Consider the line 9x+8y=-2.
Find the equation of the line that is parallel to this line and passes through the point (-3, 2).
Find the equation of the line that is perpendicular to this line and passes through the point (-3, 2).
Equation of parallel line:
Equation of perpendicular line:
Considering the definition of parallel and perpendicular line:
the equation of parallel line is y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{11}{8}[/tex].the equation of of perpendicular line is y= [tex]\frac{8}{9}[/tex]x + [tex]\frac{14}{3}[/tex].Linear equationA linear equation o line can be expressed in the form y = mx + b.
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Parallel lineParallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.
Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of parallel line in this caseIn this case, the line is 9x+8y=-2. Expressed in the form y = mx + b, you get:
8y= -2 - 9x
y= (-9x -2)÷ 8
y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{1}{4}[/tex]
Two lines are parallel if they have the same slope. So, in this case, the parallel line has a slope of -[tex]\frac{9}{8}[/tex] and has a form of: y= -[tex]\frac{9}{8}[/tex]x + b
The line passes through the point (-3, 2). Replacing in the expression for parallel line:
2= -[tex]\frac{9}{8}[/tex]× (-3) + b
2= [tex]\frac{27}{8}[/tex] + b
2- [tex]\frac{27}{8}[/tex]= b
- [tex]\frac{11}{8}[/tex]= b
Finally, the equation of parallel line is y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{11}{8}[/tex].
Equation of perpendicular line in this caseThe line is y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{1}{4}[/tex].
If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of -[tex]\frac{9}{8}[/tex]. So:
-[tex]\frac{9}{8}[/tex]× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-[tex]\frac{9}{8}[/tex])
slope perpendicular line= [tex]\frac{8}{9}[/tex]
So, the perpendicular line has a form of: y= [tex]\frac{8}{9}[/tex]x + b
The line passes through the point (-3, 2). Replacing in the expression for parallel line:
2= [tex]\frac{8}{9}[/tex]× (-3) + b
2= -[tex]\frac{8}{3}[/tex] + b
2+ [tex]\frac{8}{3}[/tex]= b
[tex]\frac{14}{3}[/tex]= b
Finally, the equation of of perpendicular line is y= [tex]\frac{8}{9}[/tex]x + [tex]\frac{14}{3}[/tex].
Learn more about parallel and perpendicular line:
https://brainly.com/question/7197064
https://brainly.com/question/11470863
https://brainly.com/question/7280013
#SPJ1
A carpenter is building a rectangular table. He wants the perimeter of the tabletop to be no more than 28 feet. He also wants the length of the tabletop to be greater than or equal to the square of 2 feet less than its width.
Create a system of inequalities to model the situation, where x represents the width of the tabletop and y represents the length of the tabletop. Then, use this system of inequalities to determine the viable solutions.
A. Part of the solution region includes a negative width; therefore, not all solutions are viable for the given situation.
B. No part of the solution region is viable because the length and width cannot be negative.
C. The entire solution region is viable.
D. Part of the solution region includes a negative length; therefore, not all solutions are viable for the given situation.
The solution from the system of inequalities is (a). Part of the solution region includes a negative width; therefore, not all solutions are viable for the given situation.
The system of inequalityLet P represent the perimeter.
So, we have:
P ≤ 28 ---- i.e. perimeter not more than 28y ≥ (x - 2)²The perimeter is calculated using:
P = 2(x + y)
So, we have:
2(x + y) ≤ 28
y ≥ (x - 2)²
Next, we plot the system of inequalities (see attachment)
From the attached graph, we have some negative x values in the shaded region.
This means that not all solutions are viable
Hence, the true statement is (a)
Read more about inequalities at:
https://brainly.com/question/25275758
#SPJ1
What is the equation of the circle with a radius of 7 and center at (6, -5)?
A (x + 6)2 + (y - 5)2 = 49
B (x - 6)2 + (y + 5)2 = 7
C (x + 6)2 + (y - 5)2 = 7
D (x - 6)2 + (y + 5)2 = 49
Answer:
D is the equation of the circle
three times the sum of x and y is increased by 5
Answer:
Here is the answer .Please mark as brainliest plshope its help you
Step-by-step explanation:
3(x+y)+5=0
3x+3y+5=0
or,3x+3y= -5
Answer:
3*(x+y) + 5
Step-by-step explanation:
This is an mathematical expression....it isi NOT an equation...the question does NOT say this is equal to zero (or anything else)
it is this 3 (x+y) + 5 or 3x + 3y + 5
Suppose that y varies inversely with x where x=4 and y=5. Solve for the constant
k and find the value of y when x=11
What is 75% of 99. Round your answer to the nearest hundredths.
Answer: 74.25
Step-by-step explanation:
75% ÷ 100 = 0.75
0.75 * 99
= 74.25
A cylinder has a base diameter of 6 cm and a height of 18 cm. What is its volume in cubic centimeters to the nearest tenths place?
Answer:
108 cm that my answer
sana makatulong
The answer is 508.9 cubed
108cm cubed is wrong
how can i solve this
Answer:
option c
Step-by-step explanation:
the first number of a exponential function is the y intercept when x = 0,
so we now the number will be 5 leaving only answers c or d
the easiest way see which one is correct is by inputting the numbers for x to find y so...
c) 5 x 2^1 = 5 x 2 = 10 so x = 1 than y = 10
d) 5 x 1/2^1 = 5 x 1/2 = 2.5 so x = 1 than y = 2.5
the table states that y = 10 when x = 1 making c correct
AND WELCOME TO BRAINLY!
In the whole number 70,819 the place value of the digit 1 is
Step-by-step explanation:
a number is a sequence of digits with every position being multiplied by increasing powers of 10.
and the whole number is then the sum of of these little multiplications.
the first position left of the decimal point is for 10⁰ (1). the second position is 10¹ (10). the third position for 10² (100). and so on.
the given number is therefore just the short version of
7×10⁴ + 0×10³ + 8×10² + 1×10¹ + 9×10⁰
and therefore, the digit 1 in this number has the value 1×10¹ = 10, which is also the place value, 10¹ = 10.
In October 2017 a pound of apples cost $1.55, while oranges cost $1.19. Two years earlier the price of apples was only $1.34 a pound and that of oranges was $1.05 a pound. What was the annual compound rate of growth in the price of apples
The annual growth rate in the price of the apple will be 7.83%.
What is the growth rate?
The growth rate is defined as the increment of any quantity over a period of time.
Given that:-
In October 2017 a pound of apples cost $1.55, while oranges cost $1.19.Two years earlier the price of apples was only $1.34 a pound and that of oranges was $1.05 a pound.The growth rate will be calculated as::-
Growth rate = Cost in 2017 / Cost in 2015
Growth rate = 1.55 / 1.34 = 1.15
The growth rate will be 15.67% for the apple in 2 years so for 1 year it will be
15.67 / 2 = 7.8%
Therefore the annual growth rate in the price of the apple will be 7.83%.
To know more about the growth rate follow
https://brainly.com/question/25849702
#SPJ1
what is 747-329 equal
Answer:
418
Step-by-step explanation:
Help !!!
Geometry and the circle
Answer:
Look at the explanation.
Step-by-step explanation:
To begin with, the center of a circle is obviously the point in the middle of the circle and it has the same distance where ever you distance the center point from a point on the edges. Hope this makes sense so far. The diameter is from one point of the circle to another point of the circle and the diameter is in the middle meaning if you folded the circle upon the diameter it should be half and half. Radii are half of the diameter. Chords of a circle are "the line segment joining any two points on the circumference of the circle".
So now:
Center is Point F, Radii could be segments FU or Segment KF, Diameter is KU, Chords of the circle could be Segment, VL, GL, or DX. I hope this is correct and hope it helps....
Answer:
Step-by-step explanation:
Center
Which point is the center is just a guess. You are intended to say F.
Radii
KF FUA radius is a line that goes from the center of a circle to the circumference.
Chord
A chord is a line segment that joins two points on the circumference. Believe it or not, the diameter of a circle is a chord.
KUDKVLGLDiameter
KU
Round 2.486.3 to The hundred this place.
Find the volume of a cylinder 9in 9in
Answer:
2290.22
Step-by-step explanation:
Formula: V=pi*r^2*h
Plug in the values:
V=pi*81*9
81*pi=~254.469
~254.469 * 9 = 2290.22
Solve by factoring y=4x^2-24x+36
Answer:
(x-3) (x-3)
Step-by-step explanation:
[tex]4x {}^{2} - 24x + 36 \\ dividing \: through \: by \: 4 \\ x {}^{2} - 6x { }^{} + 9 \\ two \: numbers \: such \: that \: when \: you \: add \: them \: they \: give \: you \: - 6 \: and \: when \: you \: multiply \: them \: they \: give \: 9 \\ the \: numbers \: are \: \: - 3 \: and \: - 3 \\ x {}^{2} - 3x - 3x + 9 \\ x( x - 3) - 3(x - 3) \\ (x - 3)(x - 3)[/tex]
A cylinder has a diameter of 5 centimeters and a height of 50 millimeters. Which of the following steps should be done
first in order to find the surface area of the cylinder?
O multiply the circumference of the circle by the height of the cylinder
o calculate the circumference of the circle
convert the diameter and the height to the same unit
o determine the radius and multiply by 2
NEXT QUESTION
ASK FOR HELP
TURN ITIN
Answer:
convert the diameter and the height to the same unit
Step-by-step explanation:
Answer: convert the diameter and the height to the same unit
Step-by-step explanation:
The surface area of a cylinder can be found with A = 2πrh + 2πr². To use this formula, all units of measurement must be the same.
This can be converting 5 centimeters to millimeters or converting 50 millimeters to 5 centimeters.
Select the correct answer.
If the graphs of the linear equations in a system are the same line, what does that mean about the possible solution or solutions of the system?
A. There is exactly one solution.
B. There is no solution.
C. There are infinitely many solutions.
D. The lines in a system cannot graph as the same line.
Answer:
c! :))
Step-by-step explanation:
i cant exactly remember how to explain it step by step, but all i remember is that i took a similar test not too long ago that had the same question!
Answer:
C. There are infinetly many solutions.
Step-by-step explanation:
A system of linear equations has infinite solutions when the graphs are the exact same line.
Ivan bought a suit on sale for $152. This price was 60% less than the original price.
What was the original price?
Work Shown:
x = original price in dollars
x - 60% of x = x - 0.60x = 0.40x = sale price in dollars
0.40x = 152
x = 152/0.40
x = 380
If there are 12 people, and each person has 3 coins, there are ____ times as many coins as people
Answer:
Step-by-step explanation:
The first three terms of an arithmetic progression are 2x, x+4, 2x - 7 respectively.
a. Find the value of x
b. Find the three terms
(6 m
c. What is the common difference?
Answer:
a) x = 7.5
b) 15, 11.5, 8
c) -3.5
Step-by-step explanation:
As there is a common difference between consecutive terms of an arithmetic progression, then:
[tex]a_3-a_2=a_2-a_1[/tex]
Given:
[tex]a_1=2x[/tex][tex]a_2=x+4[/tex][tex]a_3=2x-7[/tex]Therefore:
[tex]\implies a_3-a_2=a_2-a_1[/tex]
[tex]\implies (2x-7)-(x+4)=(x+4)-2x[/tex]
[tex]\implies 2x-7-x-4=x+4-2x[/tex]
[tex]\implies x-11=-x+4[/tex]
[tex]\implies 2x=15[/tex]
[tex]\implies x=7.5[/tex]
Inputting the found value of x into the term expressions to find the three terms of the arithmetic progression:
[tex]a_1=2(7.5)=15[/tex][tex]a_2=(7.5)+4=11.5[/tex][tex]a_3=2(7.5)-7=8[/tex]The common difference (d) is the difference between each consecutive term. To find the common difference, subtract one term from the next term:
[tex]\implies d=a_3-a_2= 8 - 11.5 = -3.5[/tex]
[tex]\implies d=a_2-a_1= 11.5-15 = -3.5[/tex]
Therefore, the common difference is -3.5
you take out a cash advance of
Answer:
$0
Step-by-step explanation:
Since there is no useful data in this question, we will fill in the blanks with what we know:
Amount of cash taken: $0
Therefore, you have taken a cash advance of $0
LOL
Please help surface area of a triangle
Answer:
A≈391.18
Step-by-step explanation:
The formula to find the surface area of a triangular prism is as follows:
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)
Plug in . .
A=ah+bh+ch+[tex]\frac{1}{2}[/tex][tex]\sqrt{ a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4}[/tex]
A = 6 * 20 + 6 * 20 + 6 * 20 + [tex]\frac{1}{2}[/tex] * [tex]\sqrt{64 + 2 * (6 * 6)2 + 2 * (6 * 6)2 - 64 + 2 *(6 * 6)2 * 64}[/tex]
A≈391.18
Answer:
391.2 square cm
Step-by-step explanation:
Surface area of triangular prisml = 20 cm
Base area = 15.6 square cm
[tex]\sf \boxed{\text{Surface area of triangular prism = Perimeter of base * l + 2*base area}}[/tex]
= (6+6+6)*20 + 2*15.6
= 18*20 + 31.2
= 360 +31.2
= 391.2 square cm
A delicatessen makes a roast-beef-on-sourdough sandwich for which you can choose from eight condiments. a. How many different types of roast-beef-on-sourdough sandwiches can the delicatessen prepare? b. What is the minimum number of condiments the delicatessen must have available if it wishes to offer at least 1000
different types of roast-beef-on-sourdough sandwiches?
Analyzing the information, it is clear that to find the solutions of the problems it is necessary to perform the calculation of mathematical arrangements.
What are arrangements?Correspond to a case of permutations, they are groupings that are formed with a number p of elements from a set of n elements. The elements of p must occupy ordered positions, where p ≤ n. The formula is:
A = n!/(n-p)!So, to solve the problems we do the following calculations:
A) 2^n =
2^8 = 256
B) We must pay attention to the statement, which asks for the minimum number of condiments required to prepare 1000 different sandwiches, so:
2^n [tex]\geq[/tex] 1000
n = 3
2^3 = 8
Find out more about arrangements here:
https://brainly.com/question/6032811
#SPJ1
Find the perimeter of the figure below
Perimeter=
If the diameter of a circle is 14 inches, which of the following is the best approximation of the area of the circle?
Answer: 153.93791 inches³
Step-by-step explanation:
Area of a circle = pi * r²
Area of a circle = pi * 7²
Area of a circle = 3.14159 * 49
Area of a circle = 153.93791 inches³
We can't see you answer choices, so select the best answer choice that is closest to 153.93791 in³
Need Help please 3rd time posting this.
Evaluate 52+[x divided3] when x=15
Answer: A. 30
Step-by-step explanation:
We will plug the value of x, 15, into the given expression. Then, we will use the order of operations, also known as PEMDAS. View attached if you need a review.
5² + (x / 3)
5² + (15 / 3)
25 + (5)
30
A. 30
PLEASE HELP!!! IMA DESPRATE!!!!!Use first and second differences to find the next three terms in the following sequence.
8, 11, 19, 35, 62,...
The next term of the given sequence using first and second differences is; 104
How to find the terms of a Sequence?We are given the sequence as;
8, 11, 19, 35, 62,.....
Thus, using the first and second differences, we have the sequence pattern as;
8 11 19 35 62 104
3 8 16 27 42
5 8 11 15
3 3 4
From the above pattern, we can see that the next term of the sequence is 104
Read more about Terms of a Sequence at;https://brainly.com/question/7882626
#SPJ1
Natalie invested $40,000 in an account paying an interest rate of 8 % compounded
continuously. Mackenzie invested $40,000 in an account paying an interest rate of
9 % compounded daily. After 20 years, how much more money would Mackenzie
have in her account than Natalie, to the nearest dollar?
%
Answer:
8000
Step-by-step explanation:
Natalie
Divide 40k by 2 to get 20k and divide 20k by 5 to get 4k we are at 10%
4k / 5 = 800 that means that every 2% is 800 now we multiply by 4x
To get 8% and we get 3200 and multiply by 20 representing the yrs
3200 x 20 = 64k + 40+ = 104k
Mackenzie
40k divide by 2 to get 50% 40k / 2 = 20k and now we divide by 5 to get 10% 20k / 5 = 4k now we divide by 10 to get the amount of each percents worth 4k / 10 = 400 we multiply by 9 to get the compounded interest
400 x 9 = 3600 multiply by 20 to get the compounded daily investment after 20yrs 3600 x 20 = 72k + 40k = 112k
112k - 104k = 8k
Robert delivers papers every morning. On Sundays he has to deliver 61 papers and on each of the other days he only has to
deliver 44 papers. How many papers does Robert deliver each week?
A. 369
B. 325
C. 413
D. 427
Answer:
B. 325
Step-by-step explanation:
y = the total value of the amount of papers he has to deliver each week
44x + 61 = y
(7 days in a week - sunday = 6 days)
44(6) + 61 = y
264 + 61 = y
325 = y