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3 years ago

If f(x)=2x^2+6,find the value of f(-3). Show all work

1 answer:

8 0

Just plug -3 where x is into the equation 2x^2 + 6 and solve
f(-3) = 2(-3)^2 + 6
f(-3) = 2(9) + 6
f(-3) = 18 + 6
f(-3) = 24

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Consider that a data set of 10 data points has a mean of 5. If every data point was doubled in the set, how might that affect th

Vesnalui [34]

Answer:

A) The mean would double to 10.

4 0

3 years ago

In a group of 25 students, 6 study both Art and Biology. 10 study Biology but not Art. 3 study neither subject. Given that a ran

olga2289 [7]

Answer:

1/2

Step-by-step explanation:

There are a total of 25 students. 3 don't study art or biology. 10 study only biology. 6 study both art and biology. This means the remaining students only study art.

1. Calculate the number of students taking art

only art: 25 - 3 - 6 - 10 = 6

number of students taking art and biology: 6

total number of students taking art: 12

2. Calculate the probability

Out of the 12 total students taking art, 6 are in art and biology.

6/12 = 1/2

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2 years ago

What is the equation of the line that passes through the point (4,−2) and has a slope of −2?

AVprozaik [17]

Answer:y=-2x+6

Step-by-step explanation:

You want to find the equation for a line that passes through the point (4,-2) and has a slope of -2.

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

To start, you know what m is; it's just the slope, which you said was -2. So you can right away fill in the equation for a line somewhat to read:

y=-2x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(4,-2). When x of the line is 4, y of the line must be -2.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: . b is what we want, the -2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (4,-2).

So, why not plug in for x the number 4 and for y the number -2? This will allow us to solve for b for the particular line that passes through the point you gave!.

(4,-2). y=mx+b or -2=-2 × 4+b, or solving for b: b=-2-(-2)(4). b=6.

6 0

3 years ago

Find the value of z.

san4es73 [151]

Answer:

Option D, 110

Step-by-step explanation:

first we find x

10x+20-80=2(2x+15)

or, x=15

now, 10x+20 = 170

so, z = 360-170-80 = 110

7 0

3 years ago

Please help please these are short answers

atroni [7]

Answer: The answers are given below.

Step-by-step explanation: The calculations are as follows:

(19) Weight of the puppy last week is

$W_\ell=2\dfrac{1}{2}~\textup{lb},$

and weight of the puppy this week is

$W_p=7\dfrac{1}{4}=\dfrac{29}{4}~\textup{lb}.$

Therefore, the weight gained by the puppy is given by

$W_g=W_p-W_\ell=\dfrac{29}{4}-\dfrac{5}{2}=\dfrac{29-10}{4}=\dfrac{19}{4}=4\dfrac{3}{4}~\textup{lb}.$

(20) Time taken in Route 1 = 1 hour 30 minutes.

Time taken in Route 2 = 1 hour 45 minutes.

Time taken in Route 3 = 1 hour 35 minutes.

Time taken in Route 4 = 1 hour 25 minutes.

Since we want to spent the least amount of time on the bus, so we will be taking route 4.

(21) Time taken by Nazia to complete her language arts homework is

$H_\ell=\dfrac{4}{9}~\textup{hr},$

and the time taken by Nazia to complete her Mathematics homework is

$H_m=\dfrac{2}{9}~\textup{hr}.$

Therefore, Nazia takes more time to complete Language Arts homework, by

$H=H_\ell-H_m=\dfrac{4}{9}-\dfrac{2}{9}=\dfrac{2}{9}~\textup{hr}.$

(22) Quantity of Aluminium collected by Maya is

$A_m=\dfrac{4}{20}=0.2~\textup{lb},$

and the quantity of Aluminium collected by her friend Abigail is

$A_a=\dfrac{7}{8}=0.87~\textup{lb}.$

Therefore,

(a) Abigail collected more aluminium

and

(b) Total Aluminium collected by both the girls is

$T=A_m+A_a=\dfrac{4}{20}+\dfrac{7}{8}=\dfrac{8+35}{40}=\dfrac{43}{40}~\textup{lb}.$

(23) Quantity of snow fall last Wednesday is

$S_w=3\dfrac{1}{4}=3.25~\textup{in.},$

and quantity of snowfall on sunday is

$S_s=3\dfrac{4}{5}=3.8~\textup{in.}.$

Therefore, quantity of snowfall was more on Sunday by

$S=S_s-S_w=3\dfrac{4}{5}-3\dfrac{1}{4}=\dfrac{19}{5}-\dfrac{13}{4}=\dfrac{76-65}{20}=\dfrac{11}{20}~\textup{in.}.$

Thus, all the questions are answered.

3 0

3 years ago