It took Emma 3/4 hour to rake the leaves. It took her 1/5 hour more to
weed the garden than it took to rake the leaves. It took her 0.2 hour
more to mow the lawn than it took to weed the garden. Discuss a
strategy you can use to find the answer. Then determine how long it
took her to do all three chores.

Answer:

x = y - 8

Step-by-step explanation:

To solve for x just subtract 8 from both sides to isolate x.

Answer:

[tex]\displaystyle \text{min} = \frac{\sqrt{3+2\sqrt{3}}}{2} - \frac{2\sqrt[4]{3}}{\sqrt{2}} \text{ at } x = \frac{\sqrt{3}}{2}\text{ and } \\ \\ \text{max} = 2\sqrt{5} -4 \text{ at } x = 4[/tex]

Step-by-step explanation:

We want to find the maximum and minimum values of the function:

[tex]\displaystyle f(x) = \sqrt{x + x^2} - 2\sqrt{x}[/tex]

On the interval [0, 4].

First, evaluate its endpoints:

[tex]\displaystyle \begin{aligned} f(0) &= \sqrt{(0)+(0)^2} - 2\sqrt{0} \\ &= 0 \\ \\ f(4) &= \sqrt{(4)+(4)^2} - 2\sqrt{(4)} \\ &= 2\sqrt{5} -4 \end{aligned}[/tex]

Recall that the extrema of a function occurs at its critical points; that is, where its derivative equals zero (or is undefined).

Take the derivative of both sides:

[tex]\displaystyle f'(x) = \frac{d}{dx}\left[ \sqrt{x + x^2} - 2\sqrt{x}\right][/tex]

Differentiate:

[tex]\displaystyle \begin{aligned} f'(x) &= \frac{1}{2\sqrt{x + x^2}} \cdot (1 + 2x) - 2\left(\frac{1}{2\sqrt{x}}\right) \\ \\ &= \frac{2x+1}{2\sqrt{x+x^2}} - \frac{1}{\sqrt{x}} \\ \\\end{aligned}[/tex]

Note that the derivative is undefined at x = 0. Hence, x = 0 is a critical point.

Solve for the zeros of the derivative:

[tex]\displaystyle\begin{aligned} \frac{2x+1}{2\sqrt{x + x^2}} - \frac{1}{\sqrt{x}} &= 0\\ \\ \frac{2x+1}{2\sqrt{x}\sqrt{1 + x }} - \frac{1}{\sqrt{x}} &= 0 \\ \\ \frac{2x+1}{2\sqrt{1+x}} - 1 &= 0\\ \\ 2x + 1 &= 2\sqrt{1+x} \\ \\ 4x^2 + 4x + 1 &= 4 + 4x \\ \\ x^2 &= \frac{3}{4} \\ \\ x= \frac{\sqrt{3}}{2} \end{aligned}[/tex]

Therefore, our only two critical points are at x = 0 and x = √3/2:

Evaluate the function at x = √3/2:

[tex]\displaystyle \begin{aligned} f\left(\frac{\sqrt{3}}{2}\right) &= \sqrt{\left(\frac{\sqrt{3}}{2} \right)+ \left(\frac{\sqrt{3}}{2}\right)^2} - 2 \sqrt{\left(\frac{\sqrt{3}}{2}\right)} \\ \\ &= \frac{\sqrt{3+2\sqrt{3}}}{2}- \frac{2\sqrt[4]{3}}{\sqrt{2}} \\ \\ &\approx -0.5900\end{aligned}[/tex]

In conclusion: the exact maximum and minimum values of f on the interval [0, 4] is:

[tex]\displaystyle \text{min} = \frac{\sqrt{3+2\sqrt{3}}}{2} - \frac{2\sqrt[4]{3}}{\sqrt{2}} \text{ at } x = \frac{\sqrt{3}}{2}\text{ and } \\ \\ \text{max} = 2\sqrt{5} -4 \text{ at } x = 4[/tex]

Answer:

Answer 1

Step-by-step explanation:

Hey here! This is your answer:

L = 9

Step-by-step explanation:

Using the formula A = wl we can figure out this question.

[tex]l=\frac{A}{W} = \frac{36}{4} =9[/tex]

Answer:

D

Step-by-step explanation:

Remember that for this kind of question, when f(x) is given as 3, then 3 is the y value of the point. So you must have a point whose value is (x,3)

There is only one point that does that. x = - 2

The answer is D

Answer:

a+b+c is the formula for calculating the perimeter of a triangle:)

Step-by-step explanation:

Answer:

0= x

Step-by-step explanation:

8= 8 + 4x +5x

Combine like terms

8 = 8+9x

Subtract 8 from each side

8-8 =8+9x-8

0 = 9x

Divide by 9

0/9 = 9x/9

0= x

Answer:

78%

Step-by-step explanation:

.94 + .78 + .62 = 2.34

2.34/3 = .78

.78 = 78%

Jeremy's weighted average is 83.6%

The grades and the weights of the grades can be represented using the following table

Subject     Final Grade   Average

Test              50%              94%

Quiz             35%               78%

Homework   15%               62%

The weighted average (w) is the sum of the product of the final grades and the average.

So, we have:

[tex]w = \sum Final\ Grade \times Avearge[/tex]

This gives

[tex]w = 50\% \times 94\% + 35\% \times 78\% + 15\% \times 62\%[/tex]

Evaluate the products

[tex]w = 47\% + 27.3\% + 9.3\%[/tex]

Evaluate the sums

[tex]w = 83.6\%[/tex]

Hence, the weighted average is 83.6%

Read more about weighted average at:

https://brainly.com/question/11408596

Answer:

$70

Step-by-step explanation:

Find how much money she has left by subtracting 30 from 100:

100 - 30

= 70

So, she has $70 left in her balance.

Answer: Circumference = 7.85 inches

Concept:

Here, we need to know the idea of circumference.

The circumference is the perimeter of a circle. The perimeter is the curve length around any closed figure.

Circumference = 2πr

r = radius

π = constant

Solve:

Given information

r = (1/2) d = (1/2) (2.5) = 1.25 inches

π = 3.14

Given formula

Circumference = 2πr

Substitute values into the formula

Circumference = 2 · (3.14) · (1.25)

Simplify by multiplication

Circumference = (2.5) · (2.14)

Circumference = [tex]\boxed {7.85 inches}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation:

Using the formulas

C=2πr

d=2r

Solving forC

C=πd=π·2.5≈7.85398in

Answer:

14,712 ft difference

Step-by-step explanation:

15,062 - 350 = 14,712

Answer:

Step-by-step explanation:

Difference in elevation is 15,062-(-350)=15,062+350=15,412

Answer:

that's sooooooo trued to me

Answer:

Point C is in the interior of angle ABD.

Answer:

I got B and C.

Step-by-step explanation:

When you rotate by 180° you turn it so that it is facing the other way (ie D is B, C is A, etc) since it's a rectangle, when you rotate by 180°, you still have the same rectangle with angles in the same corners. when you reflect across the midpoint, you are just flipping your rectangle over, and so would again have the same effect as turning it 180°.

Answer:

(x - 6)(x + 2)

Step-by-step explanation:

x^2 - 4x - 12

=x^2 - 6x + 2x - 12

=x( x - 6) + 2(x - 6)

=(x - 6)(x + 2)

Answer:

x^2 -4x-12

factorization of 12 =2×2×3 = 6×4

or in the place of 4x = we put (6-2)x

x^2-(6-2)x-12

x^2-6x+2x-12

x(x-6)+2(x-6)

(x-6) (x+2)

Answer:  1.125 miles

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

[tex]4x + 24 = 7x - 49 \\ then \: collect \: the \: same \: variable \\ 4x - 7x = - 49 - 24 \\ x = - 63 \div - 3 = 21[/tex]

Answer:

Step-by-step explanation:

Start a little more generally. Carefully find k

distance = k * speed ^2      

112 = k*40^2

112 = k * 1600                     Divide by 1600

112/1600 = k

k = 0.07

Now do the question you are asked to do.

distance = k * speed^2

distance = 0.07 * 65^2

distance = 295.75

Now having done that, you can set up a proportion.

d1 / d2 = k speed1^2/kspeed2^2      Cancel the ks

112/d2 = 40^2 / 65^2                         Cross multiply

112 * 65^2 = 40^2 * d2                      Divide by 40^2

112 * 65^2/40^2 = d2                        Expand the squares

112 * 4225 / 1600 = d2

295.75 = d2    

The second way is shorter, but I suggest the long way until you get comfortable with it.

Divide total people by total flights:

3720/31 = 120

There was 120 people on each flight

Step-by-step explanation:

A 45° angle is complementary to angle

45°+x°=90°

I hope it helped U

stay safe stay happy

Step-by-step explanation:

27=9x+2-4x

or, 27-2=9x-4x

or,25=5x

or,25/5=X

so, X=5

Answer:

D

Step-by-step explanation:

im thinking its d, because prime factorisation is a way of expressing a number as a product of its prime factors.

a isn't correct since 9 isn't is a prime number.

b isn't correct because you wouldn't use decimals typically.

c isn't correct because 1 is not a prime number.

d is the only correct solution since all the numbers listed are prime numbers.

Answer:

[tex]thank \: you[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

Let x, y, z represent the numbers of 20-cent, 35-cent, and 50-cent valentines. Then the given relations can be written as ...

  x = 1 +2y

  z = -2 +y

  0.20x +0.35y +0.50z = 4.20

__

Using the first two equations to substitute for x and y in the third equation, we get ...

  0.20(1 +2y) +0.35y +0.50(-2 +y) = 4.20

  1.25y -0.80 = 4.20 . . . . . simplify

  1.25y = 5.00 . . . . . . . . . . add 0.80

  y = 4 . . . . . . . . . . . . . . . divide by 1.25

  x = 1 +2(4) = 9

  z = -2 +4 = 2

Romeo bought 9 20-cent, 4 35-cent, and 2 50-cent valentines.

Answer:

I believe the answer is B. a^2 = c^2 - 2cx + x^2 + h^2

Step-by-step explanation:

The law of cosines states: c^2 = a^2 + b^2 - 2bc * cos(C). If we plug in the values from the diagram, we'll have (c-x)^2 = a^2 + h^2 -2ah * cos(90)

cos(90) = 0, so now we have just (c-x)^2 = a^2 + h^2

Let's expand this to c^2 -2cx + x^2 = a^2 + h^2

Isolate a^2 and we now have a^2 = c^2 -2cx + x^2 + h^2

pls vote me brainliest if i was able to help you!! <3

The coordinate of JK is (-1.7, -0.3)

The coordinate of the points that divides the line segment in the given ratio is calculated as:

[tex](x, y) = (\frac{ax_1 +bx_2}{a+b} , \frac{ay_1 +by_2}{a + b} )[/tex]

where;

a:b = 7:8

From the image;

(x₁, y₁) = (-6, 5) and,

(x₂, y₂) = (2, -5)

Substitute the given points in the equation above to calculate the coordinates of JK.

[tex](x, y) = (\frac{7(-6)+8(2)}{7+8} , \frac{7(5) +8(-5)}{7+8} )\\\\(x, y) = (\frac{-26}{15} , \frac{-5}{15} )\\\\(x,y) = (-1.7, -0.3)[/tex]

Thus, the coordinate of JK = (-1.7, -0.3)

Check the image uploaded for the plot of point K

Learn more here:https://brainly.com/question/12547932

Answer:

go to symbolab and it will simplify for you, brainly is useless with these kinds of questions. Symbolab.com very easy to use and gives you answer right away instead of have to wait for some oaf like me to solve your problems.

Step-by-step explanation:

168

this is the full process

Step-by-step explanation:

The answer is 10 times

=> 4 hundredths x 10 = 4 tenths

=> 0.04 x 10 = 0.4, which is correct

Hope that helps