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3 years ago

3) What is an equation for the line that passes through the coordinates (-1.2) and (7,6) ?

Mathematics

1 answer:

OLEGan [10]3 years ago

7 0

Answer:

$y=\frac{1}{2} x+\frac{5}{2}$

Step-by-step explanation:

First find the slope using the slope using the given points. Remember that the slope is the change in y over the change in x.

$\frac{6-2}{7- (-1)}=\frac{4}{8}=\frac{1}{2}$

So now we have the equation $y=\frac{1}{2} x+b$ , and we need to find out what b is. We can do this by pointing a point (either one, but I'll use -1,2) into the equation

$2=\frac{1}{2}(-1)+b$

Rearrange the equation so it equals b

$\frac{5}{2}=b$

Put it together and that's the final equation!

$y=\frac{1}{2} x+\frac{5}{2}$

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Factor the polynomial x2 + 2x – 3x – 6 by double grouping. Group terms with common factors: (x2 + 2x) + (– 3x – 6) Factor the GC

garik1379 [7]

We have been given a polynomial and we are asked to factor our polynomial by double grouping.

$x^{2} +2x-3x-6$

First of all we will group terms with common factors. We can see that $x^{2}$ and 2x have a common factor x. Common factor of -3x and -6 is -3.

$x^{2} +2x-3x-6$

$(x^{2} +2x)+(-3x-6)$

Now we will factor out Greatest Common Factor from each group.

$x(x+2)-3(x+2)$

After factoring out GCF from each group we got (x+2) as our common binomial. Now we will write our polynomial as a product of two binomials as:

$(x+2)(x-3)$

Therefore, our polynomial as a product of two binomials will be $(x+2)(x-3)$ .

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3 years ago

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Two Cars Start at the Same Point and travel in the Same Direction at the average speeds of 70 miles per hour, and 40 miles per h

cestrela7 [59]

Answer:

You can check it by solving it in your head. They are separating at the rate of 55-40 or 15 miles per hour. So in 1 hour or 60 minutes they'll be 15 miles apart, so in 20 minutes they'll be 5 miles apart, so in 40 minutes they'll be 10 miles apart. So it has to be 40 minutes.

Step-by-step explanation:

55t-40t=10

15t=10

15t/15=10/15

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40 Minutes

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3 years ago

Suppose f(x) = x2 and g(x) = (4x)2. Which statement best compares the graph of g(x) with the graph of f(x)?

Paha777 [63]

Answer:

Option C

Step-by-step explanation:

Given: Functions $f(x) = x^2$ and $g(x)=(4x)^2$

Now, if we compare the both equation we get,

$g(x) = 4f(x)$ as $g(x) = 4(4x^2)=16x^2=(4x)^2=f(x)$

This means that the value of g(x) is 4 times the value of f(x). So the graph of g(x) is the graph of f(x) vertically stretched by a factor of 4.

The graph shown below confirms the conclusion.

Therefore, Option C is correct.

The graph of g(x) is the graph of f(x) vertically stretched by a factor of 4.

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4 years ago

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What is 324.93 rounded to the nearest whole number

Arte-miy333 [17]

Answer:

The answer would be 325.

Hope this helps!!

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3 years ago

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How much would $14,250 be worth in a savings account after 13 years if the account has a 5.25% APY and the interest is compounde

miss Akunina [59]

Answer:

$28,188.46

Step-by-step explanation:

The formula you need is:

$A(t)=P(1+\frac{r}{n})^{nt}$

Where A(t) is the amount after the compounding, P is the initial investment, r is the interest rate, n is the number of compoundings per year, and t is the time in years. We are looking for A(t). P is $14,250; r in decimal form is .0525; n is 52 since there are 52 weeks in a year; t is 13 years. Filling in:

$A(t)=14,250(1+\frac{.0525}{52})^{(52)(13)}$

Simplifying inside the parenthesis and the exponential multiplication:

$A(t)=14,250(1.0010096154)^{676}$

Raising the number in parenthesis to the power of 676 gives us:

A(t) = 14,250(1.978137432)

Multiplying then gives us $28,188.46

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3 years ago