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3 years ago

Find an equation of the line that has the given slope and contains the given point. m=7/3 (1,6)

Mathematics

1 answer:

iris [78.8K]3 years ago

5 0

The point-slope form:

$y-y_1=m(x-x_1)$

We have the point (1, 6) and the slope m = 7/3. Substitute:

$y-6=\dfrac{7}{3}(x-1)$ use distributive property

$y-6=\dfrac{7}{3}x-\dfrac{7}{3}$ add 6 to both sides

$y=\dfrac{7}{3}x+\dfrac{11}{3}$ multiply both sides by 3

$3y=7x+11$ subtract 7x from both sides

$-7x+3y=11$ change the signs

$7x-3y=-11$

Answer:

point-slope form: $y-6=\dfrac{7}{3}(x-1)$

slope-intercept form: $y=\dfrac{7}{3}x+\dfrac{11}{3}$

standard form: $7x-3y=-11$

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Avaluate 2^3x-1 for x=1

DENIUS [597]

Answer:

4 or 7 (Check the explanation to see which one your equation actually is.

Step-by-step explanation:

One thing I want to clarify for you, It's Evaluate, not Avaluate.

Okay so, we want to find the value of 2^3x-1 and we know x = 1.

You didn't really clarify if the expression was $2^{3x-1}$ or $2^{3x}-1$ , so I'll be doing both:

For $2^{3x-1}$ , we should plug in x to get $2^{3(1)-1}$ and then simplify to get $2^{2}$ .

2 to the power of 2 or $2^{2}$ is equal to 2 * 2 or 4.

The second one, $2^{3x}-1$ , we should plug in x to get $2^{3(1)}-1$ and then to become $2^{3}-1$ . 2 to the power of 3 or $2^{3}$ is 8 and then minus 1 is 7.

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HELP ASASP PLEASE!!!!!!! What is the following simplified product? Assume x>/0

luda_lava [24]

Answer: Third option.
Please, see the detailed solution in the attache file.
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The tent shown below has fabric covering all four sides and the floor. What is the minimum amount of fabric needed to construct

fenix001 [56]

Answer:

I believe the answer is 152 ft

Step-by-step explanation:

On the side, you would find the area of the square (8x5=40). Then, you would find the area of the triangular front (6x4=24 divded by 2 so it's 12). There are two sides of each, so 24+80=104. Then, you dfind the aarea of the bottom square (6x8=48) and add them all together to make 152

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3 years ago

B is the midpoint of AC. If AB= X +5 and BC = 2X -11, find the measure of AB

Murljashka [212]

First, you know that B is the mid point, meaning AB is equal to BC. Therefore, you can set up the equation: x+5=2x-11. Then, you solve for x. Once you are done solving, you should get 16. Hope this helps!

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PLSSS HELP ME WITH MATH

labwork [276]

Step-by-step explanation:

always remember, equations and inequalities are like a scale with 2 pans (left and right).

a variable is like a placeholder, an empty spot on the pans. and the expressions on both sides are kind of the conditions for the things to put in these empty spots so that the status of the scale stays unchanged.

for an equation the scale has to stay balanced all the time.

and in an inequality one side is heavier that the other (it normally does not matter how much heavier) with "<" or ">" signs, or the scale can be also balanced with "<=" or ">=" signs. just the other side must never be heavier.

so, in our case here

2x - 5 = 3

yes, the solution (the ONLY solution, actually) is x = 4. no other value of x allows the scale to be balanced.

2x - 5 >= 3

well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = 4 is therefore a valid solution for the inequality too.

but so is every other value of x that makes the left side "heavier". what about e.g. 5 ?

2×5 - 5 >= 3

10 - 5 >= 3

5 >= 3

true, great ! so, e.g. x = 5 is also a valid solution.

what else ?

let's simplify the inequality

2x - 5 >= 3

2x >= 8

x >= 4

so, really every value of x that is greater or equal to 4 is a valid solution for the inequality.

-2x - 5 = 3

yes, the solution (the ONLY solution, actually) is x = -4. no other value of x allows the scale to be balanced.

-2x - 5 >= 3

well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = -4 is therefore a valid solution for the inequality too.

but so is every other value of x that makes the left side "heavier". what about e.g. -5 ?

-2×-5 - 5 >= 3

remember, -×- = +

10 - 5 >= 3

5 >= 3

true, great ! so, e.g. x = -5 is also a valid solution.

what else ?

let's simplify the inequality

-2x - 5 >= 3

-2x >= 8

x <= -4

a multiplication or division by a negative value flips the inequality sign, because such an operation makes a light weight heavy and a heavy weight light.

so, really every value of x that is less or equal to -4 is a valid solution for the inequality.

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