MATHEMATICS HIGH SCHOOL

Please help!!!!!!!!!!If f(x) varies directly with x2 and f(x)=10 when x=−4 , what is the value of f(x) when x = 3?
−14.4

−5.625

5.625

14.4

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

First thing, let's call f(x) "y". So y varies directly with x^2 looks like this:

y = kx^2

k is our constant of variation. We need to solve for k before we can find what we are asked to find.

Filling in:

10 = k(-4)^2 and

10 = 16 k so

k = 5/8 (reduced)

Now we will use that value of k along with the given of x = 3 to find y:

y = (5/8)(3)^2 and

y = (5/8)(9)

y = 45/8 which simplifies to

y = 5.625

Answer 2

Answer:

Final answer:

The function f(x) varies directly with x2. First, find the constant of variation, then use this constant to find the value of the function at the desired x value. The value of f(x) when x = 3 is 5.625.

Explanation:

The phrase 'f(x) varies directly with x2' implies that there is a linear relationship between f(x) and x2. That is to say, the formula will be something like f(x) = kx2 where k is the constant of variation. We can solve for k using the given condition f(x) = 10 when x = -4. By substituting these values into the equation, we get 10 = k(-4)2, which simplifies to 10 = 16k. Solving for k, we find k = 10 / 16 = 0.625.

To find the value of f(x) when x = 3, we substitute x = 3 into the formula f(x) = 0.625x2, which results in f(3) = 0.625 * 9 = 5.625.

Learn more about Direct Variation here:

brainly.com/question/34355670

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the sun's average surface temperature is 5780 k, while earth's average surface temperature is 288 k. how many times warmer, on average, is the sun's surface than earth's surface? use the equation below and round your answer to the nearest whole number.
Simplify the expression.
A student bought a pair of sunglasses in the USA.He paid $35.50 In England, an identical pair of sunglasses costs £26.99 The exchange rate is £1 = $1.42 In which country were the sunglasses cheaper, and by how much?
On a spinner p(3) =1/3 and the P(4)=2/5 What is the probabilty of getting a 3 or 4

Solve the system of equations using substitution.y = 4x + 6
y = 2x

a. (6, 3)
b. (-3, -6)
c. (3, 6)
d. (1, 2)

Answers

$y=4x+6\ny=2x\n\n4x+6=2x\n2x=-6\nx=-3\n\ny=2\cdot(-3)\ny=-6\n\n\boxed{(x,y)=(-3,-6)}$

Answer:

-3,-6

Step-by-step explanation:

Mrs. Hall records the heights of 50 students in a spreadsheet. The mean height is 68 inches. After looking at the data again, she realized that two of the 50 observations were outliers that must have been typos, 82 and 86 inches. She deleted these two observations. What is the new mean, rounded to the nearest hundredth?

Answers

So, in the situation when she still had the 50 students, the sum of their heights was

50*68=3400 (you can pretend here that all the students are 68 inches tall)

She subtracted the outliners:

3400-82-86=3232, so the new sum is 3232.

She now has to divide it by the number of the students which is now lower by 2: 48

So, 3232/48=67,33

the new mean is 67,33!

Answer:

Its 67.33 hope its helps Give me a heart plz

Step-by-step explanation:

identify whether the series infinity sigma i=1 8(5/6)^i-1 is a convergent or divergent geometric series and find the sum if possible

Answers

Answer:

The sum of infinite geometric series is:

Step-by-step explanation:

We have to find the sum of the geometric series which is given as:

$\sum^(\infty)_(i=1) 8* ((5)/(6))^i$

which could also be written as:

$8\sum^(\infty)_(i=1) ((5)/(6))^i$

As we know that any infinite series of the form:

$\sum^(\infty)_(i=1)x^i$

is convergent if |x|<1

Here we have:

x=5/6<1

Hence,the infinite series is convergent.

Also we know that for infinite geometric series the sum is given as:

$S=(a)/(1-r)$

Here we have:

a=5/6 and common ration r=5/6

Hence, the sum of series is:

$8\sum^(\infty)_(i=1) ((5)/(6))^i=8* (((5)/(6))/(1-(5)/(6)))\n\n=8* (((5)/(6))/((1)/(6)))\n\n=8* 5\n\n=40$

Hence, the sum of series is:

The sum is convergent. I'll assume the 8 isn't an attempt at using the infinity symbol, so that you have

$\displaystyle\sum_(i=1)^\infty 8\left(\frac56\right)^(i-1)$

This converges because the common ratio between terms is smaller than 1.

The sum is

$\frac8{1-\frac56}=48$

since

$\displaystyle\sum_(i=1)^\infty ar^(i-1)=a\lim_(n\to\infty)\sum_(i=1)^nr^(i-1)=a\lim_(n\to\infty)(1-r^n)/(1-r)=\frac a{1-r}$

if $|r|<1$ .

A falcon flying 55 mph crosses a lake in 1 minute. How long would it take a hummingbird flying 45 mph to cross the same lake?

Answers

The hummingbird will take 1 minute 13 seconds.

Let the time that will be taken by the hummingbird be represented by x

Note that 1 minute = 60 seconds

Based on the information given, the equation that'll be used in the question will be:

45/55 = 60/x

Cross multiply

(45 × x) = (60 × 55)

45x = 3300

x = 3300/45

x = 73.33 seconds

x = 1 minute 13 seconds

The hummingbird will take 1 minute 13 seconds.

Read related link on:

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Answer:

1 2/9 minutes

Step-by-step explanation:

55 mph

55 / 60 = 11/12

11/12 of a mile = 1 minute

45 mph

45 / 60 = 3/4

3/4 of a mile = 1 minute

11/12 divided by 3/4

11/12 * 4/3

We can cross-cancel

11/3 * 1/3 = 11/9 = 1 2/9

It takes 1 2/9 minutes for the hummingbird to cross the lake

Hope this helps!

(Please let me know if I did something wrong!)

6×2p to the second power when p=5

Answers

Answer:

3600

Step-by-step explanation:

Since the question gives you p, you replace p (which is just a placeholder) with 5.

Your equation should look like this:

$(6*2(5))^2 = 3600$

three bags of potatoes and four cases of corn cost $40. Five bags of potatoes and two cases of corn cost $34. Find the cost of one bag of potatoes and the cost of one case of corn.

Answers

Use variables and set up equations.

$3p + 4c = 40 \n 5p + 2c = 34$

Next, get one variable with equal coefficients.

$3p + 4c = 40 \n 10p + 4c = 68\ (multiplied\ both\ sides\ by\ 2)$

Then get it alone on one side.

$4c = 40-3p \n 4c = 48-10p$

Now we can use substitution. Since $40-3p = 4c$ , substitute $40-3p$ for $4c$ in the other equation and you'll get an equation with just one variable to simplify and solve.

$40-3p = 68-10p \n 40+7p = 68 \n 7p = 28 \n \boxed{p = 4}$

We can then use $p = 4$ in an earlier equation to find $c$ .

$5p + 2c = 34 \n 5*4 + 2c = 34 \n 20 + 2c = 34 \n 2c = 14 \n \boxed{c=7}$

3p + 4c = 40 ⇒ 15p + 20c = 200
5p + 2c = 34 ⇒ 15p +   6c = 102
      14c = 98
   14    14
      c = 7
          5p + 2(7) = 34
      5p + 14 = 34
      - 14 - 14
      5p = 20
   5 5
      p = 4
      (p, c) = (4, 7)

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