four big water bottles can hold 8 gallaons how much can 10 big water gallons hold

Answer:

the answer is -7+-25=-32

The inverse of g(5) and the inverse of h(x) are 2 and [tex]h^{-1}=\frac{-x-13}{4}[/tex] respectively

Inverse of a function

Given the following coordinates and function

g = {(-6, -5), (2, 5), (5,6), (6,9)}

The inverse of "g" is determined by switching the coordinates to have:

g^-1(x) =  {(-5, -6), (5, 2), (6, 5), (9,6)}

Since the value of the y-coordinate when x = 5 is 2, hence g^-1(5) = 2

Given the function expressed as:

h(x) = -4x - 13

y = -4x - 13

Replace y with x

x = -4y - 13

4y = -x - 13

y = (-x-13)/4

[tex]h^{-1}=\frac{-x-13}{4}[/tex]

Determine the composite function [tex](hoh^{-1})(-1)[/tex]

h(h(x)) = h(-4x-13)
h(h(x)) =[tex]\frac{-(-4x-13)-13}{4} \\[/tex]

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

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The dimensions of the garden with the largest area she can enclose are given by 24*14 square yards.

The area (A) of the rectangle with length L and Width W is given by,

A=L*W

The maximum of [tex]y=ax^2+bx[/tex] occurs at x = -b/2a

Let the length and width of the garden be L and W respectively.

Now let my friend use cedar fencing for one width and cheaper metal fencing for rest sides.

Rate of cedar fencing is $17/yard

Then she has to pay for cedar fencing = 17W

rate of cheaper metal fencing is $7/yard

Then she has to pay for metal fencing = 7W+7*2L = 7W+14L

Then according to condition,

17W+7W+14L = 672

24W+14L = 672

12W+7L = 336

7L = 336-12W

L = (336-12W)/7

Then the area of the rectangular garden is given by,

A = L*W

[tex]A=\frac{336-12W}{7}\times W\\A=-\frac{12}{7}W^2+48W[/tex]

So here a = -12/7 and b = 48

Then maximum of W occurs at,

W = -48/(2*(-12/7)) = (48*7)/(2*12) = 336/24 = 14

Then maximum width = 14 yards

then length (L) = (336-12*14)/7 = 168/7 = 24 yards

Hence the dimensions with the leargest area she can enclose is given by = 24 * 14 square yards.

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Answer:

29a² - 3a - 12

Step-by-step explanation:

Given expression:

(6a+2)(6a-5)-(7a-1)(a-2)

Solution:

Apply distributive property.

[tex] \rm=(6a)(6a)+(6a)(-5)+(2)(6a)+(2)(-5)-7a^2+15a-2[/tex]

[tex] \rm= 36a {}^{2} - 30a + 12a - 10 - 7a {}^{2} + 15a - 2[/tex]

Combine like terms:

[tex] \rm=(36a {}^{2} - 7a {}^{2} )+( - 30a+12a+15a)+( - 10 - 2)[/tex]

[tex] = \boxed{ \rm \: 29a {}^{2} - 3a - 12}[/tex]

Done!

Answer:

option 4 and option 3 are the answers respectively

Answer:

[tex] \sqrt{ {2}^{3} } \\ \sqrt{3} \\ .............[/tex]

Answer:

12

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{ASSUMING}[/tex]

[tex]\mathsf{x^{2y}}[/tex]

[tex]\huge\textbf{IF SO, FOLLOW THESE STEPS TO}\\\huge\textbf{SOLVE FOR YOUR RESULT}[/tex]

[tex]\mathsf{x^{2y}}\\\mathsf{= 3^{2(6)}}\\\mathsf{= 3^{2\times6}}\\\mathsf{= 3^{12}}\\\mathsf{= 3\times3\times3\times3\times3\times3\times3\times3\times3\times3\times3\times3}\\\mathsf{= 9\times9\times9\times9\times9\times9}\\\mathsf{= 81\times81\times81}\\\mathsf{= 6,561\times81}\\\mathsf{= 531,441}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{531,441}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

370 + 80x ≤ 1090

Step-by-step explanation:

By using letter variables for the unknown numbers, we can break down the question into mathematical terms:

If the cost is $370 per day and the number of days is unknown, we can substitute the number of days with a placeholder. In this case, it'll be a variable such as x. So the cost can be represented by $370y.

If the cost is $80 per hour and the number of hours is unknown, we can substitute the number of hours with a placeholder. In this case, it'll be a variable such as y. So the cost can be represented by $80x.

The questions asks for the total cost not to exceed $1090 per day. This means that we know that the number of days is 1. We're trying to find the maximum number of hours, so our equation will combine the costs of both day costs and hour costs:

$370 (1 day) + $80 (x hours) ≤ $1090 per day

The symbol is the equal to or less than symbol, meaning the combined total costs is either equal to $1090 or less than it.

To simplify this, we can rewrite it as:

370 + 80x ≤ 1090

Answer:

[tex]y=-4; y=28[/tex]

Step-by-step explanation:

The way I like to think about it, with absolute value meaning the distance is

"find which number are 16 apart from 12". Which means 28 (to the right) or -4 (to the left).

More formally, applying the definition of absolute value,

[tex]|y-12|=16 \leftrightarrow y-12=\pm16\\y-12=-16 \rightarrow y=-4\\y-12=+16 \rightarrow y=28[/tex]

The correct answer is  CI = (71.415%, 78.915%)

The correct option is (A)

A confidence interval is the mean of your estimate plus and minus the variation in that estimate.

Given:

x = 376

Sample = 500 students

CI= [(376/500-1.96 √((376/500)*(124/500)/500) , (376/500-1.96                

                                                                         √((376/500)*(124/500)/500)]

CI = (71.415%, 78.915%)

Hence, CI = (71.415%, 78.915%)

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Two (2) lines are considered to be parallel if their slopes are the same (equal) and they do not intersect.

In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts.

This ultimately implies that, two (2) lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

In conclusion, two (2) parallel lines are shown in the image attached below for more understanding,

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Answer:

C. Focus

.............

Parallel lines have equivalent slopes, so as the slope of the given line is 1, the slope of the line we want to find is also 1.

Substituting into point-slope form and rearranging into slope-intercept form,

[tex]y-2=1(x+6)\\\\y-2=x+6\\\\\boxed{y=x+8}[/tex]

The statement "the y-intercept of g is 4 units above the y-intercept of f'' is true option first is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have two functions:

f(x) = |2x - 1|   and

g(x) = |2x - 5|

After plotting on a coordinate plane.

The y-intercept of f(x) is 1

The y-intercept of g(X) is 5

Or plug x = 0 to find the y-intercept.

The y-intercept of g is 4 units above the y-intercept of f

Thus, the statement "the y-intercept of g is 4 units above the y-intercept of f'' is true option first is correct.

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Answer:

340 i am pretty sure

Step-by-step explanation:

The simplified form of the provided expression is 12x¹⁸ option second is correct.

It is defined as the combination of constants and variables with mathematical operators.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have an expression:

[tex]\rm = \sqrt{144x^{36}}[/tex]

[tex]\rm = \sqrt{(12^2)(x^{36})}[/tex]

[tex]\rm = \sqrt{(12^2)}\sqrt{(x^{36})}[/tex]

12x¹⁸

Thus, the simplified form of the provided expression is 12x¹⁸ option second is correct.

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Answer:

12x18

Step-by-step explanation:

Edge 2023

The area of the shaded part is 8.1447cm²

The formula to calculate the area of the shaded region is expressed as:
Area of the shaded region = Area of sector - Area of triangle

Determine the area of the sector

Area of sector = r²β/2

Area of sector = 14²(46π/180)/2

Area of sector = 78.64 cm²

Determine the area of triangle

Area of triangle = 1/2r²sinβ

Area of triangle = 1/2(14²sin46)

Area of triangle = 140.99/2

Area of triangle = 70.49 cm²

Area of shaded part = 78.64 cm² -  70.49 cm²

Area of shaded part = 8.1447cm²

Hence the area of the shaded part is 8.1447cm²

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The expression of the polynomials with like terms grouped together is (c) [-4x²] + 2xy²  + [10x²y + (-4x²y)]

We have:

10x²y + 2xy² - 4x² - 4x²y

Collect the like terms

- 4x² + 2xy²  + 10x²y - 4x²y

Put each group in bracket

- 4x² + 2xy²  + [10x²y - 4x²y]

Express as positives

[-4x²] + 2xy²  + [10x²y + (-4x²y)]

Hence, the expression of the polynomials with like terms grouped together is (c) [-4x²] + 2xy²  + [10x²y + (-4x²y)]

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Answer:

c

Step-by-step explanation:

Answer:

  18π ≈ 56.5 meters

Step-by-step explanation:

The length of the arc of a circle is given by the formula ...

  s = rθ . . . . where r is the radius, and θ is the central angle in radians

You are given the values of r and θ, so you only need to put them into the formula and simplify.

  s = (27 m)(2π/3) = 18π m

The length of the arc is 18π meters, about 56.5 meters.

Answer:

15

Step-by-step explanation:

0 + 1 = 1

1 + 2 = 3

3 + 3 = 6

6 + 4 = 10

10 + 5 = 15

Answer:

314 in²  (nearest whole number)

Step-by-step explanation:

Radius of a regular polygon: The distance from the center of the polygon to any vertex.  The radius of a hexagon is equal to the length of one side.

Therefore, from inspection of the given diagram:

To find the area of a regular polygon, we first need to calculate the apothem.   The apothem is the line drawn from the center of the polygon to the midpoint of one of its sides.

[tex]\textsf{Length of apothem (a)}=\dfrac{s}{2 \tan\left(\frac{180^{\circ}}{n}\right)}[/tex]

where:

Given:

Substitute the given values into the formula and solve for a:

[tex]\implies \textsf{a}=\dfrac{11}{2 \tan\left(\frac{180^{\circ}}{6}\right)}=\dfrac{11\sqrt{3}}{2}[/tex]

Area of a Regular Polygon

[tex]\textsf{A}=\dfrac{n\:s\:a}{2}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=\dfrac{6 \cdot 11 \cdot \dfrac{11\sqrt{3}}{2}}{2}[/tex]

[tex]\implies \sf A=314.3672216...[/tex]

[tex]\implies \sf A=314\:\:in^2\:\:(nearest\:whole\:number)[/tex]

Answer:

=  -10

Step-by-step explanation:

p + (-q) - 2 = x

if:

p = -3

q = 5

then:

-3 + (-5) - 2 = x

we know that:

+(-) = -

then:

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

x = -10

The value of the expression p + (-q) - 2 is -10 if the p = -3 and q = 5 the answer is -10.

It is defined as the combination of constants and variables with mathematical operators.

We have given an expression:

= P + (-q) - 2

Plug p = -3

q = 5

= -3 + (-5) - 2

= -3 - 5 - 2

= -10

Thus, the value of the expression p + (-q) - 2 is -10 if the p = -3 and q = 5 the answer is -10.

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Answer:

second and fourth option

Step-by-step explanation:

the discriminant of a quadratic equation is the easiest way to know how many solutions there will be

(discriminant: b²- 4ac)

{a discriminant of 0 means 1 solution; discriminant < 0 means no real roots, discriminant > 0 means two real roots }

so, we can quickly run b² - 4ac for each equation provided:

(note: ax² + bx + c is the formatting we use to find a, b, and c)

8² - 4(-9)(-8)

64 - 288 = -224

4² - (4)(1)(4)

16 - 16 = 0

-1² - (4)(-10)(-9)

-1 - 360 = -361

-6² - (4)(3)(3)

36 - 36 = 0

So, because the second and fourth options listed have a discriminant of 0, they have 1 real solution

hope this helps!! have a lovely day :)

Answer:

See below

Step-by-step explanation:

Slope = rise / run

           from 0,-1   to  1.5 , 0

               this is    1 / 1.5    =   2/3

y xis intercept = -1

y = 2/3 x   -1            Slope intercept form

2/3 x - y   = 1             another form

2x - 3y = 3                Standard form (I think this is 'standard form' ....yah?)

The probability will be equal to 60%.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The best thing to do here is to put it into a fraction. as 30 landed heads up, 20 (50-30) must be tails.

You can then put this into a fraction, which becomes 20/50.

To turn this into a decimal, you can then divide 1 by 50

1/50= 0.02

As you've got 22 lots of this, you then need to multiply 0.02 by 20.

0.2x20= 0.40

To find the percentage, you've then got to multiply the decimal by 100.

100x0.40= 40.

Therefore, 40% of the tosses would be tails

As you've found what one percentage is, you simply need to take this number away from 100 to find the other, rather than having to go through the process again.

100-40= 60

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Answer: 0

Step-by-step explanation:

[tex](h \circ k)(1)=h(k(1))=h(4)=\boxed{0}[/tex]