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2 years ago

Which line on the graph represents the equation y=3x-2

Mathematics

1 answer:

Vika [28.1K]2 years ago

5 0

Answer:

Line A.

Step-by-step explanation:

When you put x as zero into 3x-2, you get 3(0)-2. That equals -2. Therefore, y = -2. When x=0, that is the y-intercept, so the y-intercept is -2. Line A crosses the y-axis at -2, so line A has that y-intercept.

Slope is always y/x. On a graph, that is the number of squares UP over the number of squares ACROSS. Counting, we get, 3 squares up over 1 square across for line A. 3/1= 3. The slope is the number we multiply by x. In the equation, that is 3, because we see 3x, and no sign or space between 2 numbers automatically means we multiply. So line A also has the correct slope.

In linear equations (straight lines), the same slope and y-intercept are enough to tell you that the equation matches the line.

Therefore, the answer is A!

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If (1/4)^(x+y) = 256 and log₄(x-y) = 3, what are the exact values of x and y

andrew-mc [135]

Answer:

x = 30 and y = -34

Step-by-step explanation:

Given the following functions

(1/4)^(x+y) = 256... 1

log₄(x-y) = 3.... 2

From equation 2;

x-y = 4³

x-y = 64

x = 64 + y ... 3

Substitutw 3 into 1

From 1:

(1/4)^(x+y) = 256

(1/4)^(64+y+y) = 256

(1/4)^(64+2y) = 256

Take log₄ of both sides

64+2y log₄ (1/4) = log₄256

-(64+2y) = 4log₄4

-(64+2y) = 4

64+2y = -4

2y = -4 - 64

2y = -68

y = -34

Since

x = 64 + y .

x = 64 - 34

x = 30

Hence x = 30 and y = -34

6 0

3 years ago

Solving systems by Substitution Homework y=x+4 y=x-3

zvonat [6]

There is no solution for this equation since they have the same slope, x/1. The only difference between these two is that their y intercepts are different meaning that they will be parallel lines that will never intersect among one other. For example, think of it as two separate lines that are have the same slope and never gain more distance/units from one another.

Solve:

To solve, you have to get one of this equations into a Ax+By=C equation form, standard equation. Let’s change y=x+4 into a standard equation.

We have to get x and y together and 4 as C.
So let’s subtract x from both sides;

y=x+4
-x -x
————————
-x+y=4

This is a standard equation.

Now let’s substitute.

take the standard equation and plug in y which is x+4 since there is a equation meaning it’s y=x+4

-x+(x+4)=4

Let’s simplify this mess.

-x+x equals 0. So we are left with 4=4.

Subtract 4 from both sides and we get 0=0

This means there is no solution. Hoped this helped.

8 0

3 years ago

Veronica is choosing between two health clubs after how many months will the total cost for each health club be the same

Assoli18 [71]

Question:

Veronica is choosing between two health clubs. after how many months will the total cost for each health club be the same? yoga studio a: membership: $24.00 monthly fee: 21.50. yoga studio b: membership: $41.00 monthly fee: $17.25

Answer:

It takes 4 years for the total cost of each club to become equal

Step-by-step explanation:

Given:

For yoga studio A:

membership: $24.00

monthly fee: 21.50.

For yoga studio B:

membership: $41.00

monthly fee: $17.25

To Find:

Number of months after which the total cost for each health club be the same = ?

Solution:

Let x be the number of months of membership, and y be equal the total cost.

For Yoga club A

y = 21.50 x + 24

For Yoga club B

y = 17.25 x + 41.00

we know that the prices, y , would be equal, we can set the two equations equal to each other.

21.50 x + 24 =17.25 x+ 41.00

Grouping the like terms,

21.50x - 17.25 x= 41.00 - 24

4.25x=17

x= $\frac{17}{4.25}$

x = 4

6 0

3 years ago

From a boat on the lake, the angle of elevation to the top of a cliff is 26°35'. If the base of the cliff is 85 feet from the bo

Trava [24]

Check the picture below

now, <span>26°35' is just 26bdegrees and 35 minutes

your calculator most likely will have a button [ </span><span>° ' " ] to enter degrees and minutes and seconds

there are 60 minutes in 1 degree and 60 seconds in 1 minute

so.. you could also just convert the 35' to 35/60 degrees

so </span> $\bf 26^o35'\implies 26+\frac{35}{60}\implies \cfrac{1595}{60}\iff \cfrac{319}{12}
\\\\\\
tan(26^o35')\iff tan\left[ \left( \cfrac{391}{12} \right)^o \right]$

now, the angle is in degrees, thus, make sure your calculator is in Degree mode

5 0

3 years ago

Read 2 more answers

If Dylan buys a book that is 25% off, what percent of the original price does Dylan pay?

Schach [20]

Dylan will pay 75% of the original price.

5 0

2 years ago

Read 2 more answers