make x the subject of the formula x(a-b)=a(b-x).​

Answer:

Step-by-step explanation:

The easiest way to do this is to complete the square on the quadratic. This allows us to see what the vertex is and answer the question without having to plug in a ton of numbers to see what the max y value is. Completing the square will naturally put the equation into vertex form:

[tex]y=-a(x-h)^2+k[/tex] where h will be the time it takes to get to a height of k.

Begin by setting the quadratic equal to 0 and then moving over the constant, like this:

[tex]-4.9t^2+19.6t=-58.8[/tex] and the rule is that the leading coefficient has to be a 1. Ours is a -4.9 so we have to factor it out:

[tex]-4.9(t^2-4t)=-58.8[/tex] Now take half the linear term, square it, and add it to both sides. Our linear term is a -4, from -4t. Half of -4 is -2, and -2 squared is 4, so we add a 4 to both sides. BUT on the left we have that -4.9 out front there as a multiplier, so we ACTUALLY added on to the left was -4.9(4) which is -19.6:

[tex]-4.9(t^2-4t+4)=-58.8-19.6[/tex] and now we have to clean this up. The right side is easy, that is -78.4. The left side...not so much.

The reason we complete the square is to create a perfect square binomial, which is the [tex](x-h)^2[/tex] part from above. Completing the square does this naturally, now it's just up to us to write the binomial created during the process:

[tex]-4.9(t-2)^2=-78.4[/tex] Now, move the constant back over and set the equation back equal to y:

[tex]-4.9(t-2)^2+78.4=s(t)[/tex] and we see that the vertex is (2, 78.4). That means that 2 seconds after launch, the object reached its max height of 78.4 meters, the third choice down.

Answer:

1.11

Step-by-step explanation:

Slope of a line = (y2 - y1)/(x2-x1) = (100 - 0)/(90-0) = 100/90 = 10/9 = 1.11

Answer:

Step-by-step explanation:

Small cone:

r = 4 mm

h = 8 mm

Volume of small cone = [tex]\frac{1}{3}\pi r^{2}h[/tex]

                                    [tex]=\frac{1}{3}*\pi *4*4*8\\\\=\frac{128}{3}*\pi \ mm^{3}[/tex]

Bigger cone :

r = 8 mm

h = 16 mm

Volume of bigger cone = [tex]\frac{1}{3}*\pi *8*8*16[/tex]

                                       [tex]= \frac{1024}{3}\pi \ mm^{3}[/tex]

Volume of the space = Volume of bigger cone - volume of small cone

                                   [tex]= \frac{1024}{3}\pi-\frac{128}{3} \pi \\\\=\frac{896}{3}*\pi \\\\= \frac{896}{3}*3.14\\\\= 937.81 \ cm^{3}[/tex]

Answer:

m<EFG = 72°

m<GFH = 108°

Step-by-step explanation:

m<EFG = 2n + 16

m<GFH = 3n + 24

Linear pairs are supplementary, therefore,

m<EFG + m<GFH = 180°

Substitute

2n + 16 + 3n + 24 = 180

Add like terms

5n + 40 = 180

5n + 40 - 40 = 180 - 40 (subtraction property of equality)

5n = 140

5n/5 = 140/5 (division property of equality)

n = 28

✔️m<EFG = 2n + 16

Plug in the value of n

m<EFG = 2(28) + 16 = 72°

✔️m<GFH = 3n + 24

Plug in the value of n

m<GFH = 3(28) + 24 = 108°

Answer:

A

Step-by-step explanation:

A compressed by a factor of 1/4 in the y or vertical direction

Step-by-step explanation:

7 × 6 = 42 Answer

hope it helps

Answer:

DE ║ BC

BC = 2(DE)

Step-by-step explanation:

From the picture attached,

AD = DB [Given]

AE = EC [Given]

Therefore, points D and E will be the midpoints of the sides AB and AC.

By midsegment theorem,

Segment joining midpoints of the two sides of a triangle is parallel and measures the half of the third side of the triangle.

DE ║ BC

DE = [tex]\frac{1}{2}(BC)[/tex]

BC = 2(DE)

Answer:

Solution given:

radius [r]=3ft

height[h]=5ft

Volume of cone=⅓*πr²h

$ubstitute value

Volume of cone =⅓*3.14*3²*5=47.1ft²

Volume of cone is 47.1ft²

Answer:

the minimum production level is costing $800 (0.8×$1000) per hour for 2000 (2×1000) items produced per hour.

Step-by-step explanation:

if there is no mistake in the problem description, I read the following function :

C(x) = y = 0.3x² - 1.2x + 2

I don't know if you learned this already, but to find the extreme values of a function you need to build the first derivative of the function y' and find its solutions for y'=0.

the first derivative of C(x) is

0.6x - 1.2 = y'

0.6x - 1.2 = 0

0.6x = 1.2

x = 2

C(2) = 0.3×2² - 1.2×2 + 2 = 0.3×4 - 2.4 + 2 = 1.2-2.4+2 = 0.8

so, the minimum production level is costing $800 (0.8×$1000) per hour for 2000 (2×1000) items produced per hour.

Answer:

e s r

Step-by-step explanation:

Answer:

[tex]\frac{-1}{30} a - \frac{1}{6}[/tex]

Step-by-step explanation:

Answer:

f(p)=3p+4

Explanation:

Answer:

i guess Bis the answer bcuz, A sample space is a collection or a set of possible outcomes of a random experiment

Statement B is correct, which best defines the sample space that is " a sample space is the set of all possible outcomes for the a given situation".

A sample space is a collection or a set of possible outcomes of a random experiment. It is represented by using the symbol "s".

For example,

When we flip or toss a coin, two outcomes are possible such as head and tail. Therefore the sample space for this experiment is given as

Sample space, S = {H, T} = {Head, Tail}

According to the given option

Option B is correct. That is a sample space is the set of all possible outcomes for a given situation.

Learn more about sample space here:

https://brainly.com/question/17144524

#SPJ2

The graph above or below should answer the question.

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

Answer:

72√2

Step-by-step explanation:

3√2 × 2√8 × √3 × √6

The above can be simplified as follow:

3√2 × 2√8 × √3 × √6

Recall

a√c × b√d = (a×b)√(c×d)

3√2 × 2√8 × √3 × √6 = (3×2)√(2×8×3×6)

= 6√288

Recall

288 = 144 × 2

6√288 = 6√(144 × 2)

Recall

√(a×b) = √a × √b

6√(144 × 2) = 6 × √144 × √2

= 6 × 12 × √2

= 72√2

Therefore,

3√2 × 2√8 × √3 × √6 = 72√2

Answer:

30 degrees.

Step-by-step explanation:

Let the acute angle be x.

Then as the 2 acute angles in a right triangle sum to 90 degrees,

x = 90 - 60

= 30.

We used the information we know to give us this equation.

90°+60°+x=180°

We add 90° and 60° to give 150°

150°+x=180°

Answer:

The midpoint is (1.5, -5)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoints and divide by 2

( -3+6) /2 = 3/2 = 1.5

To find the y coordinate of the midpoint, add the y coordinates of the endpoints and divide by 2

( -5+-5) /2 = -10/2 =-5

The midpoint is (1.5, -5)

Hi!

[tex]A=(-3,-5) \ and \ B=(6,-5)\\\\Medium \ point=(\frac{-3+6}{2};\frac{-5+(-5)}{2})=\boxed{(\frac{3}{2};-5)}[/tex]

Answer:

6=b

Switch sides

b=6

Answer:

a=10 and b=6

Step-by-step explanation:

it is in picture

Please mark me as brainliest

Answer:

option A is write answer

I hope you help

Answer:

none of these

Step-by-step explanation:

it's 96000 so none

Total gasoline = 10 gallons

Gasoline left after 100 miles = 5 gallons

Gasoline used in 100 miles

= Total gasoline - Gasoline left after 100 miles

= 10 gallons - 5 gallons

= 5 gallons

Gasoline used in 1 mile

= Gasoline used in 100 miles/100

= 5 gallons/100

= 0.05 gallons

Answer:

The line of reflection is usually given in the form y = m x + b y = mx + b y=mx+by, equals, m, x, plus, b.

Step-by-step explanation:

Answer:

The line of reflection in [tex]y=mx+b[/tex] form is [tex]y=\frac{1}{3} x-2[/tex]

Step-by-step explanation:

Answer:

Square

Step-by-step explanation:

In a square,

All the four angles are equal. Each angle = 90.

All the four sides are equal.

Answer:

c = 21

Step-by-step explanation:

**I assume that side WX in my diagram (attached as an image below) is the value of C that we're looking for. ALSO, the sizes and lengths of the parallelograms are NOT to scale.**

If two parallelograms are similar, that means the lengths of the corresponding sides have EQUAL ratios.

PL corresponds with WZ. To get from 15 to 45, you would multiply 15 by 3, so the ratio of the legnths of the corresponding sides between these two parallelograms is 1:3.

With that in mind, we can apply this ratio to find WX.

We know that AP has a length of 7, so we will multiply that by 3, getting a value of 21, and 7:21 ratio is the same as 1:3.

c = 21

Hope this helps (●'◡'●)

Lets do

[tex] \\ \sf \longmapsto \: 3(x + 5) - 7 = 2(x +2) \\ \\ \sf \longmapsto \: 3x + 15 - 7 = 2x + 4 \\ \\ \sf \longmapsto \: 3x + 8 = 2x + 4 \\ \\ \sf \longmapsto \: 3x - 2x = 4 - 8 \\ \\ \sf \longmapsto \: x = - 4[/tex]

Answer: x=1 and y=0

Step-by-step explanation:

y+2x=2x

y=2x-2x

y=0

2x=2. X = 2/2

X=1

Answer:

x=1   y=0

Step-by-step explanation:

y + 2 = 2x               y = 2x - 2

y + 2x = 2

(2x - 2) + 2x = 2

4x = 4

x = 1

y + 2 = 2(1)

y + 2 = 2

y = 0

The value of m for the complex number to be purely real are 3 and -5.

The value of m for the complex number to be purely imaginary are -2 and 3.

For the complex number to be located in the second quadrant, the value of m must be less than -3 and 5.

Given the complex number:

[tex]z=\frac{m^2-m-6}{m+3}+(m^2-2m-15)i[/tex]

a) For the complex number to be purely real, then the imaginary part of the complex number must be zero that is:

[tex](m^2-2m-15)i = 0\\m^2-2m-15=0[/tex]

Factorize

[tex]m^2+5m-3m-15=0\\m(m+5)-3(m+5)=0\\(m-3)(m+5)=0\\m-3=0 \ and \ m+5=0\\m=3 \ and \ m=-5[/tex]

Hence the value of m for the complex number to be purely real are 3 and -5.

b) For the complex number to be purely imaginary, then the real part of the complex number must be zero. Hence;

[tex]\frac{m^2-m-6}{m+3}=0 \\m^2-m-6=0[/tex]

Factorize

[tex]m^2-m-6\\m^2-3m+2m-6=0\\m(m-3)+2(m-3)=0\\(m+2)(m-3)=0\\m+2=0 \ and \ m-3=0\\m=-2 \ and \ m = 3[/tex]

Hence the value of m for the complex number to be purely imaginary are -2 and 3.

c) For the complex number to be in the second quadrant, then the ratio of y to x must be negative i.e less than zero as shown:

[tex]\frac{m^2-2m-15}{\frac{m^2-m-6}{m+3} } < 0\\ \frac{m^2-2m-15(m+3)}{{m^2-m-6} }\\ \frac{(m+3)(m-5)(m+3)}{{(m-3)(m+2)} } <0\\(m+3)(m-5)(m+3) <0\\m+3<0, m-5<0 \ and \ m+3<0\\m<-3 \ and \ m<5[/tex]

Hence for the complex number to be located in the second quadrant, the value of m must be less than -3 and 5.