Consider the line y=7/4x-4.
Find the equation of the line that is perpendicular to this line and passes through the point (8,2)
Find the equation of the line that is parallel to this line and passes through the point (8,2)
Answers
Answer:
[tex]\displaystyle \perp\:y = -\frac{4}{7}x + 6\frac{4}{7} \\ \parallel\:y = 1\frac{3}{4}x - 12[/tex]
Step-by-step explanation:
Perpendicular equations have OPPOCITE MULTIPLICATIVE INVERCE RATE OF CHANGES [SLOPES], so 1¾ becomes −⁴⁄₇, and we move forward:
[tex]\displaystyle 2 = -\frac{4}{7}[8] + b \hookrightarrow 2 = -4\frac{4}{7} + b; 6\frac{4}{7} = b \\ \\ \boxed{y = -\frac{4}{7}x + 6\frac{4}{7}}[/tex]
Parallel equations have SIMILAR RATE OF CHANGES [SLOPES], so 1¾ remains as is as we proceed:
[tex]\displaystyle 2 = 1\frac{3}{4}[8] + b \hookrightarrow 2 = 14 + b; -12 = b \\ \\ \boxed{y = 1\frac{3}{4}x - 12}[/tex]
I am joyous to assist you at any time.
Related Questions
Many states run lotteries to raise money. A website advertises that it knows "how to increase YOUR chances of Winning the Lottery." They offer several systems and criticize others as foolish. One system is called Lucky Numbers. People who play the Lucky Numbers system just pick a "lucky" number to play, but maybe some numbers are luckier than others. Let's use a simulation to see how well this system works. To make the situation manageable, simulate a simple lottery in which a single digit from 0 to 9 is selected as the winning number. Any value can be picked, but for this exercise, pick 1 as the lucky number. What proportion of the time do you win? Run 60 trials using the random numbers given below, starting with the first number. 89064 27308 64568 14121 98226 65388 58732 85801 69902 78431 10380 42006
Answers
Answer:
10 percent
Step-by-step explanation:
hello,
from this question, it has been stated that the lucky number is 1
from all of these values below we are to account how many times 1 appeared in these numbers have
89064, 27308, 64568 ,14121, 98226, 65388, 58732, 85801, 69902, 78431, 10380, 42006.
the total number of 1 is 6
= 6 x 1 divided by the number of trials 60
= 6 x 1/60
= 0.1
to get the proportion, we multiply 0.1 by 100
0.1 x 100
= 10%
A wall in Marcus’s bedroom is 8 2/5 feet high and 16 2/3 feet long.If he paints 1/2 of the wall blue, how many square feet will be blue?
Answers
the area of a square patio is 196 square feet how long is each side of the patio
Answers
Answer:
[tex]14[/tex] ft
Step-by-step explanation:
Let x be the length of each side
Turn it into an algebraic expression: [tex]x^{2} = 196[/tex] 14 × 14 = 196So, x = 196I hope this helps!
Please help with this:
Answers
9514 1404 393
Answer:
Positive
Step-by-step explanation:
If thinking in the abstract doesn't work well for you, choose a couple of values that match the description:
a > 0, choose a = 1
b < 0, choose b = -1
Now, the product is ...
-4ab = (-4)(1)(-1) = 4 . . . a positive product
__
The product will be positive when the total number of minus signs of the factors is even. Here, there are 2 minus signs, so the product is positive.
Vertical Angles: Vertical angles are angles that are opposite of each other when two straight lines cross. In
the diagram in #5, ZGEF and ZMEH are a pair of vertical angles while ZFEM and ZHEG are also.
(a) Given the results of your calculations in #5, what can you say about the measure of vertical angles?
(b) Why do you think this occurs?
Answers
9514 1404 393
Answer:
vertical angles are congruentboth are supplementary to the same angleStep-by-step explanation:
Given the results of #5 are ...
∠GEF = 120, 150, 155, 135
∠FEM = 60, 30, 25, 45
∠MEH = 120, 150, 155, 135
∠HEG = 60, 30, 25, 45
__
(a) We can see that vertical angles are congruent.
(b) Each of a pair of vertical angles is supplementary to the same angle.
∠GEF and ∠MEH are both supplementary to ∠FEM and to ∠HEG
∠FEM and ∠HEG are both supplementary to ∠GEF and to ∠MEH
solve the equation:
-5|3x+8|-5=-2
Answers
Answer:
x = -2 13/15
Step-by-step explanation:
-5(3x+8)-5=-2
start by multiplying out the 5 to the numbers in the parenthesis.
= -15x-40-5=-2
subtract 5 from -40
=15x-45=-2
add the 45 to itself to get rid of it and add it to -2
=15x=43
divide 43 by 15
=2.8666666666 or -2 13/15
eight less than four times a number is twelve. what is the number? the options are, 5 , 1 , -3 , -5 , please i need a answer asap.
Answers
A professional baseball player earned $1,715,000 from
playing baseball last year.
An autobiography he had written last year sold 300,000
copies at a price of $24 each. He received 10% in
royalties on the book sales.
What was his total salary last year?
$
Answers
Answer:
The right answer is actually $2,435,000.00
Step-by-step explanation:
The reason is because you take 300,000 and times that by 24 then you get 7,200,000 then you take that and times it by 0.10 then you get 720,000 then you add that to the 1,715,000 and you get 2,435,000.
300,000 x 24 = 7,200,000
7,200,000 x 0.10 = 720,000
720,000 + 1,715,000 = 2,435,000
So, $2,435,000.00 is your answer.
The total salary last year was $2,435,000 if a professional baseball player earned $1,715,000 from playing baseball last year.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
A professional baseball player earned $1,715,000 from playing baseball last year.
The total earning from autobiography = 300,000x24
= 7,200,000
The royalty amount = 10% of 7,200,000
The royalty amount = 0.10x7,200,000
The royalty amount = 7,200,00
Total salary last year = 1,715,000 + 7,200,00
Total salary last year = $2,435,000
Thus, the total salary last year was $2,435,000 if a professional baseball player earned $1,715,000 from playing baseball last year.
Learn more about the percentage here:
brainly.com/question/8011401
#SPJ2
write each rate as a fraction in lowest terms 20 feet in 40 seconds
Answers
Answer:
1/2 feet per second.
Step-by-step explanation:
Select all the ratio that are equivalent to 8:6.
A. 4:3
B. 6:8
C. 16:12
D. 10:8
E. 7:5
Answers
4:3 and 16:12
4 times 2 is 8
3 times two is 6 therefore
4:3 has the same value
same with the second except it is 8 and 6 times 2
Answer: A and C
Step-by-step explanation: If you take the ratio and divide both sides by 2, you get the equivalent ratio 4:3. Then if you take the ratio and multiple both sides by 2, you will get the equivalent ratio 16:12. This means that both A and C are equivalent to the ratio 8:6.
Please help thank you
Answers
I can't see the whole paper the sentences is cut
Use the Distributive Property to write an expression equivalent to 5 x (3 + 4)
Answers
Answer:
15 + 20
Step-by-step explanation:
Step 1: Write expression
5 × (3 + 4)
Step 2: Distribute 5 to each term
5(3) + 5(4)
Step 3: Simplify
15 + 20
The sum of 3 and a number is 16.
Answers
Answer:
13
Step-by-step explanation:
16-3 = 13
Gillian bakes 216 cookies on Monday. She bakes 151 more cookies on Tuesday than on Monday. She bakes 85 cookies on Wednesday. How many cookies did she bake in all? Explain.
Answers
Answer:
452
Step-by-step explanation:
216+151+85=452
Which of the following is closest to 1/2 + 1/3
Answers
Answer:
The answer is 5/6.
Step-by-step explanation:
1/2=3/6, and 1/3=2/6. 2/6+3/6=5/6
The number which is closest to the addition of two fraction numbers, 1/2 + 1/3 is 0.8.
What is the fraction number?A fraction number is the number which is a part of a whole number. It is written with a numerator and denominator. Fraction number are written as,
[tex]\dfrac{a}{b}[/tex]
Here, (a) is the numerator and (b) is the denominator.
We have to find the addition of two fraction number 1/2 and 1/3. Suppose the value which is closest to 1/2 + 1/3 is n. Thus,
[tex]n=\dfrac{1}{2}+\dfrac{1}{3}\\[/tex]
Cross multiply to find the addition of two numbers,
[tex]n=\dfrac{3+2}{6}\\n=\dfrac{5}{6}\\n=0.833[/tex]
Thus, the number which is closest to the addition of two fraction numbers, 1/2 + 1/3 is 0.8.
Learn more about the fraction number here:
https://brainly.com/question/78672
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PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((
Answers
Choose the true statement.
0-2<-3
O-2» -3
O -2 = -3
Answers
Jenn swam ⅕ mile in ¼ hour. What is her unit rate in miles per hour?
Answers
Answer:
1/2 mile/1/5 hour = 5/2 mph = 2 1/2 mph
Step-by-step explanation:
Answer:
0.80mph
Step-by-step explanation:
If 1/5 = 1/4, then:
she swims 1/5 miles for every 1/4 (fourth) of an hour
per hour means 1 hour
we must covert 1/4 to 4/4 (one mile)
1/4 × 4/1 = 4/4
if we multiply by 4/1 to get to 4/4, then we must also multiply by 4/1 for 1/5 miles
1/5 × 4/1 = 4/5
Her unit rate in miles per hour is 4/5 per 1 miles, or 0.80mph
*0.80 = 4/5 because 4 × 20 = 80 and 5 × 20 = 100; 80/100 = 0.80*
This is the two that go together, but are separate questions
Answers
Answers:
Option 1)
6a + 8s = 102
14a + 4s = 150
each adult ticket costs 9 dollars
===================================================
Explanation:
6 adult tickets and 8 student tickets bring in $102, so that means 6a+8s = 102
14 adult tickets and 4 students tickets bring in $150, so 14a+4s = 150
The system of equations is
[tex]\begin{cases}6a+8s = 102\\14a+4s = 150\end{cases}[/tex]
If we multiply both sides of the second equation by -2, we get this updated system
[tex]\begin{cases}6a+8s = 102\\-28a-8s = -300\end{cases}[/tex]
Add the equations straight down
6a+(-28a) = -22a
8s+(-8s) = 0s = 0 ... the 's' terms go away
102+(-300) = -198
So we end up with the equation -22a = -198 and that solves to a = 9 after dividing both sides by -22.
Each adult ticket costs $9
If you want the value of s, then
6a+8s = 102
6(9)+8s = 102
54 + 8s = 102
8s = 102-54
8s = 48
s = 48/8
s = 6
Meaning each student ticket costs $6
Or you could use the other equation
14a+4s = 150
14(9)+4s = 150
126+4s = 150
4s = 150-126
4s = 24
s = 24/4
s = 6
We get the same value of s
A circle with radius ris inscribed inside a square with a side length s. Use 3. 14 for TT Round answer to the nearest hundredth if necessary
If s = 10 millimeters and r = 5 millimeters, calculate the area of the shaded region
square millimeters
Answers
9514 1404 393
Answer:
21.46 mm^2
Step-by-step explanation:
The area of the square is ...
A = s^2 = (10 mm)^2 = 100 mm^2
The area of the circle is ...
A = πr^2 = π(5 mm)^2 = 25π mm^2 ≈ 78.54 mm^2
Then the shaded area is ...
100 mm^2 -78.54 mm^2 = 21.46 mm^2 . . . shaded area
An average person consumes 2,000 calories each day
Answers
DOU WUL IU LI TU
23. A man and a woman share a prize of $1000 between them in the
ratio 1:4. The woman shares her part between herself, her mother
and her daughter in the ratio 2:1:1. How much does her daughter receive?DOU WUL IU LI TU
23. A man and a woman share a prize of $1000 between them in the
ratio 1:4. The woman shares her part between herself, her mother
and her daughter in the ratio 2:1:1. How much does her daughter receive?
Answers
Number of parts = 1 + 4 = 5
Sum of all parts = $1000
Each part =
= 1000 ÷ 5
= $200
Money the man got =
= 200 × 1
= $200
Money the woman got =
= 200 × 4
= $800
The womans has $800 as her share .
Total parts = 2 + 1 + 1 = 4 parts
Sum of all parts = 800
Each part = 800 ÷ 4
Each part = 200
Then ,
The woman gets =
= 200 × 2
= $400
Her mother gets =
= 200 × 1
= $200
Her daughter gets =
= 200 × 1
= $200∴ Her daughter receives $200 .
During winter vacation, you learn that a polar jet stream is traveling across the United States. The forecaster says there will be big changes in the weather as the jet stream moves past your town in Florida.Look at the map. Predict what will happen in Florida due to the jet stream. *
A) Cooler temperature
B) Sea breeze
C) Warmer temperature
D) Land breeze
Answers
Land breeze is the answer
find the equation of the linear function represented by the table below in slope-intercept form. picture of table is below
Answers
Answer:
y = 3x + 2
Step-by-step explanation:
First you want to know what the slope intercept form is. y = mx + b. Now take two points from the table and put them in the equation [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] and get the slope of 3. Now we have y = 3x + b. To find b we need to plug in any point into the equation. I chose (-1, -1). -1 = 3(-1). Solve and you get 2. Now we are left with y = 3x + 2
The equation of the line is given by: [tex]y = 3x + 2[/tex]
----------------------------
The equation of a line, in slope-intercept formula, has the following format:
[tex]y = mx + b[/tex]
In which
m is the slope, that is, how much y changes when x changes by 1.b is the y-intercept, that is, the value of y when x = 0.----------------------------
Given two points (x,y), the slope is the change in y divided by the change in x.We have points (-1, -1) and (3,11). Thus:[tex]m = \frac{11 - (-1)}{3 - (-1)} = \frac{12}{4} = 3[/tex]
Then
[tex]y = 3x + b[/tex]
----------------------------
Point (-1,-1) means that when [tex]x = -1, y = -1[/tex], and we use this to find b.
[tex]y = 3x + b[/tex]
[tex]-1 = 3(-1) + b[/tex]
[tex]b = -1 + 3 = 2[/tex]
Thus
[tex]y = 3x + 2[/tex]
A similar problem is given at https://brainly.com/question/13251894
Provide steps to the equation. :)
Answers
Answer:
C. 90°Step-by-step explanation:
Angle ABC is the sum of angles ABD and DBC as per angle addition postulate
As per given we have isosceles triangles ABD and BCD
ADC is straight angle, therefore:
2x + x = 180°3x = 180°x = 60°Triangle ABD∠BAD = ∠ABD = 1/2(180° - 2x) = 1/2(180° - 120°) = 1/2(60°) = 30°Triangle BCD∠BDC =∠ BCD = x = 60°∠DBC = 180° - 2*60° = 180° - 120° = 60°So the angle ABC∠ABC = ∠ABD + ∠DBC∠ABC = 30° + 60° = 90° What is the answer to 245 = 125 +15w
w=
Answers
Answer:
245-125=15w
120=15w
120÷15=w
w=8
What do you notice about rectangles and
parallelograms? What is the same or different between
these two polygons?
Answers
Answer:
both have four sides and equal measures with the opposite side. Parallelograms are slanted while the rectangles are straight.
On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance traveled in miles, d, to the number of hours flying, t, is t = 1/500d. How long will it take the airplane to travel 800 miles? 400 miles? 200 miles?
Answers
please refer to this...............
simplify the expression
(2x-6) - (4x+4)
Answers
Answer:
-2x - 10
Step-by-step explanation:
(2x-6) - (4x+4) multiply (4x+4) by -1 -1(4x + 4) = -4x - 4
2x - 6 - 4x - 4 Re-arrange
2x - 4x - 6 - 4
-2x - 10
A rectangle has length 4 yards more than its width. The area of the rectangle is 96 square yards. Find the
length and the width.
Answers
Answer:
Length = 12
Width = 8
Step-by-step explanation:
Area of a Rectangle = l x w
12 x 8 = 96