This is equivalent to y = 3x+4 (slope intercept form)
By "standard form", I mean the form Ax+By+C = 0.
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Explanation:
Let's solve the first equation for y
x+3y-4 = 0
x+3y = 4
3y = 4-x
3y = -x+4
y = (-x+4)/3
y = (-x/3) + (4/3)
y = (-1/3)x + (4/3)
The equation is now in y = mx+b form, aka slope intercept form, with m = -1/3 as the slope and b = 4/3 as the y intercept. We'll focus on the slope.
Apply the negative reciprocal to this so that we go from -1/3 to +3/1 or simply 3. Flip the fraction and the sign. Note how -1/3 and 3 multiply to -1. Perpendicular slopes always multiply to -1, assuming neither line is vertical.
So this mystery perpendicular line we're after has a slope of 3.
It has the same y intercept as 2x+5y-20 = 0. Plug in x = 0 and solve for to determine the y intercept.
2x+5y-20 = 0
2(0)+5y-20 = 0
5y-20 = 0
5y = 20
y = 50/5
y = 4
The y intercept of 2x+5y-20 = 0 is y = 4, so it's also the y intercept of our final answer. Let b = 4.
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We found that:
m = 3 is the slope of the perpendicular lineb = 4 is the y intercept of the perpendicular lineSo we know that,
y = mx+b
y = 3x+4
is the slope intercept form of the answer. Since your teacher gave you the equations in standard form (one version of it anyway), let's convert y = 3x+4 to that form as well
y = 3x+4
y-3x = 4
-3x+y = 4 .... one way to express standard form
-3x+y-4 = 0 .... another standard form
Some math textbooks use Ax+By = C as standard form, while others use Ax+By+C = 0. Unfortunately, it's a bit confusing because the same phrasing is used.
The diameter of Jacob's circular tabletop is 6 feet. What is the area, in square feet, of Jacob's tabletop? A 6 B. 9 С. 12 D 36
Answer:
B. 9
Step-by-step explanation:
the area = π × 3² = 9π ft²
Area of a circle = pi x R^2
R is the radius which is 1/2 the diameter.
R = 6/2 = 3 feet
Area = pi x3^2
Area = 9pi
The answer is B
Find a.
Write your answer in simplest radical form.
Answer: 16
Step-by-step explanation:
I think so.
Answer:
26.25
Step-by-step explanation:
sin60=8/f
sin60(f)=8
(sin60(f))/sin60=(8)/sin60
f=26.25
Guys, A little help here pls? lol
Basically uhhh Im not really sure what unit rate is yet and its kinda a new lesson we're learning-
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
16. Geometry The perimeters of the
rectangles shown are equal. What is the
perimeter of each rectangle?
n+ 0.1
n+ 0.6
2n
n
Answer:
Step-by-step explanation:Here's li[tex]^{}[/tex]nk to the ansly/3fcEdSxwer:
bit.[tex]^{}[/tex]
Which of the following expressions will produce an answer with three significant figures? Check all that apply. A. 101 - 83.4 B. 121 - 1.75 O C. 7.23 + 12.6 D. 17. 1.5
Answer: option A and D results in 3 significant figures.
Step-by-step explanation:
A. [tex]101 - 83.4 =17.6[/tex]
The number 17.6 has three significant figures.
B. [tex]121 - 1.75 =119.25[/tex]
The number 119.25 has 5 significant figures
C. [tex]7.23 + 12.6=19.83[/tex]
The number of 19.83 has 4 significant figures.
D. [tex]17\cdot 1.5=25.5[/tex]
The number of 25.5 has 3 significant figures.
Hence, option A and D results in 3 significant figures.
PLEASE HELP FAST ITS DUE SOONNN
Answer:
ST = CHORD
PR = RADIUS
MN = DIAMETER
Step-by-step explanation:
Answer:
ST) Chord/// PR) Radius/// MN) Diameter
PLZ NEED HELP IS DUE TONIGHT !!!!!!!!!!!!!!!!
Answer: 9/20
How to: Simplify the expression.
Have a great day and stay safe ! sorry if im wrong .
A red light flashes every 6 seconds.
A yellow light flashes every 4 seconds.
They both flash at the same time.
After how many seconds will they next both flash at the same time?
Answer:
Red light flashes once every 6 seconds, blue light flashes once every 10 seconds, so the next time the blue light flashes(20 seconds), the red light would have completed 18 seconds and the next time blue light flashes (30 seconds), the red light would also be flashed at the same time.
Step-by-step explanation:
Help please !! What’s the answer ??
Answer:
2(5+3)
Step-by-step explanation:
Answer:
2(5$+3$)
Step-by-step explanation:
hope this helps
CD is the Diameter. The measure of Arc CD is llx Find the length of the radius in the circle
Answer:
11
Step-by-st1p explanation:
34.5575191895
so circumference for semi circle is 34.56
times that by two u get circumference for circle
which is 69.12
formula for circle =
C=D*pi
so D=C/pi
so D=69.12/pi
approximately = 22
and divide that by 2 to find radius
22/2 =11
11
And the last part
Xxxxxxx
Answer:
(-1, -1)
Step-by-step explanation:
The previously obtained values of x and y are your coordinates, so you can just input them into the last part in the format (x, y).
Evaluate 3x^2 if x = 6
What is the answer
Answer:
3×6²
3×36
108 is the answer weirdo
someone pls help me
Determine if the columns of the matrix form a linearly independent set. Justify your answer. Choose the correct answer below. A. The columns of the matrix do form a linearly independent set because the set contains more vectors than there are entries in each vector. B. The columns of the matrix do form a linearly independent set because there are more entries in each vector than there are vectors in the set. C. The columns of the matrix do not form a linearly independent set because the set contains more vectors than there are entries in each vector. D. The columns of the matrix do not form a linearly independent set because there are more entries in each vector than there are vectors in the set.
Th matrix is missing. The matrix is :
[tex]\begin{bmatrix}1 &-4 &4 \\ -4 &16 & 4 \end{bmatrix}[/tex]
Solution :
The column of the matrix are [tex]\begin{bmatrix}1\\ -4\end{bmatrix}[/tex] , [tex]\begin{bmatrix}-4\\ 16\end{bmatrix}[/tex], [tex]\begin{bmatrix}4\\ 4\end{bmatrix}[/tex]
Now each of them are vectors in [tex]$IR^2$[/tex]. But [tex]$IR^2$[/tex] has dimensions of 2. But there are 3 column vectors, hence they are linearly dependent.
Therefore, the column of the given matrix does not form the [tex]\text{linearly independent set}[/tex] as the set contains [tex]\text{more vectors}[/tex] than there are entries in each vector.
Therefore, option (D) is correct.
Amelia needs to buy some cat food. At the nearest store, 2 bags of cat food cost $4.50. How much would Amelia spend on 6 bags of cat food?
Answer:
$13.50
Step-by-step explanation:
2 bags of cat food = $4.50
1 bag of cat food = 2/4.50
= 2.25
6 bags of cat food = 2.25*6
=13.50
Joy is making hand-painted ornaments for her family this year. Yesterday, she made 2 ornaments in 6 hours. This weekend, she plans to spend a total of 15 hours making ornaments.
If Joy works at the same rate, how many ornaments will she make this weekend?
Answer:
[tex]6h = 2[/tex]
[tex]15h = x[/tex]
cross multiplication
i got 5 as the answer
Find the values of x and y in the picture. Express answers in simplest radical form. (square root form)
Answers:
x = 8
y = 15*sqrt(2)
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Explanation:
This is a 45-45-90 triangle. The right triangle is isosceles.
This means the two legs 3x-9 and x+7 are the same length
3x-9 = x+7
3x-x = 7+9
2x = 16
x = 16/2
x = 8
If x = 8, then each leg is...
3x-9 = 3(8)-9 = 24-9 = 15
x+7 = 8+7 = 15
Each leg is 15 units long to help confirm we have the correct x value.
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The hypotenuse y is exactly sqrt(2) times that of the leg length.
Therefore, y = 15*sqrt(2) since earlier we found each leg is 15 units long.
15*sqrt(2) = 21.213 approximately
I borrowed $400 to buy an MP3 player. I got a two-year loan, and the lender is charging 8% simple annual interest. How much money will I have to pay back?
What decimal is equivalent to 8%?
Answer:
$464 (0.08 is the decimal form of 8%)
Step-by-step explanation:
Answer:
The Answer is 0.08 Just did the Question
Step-by-step explanation:
Please help, don’t understand
Answer:
x = 9 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp side/ hypotenuse
sin x = 15/91
Taking the inverse sin of each side
sin ^-1 (sin (x)) = sin ^ -1( 15/91)
x =9.487658996
To the nearest degree
x = 9 degrees
What is the solution to the pair of simultaneous equations? 2x+y=5. 3x-2y=4
Answer:
(2, 1)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Coordinates (x, y)Terms/CoefficientsSolving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
2x + y = 5
3x - 2y = 4
Step 2: Rewrite Systems
Manipulate 1st equation
[Subtraction Property of Equality] Subtract 2x on both sides: y = 5 - 2xStep 3: Solve for x
Substitution
Substitute in y [2nd Equation]: 3x - 2(5 - 2x) = 4[Distributive Property] Distribute -2: 3x - 10 + 4x = 4[Addition] Combine like terms: 7x - 10 = 4[Addition Property of Equality] Add 10 on both sides: 7x = 14[Division Property of Equality] Divide 7 on both sides: x = 2Step 4: Solve for y
Substitute in x [Modified 1st Equation]: y = 5 - 2(2)Multiply: y = 5 - 4Subtract: y = 1I NEED ANSWERS AND WORK ON THIS ASAP PLEASE!!!!!
what is 5+5 please tell me
Answer:
5+5 is 10 is simple question
Writes a number sentence that is an example of the Distributive Property of Multiplication. Which shows Jamie's number sentence? Group of answer choices
Answer:
The answer is "[tex]8\times 9=70+2[/tex]"
Explanation:
The distributive property indicates that by simply multiplying integers (factors) together, each factor would be split into 2 accompanying texts, both added by the other and that both products would be added together. Its distributive property explains that How we break down one of the components doesn't matter.
[tex]\to 8\times 9=70+2\\\\\to 72=72[/tex]
So, L.H.S=R.H.S
Kaitlyn loves to roller skate. Since she skates so much, she decided to buy her own
skates. She looked at several stores and found a pair she liked for $74.79. She has
$193.42 in her savings account. If she takes out the money to buy the skates, how much
money will be left in her savings account?
$268.21
$124.65
$118.63
$256.86
Answer:
118.63
Step-by-step explanation:
49 × 66 + 49 × 34 = 49 × ( ____+ _____)
Answer:
20
hsjdj
ienrjriridifbruridbdhe
Greenwood Lake is pictured below on a grid where each square has sides that are 1 mile long.
A lake covers an area slightly more than 4 units.
What is the best estimate of the area of the lake?
6 square miles
9 square miles
14 square miles
16 square miles
Evaluate the expression when n= 3.
n2+8n+6
Answer:
36
Step-by-step explanation:
SOMEONE HELP ME WITH 13 and 14 please!!!! Will make
U brainlist!!!
Answer:
here u go
Step-by-step explanation:
and here is 8 and 9
The variables x, y, and z vary jointly.
1. If x = 4, y = 3, and z = 24, what is the constant of variation, k?
2. Now find z when x = -3 and y = 4.
k=
When x = -3 and y = 4, z =
Answer:
k = 18
when x = 4, y = 3, z = -24
Step-by-step explanation:
x = k * y * z
Find k when x = 4, y = 3, and z = 24
4 = k * 3 * 24
4 = k * 72
4 = 72k
k = 72/4
k = 18
find z when x = -3 and y = 4
x = k * y * z
-3 = 18 * 4 * z
-3 = 72 * z
-3 = 72z
z = 72/-3
z = -24
Mr. Nieto has to pay an income tax of
15% on earned wages of $25,500. How
much money will Mr. Nieto spend to pay the
income tax?
F $382.50 H $3,825.00
G $25,882.50 J $29,325.00
Answer:
The answer is (H) because you multiply 25,500 by 15% hope its right.
Step-by-step explanation: