The **probability** of an adult being **unemployed** given that they are actively looking for a job is 0.22.

It should be noted that **probability** gas to do with the likelihood that something will occur.

Remember the **multiplication** rule for conditional probability:

P(B AND A)=P(B|A)P(A)

Rearranging, we see thatP(B|A)=P(B AND A)P(A)

So if we think of A as being the **event** that an adult is **actively** looking for a job and B as the event that an adult is unemployed, then we can plug in the known information to find

P(B|A)=0.04 + 0.18

≈0.22

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Type the correct answer in type the answer in the box.Consider functions fand g.f(x)=(x+1)^3g(x) = 3sqrtx + 1Evaluate the function composition.(fg)(-64) = _

f(x) = (x + 1)^3

g(x) = cubic root x + 1

f(g)(x) =

[tex]\begin{gathered} f(g(x))\text{ = (3}\sqrt[]{x}+2)^3 \\ f(g(x))\text{ = x + 6(3}\sqrt[]{x})^2\text{ + 12(3}\sqrt[]{x})\text{ + 8} \\ f(g(-64))\text{ = -64 + 6(3}\sqrt[]{-64})^2\text{ + 12(3}\sqrt[]{-64})\text{ + 8} \\ f(g(-64))\text{ = -64 + 6(16) - 48 + 8} \\ f(g(-64))\text{ = -64 + 96 - 48 + 8} \\ f(g(-64))\text{ = 104 - 112} \\ f(g(-64))\text{ = -8} \end{gathered}[/tex]result

** f(g(-64)) = -8**

Part A find the value of each variable

x=14, y=15

x=14, y=-5

x=24, y=-10

x=24, y-5

Part B

the angle measures?

100°

50°

80°

130°

**Answer:**

**Part A:**

**Option ****1**

3x + 8 = 5x - 20 (vertically opposite angles)

2x = 28

x = 14

3x + 8 + 5x + 4y = 180° (adjacent angles on a straight line)

8x + 4y = 172

Substitute x = 14 into equation to find y.

8(14) + 4y = 172

4y = 60

y = 15

Hence, x = 14 and y = 15.

**Part ****B:**

**Option ****4**

Unlabeled angle = 5x + 4y (vertically opposite angles)

Substitute x and y to find angle measure.

5(14) + 4(15) = 130°

Hence, measure of unlabeled angle is 130°.

Two motorcycle dealers sell the same motorcycle for the same original price. Dealer A advertises that the motorcycle is on sale for 7.5% off the original price. Dealer B advertises that it is reducing the motorcycle’s price by $599. When Bonnie compares the sale prices of the motorcycles in both dealers, she concludes that the sale prices are equal.

Let p represent the motorcycle’s original price.

Which equation models this situation?

0.075p = p − 599

0.925p = p + 599

0.075(p−599) = p

0.925p =

AND NO SPAM I WILL REPORT YOU AND BAN YOU IMMEADIATLEY AND HELP THIS IS DUE TODAY!! SO FAST PLS

Considering the definition of an equation, the equation **0.925p= p - 599** models the following situation: the sale prices of the motorcycles in both dealers are equal.

An equation is the **equality existing **between two algebraic expressions connected through the equals sign in which one or more unknown values appear in addition to certain known data.

The **solution **of a equation means determining the value that satisfies it and the equality is true. To solve an equation, **keep in mind**:

Being "p" the motorcycle’s original price, you know that:

Dealer A advertises that the motorcycle is on sale for 7.5% off the original price → Sale price A= 100%×p - 7.5%×p → Sale price A= (100% - 7.5%)× p → Sale price A= 92.5%p →If the sale prices are equal, the equation in this case is:

Sale price A= Sale price B

0.925p= p - 599

Finally, the equation **0.925p= p - 599** represent the situation.

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The sides of a scalene triangle have measures that are consecutive even integers. If the perimeter of this

triangle is 60 inches, what is the length of the longest side of the triangle?

**Answer: 22**

**Step-by-step explanation:**

Let the sides have lengths [tex]x-4, x-2, x[/tex]. Since the perimeter is 60,

[tex]x-4+x-2+x=60\\\\3x-6=60\\\\3x=66\\\\x=22[/tex]

So, the length of the longest side is 22 units.

can somebody please help me with this question

**Answer:**

U'(12, 15)

**Step-by-step explanation:**

Given **point U(4, 5)** is part of **figure STUVW** that is **dilated** by a **factor of 3** about the origin, you want the **coordinates of U'**.

Dilation about the origin multiplies each coordinate value by the scale factor:

U' = 3U

U' = 3(4, 5) = (12, 15)

**The coordinates of U' are (12, 15)**.

A committee of 6 is to be chosen from the 28 students in a class. If there are 10 males and 18 females in the class, in how many ways can this be done if there must be at least three females on the committee? A: 339864B: 816720C: 3060D: 18564

Hello! First, let's write some important information contained in the exercise:

committee = 6 students

class: 28 students:

- 10 males

- 18 females

Let's consider the rule: At least three females must be on the committee, so we have some cases, look:

**_F_ *** **_F_ *** **_F_ *** __ * __ * __

1st option:

3 females and 3 males

**_F_ *** **_F_ *** **_F_ *** _M_ * _M_ * _M_

4 females and 2 males

**_F_ *** **_F_ *** **_F_ *** _F_ * _M_ * _M_

5 females and 1 male

**_F_ *** **_F_ *** **_F_ *** _F_ * _F_ * _M_

6 females and 0 male

**_F_ *** **_F_ *** **_F_ *** _F_ * _F_ * _F_

Now, we have to use the formula below and find the number of possible combinations:

[tex]C_{n,p}=\frac{n!}{p!\cdot(n-p)!}[/tex]Let's calculate each option below:

1st:3 females:

[tex]C_{18,3}=\frac{18!}{3!\cdot(18-3)!}=\frac{18\cdot17\cdot16\cdot15!}{3\cdot2\cdot1\cdot15!}=\frac{4896}{6}=816[/tex]3 males:

[tex]C_{10,3}=\frac{10!}{3!\cdot(10-3)!}=\frac{10\cdot9\cdot8\cdot7!}{3\cdot2\cdot1\cdot7!}=\frac{720}{6}=120[/tex]**3 females and 3 males: 816 * 120 = 97920**

4 females:

[tex]C_{18,4}=\frac{18!}{4!\cdot(18-4)!}=\frac{18\cdot17\cdot16\cdot15\cdot14!}{4\cdot3\cdot2\cdot1\cdot14!}=\frac{73440}{24}=3060[/tex]2 males:

[tex]C2=\frac{10!}{2!\cdot(10-2)!}=\frac{10\cdot9\cdot8!}{2\cdot1\cdot8!}=\frac{90}{2}=45[/tex]**4 females and 2 males: 3060* 45 = 137700**

5 females:

[tex]C_{18,5}=\frac{18!}{5!\cdot(18-5)!}=\frac{18\cdot17\cdot16\cdot15\cdot14\cdot13!}{5\cdot4\cdot3\cdot2\cdot1\cdot13!}=\frac{1028160}{120}=8568[/tex]1 male:

[tex]C_{10,1}=\frac{10!}{1!\cdot(10-1)!}=\frac{10!}{1\cdot9!}=\frac{3628800}{362880}=10[/tex]**5 females and 1 male = 8568 * 10 = 85680**

6 females and 0 male:

[tex]C_{18,6}=\frac{18!}{6!\cdot(18-6)!}=\frac{18\cdot17\cdot16\cdot15\cdot14\cdot13\cdot12!}{6\cdot5\cdot4\cdot3\cdot2\cdot1\cdot12!}=\frac{13366080}{720}=18564[/tex][tex]C_{10,0}=\frac{10!}{0!\cdot(10-0)!}=\frac{10!}{10!}=1[/tex]**6 females and 0 male: 18564 * 1 = 18564**

To finish the exercise, we have to sum the four options:

97920 + 137700 + 85680 + 18564 = 339864

**So, right answer A: 339864.**

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 42 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 3000 aspirin tablets actually has a 6% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?

The **probability** that the entire cargo will be approved is 0.078 = 7.8% using the **Binomial probability distribution**, while 92.2% will be refused. As a result, many will be rejected.

By **Binomial probability distribution**,

P(X = x) = [tex]C_{n,x}[/tex] × [tex]p^{x}[/tex] × [tex](1-p)^{n-x}[/tex]

[tex]C_{n,x}[/tex] , various combinations of x items from a collection of n elements given by,

[tex]C_{n,x}[/tex] = n! ÷ x! (n - x)!

n=42, as 42 tablets are tested.

p=0.06 as 6% is defective.

If at most there is 1 defective piece then it will be accepted.

Therefore,

P(X ≤ 1) = P(X = 0) + P(X = 1)

P(X = x) = [tex]C_{n,x}[/tex] × [tex]p^{x}[/tex] × [tex](1-p)^{n-x}[/tex]

P(X = 0) = [tex]C_{42,0}[/tex] × [tex](0.06)^{0}[/tex] × [tex](0.94)^{42}[/tex] = 0.074

P(X = 1) = [tex]C_{42,1}[/tex] × [tex](0.06)^{1}[/tex] × [tex](0.94)^{41}[/tex] = 0.0047

Thus,

P(X ≤ 1) = P(X = 0) + P(X = 1)

P(X ≤ 1) = 0.074 + 0.0047

P(X ≤ 1) = 0.0787

The probability that the entire shipment will be approved is 0.078 = 7.8%, while 92.2% will be refused.

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what is the derivative of sqrt(9x^2-1)

**Answer:**

900

**Step-by-step explanation:**

because I know answer

The answer would be 900

Identify which method for solving systems is being described by this fact:

The intersection point of the two lines is an ordered pair (x, y) and determines the value of the solution to the system of equations.

For the** description "**The intersection point of the two lines is an ordered pair (x, y) and determines the value of the solution to the **system **of **equations**.**" **Graphing method for solving systems is in play. Option A

This is further explained below.

What isGenerally, Construct a graph using the first **equation**.

Create a **graph **using the same rectangular coordinate system for the second equation.

Find out whether the lines overlap, if they run parallel to one another, or if they are the same line.

In conclusion, Find a **solution **to the problem that we are having. In the event that the lines meet, locate the location where they do so.

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CQ.

Identify which method for solving systems is being described by this fact:

The intersection point of the two lines is an ordered pair (x, y) and determines the value of the solution to the system of equations.

answer choices

Graphing

Substitution

Elimination (adding or multiplying)

MATHEMATICAL PHRASES_____5. the quatient of y and seven is eight_____6. thrice a number is eighteen_____7. the sum of twice a number and five is nine_____8. a number decreased by seven is twenty-eight

**Explanation**

Part A: The quotient of y and seven is eight.

**Answer: y/7 =8**

Part B: Thrice a number is eighteen

**Answer: 3x = 18**

Part C: The sum of twice a number and five is nine

**Answer: 2x+5 =9**

Part D: A number decreased by seven is twenty- eight

**Answer: x-7 =28**

dentashboard/home

Town policy requires that a certain number of trees be planted for every tree that is cut down.

For example, if 8 trees are cut down, 48 trees will be planted. A homeowner is going to cut down

5 trees on his property.

Solve Problems with Ratios and Unit Rates-Instruction-Level F

How many trees will be planted when 5 are cut down?

Trees Planted

Trees Cut Down

48

8

5

This can be solved using **ratio** and proportions.

**What is ratio?**

A **ratio** in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon **ratio** is eight to six (that is, 8:6, which is equivalent to the **ratio** 4:3). Similarly, the proportion of lemons to oranges is 6:8 (or 3:4), while the proportion of oranges to overall fruit is 8:14. (or 4:7). A **ratio's** numbers can be any quantity, such as a count of persons or things, or measures of lengths, weights, time, and so forth. In most situations, both numbers must be positive. A** ratio** in mathematics illustrates how many times one number contains another.

First, we find the **ratio** of trees planted to trees cut

= 48/8 = 6

So, no. of trees to be planted when 5 trees are cut = 5x6 = 30

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Function g is a transformation of the parent function f(x) = x2. The graph of fis reflected across the x-axis, and then translated left 4 units anddown 2 units to form the graph of gWrite the equation for g in the form y = ax2 + bx + cO A. y = -x2 + 8x + 14O B. y = -x2 - 8x - 18O C. y = x2 - 8x + 18O D. y = -x2 - 8x + 14

The parent function is given as:

f(x) = x²

y = x²

The graph is reflected across the x - axis

The x axis remains the same but the y axis is negated

g(x) = -x²

It is translated 4 units left

The function g(x) becomes

g(x) = -(x - 4)²

It is the translated 2 units down

g(x) = -(x - 4)² - 2

Simplifying the above equation:

g(x) = - (x² - 8x + 16) - 2

g(x) = -x² + 8x - 16 - 2

g(x) = -x² + 8x - 18

A model of Spaceship Earth, a major tourist attraction at Epcot Center in Florida, is a sphere whose diameter is approximately 5 inches.The volume of the model sphere is approximately ___ cubic inches.Use 3.14 for pi. Round only your final answer to the nearest hundredth.

The Volume of the model sphere is given as

[tex]V_{\text{sphere}}=\frac{4}{3}\pi r^3[/tex]Given that the diameter is 5inches, the radius will be

[tex]\begin{gathered} \text{diameter,d}=2\times radius \\ r=\frac{d}{2}=\frac{5}{2}\text{inches} \\ r=2.5\text{inches} \end{gathered}[/tex]substituting r in the formula will give

[tex]\begin{gathered} V_{\text{sphere}}=\frac{4}{3}\times3.14\times(2.5)^3 \\ =\frac{4}{3}\times3.14\times76.765625 \\ =\frac{964.17625}{3} \\ =321.3922\text{cubic inches} \end{gathered}[/tex][tex]V_{\text{sphere}}=321.39\text{cubic inches}[/tex]**Hence, the volume of the model sphere is approximately ****321.39 cubic inches**

A bird is flying above a tree. You are standing 40 feet away from the tree. The angle of elevation to the top of the tree is 32°, and the angle of elevation to the bird is 42°. What is the distance from the bird to the top of the tree?

A bird is flying above a tree. You are standing 40 feet away from the tree. The angle of elevation to the top of the tree is 32°, and the angle of elevation to the bird is 42°. What is the distance from the bird to the top of the tree?

Let

A -----> you

B-----> a bird

C-----> top of the tree

see the following image

step 1

In the right triangle ABD

tan(42)=BD/AD

substitute given values

tan(42)=BD/40

BD=40*tan(42)

BD=36 ft

step 2

In the right triangle ACD

tan(32)=CD/AD

CD=AD*tan(32)

CD=40*tan(32)

CD=25 ft

step 3

Find the difference BD-CD

36-25=11 ft

therefore

the answer is 11 ftTrue or false?

Raising prices is the quickest way to resolve excess demand.

**Answer:**

this is true

**Step-by-step explanation:**

A manufacturer knows that their items have a lengths that are skewed right, with a mean of 17.6 inches, andstandard deviation of 3.3 inches.If 37 items are chosen at random, what is the probability that their mean length is greater than 18.9 inches?(Round answer to four decimal places)Question Help: D VideoSubmit Question

Answer:

The probability is 0.9999

Explanation:Given that the mean is 17.6 inches

standard deviation is 3.3/37 = 0.089

We have:

z(18.9)

[tex]z=\frac{x-\mu}{\sigma}[/tex][tex]\frac{18.9-17.6}{0.089}=14.6067[/tex]Now, we have

P(x > 18.9) = P(z > 14.6067)

= 0.9999

z(0.394) = 0.6532

(4b) If you know that you can drive 230 miles withthat much gas, how many miles per gallon doesyour bus get?Round your answer to the nearest tenth of a mile.The bus gets miles per gallon,

Given the following question:

Part A:

75 dollars to spend on gaS

Gas per gallon costs $2.80

[tex]\begin{gathered} 75\div2.80=26.7857143 \\ 26.7857143 \\ 8>5 \\ 26.8\text{ gallons of gas} \end{gathered}[/tex]**With 75 dollars you can buy "26.8 gallons of gas."**

Part B:

We know we can travel 230 miles with 26.8 gallons of gas, now we have to find out how many miles can we travel PER gallon of gas.

[tex]\begin{gathered} 230\div26.8=10.4477612 \\ 10.4477612 \\ 4<5 \\ 10.4\text{ miles per gallons} \end{gathered}[/tex]**"10.4 miles" per gallon**

diagram 10 shows a straight line PQ with point P(-4,9) and Q(12,1).

We have a line defined by two points, P(-4,9) and Q(12,1).

Knowing two points of the line, we can calculate the slope with the formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, the slope will be:

[tex]\begin{gathered} m=\frac{y_Q-y_P}{x_Q-x_P} \\ m=\frac{1-9}{12-(-4)}=\frac{-8}{12+4}=-\frac{8}{16}=-\frac{1}{2} \end{gathered}[/tex]With the slope and one point we can express the equation in slope-point form:

[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-y_Q=m(x-x_Q) \\ y-1=-\frac{1}{2}(x-12) \\ y=-\frac{1}{2}x+\frac{12\cdot1}{2}+1 \\ y=-\frac{1}{2}x+6+1 \\ y=-\frac{1}{2}x+7 \end{gathered}[/tex]The x-intercept is the value of x that makes the function f(x) become 0.

In this case, we have to find x so that y = 0.

We can replace y in the equation and calculate x as:

[tex]\begin{gathered} y=0 \\ -\frac{1}{2}x+7=0 \\ -\frac{1}{2}x=-7 \\ x=-7\cdot(-2) \\ x=14 \end{gathered}[/tex]Then, for the x-intercept is x = 14.

**Answer: **

**a) The equation of the line is y = (-1/2)*x+7**

**b) The x-intercept is x = 14.**

The line of best fit is given as y = 9 - 3x. Find the value of y when x = -3.091827

**Solution**

We are given the equation

[tex]y=9-3x[/tex]We want to find y when x = -3. We only need to put x = -3

[tex]\begin{gathered} y=9-3x \\ y=9-3(-3) \\ y=9+9 \\ y=18 \end{gathered}[/tex]**Therefore, the answer is**

A city has a population of 250,000 people. Suppose that each year the population grows by 6%. What will the population be after 5 years?Use the calculator provided and round your answer to the nearest whole number.

Answer:

The population after 5 years is approximately **337,465 people**

The population of the city is 250,000

Annual growth rate is 6%

The population after t years is:

[tex]P=P_oe^{rt}[/tex]After 5 years, t = 5 and the population becomes:

[tex]\begin{gathered} P=250000e^{\frac{6}{100}\times5} \\ \\ =250000e^{0.3} \\ \\ \approx337465 \end{gathered}[/tex]The population after 5 years is approximately 337,465 people

Given a pair of points on each line. use the slope formula to determine whether AB and CD are para el perpendicular, or neither. GH: G(14, 13) and H(-11,0) RS: R(-3, 7) and S(-4,-5)

1) Picking points G( 14,13) , H (-11, 0) and R(-3,7) , S(-4,-5) let's find their slopes using the slope formula

And R(-3,7) , S(-4,-5)

Since the condition to be parallel is share the same slope, and to be perpendicular one line must have the reciprocal and opposite slope in comparison to the first one. We can state that **neither that line is parallel nor perpendicular.**

**3) So the answer is GH is not parallel nor perpendicular.**

i need help with this pls

Hello!

What is an x-intercept:

⇒ *value of x* when the *value of y* equals '0'

[tex]8x + 5y=25\\8x+5(0)=25\\8x=25\\\\x=\dfrac{25}{8}[/tex]

x-intercept is **25/8**

What is a y-intercept:

⇒ *value of y* when the *value of x* equals '0'

[tex]8x+5y=25\\8(0)+5y=25\\5y=25\\y=5[/tex]

y-intercept is **5**

Hope that helps!

Henry purchased compact disks for $112. The compact discs cost $16 each.Which of the following equations could you use to find how many compact disks, x, Henry purchased?$16 = $112xO $112 = $16xXO $112=16$112 = x - $16

**Problem**

Henry purchased compact disks for $112. The compact discs cost $16 each.

Which of the following equations could you use to find how many compact disks, x, Henry purchased?

**Solution**

We can set up the following notation:

x= number of disks

**total cost = (number of disks)* (unitary price)**

Total cost = $112

number of disks =x

unitary price = $16

**Replacing we got:**

112 = x*16

For this case the correct equation would be given by:

**$112 = $16x**

customer account “numbers” for a certain company consists of 4 letters followed by 2 single digit numbers. how many different account numbers are possible if repetitions of letters and digits are allowed?

[tex]26^4\cdot\: 10^2=26^4\cdot\: 100=45697600[/tex]

On a recent trip, Carol's car used 7/8 of a tank of gasoline. Which decimal and percentrepresents this amount?

The fraction of gasoline used is:

[tex]\frac{7}{8}[/tex]We need to convert this fraction to decimal and to percentage to find the answer.

**Converting 7/8 to decimal: **

For this we have to do the division between 7 and 8:

Thus, the decimal form of 7/8 is **0.875**

**Converting 7/8 to percentage:**

we use the result that we previously get of 7/8 as a decimal: 0.875, and to convert it to percentage we multiply it by 100:

[tex]0.875\times100=87.5[/tex]7/8 to percentage is equal to **87.5%**

**Answer: 0.875 and 87.5%**

The table and graph show the population or Oregon

From the given **table**, it is found that:

**a. **The average population decline was of 2,250 deer a year.

**b**. The population would have reached 225 thousand deer during the years of 2017 and 2018.

The average rate of change of a function is given by the change in the output divided by the change in the input of the function. Hence, over an** interval [a,b],** the average rate of change is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

In 1984 and 2018, the **populations **are given as follows:

Hence the **rate of change** is given as follows:

r = (173.5 - 250)/34 = -2.25.

(2.25 thousand = 2,250).

For item b, the following **linear function** is built:

y = 230.5 - 1.45x.

The **amount **would be of 225 when:

230.5 - 1.45x = 225

1.45x = 5.5.

x = 5.5/1.45

x = 3.79.

Hence **between **the years of 2017 and 2018.

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Find all X such that -13 < 5x - 3 ≤ 17.

**Answer:**

-5 < x < 17/5

**Step-by-step explanation:**

add three onto all sides -10 < 5x < 17

then divide all sides by -5 < x < 17/5

When do you know you can stop the long division process when converting a fraction to a decimal number?

Division stops after a certain number of steps as the **remainder** becomes **zero** and When **division** continues as there is a remainder after every step.

a division is a process of** splitting **a specific amount into equal parts.

We can stop the** long division process** when converting a **fraction **to a decimal number.

There can be two situations in converting fractions to **decimals: **

When division stops after a certain number of steps as the **remainder **becomes zero.

When **division** continues as there is a remainder after every step.

Hence When division stops after a certain number of steps as the **remainder** becomes** zero **and When **division **continues as there is a remainder after every step.

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Colleen truman earns 5% commission on all sales in june her sales totaled 54,000$ how much did she earn in commission?

The **amount **earned as **commission** in the month of June is $2700

From the question, we have the following parameters that can be used in our computation:

Commission percentage = 5%

Total sales in the month of June = $54000

The **amount **earned as **commission** in the month of June is then calculated as

Amount = Commission percentage x Total sales in the month of June

Substitute the known values in the above equation

So, we have

Amount = 5% x 54000

Evaluate

Amount = 2700

Hence, the **commission **amount is $2700

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What is the measure of a?

In the figure below, C D bisects ∠A C B

AB=B C

∠ B E C=90° and

∠D C E=42°

Find the measure of ∠A

The measure of "a" in the above-given **right-angled triangle **is **32°**

Note that a triangle is a **three**-**sided polygon **that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.

Key properties of a **right**-**angled triangle **to note are:

To solve for "a" recall the following. It is given that:

AB = BC

∠BEC=90°

∠DCE=42°

Because CD bisects ∠ACB, Hence,

∠ACD = ∠DCB = x.............................1

∠DCE= ∠BCE + ∠DCB .....................2

= ∠BCE + x = 42° ................................3

To find ∠A, we use **deductive reasoning **to state:

∠A +∠E +∠ACD + ∠DCB + ∠BCE = 180° (Sum of **Interior Angles**)

Recall equation 1 hence, replacing ∠ACD with ∠DCB we have:

∠A +∠E +∠DCB + ∠DCB + ∠BCE = 180°

Recall equation 2, where ∠DCB = x, hence

∠A +∠E +x + x + ∠BCE = 180°

Recall equation three where 3 where ∠BCE + x = 42°, hence

∠A +∠E +x + (x + ∠BCE) = 180°

⇒ ∠A +∠E + x + 42° = 180°

Recall that ∠E = 90° so

⇒ ∠A +90° + x + 42° = 180° (**Collect like terms**)

⇒ ∠A + x = 180° - 90° - 42° = 48°; Hence

∠A + x = 48°...........................4

Recall that in Δ ABC

AB = BC (given)

Hence, ABC is an **Isosceles triangle**. Since this is true, then

⇒ ∠A = ∠ACB = 2x ...........................5 (Two angles opposite the **equal** **sides **are equal)

Substituting 2x in equation 5 into equation 4, we have

2x + x = 48°

3x = 48

x = 48/3

x = 16°

Recall that

∠A = 2x...........equation 5, hence,

∠A = 2 * 16

∠A = 32°

Learn more about the **measure of angles in a triangle:**

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