The pyramid and prism above have the same triangular base and height. The volume of the pyramid is 18 cubic inches. What is the volume of the prism?
A. 36 cubic inches
B. 72 cubic inches
C. 6 cubic inches
D. 54 cubic inches

Answers

Answer 1
The volume of a pyramid that has the same base and height as the prism it is inscribed in is exactly one-third the volume of the prism. This is true for any pyramid that can be inscribed in a prism as long as the base and height are the same1.
Since the volume of the pyramid is 18 cubic inches, then the volume of the prism is 3 times that amount which is 54 cubic inches 2.
Therefore, the answer is D. 54 cubic inches.

Related Questions

help needed fast pleaseeeeeeee. Identify the solution of the system graphed below.

Answers

The solution to the system of equations is (a) (1, 0)

Identifying the solutions to the system of equations

From the question, we have the following parameters that can be used in our computation:

The graph

The point of intersection of the lines of the graph represent the solution to the system graphed

From the graph, we have the intersection point to be

(x, y) = (1, 0)

This means that

x = 1 and y = 0

Hence, the solution to the system of equations is (a) (1, 0)

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IfmZC = 142° and m LI = 48°, find mU B.

Answers

The measure of angle of arc UB is 46°

What is arc angle relationships?

An arc is a part of the circumference.

If two arcs in circles with equal radii have the same length, then their central angles (and measures) will be equal.

To find the measure of angle of arc UB, we use the theorem that says;

angle I = 1/2( angle ZC - angle UB)

angle I = 48°

angle ZC = 142°

Therefore ;

represent angle UB by x

48 = 1/2( 142-x)

142 - x = 96

x = 142 -96

x = 46°

Therefore the measure of angle of arc UB is 46°

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Complete the following number sequence. 2, 4, 7, __, 16, __, 29, __

Answers

The completed sequence would then be: 2, 4, 7, 9, 16, 19, 29.

To complete the given number sequence, let's analyze the pattern and identify the missing terms.

Looking at the given sequence 2, 4, 7, __, 16, __, 29, __, we can observe the following pattern:

The difference between consecutive terms in the sequence is increasing by 1. In other words, the sequence is formed by adding 2 to the previous term, then adding 3, then adding 4, and so on.

Using this pattern, we can determine the missing terms as follows:

To obtain the third term, we add 2 to the second term:

7 + 2 = 9

To find the fifth term, we add 3 to the fourth term:

16 + 3 = 19

To determine the seventh term, we add 4 to the sixth term:

__ + 4 = 23

Therefore, the missing terms in the sequence are 9, 19, and 23.

By identifying the pattern of increasing differences, we can extend the sequence and fill in the missing terms accordingly.

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Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 1.9. In 1983, about 1600 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2003?

Answers

To estimate the number of people who would have died from AIDS in 2003, assuming the exponential growth model with a growth factor of 1.9, we need to calculate the exponential growth from 1983 to 2003.

First, let's calculate the number of years between 1983 and 2003:
2003 - 1983 = 20 years

Using the exponential growth formula:

N = N0 * (growth factor)^t

Where:
N0 is the initial value (number of deaths in 1983)
(growth factor) is the common ratio or growth multiplier
t is the time in years

Given:
N0 = 1600 (number of deaths in 1983)
growth factor = 1.9 (common ratio)
t = 20 (years)

Using the formula, we can calculate:

N = 1600 * (1.9)^20

Calculating this expression:

N ≈ 1600 * 6.1917364224

N ≈ 9907.58

Therefore, if the trend had continued unchecked, approximately 9908 people would have died from AIDS in the U.S. in 2003.

cosine rule problem.

Answers

Answer:

111

Step-by-step explanation:

a² = b² + c² - 2bc cos A

a² = (7√3)² + (√6)² - 2(7√3)(√6) cos 45°

a² = 49 × 3 + 6 - 14√18 × (√2)/2

a² = 153 - 42

a² = 111

a = √111

a = √n = √111

n = 111

Jacob spent 5 hours skiing and snowboarding. He skied for 2 hours 10 minutes.
How long did he spend snowboarding?

Answers

2 hr and 50 minutes

Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

Which expression is equivalent to 10f - 5f + 8 +6g +4?

Answers

The given expression, 10f - 5f + 8 + 6g + 4, simplifies to 5f + 12 + 6g when like terms are combined.

To simplify the expression 10f - 5f + 8 + 6g + 4, we can combine like terms by adding or subtracting coefficients that have the same variables:

10f - 5f + 8 + 6g + 4

Combining the terms with 'f', we have:

(10f - 5f) + 8 + 6g + 4

This simplifies to:

5f + 8 + 6g + 4

Next, we can combine the constant terms:

8 + 4 = 12

Thus, the simplified expression is:

5f + 12 + 6g

This expression is equivalent to 10f - 5f + 8 + 6g + 4.

In summary, the expression 10f - 5f + 8 + 6g + 4 simplifies to 5f + 12 + 6g after combining like terms.

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If a turtle travels 1/12 of a mile per hour how long will it take to get to a pond 5/6 of a mile away

Answers

Answer:

Step-by-step explanation:

To find the time it takes for the turtle to reach the pond, we can use the formula:

Time = Distance / Speed

Given that the turtle travels at a speed of 1/12 mile per hour and the distance to the pond is 5/6 mile, we can substitute these values into the formula:

Time = (5/6) / (1/12)

To simplify this, we can multiply the numerator by the reciprocal of the denominator:

Time = (5/6) * (12/1) = (5 * 12) / 6 = 60 / 6 = 10

Therefore, it will take the turtle 10 hours to reach the pond.

please help I'm losing braincells ​

Answers

Answer:h equals 12

Step-by-step explanation:

elsa hikes up a mountain. she hikes back down at a constant rate the table shows elsas elevation at each hour after she begins her descent

Answers

The linear equation from the given table is expressed as:

y =  -1500x + 8350

How to find the equation from the table?

The general form for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

The formula for the equation of a line through two coordinates is:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

We will take the two coordinates (1, 6850) and (2, 5350)

Thus:

(y - 6850)/(x - 1) = (5350 - 6850)/(2 - 1)

(y - 6850)/(x - 1) = -1500

y - 6850 = -1500x + 1500

y = -1500x + 1500 + 6850

y =  -1500x + 8350

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An educator wants to see how the number of absences for a student in her class affects the student’s final grade. The data obtained from a sample are shown.
Test at :a 05.XCV=0.811 No. of absences -\ 10, final grade 70

Answers

By conducting a statistical test with the provided data and using a significance level of 0.05 and a critical value of 0.811, the educator can determine whether the number of absences significantly affects the final grade of the students.

To analyze the relationship between the number of absences and the final grade of students, an educator collected data from a sample. The obtained data reveals that for 10 absences, the corresponding final grade was 70. In order to determine whether the number of absences significantly impacts the final grade, a statistical test is needed.

The information provided, "Test at α = 0.05, XCV = 0.811," suggests that the educator is referring to a significance level (α) of 0.05 and the critical value (XCV) associated with this level is 0.811.

To conduct a hypothesis test, the educator needs to set up the null (H0) and alternative (Ha) hypotheses. In this case, the null hypothesis would assume that the number of absences does not have a significant effect on the final grade. The alternative hypothesis would assume that the number of absences does have a significant effect on the final grade.

Using the obtained data, the educator would perform the statistical test, such as a correlation analysis or a regression analysis, to determine the strength and significance of the relationship between absences and final grade.

If the test statistic (such as the correlation coefficient or regression coefficient) exceeds the critical value, the null hypothesis would be rejected, suggesting that the number of absences does have a significant impact on the final grade.

The educator can then interpret the results, considering factors such as the direction and strength of the relationship. Additionally, they may explore other variables or factors that could be influencing the final grade and further refine their analysis.

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debbie wants tp compare the simple interest to compound interest on 60,000 investment

Answers

Answer:

this question is incomplete

Simplify the expression to a polynomial in standard form (x^2+3x+3) (-2x^2-x+6)

Answers

The polynomial [tex](x^2 + 3x + 3) * (-2x^2 - x + 6)[/tex] simplifies to [tex]-2x^4 - 7x^3 - 3x^2 + 33x + 18.[/tex]

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication operations. It is defined as a sum of terms, where each term consists of a variable raised to a non-negative integer exponent, multiplied by a coefficient.

The general form of a polynomial is:

P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x + a₀

To simplify the expression[tex](x^2 + 3x + 3) * (-2x^2 - x + 6)[/tex], we need to perform the multiplication and combine like terms.

First, we multiply each term in the first polynomial by each term in the second polynomial:

[tex](x^2 + 3x + 3) * (-2x^2 - x + 6) = x^2 * (-2x^2 - x + 6) + 3x * (-2x^2 - x + 6) + 3 * (-2x^2 - x + 6)[/tex]

Expanding each term, we get:

=[tex](-2x^4 - x^3 + 6x^2) + (-6x^3 - 3x^2 + 18x) + (-6x^2 - 3x + 18)[/tex]

Now, we combine like terms:

=[tex]-2x^4 + (-x^3 - 6x^3) + (6x^2 - 3x^2 - 6x^2) + (18x + 18x - 3x) + 18[/tex]

Simplifying further:

=[tex]-2x^4 - 7x^3 - 3x^2 + 33x + 18[/tex]

The simplified expression in polynomial standard form is:

-2x^4 - 7x^3 - 3x^2 + 33x + 18

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A small grocery store selling jugs of milk, loafs of bread and pieces of cheese sold a total of 224 of those three items today. It sold
three times as many loafs of bread as jugs of milk, and it sold 4 times as many pieces of cheese as loafs of bread.
a) Write an equation that represents the information.
b) Solve the equation in (a) to find the number of jugs of milk, loafs of bread, and pieces of cheese the store sold today

Answers

Answer:  the store sold 14 jugs of milk, 42 loaves of bread, and 168 pieces of cheese today.

Step-by-step explanation:

a) Let's represent the number of jugs of milk as 'm', the number of loaves of bread as 'b', and the number of pieces of cheese as 'c'. According to the given information:

The total number of items sold today is 224. Therefore, we can write the equation:

m + b + c = 224

The store sold three times as many loaves of bread as jugs of milk. We can write this as:

b = 3m

The store sold four times as many pieces of cheese as loaves of bread. We can write this as:

c = 4b

b) Now, let's solve the equation:

Substituting the value of 'b' from equation (2) into equation (3):

c = 4(3m)

c = 12m

Substituting the values of 'b' and 'c' from equations (2) and (3) into equation (1):

m + 3m + 12m = 224

16m = 224

m = 224 / 16

m = 14

Using the value of 'm' in equation (2):

b = 3m

b = 3(14)

b = 42

Using the value of 'b' in equation (3):

c = 4b

c = 4(42)

c = 168

Answer:

Step-by-step explanation:

a) Let's denote the number of jugs of milk as 'x', the number of loaves of bread as 'y', and the number of pieces of cheese as 'z'.

Based on the given information, we can form two equations:

1) The total number of items sold today is 224:

x + y + z = 224

2) The store sold three times as many loaves of bread as jugs of milk:

y = 3x

3) The store sold four times as many pieces of cheese as loaves of bread:

z = 4y

b) To solve the equations and find the number of jugs of milk, loaves of bread, and pieces of cheese the store sold today, we will substitute equation (2) and equation (3) into equation (1):

x + y + z = 224

x + 3x + 4y = 224

4x + 4y = 224

Now, substitute y = 3x into the equation:

4x + 4(3x) = 224

4x + 12x = 224

16x = 224

Divide both sides by 16:

x = 224 / 16

x = 14

Now substitute the value of x back into equation (2) to find y:

y = 3x

y = 3(14)

y = 42

Finally, substitute the value of y into equation (3) to find z:

z = 4y

z = 4(42)

z = 168

Therefore, the store sold 14 jugs of milk, 42 loaves of bread, and 168 pieces of cheese today.

GEOMETRY 50POINTS

find x to the nearest hundredth.

TYSM​

Answers

Answer:

It's 18.37

Step-by-step explanation:

I'm smart trust me.

SOMEONE SOLVE THUS PLEASE ILL GIVE U THIRTY BRAINILY POINTS U WILL BE RICH PLEACE ANSWER I AM IN DESPERATE NEED THANK YOU SO MUCH

Answers

The degree of f(x) is 5, and the leading coefficient is negative. There are 3 distinct real zeros and 2 relative maximum values.

How to obtain the zeros of a function?

From the graph of a function, the zeros of the function are the x-intercepts, that is, the values of x for which the graph crosses or touches the x-axis.

The function in this problem has three distinct zeros, given as follows:

2 with even multiplicity, as the graph turns at the x-axis.1 with odd multiplicity, as the graph crosses the x-axis.

Hence the degree of the function is given as follows:

2 x 2 + 1 = 5.

The leading coefficient is negative, as the function has an odd degree, but increases to left and decreases to right.

The relative maximums of the functions are the points where the function makes a downward turn, changing from increasing to decreasing, hence there are two points.

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What number completes the sequence below? Enter your answer in the input
box at the bottom.
8——-4
16——8
24——12
32——?

Answers

Answer:

16

Step-by-step explanation:

the numbers on the right of the arrow are half the value of the corresponding numbers on the left, then

32 → [tex]\frac{1}{2}[/tex] (32)

32 → 16

he table represents the total miles traveled, y, after a number of hours, x.

Hours, x
Miles, y
2.5
150
4.0
240
5.5
330
7.0
420

Which linear equation represents the situation?

y = 60 x
y = 60 x + 480
y = 4 x + 240
y = 270 x

Answers

Answer:

the answer is y=mx+c

Step-by-step explanation:

where the answer is the coefficient of the gradient which is x

Hungry Harry is a giant ogre with an even bigger appetite. After Harry wakes up from hibernation, his daily hunger � ( � ) H(t)H, left parenthesis, t, right parenthesis (in kg kgstart text, k, g, end text of pigs) as a function of time � tt (in hours) can be modeled by a sinusoidal expression of the form � ⋅ cos ⁡ ( � ⋅ � ) + � a⋅cos(b⋅t)+da, dot, cosine, left parenthesis, b, dot, t, right parenthesis, plus, d. When Harry wakes up at � = 0 t=0t, equals, 0, his hunger is at a maximum, and he desires 30 kg 30 kg30, start text, space, k, g, end text of pigs. Within 2 22 hours, his hunger subsides to its minimum, when he only desires 15 kg 15 kg15, start text, space, k, g, end text of pigs. Find � ( � ) H(t)H, left parenthesis, t, right parenthesis.

Answers

The equation for Harry's hunger in terms of time can be written as,H(t) = 7.5.cos(π.t) + 22.5

Given:Hunger of Harry as a function of time,H(t)H(t) can be modeled by a sinusoidal expression of the form,a⋅cos(b⋅t)+da⋅cos(b⋅t)+d, where Harry wakes up at t=0t=0t=0, his hunger is at a maximum, and he desires 30 kg 30 kg30, start text, space, k, g, end text of pigs.

Within 2 22 hours, his hunger subsides to its minimum, when he only desires 15 kg 15 kg15, start text, space, k, g, end text of pigs.

Therefore, the equation of the form for H(t)H(t) will be,H(t) = A.cos(B.t) + C where, A is the amplitude B is the frequency (number of cycles per unit time)C is the vertical shift (or phase shift)

Thus, the maximum and minimum hunger of Harry can be represented as,When t=0t=0t=0, Harry's hunger is at maximum, i.e., H(0)=30kgH(0)=30kg30, start text, space, k, g, end text.

When t=2t=2t=2, Harry's hunger is at the minimum, i.e., H(2)=15kgH(2)=15kg15, start text, space, k, g, end text.

According to the given formula,

H(t) = a.cos(b.t) + d ------(1)Where a is the amplitude, b is the angular frequency, d is the vertical shift.To find the value of a, subtract the minimum value from the maximum value.a = (Hmax - Hmin)/2= (30 - 15)/2= 15/2 = 7.5To find the value of b, we will use the formula,b = 2π/period = 2π/(time for one cycle)The time for one cycle is (2 - 0) = 2 hours.

As Harry's hunger cycle is a sinusoidal wave, it is periodic over a cycle of 2 hours.

Therefore, the angular frequency,b = 2π/2= π

Therefore, the equation for Harry's hunger in terms of time can be written as,H(t) = 7.5.cos(π.t) + 22.5

Answer: H(t) = 7.5.cos(π.t) + 22.5.

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In random sampling, the probability of selecting an item from the population is:

Select one:
a. Un-Known
b. One
c. known
d. undefined
e. Un-decided


Note: Answer D is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.

Answers

Answer: c. known

Step-by-step explanation:

In random sampling, the probability of selecting an item from the population is known. This probability can be calculated based on the sampling method and the characteristics of the population being sampled. Random sampling ensures that each item in the population has an equal chance of being selected, making the probability of selection known and calculable.

50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

Answer:

BC = 24 (D)

Step-by-step explanation:

Special Right Triangles (30-60-90 triangle)

Write an inequality and solve.

Negative one hundred eighty three is at least nine more than 24 times a number.

Answers

Answer:    -8 ≥ x

Step-by-step explanation:

Let x be the number, we set up an inequality:

-183 ≥ 9 + 24x    [we use ≥ to present "at least"]

-192 ≥ 24x

  -8 ≥ x


Geometry Final Exam
A jar of kosher dill spears is filled to the brim with a vinegar based pickling liquid and then
sealed. The base of the cylindrical jar has an area of 45 cm² and the height of the jar is
13 cm. When the pickles are opened, all the pickle juice is drained into a measuring cup,
amounting to 160 cm³ of pickle juice. Find the total volume of the dill spears.

Answers

The total volume of the dill spears is approximately 160 cm³.

To find the total volume of the dill spears, we'll need to determine the volume of the pickling liquid and subtract it from the total volume of the jar.

Given information:

Base area of the jar = 45 cm²

Height of the jar = 13 cm

Pickle juice drained = 160 cm³

First, let's calculate the volume of the jar:

The volume of a cylinder can be found using the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder.

The base area of the jar is given as 45 cm², which means πr² = 45.

So, we can find the radius (r) of the base using the formula r = √(45/π).

Let's calculate the value of r:

r = √(45/π) ≈ 3.79 cm

Now we can find the volume of the jar:

V_jar = πr²h

= π(3.79)²(13)

≈ 1818.73 cm³

Next, let's calculate the volume of the pickling liquid:

Given that 160 cm³ of pickle juice was drained, the volume of the pickling liquid is equal to the volume of the jar minus the volume of the drained pickle juice.

V_pickling_liquid = V_jar - 160

≈ 1818.73 cm³ - 160 cm³

≈ 1658.73 cm³

Finally, to find the total volume of the dill spears, we need to subtract the volume of the pickling liquid from the volume of the jar:

Total volume of dill spears = V_jar - V_pickling_liquid

≈ 1818.73 cm³ - 1658.73 cm³

≈ 160 cm³

Therefore, the total volume of the dill spears is approximately 160 cm³.

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Como se llama un ángulo de 192 grados?

Answers

Answer:

reflex angle

Step-by-step explanation:

the angle of 192 degrees is called a reflex angle

The functions f(x) and g(x) are graphed.
1(x) 5
32
1
-6-5-4-3-2-11-
-2-
-3-
3458
-4
2 3 4
g(x)
Which represents where f(x) = g(x)?
Of(0) = g(0) and f(2)= g(2)
Of(2)= g(0) and f(0) = g(4)
Of(2)= g(0) and f(4) = g(2)
Of(2)= g(4) and f(1) = g(1)

Answers

Answer: the answer is -4

Step-by-step explanation: the reason why the answer is -4 becaue all of the option is in correct.

An important part of the customer service responsibilities of a company relates to the speed with which troubles in residential service can be repaired. Suppose that past data indicate that the likelihood is 0.70 that service troubles can be repaired on the same day they are reported. For the first five troubles reported on a given day, what is the mean of the distribution used in this problem?

Select one:

A.
350


B.
3.5


C.
0.35


D.
0.7143


E.
3500

Answers

The mean of the distribution used in this problem is 3.5.The answer is B. 3.5.

To find the mean of the distribution used in this problem, we need to calculate the expected number of troubles that can be repaired on the same day out of the first five reported. The likelihood of a trouble being repaired on the same day is given as 0.70.

The expected number of troubles repaired on the same day can be calculated by multiplying the probability of each event by the number of trials. In this case, we have five trials (the first five troubles reported) and a probability of 0.70 for each trial.

Expected number of troubles repaired on the same day = Probability of repair on the same day * Number of trials

= 0.70 * 5

= 3.5

This means that, on average, out of the first five troubles reported, we can expect 3.5 of them to be repaired on the same day based on the past data and the given likelihood. So, the correct answer is B. 3.5.

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Colin and Paul have played 38 tennis matches.
Colin has won 20 times.
Paul won the rest.
a) Estimate the probability that Colin wins.
b) Estimate the probability that Paul wins.

Answers

Answer:

P(Colin) = 20/38

P(Paul) = 18/38

Step-by-step explanation:

Colin won 20 times out of 38, so the probability that he wins would be 20/38 (or 10/19 simplified).

Paul won 18 times out of 38, so the probability that he wins would be 18/38 (or 9/19 simplified).

Answer:

a) Probability of Colin winning = 10/19

b) Probability of Paul winning = 9/19

Step-by-step explanation:

Total number of matches = 38

Colin won 20,

Paul won the rest so, 38 - 20 = 18

Paul won 18 matches,

From this data, we calculate the probabilities of Colin or Paul winning,

a) Estimate the probability that Colin wins.

Colin won 20 out of 38 matches, so his probability of winning is,

20/38 = 10/19

Probability of Colin winning = 10/19

b) Estimate the probability that Paul wins

Paul won 18 out of 38 matches, so his probability of winning is,

18/38 = 9/19

Probability of Paul winning = 9/19

24°
Solve for c.
= [?]°
C =
60% C
Enter

Answers

Answer:

  96°

Step-by-step explanation:

You want the value of angle C in the diagram with two parallel lines and a triangle between them.

Angle sum theorem

The sum of angles in a triangle is 180°, so the missing angle in the triangle is ...

  180° -60° -24° = 96°

Alternate interior angles

Angle C and the one we just found are alternate interior angles with respect to the parallel lines and the transversal that forms those angles. As such, they are congruent:

  C = 96°

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Given that g(x)=2x^2 - 2x + 9 , find each of the following.

a) g(0)
b) g(- 1)
c) g(2)
d) g( - x)
e) g(1 - t)

Answers

Answer:

Step-by-step explanation:

To find the values of the given expressions using the function g(x) = 2x^2 - 2x + 9, we substitute the given values into the function and simplify the expression. Let's calculate each of the following:

a) g(0)

To find g(0), substitute x = 0 into the function:

g(0) = 2(0)^2 - 2(0) + 9

g(0) = 0 - 0 + 9

g(0) = 9

b) g(-1)

To find g(-1), substitute x = -1 into the function:

g(-1) = 2(-1)^2 - 2(-1) + 9

g(-1) = 2(1) + 2 + 9

g(-1) = 2 + 2 + 9

g(-1) = 13

c) g(2)

To find g(2), substitute x = 2 into the function:

g(2) = 2(2)^2 - 2(2) + 9

g(2) = 2(4) - 4 + 9

g(2) = 8 - 4 + 9

g(2) = 13

d) g(-x)

To find g(-x), substitute x = -x into the function:

g(-x) = 2(-x)^2 - 2(-x) + 9

g(-x) = 2x^2 + 2x + 9

e) g(1 - t)

To find g(1 - t), substitute x = 1 - t into the function:

g(1 - t) = 2(1 - t)^2 - 2(1 - t) + 9

g(1 - t) = 2(1 - 2t + t^2) - 2 + 2t + 9

g(1 - t) = 2 - 4t + 2t^2 - 2 + 2t + 9

g(1 - t) = 2t^2 - 2t + 9

Therefore:

a) g(0) = 9

b) g(-1) = 13

c) g(2) = 13

d) g(-x) = 2x^2 + 2x + 9

e) g(1 - t) = 2t^2 - 2t + 9

GEOMETRY 50POINTS

determine what type of triangle they will form.

BRILLIANT for the best answer ​

Answers

Answer:

acute triangle

Step-by-step explanation:

for the given sides to form a triangle

the sum of any 2 sides must be greater than the third side

given 56 , 90 , 100

56 + 90 = 146 > 100

56 + 100 = 156 > 90

90 + 100 = 190 > 56

the condition is met so the 3 lengths will form a triangle.

let a = 56 , b = 90 and c = 100 , where c represents the longest of the 3 sides , then

• if a² + b² = c² , then triangle is right

• if a² + b² > c² , then triangle is acute

• if a² + b² < c² , then triangle is obtuse

a² + b² = 56² + 90² = 3136 + 8100 = 11,236

c² = 100² = 10, 000

since a² + b² > c² , then triangle is acute

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