Please answer this multiple choice question CORRECTLY for 30 points and brainliest!!!

Please Answer This Multiple Choice Question CORRECTLY For 30 Points And Brainliest!!!

Answers

Answer 1

Answer:

D

Step-by-step explanation:

The 3 angles on the right form a straight angle, thus they sum to 180°

Subtract the 2 given angles from 180 to find measure of third angle ( which is the angle inside the triangle )

third angle = 180° - (70 + 60)° = 180° - 130° = 50°

The sum of the 3 angles in a triangle = 180°

Subtract the 2 known angles from 180 for measure of x

x = 180° - (50 + 60)° = 180° - 110° = 70° → D


Related Questions

Need help fast!!!!!!!!!!! Discuss how to convert the standard form of the equation of a circle to the general form. 50 points

Answers

Answer:

Step-by-step explanation:

The standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where h, k an r are real numbers that can be added at the end.

First, to get to the general form of a circle, you have to expand the binomials. Meaning,

[tex](x-h)^2=x^2-2xh+h^2[/tex] and

[tex](y-k)^2=y^2-2yk+k^2[/tex].

After you do this, then the h^2, k^2, and r^2 terms can be added together to give you one number. Then put everything else in descending order, like this:

[tex]x^2+y^2-(2h)x-(2y)k+(h^2k^2r^2)=0[/tex]

It's very hard to describe when there are no values assigned to the h, k, and r in the equation.

Basic idea:

Expand the binomials and add like terms, setting the whole thing equal to 0.

A solid machine part is to be manufactured as shown in the figure The part is made by cutting a small cone off the top of a larger cone The small cone has a base radius of 3 inches and a height of 5 inches. The larger cone has a base radius of 9 inches and had a height of 15 inches prior to being cut What is the volume of the resulting part illustrated in the fiqure?

Answers

Answer:

The exact volume of the part is 390pi in.^3

Using pi = 3.14, the approximate volume of the part is 1224.6 in.^3

Step-by-step explanation:

Find the volume of the large cone and the volume of the small cone. The subtract the small volume from the large volume.

Large cone:

V = (1/3)(pi)r^2h

V = (1/3)(pi)(9 in.)^2(15 in.)

V = 405pi in.^3

Small cone:

V = (1/3)(pi)r^2h

V = (1/3)(pi)(3 in.)^2(5 in.)

V = 15pi in.^3

Difference in volumes:

volume of part = 405pi in.^3 - 15pi in.^3 = 390pi in.^3

The exact volume of the part is 390pi in.^3

Using pi = 3.14, the approximate volume of the part is 1224.6 in.^3

If the frequency of a sound decreases, what happens to the wavelength?

Answers

Answer: The wavelength increases

Step-by-step explanation:

As frequency increases, wavelength decreases. Frequency and wavelength are inversely proportional. This basically means that when the wavelength is increased, the frequency decreases and vice versa.

Hope that this helps! Have a great day!

Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample.

A converse statement is formed by exchanging the hypothesis and conclusion of the conditional.

A) a non-converse statement is not formed by exchanging the hypothesis and conclusion of the conditional. True
B) A statement not formed by exchanging the hypothesis and conclusion of the conditional is a converse statement. False; an inverse statement is not formed by exchanging the hypothesis and conclusion of the conditional.
C) A non-converse statement is formed by exchanging the hypothesis and conclusion of the conditional. False; an inverse statement is formed by negating both the hypothesis and conclusion of the conditional.
D) A statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement. True

Answers

Answer:

D is the contrapositive.

Step-by-step explanation:

Contrapositive of if A then B is if not B then not A

Answer:

Option D is correct here.

Step-by-step explanation:

A conditional statement is in the form of if p then q.

A contrapositive statement is when we interchange the hypothesis and conclusion of the sentence and negate both of them. It is in the form of - if not q then not p.

Given statement here is - A converse statement is formed by exchanging the hypothesis and conclusion of the conditional.

This is a true statement. It is the definition of converse statement.

Its contrapositive will be : A statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement.

So, here option D is the contrapositive that is also true.

Help with vectors! Write each vector in terms of a, b or a and b. Please explain how to do this! I don't know!​

Answers

Answer:

see explanation

Step-by-step explanation:

Find equivalent routes for the directed lines, that is

(a)

FE = FA + AB + BE = b + a - 3b = a - 2b

(b)

BC = BE + ED + DC = - 3b + a + 2b = a - b

(c)

FC = FA + AB + BE + ED + DC

     = b + a - 3b + a + 2b = 2a

A rectangle has a length of 9 centimeters and a width of x centimeters. The perimeter of the rectangle is 28 centimeters. What is the value of x?

NEED HELP!!

Answers

Answer:

x=5

Knowing that the length of the rectangle is 9, we can simply multiply this by 2 since there are two sides that will equal the same. This gets us 18. If we subtract that from 28, we get 10. There are four sides in a rectangle, meaning we have two sides left. This leaves us to divide 10 by two to get a final answer of the width of the retangle being 5 centimeters.

Final answer:

The value of x, which represents the width of the rectangle, can be found by inserting the given length and perimeter into the perimeter formula of a rectangle, P = 2L + 2W. Then, solve for W to get the value of x.

Explanation:

The first step to solve this problem is to understand the formula for the perimeter of a rectangle. This formula is P = 2L + 2W, where P is the perimeter, L is the length and W is the width. We know that the length (L) is 9 cm and the perimeter (P) is 28 cm based on the problem given. We are looking to find the value for x which represents the width (W).

Let's substitute the given values into the formula:
28 = 2(9) + 2W.

This simplifies to:
28 = 18 + 2W.

Now, let's solve for W by subtracting 18 from both sides of the equation:
10 = 2W.

To isolate W, divide both sides of the equation by 2:
W = 5
So, the value of x, which represents the width of the rectangle, is 5 cm.

Learn more about Solving for Variables here:

https://brainly.com/question/32610670

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Help!! I cant figure this out for some reason

Answers

Answer:

x³ - 6x² + 18x - 10

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

= x³ - 2x² + 12x - 6 - (4x² - 6x + 4)

= x³ - 2x² + 12x - 6 - 4x² + 6x - 4 ← collect like terms

= x³ - 6x² + 18x - 10

A bag contains purple marbles and blue marbles ,27 in total . The number of purple marbles is 3 less than 4 times the number of blue marbles . How many purple marbles are there

Answers

[tex]p+b=27\\p=4b-3\\\\4b-3+b=27\\5b=30\\b=6\\\\p+6=27\\p=21[/tex]

21

Final answer:

To determine the number of purple marbles, we can use a system of linear equations derived from the problem's conditions. Solving these gives us 21 purple marbles in the bag.

Explanation:

To solve the problem, let's denote the number of blue marbles as x and the number of purple marbles as y. According to the problem, the total number of marbles is 27, which is our first equation, x + y = 27. Additionally, the number of purple marbles is 3 less than 4 times the number of blue marbles, giving us a second equation, y = 4x - 3.

Now, we'll solve for x using substitution. We place the expression for y from the second equation into the first equation:

x + (4x - 3) = 27

5x - 3 = 27

5x = 30

x = 6

Since x is 6, we can find y by substituting back into the second equation:

y = 4(6) - 3

y = 24 - 3

y = 21

There are therefore 21 purple marbles in the bag.

What was the sensitive, well-insulated tool Willard F. Libby used to date artifacts with known ages?

A. X-ray machine
B. Richter scale
C. Geiger-Müller tubes
D. petri dish

{Full explanation, no spam answers, please! Thank you!}

Answers

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

[tex]\text{Question reads: What was the sensitive, well-insulated tool Willard F.}[/tex] [tex]\text{ Libby used to date artifacts with known ages?}[/tex]

[tex]\bf{Choices\downarrow}\\\bf{A) X-ray\ machine}\\\bf{B) Richter\ Scale}\\\bf{C)Geinger-Muller\ tubes}\\\bf{D)Petri\ dish}[/tex]

[tex]\boxed{\boxed{\bf{Answer: C. Geiger-Muller\ tubes}}}\checkmark[/tex]

[tex]\text{Your explanation}\downarrow[/tex]

[tex]\text{The people of the University of Berkeley were succeeding to make a(n)}[/tex] [tex]\text{energy to make the interest for the atomic energy force.}[/tex][tex]\text{. Some people thought this was delicate to handle.}[/tex]

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

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

C. Geiger-Müller tubes

Step-by-step explanation:

Geiger-Müller tubes was the sensitive, well-insulated tool Willard F. Libby used to date artifacts with known ages.

Use Cavalieri's Principle to calculate the exact volume of an oblique cylinder with a height of 20 centimeters and a circular base with a radius of 10 centimeters.

Answers

Answer:

The exact volume of an oblique cylinder is [tex]V=2,000\pi\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The Cavalieri's principle states that if two or more figures have the same cross-sectional area at every level and the same height, then the figures have the same volume

so

The volume of the oblique cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]h=20\ cm[/tex]

[tex]r=10\ cm[/tex]

substitute

[tex]V=\pi (10)^{2} (20)[/tex]

[tex]V=2,000\pi\ cm^{3}[/tex]

Answer:

the volume of an oblique cylinder is V=2,000\pi\ cm^{3}

Tamie uses 3/4 of a cup of water with 1/8 of a pound of flour to make a paste for a sculpture she is creating. How many cups of water does she need to mix with 1 pound of flour to create the same paste?

Answers

For this case we can raise a rule of three:

[tex]\frac {3} {4}[/tex]cup of water ---------> [tex]\frac {1} {8}[/tex] pound of flour

x --------------------------------- > 1 pound of flour

Where:

x: Represents the amount of water that Tamie must use with 1 pound of flour.

[tex]x = \frac {1 * \frac {3} {4}} {\frac {1} {8}}\\x = \frac {\frac {3} {4}} {\frac {1} {8}}\\x = \frac {3 * 8} {4 * 1}\\x = \frac {24} {4}\\x = 6[/tex]

So, Tamie should use 6 cups of water

Answer:

6 cups of water

Find the volume of the cylinder in terms of π.

Cylinder height = 11 in.
Cylinder radius = 5 in.

Answers

Hello There!

The volume for a cylinder is Pi*r^2*h

We are going to leave our Answer in terms of pi so first we need to square our radius which we know is 5

Our radius is 25 because we squared 5. Next, we need to multiply 25 by our height which is 11.

25 multiplied by 11 is 275 so our Answer would be 275[tex]\pi[/tex]

Will mark the BRANLIEST.

Beverly has $50 to spend at an amusement park. Admission to the park is $15. She plans to spend $10 on food. Each ride costs $1.50. What is the maximum number of rides she can ride?

1. Define a variable for this situation.
2. Write an inequality to represent the possible number of rides she can ride.
3.Solve the inequality from #2 to determine the maximum number of rides she can ride.
4.5. If Beverly rides the maximum number of rides possible, will she have spent the entire $50? If she has not spent the entire $50, how much money is left over? Support your answer with an explanation and/or calculations.

Answers

Answer:

see below

Step-by-step explanation:

Let r = number of rides

total amount of money spent has to be less than  or equal to 50

costs are admission and food and rides

rides cost 1.50 each

50≥ admission + food + rides

50 ≥ 15 +10 + 1.50r

Combine like terms

50 ≥25 + 1.50 r

Subtract 25 from each side

50-25 ≥25-25 + 1.50 r

25  ≥ 1.50 r

Divide by 1.5 on each side

25/1.5 ≥ 1.5r/1.5

50/3  ≥ r

Changing this to a mixed number

16 2/3  ≥r

We can only take a whole number of rides

r = 16

Beverly has not spent all of her 50 dollars since there was a fraction for the rides

cost =  15 +10 + 1.50r

        15+10 + 1.5*16

            25+24

           49

She has 1 dollar left

1. Use the correct order of operation to solve the following problem: 3 × (50 – 62) ÷ 2 A. 69 B. 18 C. 21 D. 57

Answers

Answer:

The correct answer is option B.  -18

Step-by-step explanation:

It is given an expression : 3 × (50 – 62) ÷ 2

To find the answer we have to use BODMAS principle

BODMAS means that the order of operations

B- Bracket, O - of , D - Division, M - Multiplication, A - Addition and  

S - Subtraction

To find the correct option

Step 1: Do the bracket first

3 × (50 – 62) ÷ 2 =  3 × (-12) ÷ 2

(Multiplication and division are in the order of appearance)

Step 2: Multiplication  

3 × (-12) ÷ 2 = -36  ÷ 2  

Step 3 : Division

-36 ÷ 2 = -18

The correct option is option B.  -18

Answer:

=-18

Step-by-step explanation:

3×(50-62)÷2

Using PEMDAS,  we first evaluate the parentheses. 50-62=-12

The new expression becomes

3×⁻12÷2

We now perform the multiplication in the order in which they occur.

3×-12=-36 and -36÷2= -18

=-18

NEED HELP WITH A MATH QUESTION

Answers

Answer:

1/5 or 20%

Step-by-step explanation:

Since the customer ordered a cold drink, that reduces our sampling population to 25 (8 + 12 = 5).

Out of those 25 people, 5 ordered a large size.

So, the probability that someone who has ordered a cold drink ordered a large one is 5 out of 25...

P = 5 / 25 = 1/5 or 20%

1/5 or 20%

Have a great day

A mixture of 30 liters of paint is 25% red tint, 30% yellow tint and 45% water. 8 liters of yellow tint are added to the original mixture.

Answers

Answer:

Yellow Paint: 0.44736842105%

Red Paint: 0.19736842105%

Water: 0.35526315789%

Step-by-step explanation:

Yelow:

30 x 0.3 = 9

8 + 9 = 17

30 + 8 = 38

17/38 = 0.44736842105%

Red:

30 x 0.25 = 7.5

7.5/38 = 0.19736842105%

Water:

30 x 0.45 = 13.5

13.5/38 = 0.35526315789%


I believe it’s 0.3552%

A prong horn runs 59 miles per hour, what is the speed in feet per second,to the nearest whole number

Answers

Step-by-step explanation:

59 mi/hr × (5280 ft/mi) × (1 hr / 3600 s) = 86.53 ft/s

Rounded to the nearest whole number, the speed is approximately 87 ft/s.

If $6500 is invested at a rate of 6% compounded continuously, find the balance in the account after 3 years

Answers

[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$6500\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &3 \end{cases} \\\\\\ A=6500e^{0.06\cdot 3}\implies A=6500e^{0.18}\implies A\approx 7781.91[/tex]

Add.

(6x3+3x2−2)+(x3−5x2−3)

Express the answer in standard form.

Answers

Answer:

[tex]7x^3-2x^2-5[/tex]

Step-by-step explanation:

We need to add the two terms.

[tex](6x^3+3x^2-2)+(x^3-5x^2-3)[/tex]

Solving,

Combine the like terms and adding those terms

[tex](6x^3+3x^2-2)+(x^3-5x^2-3)\\=6x^3+3x^2-2+x^3-5x^2-3\\=6x^3+x^3+3x^2-5x^2-2-3\\=7x^3-2x^2-5[/tex]

So, the answer is:

[tex]7x^3-2x^2-5[/tex]

Which of the following functions corresponds to the above sinusoid?

A. 10 cos πx - 5
B. -5 sin x - 5
C. -10 cos πx/2 - 0.5
D. 10 sin πx - 5

Answers

Answer:

d

Step-by-step explanation:

Answer:

Option d

Step-by-step explanation:

Consider the parent function y =sinx which has amplitude 1 and period 2pi.

Compare this with out graph passing through 3 points given as

(0.5,5) (1.5,-15) and (0,5)

Since maximum value is 5 and min value is -15 amplitude = 1/2 (20) = 10

Also period =2 instead of 2pi.

Hence pi must be coefficient for x

Also the curve does not pass through origin but passes through (0,-5)

So vertical shift of 5 units down.

Hence the curve equation is

[tex]y=10sin \pi x -5[/tex]


4. The cosine function can be made to have the same values as the sine function for each angle by including a shifted _______ in the calculation.

A. amplitude
B. wavelength
C. period
D. phase

Answers

Answer: Option D

phase

Step-by-step explanation:

By definition, the cosine function has the following form

[tex]y = cos (x - \phi)[/tex]

Where [tex]\phi[/tex] is known as the phase angle

By definition the sinx function is equal to the cosx function with a phase shift of [tex]\frac{\pi}{2}[/tex]

So if we have the function

[tex]y = cos (x - \phi)[/tex] and we want to transform it into the function [tex]y=sin(x)[/tex] then [tex]\phi = \frac{\pi}{2}[/tex]

Finally

[tex]y = cos(x - \frac{\pi}{2})=sin(x)[/tex]

the answer is the option D

Final answer:

The cosine function aligns with the sine function by introducing a phase shift, typically represented by phi (φ), indicating that D. phase is the correct answer.

Explanation:

The cosine function can be made to have the same values as the sine function for each angle by including a shifted phase in the calculation. This shift is referred to as a phase shift and is typically represented by the Greek letter phi (φ).

In the context of trigonometric functions, a phase shift will slide one function over to match that of another.

Specifically, when the sine function is shifted left by 90 degrees (π/2 radians), it aligns perfectly with the cosine function, indicating that the sine and cosine are out of phase by 90 degrees.

Thus, the correct answer is D. phase.

simplify. -x/17 = -0.9
a. -15.3
b. 15.3
c. 153
d. -153

Answers

Answer:

[tex]\large\boxed{b.\ 15.3}[/tex]

Step-by-step explanation:

[tex]-\dfrac{x}{17}=-0.9\qquad\text{multiply both sides by (-17)}\\\\(-17\!\!\!\!\!\diagup^1)\left(-\dfrac{x}{17\!\!\!\!\!\diagup_1}\right)=(-17)(-0.9)\qquad{/(-)(-)=(+)/}\\\\x=15.3[/tex]

the values in the table represent an exponential function.what is the common ratio of the associated geometric sequence
x y
1 8
2 32
3 128
4 512
5 2048


A.4 B.24 C.40 D.8

Answers

Answer:

  A.  4

Step-by-step explanation:

The common ratio will be the ratio of any adjacent pair of y-values:

  32/8 = 128/32 = 512/128 = 2048/512 = 4

suppose that y varies inversely with x, and y=0.2 when x=8. what is the equation for the inverse variation​

Answers

Answer:

xy = 1.6

Step-by-step explanation:

The equation for inverse variation is

xy = k  where k is the constant of variation

8 * .2 = k

1.6 = k

xy = 1.6

Find the value of x in the following equation: x/2 + 2x/5 = 18 A. x = 11/2 B. x = 2 C. x = 255/7 D. x = 20

Answers

Answer: x = 20

Step-by-step explanation:

Multiply by 10 ( next LCF )

10 ( x / 2 + 2x / 5 ) = 18 * 10

5x + 4x = 180

9x = 180

x = 20

Answer:

[tex]\dfrac{x}{2} + \dfrac{2x}{5} = 18[/tex] has the unique solution x = 20.

Step-by-step explanation:

The equation has the equivalences

[tex]\displaystyle\frac{x}{2} + \frac{2x}{5} = 18 \Leftrightarrow x\left( \frac{1}{2} + \frac{2}{5} \right) = 18 \Leftrightarrow x \left( \frac{9}{10} \right) = 18 \Leftrightarrow x = 18 \cdot \frac{10}{9} = 20.[/tex]

Question is in picture, please please help

Answers

Answer:

  b.  42.875 units³

Step-by-step explanation:

The volume of a cuboid is the product of its edge dimensions (length×width×height):

  (3.5 units)(3.5 units)(3.5 units) = 3.5³ units³ = 42.875 units³

GEOMETRY PLS HELPPPPPP

Answers

ANSWER

(0,2)

EXPLANATION

The mapping point A has coordinate (0,2).

We want to find the coordinates of this point after a rotation of -90° about the origin.

In other words, we want to find the image of this point after a rotation of 90° anticlockwise.

The rule is

[tex](x,y) \to( - y,x)[/tex]

This implies that

[tex](2,0) \to(0,2)[/tex]

A merchant has coffee worth $60 a pound that she wishes to mix with 50 pounds of coffee worth $90 a pound to get a mixture that she will sell for $70 a pound. How many pounds of the &60 coffee should be used?

Answers

Answer:

  100 lbs

Step-by-step explanation:

Let x represent the number pounds of $60 coffee that should be used to create the mix. The total cost of the mix will be ...

  60x + 90·50 = 70(x+50)

  60x +4500 = 70x +3500 . . . . simplify

  1000 = 10x . . . . . . . . . . . . . . . . subtract 3500+60x

  100 = x . . . . . . . . . . . . . . . . . . . divide by 10

The merchant should use 100 pounds of the $60 coffee.

_____

The cost of the mix parts and the total mix is figured from ...

  (dollars/lb)×(lbs) = dollars

An initial investment of $100 is now valued at $150. The annual interest rate is 5%, compounded continuously. The equation 100e0.05t = 150 represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use your calculator and round to the nearest whole number. Years

Answers

Answer:

[tex]8\ years[/tex]  

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=?\ years\\ P=\$100\\A=\$150\\ r=0.05[/tex]  

substitute in the formula above  

[tex]150=100(e)^{0.05*t}[/tex]  

[tex]1.5=(e)^{0.05*t}[/tex]  

Applying ln both sides

[tex]ln(1.5)=(0.05t)ln(e)[/tex]  

[tex]ln(1.5)=(0.05t)[/tex]  

[tex]t=ln(1.5)/(0.05)[/tex]  

[tex]t=8\ years[/tex]  

Answer:

If you need all the answers for that assignment:

Step-by-step explanation:

1. Consider 8^x-4 = 8^10

Because the (blank a) are equal , the (blank b) must also be equal.

Answer: Bases, Exponents

The solution to the equation is 14

2.What equation is equivalent to 9^(x-3)=729?

Answer 3^x - 3 = 3^6  

Solve: 9x - 3 = 729

Answer: x = 6

3. To solve 5(2^x+4)=15, first divide each side by

Answer: 5

Solve 5(2^x+4) = 15. Round to the nearest thousandth.

Answer: -2.415

4. Which of the following is the solution of 5e^2x- 4 = 11?

Answer: x=In3/2

5. Select all of the potential solution(s) of the equation 2log5x = log54.

Answer: 2,-2

What is the solution to 2log5x = log54?

Answer: 2

6. Which equation is equivalent to log5x3 - logx2 = 2?

Answer: 10^log5^3/x^2=10^2

Solve: log5x3 - logx2 = 2

Answer: 20

7. What is the solution to ln (x2 - 16) = 0?

Answer: x=+-(17)

8. Solve: ln 2x + ln 2 = 0

Answer: ¼

Solve: e^ 2x+5 = 4

Answer: x=(In4) - 5/2

9. Consider the equation log(3x - 1) = log2(8). Explain why 3x - 1 is not equal to Describe the steps you would take to solve the equation, and state what 3x - 1 is equal to.

Answer: The bases are not the same, so you cannot set 3x - 1 equal to 8.You can evaluate the logarithm on the right side of the equation to get .You can use the definition of a logarithm to write 3x - 1 = 1000.

10. An initial investment of $100 is now valued at $150. The annual interest rate is 5%, compounded continuously. The equation 100e^0.05t = 150 represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use your calculator and round to the nearest whole number.

Answer: 8

Which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle?A. 8, 10, 14B. 9, 12, 15C. 10, 14, 17D. 12, 15, 19

Answers

Answer:

  A.  8, 10, 14

Step-by-step explanation:

As a rough cut, a triangle will be obtuse if the longest side is about 1.4 or more times the length of the second-longest side. This derives from the relationship in an isosceles right triangle, where the hypotenuse is √2 ≈ 1.414 times the length of the two equal-length sides. If one side is shorter than the other, and the hypotenuse is still 1.414 times the length of the second-longest side, then the triangle is no longer a right triangle, but is an obtuse triangle.

Here, the first selection has a middle-length side of 10 and a longest side of 14, about 1.4 times 10. It is an obtuse triangle.

_____

More rigorously, you can see if the sum of the squares of the short sides is less than the square of the longest side. If so, the triangle is obtuse. (The Law of Cosines will tell you the angle opposite the longest side must have a negative cosine, so must be greater than 90°.)

Our answer choices are ...

  A. 8^2 + 10^2 = 164 < 14^2 = 196 . . . . . obtuse

  B. 9^2 + 12^2 = 225 = 15^2 . . . . . . . . . . right

  C. 10^2 +14^2 = 296 > 17^2 = 289 . . . . . acute

  D. 12^2 +15^2 = 369 > 19^2 = 361 . . . . . acute

Answer:

A) 8, 10 and 14

correct on edg2020 :)

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