In the following figure AEDC is a square, BA= BC and AE = AC. The area of AEDC is 25 cm² and angle B=90°, Calculate the length of AB. ​

The exterior angle of the triangle is 62°.

What is triangle?

A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.

Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.

Let us take the triangle as ABC.

Here \(m\angle C\)= 180-(5x-3)° [Because straight line angle is 180°].

We know that sum of all angles in triangle is add upto 180° Then,

=> \(m\angle A+m\angle B+m\angle C\)=180

=> 43°+3x°+180-5x+3=180°

=> -2x=180-180-43-3

=> -2x=-46

=> x=13°

Now exterior angle ,

=> 5x-3

=> 5*13-3

=> 65-3

=> 62°

Hence the exterior angle of the triangle is  62°.

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Answer:

9?maybe

Step-by-step explanation:

Answer:

\(x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}\)

Step-by-step explanation:

Given trigonometric equation:

\(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

To solve the equation for x in the given interval [0, 2π), first rewrite the equation in terms of sin x and cos x using the following trigonometric identities:

\(\boxed{\begin{minipage}{4cm}\underline{Trigonometric identities}\\\\$\tan \left(\dfrac{\theta}{2}\right)=\dfrac{1-\cos \theta}{\sin \theta}$\\\\\\$\csc \theta = \dfrac{1}{\sin \theta}$\\ \end{minipage}}\)

Therefore:

              \(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

\(\implies 2 \left(\dfrac{1-\cos x}{\sin x}\right)- \dfrac{1}{\sin x}=0\)

  \(\implies \dfrac{2(1-\cos x)}{\sin x}- \dfrac{1}{\sin x}=0\)

\(\textsf{Apply the fraction rule:\;\;$\dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}$}\)

\(\dfrac{2(1-\cos x)-1}{\sin x}=0\)

Simplify the numerator:

\(\dfrac{1-2\cos x}{\sin x}=0\)

Multiply both sides of the equation by sin x:

\(1-2 \cos x=0\)

Add 2 cos x to both sides of the equation:

\(1=2\cos x\)

Divide both sides of the equation by 2:

\(\cos x=\dfrac{1}{2}\)

Now solve for x.

From inspection of the attached unit circle, we can see that the values of x for which cos x = 1/2 are π/3 and 5π/3. As the cosine function is a periodic function with a period of 2π:

\(x=\dfrac{\pi}{3} +2n\pi,\; x=\dfrac{5\pi}{3} +2n\pi \qquad \textsf{(where $n$ is an integer)}\)

Therefore, the values of x in the given interval [0, 2π), are:

\(\boxed{x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}}\)

Answer:

the asnwer is p is less than or equal to -6.

Step-by-step explanation:

The reasonfro that is becuase when u have a negative variable you have to divide both sides by a negative, which will flip the symbol making it less than in this case rather than greater than. Hope this works mark as brainliest pls

that what i got but check the sign well

Answer:

y = 3. last option is correct answer for 2nd question.

Step-by-step explanation:

f(x) just means y.

horizontal asymptote is y = 'something.'

the graph crosses y = 4, so y = 4 cannot be asymptote.

y = 3 is since the graph never quite touches it.

as for ∞, we see that as x approaches -∞, y almost reaches 3. but not quite. also, as x approaches +∞, y approaches +∞.

so the last option is the correct answer.

The number of gallons is 4.1

From the information given, we have that;

1 gallon of paint is equivalent to 150 square feet

Since we have 2 doors, the area of a rectangular prism is

Area = lw

Area =20(15)

Area = 300 (2) = 600 ft²

For the window, we have;

Area = 3(5) = 15

The total area of the wall is;

Total area = 615 ft²

Then, if;

1 gallon = 150 square feet

x = 615  square feet

cross multiply

x = 4. 1 gallons

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Answer:

About 1.05 US quart

Answer:

One liter is like 1.05668821 quarts and just round it to whatever your teacher wants

Answer:

  see below

Step-by-step explanation:

There are a few relevant relations involved:

AB is a diameter, so arcs AB are 180°.

a) BC is the supplement to arc AC: 180° -140° = 40°

b) BG is the supplement to AG: 180° -64° -38° = 78°

c) ∠1 has the measure of BC: 40°

d) ∠2 is inscribed in a semicircle, so has measure 180°/2 = 90°

e) ∠3 is half the measure of arc AE: 64°/2 = 32°

f) ∠4 is half the sum of arcs AG and BC: ((64°+38°) +40°)/2 = 71°

g) ∠5 is half the difference of arcs AC and EG: (140° -38°)/2 = 51°

h) ∠6 is half the sum of arcs EAC and BG: ((140°+64°) +78°)/2 = 141°

i) ∠7 is the difference of exterior angle 4 and interior angle 1: 71° -40° = 31°

j) ∠8 is the measure of arc AC: 140°

k) ∠9 is the supplement to arc AC: 180° -140° = 40°

l) ∠10 is the complement of angle 7: 90° -31° = 59°

Answer:

1 and 3,  if im wrong i am sorry I have not don this in a long time

Step-by-step explanation:

Answer:

I can't read the numbers correctly but a supplementary angles are angle that equal 180*

Hope this helped a little :)

Step-by-step explanation:

The pattern is empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty.

Given that, there are 6 pails in a row. The first 3 pails are filled with water.

The easiest way to solve this problem is to empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty. This will create the desired pattern of full, empty, full, empty, full, empty.

Therefore, empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty.

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Answer:

2/3

Step-by-step explanation:

Do you need an explanation?

The similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other. When two shapes are similar, one can be obtained from the other by uniformly scaling (enlarging or reducing) the shape.

Given that the shape EFGH is a smaller shape of JKLM, and they are similar, then:

the measure of angle Z is equal to 65°

the side EF corresponds to JK and side FG corresponds to KL, so:

8/20 = 11/x

x = (11 × 20)/8 {cross multiplication}

x = 27.5

the side EF corresponds to JK and EH corresponds to JM, so:

8/20 = y/30

y = (30 × 8)/20 {cross multiplication}

y = 12

Therefore, the similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

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Answer:

Step-by-step explanation:

50

-1.96 and 1.96 are the essential z values for a two-tailed test with a significance level of 0.05.

A null hypothesis is a statistical hypothesis that presupposes that there is no link between two variables in a population or that there is no meaningful difference between two populations. It serves as the beginning point of a statistical hypothesis test and is typically marked as H0. A null hypothesis serves as a reference point against which the alternative hypothesis may be compared. The alternative hypothesis is accepted if there is sufficient evidence from the data to reject the null hypothesis. The null hypothesis is not rejected if there is insufficient evidence in the data to support it.

Using a significance threshold of 0.05, we may use a conventional normal distribution table or calculator to get the essential z value. The value that corresponds to the 0.025 percentile is the crucial z value (or the 0.975 percentile, depending on the direction of the alternative hypothesis).

The z value for the 0.025 percentile, as determined by a typical normal distribution table, is -1.96.

Hence, -1.96 and 1.96 are the essential z values for a two-tailed test with a significance level of 0.05.

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the values of x where f(x) = 1 for the function y = x^2 - 2x + 1 are x = 0 and x = 2.

general steps to find all values of x where f(x) = 1 for a given function y = f(x):

1. Set f(x) equal to 1: f(x) = 1.
2. Solve the equation for x. This may involve algebraic manipulation or using techniques such as factoring, completing the square, or using the quadratic formula, depending on the form of the equation.
3. If the equation has multiple solutions, list them all as the values of x where f(x) = 1. If the equation has no solutions, then there are no values of x for which f(x) = 1.

For example, if the function is y = x^2 - 2x + 1, then setting f(x) = 1 gives:

x^2 - 2x + 1 = 1

Simplifying this equation by subtracting 1 from both sides, we get:

x^2 - 2x = 0

Factoring out x, we get:

x(x - 2) = 0

This equation is satisfied when either x = 0 or x = 2. Therefore, the values of x where f(x) = 1 for the function y = x^2 - 2x + 1 are x = 0 and x = 2.

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The value of x is x = -3.

What is solving an equation?

Finding an equation's solutions, or the values that satisfy the condition given by the equation, is known as solving an equation in mathematics. Solutions often consist of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.

Consider the given equation,

27 = (1/3)^x

This equation can be written as,

\(27 = \frac{1^x}{3^x}\)

Here 1^x

1\(27 = \frac{1}{3^x}\)

Take 3^x on numerator.

\(27 = 3^-^x\)

Now 27 can be written as,  \(27 = (3)(3)(3) = 3^3\)

⇒ \(3^3 = 3^-^x\)

Applying the exponent rule: \(a^b=a^c\) ⇒ b = c

So we get,

3 = -x

Multiply both sides by -1.

-3 = x

x = -3

Hence the value of x is x = 3.

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Answer:

Step-by-step explanation:

Rate (slope) of miles per gallon of gas: m = \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

(0, 0)

(2, 50)

\(m_{carA}\) = 25 mi/gal.

(0, 0)

(3, 60)

\(m_{carB}\) = 20 mi/gal.

Car B use less gasoline.

Step-by-step explanation:

31 + 6x + x + 16 = 180

7x + 47 = 180

7x = 180 - 47

x = 133/7

x = 19

Answer:

(2, -1)

Step-by-step explanation:

I just plugged (y-x<-3) into desmos (if you haven't used desmos, use it. Its a lifesaver) and the only coordinate pair that was part of the line, is (2,-1)

Hope that helps!

Answer:

(6,2)

coz if y=2 & x=6

then substitute in to the equation

and we get 2-6=-4

so -4 is less than -3; in number line. thats it!!!!!

Answer:

C

Step-by-step explanation:

Since C is the largest half, then C is part of the largest whole.

Answer: C

Answer:it took  the particle 50,000,000 seconds to travel the specified distance

Step-by-step explanation:

Given that distance = Rate x time

Distance traveled by Particle= 9.0×10^12 meters

and rate= 1.8×105 meters per second

Time taken for particle to travel the specified distance  using our equation that

distance = Rate x time

time = Distance / Rate

=9.0×10^12 meters/ 1.8×105 meters per second

=50,000,000 seconds

Answer: The 3/8 image will go with the answer 3/4 x 1/2. The The 3/16 image will go with the answer 1/4 x 3/4. And finally, the 4/9 image goes with the answer 2/3 x 2/3. You’re welcome. :)

Step-by-step explanation:

Answer:

4 + 4 + 4 = 12

Step-by-step explanation:

Perimeter (P) = a + b + c (a, b, c being all the sides, which are all equal to 4)

The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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The computation of the profitability ratios for Western Bookkeeping and Tax Service is as follows:

Profitability ratios are the financial ratios that evaluate an entity's ability to convert its earnings (revenue) into profit versus different criteria.

Some of the common profitability ratios include:

Stockholders' equity = $442,600

Total assets = $640,000

Net sales = $480,000

Net income = $36,000

Profit margin ratio = Net income/Net Sales x 100

= $36,000/$480,000 x 100

= 7.5%

= 8%

Return on equity ratio = Net income/Shareholders' Equity x 100

= $36,000/$442,600 x 100

= 8.13%

= 8%

Asset turnover ratio = Net Sales/Total Assets

= $480,000/$640,000

= 0.75

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Answer:

y = -1

Step-by-step explanation:

The word sofa begins with an open syllable.

Phonetics is the study of the sound of words/ speeches. This branch of linguistics deals with how words and letters sound and classifies them accordingly.

The easiest way to detect an open and closed syllable is by identifying the position or use of the vowels and consonants in a syllable. This makes the word "sofa" an open syllable.

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