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2 years ago

Use the diagram to find the measure of each of the angles.

Mathematics

2 answers:

just olya [345]2 years ago

8 0

Angle AQB is x = 90

Angle ASB is x = 90

Angle ALB is x = 90

Angle ATB is x = 90

Angle ARB is x = 90

<span>BWD is x < 90</span>

Elis [28]2 years ago

7 0

Answer:

If an angle is inscribed in a semicircle, it will be half the measure of a semicircle (180°), that is, measuring 90 degrees.

According to the given diagram,

Q, S, L, T, R and W are the points of the circumference of the circle having center O,

Also, AB is the diameter of the given circle,

∠AQB, ∠ASB, ∠ALB, ∠ATB, ∠ARB and ∠AWB are the angles on the semicircle,

Thus, by the above property,

m∠AQB = 90°

m∠ASB = 90°

m∠ALB = 90°

m∠ATB = 90°

m∠ARB = 90°

m∠AWB = 90°

If m∠BWD = x

Since, By the diagram,

m∠BWD < m∠AWD

⇒ m∠BWD < 90°

⇒ x < 90°

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Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that

mezya [45]

Answer:

The formula to the sequence

-5, 10/3, -20/9, 40/27, -80/81, ...

(-1)^n. 5×2^(n-1). 3^(1-n)

For n = 1, 2, 3, ...

Step-by-step explanation:

The sequence is

-5, 10/3, -20/9, 40/27, -80/81, ...

By inspection, we see the following

- The numbers are alternating between - and +

- The numerator of a number is twice the numerator of the preceding number. The first number is 5.

- The denominator of a number is 3 raised to the power of (1 minus the position of the number)

Using these, we can write a formula for the sequence.

(-1)^n for n = 1, 2, 3, ... takes care of the alternation between + and -

5×2^(n-1) for n = 1, 2, 3, ... takes care of the numerators 5, 10, 20, 40, ...

3^(1-n) for n = 1, 2, 3, ... takes care of the denominators 1, 3, 9, 27, ...

Combining these, we have the formula to be

(-1)^n. 5×2^(n-1). 3^(1-n)

For n = 1, 2, 3, ...

8 0

2 years ago

Find the sum (3.2+4x)+(18.25+6x)=

tatiyna

Answer: -2.145

Step-by-step explanation:

(3.2+4x)+(18.25+6x)=

Simplifying

(3.2 + 4x) + (18.25 + 6x) = 0

Remove parenthesis around (3.2 + 4x)

3.2 + 4x + (18.25 + 6x) = 0

Remove parenthesis around (18.25 + 6x)

3.2 + 4x + 18.25 + 6x = 0

Reorder the terms:

3.2 + 18.25 + 4x + 6x = 0

Combine like terms: 3.2 + 18.25 = 21.45

21.45 + 4x + 6x = 0

Combine like terms: 4x + 6x = 10x

21.45 + 10x = 0

Solving

21.45 + 10x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-21.45' to each side of the equation.

21.45 + -21.45 + 10x = 0 + -21.45

Combine like terms: 21.45 + -21.45 = 0

0 + 10x = 0 + -21.45

10x = 0 + -21.45

Combine like terms: 0 + -21.45 = -21.45

10x = -21.45

Divide each side by '10'.

x = -2.145

Simplifying

x = -2.145

8 0

2 years ago

Read 2 more answers

Please answer all of them need this

VikaD [51]

First Question

For a better understanding of the solution provided here please find the first attached file which has the diagram of the the isosceles trapezoid.

We dropped perpendiculars from C and D to intersect AB at Q and P respectively.

As can be seen in $\Delta BCQ$ , we can easily find the values of CQ and BQ.

Since, $Sin(75^0)=\frac{CQ}{8}$

$\therefore CQ=8\times Sin(75^0)\approx 7.73$ ft

In a similar manner we can find BQ as:

$Cos(75^0)=\frac{BQ}{8}$

$BQ\approx2.07$ ft

All these values can be found in the diagram attached.

Thus, because of the inherent symmetry of the isosceles trapezoid, PQ can be found as:

$PQ=22-(AP+QB)=22-(2.07+2.07)=17.86$

Let us now consider $\Delta AQC$

We can apply the Pythagorean Theorem here to find the length of the diagonal AC which is the hypotenuse of $\Delta AQC$ .

$AC=\sqrt{(AQ)^2+(QC)^2}=\sqrt{(AP+PQ)^2+(QC)^2}=\sqrt{(2.07+17.86)^2+(7.73)^2}\approx21.38$ feet.

Thus, out of the given options, Option B is the closest and hence is the answer.

Second Question

For this question we can directly apply the formula for the area of a triangle using sines which is as:

Area= $\frac{1}{2}$ (First Side)(Second Side)(Sine of the angle between the two sides)

Thus, from the given data,

Area= $\frac{1}{2}\times 218.5\times 224.5\times sin(58.2^0)\approx20845$ $m^2$

Therefore, Option D is the correct option.

Third Question

For this question we will apply the Sine Rule to the $\Delta ABC$ given to us.

Thus, from the triangle we will have:

$\frac{AB}{Sin(\angle C)}=\frac{BC}{Sin(\angle A)}$

$\frac{c}{Sin(\angle C)}=\frac{a}{Sin(\angle A)}$

$\frac{17}{Sin(25^0)}=\frac{a}{Sin(45^0)}$

This gives $a$ to be:

$a\approx28.44$

Which is not close to any of the given options.

Fourth Question

Please find the second attachment for a better understanding of the solution provided her.

As can be clearly seen from the attached diagram, we can apply the Cosine Rule here to find the return distance of the plane which is CA.

$AC=\sqrt{(AB)^2+(BC)^2-2(AB)(BC)\times Cos(\angle B)}$

$\therefore AC=\sqrt{(172.20)^2+(111.64)^2-2(172.20)(111.64)\times Cos(177.29^0)}\approx283.8$ miles.

Thus, Option D is the answer.

8 0

2 years ago

Read 2 more answers

On a certain route, an airline carries 7000 passengers per month, each paying $30. A market survey indicates that for each $

KengaRu [80]

Answer:

The ticket price that maximizes revenue is $50.

The maximum monthly revenue is $250,000.

Step-by-step explanation:

We have to write a function that describes the revenue of the airline.

We know one point of this function: when the price is $30, the amount of passengers is 7000.

We also know that for an increase of $1 in the ticket price, the amount of passengers will decrease by 100.

Then, we can write the revenue as the multiplication of price and passengers:

$R=p\cdot N=(30+x)(7000-x)$

where x is the variation in the price of the ticket.

Then, if we derive R in function of x, and equal to 0, we will have the value of x that maximizes the revenue.

$R(x)=(30+x)(7000-100x)=30\cdot7000-30\cdot100x+7000x-100x^2\\\\R(x)=-100x^2+(7000-3000)x+210000\\\\R(x)=-100x^2+4000x+210000\\\\\\\dfrac{dR}{dx}=100(-2x)+4000=0\\\\\\200x=4000\\\\x=4000/200=20$

We know that the increment in price (from the $30 level) that maximizes the revenue is $20, so the price should be:

$p=30+x=30+20=50$

The maximum monthly revenue is:

$R(x)=(30+x)(7000-100x)\\\\R(20)=(30+20)(7000-100\cdot20)\\\\R(20)=50\cdot5000\\\\R(20)=250000$

3 0

2 years ago

If five friends want to share 1.25 of a pizza evenly how much pizza would each person get

Amanda [17]

1.25 /5

12/5 = 2 with 2 left over

25/5 = 5

2 numbers

1.25 /5 = .25

Each person gets .25 of a pizza

4 0

2 years ago

Read 2 more answers