Identify the vertex of the parabola. (EASY! 10 Points)

Total surface area of right triangular prism is 750cm²

A right triangular prism is a three-dimensional geometric shape with three rectangular faces connecting the edges of its two parallel, congruent triangular bases.

Area of the two opposite side triangles (A₁) = 2 × ( [tex]\frac{1}{2}[/tex] × 12 × 5)

Area of the two opposite side triangles (A₁) = 60 cm²

Area of upper, lower and side rectangles (A₂) = (5×23) + (12×23) + (13×23)

Area of upper, lower and side rectangles (A₂) = 115 + 276 + 299

Area of upper, lower and side rectangles (A₂) =  690 cm²

Total surface area of right triangular prism = A₁ + A₂

Total surface area of right triangular prism = 60 + 690

Total surface area of right triangular prism = 750 cm²

Therefore, the total area of the right triangular prism is 750cm²

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Hello!

1= 122

2= 58

3= 58

4= 122

5= 122

6= 58

7= 58

8= 122

To find angle 2, you subtract 122 from 180 because angles 1 and 2 are supplementary angles. You can find angle 3 by using the vertical angles theorem. This means that angle 2 and 3 are congruent to each other. You can use the same for angle 4, meaning 1 and 4 are also congruent. You can use the alternate interior angles theorem to prove that 3 and 6 are congruent and then use the vertical angles theorem to prove that 6 and 7 are congruent. You can find angles 5 and 8 by proving that 5 is congruent to 4 using the alternate interior angles theorem and then once again using the vertical angles theorem to prove that angle 5 is congruent to angle 8. Let me know if this is too hard to understand, I will happily simplify it.

The expansion of the multiplication is [tex]-16+12\sqrt{3}[/tex] and [tex]5-13\sqrt{5}[/tex]

Irrational numbers are real numbers that cannot be represented as simple fractions. If N is irrational, it is not equal to p/q, where p and q are integers and q is not equal to zero. [tex]\sqrt{2}, \sqrt{3}[/tex] are two examples.

distributive law

This property states that multiplying the total of two or more addends by a number produces the same result as multiplying each addend separately by the number and then putting the products together.

That is A(B+C)=AB+AC

According to the given information:

[tex](-2\sqrt{3} +2)(\sqrt{3}-5) = -2\sqrt{3}*\sqrt{3} + 10\sqrt{3} +2\sqrt{3} -10[/tex]

                                 =[tex]-6+12\sqrt{3}-10[/tex]

                               = [tex]-16+12\sqrt{3}[/tex]

[tex](-2-3\sqrt{5})(5-\sqrt{5}) = -10+2\sqrt{5}-15\sqrt{5}+3*5[/tex]

                               = [tex]-10-13\sqrt{5}+15[/tex]

                              =[tex]5-13\sqrt{5}[/tex]

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The quadratic function that models the height h of the ball after t seconds in flight is h(t) = -16t² + 70t + 3.5

A quadratic function is a type of function in algebra that involves a variable raised to the power of 2, or squared. The general form of a quadratic function is:

f(x) = ax² + bx + c

where f(x) represents the output of the function for a given input x, a, b, and c are constants that determine the shape and position of the function, and x is the input variable.

The graph of a quadratic function is a parabola, which is a curved shape that opens upwards if the coefficient a is positive, and downwards if the coefficient a is negative. The vertex of the parabola is the point at which the function reaches its minimum or maximum value, depending on the direction of the opening of the parabola. The x-coordinate of the vertex is given by:

x = -b/2a

The height h of the ball after t seconds in flight can be modeled by the quadratic function:

h(t) = -16t² + vt + s

where v is the initial velocity of the ball, s is the initial height of the ball, and -16 is the acceleration due to gravity in feet per second squared.

In this case, we know that the ball is hit with an initial velocity of 70 ft/s and is 3.5 ft off the ground, so we can substitute these values into the equation:

h(t) = -16t² + 70t + 3.5

Therefore, the quadratic function that models the height h of the ball after t seconds in flight is:

h(t) = -16t² + 70t + 3.5

Note that this function is only valid until the ball reaches its maximum height and starts falling back down to the ground.

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Evan sold half his story books and then bought 17 more. Evan had thirty bucks.

A mathematical statement is known as an equation, and the equal sign ('=') connects two expressions. At least one unknown variable must be determinable. For instance, an equation is 3x - 8 = 16. We achieve x = 8.

We will sοlve the prοblem by fοrming a οne variable equatiοn.

Let's say Evan started out with a lot of problems. Evan gave up half of his regular wares. He split two separate cakes.

He now has (x-x/2)=x/2 straight numbers.

He then gained 17 pounds.

Sο subsequent to purchasing 17 bοοks he has nοw (x/2+17) story bοοks

Given number οf stοry bοοks he has right nοw is 32.

By equating the two, we can construct a equation for one variable.

(x/2+17) = 32 Solving for x will be the equation:

(x/2+17) = 32; x/2 = 32- 17; x/2 = 15; x = 152; x = 30.

According to the initial equation, Evan had 30 books.

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Answer:

Yes, Alexa is correct.

Step-by-step explanation:

Counting by 8 means adding 8 repeatedly. The first multiple of 8 is 8 (1 x 8), the second multiple is 16 (2 x 8), the third multiple is 24 (3 x 8), the fourth multiple is 32 (4 x 8), and the fifth multiple is 40 (5 x 8). So, by counting by 8 five times, Alexa can find the fifth multiple of 8 which is 40.

The probabilities that select an incorrect choice are

a) P(correct) = 1/6 b) P(incorrect) = 5/6 c) P(correct) = 1/3 d) P(incorrect) = 2/3.

What is probability?

Probability is a measure of the likelihood or chance that a particular event will occur. It is a way of quantifying uncertainty, and is expressed as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain.

What are events in probability?

In probability, an event refers to an outcome or a set of outcomes of a random experiment or a process. A random experiment is an experiment or a process that has multiple possible outcomes, and the outcome of the experiment is uncertain or unpredictable.

a) The probability of selecting the correct choice from six possible choices is 1 out of 6, or 1/6, since there is only one correct answer among the six options.

b) The probability of selecting an incorrect choice from six possible choices is 5 out of 6, or 5/6, since there are five incorrect answers among the six options.

c) If three choices can be eliminated, then there are only three options left, with one correct answer among them. Therefore, the probability of selecting the correct choice from the remaining options is 1 out of 3, or 1/3.

d) Similarly, if three choices can be eliminated, then there are three options left, with two incorrect answers among them. Therefore, the probability of selecting an incorrect choice from the remaining options is 2 out of 3, or 2/3.

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Answer:

Because you are spending your time doing other things

Step-by-step explanation:

most of the time people waste time in school because they are busy doing other things and they probably don't think school is important.

a way to stop wasting time in school is to pay attention more in class and start developing a desire to learn.

:) i hope this helps lol

Answer:

For more opportunities to go to college, graduating college gets you a degree, the better degree the better job opportunities, the better job opportunities the more money earned. Your in school for money, the best end goal.

The vertex is (4,1), and the parabola opens b since the coefficient of the squared term is negative. The axis of symmetry is x=4, and the domain is all real numbers. The range is (-∞, 1], since the maximum value is 1.

A parabola is a symmetrical U-shaped curve that can be formed by intersecting a cone with a plane parallel to one of its sides. It is a type of quadratic function, which can be expressed in the form of y = ax^2 + bx + c, where "a" is the coefficient of the squared term, "b" is the coefficient of the linear term, and "c" is the constant term.

f(x) = x²+8x-3

To complete the square, we need to add and subtract the square of half the coefficient of x:

f(x) = (x²+8x+16) - 19 --> (x+4)² - 19

So, the equation in vertex form is: f(x) = (x+4)² - 19.

The vertex is (-4,-19), and the parabola opens upwards since the coefficient of the squared term is positive. The axis of symmetry is x=-4, and the domain is all real numbers. The range is [-19, ∞), since the minimum value is -19.

f(x)=-2x² + 16x-31

To complete the square, we need to factor out the leading coefficient of -2, and then add and subtract the square of half the coefficient of x:

f(x) = -2(x² - 8x + 16) - 31 + 32 --> -2(x-4)² + 1

So, the equation in vertex form is: f(x) = -2(x-4)² + 1.

The vertex is (4,1), and the parabola opens downwards since the coefficient of the squared term is negative. The axis of symmetry is x=4, and the domain is all real numbers. The range is (-∞, 1], since the maximum value is 1.

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Step-by-step explanation:

4n - 3 = 0

4n = 0 + 3

4n = 3

[tex]n \: = \frac{3}{4} [/tex]

Answer:

D. -22.25

Step-by-step explanation:

First, we need to simplify the expression inside the parentheses

|-3.5| = 3.5

Next, we can simplify the expression inside the parentheses:

-7 ÷ |-3.5| = -2

Now we can simplify the entire expression:

3/10^2 - 17 + (-2) x 2.67 = 0.09 - 17 - 5.34 = -22.25

The three true statements are

Step-by-step explanation:

Standard form for a circle is  ( x -h)^2 + ( y-k)^2 = r^2

     h, k   is the center      r is the radius

x^2 -2x + y^2 = 8     arrange into standard form ( complete the square for 'x')

(x-1)^2 + y^2 = 8+1

(x-1)^2 + y^2 = 9        shows center is at   1, 0

                                   radius = 3

 So

The radius of the circle is 3 units.

The center of the circle lies on the x-axis    (1,0 is on the x axis)

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Answer:

B: y ≥ 2r-4.

Step-by-step explanation:

To solve for y, we need to isolate y on one side of the inequality. First, we can simplify the left side of the inequality by dividing both sides by 2:

2x - y ≤ 4

Then, we can subtract 2x from both sides to get:

-y ≤ -2x + 4

Finally, we need to isolate y by multiplying both sides by -1 and flipping the direction of the inequality:

y ≥ 2x - 4

Now we can see that the equivalent inequality is option B: y ≥ 2r-4.

Step-by-step explanation:

the angle at Y = 1/2 × (arc angle WZ - arc angle ZX).

so,

42 = (arc angle WZ - 51)/2

84 = arc angle WZ - 51

135° = arc angle WZ

the arc angle WX is the remainder of the whole circle to the sum of the arc angles WZ and ZX :

arc angle WX = 360 - 135 - 51 = 174°

Erin's capital gains are the sum of her long-term capital gains (LTCG) and short-term capital gains (STCG), which is $2,600 + $24,400 = $27,000.

Erin's capital losses are the sum of her long-term capital losses (LTCL) and short-term capital losses (STCL), which is ($9,600) + ($15,600) = ($25,200).

Since Erin's capital gains exceed her capital losses, she has a net capital gain of $27,000 - $25,200 = $1,800.

The nature of Erin's capital gains and losses are as follows:

Answer: $5.40

Step-by-step explanation:

First, let's calculate the tax for each purchase and then find the total amount paid by Dave and James.

For Dave:

Basketball cost = $15

Tax = 8% of $15 = 0.08 * 15 = $1.20

Total amount paid by Dave = Cost + Tax = $15 + $1.20 = $16.20

For James:

Football cost = $20

Tax = 8% of $20 = 0.08 * 20 = $1.60

Total amount paid by James = Cost + Tax = $20 + $1.60 = $21.60

Now, let's find the difference between the amounts paid by Dave and James.

Difference = Amount paid by James - Amount paid by Dave = $21.60 - $16.20 = $5.40

So, the difference in the amounts paid by Dave and James, including tax, is $5.40.

If TV cable company has 2400 subscribers who are each paying ​$16 per month, charging $52 per month will yield a maximum revenue of $98,304.

To find the rate that will yield the maximum revenue, we can use the formula:

r = -b / 2a

where r is the rate, a is the coefficient of the quadratic term, and b is the coefficient of the linear term in the revenue equation.

The revenue equation is:

R = (2400 + 120x)(16 - 0.5x)

Expanding and simplifying, we get:

R = -0.5x^2 + 52x + 38400

So, a = -0.5 and b = 52. Plugging these values into the formula, we get:

r = -52 / 2(-0.5) = 52

This means that the company should charge $52 per month to maximize revenue. To find the maximum revenue, we can plug this value into the revenue equation:

R = (2400 + 120(52))(16 - 0.5(52)) = $98,304

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Answer: X= -4

Step-by-step explanation:

Answer:

7.38%

Step-by-step explanation:

Answer:

The correct answers for this question are:

A. Diagonals bisect each other.

C. Opposite angles are congruent.

D. Opposite sides are parallel.

E. Consecutive angles are supplementary. Those are the statements that describe properties of parallelograms. They are also belong to the family of quadrilateral.

Step-by-step explanation:

Step-by-step explanation:

To solve for x, we'll first need to simplify the equation by combining like terms:

0.6x - 5 = 0.1x + 7

0.6x - 0.1x = 7 + 5

0.5x = 12

x = 12 / 0.5

x = 24

Therefore, the value of x that makes the equation true is 24.

Answer:

29°

Step-by-step explanation:

In the first triangle,

46 + 30 + x = 180 (Angle sum property)

76 + x = 180

x = 180 - 76

x = 104

In the second triangle,

47 + 104 + y = 180

151 + y = 180

y = 29

Thus, the required angle is 29°.

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Answer:

the answer is 29 degrees

Step-by-step explanation:

look at the picture below

The radius οf the rain barrels is apprοximately 40.03 cm.

A value knοwn as the square rοοt οf a number is οne that, when multiplied by itself, yields the οriginal number. An alternative tο square rοοting a number is tο use it. Therefοre, the cοncepts οf squares and square rοοts are cοnnected. The οriginal number is equal tο the square rοοt οf any integer, which is equivalent tο a number.

The tοtal surface area is given as 40,212 square centimeters. Therefοre, we can write the equatiοn:

[tex]2\pi r^2 +\pir^2 + 4\pi r^2 + \pi r^2 = 40212[/tex]

Simplifying this equatiοn, we get:

[tex]8\pi r^2 = 40212[/tex]

Dividing bοth sides by 8π, we get:

[tex]r^2 = 1602.62[/tex]

Taking the square rοοt οf bοth sides, we get:

r ≈ 40.03 cm

Therefοre, the radius οf the rain barrels is apprοximately 40.03 cm.

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The two forms of the expression

[tex] \frac{ {x}^{5} }{ {x}^{10} } [/tex]

when simplified are

[tex] = {x}^{ - 5} [/tex]

x exponents negative 5 and

[tex]\frac{1}{ {x}^{5} } [/tex]

numerator 1 over denominator x exponents 5.

Given:

[tex] \frac{ {x}^{5} }{ {x}^{10} } [/tex]

When we have the same base but different powers in indices division, one of the bases is chosen and the powers are subtracted.

[tex] = {x}^{5 - 10} [/tex]

[tex] = {x}^{ - 5} [/tex]

[tex] = \frac{1}{ {x}^{5} } [/tex]

Therefore, the simplified expressions are x exponents negative 5 and numerator 1 over denominator x exponents 5.

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The lowest odd integer is [tex]35[/tex] followed by the next two odd integers in a row,[tex]37[/tex] and [tex]39[/tex] Thus, these are three consecutive odd integers.

Numbers that can be positive, negative, or zero but are not fractions are said to be integers. All mathematical operations, such as addition, subtraction, multiplication, and division, can be performed on integers. There are integer occurrences of [tex]1, 2, 5, 8, -9[/tex], and so on. [tex]Z[/tex] represents a number.

The variable for the lowest odd integer should be defined first. Assume that [tex]x[/tex] is the lowest odd number.

Since there is always a [tex]2[/tex] difference between two successive odd integers, the following two would be [tex]x+2[/tex] and [tex]x + 4[/tex]

The problem statement states that twice the smallest number [tex](2x)[/tex] is [tex]45[/tex]less than the total of twice the largest number  [tex]2(x+4)[/tex] and twice the middle number [tex](x+2).[/tex]

[tex]2x = (x+2) + 2 (x+4) ) - 45[/tex]

When we simplify and find x, we obtain:

[tex]2x = x + 2 + 4x + 8 - 45[/tex]

[tex]2x = 3x - 35[/tex]

[tex]x = 35[/tex]

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The length of the ramp we need to build should be at least 38.61 feet to pass code.

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles.

We can use trigonometry to solve the problem. Let x be the length of the ramp we need to build. Then, the angle the ramp makes with the ground is given by:

sin(theta) = opposite/hypotenuse

where theta is the angle the ramp makes with the ground, opposite is the vertical increase of 10 feet, and hypotenuse is the length of the ramp x.

Solving for x, we get:

x = opposite/sin(theta) = 10/sin(15)

Using a calculator, we can evaluate sin(15) to be approximately 0.2588. Then, we can divide 10 by 0.2588 to get:

x ≈ 38.61

Therefore, the length of the ramp we need to build should be at least 38.61 feet to pass code.

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In order for the account value to reach $91,000 in 12 years, Fwam would therefore need to invest $39,165.95, to the closest hundred dollars, assuming the interest rate is 5.9% compounded daily.

In exchange for using borrowed funds or assets, a borrower must pay the lender interest. It is charged for a certain duration of time, typically until the loan is fully returned, and is typically stated as a percentage of the amount borrowed. This fee is known as the interest rate. For instance, if a bank lends you $1,000 at a 5% annual interest rate, after a year of borrowing the money you would still owe the bank $50 more in interest. The creditworthiness of the borrower, the risk of the loan, and current market conditions are frequently used to establish the interest rate.

given

We know that Fwam expects the account to be worth $91,000 in 12 years and that the interest rate is 5.9% compounded daily in this situation.

We must convert the interest rate and the time period to the proper units before we can use the formula.

We begin by converting the 5.9% yearly interest rate to a daily rate:

daily rate is equal to (1 + 0.059/365)(365/365)-(1-1) = 0.00015999.

4,380 days in 12 years, or 365 days per year.

We can now enter the values into the formula to find P:

$91,000 = P × 2.3226

P = $39,165.95

In order for the account value to reach $91,000 in 12 years, Fwam would therefore need to invest $39,165.95, to the closest hundred dollars, assuming the interest rate is 5.9% compounded daily.

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The volume of cylinder is 191 cubic centimeters.

What is volume?

The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.

Here cylinder with height 6 cm ,

Volume = 128 cubic centimeters.

Now using volume of cylinder formula then,

=> Volume V =

=> 128 = 3.14**6

=>  =  = 6.79406

=> r = 2.6 cm.

Now volume of cylinder with height 9 cm is ,

=> Volume V = 3.14**9 = 191 cubic centimeters.

Hence the volume of cylinder is 191 cubic centimeters.

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Answer:

34

Step-by-step explanation:

5+5+2=12

12+6+3=21

21+8+5=34

Answer:45

Step-by-step explanation:

5+5(8)=45