Complete the square to write 16t² - 96t + 48 = 0

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Step-by-step explanation:

L = 6t+5

H = √t

A = L*H

= (6t+5) *√t = 6t√t + 5√t

A'(t) = 6t * 1/2*√t + √t * 6 + 5/2*√t

= 6t/2√t + 6√t + 5/2√t

Expression for the rate of change of the area with respect to time will be,

A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex] cm per second

It's given in the question,

      (6t + 5) cm

       [tex]\sqrt{t}[/tex] cm

Area of the rectangle is given by,

Area = Length × Height

A = (6t + 5)(√t)

A = [tex]6t^{\frac{3}{2}}+5t^\frac{1}{2}[/tex]

Now find the derivative of area (A) with respect to time (t).

[tex]\frac{dA}{dt}=\frac{d}{dt}(6t^{\frac{3}{2}}+5t^\frac{1}{2})[/tex]

A' = [tex](6\times \frac{3}{2})t^\frac{1}{2}+\frac{5}{2} t^{-\frac{1}{2}}[/tex]

A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex]

     Therefore, expression for the rate of change of the area will be,

A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex]

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Answer:

562

Step-by-step explanation:

Plug in the values of x, y, and z provided.

(5(5)-1)^2-2(7)

Solve.

(25-1)^2-14

(24)^2-14

576-14

562

Answer: 562

Step-by-step explanation:

(5x+y)^2-2z

first put in the known values. (5(5)+(-1))^2-2(7)

(25+-1)^2-14

Second, do 25+-1=24

(24)^2-14

Third, do 24 squared

576-14

Subtract

562

Answer: x=7

Step-by-step explanation:

Answer:

!7 hope this helps:)

Step-by-step explanation:

Answer:

Slope = -2/7; Y intercept = +2

Step-by-step explanation:

First, for this particular question - we want to convert the equation to slope intercept form! You may recognize it already, it looks like this:

y = mx + b

Here's how:

[tex]2x+7y=14\\2x+7y - 2x = -2x+14\\7y=-2x+14\\\frac{7y}{7} =\frac{-2x+14}{7} \\y = \frac{-2}{7}x+2[/tex]

The above shows this equation in slope intercept form: y = -2/7x + 2.

The slope of this line is -2/7 while the y intercept is 2!

*Note*: In the slope-intercept formula, m stands for the slope, and the b is the intercept!

Hope I was of assistance! Algebra can be a little difficult but you'll get it! Have a nice day and spread the love! <3

Answer:

C. 45 + 7h = g

Step-by-step explanation:

This one would be correct because you have to add 7 points to the 45 points she would get on average without studying, without forgetting to multiply 7 by the number of hours that Isabella studied.

Example:

Let's say that Isabella studied for 3 hours. We could replace the h for the number of hours that she studied.

45 + 7(3) = g

Now you just have to solve the equation.

45 + 21 = g

Following the rules of PEMDAS, you would get rid of the parenthesis first by multiplying 7 times 3. Now you just have to add and you will have your answer for g.

g = 66

Answer:

It's A.

Step-by-step explanation:

Answer:

10 inches

Step-by-step explanation:

1,000 / 100 = 10

Answer:

7

Step-by-step explanation:

one bag of candy for every three people

12 ÷ 4 = 3

21 ÷ 7 = 3

Answer:

7  

Step-by-step explanation:

Apply proportions:

People/bag of candy

[tex]\frac{12}{4}[/tex]

For 21 people

[tex]\frac{21}{x}[/tex]

Equal both expressions

[tex]\frac{12}{4} =\frac{21}{x}[/tex]

Solve for x:

[tex]x=21\frac{12}{4} \\x= \frac{21}{3} \\x=7[/tex]

You should purchase 7 bags of candy

Answer:

yes they are equivalent

Answer:

pls help

Step-by-step explanation:

Answer:

x= 3, y= 8

or x= -1, y= 0

Step-by-step explanation:

y= 2x² -2x -4 -----(1)

y -2x= 2

y= 2x +2 -----(2)

Substitute (1) into (2):

2x² -2x -4= 2x +2

2x² -2x -4 -2x -2= 0 (bring all terms to the left)

2x² -4x -6= 0 (simplify)

x² -2x -3= 0 (÷2 on both sides)

(x -3)(x +1)= 0 (factorise)

x -3= 0 or x +1= 0

x= 3 or x= -1

Substitute into (2):

y= 2(3) +2 or y= 2(-1) +2

y= 6 +2 or y= -2 +2

y= 8 or y= 0

Answer:1.20/5

Step-by-step explanation:

Answer:

9/10 or in decimal form 0.9

Step-by-step explanation:

Answer:

He Won 26 Box trolls and 11 Pikachus

Step-by-step explanation:

You subtract 37-11 which would get you 26

Answer:

Not too sure because I don't know how it works for your site but drag the B dot to the A dot and drag that A dot to the C dot so their all going through the lines while being connected.

(sorry if its incorrect had a hard time reading the picture)

Answer:

Y=30

Step-by-step explanation:

we know that Y+150=180 as it is a linear pair

so, Y= 108-150

which will be 30

Answer:

if u get it pls tell me

Step-by-step explanation:

Answer:

line A is steeper.

Line A´s slope is 1, while line d´s slope is 2/5

Given:

In September, John sold 32 prints of his artwork for $126.

In October, he sold 48 prints of his artwork for $240.

To find:

The cost per print expressed as a slope.

Solution:

Let y be the cost of x prints.

The relationship between the number of poster prints and total earnings is linear.

In September, John sold 32 prints of his artwork for $126. So, the line passes through (32,126).

In October, he sold 48 prints of his artwork for $240. So, the line passes through (48,240).

Now, the slope of the line is

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{240-126}{48-32}[/tex]

[tex]m=\dfrac{114}{16}[/tex]

[tex]m=7.125[/tex]

The slope of the linear function 7.125.

Therefore, the cost of per print is $7.125.

Answer:

x = 6

Step-by-step explanation:

5 times x is 5x, 5 times 9 is 45; 5x+49-4; 49 minus 4 is 45; 5x+45 = 75; now minus 45 from each side so it would now be 5x = 30; now divide; 30/5 = 6.

Answer: wut yea i think it's six too.

The answer is 4 because look at this: ♥ ♥

That's 2 hearts

If you add 2 more:

♥ ♥ ♥ ♥

1  2  3  4 --> 4 hearts!

♥ ♥ + ♥ ♥ = ♥ ♥ ♥ ♥

So, 2 + 2 = 4.

Ok :

Answer:

In triangles DEF and OPQ, ∠D ≅ ∠O, ∠F ≅ ∠Q, and segment DF ≅ segment OQ. Is this information sufficient to prove triangles DEF and OPQ congruent through SAS? Explain your answer.

Step-by-step explanation:

can  you help me?

Answer:

25.748

Step-by-step explanation:

If you multiply 4.1 by 3.14, your answer comes out to 12.874. Multiply that by 2 and you get your answer of 25.748. Hope this helps.

Answer:

54/35 is a rational number!

Have a great rest of your day!

Answer:

Yes and no

Step-by-step explanation:

The number 54 is a rational number if 54 can be expressed as a ratio, as in Rational. A quotient is the result you get when you divide one number by another number. Although the 54 is good the 35 is not due to it if you had to choose if it was or not you can say yes but it determines the question.

Answer:

Step-by-step explanation:

Let the initial money in the account be y.

Lexi withdrew $150 from the stand's bank account to buy supplies. This will be:

= y - $150

Later, she deposited $437 from the day's sales. The money in the account will now be:

= y - $150 + $437

= y + $287

The total change in the stand's bank account relative to where it started will be the initial amount + $287.

Answer:

287

Step-by-step explanation:

Answer:

10+(-4)=6

Step-by-step explanation:

Answer:

-4 + 10

Step-by-step explanation:

Answer:

We have the equation:

(ax^2 + 3x + 2b) - (5x^2+bx-3c)=  3x^2 - 9

First, move all to the left side.

(ax^2 + 3x + 2b) - (5x^2+bx-3c) - 3x^2 + 9 = 0

Now let's group togheter terms with the same power of x.

(a - 5 - 3)*x^2 + (3 - b)*x + (2b + 3c + 9) = 0.

This must be zero for all the values of x, then the things inside each parenthesis must be zero.

1)

a - 5 - 3 = 0

a = 3 + 5 = 8.

2)

3 - b = 0

b = 3.

3)

2b + 3c + 9 = 0

2*3 + 3c + 9 = 0

3c = -6 - 9 = -15

c = -15/3 = -5

Then we have:

a = 8, b = 3, c = -5

a + b + c = 8 + 3 - 5 = 6