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This is because we have two pairs of congruent sides (AB = CD and AC = CA) with a pair of congruent angles between them. Those angles are the alternate interior angles BAC and DCA

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Similar to reason 2, but the converse means we go in reverse more or less. The original theorem states that if we have parallel lines, then the alternate interior angles are congruent. This time we know the alternate interior angles are congruent, so we conclude the lines are parallel.

Answer:

see below

Step-by-step explanation:

Reason 4 is SAS  AB = CD, BAC = DCA  and AC = CA so we have Two sides and the included angle

Reason 6 is if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

Answer:

triangle pythagora

Step-by-step explanation:

the pythagora is made by someone special names albert and you ahve to amke three sides a b and c

This question is incomplete, here is the complete question:

Suppose in the next year, 2007, College D's expenses and enrollment remain about the same, but in addition to their current revenues, they receive an additional $50,000,000 grant. This would allow them to reduce average tuition by how much?

A) $1388.89

B) $3571.43

C) $5555.56

D) $9500.00

E) $25888.89

number of students = 36,000

Answer: A) $

1388.89

Step-by-step explanation:

the college received additional grant which is $50,000,000

and the number of students is 36,000,

and we also know that expenses and enrollment remained the same.

So if we have more money (grants) and nothing changed (expenses remain the same)

dividing the grant by the number of students will show just how much the average tuition fee would be reduced

therefore R = G/n

R = 50,000,000 / 36000

R = 1,388.888 ≈  $1388.89

Answer:

1057

Step-by-step explanation:

tower is 60 feet high.

angle of 3.25 degrees.

3.25/360 * 2 * pi * r = the arc length of this angle.

that would be equal to 0.0567232007* r

if we assume the arc length and the height of the tower are approximately equal, then 0.0567232007 * r = 60

solving for r, we get r = 60/0.0567232007 = 1057.768237 feet.

that's about how far the tower is from the observer.

since the arc length is going to be a little longer than the length of the chord formed by the flagpole, this means that the distance of 1057.768237 meters is going to be a little less than the actual distance.

Answer:

≈ 1058 ft

Step-by-step explanation:

Use of arc formula: s=rθ

Given:

r= s/θ= 60/0.0567 ≈ 1058 ft

Answer:

Assuming that the null hypothesis is true and that the new cancer drug shrinks tumors by the same amount as the gold-standard drug, the probability that the test will lead the researcher to this decision = 95%

Step-by-step explanation:

The nulll hypothesis is correct and we are not rejecting it, which means we are making the correct decision.

P(not rejecting the null | null hypothesis is true)

= 1 - P(rejecting null hypothesis | null hypothesis is true)

= 1 - P(type I error)

P(type I error) = significance level of the test = 0.05

P(not rejecting the null | null hypothesis is true)

= 1 - 0.05

= 0.95

= 95%

Hope this Helps!!!

Answer: C. y ≤ 2/3x + 1/5

Step-by-step explanation: From 1/5 on the y coordinate plane go up 2 and right 3 and it perfectly matches, so it would be C. 100% on Edge2020.

Answer:

C

Step-by-step explanation:

just did the test.

Answer:

cot(A-B) = 3/19

Step-by-step explanation:

The formula for cot(A-B) = (Cot A Cot B + 1 ) / (Cot B - Cot A)

we know that cot A = 1/ Tan A

Given

tan A=2/3

therefore cot A = 1/ tan A = 1/2/3 = 3/2

tan B= -3/5  

cot B = 1/ tan B = 1/-3/5 = -5/3

Thus,

(Cot A Cot B + 1 ) = (3/2)*(-5/3 )+ 1 = -5/2 +1 = (-5+2)/2 = -3/2

(Cot B - Cot A) = -5/3 -3/2 = (-5*2) + (-3*3) / 2 = -10 -9/2 = -19/2

Thus,

cot(A-B) = (Cot A Cot B + 1 ) / (Cot B - Cot A) = -3/2  / -19/2 = 3/19

Thus,

cot(A-B) = 3/19

Answer:

C.  (x - 9)(x^2 + 9x + 81).

Step-by-step explanation:

The cube identities are

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Checking against the list the one that fits is the difference formula:

x^2 - 9^2 = (x - 9)(x^2 + 9x + 81).

a=1, b = 9, ab = 1 *9 = 9.

Answer:

B

Step-by-step explanation:

the hotpotuse is always the biggest

the rest is pretty easy to determine

The orders that the sides of the triangle ABC from longest to shortest length will be AB, BC, and AC.

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry. A right-angled triangle is a triangle having one of its angles with a measure of 90°. The slanted side of that triangle is called Hypotenuse and it is the longest side in that triangle.

If one of the angle is of 90°  then the triangle is right angled triangle.

We can see that the Hypotenuse is always the biggest side among all the sides.

Then the perpendicular side BC is the second biggest and then the base of the triangle.

Therefore, the order must be AB > BC > AC.

The orders that the sides of the triangle ABC from longest to shortest length will be AB, BC, and AC.

Learn  more about  right angled triangle here:

https://brainly.com/question/27190025

#SPJ5

Answer:

-3x-11

Step-by-step explanation:

First deduct 7x from 4x   4x-7x=-3x

Next  proceed the expression -8-3=-11

So the result is -3x-11

Answer:

Tan<C=2.4

Step-by-step explanation:

Opp=36

Adj=15

Tan<C=opp/adj

Tan<C=36/15

Tan<C=2.4

Hope this helps :) ❤

They got 5 yards on 3 plays. For total yards multiply the 3 plays by 5 yards. The first play was negative, so add the negative value.  The answer is A.

Answer:

A

Step-by-step explanation:

Answer:

Check the answers to the questions below

Step-by-step explanation:

a) If [tex]\mu_1[/tex] is the average learning rate of the 6th graders without background noise level and [tex]\mu_2[/tex] is the average learning rate of the 6th graders with background noise level

The Null Hypothesis is that the learning rate of the 6th graders is not affected by the background noise level.

Null hypothesis, [tex]H_0: \mu_1 = \mu_2[/tex]

b) The Alternative Hypothesis is that the learning rate of the 6th graders is affected by the background noise level.

Alternative hypothesis, [tex]H_a: \mu_1 \neq \mu_2[/tex]

c) Assumptions that must be met about the data before she can correctly use independent t-test

There must be random selection of the 6th graders

That the two groups are normally similar in their learning abilities

The division of students into the two groups should be at random

d) She has to  make these assumptions to prevent bias and inaccuracy of results. If these assumptions are not made, the outcome of the experiment may not reflect the true effect of background noise on the learning of the 6th graders.

She can still get accurate results if she include some bias in the selection to prove a particular result.

Answer:

50% chance.

Step-by-step explanation:

There are 3 numbers that are either greater than 4 or less than 2. They are 1, 5, and 6. There is a 3/6 chance you roll one of them or 50% chance.

Hey there! :)

Answer:

P(greater than or less than 2) = 50%.

Step-by-step explanation:

Numbers greater than 4: 5, 6

Numbers less than 2: 1

Total of 3 numbers that fit the criteria. Therefore:

P(greater than 4 or less than 2) = # of numbers / total

P(greater than 4 or less than 2) = 3 / 6 = 1 / 2

Convert fraction to percent:

1/2 × 100 = 50%

Step-by-step explanation:

|S450(2)

(3)

(4)1m3+1AB is a vertical pole with B at the ground level

and A at the top. A man finds that the angle of

elevation of the point A from a certain point C600.He moves away from the pole along the lineCD- 7m

.From D the angle of elevation of the point Aon the ground isBC to a point D such that.Then the height of the pole is (1)7/3

7/3

7/3

7/3V33+1m

i hope this help

Answer:

5676039

Step-by-step explanation:

-14² + 5675843

Solve for exponent.

196 + 56758

Add the numbers.

= 5676039

[tex]50/20=20/x\implies50x=400\implies\boxed{x=8\mathrm{ft}}[/tex]

Hope this helps.

The length of the shadow cast by the flag pole is 6.4 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that;

Height of building= 50 foot

Shadow= 20foot

Now,

Let x be the length of the shadow cast by the flag pole. Then we have:

2050​=x20​

Cross-multiplying, we get:

50x=20×20

Dividing both sides by 50, we get:

x=5020×20​

Simplifying, we get:

x=58​×4

Multiplying, we get:

x=6.4

Therefore, by the proportion the answer will be 6.4 feet.

More can be learned about proportions at;

brainly.com/question/24372153

#SPJ2

Answer:

Step-by-step explanation:

hello,

I assume that you want to develop the expression

[tex](7x-3)(4x^2-3x-6)=7x(4x^2-3x-6)-3(4x^2-3x-6)\\= 28x^3-21x^2-42x-12x^2+9x+18\\\\=28x^3-33x^2-33x+18[/tex]

hope this helps

Answer:  A) 0.5

Step-by-step explanation:

The denominator should be in the form 1 + e sin θ

Currently the denominator is: 2 + 1 sin θ

Divide the denominator by 2 to get:  1 + 0.5 sin θ

Thus, e = 0.5

Answer:

Selected option is correct

Step-by-step explanation:

Triangle BDE and BAC are similar because of the two pairs of equal angles (AA)

1. angle B

2. angle BDE = angle BAC

Answer:

5

Step-by-step explanation:

[tex]\frac{6}{7}=0.857142857142857142857142...[/tex]

Or 0.857142 with "857142" recurring.

The hundredths place is the second decimal place of a number. In this case, it would be 5.

Answer:

The answer is option 3.

Step-by-step explanation:

In order to solve the equation, you have to add 0.2 to both sides to eliminate -0.2 on the left side and make x the subject :

[tex]4x - 0.2 = 1.9[/tex]

[tex]4x - 0.2 + 0.2 = 1.9 + 0.2[/tex]

[tex]4x = 2.1[/tex]

Answer:

Add 0.2 to both sides of the equation

Step-by-step explanation:

4x-0.2=1.9

+0.2   +  0.2

4x=2.1

:4     :4

x=2.1/4

Answer:

£1.53 per litre

Step-by-step explanation:

original = 1.02

if it is increased by 2/3 then we do 1.02 / (2/3) =£1.53 per litre

Answer:

Option (4)

Step-by-step explanation:

Surface area of a prism = 2B + P×h

where B = Area of the triangular base

P = perimeter of the triangular base

h = height of the prism

B = [tex]\frac{1}{2}(\text{leg 1})(\text{leg 2})[/tex]

Since, (Hypotenuse)² + (Leg 1)² + (Leg 2)² [Pythagoras theorem]

(20)² = (12)² + (Leg 2)²

Leg 2 = [tex]\sqrt{400-144}[/tex]

          = 16 units

Therefore, B = [tex]\frac{1}{2}\times 12\times 16[/tex]

                     = 96 units²

P = 12 + 16 + 20

P = 48 units

h = 7.5 units

Surface area of the prism = 2(96) + (48×7.5)

                                           = 192 + 360

                                           = 552 units²

Therefore, surface area of the given triangular prism = 552 units²

Option (4) will be the answer.

Answer:

Step-by-step explanation:

Since 15 liters of water flow through a water pipe and enter a tank within 4.5 minutes, the same amount of water would flow through a similar pipe at the same time. Therefore, if two similar water pipes are used, the volume of water that would flow into the tank in 4.5 minutes is 15 × 2 = 30 liters

Therefore, the time it will take to pump 727.5 liters of water into a water tank using 2 similar water pipes is

(727.5 × 4.5)/30 = 109.125 minutes

Answer:

All angles in any quadrilateral adds up to 360°

Step-by-step explanation:

We can prove this by using 180(n - 2)

n = 4 for a quadrilateral

180(4 - 2)

180(2)

360°

So, 360 - (125 + 67 + 80) = 88°

Answer:

See below

Step-by-step explanation:

The interior angles of a quadrilateral (having 4 sides) add up to 360 degrees.

=> So, to find x, we'll simply subtract the rest if the angles from 360

So,

=> x = 360-125-67-80

=> x = 88 degrees

Answer: 1620

Step-by-step explanation:

Answer:

1,620 words

Step-by-step explanation:

If you know that she can text message about 54 wpm and that she types at this rate of 30 minutes, you would simply multiply 54 by 30.

Hope that helps!

Don't forget to rate and thanks!

Answer:

the minimum sample size n = 11.03

Step-by-step explanation:

Given that:

approximate value of the population standard deviation [tex]\sigma[/tex] = 49

level of significance ∝ = 0.01

population mean = 38

the minimum sample size n = ?

The minimum sample size required can be determined by calculating the margin of error which can be re[resented by the equation ;

Margin of error = [tex]Z_{ \alpha /2}} \times \dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]38 = \dfrac{2.576 \times 49}{\sqrt{n}}[/tex]

[tex]\sqrt{n} = \dfrac{2.576 \times 49}{38}[/tex]

[tex]\sqrt{n} = \dfrac{126.224}{38}[/tex]

[tex]\sqrt{n} = 3.321684211[/tex]

[tex]n= (3.321684211)^2[/tex]

n ≅ 11.03

Thus; the minimum sample size n = 11.03

Answer: x=48°

Step-by-step explanation:

The 3 angles of the triangle add up to 180°. We can set the angles to 180 and solve.

47+85+x=180               [combine like terms]

132+x=180                    [subtract both sides by 132]

x=48

Answer:

x=48

Step-by-step explanation:

Total sum of angles in a triangle =180

47+85+x=180

132+x=180

x=180-132

x=48