How can 2182 be written as the sum of four consecutive whole numbers?

Answer:

x = {2,3,4}    (if x can only be positive whole numbers)

Step-by-step explanation:

For a triangle exists, the side lengths of the triangle must be such that the sum of the two shorter sides must be greater than the third side.

This also is equivalent to any two sides must have a sum greater than the third side.

So

7+10 > x^2, => x^2 < 17 => x < sqrt(17)     (maximum)

7+x^2 > 10, => x^2 >3 => x > sqrt(3)

Therefore

sqrt(3) < x < sqrt(17)

If x must be an integer,

2< x < 4, or x = {2,3,4}

Answer:

The value of cos theta for 0° < theta < 90° will be 20 / 29

Step-by-step explanation:

To solve this problem we can express three trig functions as ratios involving the sides of a right-angle triangle,  the adjacent side, the opposite side and the hypotenuse. In this case sin θ = a / c, such that a = 21 and c = 29.

By Pythagorean Theorem,

[tex]b = \sqrt{c^2-a^2} = \sqrt{29^2-21^2} = \sqrt{841-441} = \sqrt{400} = 20[/tex]

Therefore cos θ = b / c = 20 / 29. This is the cosine ration of the adjacent side over the hypotenuse.

Answer:

10 meters

Step-by-step explanation:

From your question, it seems we are dealing with a triangle and we are given the two legs of the triangle.

The given dimensions are:

7 meters and 7 meters.

Required:

Here, we are required to find the third side of the triangle which is the hypotenus.

Using Pythagoras theorem:

a² + b² = c²

Where a = 7 & b = 7

Thus, we have:

7² + 7² = c²

c² = 49 + 49

c² = 98

Take the root of both sides

√c² = √98

c = √98

c = 9.899

c ≈ 10 meters

Therefore the length of the unknown side is approximately 10 meters

The relation { (3,4), (-3, 8), (6,8) } is a function.

====================================================

Explanation:

Choice A can be ruled out because we have x = -3 repeat itself for different y values. For any x input, there must be exactly one y output. This is assuming the x value is in the domain of course.

Choice C can be ruled out for similar reasoning. This time x = 3 repeats.

Choice D is the same story, but we go back to x = -3 showing up twice.

Choice B is the only thing left. Each x value is unique or only written one time. This graph passes the vertical line test. The other graphs fail the vertical line test (it is possible to draw a vertical line through more than one point).

Answer:

:)

Step-by-step explanation:

y=6x-3

y=-3

-3=6x-3

-3=6x-3

+3     +3

=6x

Answer:

Step-by-step explanation:

y=6x-3

y=-3

6x-3=-3

6x=-3+3

6x=0,

x=0

y=-3

so solution is point (0,-3)

Answer:

(2, 2), (5, 3), (9, 4), and (13, 5).

Step-by-step explanation:

The inverse of a function makes it so that the x-values become y-values, and y-values become x-values.

The current coordinates are (2, 2), (3, 5), (4, 9), and (5, 13).

If the function were inversed, the coordinates would be (2, 2), (5, 3), (9, 4), and (13, 5).

Hope this helps!

Answer:

33x-6x(square)-45

Step-by-step explanation:

(2x-5)(9-3x)

= 2x(9-3x) + -5(9-3x)

= 18x-6x(square) - 45+15x

= 33x-6x(square)-45

Answer:

8x^3 - 26x^2 + 17x - 5.

Step-by-step explanation:

(2x - 5)(4x^2 - 3x + 1)

= (2x * 4x^2) + (-5 * 4x^2) + (2x * -3x) + (-5 * -3x) + (2x * 1) + (-5 * 1)

= 8x^3 + (-20x^2) + (-6x^2) + 15x + 2x - 5

= 8x^3 - 26x^2 + 17x - 5.

Hope this helps!

Answer:

25

Step-by-step explanation:

Given that the ratio is 4 : 5 = 4x : 5x ( x is a multiplier ), then

4x - 2 : 5x = 2 : 3

Expressing the ratio in fractional form

[tex]\frac{4x-2}{5x}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

3(4x - 2) = 10x , distribute left side

12x - 6 = 10x ( subtract 10x from both sides )

2x - 6 = 0 ( add 6 to both sides )

2x = 6 ( divide both sides by 2 )

x = 3

Thus initially there were

4x + 5x = 9x = 9(3) = 27 pieces of fruit

2 apples were removed, leaving 25

Answer:

25

Step-by-step explanation:

4 : 5. is ratio before two apples were removed.

2 : 3. is ratio after two apples were removed.

combing the two statements will give you the following mathematical statement:

4x-2:5x=2:3 solve for x

3(4x-2)=5x*2

12x - 6=

2x=6

x=3

then 4x + 5x = total ñô fruit

4(3) + 5(3) = total ñô fruit

27= total ñô fruit

remaining fruit=total ñô fruit - 2

remaining fruit=27-2

remaining fruit=25

Answer:

Read this for more help!

Step-by-step explanation:

That is okay if you do not understand the formula. We all have troubles with math in one spot or in another. With the a²+b²=c², we would have to go really slowly. Just for you!

Let´s do an example. Say we have a triangle, and for this we need to know our square roots! Say we have this triangle, and it has both a 3 and a 4 on its sides. Now a triangle had 3 sides. 2 sides are smaller, and then it would have a larger side, which is called the hypotenuse! That is the side we would need to figure out, because the hypotenuse is the largest side of the triangle, and we only have the smaller sides(3 and 4).

So we need to work with the formula.

So let us plug the example into the formula.

There is no specific order to how we would be putting the sides in. 3 could be b or it could be a. Same goes for the 4. It really does not matter because you would be getting the same answer no matter what.

a²+b²=c²

3²+4²=c²  

3²=9

4²=16

We need to add the two of those numbers, both 9 and 16 and we get 25. That is c². But we need c, because the hypotenuse is only c. So we need to take the square root of 25. And we get 5!

I will show you the equation again with 3 and 4 reversed.

4²+3²=c²

4²=16

3²=9

Like what we did above, we would get 25. And then take the square root! Same answer, so it really doesn't matter!

If you still do not understand this topic, you can always ask someone else who does, or go on khan academy, or search for more topics like this on BRAINLY! I hope this helped!

31

because 15 +16 :31

[tex]. = y1 = \times [/tex]

Answer:

69

Step-by-step explanation:

A triangle has a 180 degree angle so you do 180-111=69

Answer: x=24

Step-by-step explanation:

lets say 94 is ∠ a

41 is ∠ b

___ ∠  c

111∠ d

x ∠ e

so with that you will figure out that ∠  c is to find X

108-94-41= 45

so ∠ c is 45

now you can ∠a ∠ b∠ c

with that yo take

108-111-45=24

So X=24

Answer:

Mean = 2.14

Standard deviation = 2.40

Step-by-step explanation:

The calculation of mean and standard deviation is shown below:-

[tex]X = .07\times0 + 0.20\times 1 + 0.38\times 2 + 0.22\times 3 + 0.13\times 4\\\\ = 0 + 0.2 + 0.76 + 0.66 + 0.52[/tex]

= 2.14

So, the mean is 2.14

Now, For computing the standard deviation first we need to find out the variance which is shown below:-

Variance is

[tex]Var(X) = P(X^2) - [P(X)]^2\\\\ P(X^2) = .07\times (0^2) + .20\times (0^1) + .38\times (0^2) + .22\times (0^3) +0.13\times (0^4)[/tex]

After solving the above equation we will get

= 5.78

Now, the standard deviation is [tex]= \sqrt{Variance}[/tex]

[tex]= \sqrt{5.78}[/tex]

= 2.404163056

or

= 2.40

Answer:

{-0.5, 0.1}

Step-by-step explanation:

[tex]x = \frac{8 \pm \sqrt{(-8)^2 - 4 \cdot -20 \cdot 1}}{-40} = \frac{8 \pm 12}{-40}[/tex]

so x is 20/-40 = -0.5 or x = -4/-40 = 0.1

Answer:

950.33 ft³

Step-by-step explanation:

The volume of a cylinder is denoted by: V = πr²h, where r is the radius and h is the height.

Here, the radius is r = 5.5 ft and the height is h = 10 ft. Plug these into the formula:

V = πr²h

V = π * 5.5² * 10 ≈ 950.33 ft³

The answer is thus 950.33 ft³.

~ an aesthetics lover

Answer:

1/5 or 20%

Step-by-step explanation:

This problem can be easily solved by finding the probability of her picking one matching pair to leave in the suitcase (which results in pulling out exactly two matching pairs)

For the first sock, it does not matter what sock she picks.

For the second sock, there is only 1 out of the 5 socks left that would match the first one picked. Therefore, the probability that she pulls out exactly two matching pairs is 1/5 or 20%

Answer:

Step-by-step explanation:

If you translate the triangle BCD in such a way that vertex B maps onto vertex W, you'll realize that with rotation, you'll map the whole BCD triangle onto triangle WXY.

On the other hand, reflections can't be used here, because the sides of both triangles are not in opposite positions.

Therefore, the right answer is the third choice.

Answer:

14

Step-by-step explanation:

7x2=14

Answer:

25 ( A)

pls mark me as BRAINLIEST

stay at home stay safe

and keep rocking

Answer:

A

Step-by-step explanation:

The first ten primes are

2,3,5,7,11,13,17,19,23,27

so the number is

2*3*5*7*11*13*17*23*27

so

2*11 is 22, so 22 divides the number

2*3 is 6, so 6 divides the number

2 is there so 2 divides the number

So the only one is 25.

Answer:

7

Step-by-step explanation:

Quadratic Equation: 3x² - 24x + 72

The form we are to convert the equation to:

3x² - 24x + 72

a(x + b)² + 72

3(x² - 8x + 24)

Step 1

Make the Quadratic equation (x² - 8x) in the bracket factorisable using completing the square method

3( x² - 8x +(- 8/2)²) + 24

3( x² - 8x + 16 = -24 + 16

3( x² - 8x + 16 + 8 = 0)

3( x² - 8x + 16) + 8

3( x² - 4x + 4x + 16) + 8

3( x(x - 4) -4(x - 4) + 8

3((x - 4)(x - 4) )+ 8

3( (x - 4)² + 8

Using this form

a(x + b)² + c

a = 3

b = -4

c = 8

We were asked to add up constants a, b, c

Therefore,

3 +(-4) + 8

= 7

Answer:

[tex] s = 5.8 [/tex]

Step-by-step Explanation:

Given:

∆RST,

m < T = 17°

t = RS = 5

m < S = 20°

s = RT = ?

Apply the Law of Sines to find s

[tex] \frac{s}{sin(S)} = \frac{t}{sin(T)} [/tex]

[tex] \frac{s}{sin(20)} = \frac{5}{sin(17)} [/tex]

Multiply both sides by sin(20) to make s the subject of formula.

[tex] \frac{s}{sin(20)}*sin(20) = \frac{5}{sin(17)}*sin(20) [/tex]

[tex] s = \frac{5*sin(20)}{sin(17)} [/tex]

[tex] s = 5.8 [/tex] (to nearest tenth)

Answer:

Step-by-step explanation:

Given that:

Sample size n = 11

Sample Mean X = 26500

standard deviation = 6000

Population mean [tex]\mu[/tex] = 31000

the null and alternate hypotheses are being stated as follows:

[tex]H_o : \mu = 31000[/tex]

[tex]H_1 : \mu \neq 31000[/tex]

The value of the test statistic can be computed as:

[tex]Z = \dfrac{\bar x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \dfrac{26500 - 31000}{\dfrac{6000}{\sqrt{11}}}[/tex]

[tex]Z = \dfrac{-4500}{\dfrac{6000}{3.3166}}[/tex]

Z = −2.4875

Z = −2.49

The degree of freedom df = n- 1

The degree of freedom df = 11 - 1

The degree of freedom df = 10

At the level of significance ∝ = 0.05

[tex]t_{\alpha/2}[/tex] = 0.025

From the t distribution table at [tex]t_{\alpha/2, 10}[/tex] and critical value = -2.49;

The p-value =  0.0320

Decision Rule: Reject null hypothesis if p -value is lesser than the level of significance

Conclusion:We reject the null hypothesis , therefore, we conclude that there is no sufficient information to that the mean tuition and fees for private colleges is different from $31,000

Answer:

Hey there!

That would be the SAS postulate.

This states that one angle is congruent and between two congruent sides.

Hope this helps :)

Answer:

-60.X + 32 = 32.r – 60

Because we only have one equation for 2 unknowns.

Step-by-step explanation:

All the equations have solution for r but the one that has 2 unknowns (r and X).

That is because we only have one equation and 2 unknowns.

Then, we only can express one unknown in function of the other and have an indeterminate solution.

Answer:

48

Step-by-step explanation:

FB:BS=2:1

[tex]\frac{FB}{BS} =\frac{2}{1} \\add~1~to~both~sides\\\frac{FB}{BS} +1=\frac{2}{1} +1=3\\\frac{FB+BS}{BS} =3\\\frac{FS}{BS} =3\\FS=3 \times~BS\\FS=3 \times~16=48[/tex]

Answer:

48

Step-by-step explanation:

Answer:

AQ = 20 units

Step-by-step explanation:

I tried figuring in the pic below..

Similar triangles are triangles whose corresponding measures are proportional. All of their corresponding angles are also congruent. There are theorems and postulates that prove triangle similarity. Usually they requrie at least three parts of each triangle. The symbol for similarity is ~.

We have two triangles in the figure. ΔAQR and ΔABC. We will prove first that they are similar.

Answer:

20

Step-by-step explanation:

RQ is 1/2 of CB, so 2(2p+3)=6p-4. This would make p=5. Then, 5*4=20.

(also it is right on edgenuity)

Answer:

  3.5 times as large

Step-by-step explanation:

The ratio can be written using a colon or a fraction bar. In the latter case, simplifying the fraction gives you your answer:

  a : b = 7 : 2 = 7/2

'a' is 7/2 = 3.5 times as large as 'b'

Answer:

xy = 32

x = 1/2y.

Step-by-step explanation:

Let's say the two numbers are x and y.

The product of them is 32, so x times y is 32.

xy = 32.

x is 1/2 of y. So...

x = 1/2y

Your two systems are xy = 32 and x = 1/2y.

Hope this helps!

Answer:

The answer is A on edg 2021

Answer:

∠A = 35°

Step-by-step explanation:

From the question above,

Sum of Angles on a straight line = 180°

180° = ∠BDE + ∠ADE

∠BDE = 105°

∠ADE = 180° - 105°

∠ADE = 75°

To find Angle ∠EBC and ∠DEB are alternate angles, this means that they are equal to each other

Hence, ∠EBC = ∠DEB

30° = 30°

Sum of Angles on a straight line = 180°

180° = ∠DEB + ∠BEC + ∠DEA

180° = 30° + 80° + ∠DEA

∠DEA = 180° -(30+ 80)°

∠DEA = 180° - 110°

∠DEA = 70°

It is important to note that the sum of Angles in a triangle = 180°

180° = ∠ADE + ∠DEA + ∠A

∠ADE = 75°

∠DEA = 70°

180° = 75° + 70° + ∠A

∠A = 180° - (75° + 70°)

∠A = 180° - 145°

∠A = 35°

Answer:

a   4/17

Step-by-step explanation:

if you add them all up, you get 34. 8 out of 34 reduced is 4/17

Answer:

4/17

Step-by-step explanation:

8 black marbles, 12 clear marbles, and 14 blue marbles = 34 marbles

P( black) = number of black/ total

              = 8/34

              =4/17

Answer: im having the same problem

Step-by-step explanation: