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4 years ago

Please help me out! Factor the expression. 3x^2-14x-24

Mathematics

1 answer:

valkas [14]4 years ago

8 0

Split the second term in 3x^2 - 14x - 24 into two terms

3x^2 + 4x - 18x - 24

Factor out the common terms in the first two term, then in the last two terms;

x(3x + 4) - 6(3x + 4)

Factor out the common term 3x + 4

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Find the slope and y-intercept for the two linear functions. Linear Functions Identify the slope of the line given in the table:

Natalija [7]

ANSWER

See explanation

EXPLANATION

The table contains these two points (-4,-3) and (2,-4.5)

The slope of this line is given by;

$m = \frac{rise}{run}$

$m = \frac{ - 4.5 - - 3}{2 - - 4} = \frac{ - 1.5}{6}$

$m = - \frac{1}{4}$

The y-intercept can be obtained by finding the equation of the line in the form:

$y = mx + c$

We plug in the slope and the point (-4,-3) to find c.

This implies that,

$- 3 = - \frac{1}{4} \times - 4 + c$

$- 3 = 1 + c$

$c = - 3 - 1 = - 4$

Hence the y-intercept is -4.

The given line is

$y = \frac{3}{2} x + 1$

This is already in the slope intercept form:

The slope is

$m = \frac{3}{2}$

The y-intercept is c=1

5 0

3 years ago

Read 2 more answers

Determine the sum of the terms in the series 25 + 30 + 35 + ⋯ + 245. Show your work.

scoray [572]

Answer:

6075

Step-by-step explanation:

Given series is: 25 + 30 + 35 + ⋯ + 245.

Here, first term (a) = 25
Common difference (d) = 5
Last term $(a_n) = 245$

First we find the number of terms that this series has by the following formula:

$a_n = a+(n-1)d$

Plugging the values of a, d and $a_n$ , we find.

$245 = 25+(n-1)5$

$\implies 245 - 25=(n-1)5$

$\implies 220=(n-1)5$

$\implies \frac{220}{5}=n-1$

$\implies 44=n-1$

$\implies 44+1=n$

$\implies\red{\bold{ n=45}}$

Thus, the given series contains 45 terms.

Next, we find the sum of the given series using the formula given below.

$S_n = \frac{n}{2}(a+a_n)$

$\implies S_{45}= \frac{45}{2}(25+245)$

$\implies S_{45}= \frac{45}{2}(270)$

$\implies S_{45}=45*135$

$\implies\orange{\boxed{\boxed{\boxed{\bold{ S_{45}=6075}}}}}$

6 0

2 years ago

Gregg home is 1.8 miles from his school. There is a music store half way between his school and home. Today Greg wants to stop a

masya89 [10]

The music store is 1/2 , so:
1.8 ÷ 2 or 1.8 x 1/2
= 0.9
The music store is 0.9 miles from school (from home)

8 0

3 years ago

What’s the answer hurry

Rina8888 [55]

Answer:

Choice C: Lauren is faster than Kevin, slower than Jeremy.

Step-by-step explanation:

Ok, so it directly says that Jeremy is going at y=12x, or 12 miles per hour. To find how fast Kevin is riding, take two points of the table and use the slope formula to get the speed(.

Slope Formula: (y2-y1) / (x2-x1)

So lets take the table plots (2, 22) and (4, 33) to do this.

(y2-y1) / (x2-x1)

(33-22) / (4-2)

(11) / (2)

The speed of Kevin is 5.5 miles by hour.

Then, it asks for how fast Lauren is going, saying she is twice as fast as Kevin. Therefore, simply do:

5.5 * 2 = 11 miles per hour

To get the third biker's speed.

Now, with all of the speeds of the bikers, we can now compare them. Here's a listing of their speeds to make things easier to compare:

Jeremy: 12 mph

Kevin: 5.5 mph

Lauren: 11 mph

From this, we can see that Lauren is the second fastest. She is slower than Jeremy but faster than Kevin. Therefore, the correct answer choice is C.

6 0

3 years ago

Ivy is building a new L-shaped desk for her room. She wants to make sure it is large enough to hold all her supplies. The dimens

lozanna [386]

Answer: the answer is C

Step-by-step explanation:

8 0

3 years ago