Identifying relationships from diagrams

Answer:

Step-by-step explanation:

Hello,

First of all, we know that the solution of the following equation

   [tex]ax^2+bx+c=0[/tex]

are

   [tex]\dfrac{-b\pm\sqrt{b^2-4ac}}{2a} \ \text{ when } \Delta=b^2-4ac \geq 0[/tex]

I would suggest that you try to apply this formula first and check the solution only after you try.

Let's apply it in this case, we have:

[tex]a=4\sqrt{5} \\ \\ b=-24 \\ \\ c= -9\sqrt{5}[/tex]

[tex]\Delta=b^2-4ac=24^2+4*9*5=1296 \\ \\ \sqrt{\Delta}=36 \ \text{ and the solutions are } \\ \\ \\ x_1=\dfrac{24-36}{8\sqrt{5}}=\dfrac{-12}{8\sqrt{5}}=\boxed{\dfrac{-3}{2\sqrt{5}}} \\ \\x_2=\dfrac{24+36}{8\sqrt{5}}=\dfrac{60}{8\sqrt{5}}=\boxed{\dfrac{15}{2\sqrt{5}}}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

8(6-x)

Step-by-step explanation:

Both 48 and 8 can be divisible by 8.

48 ÷ 8 = 6

8 ÷ 8 = 1

Therefore you get the answer 8(6-x)

as the simplest form.

Hope this helps.

Answer:

A

Step-by-step explanation:

We know that because the second plane flies 15 miles less, it has to be either A or B, because they have -15 at the end.

It cannot be B, because in B, the second plane has a -w in the equation. However, in the word problem, the second plane flies with the wind, not against it. Therefore, it must be A.

Answer: 3 x minus 3 + 4 = 2 minus x minus 3

              3 x + 1 = negative x minus 1

Step-by-step explanation:

             A and D. Edge 2020

The required equation that Samuel used is 3x -3 + 4 =2- x -3. option A is correct.

Samuel is solving the equation 3 (x minus 1) + 4 = 2 minus (x + 3). Which equivalent equations might Samuel use, is to be determined.

The equation is the relationship between variables and represented as[tex]y = ax +b[/tex]  is an example of a polynomial equation.

Given equation is [tex]3(x-1) +4 =2 -(x+3)[/tex]
Simplification of the above equation,
opening the parenthesis on both sides
step 1⇒ 3x - 3 + 4 = 2 - x - 3
step 2⇒ 3x + 1 = -x - 1
Transposition of -x to the left side and +1 to the right side
step 4 ⇒ 3x +x = -1 -1
                  4x = -2
Transposition of 4 to the denominator of -2.
step 5⇒ x = -2/4
               x = -1/2

Thus , Step 1 3x -3 + 4 =2- x -3 is the equivalent equation used by the samuel.

Learn more about the equation here:

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Answer:

iii) 5.7

iv) 27.85

vii) 0.609

viii) 40.0709

Step-by-step explanation:

hope this helps

The 210 angles in the standard position are shown in figure (A) option (A) is correct.

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

It is given that:

The measure of the angle:

= 210 degrees

The reference angle can be defined as the angle formed between the terminal side and the x-axis, known as the reference angle.

The angle between the x-axis and the y-axis is 90 degrees.

The angle between the y-axis and the negative x-axis is 90 degrees.

The angle between the negative x-axis and the arrow shown in the coordinate plane is 30 degrees.

Thus, the 210 angles in the standard position shown in figure (A) option (A) is correct.

Learn more about the angle here:

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Answer:

14

Step-by-step explanation:

7x2=14

Complete question :

WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in:

a. More than 20 minutes? b. For 20 minutes or less

Answer: 0.0764 ; 0.9236

Step-by-step explanation:

Mean (m) = 15 minutes

Standard deviation (sd) = 3.5

Z - score :

Z = (x - m) / sd

A) more than 20 minutes

P(X > 20) ; x = 20

Z > (20 - 15) / 3.5 = 5/3.5 = 1.429

P(z > 1.429) = 0.5 - P(0<z<1.43)

Using the z-table: 1.43 = 0.4236

0.5 - 0.4236 = 0.0764

2) 20 minutes or less :

P(X <= 20) ; x = 20

Z < (20 - 15) / 3.5 = 5/3.5 = 1.429

P(z < 1.429) = 0.5 + P(0<z<1.43)

Using the z-table: 1.43 = 0.4236

0.5 + 0.4236 = 0.9236

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:

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:

hello:

Step-by-step explanation:

If f(x) = -8x - 6 and g(x) = x+8 ,  (f • g) (- 7)= f(g(-7))

but g(-7)=-7+8=1

(f • g) (- 7)= f(1) =-8(1)-6 =-14

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:

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:

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:

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:

the numbers of cars pf various colors in a parking lot

Answer:  The speed of a car as it changes during a time.

B is the best example of continuous data.

Step-by-step explanation:  The contrast between the definitions of continuous data  vs. discreet data is that discrete data is counted, continuous data is measured.

A speedometer measures speed continuously, time is measured continuously.

Time can, however, be reported as discreet measurements in situations where that kind of data is needed. (not in this question)

A Number of cars is discreet.

Data from different workers or different days is not continuous.

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:

∠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:

  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'

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:

let the parabola be y=a(x+5)²+0

or y=a(x+5)²

∵ it passes through (-3,1)

1=a(-3+5)²

4a=1

a=1/4

so parabola is y=1/4(x+5)²

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:

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:

The cost C, of hosting the banquet with the services of Caterer One is;

C = $ 45·n

The cost C, of hosting the banquet with the services of Caterer Two is;

C = $250 +  $ 28·n

The cost C, of hosting the banquet with the services of Caterer Three is;

C = $500 +  $ 20·n

Step-by-step explanation:

The information includes;

The amount available to the group for the banquet = $120

The number of people attending the banquet = n

The cost incurred in hosting the banquet = C

The major costs in hosting the banquet are hall rental and caterer

The cost per caterer are as follows;

Caterer One

The cost per person including the hall = $45

Therefore, the cost incurred, C, in hosting the banquet using caterer one is equal;

C = n × $45 = $ 45·n

Caterer Two

The hall rental = $250

The cost per person = $28

Therefore, the cost incurred, C, in hosting the banquet using caterer two is equal;

C = $250 +  n × $28 = $250 +  $ 28·n

Caterer Three

The hall rental = $500

The cost per person = $20

Therefore, the cost incurred, C, in hosting the banquet using caterer three is equal;

C = $500 +  n × $20 = $500 +  $ 20·n.

Answer:

The cost C, of hosting the banquet with the services of Caterer One is;

C = $ 45·n

The cost C, of hosting the banquet with the services of Caterer Two is;

C = $250 +  $ 28·n

The cost C, of hosting the banquet with the services of Caterer Three is;

C = $500 +  $ 20·n

Step-by-step explanation:

The information includes;

The amount available to the group for the banquet = $120

The number of people attending the banquet = n

The cost incurred in hosting the banquet = C

The major costs in hosting the banquet are hall rental and caterer

The cost per caterer are as follows;

Caterer One

The cost per person including the hall = $45

Therefore, the cost incurred, C, in hosting the banquet using caterer one is equal;

C = n × $45 = $ 45·n

Caterer Two

The hall rental = $250

The cost per person = $28

Therefore, the cost incurred, C, in hosting the banquet using caterer two is equal;

C = $250 +  n × $28 = $250 +  $ 28·n

Caterer Three

The hall rental = $500

The cost per person = $20

Therefore, the cost incurred, C, in hosting the banquet using caterer three is equal;

C = $500 +  n × $20 = $500 +  $ 20·n.

Answer:

5

Step-by-step explanation:

(0.000064)^5/6 divided by (0.00032)^6/5

(0.00032)^6/5=(0.000064)

and

(0.000064)^6/5=(0.00032)

so now we have (0.00032) divided by (0.000064)

which is 5!

hope this helps!

Answer: yes

Step-by-step explanation: no

Answer:

[tex]\boxed{\sf y=6}[/tex]

Step-by-step explanation:

There are 5 identical squares.

The area of one square is [tex]\sf s^2[/tex].

[tex]\sf{y^2 } \times \sf{5}[/tex]

[tex]\sf 5y^2[/tex]

The area of the whole shape is 180 cm².

[tex]\sf 5y^2=180[/tex]

Solve for y.

Divide both sides by 5.

[tex]\sf y^2=36[/tex]

Take the square root on both sides.

[tex]\sf y=6[/tex]

Answer:

25 ( A)

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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:

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!

I hope this helps you

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!