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3 years ago

Slope 8 ; through (4,3)

Mathematics

1 answer:

Reptile [31]3 years ago

7 0

Answer:

y=8x-29

Step-by-step explanation:

Since we know the slope (m) is 8, we can plug it in the slope-intercept formula y=mx+b, making y=8x+b.

Now we need to find the y-intercept (b). To do that, you would need to plug in the points given to you, which were (4,3).

x=4, y=3... so 3=8(4)+b

Now you can solve for the variable b to find the y-intercept.

3=8(4)+b, multiply...

3=32+b, subtract 32 on both sides...

-29=b

Therefore, the y-intercept, or b, is -29.

The equation would be y=8x-29

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Carlos wants to practice piano 2 hours each day. He practices piano for 3/4 hour before school and 7/10 hour when he gets home.

kiruha [24]

Answer

Find out the how many hours has Carlos practiced piano .

To prove

As given

$He\ practices\ piano\ for\ \frac{3}{4}\ hour\ before\ school.$

$\frac{7}{10}\ hour\ when\ he\ gets\ home.$

Than

$Total\ hours\ carlos\ practiced\ piano = \frac{3}{4} + \frac{7}{10}$

L.C.M of (4,10) = 20

$Total\ hours\ carlos\ practiced\ piano = \frac{3\times 5+7\times 2}{20}$

$Total\ hours\ carlos\ practiced\ piano = \frac{15+14}{20}$

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Therefore the total hours Carlos practiced piano is 1.45 hours .

4 0

3 years ago

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Determine the quadratic function f whose graph is given. The vertex is (1,-3) and y-intercept is -2

Nesterboy [21]

Answer:

Vertex form: $f(x)=(x-1)^2-3$

Standard form: $f(x)=x^2-2x-2$

Step-by-step explanation:

A quadratic function in vertex form is $f(x)=a(x-h)^2+k$ where $(h,k)$ is the vertex.

We are given $h=1,k=-3$ .

Let's plug that in:

$f(x)=a(x-1)^2-3$ .

Now let's find $a$ .

We will use the $y$ -intercept $(0,-2)$ to find $a$ .

$f(0)=a(0-1)^2-3$

$-2=a(0-1)^2-3$

$-2=a(-1)^2-3$

$-2=a(1)-3$

$-2=a-3$

$1=a$

So the function in vertex form is:

$f(x)=(x-1)^2-3$ .

In standard form, we will have to multiply and combine any like terms.

Let's do that:

$f(x)=(x-1)(x-1)-3$

$f(x)=x^2-x-x+1-3$

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3 years ago

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3 years ago

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Ksivusya [100]

Answer:

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