An empty swimming pool is shaped like a rectangular prism with a length of 18 feet and a width of 9 feet. once water begins to be pumped into the pool, the depth of the water increases at a rate of 0.5 foot per hour.

The value of x in the angles is equal t0 15

To solve this problem, we can simply apply the theorem that states the sum of angles in a straight line is equal to 180 degrees.

This implies that;

[tex]AOF + FOG + GOB = 180^0[/tex]

substituting the values into the equation;

[tex]AOF + FOG + GOB = 180^0\\(5x -15) + 90 + 2x = 180[/tex]

Let's solve for x

[tex]5x - 15 + 90 + 2x = 180\\7x + 75 = 180\\7x = 105\\x = 15[/tex]

The value of x that makes the angles equal to 180 degrees is 15.

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The expression for [tex]\sqrt{-27}[/tex] is 3i[tex]\sqrt{3}[/tex]

What is an expression?

Expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

given [tex]\sqrt{-27}[/tex] we know that

3 multiplied by 9 gives 27 and the square root of 9 is 3

we can write

[tex]\sqrt{-3(3)(3)}[/tex]

or [tex]3\sqrt{-3}[/tex]

square root of minus gives iota

we get,

[tex]3i\sqrt{3}[/tex]

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Answer:

sinTheta = 24/25

cotTheta = 7/24

cscTheta = 25/24

Step-by-step explanation:

Use pythagorean thm or pythagorean triples to find the missing side of the triangle.

7^2 + x^2 = 25^2

49 + x^2 = 625

x^2 = 576

x = 24

The third side of the triangle is 24. We'll need this in a sec.

The marked angle is called theta. That 0 with a belt is greek letter theta. They could just call it angleA or angleB or whatever. Its name is just theta no big deal.

25 is the hypotenuse (longest side). The side that's 7 units long is one of the pieces that makes up AngleTheta. So the 7 is "adjacent" to theta. The other leg, 24, is "opposite" from theta.

sinTheta is a ratio. It is OPPOSITE/HYPOTENUSE

sinTheta = 24/25

cotTheta is tanTheta flipped over.

tanTheta is OPP/ADJACENT

so...

cotTheta =

ADJ/OPP

=7/24

Last, cscTheta is sinTheta flipped over.

We already found sinTheta, so flip it over.

cscTheta = 25/24

SOH-CAH-TOA is supposed to help you memorize the ratios for sine (opp/hyp), cos (adj/hyp), and tan (opp/adj).

The math word for "flipped over" is reciprocal.

csc is the reciprocal of sin

sec is the reciprocal of cos.

cot is the reciprocal of tan.

Good luck! Hope this helps!

The composite functions of  (f o g)(x), (g o f)(x) and their domains in the function f( x ) = x² + x and  g( x ) = 1/(x+1) are (x+2) / (x+1)², Domain: {x|x ≠ -1 } and 1/(x² + x + 1 ), Domain: {x|x ∈ R } respectively.

A function is simply a relationship that maps one input to one output.

Given the data in the question;

First, set up the composite result function (f o g)(x).

(f o g)(x) = f( g(x) )

f( x ) = x² + x

f( g(x) ) = f( 1/(x+1) )  = ( 1/(x+1) )² + 1/(x+1)

Apply product rule to simply

f( g(x) ) = 1² /(x+1)² + 1/(x+1)

f( g(x) ) = (1 + x + 1 )/ (x+1)²

f( g(x) ) = (x+2) / (x+1)²

Next, find the domain by equating the denominator to 0 and solve for x.

x + 1 = 0

x = -1

Domain: {x|x ≠ -1 }

For (g o f)(x), set up the composite result function (g o f)(x).

(g o f)(x) = g( f(x) )

g( x ) = 1/(x+1)

g( f(x) ) = g( x² + x ) = 1/( (x² + x) + 1 )

g( f(x) ) = 1/( (x² + x) + 1 )

g( f(x) ) = 1/(x² + x + 1 )

Next, find the domain by equating the denominator to 0 and solve for x.

x² + x + 1 = 0

x = ( -1±√(1² - 4 ×(1×1) ) / (2 × 1 )

x = (-1±i√3)/2

x = (-1+i√3)/2, (-1-i√3)/2

Hence,

Domain is set of all real numbers.

Domain: {x|x ∈ R }

Therefore the composite functions and their domain are (x+2) / (x+1)², Domain: {x|x ≠ -1 } and 1/(x² + x + 1 ), Domain: {x|x ∈ R }.

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Answer:

y > 15

Step-by-step explanation:

y + 7 > 22 ( subtract 7 from both sides )

y > 15

For 1 xylobar and 2 yackities Dado would pay $0.61   .

In the question ,

it is given that

Zimak paid $1.75 for 3 xylobars and 5 yackities .

let the price of 1 xylobar = x

and let the price of 1 yackities = y

According to the question

3x+5y=1.75    ...(i)

Jeejunu paid $1.88 for 4 xylobars and 1 yackity .

So , equation becomes

4x+y=1.88    ...(ii)

y = 1.88-4x

substituting it in equation (i), we get

3x + 5(1.88 - 4x) = 1.75

3x + 9.4 - 20x = 1.75

20x-3x = 9.4 - 1.75

17x = 7.65

x = 7.65/17

x = 0.45

So, the price of 1 xylobar = $0.45

put x = 0.45 in y= 1.88-4x , we get

y = 1.88 - 4(0.45)

y = 1.88 - 1.8

y = 0.08

So , the price of 1 yackity is $0.08   .

So, For 1 xylobar and 2 yackities , Dado would pay

= x+2y

= 0.45 + 2(0.08)

= 0.45+0.16

= 0.61

Therefore , for 1 xylobar and 2 yackities Dado would pay $0.61   .

The given question is incomplete , the complete question is

Zimak bought 3 xylobars and 5 yackities from the intergalactic candy store for $1.75 . Jeejunu paid  $1.88 and got 4 xylobars and 1 yackity . How much would dado pay for 1 xylobar and 2 yackities ?

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The required problems on probability application are detailed below.

Probability is the study of chance represented as a proper fraction between 0 and 1 .  

The manufacturing process of a particular rugby ball consists of two parts, a leather covering and a rubber bladder. The probabilities of defect in the leather covering is 5% and the probability of the rubber bladder is 15% respectively. What is the probability that the assembled Rugby ball will not have any defect.

Let A and B denote the event that  a rugby ball is defective due to defects in the leather covering and the rubber bladder respectively.

Then we can say that  P(A) = 5 / 100 = 1 / 20  and

P(B) = 15 / 100 = 3 / 20

Therefore  P(A') = 1 - 1/20 = 19/20 and P(B') = 1 - 3 / 20 = 17 / 20.

P(A') and  P(B') gives us the probabilities that the rugby ball will not have defective parts respectively.

Therefore the probability that the assembled product will not have any defect is:

P(A') ×  P(B')

[tex]=\frac{19}{20} \times \frac{17}{20}\\\\=\frac{323}{400} \\\\=0.8075[/tex]

Therefore the probability that the rugby ball will not have any defect is 80.75% .

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Answer:

b

Step-by-step explanation:

Answer: the answer is ..

Step-by-step explanation: fec r/sm mkdnjervc

Mathematical expressions known as linear inequalities compare two expressions using the inequality symbol. The expression may be either a numerical or an algebraic expression, or it may be both.

Addition, subtraction, multiplication, and division are the four types of operations that can be performed on linear inequalities. Equivalent inequality refers to linear inequalities with the same solution. Both equality and inequality are subject to laws. For inequality involving smaller than or equal to () and greater than or equal to (), all the principles listed below apply. Let's look at some of the key inequality rules for all these operations before learning how to solve linear inequalities.

As with multi-step linear equations, start by separating the variable from the constants when resolving multi-step linear inequalities with one variable. According to the laws of inequality, it is crucial that we remember to flip the inequality sign when multiplying or dividing with negative values while resolving multi-step linear inequalities.

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Answer:

0.1037

Step-by-step explanation:

well, the difference is 39.14 - 38 = 1.14, so that's the tax.

if we take 38 to be the 100%, just the listed price alone, what is 1.14 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 38 & 100\\ 1.14& x \end{array} \implies \cfrac{38}{1.14}~~=~~\cfrac{100}{x} \implies 38x=114\implies x=\cfrac{114}{38}\implies x=3[/tex]

The sequence of transformation that exhibits the similarity between the rectangles ABCD and rectangle A'B'C'D' is the option C.

C. Rectangle ABCD is reflected across the y-axis and then dilated by a scale factor of 2 with the center of dilation at the origin to obtain rectangle A'B'C'D'

A reflection transformation of an object gives or produces the mirror image of the object about a specified line.

The coordinates of the points of the rectangle ABCD obtained from the graph are; A(-4, -4), B(-4, 4), C(2, 4), and D(2, -4).

The coordinates of the image of the rectangle ABCD (rectangle (A'B'C'D') are; A'(8, -8), B'(8, 8), C'(-4, 8) and D'(-4, -8)

The coordinates of the reflection of the point (x, y), following a reflection across the y-axis is the point (-x, y)

The vertices of the image of rectangle ABCD formed following a reflection across the x-axis are therefore;

A(-4, -4)  [tex]\underrightarrow{R_{x-axis}}[/tex] A''(4, -4)

B(-4, 4)  [tex]\underrightarrow{R_{x-axis}}[/tex] B''(4, 4)

C(2, 4)  [tex]\underrightarrow{R_{x-axis}}[/tex] C''(-2, 4)

D(2, -4) [tex]\underrightarrow{R_{x-axis}}[/tex] D''(-2, -4)

The coordinates of the point (x, y) following a dilation by a scale factor of k, with the center of dilation at the origin is (k·x, k·y)

The dilation of the image of the rectangle ABCD by a scale factor of 2 gives;

A''(4, -4)  [tex]\underrightarrow{D_{2}}[/tex] (2×4, 2×(-4)) = A'(8, -8)

B''(4, 4)  [tex]\underrightarrow{D_{2}}[/tex] (2×4, 2×(4)) = B'(8, 8)

C''(-2, 4)  [tex]\underrightarrow{D_{2}}[/tex] (2×(-2), 2×(4)) = C'(-4, 8)

D''(-2, -4)  [tex]\underrightarrow{D_{2}}[/tex] (2×(-2), 2×(-4)) = D'(-4, -8)

The points of the image of rectangle ABCD following a a reflection and a dilation are A'(8, -8), B'(8, 8), C'(-4, 8) and D'(-4, -8), which are the same as the coordinates of the points of the given rectangle A'B'C'D'

The correct option is therefore option C;

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Step-by-step explanation:

Translate this sentence into an equation. The difference of Janelle's height and 9 is 65. Use the variable j to represent Janelle's height.

j - 9 = 65

to solve:

j - 9 = 65

add 9 to both sides:

j - 9 + 9 = 65 + 9

j = 74

Answer: $3.20 is the sales tax

Step-by-step explanation:

[tex]\frac{8x40}{100} =3.2[/tex] (8 times 40 divided by 100)

please mark brainliest if this helped :)

[tex]=2t+5x+3-9t-4x+7\\=2t-9t+5x-4x+3+7\\=-7t+x+10[/tex]

Be aware I used the plus sign for 3 since you DID NOT insert the sign. For Future purposes Be careful.

Answer: -7t+x+10 (if the 3 in your equation is positive)

Step-by-step explanation: Add all like variables and integers.

Answer:

w is 59

Step-by-step explanation:

63-4 =59 and this should be the answer your looking for

Answer:

w=12

Step-by-step explanation:

63+4w+15

collect like terms

63-15=4w

48=4w (divide all through by 4)

w=12

Answer:

To what please

Step-by-step explanation:

I am here to help you so please send your questions

Answer: 7921   123569 5410

Step-by-step explanation:

1. 7912

2. 123569

3. 5210

Answer:

3.75 cups of flour

2.5 cups of sugar

1.25 cups of butter

Step-by-step explanation:

Hello!

Let the amount of sugar used be x:

The total sum of ingredients should be 7.5 cups, so we can add x, 1.5x, and 0.5x and set it to 7.5.

Clifford needs 2.5 cups of sugar.

The amount of flour can be found by multiplying 2.5 by 1.5: 3.75 cups

The amount of butter can be found by multiplying 2.5 by 0.5: 1.25

Clifford needs 3.75 cups of flour, 2.5 cups of sugar, and 1.25 cups of butter.

Answer:

121

Step-by-step explanation:

11^6/11^4

= 11^(6-4)

= 11^2

= 121

Solution

The diagram below shows what is needed

As shown above

distance between points A and B is

distance between points C and D is

The 10th figure will have 19 blocks.

An arithmetic progression (AP) is a sequence in which the differences between each successive term are the same. The formula Tₙ = a+(n-1)d finds the general term (or) nth term of an AP whose first term is 'a' and the common difference is 'd'.

In the given figures,

Figure 1 has 1 block.

Figure 2 has 3 blocks.

Figure 3 has 5 blocks.

We have to find the number of blocks in the 10th figure.

The number of blocks in the figures are forming an arithmetic progression of 1,3,5.....with a common difference of 2.

So the 10th term of AP can be calculated as,

[tex]T_{10} = 1 + (10 -1)2[/tex]

[tex]T_{10} = 1 + 9*2[/tex]

[tex]T_{10} = 19[/tex]

Therefore, the 10th figure will have 19 blocks.

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Step 1

State the compound interest formula

where;

Step 2

Find the amount after 22 years

Answer;

The length and breadth should be 2 feet each and height should be 3 feet to minimize the cost of the materials.

Let consider the length of the box =x

considering a square bottom ,

length = breadth = x

and let the height  =h

The surface area of the box is

SA = x² + 4xh      ( box is open from top )

cost of 1sq feet material for bottom =$3    

cost of 1sq feet material for sides =$1    

The cost functions can be written as

C =  3x² + 1(4xh)

C =   3x² + 4xh

Also the volume equation is

x²h = 12

h = 12/x²

substituting the value of h into the cost function.

C =  3x² + 4x (12/x²)

C =  3x² + 48/x

C = (3x³ + 48)/ x

Take the derivative of C and set it equal to zero. So we get

6x³ - 48 = 0

x³ = 48/6 = 8

x = 2

∴ h = 12/x²

h = 12/4

h = 3

This is the value of x and h that minimizes the cost.

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The ordered pair which is a solution to the system of linear equations is: A. (3, 0).

In order to determine a solution to the system of linear equations, we would have to test the given ordered pairs by substituting their values into the linear equations as follows;

For ordered pair (3, 0), we have:

y = −x + 3

0 = -3 + 3

0 = 0 (True).

2x − y = 6

2(3) - 0 = 6

6 - 0 = 6

6 = 6 (True).

For ordered pair (3, -1), we have:

y = −x + 3

-1 = -3 + 3

-1 = 0 (False).

For ordered pair (0, 3), we have:

y = −x + 3

3 = 0 + 3

3 = 3 (True).

2x − y = 6

2(0) - 3 = 6

0 - 3 = 6

-3 = 6 (False).

For ordered pair (-1, 3), we have:

y = −x + 3

3 = -1 + 3

3 = 2 (False).

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By evaluating f(x) in x = 3, we will get that:

f(3) = 4

Thus the correct option is D:

Here we have the following function:

[tex]f(x) = x + \frac{\sqrt{x + 1} }{x - 1}[/tex]

We want to get f(3), and to get that, we just need to replace all the "x" in the equation by the number 3, we will get:

f(3) = 3 + (3 + 1)/(3 - 1)

f(3) = 3 + √4/2 = 4

With this, we can conclude that the correct option is D:

f(3) = 4.

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