Joan can mow a 7- acre field in 5 hours. How long would it take her to mow a 5.6- acre field?

[tex]x = \frac{ac + b}{2c - ab} [/tex]

Refer to the attachment for step by step explaination.

Answer:

[tex]x=\frac{b+ax}{2c-ba}[/tex]

Step-by-step explanation:

When given the following expression, one is asked to solve for (x):

[tex]\frac{2x-a}{b}=\frac{ax+1}{c}[/tex]

Use cross products to rid the variable in the denominator,

[tex]c(2x-a)=b(ax+1)[/tex]

Simplify, distribute, multiply every term in the parenthesis by the term outside of it,

[tex]2xc-ac=bax+b[/tex]

Inverse operations, collect all terms with variable (x) on one side of the equation:

[tex]2xc-ac = bax + b\\\\2xc - bax = b + ac[/tex]

Factor, remove a like term that exists in both of these expressions,

[tex]x(2c-ba)=b+ax[/tex]

Inverse operations,

[tex]x=\frac{b+ax}{2c-ba}[/tex]

Answer:

26

Step-by-step explanation:

Let x represent the missing number

[tex] 8\frac{11}{15} = 7\frac{x}{15} [/tex]

Convert both fractions to improper fractions

[tex] \frac{131}{15} = \frac{105 + x}{15} [/tex]

Cross multiply

[tex] 15(105 + x) = 15(131) [/tex]

[tex] 1,575 + 15x = 1,965 [/tex]

Subtract both sides by 1,575

[tex] 15x = 1,965 - 1,575 [/tex]

[tex] 15x = 390 [/tex]

Divide both sides by 15

[tex] x = \frac{390}{15} [/tex]

x = 26

Answer:

Karen: 15; Dale: 9; Tom: 60

Step-by-step explanation:

"Karen and Dale and Tom sent a total of 84 messages during the weekend."

k + d + t = 84

"Dale sent six fewer messages than Karen"

d = k - 6

"Tom sent four times as many as Karen."

t = 4k

Substitute k - 6 for d and 4k for t in the first equation.

k + d + t = 84

k + k - 6 + 4k = 84

6k - 6 = 84

6k = 90

k = 15

d = k - 6 = 16 - 6 = 9

t = 4k = 4(15) = 60

Answer: Karen: 15; Dale: 9; Tom: 60

Answer:

It will take 25.6 years for the mass of the sample to reach 400 grams.

Step-by-step explanation:

Element X is a radioactive isotope such that every 25 years, its mass decreases by half.

This means that the amount of the substance after t years can be modeled by a function in the following format:

[tex]A(t) = A(0)(0.5)^{\frac{t}{25}}[/tex]

In which A(0) is the initial amount.

Initial mass of a sample of Element X is 910 grams.

This means that [tex]A(0) = 910[/tex]

So

[tex]A(t) = A(0)(0.5)^{\frac{t}{25}}[/tex]

[tex]A(t) = 910(0.5)^{\frac{t}{25}}[/tex]

How long would it be until the mass of the sample reached 400 grams?

This is t for which [tex]A(t) = 400[/tex]

So

[tex]A(t) = 910(0.5)^{\frac{t}{25}}[/tex]

[tex]400 = 910(0.5)^{\frac{t}{25}}[/tex]

[tex](0.5)^{\frac{t}{25}} = \frac{400}{910}[/tex]

[tex](0.5)^{\frac{t}{25}} = 0.43956[/tex]

[tex]\log{(0.5)^{\frac{t}{25}}} = \log{0.43956}[/tex]

[tex]\frac{t}{25}\log{0.5} = \log{0.43956}[/tex]

[tex]t = \frac{25\log{0.43956}}{\log{0.5}}[/tex]

[tex]t = 25.6[/tex]

It will take 25.6 years for the mass of the sample to reach 400 grams.

Answer:

29.6

Step-by-step explanation:

Answer:

j/3

Step-by-step explanation:

quotient is division

j/3

Answer:

9.1

Step-by-step explanation:

what is the length of x of the side of the triangle below?

Answer:                                                                    

14 and 1

Explanation:

14 + 14 + 1 + 1 = 30

14 x 1 = 14

The perimeter is the sum of all 4 sides. Divide the perimeter in half fo the some of one length and one width:

Length + width = 15

Area is length x width

Find 2 numbers that when added equal 15 but when multiplied equal 14

15 + 0 = 15, 15 x 0 = 0

14 + 1 = 15, 14 x 1 = 14

The answer is 14 ft long by 1 ft wide

Answer:

24 inches

Step-by-step explanation:

Answer:

7.5 or 7 1/2

Step-by-step explanation:

since in the original you divide by 4 and multiply by 5,

the same rule applies for the second.

6/4=1.5x5=7.5

Answer:

D-780 squared inches

Step-by-step explanation:

you multiply 2(l)(w)+2(l)(h)+2(w)(h)

Answer:

Last option 780.

Step-by-step explanation:

To get the surface area for this you will need to get the area of each square that you see is in the net version. Once you do that you add them all together. Here is the math. . .

(4*25)+(4*10)+(4*25)+(10*25)+(10*25)+(4*10) = 780 total surface area.

If this looks confusing just look at the net version of the rectangular prism and you can see there is a duplicate of the different dimension triangles. These areas would be (4*25), (4*10), (10*25). There are a total of 3 different size triangles and all of them have duplicates. So we just multiply everything by 2

(4*25)+ (4*10)+(10*25) = 390 now multiply that by 2 and you get 780 again.

Hope the explanation helps :)

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The center of dilation is point S, so S' is at the same location. The other points move to 5/3 of their distance from S.

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Explanation:

We have n = 5 sides. This means the interior angles sum up to...

S = 180(n-2)

S = 180(5-2)

S = 180(3)

S = 540

All five interior angles of this pentagon add up to 540 degrees.

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Explanation:

That calculation you wrote out would only apply if each lamb ate 1 full bale of alfalfa.

Instead, each lamb eats 1/8 of a bale. So you'll divide the 1596 value by 8 to get 1596/8 = 199.50

This is the same as saying (1/8)*1596 = 0.125*1596 = 199.50

---------------------

Or we can think of it like this

1 day = 1/8 bale of alfalfa

168*(1 day) = 168*(1/8 bale of alfalfa)

168 days = 21 bales of alfalfa

This says that one lamb will eat 21 bales of alfalfa over the course of 168 days

At $9.50 per bale, the total cost for one lamb is 9.50*21 = 199.50 dollars

This cost applies to one lamb only. So if you had say 3 lambs overall, then you'd multiply that by 3.

Answer:

Step-by-step explanation:

Take angle A as reference angle

using sin rule

sin A=opposite/hypotenuse

sin A=10/13

sin A=0.76

[tex]sin^{-1}[/tex] 0.76=49.46 degree

A=49.5 degree

Answer:

Solution given:

Annie needs 250 lb of cement to fix the outer step.

Each bag hold 40 lb of cement.

Now

40 lb =1bag

we need

250lb= ? bag.

we have

no of bag =needed lb/1 bag's lb=250/40=250/40=6.25

we do not need more than 7 bags

Annie needs 7 bags.

So

The required inequality is:

b≥7.

Step-by-step explanation:

100%-3%=97%

$1500*97%=$1455

Answer:

Undefined

Step-by-step explanation:

This equation is just a vertical line, so the slope is undefined.

Answer:

21 flowers

Step-by-step explanation:

because if dora can plant 18 plants then Charlie can plant 21 flowers

Check the picture below.

so we know the radius of the semicircle is 2 and the rectangle below it is really a 4x4 square, so let's just get their separate areas and add them up.

[tex]\stackrel{\textit{area of the semicircle}}{\cfrac{1}{2}\pi r^2}\implies \cfrac{1}{2}(\stackrel{\pi }{3.14})(2)^2\implies 3.14\cdot 2\implies 6.28 \\\\\\ \stackrel{\textit{area of the square}}{(4)(4)}\implies 16 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{sum of both areas}}{16+6.28=22.28}~\hfill[/tex]

Answer:

OMGGGG OMGGG I NEEDTHIS QUESTION TOOOOOO

Answer:

linearly because the  table shows that the daisies increased by the same amount each month

Step-by-step explanation:

Answer:

Linearly, because the table shows that the daisies increased by the same amount each month

Step-by-step explanation:

Take the second term and subtract the first term for the output

13.1 -10 = 3.1

Do the same for the third and the second

16.2 -13.1 = 3.1

And the fourth and third

193. -16.2 = 3.1

This is a linear increase since we add the same amount each time

Answer:

$639

Step-by-step explanation:

$450 * .14 = 63

63 * 3 = 189

450 + 189 = 639

Answer:

wheres the photo

Step-by-step explanation:

Answer:

Option C

4w + 4(8)

=4w + 32.

Answer:

Thus this mixture contains 184 pints of Zesty lemon tea.

Answer:

hlw its jess your ans is here ↑ ↓

:- 150 rotation and the other 30 rotation about the same point is equivalent to 150+30 = 180

rotation about that point

Answer:

B)10

Step-by-step explanation:

Because this is a right angle(indicated by the red box) the total measure should be 90°.

And based on that we say 5X +40=90

Subtract 40 from both sides to get 5x=50

And then divide both sides by 5 to get x=10

Answer:

x = 10°

Step-by-step explanation:

5x° + 40° = 90°

5x° = 90°-40°

5x°=50°

x°= 50°/5

x = 10°

Answer:

i don't now to arrange thats

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Explanation:

The set {1, 2}U{2, 6, 7, 9}U{5, 6, 7} simplifies to {1,2,5,6,7,9} after we combine everything and sort the values. We toss any duplicates.

Let B = {1,2,5,6,7,9}

There are 6 items in set B out of 10 items in set A.

The probability of landing in set B, if you pick something randomly from A, is 6/10 = 3/5

Answer:

3/5

Step-by-step explanation:

Answer:

243.

Step-by-step explanation:

they are multiplying by -3.

3x(-3)= -9

-9x(-3)= 27

27x(-3)= -81

so you would do -81x(-3) which equals 243.