j
|a| = √(−9)² + (12)²
|a| = √81 + 144 = √225
|a| = 15
To find |a − b|, first subtract b from a and find the magnitude of the resultant,a - b = −9i + 12j - (6i + 4j)
a - b = −9i - 6i + 12j - 4j
a - b = −15i + 8j
Now use the formula to find the magnitude of a vector,
|a − b| = √(-15)² + (8)²
|a − b| = √225 + 64 = √289
|a − b| = 17
Hence the values of a + b, 6a + 9b, |a|, and |a − b| are −3i + 16j, 0i + 108j, 15 and 17 respectively.
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AArea of a circle Take a rope, tie it at one corner of a door knob and then. find out how much area can be covered if you cart move around. Also mention the name of 2D figure obtained. Tie a stone on one end of the rope and then rotate it. . Find the area of obtained figure take the length of rope as a radius.
Answer:
A=113 cm²
Step-by-step explanation:
If the length of the rope is 6 cm
then the radius of the circle we draw is 6 cm.
Area of the circle is A = π·r²
A = π·6² ≈ 3.14· 36 ≈ 113cm²
Austin keeps a right conical basin for the birds in his garden as represented in the diagram. The basin is 40 centimeters deep, and the angle between the sloping sides is 77°. What is the shortest distance between the tip of the cone and its rim?
177.8 centimeters.
What is the formula for cos θ?The symbol for it is Cosθ, and it has the following form: adjacent/hypotenuse = cosθ. In other words, it divides the length of the hypotenuse by the length of the neighboring side, which is the side next to the angle (the longest side of a right triangle).When working with right-angled triangles, the Cos Theta Formula is particularly helpful. The Cosine of an angle in a right triangle is always equal to the hypotenuse's length divided by the length of the neighboring side. This makes it an excellent tool for resolving Cosine-related issues.The shortest distance between the tip of the cone and its rim:
cos θ= base/Hypotenuse
cos 77°=[tex]\frac{40}{H}[/tex]
[tex]0.22495=\frac{40}{H}[/tex]
[tex]H=177.8[/tex]
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The shortest distance between the tip of the cone and its rim exits 51.11cm.
What is the shortest distance between the tip of the cone and its rim?If you draw a line along the middle of the cone, you'd finish up with two right triangles and the line even bisects the angle between the sloping sides. The shortest distance between the tip of the cone and its rim exists in the hypotenuse of a right triangle with one angle calculating 38.5°. So, utilizing trigonometry and allowing x as the measurement of the shortest distance between the tip of the cone and its rim.
Cos 38.5 = 40 / x
Solving the value of x, we get
Multiply both sides by x
[tex]$\cos \left(38.5^{\circ}\right) x=\frac{40}{x} x[/tex]
[tex]$\cos \left(38.5^{\circ}\right) x=40[/tex]
Divide both sides by [tex]$\cos \left(38.5^{\circ}\right)$[/tex]
[tex]$\frac{\cos \left(38.5^{\circ}\right) x}{\cos \left(38.5^{\circ}\right)}=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]
simplifying the above equation, we get
[tex]$x=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]
x = 51.11cm
The shortest distance between the tip of the cone and its rim exits 51.11cm.
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Find how many matches Peter won. plss answwer (ಥ _ ಥ)
Answer:
10 is the right answer...
Step-by-step explanation:
thanks
mark me as brainlist....
the sum of two numbers is 123. when the larger number is added to 5 times the smaller, the sum is 343. find the numbers.
The two numbers are 68 and 55.
Given that the sum of two numbers is 123. when the larger number is added to 5 times the smaller, the sum is 343.
We need to find the numbers,
Let's call the two numbers x and y. According to the given information, we have the following two equations:
x + y = 123 (The sum of the two numbers is 123)
x + 5y = 343 (When the larger number is added to 5 times the smaller, the sum is 343)
Now, we can solve these two equations simultaneously to find the values of x and y.
Let's rearrange equation 1 to express x in terms of y:
x = 123 - y
Substitute this value of x into equation 2:
(123 - y) + 5y = 343
Now, solve for y:
123 + 4y = 343
4y = 343 - 123
4y = 220
y = 220 / 4
y = 55
Now that we have the value of y, we can find the value of x using equation 1:
x = 123 - y
x = 123 - 55
x = 68
So, the two numbers are 68 and 55.
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Which graph represents a reflection across the x-axis of g(x) = Three-fourths(3)x?
See attached images for the graph.
Given △BAD AB = 3x - 4 ED = 24 CA = 12 BE = 3x Find x to the nearest hundredth.
Answer:
x = 10.67
Step-by-step explanation:
The triangles shown are similar, so corresponding sides are proportional. This lets us write a relation that can be solved for x.
SetupFor the given figure, we can write the proportion ...
AB/CA = DB/ED . . . . . . where DB = ED +BE
(3x-4)/12 = (24 +3x)/24 . . . . . . substitute given values
SolutionMultiplying by 24 gives ...
2(3x -4) = 3x +24
6x -8 = 3x +24 . . . . . eliminate parentheses
3x = 32 . . . . . . . . add 8-3x
x = 32/3 = 10 2/3 ≈ 10.67 . . . . . divide by 3 and convert to decimal
The value of x to the nearest hundredth is 10.67.
A bag contains 3 red marbles, 7 blue marbles, and 2 green marbles. what is the probability of choosing a blue marble when one marble is drawn?
Answer: 7/12
Step-by-step explanation: There is a total of 3+7+2 = 12 marbles in the bag. 7 are blue marbles so there is a 7/12 chance of getting a blue marble when one marble is drawn.
Answer:
7/12
or an 84%
Step-by-step explanation:
A soap company started a promotion in which each packet of detergent powder will have 20% extra powder at the
same price, Jenna buys a 2 kg packet of the detergent powder. How much total detergent powder will be in the packet?
2.4kg.,
..
hope it helps
In a certain company, there were five candidates running for President. After the vots were tallied, it turned out that Victor, like in the election, finished in thir place, and david beat him. Greg said that he didn't come in first, but he also didn't come in last. Mac in an interview, said that in this election he wasn't able to win, but at least he was one place hight than his old rival Bill. What place did each candidate come in?
Considering the situation described, the classification of the elections is given as follows, according to their order of finish:
David, Greg, Victor, Mac, Bill.
How to find the classification of the elections?We take the situation that is described, and build the classification from it. The classification has the following format:
P1 - P2 - P3 - P4 - P5
With P1 being the first placed candidate, P2 being the second placed candidate, and so on until P5 which is the fifth placed candidate.
From the text given in this problem, we have that:
Victor finished in third place, and David beat him, hence P3 = Victor, David = P1 or P2.Greg didn't come in first nor in last, hence, considering that Victor is P3, Greg = P2 or P4.Mac didn't win, but he finished higher than Bill, hence, considering that Mac didn't win and that Victor is P3, Mac = P4, Bill = P5.From the bullet points above, we can conclude that David = P1, Greg = P2.Hence the classification of the election is given by:
David, Greg, Victor, Mac, Bill.
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A coin-operated drink machine was designed to discharge a mean of 7 ounces of coffee per cup. In a test of the machine, the discharge amounts in 18 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 7.04 ounces and 0.17 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.1 level of significance, to conclude that the true mean discharge,u, differs from ounces? Perform a two-tailed test. Then fill in the table below. I need the two critical values at the 0.1 level of significace. Also need the answers to al other questions and whether we accpe for reject.
Using the t-distribution, it is found that since the test statistic is between -1.7341 and 1.7341, we do not reject(accept) the null hypothesis, hence there is not enough evidence to conclude that the true mean discharge differs from 7 ounces.
What are the hypothesis tested?At the null hypothesis, it is tested if the mean is of 7 ounces, that is:
[tex]H_0: \mu = 7[/tex]
At the alternative hypothesis, it is tested if the mean is different of 7 ounces, that is:
[tex]H_1: \mu \neq 7[/tex]
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The values of the parameters are given by:
[tex]\overline{x} = 7.04, \mu = 7, s = 0.17, n = 18[/tex]
Hence the value of the test statistic is found as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{7.04 - 7}{\frac{0.17}{\sqrt{18}}}[/tex]
t = 1
What is the decision?Considering a two-tailed test, as we are testing if the mean is different of a value, with 18 - 1 = 17 df and a significance level of 0.1, the critical value is of [tex]t^{\ast} = 1.7341[/tex]
Since the test statistic is between -1.7341 and 1.7341, we do not reject(accept) the null hypothesis, hence there is not enough evidence to conclude that the true mean discharge differs from 7 ounces.
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Select the correct answer. What is the value of the limit ? lim x 5 square x^2 +4
By direct evaluation, we will see that the limit is equal to 29.
How to find the limit?Here we want to find the limit of the given expression when x tends to 5.
[tex]\lim_{x \to \ 5} x^2 + 4[/tex]
We can directly evaluate the expression in x = 5 and see if we get a real value different than zero.
By direct evaluation, we get:
[tex]\lim_{x \to \ 5} x^2 + 4 = 5^2+ 4 = 29[/tex]
Notice that the limit does give a whole number, then in this way, we conclude that the limit of the given expression when x tends to 5 is equal to 29.
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Answer:
square 29
Step-by-step explanation:
Rounding off 6 400mm
The rounding off a given number implies approximating the number to the required value. Thus the answer to the given question is 6 000 mm.
Rounding off a given number implies approximating the number to the required value. This can be done in two major ways: rounding up or rounding down.
Rounding up implies considering the required digit if it is up to or greater than 5, which turns to 1. Rounding down requires no consideration of digits less than 5 which turns to 0.
Thus considering the given question, Since the second digit is 4 which is lesser than 5, then it turns to a zero. So that;
rounding off 6 400 mm would give 6 000 mm.
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How many natural numbers between $150$ and $300$ are divisible by $9$?
Answer:
There are 17 natural numbers divisible.
There are 17 natural numbers between 150 and 300 that are divisible by 9.
To find the number of natural numbers between 150 and 300 that are divisible by 9, we need to find the count of multiples of 9 within this range.
The first multiple of 9 greater than or equal to 150 is 153 (9 x 17), and the last multiple of 9 less than or equal to 300 is 297 (9 x 33).
Now, we can calculate the number of multiples of 9 between 153 and 297 (inclusive):
Number of multiples of 9 = (Last multiple - First multiple) / 9 + 1
Number of multiples of 9 = (297 - 153) / 9 + 1
Number of multiples of 9 = 144 / 9 + 1
Number of multiples of 9 = 16 + 1
Number of multiples of 9 = 17
So, there are 17 natural numbers between 150 and 300 that are divisible by 9.
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Find the producer surplus at the equilibrium point. 3) s(x) = x 3, 0 k x k 3; x = 3
The producer surplus at the equilibrium point is 1.0146
An equilibrium (or equilibrium point) of a dynamical machine-generated via an autonomous machine of everyday differential equations (ODEs) is a solution that doesn't change with time.
Equilibrium is the country in which the marketplace delivers and calls for stability each different, and as a result, expenses turn out to be solid. usually, an over-deliver of products or services reasons charges to head down, which leads to higher demand—at the same time as a below-supply or scarcity reasons costs to head up resulting in fewer calls.
The equilibrium equations (balance of linear momentum) are given in index form as(1.4)σji,j+bi=ρu¨i, I,j=1,2,3where σij are additives of (Cauchy) stress, ρ is mass density, and bi is body force additives.
Producer Surplus = area of shadestportion
Area of shaded portion = free of rect minus area of OneD
Aves of OABO=Now serving from
"[3√74-3/5]
= √(x+3)" de
=2 (2√6-√5)
(Jon= √46 = Fure=456-255
(x+3)+1
Area of rectangle OA BC =316
= 3√6
producer surplus = 3√6 - (ure -2√5)
= 2√3-66
= 1.0146
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particular company's net sales, in billions, from 2008 to 2018 can be modeled by the expression t2 + 14t + 85, where t is the number of years since the end of 2008. What does the constant term of the expression represent in terms of the context?
The constant in the expression represents that the company earned 85 billion dollars in 2008.
What does the constant represent?The expression given in the question is known as a quadratic function. A quadratic function is a function that usually has a single variable and it is raised to the power of 2. The graph of a quadratic function is a curve called a parabola. Parabolas may curve upward or downward
An example of a quadratic function is ax² + bx + c
Where: a,b, c are real numbers not equal to zero
c = constant.
The constant in this question is 85. It is the amount earned in 2008
Here are the options:
The company earned 85 billion dollars from 2008 to 2018
The company earned 85 billion dollars in 2008
The company earned 14 billion dollars from 2008 to 2018.
The company earned 14 billion dollars in 2008.
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Which test point holds true for the inequality 3/2y-2x>=1? Where does the shaded area lie for this inequality? The test point holds true for this inequality. The shaded area for the inequality lies the boundary line.
The test That holds true for this inequality is given as 1/4 and 1
How to solve for the inequality3/2 y - 2x > 1
The goal is to make y the subject
then
3/2 y > 2x + 1
We have to divide through the equation by 3/2
Such that y > 4/3 x + 2/3
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The volume of a cylindrical can of beans is 45 π cubic centimeters. if the diameter is 6 centimeters, what is the height of the can in centimeters?
Answer:
h = 5 cm
Step-by-step explanation:
Givens
d = 6cm
V = 45cubic cm
Formula
V = pi * r^2 h substitute values into the formula
Solution
d = 2*r
6 = 2*r Divide both sides by 2
6/2 = 2r / 2
3 = r
45 pi cm^3 = pi * (3)^2 * h Divide both sides by pi
45 pi/pi = pi * 9 * h / pi
45 = 9h Divide both sides by 4
45/4 = 9h/9
5 cm
Use special right triangles to find the value of the variables no decimal answers
Step-by-step explanation:
This is trigonometry. Focusing on Y initially, we can see that Y is the opposite, and 32 is the hypotenuse. Therefore, we must use sin:
[tex] \sin(60) = \frac{y}{32} [/tex]
[tex]y = \sin(60) \times 32[/tex]
[tex]y \approx28[/tex]
Next X. We can see that X is the adjacent, and 32 is the hypotenuse, so we must use cos:
[tex] \cos(60) = \frac{x}{32} [/tex]
[tex]x = \cos(60) \times 32[/tex]
[tex]x = 16[/tex]
Now let's look at A. We can see that a is the adjacent, and 12 is the opposite, so we must use tan:
[tex] \tan(60) = \frac{12}{a} [/tex]
[tex]a = \frac{12}{ \tan(60) } [/tex]
[tex]a \approx7[/tex]
Now, B. We can see that B is the hypotenuse, and 12 is the opposite, so we must use sin:
[tex] \sin(60) = \frac{12}{b} [/tex]
[tex]b = \frac{12}{ \sin(60) } [/tex]
[tex]b \approx14[/tex]
Answer:
Below in bold.
Step-by-step explanation:
The first triangle is a 30-60-90 triangle,
so the sides are in the ratio 2 : 1 : √3, where 2 is the hypotenuse, the 1 is adjacent to 60 degree angle and the √3 is opposite the 60 degree angle.
So x = 1/2 * 32 = 16
and y = 16√3 or 27.71 to nearest hundredth.
The second one is the same special triangle, so
√3/2 = 12/b
b = 24/√3
= 8√3 or 13.86 to nearest hundredth.
a = 1/2 b = 4√3 or 6.93 to nearest hundredth.
PLS SOLVE ASAP. I will mark brainlest.
Answer:
• [tex](w \cdot u) (7)[/tex] = [tex]\bf 8[/tex]
• [tex](u \cdot w) (7)[/tex] = [tex]\bf 22[/tex]
Step-by-step explanation:
We are given:
[tex]u(x) = x^2 + 6[/tex]
[tex]w(x) = \sqrt{x + 9}[/tex].
• [tex](w \cdot u) (7)[/tex]. read as "w of u of 7", means we have to input 7 into the function [tex]u(x)[/tex], and use the output we get as input for the function [tex]w(x)[/tex] :
[tex](w \cdot u) (7)[/tex]
⇒ [tex]w(u(7))[/tex]
⇒ [tex]w(7^2 + 6)[/tex]
⇒ [tex]w(55)[/tex]
⇒ [tex]\sqrt{55 + 9}[/tex]
⇒ [tex]\sqrt{64}[/tex]
⇒ [tex]\bf 8[/tex]
• Similarly, we can evaluate [tex](u \cdot w) (7)[/tex] :
[tex](u \cdot w) (7)[/tex]
⇒ [tex]u(w(7))[/tex]
⇒ [tex]u(\sqrt{7 + 9})[/tex]
⇒ [tex]u(\sqrt{16})[/tex]
⇒ [tex]u(4)[/tex]
⇒ [tex]4^2 + 6[/tex]
⇒ [tex]\bf 22[/tex]
The answers are :
(w o u)(7) = 8
(u o w)(7) = 22
To find the first answer, substitute u(x) in w(x), and set x = 7.
u(7) = 7² + 6 u(7) = 49 + 6u(7) = 55w(u(7)) = √(55 + 9)w(u(7)) = √64w(u(7)) = 8(w o u)(7) = 8To find the second answer, substitute w(x) in u(x), and set x = 7.
w(7) = √(7 + 9)w(7) = √16w(7) = 4u(w(7)) = 4² + 6u(w(7)) = 16 + 6u(w(7)) = 22(u o w)(7) = 22The hollenbecks own a square lot with area 3600 square meters. they plan to fence just three sides of this lot. how many meters of fence must they purchase?
Answer: 180 meters
Step-by-step explanation: To solve this we need to find the square root of 3600. 6x6 = 36 so we know the square root is 60. That means that each side of the square lot is 60 meters. If they fence 3 sides they will need to purchase 60x3= 180 meters of fence.
The slope-intercept form given (6,-5) & perpendicular to -5x - 7y = -17.
Answer:
[tex]y=\dfrac{7}{5}x-\dfrac{67}{5}[/tex]
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
m is the slope.b is the y-intercept.Rearrange the given equation so that it is in slope-intercept form:
[tex]\implies -5x-7y=-17[/tex]
[tex]\implies -7y=5x-17[/tex]
[tex]\implies y=-\dfrac{5}{7}x+\dfrac{17}{7}[/tex]
Therefore, the slope of the given equation is -⁵/₇.
If two lines are perpendicular to each other (at right angles), the product of their slopes will be -1. Therefore, their slopes will be negative reciprocals of each other.
Therefore, the slope of the line perpendicular to the given equation is:
[tex]\sf m=\dfrac{7}{5}[/tex]
Substitute the found slope and the given point (6, -5) into the slope-intercept formula and solve for b:
[tex]\implies -5=\dfrac{7}{5}(6)+b[/tex]
[tex]\implies -5=\dfrac{42}{5}+b[/tex]
[tex]\implies b=-\dfrac{67}{5}[/tex]
Substitute the found slope and the found value of b into the slope-intercept formula to create the equation for the perpendicular line:
[tex]\implies y=\dfrac{7}{5}x-\dfrac{67}{5}[/tex]
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