A right triangle ABC is shown below:
The are of the triangle above will equal one-half of a rectangle that is 5 units long and __ units wide. (Input only whole numbers, such as 8) (1 point)

Answer:

ASA

Step-by-step explanation:

..................

To prove ABC = ADC, We use ASA triangle postulate.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

The similarity of triangles on the other hand is when the corresponding angles are equal but the corresponding sides are not equal but they have the same common ratio.

From the given diagram a quadrilateral ABCD is given,

Line segment AC divides quadrilateral ABCD into two triangles namely

ABC and ADC, and both have a common side AC.

m∠BAC ≅ m∠DAC and m∠BCA ≅ m∠DAC.

Therefore, Triangle ABC and ADC are congruent by ASA, with two angles and a side included between them.

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Answer:

The upper 20% of the weighs are weights of at least X, which is [tex]X = 0.84\sigma + \mu[/tex], in which [tex]\sigma[/tex] is the standard deviation of all weights and [tex]\mu[/tex] is the mean.

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.

Upper 20% of weights:

The upper 20% of the weighs are weighs of at least X, which is found when Z has a p-value of 0.8. So X when Z = 0.84. Then

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

[tex]0.84 = \frac{X - \mu}{\sigma}[/tex]

[tex]X = 0.84\sigma + \mu[/tex]

The upper 20% of the weighs are weights of at least X, which is [tex]X = 0.84\sigma + \mu[/tex], in which [tex]\sigma[/tex] is the standard deviation of all weights and [tex]\mu[/tex] is the mean.

Answer:

See Below.

Step-by-step explanation:

We want to verify the identity:

[tex]\displaystyle \frac{\sin x}{1 - \cos x} - \cot x = \csc x[/tex]

We can multiply the fraction by 1 + cos(x):

[tex]\displaystyle \frac{\sin x(1+\cos x)}{(1 - \cos x)(1+\cos x)} - \cot x = \csc x[/tex]

Difference of Two Squares:

[tex]\displaystyle \frac{\sin x(1+\cos x)}{1-\cos^2 x} - \cot x = \csc x[/tex]

From the Pythagorean Theorem, we know that sin²(x) + cos²(x) = 1. Rearranging, we acquire that sin²(x) = 1 - cos²(x). Substitute:

[tex]\displaystyle \frac{\sin x(1+\cos x)}{\sin^2 x} - \cot x = \csc x[/tex]

Cancel:

[tex]\displaystyle \frac{ 1 + \cos x}{\sin x}-\cot x = \csc x[/tex]

Let cot(x) = cos(x) / sin(x):

[tex]\displaystyle \frac{ 1 + \cos x}{\sin x}-\frac{\cos x}{\sin x} = \csc x[/tex]

Combine Fractions:

[tex]\displaystyle \frac{ 1 + \cos x - \cos x}{\sin x}= \csc x[/tex]

Thus:

[tex]\displaystyle \frac{1}{\sin x}=\csc x = \csc x[/tex]

Hence proven.

Answer:

3

Step-by-step explanation:

25 divided by 5 is 5

therefor 15 divided by 5  is 3

15/25 = 3/5

Answer:

3

Step-by-step explanation:

[tex]\frac{15}{25} =\frac{?\\}{5}[/tex]      25 divided by ? = 5? The number 5 so divide 15 as well

15 ÷ 5 = 3

[tex]\frac{15}{25} =\frac{3}{5}[/tex]

Hence, 3 is the answer

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Answer:

Step-by-step explanation:

sorry im not sure

Answer:

D

5 sq.rt. 3

Step-by-step explanation:

use the pythagorean theorem: a^2 + b^2 =c^2

5^2 + x^2 = 10^2

25+ x^2 =100

x^2 = 100 - 25

x^2 =75

x = [tex]\sqrt{75}[/tex]

x = 5 [tex]\sqrt{3}[/tex]

Answer:

A=B=C... wouldn't both B and C be equal to A? Also I can't see the statements.

Answer:

Well the volume is 1570.8 cubed. but i don't know what it would be in your range of answers.

Step-by-step explanation:

Answer:

A) -8x+2

Step-by-step explanation:

-8x + 7 - 5 - 5x + 5x

-8x -5x + 5x + 7 - 5

- 8x+2

Answer:

$4800

Step-by-step explanation:

SI=PRT DIVIDED BY 100..

So it is going to be 400×2×6 divided by 100 which will be 4800

Answer:

1. 35 degrees

2. 44 degrees

Step-by-step explanation:

1). 35 degree

180-59=121

121+24+ m<1= 180

m<1= 35 degree

2) m<CED= 45 degree

As CED is a right angled triangle, one angle is of 90 degree while other 2 angles are of 45 degree which makes a sum of 180.

Answer:

F (5,-8)

Step-by-step explanation:

By rearranging,

y= 4x-28

Substitute each of the x values of the answers, eventually you will get to F and discover that when x = 5, y= -8

y= 4(5) - 28

y= -8

So, when x= 5, y= -8,

Point F is  (5,-8)

Answer:

We don't have sufficient evidence to support the claim

Step-by-step explanation:

Null hypothesis:

[tex]H_0: p = 0.276[/tex]

Alternate hypothesis:

[tex]H_1: p < 0.276[/tex]

The P-value is 0.3064

0.3064 probability of finding a sample proportion lower than the one found.

The p-value is higher than the significance level of 0.05, which means that there is no sufficient evidence to support the claim.

Answer:

The absolute maximum on the interval 0 < x < 3 is at x = 2 and f(2) = 0. Since x = 2 can only give an absolute maximum, so there is no absolute minimum.

Step-by-step explanation:

f(x) = (-x + 2)⁴

to find the absolute maximum and minimum values, we differentiate f(x) with respect to x.

So df(x)/dx = f'(x) = 4(-x + 2)³

The maximum and minimum values are obtained when f'(x) = 0

So,  4(-x + 2)³ = 0

⇒  (-x + 2)³ = 0

⇒ -x + 2 = 0

-x = -2

x = 2

Now, f(2) = (-2 + 2)⁴ = 0⁴ = 0

So, the absolute maximum on the interval 0 < x < 3 is at x = 2 and f(2) = 0. Since x = 2 can only give an absolute maximum, so there is no absolute minimum.

Answer:

If you take 5 sweet out of the basket, then the ratio of the number of chocolate to the number of sweet left in the basket is. \frac{5} {30 - 5} = 5/25 = 1/5

Step-by-step explanation:

Answer:  it is c which is the function was stretched by all the factor of 2

hope this help

Answer:

C 80 R36

Step-by-step explanation:

See attached image for explanation.

Answer:

1/4

Step-by-step explanation:

4 divide in half so should be 1/4

Answer:

Step-by-step explanation:

Answer:

i think its b

Step-by-step explanation:

Answer:

C. The mean of the data set is 8.

Step-by-step explanation:

From the dot plot we can make a frequency table as follows:

Number of books read                      Frequency

       6                                                       2  

       7                                                       2

       8                                                       2

       9                                                       2

       10                                                      2

Since, the number of dots are  10 or then sum of the frequencies is 10.

           Hence, the number of observations are 10.

Also, the median of the set is: 8

Now, the mean is calculated as:

                  Hence, Mean of the data set is: 8

Now, the range of the data set is the difference between the minimum and the maximum value.

                  Hence, range=10-6=4

           The range of the data set is 4.

Answer:

c

Step-by-step explanation:

Answer:

substitute means to use or add in place of something.

Step-by-step explanation:

Example: Substitute 1 for x: therefore x now is equal to 1.

Answer:

Margo will pay $ 44 in interest.

Step-by-step explanation:

Given that Margo borrows $ 1600, agreeing to pay it back with 3% annual interest after 11 months, to determine how much interest will she pay, the following calculation must be performed:

3/12 x 11 = 0.25 x 11 = 2.75

1600 x 1.0275 = X

1644 = X

1644 - 1600 = 44

Therefore, Margo will pay $ 44 in interest.

Answer:

94 degrees

Step-by-step explanation:

Answer:

1.) No ;

2.) - 0.931

3.) 0.1785

Step-by-step explanation:

Given :

μ = 84.3 ; xbar = 81.9 ; s = 17.3

H0 : μ = 84.3

H1 : μ < 84.3

The test statistic :

(xbar - μ) ÷ (s/√(n))

(81.9 - 84.3) / (17.3/√45)

-2.4 / 2.5789317

= - 0.9306

= - 0.931

Using the test statistic, we could obtain the Pvalue : df = n - 1 ; df = 45 - 1 = 44

Using the Pvalue calculator :

Pvalue(-0.9306, 44) = 0.1785

Using α = 0.05

The Pvalue > α

Then we fail to reject H0; and conclude that there is no significant evidence to support the claim that the mean waiting time is less than 84.3

Answer:

(3x + 4)^2

Step-by-step explanation:

9x^2 + 24x + 16

Let's use middle term break method to factor this polynomial.

In Quadratic Factorization using Splitting of Middle Term which is x term is the sum of two factors and product equal to last term. Factor each pair by finding common factors.

we nee two number which give 144 wh3n multiplied and 24 when added.So, 12 and 12 is the number because 12*12=144 and 12+12=24.

9x^2 + (12+12)x +16

9x^2 +12x +12x +16

take common

3x(3x + 4) +4(3x +4)

take (3x + 4) as common

(3x +4)(3x*1 +4*1)

(3x +4)(3x +4)

(3x +4)^2

Answer:

2 (17+12x)

Step-by-step explanation:

See image below:)

Answer:

The average rate of change is 28.57

Step-by-step explanation:

Given

See attachment for graph

Required

The average rate of change from 0 to maximum profit

At 0, we have:

[tex](x_1,y_1) = (32,0)[/tex]

At maximum, we have:

[tex](x_2,y_2) = (60,800)\\\\[/tex]

The average rate of change (m) is calculatd as:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]m = \frac{800 - 0}{60 - 32}[/tex]

[tex]m = \frac{800}{28}[/tex]

[tex]m = 28.57[/tex] --- approximated