The Garcia family and the Lee family each used their sprinklers last summer. The Garcia family's sprinkler was used for 40  hours. The Lee family's sprinkler was used for 20  hours. There was a combined total output of 2000L  of water. What was the water output rate for each sprinkler if the sum of the two rates was 60L  per hour?

Answer:

[tex]a_n=-3a_{n-1}[/tex] where [tex]a_1=2[/tex]

Step-by-step explanation:

Recursive means you want to define a sequence in terms of other terms of your sequence.

The common ratio is what term divided by previous term equals.

The common ratio here is -6/2=18/-6=-54/18=-3.

Or in terms of the nth and previous term we could say:

[tex]\frac{a_n}{a_{n-1}}=r[/tex]

where r is -3

[tex]\frac{a_n}{a_{n-1}}=-3[/tex]

Multiply both sides by the a_(n-1).

[tex]a_n=-3a_{n-1}[/tex] where [tex]a_1=2[/tex]

Answer:

see explanation

Step-by-step explanation:

A recursive rule allows us to obtain any term in the sequence from the previous term.

These are the terms of a geometric sequence with common ratio r

r = - 6 ÷ 2 = 18 ÷ - 6 = - 54 ÷ 18 = - 3

Thus to obtain a term in the sequence multiply the previous term by - 3

[tex]a_{n+1}[/tex] = - 3 [tex]a_{n}[/tex] with a₁ = 2

Answer:

C (2, -5/2)

Step-by-step explanation:

To find the midpoint of two points

mid = (x1+x2)/2, (y1+y2)/2

       = (2+2)/2, (4+-9)/2

       = 4/2, -5/2

       =2,-5/2

Answer:

A. Parabola

Step-by-step explanation:

Parabola best describes the locust of points equidistant from a given directrix and focus.

Parabola is the curve that best describes the locus of points equidistant from a given directrix and focus. This can be obtained by understanding what a parabola is.

The equation is y² = 4ax, when directrix is parallel to the y-axis, a is distance from origin to focus.

Hence parabola is the curve that best describes the locus of points equidistant from a given directrix and focus.

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For this case we have that a percentage equivalent to[tex]\frac {1} {8}[/tex]is given by:

[tex]x = \frac {1} {8} * 100 =[/tex] 12.5%

Then, according to the steps, it is observed that Harriet made an incorrect division, deboa multiply. So, the second step is the wrong one.

Answer:

Option B

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}[/tex]

[tex]\bf A=5000\left(1+\frac{0.08}{12}\right)^{12\cdot 15}\implies A=5000(1.00\overline{66})^{180}\implies A\approx 16534.61[/tex]

Answer:

B

Step-by-step explanation:

Given

6x³ + 6 ← factor out 6 from each term

= 6(x³ + 1)

x³ + 1 is a sum of cubes and factors as

x³ + 1 = (x + 1)(x² - x + 1)

Hence

6x³ + 6 = 6(x + 1)(x² - x + 1)

With factor (x + 1) → B

Answer:

b) x + 1

Step-by-step explanation:

you can either

1) take (6x³ + 6) and divide by all the choices to see which one gives you a factor. You will realize that if you divide this by option b, you will be able to factorize the equation as follows:

(6x³ + 6) = 6(x+1)(x²−x+1)

Hence option b is a factor

or

2) (my preferred method), utilize the properties of functions and roots.

Let function f(x) = 6x³ + 6

any value of a which gives f(a) = 0 is a root , i.e (x-a) is a factor.

In this case, lets consider option b

let x + 1 = 0 -------> or x = -1

substitute this into the function f(x)

f(-1) = 6 (-1)³ + 6

f(-1) = -6 + 6 = 0

hence x = -1 is a root , or (x+1) is a factor.

as a sanity check, lets try choice a) x -1

let x - 1 = 0 -------> or x = +1

substitute this into the function f(x)

f(1) = 6 (1)³ + 6

f(1) = 6 + 6 = 12 ≠0

hence x = 1 is NOT a root , or (x-1) is NOT a factor.

You can do the same for c and d and find that they too are NOT factors.

Answer:

(f-g)(x) = x-3

Step-by-step explanation:

Given

f(x) = 3x-2

and

g(x) = 2x+1

We have to find (f-g)(x)

So,

(f-g)(x) = f(x)-g(x)

= 3x-2 - (2x+1)

= 3x-2-2x-1

=x-3

Hence,

(f-g)(x) = x-3

Answer:

( f - g ) ( x ) = x - 3

Step-by-step explanation:

We are to find [tex] ( f - g ) ( x ) [/tex] given that [tex] f ( x ) = 3 x - 2 [/tex] and [tex] g ( x ) = 2 x + 1 [/tex].

So basically we have to subtract the function g from function f.

[tex] ( f - g ) ( x ) = f(x) - g(x) [/tex]

Substituting the given functions in the above equation to get:

[tex] ( f - g ) ( x ) = (3x - 2) - (2 x + 1 ) [/tex]

[tex] ( f - g ) ( x ) = 3x - 2 - 2 x - 1  [/tex]

[tex] ( f - g ) ( x ) = 3x - 2 x - 2 - 1  [/tex]

[tex] ( f - g ) ( x ) = x - 3 [/tex]

Answer:

x =  -12.42    or  x = 2.42

Step-by-step explanation:

x^2 + 10x - 13 = 17

To solve this using the completing the square method, we will follow the  steps below;

First, we will add 13 to both side of the equation, we want only the x variable to be on the left-hand side of the equation

x^2 + 10x - 13 + 13 = 17 + 13

x^2 + 10x  = 30

The next step is to add both-side of the equation  by square of half of the coefficient of x (that is ; half of 10 is 5, then we will add 5²  to both-side of the equation)

x^2 + 10x + 5²  = 30 + 5²

Then we can now factorize the left-hand side of the equation and at the same time simplify the right-hand side of the equation

(x + 5)²   =   30 + 25

(x + 5)²   = 55

We will then take the square root of both-side of the equation

√(x + 5)²   = ±√55

x + 5  =  ±√55

To get the value of x, we will subtract 5 from both-side of the equation

 x + 5 - 5   =  ±√55 - 5

x =  ±√55  -  5

Either x = + √55 -5  = 7.42 -5 = 2.42

OR

x = -√55 - 5   = -7.42 - 5 = -12.42

Therefore either x =  -12.42    or  x = 2.42

 x =  -12.42    or   2.42

The answer is 84 degrees because d and f both are 48 degrees so that adds up to 96. So that means you add 84 plus 96 which is 180 so the answer is 84 degrees.

Answer. The answer is 84

Answer:

b

becasue to find his current weight you would use what you know and the amount of lbs he added (represented as x)

96 + x

Step-by-step explanation:

Answer:

[tex]\large\boxed{f^{-1}(x)=\dfrac{x+4}{3}=\dfrac{1}{3}x+\dfrac{4}{3}}[/tex]

Step-by-step explanation:

[tex]f(x)=3x-4\to y=3x-4\\\\\text{exchange x to y and vice versa}\\\\x=3y-4\\\\\text{solve for y}\\\\3y-4=x\qquad\text{add 4 to both sides}\\\\3y=x+4\qquad\text{divide both sides by 3}\\\\y=\dfrac{x+4}{3}[/tex]

Answer: 3p+5=11

Step-by-step explanation:

3p+5=11

-5 -5

3p=6

3p/3=6/3

P=2

$2

The cost of each pencil is $2.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Number of pencils = 3

Number of notebook = 1

Cost of a notebook = $5

Total cost = $11

Let number of pencil be p.

Lela purchased three mechanical pencils and a notebook is

⇒ [tex]3p+5=11[/tex]

⇒ [tex]3p=11-5[/tex]

⇒ [tex]3p=6[/tex]

⇒ [tex]p=\frac{6}{3}[/tex]

⇒ [tex]p=2[/tex]

Hence we can conclude that the cost of each pencil is $2.

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So you're asking to evaluate this equation?

mk/m+k for m = 6 and k = 2

Answer:

[tex]\frac{2x-y}{x(x-y)}[/tex]

Step-by-step explanation:

To express as a single fraction

multiply numerator/denominator of [tex]\frac{1}{x}[/tex] by (x - y) and

multiply numerator/ denominator of [tex]\frac{1}{x=y}[/tex] by x

= [tex]\frac{x-y}{x(x-y)}[/tex] + [tex]\frac{x}{x(x-y)}[/tex]

Add the numerators leaving the denominator

= [tex]\frac{2x-y}{x(x-y)}[/tex]

Answer:

Option D is correct.

Step-by-step explanation:

Original Price of car = $38,000

Current Price of car = $28,500

The residual value of Sally's leased car = x = ?

Residual value * Original Price = Current Price

x * 38,000 = 28,500

x = 28,500/38,000

x = 0.75

Since we need to find percentage

Multiply the residual value with 100 i.e,

0.75 * 100 = 75%

Option D is correct.

Answer:

[tex]x=\sqrt[3]{10}-2[/tex]

Step-by-step explanation:

The composite function (f(x+1)) is moved in the x-axis by -1, you know this by solving x+1=0.

The equivalent expresion for f(x+1) is

[tex]f(x+1)= (x-1+3)^{3}+4[/tex]

[tex]f(x+1)=(x+2)^{3}+ 4[/tex]

Eval the above expression in g(x)

[tex]g(x)=(x+2)^{3}+4-2[/tex]

We must find x that gives g(x)=12

The equation is the following

[tex]12=(x+2)^{3}+2[/tex]

Grouping terms>

[tex](x+2)^{3} =10[/tex]

To solve for x, must apply cubic root in both sides of equation:

[tex]\sqrt[3]{(x+2)^{3} } =\sqrt[3]{10}[/tex]

it then turns in the following>

[tex]x+2=\sqrt[3]{10}\\[/tex]

Giving the stated answer

Answer:

I think it may be B, but double check

Answer:

B and D

Step-by-step explanation:

Considering the multiple choices and let us assume that x = 2,

Option A would be equal to [tex]\frac{3}{4}x[/tex],

so if x = 2, then;

        [tex]\frac{3}{4}x[/tex] = 1.5 (which is less than x)

Option B would give [tex]\frac{5}{4} x[/tex],

so if x = 2, then;

       [tex]\frac{5}{4} x[/tex] = 2.5 ( which is greater than x)

From option C,

      [tex]\frac{7}{8} x[/tex] = 1.75 (which is less than x)

From option D,

     [tex]\frac{9}{8} x[/tex] = 2.25 ( which is greater than x)

So, options B and D are expressions whose values are greater than x.

Answer:

Step-by-step explanation:

We know: the angles measures in a triangle add up to 180°.

(look at the picture)

z + 50 + 60 = 180

z + 110 = 180    subtract 110 from both sides

z = 70°

x + 50 + 70 = 180

x + 120 = 180         subtract 120 from both sides

x = 60°

Angles x, y and z are on one side of a straight line. Therefore they add to 180°.

x + y + z = 180

60 + y + 70 = 180

y + 130 = 180         subtract 130 from both sides

y = 50°

Answer:

x = 60°, y = 50°

Step-by-step explanation:

We know: the angles measures in a triangle add up to 180°.

z + 50 + 60 = 180

z + 110 = 180    subtract 110 from both sides

z = 70°

x + 50 + 70 = 180

x + 120 = 180         subtract 120 from both sides

x = 60°

Angles x, y and z are on one side of a straight line. Therefore they add to 180°.

x + y + z = 180

60 + y + 70 = 180

y + 130 = 180         subtract 130 from both sides

y = 50°

5x^4

Step-by-step explanation:

simply we take 5x^4 bec. it can be divided by 40 and 135

Check the picture below.

Answer:

Step-by-step explanation:

The cost function is

[tex]C=10n+150[/tex]

Where [tex]n[/tex] is the number of buckets of apples sold.

The revenue is defined as

[tex]r=15n[/tex]

The image attached shows both functions graphed in the same coordinate system. According with the graph, the break-even point is at (30,450), that is, 30 of buckets sold and $450 of revenue and cost.

In other words, we need to sell 30 buckets to have the cost and revenue equals.

Therefore, the answer is A.

Answer:

5/6 (if including 3)       4/6 (not including 3)

Step-by-step explanation:

1 and 2 are less than 3

4 and 6 are even

that leaves 5 and 3.

so 4 of the numbers are even or less than 3

Probability of rolling even number or number less than 3 is 2/3.

Probability is defined by the possibility of the event to happen which is ratio of no. of favorable outcomes and the total no. of outcomes.

Probability of event = P(E) = No. of favorable outcomes/Total No. of outcomes

Here given that the dice is fair and six-sided is rolled.

Total no. of outcomes by rolling the dice=6 i.e. {1,2,3,4,5,6}

No. of favorable outcomes of getting even no. =3 i.e. {2,4,6)

Probability of rolling an even no.=P(even)= No. of favorable outcomes/Total No. of outcomes = 3/6

No. of favorable outcomes of getting no. less than 3 =2 i.e. {1,2}

Probability of rolling no. less than 3=P(<3) =No. of favorable outcomes/Total No. of outcomes = 2/6

No. of favorable outcomes of getting even no and number less than 3 =1 i.e. {2}

Probability of rolling an even no. and no. less than 3 =P(even and <3) = P(even ∩ <3)= No. of favorable outcomes/Total No. of outcomes = 1/6

As we know P(A∪B)=P(A)+P(B)-P(A∩B)

Probability of rolling an even no.or no. less than 3 = P(even or <3) = P(even ∪ <3)= P(even)+P(<3)-P(even ∩ <3)

=(3/6)+(2/6)-(1/6)

=4/6

=2/3

Therefore probability of rolling even number or number less than 3 is 2/3.

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Answer: 245 [tex]in^{2}[/tex]

Step-by-step explanation:

You can find the Surface Area of a figure by adding up the areas of each shape.

First you have to find the area of the base.

7×7 = 49

Then you can find the area of the 4 triangles that complete the pyramid.

Formula for area of a triangle: [tex]\frac{1}{2} bh[/tex] (one half of base times height)

[tex]\frac{1}{2} (14*7) = x\\\frac{1}{2} 98 = x\\x = 49[/tex]

Since all the triangles are the same, you only have to calculate that once.

Now you just add everything together, and that's your surface area.

[tex]49+49+49+49+49= 245[/tex]

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Answer:  245

Step-by-step explanation:

first you have to 7 for the square which = 14

then after that you do 1/2 b x h = 1/2  7 x 14= 3.5 x 14= 49 but then you have 4 triangles so 49 x 4=196.     Then  49 + 196= 245  

Answer:

Osvoldo does not meet his goal

He had to have eaten at least 66 grams of whole grains to meet his goal.

Step-by-step explanation:

step 1

Find out the 30% of the grams of carbohydrates that Osvoldo ate today

Remember that

30%=30/100=0.30

so

0.30(220)=66 grams

step 2

Compare the 30% of the grams of carbohydrates that Osvoldo ate today with the 55 grams of whole grains

we know that

To Osvoldo meet his goal the 55 grams of whole grain must be greater than or equal to the 30% of the grams of carbohydrates that Osvoldo ate today

55 < 66

therefore

Osvoldo does not meet his goal

He had to have eaten at least 66 grams of whole grains to meet his goal.

[tex]\bf \sqrt{x+11}-x=-1\implies \sqrt{x+11}=x-1\implies \stackrel{\textit{squaring both sides}}{(\sqrt{x+11})^2=(x-1)^2} \\\\\\ x+11=\stackrel{\mathbb{F~O~I~L}}{x^2-2x+1}\implies 11=x^2-3x+1\implies 0=x^2-3x-10 \\\\\\ 0=(x-5)(x+2)\implies x= \begin{cases} 5\\ -2 \end{cases}[/tex]

Gives x = -5 or x = 2.

Learn how to solve radical equations step by step by isolating terms and squaring, resulting in solutions to the given equation.

To solve the equation (square root of x+11)-x=-1, follow these steps:

Answer:

y  ≥ 14.

Step-by-step explanation:

y - 27 ≥ -13 Add 27 to both sides:

y  ≥ 14 (answer).

For this case we must find the solution of the following inequality:

[tex]y-27 \geq-13[/tex]

We must add 27 to both sides of the inequality:

[tex]y \geq-13 + 27[/tex]

We know that different signs are subtracted and the sign of the major is placed.[tex]y \geq14[/tex]

So, the solution is [tex]y \geq14[/tex]

Answer:

Option C

Answer:

36x² + 24x + 4

Step-by-step explanation:

Given

(6x + 2)² = (6x + 2)(6x + 2)

Each term in the second factor is multiplied by each term in the first factor, that is

6x(6x + 2) + 2(6x + 2) ← distribute both parenthesis

= 36x² + 12x + 12x + 4 ← collect like terms

= 36x² + 24x + 4

Answer:

x=7

Step-by-step explanation:

The given equation is:

[tex]\frac{x}{3}+\frac{x}{6} = \frac{7}{2}[/tex]

Multiplying both sides by LCM of 3 and 6

So,

[tex]\frac{x}{3}*6+\frac{x}{6}*6 = \frac{7}{2}*6\\2x+x=7*3\\3x=21\\\frac{3x}{3} =\frac{2}{3}\\ x=7[/tex]

Hence, the solution of the equation is x=7 ..

Answer: x = 7

Step-by-step explanation:

(x/3)+(x/6)=7/2

add variables

(2x+x)/6=7/2

combine like terms

3x/6=7/2

simplify

x/2=7/2

multiply denominators by 2

x=7

Answer:

4

Step-by-step explanation:

-36-9+14-31+66

=4

Since + - = - and - - = +

Answer:

Step-by-step explanation:

Look at the picture.

We know: the sum of the angles measure in the triangle is 180°. Therefore we have the equation:

[tex]35^o+35^o+\alpha=180^o[/tex]

Solve it:

[tex]70^o+\alpha=180^o\qquad\text{subtract}\ 70^o\ \text{from both sides}\\\\\alpha=110^o[/tex]

Angle α and β = x are the supplementary angles. Supplementary angles add up to 180°. Therefore:

[tex]\alpha+\beta=180^o[/tex]

[tex]110^o+\beta=180^o\qquad\text{subtract}\ 110^o\ \text{from both sides}\\\\\beta=70^o[/tex]

[tex]\beta+\gamma+\gamma=180^o[/tex]

[tex]70^o+2\gamma=180^o\qquad\text{subtract}\ 70^o\ \text{from both sides}\\\\2\gamma=110^o\qquad\text{divide both sides by 2}\\\\\gamma=55^o[/tex]