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3 years ago

Solve for x: one over eight (8x + 15) = 24

Mathematics

2 answers:

Vsevolod [243]3 years ago

8 0

The answer is 177/8 or one hundred seventy seven over eigth.

1/8(8x + 15) = 24

Multiply both sides by 8:
8* 1/8(8x + 15) = 8 * 24
8x + 15 = 192

Subtract 15 from both sides:
8x +15 - 15 = 192 - 15
8x = 177

Divide both sides by 8:
8x/8 = 177/8
x = 177/8

UkoKoshka [18]3 years ago

7 0

I hope this helps you

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CaHeK987 [17]

It’s not a function as there are more than one value of y fir each value if x

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3 years ago

Match the parabolas represented by the equations with their foci.

Elenna [48]

Function 1 $f(x)=- x^{2} +4x+8$

First step: Finding when $f(x)$ is minimum/maximum
The function has a negative value $x^{2}$ hence the $f(x)$ has a maximum value which happens when $x=- \frac{b}{2a}=- \frac{4}{(2)(1)}=2$ . The foci of this parabola lies on $x=2$ .

Second step: Find the value of y-coordinate by substituting $x=2$ into $f(x)$ which give $y=- (2)^{2} +4(2)+8=12$

Third step: Find the distance of the foci from the y-coordinate
$y=- x^{2} +4x+8$ - Multiply all term by -1 to get a positive $x^{2}$
$-y= x^{2} -4x-8$ - then manipulate the constant of y to get a multiply of 4
$4(- \frac{1}{4})y= x^{2} -4x-8$
So the distance of focus is 0.25 to the south of y-coordinates of the maximum, which is $12- \frac{1}{4}=11.75$

Hence the coordinate of the foci is (2, 11.75)

Function 2: $f(x)= 2x^{2}+16x+18$

The function has a positive $x^{2}$ so it has a minimum

First step - $x=- \frac{b}{2a}=- \frac{16}{(2)(2)}=-4$
Second step - $y=2(-4)^{2}+16(-4)+18=-14$
Third step - Manipulating $f(x)$ to leave $x^{2}$ with constant of 1
$y=2 x^{2} +16x+18$ - Divide all terms by 2
$\frac{1}{2}y= x^{2} +8x+9$ - Manipulate the constant of y to get a multiply of 4
$4( \frac{1}{8}y= x^{2} +8x+9$

So the distance of focus from y-coordinate is $\frac{1}{8}$ to the north of $y=-14$
Hence the coordinate of foci is (-4, -14+0.125) = (-4, -13.875)

Function 3: $f(x)=-2 x^{2} +5x+14$

First step: the function's maximum value happens when $x=- \frac{b}{2a}=- \frac{5}{(-2)(2)}= \frac{5}{4}=1.25$
Second step: $y=-2(1.25)^{2}+5(1.25)+14=17.125$
Third step: Manipulating $f(x)$
$y=-2 x^{2} +5x+14$ - Divide all terms by -2
$-2y= x^{2} -2.5x-7$ - Manipulate coefficient of y to get a multiply of 4
$4(- \frac{1}{8})y= x^{2} -2.5x-7$
So the distance of the foci from the y-coordinate is - $\frac{1}{8}$ south to y-coordinate

Hence the coordinate of foci is (1.25, 17)

Function 4: following the steps above, the maximum value is when $x=8.5$ and $y=79.25$ . The distance from y-coordinate is 0.25 to the south of y-coordinate, hence the coordinate of foci is (8.5, 79.25-0.25)=(8.5,79)

Function 5: the minimum value of the function is when $x=-2.75$ and $y=-10.125$ . Manipulating coefficient of y, the distance of foci from y-coordinate is $\frac{1}{8}$ to the north. Hence the coordinate of the foci is (-2.75, -10.125+0.125)=(-2.75, -10)

Function 6: The maximum value happens when $x=1.5$ and $y=9.5$ . The distance of the foci from the y-coordinate is $\frac{1}{8}$ to the south. Hence the coordinate of foci is (1.5, 9.5-0.125)=(1.5, 9.375)

8 0

3 years ago

3y +(-2) +48=180 solve for y

GalinKa [24]

Answer:

The answer to the problem is

y = 134/3

Step-by-step explanation

7 0

3 years ago

Brainliest goes to whoever answers correctly try to show work ONLY if you can also if you want more points answer my other quest

dolphi86 [110]

Answer:

Hi, there the answer is C. y=33/2x+425

I tried uploading a picture on how I got, but it keep saying I'm using offensive word, which I didn't but trust me the answer is right

Step-by-step explanation:

5 0

3 years ago

our goal is to run a mean of 45 minutes per day for a week. For the first six days, you run 38, 40, 40, 42, 43, and 50 minutes.

oksano4ka [1.4K]

Answer:

62 minutes.

Step-by-step explanation:

To find the mean, you need to <u>add</u> together all of your values (the minutes) and <u>divide</u> them by the number of values (how many sets of minutes given).

So, choosing to add 62 minutes:

38 + 40 + 40 + 42 + 43 + 50 + 62 = 315

There are 7 sets of minutes in total, so we then divide 315 by 7.

315/7 = 45 minutes

Therefore, running 62 minutes on the seventh day would cause you to run a mean of 45 minutes per day for the week.

6 0

3 years ago