Select the correct answer.
Given: ΔABC
Prove: The sum of the interior angle measures of ΔABC is 180°.

Answer:

x + 5y = 237

5x + 5y = 465

Step-by-step explanation:

Let

x = length of cardio class

y = length of weightlifting class

x + 5y = 237 (1)

5x + 5y = 465 (2)

Using elimination method

Subtract (1) from (2) to eliminate y

5x - x = 465 - 237

4x = 228

x = 228/4

x = 57 minutes

Substitute x = 57 into (1)

x + 5y = 237 (1)

57 + 5y = 237

5y = 237 - 57

5y = 180

y = 180/5

y = 36 minutes

x = length of cardio class = 57 minutes

y = length of weightlifting class = 36 minutes

Answer:6

Step-by-step explanation:

Answer:

16/25

Step-by-step explanation:

To find the probability that she gets both questions right, multiply the probabilities together:

4/5 x 4/5

= 16/25

So, the probability that she answers both correctly is 16/25

Answer:

x = 2

Step-by-step explanation:

[tex]y = {x}^{2} - 4x + 7 \\ y = (x - 2) {}^{2} - 4 + 7 \\ y = {(x - 2)}^{2} + 3[/tex]

Therefore, axis of symmetry is x = 2

The solution is: x=2, is the axis of symmetry for the function f(x)=7−4x+x2.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

Here, we have,

f(x)=7−4x+x^2

Rewriting as

f(x)  = x^2 -4x+7

a =1  b -4  c=7

The axis of symmetry is:

h = -b/2a

 = -(-4)/ 2(1)

 = 4/2(1)

 = 4/2  

 =a

The axis of symmetry is x=2.

Hence, The solution is: x=2, is the axis of symmetry for the function f(x)=7−4x+x2.

To learn more on function click:

brainly.com/question/21145944

#SPJ7

Answer:

2y -6

Step-by-step explanation:

5y-3(y + 2)

Distribute

5y -3y - 6

Combine like terms

2y -6

Answer:

73.0m

Step-by-step explanation:

see the attachment. Hope it helps.

Step-by-step explanation:

....

I Dont Known........

Answer:

16 full cases

Step-by-step explanation:

4 quarts to a gallon

50 gallons is 200 quarts (50 x 4)

200 quarts / 12 quarts per case = 16.66667 (.66667 isn't a full case)

so, it's 16

Answer:

(3x-2)^2+8= 9x^2-12x+12

Answer:

Kindly check explanation

Step-by-step explanation:

If the null is rejected, then we conclude that the average Consumption of beer and cider by customers who are 21 years and above is greater than 26.1

A type 1 error is committed if the null hypothesis is incorrectly rejected ; this means we will be concluding that customers who are 21 years and older have higher average Consumption when they actually do not. This may lead to a restriction on beer consumption in the city when there actually isn't a need for it.

For type 2 error, a false null is incorrectly accepted, in this scenario, we are saying that the consumption of beer and cider is not beyond the mean value when in actual sense it is.

Answer:

A: y < -2x - 1

Step-by-step explanation:

First, to figure out which part of the graph to be looking at, you will look at the shaded region as the solution area.

So, the solution area is to the left of the line. Said line is a dotted line which means that the points on the line can not be a solution.

If the points on the line can not be a solution then it eliminates answer choices C and D because y can not equal the other side of the inequality.

Now, we will bring the shaded region back into focus to find out if y is greater than or less than the other side. The shaded area is "below" the line so it is less than -2x - 1.

To ensure this is correct, plug two points into the inequality we just chose, one from the shaded region and one not, just to make sure the answer is correct.

I picked (-3,4) to test. So plug them into the inequality to get:

4 < -2 (-3) - 1

So 4 < 6 - 1 which is correct.

Then from the other side of the line I picked (5,2)

2 < -2 (5) - 1

2 < -10 - 1

2 < -11 is not true so the inequality that we found was correct.

Answer:

$3.50

Step-by-step explanation:

Given:

$10 for a 6, $7 for a 5, $4 for a 4, and no payoff otherwise

P(6) = 1/6 ; p(5) = 1/6 ; p(4) = 1/6 ; p(1,2or3) = 3/6 = 1/2

P(x) ____ 1/6 _____ 1/6 _____1/6 _____1/2

x______ 10 _______ 7 _____ 4 _______ 0

Expectwd value ; E(x)

Σx*p(x) = (1/6 * 10) + (1/6 * 7) + (1/6 * 4) + (1/2 * 0)

E(x) = 3.50

Answer:

x = 2.8

Step-by-step explanation:

sin = opp/hyp

hyp = opp/sin

x = 2.4/sin60

x = 2.771281292110204

rounded

x = 2.8

Answer:

y=2x+14

Step-by-step explanation:

y=2x+2.3+8=2x+14

Answer:

m<4 = 52°

m<BFD = 98°

Step-by-step explanation:

m<1 = (3x)°

m<2 = (5x - 7)°

m<3 = (4x + 15)°

m<AFD = 128°

✔️Find m<4:

m<4 = 180° - m<AFD (angles on a straight line)

Substitute

m<4 = 180° - 128°

m<4 = 52°

✔️m<BFD = m<2 + m<3

Substitute

m<BFD = (5x - 7)° + (4x + 15)°

We need to find the value of x.

Create an equation to find x.

m<1 + m<2 + m<3 = m<AFD (angle addition postulate)

Substitute

3x + 5x - 7 + 4x + 15 = 128°

Add like terms and solve for x

12x + 8 = 128

12x + 8 - 8 = 128 - 8

12x = 120

12x/12 = 120/12

x = 10

m<BFD = (5x - 7)° + (4x + 15)°

Plug in the value of x

m<BFD = 5(10) - 7 + 4(10) + 15

m<BFD = 50 - 7 + 40 + 15

m<BFD = 98°

Answer:

Not a 70%, but a 72.5% (or a 73%)

Step-by-step explanation:

Assuming that the 65% is the first grade and the 80% is your second, adding both numbers and dividing by 2 will get you 72.5%.

The best possible grade you can get from that 65% is an 82.5%, or 83% if you round the grade up. 100+65=165÷2 will get you 82.5.

Answer:

I'd use A = πr^2

The area is 28.3 if we're using 3.14 as pi (rounded to the nearest tenth)

Step-by-step explanation:

Z 00m

336"083"2553

(wZE2XQ) are

please edit your question man

Answer:

x = 43.7°

Step-by-step explanation:

Reference angle (θ) = x°

Opposite side length = 43

Adjacent side length = 45

Apply the trigonometric function, TOA, which is:

Tan θ = Opp/Adj

Substitute

[tex] Tan(x) = \frac{43}{45} [/tex]

[tex] x = Tan^{-1}(\frac{43}{45}) [/tex]

x = 43.7° (nearesth tenth)

Answer:

300 computers

Step-by-step explanation:

So I divided 1500 out of a 100 and got 15, then I multiply 15 to 20 and got 300.

(I am a high schooler so I hope this is 3rd grade math because I notice you are a college student and I hope this not some college tricky math, if you get this wrong I am truly sorry)

Answer:

x=6

Step-by-step explanation:

Answer:

∠2=92°

Step-by-step explanation:

Using an angle formula, -8x+144=2x+74

Simplification:

-8x+144=2x+74

-8x+70=2x

70=10x

x=7

Therefore, each angle is 88°

Now, because ∠2 is adjacent to one of 88°, they add up to 180°

Therefore,

180°=88°+∠2

∠2=92°

Answer:

Step-by-step explanation:

First of all, I'm having a bit of trouble seeing what the exponent on the leading term in the distance is, but I think its an x-squared so that's what I used to solve this. Keep in mind that you do NOT get a number answer here; you get another expression in terms of x for an "answer".

Let's simplify down the rate first by multiplying. What I did was put the denominator under each of the terms in the numerator and then simplified by dividing each term:

[tex]r=\frac{2x^2}{2x}-\frac{5x}{2x}-\frac{3}{2x}[/tex] which simplifies to

[tex]r=x-2.5-\frac{3}{2x}[/tex] Now let's get rid of that denominator there by multiplying everything by 2x to get

[tex]r=2x^2-5x-3[/tex] and we're ready to solve for time.

If d = rt, then

[tex]t=\frac{d}{r}[/tex] so filling in:

[tex]t=\frac{6x^2+3x}{2x^2-5x-3}[/tex] and we can divide this using the method of long division. It would be impossible to show you how to do that here in this forum, but when you divide, you get

[tex]t=3+\frac{18x+9}{2x^2-5x-3}[/tex] ...as crazy as that seems.

Answer:

Step-by-step explanation:

Add all the socks in the drawer to get a denominator

12

blue socks can be picked out of the

36

total socks, so

12

36

Then you take away one sock from the top and bottom, so you now have

11

35

Multiply the two numerators (

12

and

11

), then multiply the denominators (

36

and

35

), then divide the numerator by the denominator,

132

1260

, to get your answer.

Answer:

6/10

Step-by-step explanation:

1st step: 4+6=10

9514 1404 393

Answer:

  6

Step-by-step explanation:

Any of the three can be in first place.

Any of the remaining two can be in 2nd place.

The remaining swimmer will be in 3rd place.

There are 3 × 2 × 1 = 6 possible orderings of the swimmers.

Answer:

a. 97.72% of the observations are less than 33

b. Approximately 977 observations are less than 33.

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.

Mean of 25 and a standard deviation of 4.

This means that [tex]\mu = 25, \sigma = 4[/tex]

a. Approximately what percentage of the observations are less than 33?

The proportion is the p-value of Z when X = 33. So

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

[tex]Z = \frac{33 - 25}{4}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772

0.9772*100% = 97.72%

97.72% of the observations are less than 33.

b. Approximately how many observations are less than 33?

Out of 1000:

0.9772*1000 = 977.2

Approximately 977 observations are less than 33.