Write 84 as a product of primes.
Use index notation when giving your answer

Using the tangent theorem and the inscribed angle theorem, we have:

a. m∠SQT = 74°; b. m∠RQS = 16°.

Angle formed at the point of tangency between the tangent and the radius of a circle = 90 degrees based on the tangent theorem.

The inscribed angle theorem states that, measure of inscribed angle = 1/2(measure of intercepted arc).

a. Find m(SQT):

m∠RQT = 90° [tangent theorem]

m(QR) = 180° [semicircle]

m(QRS) = 212° [given]

m(RS) = m(QRS) - m(QR) = 212 - 180 = 32°

m∠RQS = 1/2[m(RS)] [inscribed angle theorem]

m∠RQS = 1/2(32)

m∠RQS = 16°

m∠SQT = m∠RQT - m∠RQS = 90 - 16

m∠SQT = 74°

b. m∠RQS = 1/2(32)

m∠RQS = 16°

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Answer:

see below

Step-by-step explanation:

If it decreases at  10.5 % per year then 89.5 % remains

Value =      y =  35 300 ( .895)^x

value when x = 5.5      y =  $ 19177.92

Answer:

13

Step-by-step explanation:

26.5 - 13.5 = 13

The geometry is defined by the combination of rectangular prism and half-cylinder. Then the volume of the composite geometry will be 796.94 cubic mm.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The graph is given below.

The geometry is defined by the combination of rectangular prism and half-cylinder. Then the volume of the composite geometry will be

Volume = [(πr²/2) + a x b] x h

Volume = [(π x 4.5²/2) + 9 x 2] x 16

Volume = [10.125π + 18] x 16

Volume = 48.808 x 16

Volume = 796.938

Volume ≅ 796.94 cubic mm

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Answer:

a) 29.45 cm (2 dp)

b) 220.89 cm² (2 dp)

Step-by-step explanation:

Formula

[tex]\textsf{Arc length}=r \theta[/tex]

[tex]\textsf{Area of a sector}=\dfrac{1}{2}r^2 \theta[/tex]

[tex]\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in radians)}[/tex]

Calculation

Given:

[tex]\begin{aligned}\implies \textsf{Arc length} & =r \theta\\& = 15\left(\dfrac{5 \pi}{8}\right)\\& = \dfrac{75}{8} \pi \\& = 29.45\: \sf cm\:(2\:dp)\end{aligned}[/tex]

[tex]\begin{aligned} \implies \textsf{Area of a sector}& =\dfrac{1}{2}r^2 \theta\\\\ & = \dfrac{1}{2}(15^2) \left(\dfrac{5 \pi}{8}\right)\\\\& = \dfrac{225}{2}\left(\dfrac{5 \pi}{8}\right)\\\\ & = \dfrac{1125}{16} \pi \\\\& = 220.89 \: \sf cm^2\:(2\:dp)\end{aligned}[/tex]

Answer:

x = 63

Step-by-step explanation:

Answer:

63°

Step-by-step explanation:

Applying the Angle Sum of Quadrilaterals,

You should plot the total distance traveled from the base camp on the x-coordinate while the elevation should be plotted on the y-coordinate.

A graph simply refers to a type of chart which is commonly used to graphically represent data on both the vertical and horizontal lines of a cartesian coordinate (x-coordinate and y-coordinate).

In this scenario, you would plot the total distance traveled from the base camp on the x-coordinate while the elevation of the camps would be plotted on the y-coordinate as shown in the image attached below.

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Step-by-step explanation:

the surface area consists of 6 individual areas :

front and back (both are equal)

left and right (both are equal)

top and bottom

front and back are trapezoids.

the area of a trapezoid is

(base 1 + base 2)/2 × h

the bases are the 2 parallel sides.

in our case the area of one trapezoid is

(5 + 19)/2 × 12.1 = 145.2 ft²

front and back together then are 290.4 ft².

left and right are 8×14 rectangles:

8×14 = 112 ft²

together they are 224 ft².

the bottom is a 5×8 rectangle :

5×8 = 40 ft²

the top is a 19×8 rectangle :

19×8 = 152 ft²

so, the total surface area is

290.4 + 224 + 40 + 152 = 706.4 ft²

The computation of the word problem shows that the oranges that John will have in 12 weeks will be 70 oranges.

The word problem will be that John has 10 oranges and buys 5 more oranges every week. How many oranges will John have in 12 weeks?

The computation will be:

= 10 + 5x

where x= number of weeks.

= 10 + 5x

= 10 + 5(12)

= 10 + 60

= 70 oranges

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Here is the basic salary-to-hourly formula for this method: First, divide the employee’s annual salary by 52 weeks (the number of weeks in a year). Divide the weekly wages by 40 hours.

3

Step-by-step explanation:

there are 6 solutions, 3 contain 2 heads, i think. dont judge me if its wrong.

Answer:

D. a=1 and b=4

Step-by-step explanation:

x^2-2x+(-2/2)^2 =3+(-2/2)^2

x^2-2x+(-1)^2=3+(-1)^2

x^2-2x +1 =4

(x-1)^2=4

Therefore a=1 and b=4

Answer 27 in^2:

Step-by-step explanation:

Step-by-step explanation

Here ...I'm not too sure about the question as you have written

P = 2 ( 1 + 6 ) and ask to solve for L ...

.So I guess the question you have written is wrong .. ...and I guess there should be L in the place of 1.

...So let me correct the question....

P = 2 ( l + 6 )

P = 2l + 12

P - 2l = 12

- 2l = 12 - P

- 2l = - P + 12

Change the sign of both side of the equation...

2l = P + 12

divide both side by the same number...

L = ( P + 12 ) ÷ 2

[tex]l = \frac{1}{2} p - 12 \times \frac{1}{2} \\ [/tex]

Calculate the product of rational numbers...

[tex]l = \frac{1}{2} p - 6 \\ [/tex]

Step-by-step explanation:

it's either 3 or 2 probably

Answer:

sin Θ = 11/19

Step-by-step explanation:

19 is the hypotenuse.

The legs are 11 and 4√15.

sin Θ = opp/hyp

For angle Θ, 11 is the opposite leg.

sin Θ = 11/19

Answer:

11/19 the other guys is correct

Step-by-step explanation:

Answer:

(5,36)(8,48)slope = (48 - 36) / (8 - 5)

Step-by-step explanation:

Answer: Equation of the system is y = 4x + 16 and in function form is f(x) = 4x + 16.

Explanation

Answer:

The system of equation has infinite solution.

Step-by-step explanation

2x + y = 3

6x = 9 – 3y

First we re-write the second equation in standard form

So, we add 3y both sides

6x+3y=9 ---------------- (2)

2x+y = 3-----------------  (1)

3(2x)+3y = 3(3)

6x+3y=9

6x-6x + 3y-3y = 9-9

0=0

LHS=RHS

This is true statement. If statement is true then infinite number of many solution.

Answer:

infinite

Step-by-step explanation:

acellus

Answer: 104 degrees

Step-by-step explanation:

Answer:

[tex]x=-72[/tex]

Step-by-step explanation:

[tex]-\frac{x}{8}-11=-2\\ -\frac{x}{8}=9\\ -x=72\\x=-72[/tex]

Answer:

The Surface area will double and the volume will triple.

Step-by-step explanation:

This is because the dimensions will cause the shape to double in surface area and triple in volume as surface area is in a two-dimensional space while volume is in a 3-dimensional plane.

Answer:

See below ~

Step-by-step explanation:

Subpart (h) :

⇒ By doubling the dimensions of a rectangular prism, the surface area becomes 2 times the original value

===========================================================

Subpart (i) :

⇒ By doubling the dimensions of a rectangular prism, the volume becomes 8 times the original value

For two matrices to be multiplicative inverse of each other, the product of the matrix must be equal to an identity matrix I.

For two matrices to be multiplicative inverse of each other, the product of the matrix must be equal to an identity matrix I.

Since the 2 by 2 matrix is given, hence the resulting value of I must be a 2 by 2 matrix.

Multiply the row of the first matrix with the column of the second to have:

[tex]\left[\begin{array}{ccc}-3&7\\-2&5\\\end{array}\right] \left[\begin{array}{ccc}-5&-7\\-2&3\\\end{array}\right] =\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

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original equation

[tex]\frac{x}{2}-\frac{3x}{4}+\frac{x}{6}=-\frac{2}{3}[/tex]

multiply by lcd

[tex]12(\frac{x}{2})-12(\frac{3x}{4})+12(\frac{x}{6}) =-12(\frac{2}{3})\\\\6x-9x+2x=-8[/tex]

isolate for x

[tex]-1x=-8\\\\x=8[/tex]

verify

[tex]\frac{8}{2}-\frac{3(8)}{4}+\frac{8}{6}=-\frac{2}{3}\\\\4-6+\frac{4}{3}=-\frac{2}{3}\\\\4-2+\frac{4}{3}=-\frac{2}{3}\\\\-\frac{2}{3}=-\frac{2}{3}\\\\LS=RS[/tex]

Part A: She needs to collect different types of data to form her classmates. It will help her to find which student spends the most time playing musical instruments.

Part B: Yes, it is a statistical question.

Zoe needs two main data from each of her classmates.

1. Name of her classmates.

2. Which student spends how much time playing musical instruments.

After that, she can make a graph or a chart in order to understand which student spends more time playing musical instruments.

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Answer:

1) 1/2or 50%
2) 38/50 or 76%
3) 38/60 or 63%
4) not sure tbh

Step-by-step explanation:

Answer:

y1: Ann

y2: Damian

y3: Adam

y4: Debbi

Step-by-step explanation:

Answer:

The total price David paid for the computer is $933.12

Step-by-step explanation:

The cost of the computer will be $1,080 with 20% off and 8% sales tax.

20% of 1080 is 1080(0.20)=216 this means 216 is 20% of 1080, so with the discount the price will be 1080-216=$864

Now we have to find 8% of 864.

864(0.08)=$69.12

So the total price will be 864+69.12= $933.12

answer : -40/41

steps:

soh cah toa

sin is soh

meaning opposite/hypotenuse

opposite is 9 and

hypotenuse is 41

now you can treat it like a triangle and use the pythagorean theorem

a^2 + 9^2 = 41^2

a^2 + 81 = 1681

a^2 = 1600

a = 40

in soh cah toa

cos is adjacent/hypotenuse so

cos is 40/41

its in quadrant 2 so its negative

-40/41

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Answer:The third option is correct

Step-by-step explanation:

Answer:

(y³ - 2) (x² - 2).

Step-by-step explanation:

x²y³ - 2y³ - 2x² + 4

= y³ (x² - 2) - 2(x² - 2)

(x² - 2) is common to both parts so we have:

(y³ - 2) (x² - 2)