Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle?

The triangle is acute because 22 + 52 > 42.
The triangle is acute because 2 + 4 > 5.
The triangle is not acute because 22 + 42 < 52.
The triangle is not acute because 22 < 42 + 52.

Answers

Answer 1

9514 1404 393

Answer:

  The triangle is not acute because 2² + 4² < 5²

Step-by-step explanation:

The square of the hypotenuse of a right triangle with the given short sides would be 2² +4² = 20. So, that hypotenuse would be √20, about 4.47. The long side of this triangle is longer than that, so the angle opposite is larger than 90°. The triangle with sides 2, 4, 5 is an obtuse triangle.

  The triangle is not acute because 2² + 4² < 5²

Which Best Explains Whether A Triangle With Side Lengths 2 In., 5 In., And 4 In. Is An Acute Triangle?The
Answer 2

The triangle is not acute because 22 + 42 < 52.

Option C is the correct answer.

What is a triangle?

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

To determine if a triangle is acute, we need to check whether all three angles of the triangle are acute angles (less than 90 degrees).

Pythagorean theorem,

- If the square of the length of the hypotenuse is greater than the sum of the squares of the other two sides, then the triangle is acute.

- If the square of the length of the hypotenuse is less than the sum of the squares of the other two sides, then the triangle is obtuse.

Now,

The triangle with side lengths 2 in., 5 in., and 4 in. is not a right triangle.

So we can't use the Pythagorean theorem directly.

Now,

We can check if the sum of the squares of the two shorter sides is greater than the square of the longest side.

2² + 4² = 4 + 16 = 20

5² = 25

Since 20 < 25, we know that the triangle is not acute.

Therefore,

The triangle is not acute because 22 + 42 < 52.

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Related Questions

6. A company builds a model of its earning, and finds that its profit fits the linear model()=5―2500 Where p is the profit in dollars and q is the quantity of its product sold. a) Explain what the slope and y-intercept mean in the context of the problem. Be specific and answer in complete sentence. (2 points)

Answers

Answer:

The slope of 5 means that for each product sold, the profit increases by 5, and the intercept of -2500 means that if no products are sold, the company loses 2500.

Step-by-step explanation:

Linear function:

A linear function has the following format:

[tex]y = mx + b[/tex]

In which m is the slope, that is, by how much y changes for each unit of x, and b is the y-intercept, which is the values of y when x = 0.

In this question:

[tex]p(q) = 5q - 2500[/tex]

p is the profit in dollars and q is the quantity of its product sold.

a) Explain what the slope and y-intercept mean in the context of the problem.

The slope of 5 means that for each product sold, the profit increases by 5, and the intercept of -2500 means that if no products are sold, the company loses 2500.

6. a semicircle has as its diameter the hypotenuse of a right triangle shown below. determine the area of the semicircle to the nearest tenth of a square centimeter. show how you arrived at your answer.

Answers

Answer:

[tex]A = 137.3cm^2[/tex]

Step-by-step explanation:

Given

See attachment

Required

The area of the semicircle

First, we calculate the hypotenuse (h) of the triangle

Considering only the triangle, we have:

[tex]\cos(68) = \frac{7}{h}[/tex] --- cosine formula

Make h the subject

[tex]h = \frac{7}{\cos(68)}[/tex]

[tex]h = \frac{7}{0.3746}[/tex]

[tex]h = 18.7[/tex]

The area of the semicircle is then calculated as:

[tex]A = \frac{\pi h^2}{8}[/tex]

This gives:

[tex]A = \frac{3.14 * 18.7^2}{8}[/tex]

[tex]A = \frac{1098.03}{8}[/tex]

[tex]A = 137.3cm^2[/tex]

4n-6 in as a undistributed expression

Answers

Answer:

2( 2n-3)

Step-by-step explanation:

4n-6

2*2 n - 2*3

Factor out the greatest common factor

2( 2n-3)

PLEASE HELP ME WITH THIS ONE QUESTION
How many combinations without repetition are possible if n = 4 and r = 3?

A) 16
B) 12
C) 3
D) 4

Answers

Given:

[tex]n=4[/tex] and [tex]r=3[/tex].

To find:

The combinations without repetition are possible if [tex]n=4[/tex] and [tex]r=3[/tex].

Solution:

Combination of selecting r item from total n items is:

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

We have [tex]n=4[/tex] and [tex]r=3[/tex]. By using the above formula, we get

[tex]^4C_3=\dfrac{4!}{3!(4-3)!}[/tex]

[tex]^4C_3=\dfrac{4\times 3!}{3!1!}[/tex]

[tex]^4C_3=4[/tex]

Therefore, the correct option is D.

Answer:

Step-by-step explanation:

khalil has a circular cake that he plans to share equally betweeb himself and 5 friends. if tge cake is 8 inched in a diameter, what will be the length of the arc of each slice of cake.

Answers

Answer:

4.2

Step-by-step explanation:

The length of the arc of each slice of cake will be 4.18 inches if Khali shares the cake between him and 5 friends equally.

What is the circumference of a circle?

The circumference is the length of the outer boundary of the circle. It can be calculated as under:

Circumference=2πr

How to find length of arc?

We have been given that the diameter of the cake is 8 inches So, the radius becomes 4 inches. We have to calculate the circumference of the cake. so the circumference becomes:

Circumference=2π(4)=8π

=8*22/7

=25.1

Then we have to divide it into 6 people so it will be 25.1/6=4.18 inches.

Hence the length of the arc will be 4.8 inches.

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the solution set for -2x[tex]-2x^{2}+12x=0[/tex]

Answers


Mark Brainliest please
Answer : x = 0 or x = 6


Explanation:
−2x^2 + 12x = 0. By can be written as
2x × ( −x ) + 2x × 6 = 0

or,

2x ( − x + 6 ) = 0

As product of 2x and (−x+6) is zero,

therefore

either 2x = 0 i.e. x = 0

or −x +6 = 0. i.e. x = 6

Find the percent of decrease from 46 songs to 41 songs. Round to the nearest tenth of a percent if necessary.
percent of decrease
%

Answers

Answer:

10.9 %

Step-by-step explanation:

46 - 41 = 5

5/46 * 100% = 10.8695652174%

Rounded

10.9 %

How many times bigger is a group of 20 coins than a group of 5 coins

Answers

Answer:

It is there difference:

20-5

15

A local hamburger shop sold a combined total of 393 hamburgers and cheeseburgers on Thursday. There were 57 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Thursday? ​

Answers

Answer:

H+C = 393

H - 57 = C

~~~~~~~~~~~~~~~~

H + H - 57 = 393

2H = 450

H = 225

C = 168

Step-by-step explanation:

Joe drives for 3 hours and covers 201 miles. In miles per hour, how fast was he driving?​

Answers

Answer:

50

Step-by-step explanation:

graph the
function f(x)=10(2)x

Answers

Answer:

G.o.o.g.l.e

Step-by-step explanation:

If you search up 'f(x)=10(2)x' on g.o.o.g.l.e it will draw the graph for you.

If this helps you, please give brainliest!

What is the y-intercept of this quadratic function? f(x)= -x^2

Answers

Answer:

x-intercept(s):  

( 0 , 0 )

y-intercept(s):  

( 0 , 0 )

Step-by-step explanation:

Answer:

(0,0)

Step-by-step explanation:

This has no real starting point. The x-intercept as well as the y-intercept is (0,0).

reflectiion across y=x​

Answers

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The reflection across y=-x swaps the coordinates and negates both of them. The first-quadrant figure becomes a third-quadrant figure.

  (x, y) ⇒ (-y, -x)

Please help me solve this. I keep getting the answer weong

Answers

Answer:

21 is the answer I think sike I lied ik its not im just trying get this over with

You can use this formula to work out the area of a triangle when you know two sides and the angle inbwtween them :

1/2 x a x b x sin(C)

where a and b are the two sides you know and C is the angle in between them.

So here a = 7, b = 14, C = 125.

Area = 1/2 x 7 x 14 x sin(125) = 40.138...

= 40.1 (nearest 10th)

A zoo is designing a giant bird cage consisting of a cylinder of radius rr feet and height hh feet with a hemisphere on top (no bottom). The material for the hemisphere costs 2020 per square foot and the material for the cylindrical sides costs 1010 per square foot; the zoo has a budget of 45004500. Find the values of rr and hh giving the birds the greatest space inside assuming the zoo stays within its budget. Note: surface of a cylinder's side 2πrh2πrh, surface of a sphere 4πr24πr2, volume of a cylinder's side πr2hπr2h, volume of a sphere 43πr343πr3

Answers

Answer:

r  =  42,32 ft

h  = 84.8 ft

Step-by-step explanation:

We are going to apply Lagrange multipliers method

The greatest space   means  maximum volume

V(cage)  =  Vol. of the cylinder + volume of the hemisphere

V(cylinder )  = π*r²*h

V(sphere) = (4/3)*π*r²   ⇒  V(hemisphere) = (2/3)*π*r³

V(cage) =  π*r²*h  +  (2/3)*π*r³

Associated costs:

Costs =  cost of cylinder  + cost of hemisphere

Area of the cylinder  =  Lateral area   ( no bottom no top)

Area of the cylinder  =  2*π*r*h

Area of hemisphere  =  2*π*r²

A(r,h)  =   2*π*r*h  +  2*π*r²

C(r , h ) =  10* 2*π*r*h  + 20* 2*π*r²    C(r , h ) =  20*π*r*h  + 40*π*r²

4500 = 20*π*r*h  + 40*π*r²

20*π*r*h  + 40*π*r² -  4500  =  0         20*π*r*h  + 40*π*r² -  4500 = g(r,h)

V(cage) =  π*r²*h  +  (2/3)*π*r³

δV/δr  =  2*r*π*h  + 2*π*r²                       δg(r,h)/δr  =   20*π*h + 80*π*r

δV/δh  =  π*r²                                            δg(r,h)/δh =   20*π*r

δV/δr  = λ*  δg(r,h)/δr

2*r*π*h  + 2*π*r² =  λ* 20*π*h + 80*π*r

2*r*π* ( h + r )  =  20*π*  λ* ( h + 4*r)

r* ( h + r )  = 10*λ* ( h + 4*r)                        (1)

δV/δh  = λ*  δg(r,h)/δh

π*r²  =  20*λ*π*r        r  =  20*λ                  (2)

20*π*r*h  + 40*π*r² -  4500 = 0                 (3)

We need to sole the system of equation 1 ; 2 ; 3

r = 20*λ   plugging that value in equation  1

20*λ ( h  +   20*λ  ) =  10*λ* ( h + 4*r)  

2( h  +  20*λ  ) =   ( h + 4*20*λ)  

2*h  + 40*λ  =  h + 80*λ

h  = 40*λ

20*π*r*h  + 40*π*r² -  4500 = 0  

20*π*20*λ*40*λ  + 40*π+400λ²  - 4500  = 0

16000*π*λ²  +  16000*π*λ²  = 4500

32000*π*λ² = 4500

320*π*λ² = 4500

λ² = 4500/1004,8               λ² = 4.48          λ  = 2.12

Then

r  =  20* λ         r  =  42,32 ft

h  = 40* λ         h  = 84.8 ft

A picture frame (see figure) has a total perimeter of 3 feet. The width of the frame is 0.64 times its length. Find the dimensions of the frame. (Round your answers to two decimal places.)

Answers

Answer:

[tex]\approx 0.59\text{ ft by }0.91\text{ ft}[/tex]

Step-by-step explanation:

Let [tex]\ell[/tex] represent the length of the rectangle. The width can be represented as [tex]0.64\ell[/tex].

The perimeter of a rectangle with lengths [tex]l[/tex] and [tex]w[/tex] is given by [tex]p=2l+2w[/tex].

Thus, we have:

[tex]2\ell+2(0.64\ell)=3,\\2\ell +1.28\ell=3,\\3.28\ell=3,\\\ell=0.91463414634\approx 0.91[/tex]

The width is then [tex]0.64(0.91463414634)=0.58536585365\approx 0.59[/tex].

find the slope from the graph. Leave the answer as a reduced fraction. *
I attached a picture below: I will give brainliest

Answers

Answer:

Slope = -2

Step-by-step explanation:

Point 1 (-1, 2)

Point 2 (1, -2)

Formula to find slope = y2 - y1 / x2 - x1

Slope = 2-(-2) / -1-1

Slope = 4 / -2

Slope = -2

Let x be a real number such that x + (1/x) is an integer. Prove that (x^n) + 1/(x^n) is an integer for every positive integer n.

Answers

Answer:

sim eu também preciso desta respota

There are 9 students in a class: 7 boys and 2 girls.
If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a boy?

Answers

Answer: 9/7

Step-by-step explanation:

A road has a scale of 1:50 000 The length of a road on the map is 8.5cm.Work out the length of the real road in kilometres

Answers

Answer:

ok so

8.5*150000

1275000 cm into kilometers is

12.75 kilometers

Hope This Helps!!!

Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 9.6 minutes and a standard deviation of 2.3 minutes. For a randomly received emergency call, find the following probabilities. (For each answer, enter a number. Round your answers to four decimal places.)

a. between 5 and 10 min
b. less than 5 min
c. more than 10 min

Answers

Answer:

a) 0.5447

b) 0.0228

c) 0.4325

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normal distribution with a mean of 9.6 minutes and a standard deviation of 2.3 minutes.

This means that [tex]\mu = 9.6, \sigma = 2.3[/tex]

a. between 5 and 10 min

This is the p-value of Z when X = 10 subtracted by the p-value of Z when X = 5. So

X = 10

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{10 - 9.6}{2.3}[/tex]

[tex]Z = 0.17[/tex]

[tex]Z = 0.17[/tex] has a p-value of 0.5675

X = 5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{5 - 9.6}{2.3}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a p-value of 0.0228

0.5675 - 0.0228 = 0.5447 probability that a randomly received emergency call is between 5 and 10 minutes.

b. less than 5 min

p-value of Z when X = 5, which from item a), is 0.0228, so 0.0228 probability that a randomly received emergency call is of less than 5 minutes.

c. more than 10 min

1 subtracted by the p-value of Z when X = 10, which, from item a), is of 0.5675.

1 - 0.5675 = 0.4325

0.4325 probability that a randomly received emergency call is of more than 10 minutes.


1. Determine the length and perimeter of Laura's property.
(5)

Answers

9514 1404 393

Answer:

length: 40 mperimeter: 136 marea: 653 m²volume: 6.52 m³

Step-by-step explanation:

1.

The outer dimensions of the property are 20 squares (length) by 14 squares. Each square is 2 m on a side, so the overall length of the property is ...

  (20 squares)×(2 m/square) = 40 m . . . . length

The overall width of the property is ...

  (14 squares)×(2 m/square) = 28 m . . . . width

Then the perimeter is ...

  P = 2(length + width) = 2(40 +28) m = 136 m . . . . perimeter

__

Additional comment

We have computed the perimeter as though the plot were a rectangle. If you carefully consider the total length of horizontal edges and the total length of vertical edges, you see that those totals are the same as they would be for a 20×14 square (40×28 m) rectangle.

_____

2.

The area of open ground is perhaps most easily computed by finding the area that must be subtracted from the overall 20×14 square rectangle. Those exclusions will be (in dimensions of squares) ...

lower right corner: 8 wide by 3 high = 24 squaresfish pond: 2 wide by 3 high = 6 squaresveranda: 4 wide by 4 high = 16 squareshouse: 9 wide by 7 high = 63 squarespavement: 4 wide by 2 high = 8 squares

The total area of exclusions is 24+6+16+63+8 = 117 squares. The bounding rectangle is 20 by 14 = 280 squares, so the open ground is ...

  280 squares - 117 squares = 163 squares

At (2 m)(2 m) = 4 m² per grid square, that's an area of ...

  (163 squares)(4 m²/square) = 652 m²

The surface area of the open ground is 652 m².

_____

3.

The volume is given by the formula ...

  V = Bh

where B is the base area and h is the height.

1 cm = 1/100 m = 0.01 m thickness. That means the total volume is ...

  V = (652 m²)(0.01 m) = 6.52 m³

6.52 cubic meters of topsoil are needed to cover the open ground to a depth of 1 cm.

find the value of x if 3x over 2 equals to 3 ​

Answers

Answer:

x = 2

Step-by-step explanation:

3x/2 = 3/1

cross-multiply to get:

3x = 6

divide each side by 2 to get:

x = 2

Noah is ordering a taxi from an online taxi service. The taxi charges $2.50 just for the pickup and then an additional $2 per mile driven. How much would a taxi ride cost if Noah is riding for 4 miles? How much would a taxi ride cost that is mm miles long?

Answers

Answer:

$10.50

Step-by-step explanation:

We can make an equation

2.50+2x=?

x=4 because we are riding 4 miles.

so it's 2.5+2*4=?

let's solve

2.5+8=$10.50

The Cost of the taxi ride for 4 miles is $10.50 and Charge for m miles is 2.50 + 2m

Given:

Pick up charge = $2.50

Charge per mile = $2

Number of miles = 4

Cost of the taxi ride for 4 miles = Pick up charge + (Charge per mile + Number of miles)

= 2.50 + (2 × 4)

= 2.50 + 8

= $10.50

Charge for m miles = Pick up charge + (Charge per mile + Number of miles)

= 2.50 + (2 × m)

= 2.50 + 2m

Therefore, Cost of the taxi ride for 4 miles is $10.50 and Charge for m miles is 2.50 + 2m

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A, B, and C are collinear points:
B is between A and C.
If AB = 3x + 4, BC = 4x - 1, and AC = 6x + 5,
find AC.

Answers

9514 1404 393

Answer:

  AC = 17

Step-by-step explanation:

The segment sum theorem tells you ...

  AB +BC = AC

Substituting the given expressions, we have ...

  (3x +4) +(4x -1) = (6x +5)

  x = 2 . . . . . . . . . . . . . . . . . . subtract 3+6x from both sides

  AC = 6x +5 = 6(2) +5

  AC = 17

_____

  AB = 10, BC = 7

Choose the equation of the line that is parallel to the x-axis.
x = 4
x + y = 0
x = y
y = 4

Answers

Y= 4, because the line is graphed horizontally
y = 4
When y = 0 the line falls on the x axis, so when y = 4, it will move up 4 spaces and be parallel to the x axis.
Hope this helps!!

Cho mặt bậc hai
z=\sqrt(x^(2)+y^(2))

. Đây là mặt gì?

Answers

Answer:

ñkxkdbdidvdv

Step-by-step explanation:

hsu3jdjfiebdic ic8 e

\left(a+b\right)^2 hihihihihiihihihihihih

Answers

Consider, we need to find the expanded form of the given expression.

Given:

The expression is:

[tex]\left(a+b\right)^2[/tex]

To find:

The expanded form of the given expression.

Solution:

We have,

[tex]\left(a+b\right)^2[/tex]

It can be written as:

[tex]\left(a+b\right)^2=(a+b)(a+b)[/tex]

Using distributive property of multiplication over addition, we get

[tex]\left(a+b\right)^2=a(a+b)+b(a+b)[/tex]

[tex]\left(a+b\right)^2=a(a)+a(b)+b(a)+b(b)[/tex]

[tex]\left(a+b\right)^2=a^2+ab+ab+b^2[/tex]

[tex]\left(a+b\right)^2=a^2+2ab+b^2[/tex]

Therefore, the expanded form of the given expression is [tex]a^2+2ab+b^2[/tex].

the sum of 1+2-3-4+5+6-7-8+9+10-...+1378

Answers

Answer:

1389

Step-by-step explanation:

hope this helps?

1389 100% ok so pls give me points

Find the sine of ZF.
H
2/2
3/3
F
Write your answer in simplified, rationalized form. Do not round.
sin (F) =

Answers

Answer:

1/9 √57

Step-by-step explanation:

the length of HG = √(3√3² - 2√2²)

= √(27-8) = √19

sin L F = HG/GF = √19/ 3√3

= 1/9 √57

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What role does the law of supply and demand play in a command economy?.The law of supply and demand functions in reverse because a command economy is the opposite of a market economy.B. The law of supply and demand applies to a command economy as much as it does to other economies.C. The law of supply and demand does not apply because in a command economy, the government controls the market. D. The law of supply and demand functions the same way as in other economies, but the government sets the prices. A farmer tested the soil in a field and found that there was a high nitrate salt concentration. The farmer then grew a crop in this field. After the crop was removed, the soil was tested again. The nitrate salt concentration had decreased. In the sale, Mo buys a jacket for $63.The original price was reduced by 25%.Calculate the original price of the jacket. The distance between two points is 10 units, if the coordinates of one of the endpoints are (4, -7), find x if the coordinates of the other endpoint are (x, 1). an object that is 15 cm tall is placed 44 cm in front of a diverging lens. A virtual image appears -14cm in front of the lens. determine the focal length of the lens .SHOW YOUR WORK.A) 0.09cmB)-20.53cmC)10.6cmD)-0.04cm Then, use the information you have learned from the article and throughout the lesson to complete this charting activity. Three topics are provided; you can include up to two more of interest. Include informed opinion about how and whether the changes occurring in the South represented successes or failures in Reconstruction. Then, write an editorial evaluating progress (or lack thereof). Be sure your editorial is clear in its stance, and cite specific examples to support your opinion. Groundwater levels within an aquifer generally rise and fall due to the annual rain cycle, but prolonged periods of rainfall can causeflooding that can last for weeks. Groundwater flooding occurs when water levels in the ground rise above the land surface.Where does the type of flooding caused by groundwater levels most likely to occur?es )A)rural areasB)above an aquiferC)below an aquiferD)Daquifers never overfill A desk is on sale for $368 , which is 36% less than the regular price.What is the regular price? PLEASE SHOW EXACTLY HOW TO DO THIS Thesaying "Whoso is aman must be a nonconformist" is based on whose transcendentalist belief? ARalph Waldo EmersonB.Amos Bronson AlcottHenry David ThoreauMargaret Fuller ANSWER ASAP PLS!!!!!A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:f(n) = 10(1.02)nPart A: When the scientist concluded his study, the height of the plant was approximately 11.04 cm. What is a reasonable domain to plot the growth function? (4 points)Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)Part C: What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent? (4 points) Paulo comprou 60 mas e 24 laranjas. Ele pretende organizar essas frutas em embalagens plsticas. Em cada embalagem plstica ele colocar apenas um tipo de fruta e na maior quantidade possvel, para que todas as embalagens fiquem com a mesma quantidade de frutas. Qual a quantidade de embalagens plsticas que Paulo ir precisar para organizar essas frutas? 7. 12. 84. 120.