Bella can rake the leaves in 3 hours and Jordan can complete the same task in 4 hours. If they work together, how long will it take Bella and Jordan to rake the leaves? Round your answer to the nearest hundredth of an hour.

[tex]x^2-x-42=0\\x^2+6x-7x-42=0\\x(x+6)-7(x+6)=0\\(x-7)(x+6)=0\\x=7 \vee x=-6[/tex]

Answer:

The roots are 7 and -6.

Keys:

When you see a ± in a quadratic equation, you will have multiple solutions; more than one.

Step-by-step explanation:

solve the main expression

[tex]x^2-x-42=0\\x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \left(-42\right)}}{2\cdot \:1}\\\rightarrow \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \left(-42\right)}\\=\sqrt{\left(-1\right)^2+4\cdot \:1\cdot \:42}\\\rightarrow \left(-1\right)^2\\=1^2\\=1\\\rightarrow 4\cdot \:1\cdot \:42\\=168\\=\sqrt{1+168}\\=\sqrt{169}\\=\sqrt{13^2}\\=13\\x_{1,\:2}=\frac{-\left(-1\right)\pm \:13}{2\cdot \:1}[/tex]

solve for x₁

[tex]\frac{-\left(-1\right)+13}{2\cdot \:1}\\=\frac{1+13}{2\cdot \:1}\\=\frac{14}{2\cdot \:1}\\=\frac{14}{2}\\=7[/tex]

solve for x₂

[tex]\frac{-\left(-1\right)-13}{2\cdot \:1}\\=\frac{1-13}{2\cdot \:1}\\=\frac{-12}{2\cdot \:1}\\=\frac{-12}{2}\\=-\frac{12}{2}\\=-6[/tex]

Using it's concept, it is found that the probability that a person chosen at random from this group has brown or green eyes is of [tex]\frac{13}{25}[/tex].

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching the problem on the internet, it is found that the group has 20 + 6 + 17 + 7 = 50 people, of which 20 + 6 = 26 have brown or green eyes, hence the probability is given by:

p = 26/50 = 13/25.

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The asked sum of multiples of five from 10 to 75, inclusive, is 595.

To find the sum of multiples of five from 10 to 75, inclusive, we can use the formula for the sum of an arithmetic series:

Sum = (n/2) * ([first term] + [last term])

Following the given case, the first term (a) is 10, the last term (l) is 75, and the common difference (d) between consecutive terms is 5 (since we are considering multiples of five).

The number of terms (n) can be calculated as:

n = (last term - first term) / common difference + 1

Let's calculate the number of terms first:

n = (75 - 10) / 5 + 1

n = 65 / 5 + 1

n = 13 + 1

n = 14

Now, we can determine the sum of the multiples of five:

Sum = (14/2) * (first term + last term)

Sum = 7 * (10 + 75)

Sum = 7 * 85

Sum = 595

Therefore, the asked sum of multiples of five from 10 to 75, inclusive, is 595.

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Answer: 19.7

Step-by-step explanation:

By the Pythagorean theorem,

[tex](BD)^{2}=8^{2}+18^{2}\\\\(BD)^{2}=388\\\\BD=\sqrt{388} \approx \boxed{19.7}[/tex]

Answer:

slope = 1

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 9 ) and (x₂, y₂ ) = (- 4, 2 )

m = [tex]\frac{2-9}{-4-3}[/tex] = [tex]\frac{-7}{-7}[/tex] = 1

Both lines are parallel because: A. both lines have a slope of 4/3.

The slope of a line = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

The slope of parallel lines are the same, while the slope of perpendicular lines are negative reciprocals.

Slope of AB = 4 units/3 units = 4/3

Slope of CD = 4 units/3 units = 4/3

Both lines have the same slope, therefore, they are parallel to each other.

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Answer:

[tex]h(x) = \frac{1}{4} x[/tex]

Step-by-step explanation:

To find the inverse of a function, the steps are:

In this case, since h(x) is the inverse function of f(x), we can replace x with h(x) in step 3.

_____

f(x)= 4x

Let y= f(x) [tex]\textcolor{steelblue}{\text{ - step 1}}[/tex]

y= 4x

Divide both sides by 4:

[tex] \frac{1}{4} y = x[/tex]

[tex]x = \frac{1}{4} y \: \: \: \textcolor{steelblue}{\: \text{ - step 2}}[/tex]

Replace x with h(x) and y with x:

[tex]\bf{h(x) = \frac{1}{4} x} \: \: \: \textcolor{steelblue}{\: \text{ - step 3}}[/tex]

Additional:

For a similar question on inverse functions, do check out the following!

Answer:

b =22

Step-by-step explanation:

The formula to calculate the area of a trapezoid:

1/2*(a+b)*h : (a: base, b: base, h: height)

The formula to calculate the area of a triangle:

1/2*a*h (a: base, h: height)

All inputs are given for trapezoid so let's first find the area of trapezoid then we can find the value of b:

1/2*(10+12)*7 = 77 cm^2 is the area of trapezoid

now for the area of triangle:

1/2*b*7 = 77 (it was given that the areas are equal)

first we multiply both sides by 2

7*b = 154 now divide both sides by 7

b = 22

Answer:

=> Expand by applying the FOIL method

[tex]2x\cdot \:3x+2x\left(-8\right)-7\cdot \:3x-7\left(-8\right)[/tex]

=> combine like terms

[tex]6x^2-37x+56[/tex]

Answer:

Answer is A 216

Step-by-step explanation:

252×6=1512

1512÷7=216

Answer:

2

Step-by-step explanation:

2 can go into 12,2, and 84

To obtain the greatest common divisor of (g.c.d) we must do it in simultaneous decomposition.

This method consists of extracting the common and uncommon prime factors, then

  [tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{12 \ \ \ 2 \ \ \ 84}\\ \ 6 \ \ \ 1 \ \ \ 42 \end{matrix}\right|\begin{matrix} 2\\ \: \end{matrix} \end{gathered}$}[/tex]

As we can see the number 2, is the only common prime number.

The greatest common factor of 12, 2, and 84 is 2.

Translation: please help it's due today

Would love to help but there is no question to answer

Answer:

Step-by-step explanation:

The total number of counters in the bag is 5 + 3 = 8.

and only 5 are red.

Then

the probability of obtaining a red counter is :

[tex]= \frac{5}{8} = 0.625[/tex]

Answer:

2/9

Step-by-step explanation:

Answer:

The ans of first one is 0/8 = 0

and 6÷0 = undefined....hope this helps:)

Answer:

15, 21, 27, 33, 39, 45, 51 67, 59, 51, 43, 35, 27, 19

20, 27, 34, 41, 48, 55, 62 64, 58, 52, 46, 40, 34, 28

66, 60, 54, 48, 42, 36, 30 6, 12, 18, 24, 30, 36, 42

72, 68, 64, 60, 56, 52, 48 5, 13, 21, 29, 37, 45, 53

50, 47, 44, 41, 38, 35, 32 12, 15, 18, 21, 24, 27, 30

60, 55, 50, 45, 40, 35, 30 19, 22, 25, 28, 31, 34, 37

54, 52, 50, 48, 46, 44, 42 8, 9, 10, 11, 12, 13, 14

69, 62, 55, 48, 41, 34, 27 2, 9, 16, 23, 30, 37, 44

24, 26, 28, 30, 32, 34, 36 3, 7, 11, 15, 19, 23, 27

52, 50, 48, 46, 44, 42, 40 16, 19, 22, 25, 28, 31, 34

70, 65, 60, 55, 50, 45, 40 55, 54, 53, 52, 51, 50, 49

4, 12, 20, 28, 36, 44, 52 11, 15, 19, 23, 27, 31, 35

21, 28, 35, 42, 49, 56, 63 61, 60, 59, 58, 57, 56, 55

10, 15, 20, 25, 30, 35, 40 18, 19, 20, 21, 22, 23, 24

25, 33, 41, 49, 57, 65, 73 58, 56, 54, 52, 50, 48, 46

yan yung bilang TXS me later ;-)

Answer: I think the answer is A (4,6)

Step-by-step explanation:

Because point B is translated up you have to move the whole shape and pint D would end up at (4,6)

Answer:

a) k = 10              b) k = 7.5

Step-by-step explanation:

( 5k+ 20 ) + ( 7k + 40 ) = 180

12k + 60 = 180

12k = 120

k = 10

40 + ( 12k + 10) + 180 - ( 8k + 80 ) = 180

50 + 12k + 180 - 8k - 80 = 180

50 + 12k -8k - 80 = 0

50 + 4k - 80 = 0

30 = 4k

k = 7.5

Answer:

22 plants

Step-by-step explanation:

Because 6/3 is 2/1 so 11 seed packets will grow 22 plants.

Step-by-step explanation:

5 - 3x = -6 ( x + 2 )

5 - 3x = -6x - 12

-3x + 6x = - 12 - 5

3x = - 17

[tex]x = - \frac{17}{3} .. \\ [/tex]

Answer:

Exact Form:

x = −17/3

Decimal Form:

x = − 5.6

Mixed Number Form:

x = − 5  2/3

Answer: 1/16

Step-by-step explanation:

Given that there are 4 green marbles, when Dan takes a marble the first time, the probability is 1/4 as there are 4 green marbles. When he puts it back and draws another one, the probability is still 1/4 because Dan didn't take the marble out of the bag(this is known as with replacement)

∴ the total probability of drawing 2 green marbles with replacement is 1/4 × 1/4= 1/16

Hope this helps

The purchase of the hydroponic system by Ingrid Nilsen for $4,000 with a 20% down payment at 10% APR for 36 months, and the related calculations, are as follows:

a) down payment = $800.00 ($4,000 x 20%)

b) amount financed = $3,200 ($4,000 - $800)

c) monthly payment = $103.25

d) total amount repaid = $4,517

e) finance charge = $517

The amount of the periodic payment, finance charge, and total repayment can be computed using an online finance calculator as follows:

Auto Price = $4,000

Loan Term = 36 months

Interest Rate = 10%

Down Payment = $800 ($4,000 x 20%)

Monthly Payment  = $103.25

Total Loan Amount $3,200.00

Upfront Payment = $800.00 ($4,000 x 20%)

Total of 36 Loan Payments = $3,717. ($103.25 x 36)

Total Loan Interest = $517

Total Cost (price, interest, tax, fees) = $4,517

Thus, Ingrid Nilsen repaid a total of $4,517 with $517 in interest (finance charge).

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Answer:

t=0

Step-by-step explanation:

First, we expand everything. The left-hand side is -3(2t) - 1(-3), and we expand it to be -6t+3. The right-hand side is t+t+t+3, and we can reduce it to 3t+3. Now that we have both sides of the equation, we set them to each other.

-6t+3=3t+3 (subtract 3 on both sides)
-6t=3t (add 6t to both sides)
9t =0 (divide by 9)
t=0