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[tex]3y - 4x = - 8[/tex]
Add sides 4x
[tex]3y - 4x + 4x = 4x - 8[/tex]
[tex]3y = 4x - 8[/tex]
Divide sides by 3
[tex] \frac{3}{3} y = \frac{4}{3} x - \frac{8}{3} \\ [/tex]
[tex]y = \frac{4}{3} x - 8 \\ [/tex]
This is the slope-intercept form of the line.
We that the coefficient of the x in slope-intercept form , is the slope of the line.
Thus ;
[tex]slope = \frac{4}{3} \\ [/tex]
_________________________________
Remember from now on ;
Multiply of the slopes of the lines which are perpendicular to each other equal -1 .
Suppose the slope of the line which question asked is m.
So :
[tex] \frac{3}{4} \times m = - 1 \\ [/tex]
Multiply sides by 4
[tex]4 \times \frac{3}{4} \times m = 4 \times ( - 1) \\ [/tex]
[tex]3m = - 4[/tex]
Divide sides by 3
[tex] \frac{3}{3} m = \frac{ - 4}{3} \\ [/tex]
[tex]m = - \frac{4}{3} \\ [/tex]
Done...
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The ratio of apples to oranges in a basket of fruit is 2:7. There are 21 oranges in the
basket. How many apples are in the basket?
Answer:
6
Step-by-step explanation:
The given ratio specifies the number of apples to be found in the basket
for a given number of oranges.
Correct response:
The number of apples in the basket are 6 applesMethods of calculationThe given ratio of apples to oranges in the basket of fruits = 2:7
The number of oranges = 21 oranges
Required:
The number of apples in the basket.
Solution:
The given ratio can be expressed as follows;
[tex]\mathbf{\dfrac{Number \ of \ apples}{Number \ of \ oranges}} = \dfrac{2}{7} [/tex]Which gives;
[tex]\dfrac{Number \ of \ apples}{21} = \dfrac{2}{7} [/tex]
7 × (Number of apples) = 2 × 21
[tex]Number \ of \ apples = \dfrac{2 \times 21}{7} = 6[/tex]
The number of apples in the basket = 6 applesLearn more about ratios here:
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Suppose that you borrow $11000 for 4 years at 6% toward the purchase of a car. Find the monthly payments and the total interest for the loan.
Answer:
The monthly payments ≅ $258.335
The total interest of the loan ≅ $1400.095
Step-by-step explanation:
The rule of the monthly payments is
[tex]M.P=\frac{P(\frac{r}{n})}{1-(1+\frac{r}{n})^{-nt}}[/tex] , where
P is the initial amountr is the rate in decimaln is the period in a yeart is the number of years∵ You borrow $11000
∴ P = 11000
∵ It will be for 4 years
∴ t = 4
∵ The rate is 6%
∴ r = 6% = [tex]\frac{6}{100}[/tex] = 0.06
∵ It is a monthly payment
∴ n = 12
→ Substitute these values in the rule above
∴ [tex]M.P=\frac{11000(\frac{0.06}{12})}{1-(1+\frac{0.06}{12})^{-12(4)}}[/tex]
→ Use your calculator to find the answer
∴ M.P = 258.3353195
∴ The monthly payments ≅ $258.335
→ The total interest of the loan is the difference between the total
of the monthly payments and the initial amount
∴ The total interest of the loan = T.M.P - P
∵ The total of the monthly payments = M.P × t × n
∴ The total of the monthly payments = 258.3353195 × 4 × 12
∴ The total of the monthly payments = $12400.09534
∵ The initial amount P = $11000
∴ The total interest of the loan = 12400.09534 - 11000
∴ The total interest of the loan = 1400.095
∴ The total interest of the loan ≅ $1400.095
Divied. Reduce the awnser to lowest terms 4/5 divided by 16/15
Answer:
B:3/4
Step-by-step explanation:
4/5÷16/15= 4/5×15/16= 60/80.
And take 60/80 ÷ 2= 3/4
can sommeone please answer this
Answer:
x= 8
z= 116 degrees
Step-by-step explanation:
the two given angle measures are vertical angles so they are equal to each other, the equation is: 12x-32 = 11x-24
simplify this to get: x= 8
plug the value of x into either of the given equations, I will use the first one: 12(8) - 32
this means that the angle of one of them is 64
and since z and 12x-32 make a straight angle (180 degrees)
you can subtract 64 from 180 to find z
this gives you 180-64 = 116
Linear combination of matrices
Step-by-step explanation:
2B=
10 8 6
0 -6 6
4 12 14
6C=
24 30 36
42 0 18
6 -12 0
so 2B+6C=. 34 38 42
42 -6 24
10 0 14
how do you solve
x2 - 4xy + 4y
Answer: x2-4xy+4y=2xy-5y+2y
Step-by-step explanation:
what’s the unit rate for 10 1/3 miles per 1/6 hour
Points J, K, and L are collinear one, and JL: LK = J is located at (-3,5), K is located at (1,-10) and Lis located at (x, y). What are the values of x and y?
9514 1404 393
Answer:
L = (x, y) = (1/5, -7)
Step-by-step explanation:
The given relation tells you ...
(L -J)/(K -L) = 4/1
Cross-multiplying, we have ...
L -J = 4(K -L)
5L = 4K +J . . . . add 4L+J
L = (4K +J)/5
L = (4(1, -10) +(-3, 5))/5 = (4-3, -40+5)/5
L = (x, y) = (1/5, -7)
Which of the following statements is true concerning ABC below?
Answer:
A is the answear. so jst pick A
Which of the following should come next at the end of this row of letters? XOOOOXXOOOXXX:
a. oxxx, b. ooxx, c. xooo
Answer:
b
Step-by-step explanation:
The correct option that should come next at the end of this row of letters is OOXX.
What is a sequence?A sequence can be defined as an arrangement of letters or numbers in a particular manner.
If you look at the given sequence it can be seen as the set of 5 letters where X is starting the set while O is ending the series. Also, the number of X will tend to increase in the next set as well while the number of O will be reduced. Therefore, the series can be seen as,
XOOOO XXOOO XXXOO XXXXO
Thus, the correct option that should come next at the end of this row of letters is OOXX.
Learn more about Sequence:
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1 2 3 4 5 6 7 8 9 10 which of the following could be the number shown on the number line a.38 b.37 c.35 d.30
Subtract the rational expressions x/x+1 - 2/x
Answer:
(2x-2)/x
Step-by-step explanation:
x/x-2/x+1
LCM is x
(x-2+x)/x
(2x-2)/x
If g(x) =5-9x and f(x) = 5+ 3x
Find g(2)
Find f(g(2))
Answer:
Step-by-step explanation:
g(2)= 5-9(2)
= -13
f(g(2))= 5+3(-13)
= -34
Answer:
g(2) = -13
f(g(2)) = -34
Explanation:
For g(2), just substitute 2 in for the x, multiply, and simplify.
g(x) = 5-9(x)
g(2) = 5-9(2) = 5-18 = -13
For f(g(2)), substitute this output in for x, multiply, and simplify.
f(x) = 5 + 3(x)
f(g(2)) = 5 + 3(g(2)) = 5 + 3(-13) = 5-39 = -34
In 1902, the yearly attendance at a major league baseball park was 3.4 × 105 people.
One hundred years later, the yearly attendance was 1.7 × 106 fans.
How many times greater was the attendance in 2002 than in 1902? Enter your answer in the box.
Answer:
The number of attendance is 5 times greater than in 1902.
Step-by-step explanation:
Since we have given that
Number of attendance at a major league baseball park in 1902 =
Number of attendance at a major league baseball park in 2002 =
We need to find the number of times that the attendance in 2002 is greater than in 1902.
So, number of times becomes,
Hence, the number of attendance is 5 times greater than in 1902.
5 x 7 = 7 x 5
What algebraic property is illustrated above?
A. commutative property of multiplication
B. associative property of multiplication
C. distributive property
D. transitive property
Answer:
A. commutative property of multiplication
Step-by-step explanation:
The commutative property of multiplication ,
States that when two numbers are being multiplied, their order can be changed without affecting the product.
EDGE 2020
Which trigonometric functions have the same maximum value?
y = arcsinx and y = arccosx
y = arcsinx and y = arctanx
y = arctanx and y = arcsecx
y = arccosx and y = arcsecx
Answer:
D. y = arccosx and y = arcsecx
Step-by-step explanation:
got it right on edge :)
Answer:
The trigonometric function which have the same maximum value is:
y = arcsinx and y = cos x
Concept:
What are Inverse trigonometric functions?
Inverse trigonometric functions are represented as arcsinx, arccosx, arcsecx, and so on.
The trigonometric functions that are used to calculate an angle from any of the angle's trigonometric ratios are called inverse functions.
The formula which is used to in inverse trigonometric equations are:
arcsinx = -arcsinx
arccosx = pi-arccosx
arctanx = -arctanx
arcsecx = pi - arcsecx
Solution:
The maximum values we obtain from the following equations are:
arcsinx = -1 to 1
arccosx = -1 to 1
arctanx = -pi/2 to pi/2
arcsecx = ∞
So the trigonometric functions which have the same maximum value is arcsinx and arccosx.
Learn more about "inverse trigonometric functions" here-
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how do i put this into factored form? (x-4)^2-9=0
Answer:
x=7,1
Step-by-step explanation:
Use Math Way
What is an equation of the line passes through the points (-6,2) and (6,-2)?
Answer:
The equation for the question above is y = -1/3x.
Find the slope (3, 7) (-2, 7)
Answer:
(-5,0)
Step-by-step explanation:
The X coordinates go down by five = -5
The Y coordinates don't change = 0
I'm pretty sure this is right :)
Hope it helped!
Answer:
Answer BelowStep-by-step explanation:
Hope this helps! <3
How do you do this question?
Exact value: [tex]c = \frac{-11+\sqrt{165}}{22}[/tex]
Approximate value: c = 0.08387
Round the approximate value however you need to
==============================================
Work Shown:
Let x = 1+c
[tex]\displaystyle S = \sum_{n=2}^{\infty}(1+c)^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}x^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}\frac{1}{x^n}\\\\\\\displaystyle S = \frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^4}\ldots\\\\\\[/tex]
We have an infinite geometric series here. The first term is a = 1/(x^2). The common ratio is r = 1/x.
Each new term is found by multiplying the previous term by 1/x.
Assuming -1 < r < 1 is true, the infinite geometric sum is
[tex]S = \frac{a}{1-r}\\\\\\S = \frac{1/x^2}{1-1/x}\\\\\\S = \frac{1/x^2}{x/x-1/x}\\\\\\S = \frac{1/x^2}{(x-1)/x}\\\\\\S = \frac{1}{x^2}\div\frac{x-1}{x}\\\\\\S = \frac{1}{x^2}*\frac{x}{x-1}\\\\\\S = \frac{1}{x^2-x}\\\\\\[/tex]
Plug in S = 11 and solve for x
[tex]S = \frac{1}{x^2-x}\\\\11 = \frac{1}{x^2-x}\\\\11(x^2-x) = 1\\\\11x^2-11x = 1\\\\11x^2-11x-1 = 0\\\\[/tex]
Use the quadratic formula to find the two solutions
[tex]x = \frac{11+\sqrt{165}}{22} \approx 1.08387\\\\x = \frac{11-\sqrt{165}}{22} \approx -0.08387\\\\[/tex]
Using these x values, we find that the corresponding r values are
r = 1/x = 1/(1.08387) = 0.92262
r = 1/x = 1/(-0.08387) = -11.92321
The first r value makes -1 < r < 1 true, but the second r value does not. So we will be ignoring the solution x = -0.08387
----------------------------------------------
Using the solution that corresponds to x = 1.08387, we find the value of c is
[tex]x = c+1\\\\c = x-1\\\\c = \frac{11+\sqrt{165}}{22}-1\\\\c = \frac{11+\sqrt{165}}{22}-\frac{22}{22}\\\\c = \frac{11+\sqrt{165}-22}{22}\\\\c = \frac{-11+\sqrt{165}}{22}\\\\c \approx 0.08387\\\\[/tex]
Evaluate the expression.
10.56÷3−1.9=
Ryan picked 7 apples.David picked 4 times as many apples.How manyapples did he picked
Answer:
28
Step-by-step explanation:
7*4
Which fraction is equivalent to 2/6?
Answer:3/9
Step-by-step explanation: 2/6=1/3. And 1/3x3=3/9
1. Pedro bought seven dozen candy bars to give out on Halloween night. He gave each trick-or-treater two candy
bars. At the end of the night, he had 14 candy bars left. How Many Trick-or-treaters did he have
Answer:
28 or it is 42
Step-by-step explanation:
Answer:
35
Step-by-step explanation:
First, you need to know 7 dozen, which is 7*12, which equals 84. Altogether, Pedro had 84 candy bars. He had 14 candy bars left over. 84-14=70 He used 70 candy bars. He gave 2 to each trick-or-treater, so do 70/2=35. He had 35 trick-or-treaters.
not sure need help
Answer:
8.2
Step-by-step explanation:
Mel drove 432 miles during his trip. He drove an average of 72 miles per hour. How long was his trip?
Answer:
6h
Step-by-step explanation:
If he drove 72 mph and you know how long he drove, just need to divide:
[tex]Distance / Speed = Time[/tex]
Therefore:
[tex]432 / 72mph = 6h[/tex]
Answer:
hi its just like the dood above me said *dude sorry if i was late
Step-by-step explanation:
(x7) - 3 = 4
What does x =
How do I solve for x
x divided by 7 - 3 = 4
how do i find out what X equals
Answer:
detailed one
Please mark as the BRAINLIEST
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What is the y-intercept of the function y= -1/2cos(3/2x)
Answer: (0,-1/2)
Step-by-step explanation:
Edge :-)
Answer: (0,-1/2)
Step-by-step explanation:
enrico is laying 1-ft tiles ok a square bathroom floor. if he needs 81 tiles to cover the floor, how many tiles run along each wall?
Answer:
9
Step-by-step explanation:
you would need to find the square root of the total amount of tiles. luckily 81 is a square number meaning the answer is each side is 9 tiles long.
Which of the following statements best describes the effect of replacing the graph of f(x) with the graph of f(x) + 4? (1 point)
The graph shifts 4 units up.
The graph shifts 4 units down.
The graph shifts 4 units left.
The graph shifts 4 units right.
Answer:
C The graph shifts 4 units left.
Step-by-step explanation:
Answer: its A
Step-by-step explanation:
i took the test on flvs lol