The base is a 45 45 90 triangle with a leg of 5 in. The height is 1.8 what’s the volume of the prism

Answer:

Step-by-step explanation:

To solve the given quadratic equation, we simplified and factored it, yielding solutions x = 0 and x = 17. For the data in the table, an exponential function is suggested by the consistent ratio between y-values. Algebraically solving the system of equations results in two solutions: (5, 35) and (-4, 8).

Formula to Solve the Equation

To solve the equation x squared minus 21 x equals negative 4 x, you'll first want to rewrite it in standard form. Moving all the terms to one side gives us [tex]x^2 - 21x + 4x = 0[/tex], which simplifies to [tex]x^2 - 17x = 0[/tex]. To find the solutions, we can factor out an x, giving us x(x - 17) = 0. This yields two solutions: x = 0 and x = 17.

Model the Data in the Table

Looking at the data given, we see that each y-value seems to be a multiple of the previous y-value. This suggests an exponential function might be a better fit than a linear one. To confirm, you can divide each y-value by the previous y-value and observe if the ratios are consistent. Calculating the ratios between consecutive y-values in the table, we see that the ratio is consistently around 4, confirming that an exponential model is appropriate.

Solve the System of Equations Algebraically

To solve the system [tex]y = x^2 + 2x[/tex]and y = 3x + 20, set the right sides of the equations equal to each other:[tex]x^2 + 2x = 3x + 20[/tex]. Bringing all terms to one side gives us the quadratic equation[tex]x^2 - x - 20 = 0[/tex]. Factoring the quadratic equation we get (x - 5)(x + 4) = 0, which gives us two solutions for x: x = 5 or x = -4. Substituting these back into either original equation provides the related y-values, thus giving us two solutions for the system: (5, 35) and (-4, 8).

Answer:

A) g(x)=x2−12x+31

Answer:

Because in one way or another, you would lose money.

Step-by-step explanation:

Sometimes, it is a good idea to underprice a house when selling it, specially when there is a hot market to start a bidding war. If this is not the case, when the prices go down, it means that the seller must adjust his prices to the market; meaning that the lower the prices are, the lower the underpricing should be, so the seller would lose money.

The elimination method is used for solving linear systems of equations.It is way of solving a linear system of equations.In the elimination method we either add or subtract the equations to get an equation in one variable.The main concept behind elimination method is to create terms with opposite coefficients because they cancel each other when added.

When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.

When Heather has to solve this system of equations using elimination her first step will be to make the coefficients of x or y the same   so that one of the variable is eliminated on addition or subtraction of the equations.

Answer:

Step-by-step explanation:

We have to find the values of the given trigonometric ratios at the angle indicated. Thus,

(A) The given trigonometric function is:

[tex]cos270^{\circ}[/tex]

Since, the function lies in Quadrant III, therefore the value of the function will be negative.

Also, [tex]cos270^{\circ}=-(0)=0[/tex]

(B) The given trigonometric function is:

[tex]sin270^{\circ}[/tex]

Since, the function lies in Quadrant III, therefore the value of the function will be negative.

Also, [tex]sin270^{\circ}=-1[/tex]

(C) The given trigonometric function is:

[tex]tan270^{\circ}[/tex]

Since, the function lies in Quadrant III, therefore the value of the function will be negative.

Also, [tex]tan270^{\circ}=undefined[/tex]

(D) The given function is:

[tex]cos0^{\circ}[/tex]

Since, the function lies in Quadrant I, therefore the value of the function will be positive.

Also,  [tex]cos0^{\circ}=1[/tex]

(E) The given function is:

[tex]sin0^{\circ}[/tex]

Since, the function lies in Quadrant I, therefore the value of the function will be positive.

Also,  [tex]sin0^{\circ}=0[/tex]

(F) The given function is:

[tex]tan0^{\circ}[/tex]

Since, the function lies in Quadrant I, therefore the value of the function will be positive.

Also,  [tex]tan0^{\circ}=0[/tex]

Given is a circle O with tangent AB and secant OB.

Given is OA = 21 units and BC = 14 units.

From the diagram, OB = OC + BC.

OC and OA, both are radius, so OC = OA = 21 units.

Now OB = 21 + 14 = 35 units.

In right triangle ΔOAB, using Pythagorean theorem;

OA² + AB² = OB²

⇒ (21)² + AB² = (35)²

⇒ 441 + AB² = 1225

⇒ AB² = 1225 - 441  = 784 square units

⇒ AB = [tex]\sqrt{784} =28[/tex]

⇒ AB = 28 units.

Hence, final answer is AB = 28 units.

Answer:

the cost is [tex]\$6[/tex]

Step-by-step explanation:

observing the graph

we know that

For the interval of x------> [tex](0,1][/tex] -----> the cost is [tex]\$0[/tex]

For the interval of x------> [tex](1,3][/tex] -----> the cost is [tex]\$4[/tex]

For the interval of x------> [tex](3,4][/tex] -----> the cost is [tex]\$6[/tex]

For the interval of x------> [tex](4,infinite)[/tex] -----> the cost is [tex]\$10[/tex]

In this problem we have

[tex]3[/tex] hours and [tex]45[/tex] minutes

therefore

the value of x belong to the interval [tex](3,4][/tex]

the cost is [tex]\$6[/tex]

It will take 24 minutes to fill the tub when both the faucet is running and the drain is open. The calculation is done using rates and subtraction.

This problem can be approached with the concept of rates. The rate at which the bathtub fills is 1 tub per 8 minutes or 1/8 tubs/min. Similarly, the rate at which it drains is 1 tub per 12 minutes or 1/12 tubs/min. When the faucet is running and the drain is open, the net rate is the fill rate minus the drain rate.

So, (1/8 - 1/12) tubs/minute = 1/24 tubs/minute. Thus, it will take 24 minutes to fill the bathtub with both the faucet running and the drain open.

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The colon will blink 8400 times in 2 hours and 20 minutes.

Since the colon blinks every second. And we know that there are 60 minutes in an hour and there are 60 seconds in a minute.

Thus, we can say:

1 minutes = 60 seconds

1 hour = 60 minutes = 3600 seconds

Note: 60 minute = (60 * 60) seconds = 3600 seconds

Thus, in 2 hours and 20 minutes, we have:

2 hours + 20 minutes = (2 * 3600) + (20 * 60)

                                   = 7200 + 1200

                                   =  8400 second

Therefore, the colon will blink 8400 times in 2 hours and 20 minutes.

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Final answer:

To find out if the ratios 1/9 and 6/54 form a proportion, calculate their cross-products. Since both cross-products are equal (54 = 54), they do form a proportion.

Explanation:

The question asks if two given ratios form a proportion. To determine whether ratios form a proportion, you can compare the cross-products of the ratios. If the cross-products are equal, the ratios do form a proportion. For the given ratios 1/9 and 6/54, we will calculate the cross-products:

For the first ratio, 1 times 54 equals 54.

For the second ratio, 9 times 6 equals 54.

Since both cross-products are equal (54 = 54), the ratios 1/9 and 6/54 do indeed form a proportion.

To write a proportion by setting two ratios equal to one another with the unit 'meters', an example would be 1/20 = 1/5.5. When working with unit scales or unit rates, such as in map readings or speed, you compare two measurements where one of the ratios is typically a value of 1, like the example provided 55 miles per hour, which is written as 55/1 miles/hour.

The probability of selecting correct options is 1/3.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Mathematically -

P[E] = n[E]/n[S]

Given are first 2 questions on a multiple choice test such that each of the question has 3 possible answers.

Now, there are two questions, with three possible answers, this means that we have total of 6 elements in a sample space. Let [A] represent the event of selecting correct options. Then there could be only 2 possible answers from the given six. Therefore, the probability of the event [A] would be :

P[A] = n[A]/n[S]

P[A] = 2/6

P[A] = 1/3

Therefore, the probability of selecting correct options is 1/3.

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1/2(z+18) is the expression of 1/2z+9 when 1/2 is factored out.

A fraction represents a part of a whole.

Given,

The expression is 1/2 z+9

A factor is a number that divides another number, leaving no remainder.

The given expression is one by two times of z plus nine.

1/2 z+9

Now we need to take 1/2 as common from the expression

1/2(z+18)

Hence, 1/2(z+18) is the expression of 1/2z+9 when 1/2 is factored out.

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The estimated amount of fabric that the umbrella has is approximately [tex]\(112 + 32\sqrt{2}\)[/tex] square feet.

To estimate the amount of fabric that the umbrella has, we first need to find the total surface area of the regular octagonal pyramid.

A regular octagonal pyramid consists of 8 congruent isosceles triangles as its lateral faces and a regular octagon as its base.

Given:

- Side length of the octagon (s) = 4 feet

- Slant height of the pyramid (l) = 5 feet

First, let's calculate the area of one of the lateral faces (isosceles triangle) using the formula for the area of a triangle:

[tex]\[ \text{Area of one lateral face} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

In this case, the base of the triangle is the side of the octagon, s=4 feet, and the height is the slant height of the pyramid, l=5 feet. Therefore:

[tex]\[ \text{Area of one lateral face} = \frac{1}{2} \times 4 \times 5 = 10 \text{ square feet} \][/tex]

Since there are 8 congruent lateral faces on the octagonal pyramid, the total area of the lateral faces is:

[tex]\[ \text{Total area of lateral faces} = 8 \times 10 = 80 \text{ square feet} \][/tex]

Now, let's calculate the area of the base (regular octagon). The formula for the area of a regular octagon is:

[tex]\[ \text{Area of octagon} = 2 \times (1 + \sqrt{2}) \times s^2 \]\[ \text{Area of octagon} = 2 \times (1 + \sqrt{2}) \times 4^2 \]\[ \text{Area of octagon} \approx 2 \times (1 + \sqrt{2}) \times 16 \]\[ \text{Area of octagon} \approx 32 \times (1 + \sqrt{2}) \][/tex]

Now, we can calculate the total surface area of the regular octagonal pyramid by adding the area of the lateral faces and the area of the base:

[tex]\[ \text{Total surface area} = \text{Area of lateral faces} + \text{Area of octagon} \]\[ \text{Total surface area} = 80 + 32 \times (1 + \sqrt{2}) \]\[ \text{Total surface area} \approx 80 + 32 \times (1 + \sqrt{2}) \]\[ \text{Total surface area} \approx 80 + 32 + 32\sqrt{2} \]\[ \text{Total surface area} \approx 112 + 32\sqrt{2} \][/tex]

Answer:

205 cubic units

Step-by-step explanation:

Given : The expression 100 + 20m gives the volume of water in Eduardo’s pool (in liters) after Eduardo spends m minutes filling his pool.

To Find: What is the volume of water in Eduardo’s pool after he fills it for 5.25 minutes?

Solution:

Expression: Volume of water in pool after m minutes= 100 + 20m

Volume of water in pool after m minutes = 100 + 20m

Where m is the number of minutes spent in filling pool.

Now we are supposed to find the volume of water in Eduardo’s pool after he fills it for 5.25 minutes

Substitute m = 5.25

Volume of water in pool after m minutes= 100 + 20(5.25)

                                                                  =205

Thus the volume of water in Eduardo’s pool after he fills it for 5.25 minutes is 205 cubic units.

A perimeter of 24 feet is achieved in this optimal scenario.

For an area of 36 square feet, we can factor this into pairs: (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6). Since we are looking for the minimum perimeter, the closest factors will yield the smallest perimeter, which in this case is the pair (6, 6). Therefore, a rectangle with the dimensions 6 feet by 6 feet will not only satisfy the area requirement of 36 square feet but will also have the minimum perimeter, which is 24 feet.

The perimeter (P) of a rectangle is calculated by the formula P = 2(l + w), where 'l' is the length and 'w' is the width. Given our dimensions, P = 2(6 + 6) = 24 feet. The square shape of the rectangle, which is a special case where the length and width are equal, is what minimizes the perimeter for a given area.

The rectangle with an area of 36 square feet that has minimal perimeter is actually a square with dimensions of 6 feet by 6 feet.

To find the length and width of a rectangle with an area of 36 square feet that has the minimum perimeter, we need to follow these steps:

Thus, the dimensions that yield the minimum perimeter are 6 feet by 6 feet. This results in a square having the smallest possible perimeter for the given area.