1. What is the magnitude and direction of RS with tail and head points R(4, -6) and S(-2, 1)?
a.9.2 units, 49.4° south of east
b.10.4 units, 40.6 ° south of east
c.9.2 units, 49.4 ° north of west
d. 10.4 units, 40.6 ° north of west

Answer:

b = 25°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

b + 110° + 45° = 180°

b + 155° = 180° ( subtract 155° from both sides )

b = 25°

Answer:

∠ YZX ≈ 19.7°

Step-by-step explanation:

using the sine ratio in the right triangle.

sin YZX = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{XY}{YZ}[/tex] = [tex]\frac{7.5}{22.3}[/tex] , then

∠ YZX = [tex]sin^{-1}[/tex] ( [tex]\frac{7.5}{22.3}[/tex] ) ≈ 19.7° ( to 3 significant figures )

Step-by-step explanation:

every triangle inscribed into a circle with the baseline being a diameter of the circle must be a right-angled triangle.

therefore,

angle XVY = 90°.

for VY we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse (the line opposite of the 90° angle, in our case XY).

XY = 2×ZY = 2×17 = 34.

so,

34² = 30² + VY²

VY² = 34² - 30² = 1156 - 900 = 256

VY = 16

Answer:

  6.2 units

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relations between trig functions and sides of a right triangle.

To find the value of x in this figure, we need to know the length of the common segment between the two triangles. That segment is opposite the 53° angle, so can be found using the sine relation:

  Sin = Opposite/Hypotenuse

  Opposite = Hypotenuse × Sin = 30·sin(53°) ≈ 23.9591

__

The side marked x is adjacent to the marked angle in that triangle, so the relevant relation is ...

  Cos = Adjacent/Hypotenuse

  Adjacent = Hypotenuse × Cos = 23.9591·cos(75°) ≈ 6.20106

The length of the side marked x is about 6.2 units.

Answer:

The answer is 15 cm.

Step-by-step explanation:

y= k/x

x= width

y= length

So there for;

x= 5

y= 12

Which means that;

12= k/5

k= 60

And then;

y= 60/x

Which then finally means that;

y= 60/4

60/4= 15 cm

The distance between the two buildings is 844.23 feet apart, we go this answer by simply applying the SOH CAH TOA method

Given Data

Applying the SOH CAH TOA Approach we have

Tan  θ = Opp/Adj

Substituting our given data we have

Tan 35 = 400/x

0.4738 = 400/x

make x subject of the formula we have

x = 400/0.4738

x = 844.23 feet

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Answer:

length = 44 ft.

Step-by-step explanation:

A = lw

[tex]880 = 20l\\[/tex]

Solving for l gives us l = 44 ft.

Answer: 166 feet^2

Step-by-step explanation:

The equation for surface area is 2(wl+hl+hw). So that would be:
Surface Area = 2×(5×7 + 5×4 + 7×4) = 166 feet^2

Answer:16 square cm

Step-by-step explanation: Surface area = base, height (Side 1 + Side 2+ Side 3) H = Side 1 = 5 cm

Side 2 = 7cm

Side 3 = 4cm (add all these numbers ) = 16 Square cm

Step-by-step explanation:

please mark me as brainlest

ans

[tex] \frac{3x}{x + 4} [/tex]

Answer:

False

Step-by-step explanation:

45/100 × 72 = 32.4

45/72 × 100 = 62.5

62.5 ≠ 32.4

Answer:

false

Step-by-step explanation:

45/100x72=32.4%

45/72X100=62.5%

Answer:

3

Step-by-step explanation:

these are 2 similar triangles (all 3 pairs of corresponding angles are equal in their pair, and the lengths of corresponding sides have the same ratio in every pair of corresponding sides and other lengths).

and they are also right-angled triangles.

so, what else do we know about them ?

PQ = 18

RT = 6

ST = QT + 9

therefore

QT = ST - 9

and

QR = QT + RT = ST - 9 + 6 = ST - 3

due to the principles of cumulative triangles

PQ/ST = QR/RT = 18/ST = (ST - 3)/6

108/ST = (ST - 3)

108 = (ST - 3)ST = ST² - 3ST

ST² - 3ST - 108 = 0

we can the write

x² - 3x - 108 = 0

and the solution for such a squared equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -3

c = -108

x = (3 ± sqrt(9 - 4×1×-108))/2 = (3 ± sqrt(441))/2 =

= (3 ± 21)/2

x1 = (3+21)/2 = 24/2 = 12

x2 = (3-21)/2 = -18/2 = -9

a negative solution for real lengths is not valid, so we know

x = ST = 12

so,

QR = ST - 3 = 12 - 3 = 9

and then

QT = QR - RT = 9 - 6 = 3

Answer:

Emma began her journey at 7:30 a.m., at 8 a.m. she was 20 miles away, she stayed for an hour and a half, she left at 10 a.m., she was 7.5 miles from her house at 11:45, she traveled 80 miles total

Step-by-step explanation:

please let me know what you don't understand here. because this is really simple.

the distance from home is increasing and then decreasing when she is traveling.

the rate of distance per time would give us even the speed with which she was traveling.

when there is no change in the distance over time, that means she was "stationary" - either at home or at her grandmother's place.

so, let's answer the questions :

(a)

movement started at 7:30am (that is when she began her journey).

(b)

20 miles

you pick 8am on the time scale and move straight up until you hit the curve. and then you check what value is at that point all the way to the left on the distance scale : 20.

(c)

from 8:30am to 10am = 1.5 hours.

we see this by the interval on the time scale for which the curve is totally flat (a horizontal line) = no change in distance from home during that time.

(d)

at 10am

that is when the curve indicates the begin of a change in the distance to home.

(e)

7.5 miles.

this is the point marked by a star on the graph.

down on the time scale this point shows 11:45am, and on the left side in the distance scale it shows 7.5 miles (the middle between 5 and 10 miles).

so, at that time she was still 7.5 miles away from home.

(f)

she traveled 40 miles to her grandmother (the left part of the curve from 0 distance until it turns flat), and then 40 miles back home (the right part of the curve from 40 distance all the way down to 0).

so, in total she traveled

40 + 40 = 80 miles

Answer:

50²

Step-by-step explanation:

(2×10⁵) ÷ (4×10²)

2 × 100000 ÷ 4 × 100

200000 ÷ 400

= 500

= 50²

A number line is a representation of a graded straight line. The number √128  will lie between 11.3 and 11.4.

A number line is a representation of a graded straight line that serves as an abstraction for real numbers, which are represented by the letter R. A real number is considered to correspond to every point on a number line, and a point to every real number.

In order to know the location of the √128, we need to write the number  √128 in decimal form, therefore, the value of √128 can be written as,

[tex]\sqrt{128} = 11.3137 \approx 11.31[/tex]

Now, on the number line if we plot √128 we will see that it will lie between 11.3 and 11.4, as shown below.

Hence, the number √128  will lie between 11.3 and 11.4.

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Answer:

Q1. 95 degrees  

Q2. 100 degrees

Step-by-step explanation:

When you create a triangle, all angle measures must equal 180 degrees.

So, using that information, take 180 and subtract both of the other values.

180 - 25 = 155

155 - 60 = 95

When two angles are supplementary, the sum of their angle measures equal 180, or a straight angle.

Using that information, take 180 and subtract 80.

180 - 80 = 100

Answer:

[tex]\frac{7\pi }{4}[/tex] radians

Step-by-step explanation:

to convert degrees to radians

radians = degrees × [tex]\frac{\pi }{180}[/tex] , then

radian measure = 315° × [tex]\frac{\pi }{180}[/tex] ( cancel 315 and 180 by 45 )

                          = 7 × [tex]\frac{\pi }{4}[/tex]

                         = [tex]\frac{7\pi }{4}[/tex]

315 degrees is equal to 5.49779 radians.

To convert degrees to radians, you need to multiply the degree measure by the conversion factor of π/180.

Let's convert 315 degrees to radians:

315 degrees × (π/180)

315×3.14 /180

= 5.49779 radians

Therefore, 315 degrees is equal to 5.49779 radians.

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Answer:

[tex] (x + 6 {)}^{6} = {x}^{6 } + 36{x}^{5} + 540{x}^{4} + 4320 {x}^{3} + 19440{x}^{2}+ 46656{x}^{} + 46656 [/tex]

Step-by-step explanation:

we want to solve the following binomial:

[tex](x + 6 {)}^{6} [/tex]

There is a handy way to expand powers of binomials which is known as binomial theorem . and it describes the algebraic expansion of powers of a binomial. binomial theorem is given by

[tex] \displaystyle (a + b {)}^{n} = \sum _{k = 0 }^{n} \binom{n}{k} {a}^{n - k} {b}^{k} [/tex]

comparing (x+6)⁶ to (a+b)ⁿ , we get

now substitute them on the formula which yields:

[tex] \displaystyle (x + 6 {)}^{6} = \sum _{k = 0 }^{n} \binom{6}{k} {x}^{6 - k} \cdot {6}^{k} [/tex]

converting the summation notation into sum yields:

[tex] \displaystyle (x + 6 {)}^{6} = \binom{6}{0} {x}^{6 - 0} \cdot {6}^{0} + \binom{6}{1} {x}^{6 - 1} \cdot {6}^{1} + \binom{6}{2} {x}^{6 - 2} \cdot {6}^{2} + \binom{6}{3} {x}^{6 - 3} \cdot {6}^{3} + \binom{6}{4} {x}^{6 - 4} \cdot {6}^{4} + \binom{6}{5} {x}^{6 - 5} \cdot {6}^{5} + \binom{6}{6} {x}^{6 - 6} \cdot {6}^{6} \\ \implies(x + 6 {)}^{6} = \binom{6}{0} {x}^{6 } \cdot 1 + \binom{6}{1} {x}^{5} \cdot {6} + \binom{6}{2} {x}^{4} \cdot 36+ \binom{6}{3} {x}^{3} \cdot 216 + \binom{6}{4} {x}^{2} \cdot 1296+ \binom{6}{5} {x}^{} \cdot 7776+ \binom{6}{6} {x}^{0} \cdot 46656 \\ \implies(x + 6 {)}^{6} = 1 \cdot {x}^{6 } \cdot 1 + 6 \cdot{x}^{5} \cdot {6} + 15 \cdot {x}^{4} \cdot 36+ 20 \cdot {x}^{3} \cdot 216 + 15 \cdot{x}^{2} \cdot 1296+ 6 \cdot {x}^{} \cdot 7776+ 1 \cdot {x}^{0} \cdot 46656 \\ \implies \boxed{ (x + 6 {)}^{6} = {x}^{6 } + 36{x}^{5} + 540{x}^{4} + 4320 {x}^{3} + 19440{x}^{2}+ 46656 {x}^{} + 46656 }[/tex]

and we're done!

Answer:

-13

Step-by-step explanation:

Answer:

period = 2π

Step-by-step explanation:

the period is the distance from one point on the waveform to the corresponding point on the next wave.

there is a maximum at 2π and a corresponding maximum at 4π

period = 4π - 2π = 2π

Answer: ∠A=144°

Step-by-step explanation:

∠A and ∠B are alternate exterior angles. Alternate exterior angles are congruent to each other. That means ∠A=∠B. Since we are given the measures of ∠A and ∠B, all we have to do is set them equal to each other.

10x+24=6x+72          [subtract both sides by 6x]

4x+24=72                  [subtract both sides by 24]

4x=48                         [divide both sides by 4]

x=12

Now that we found x, we need to plug it into ∠A.

10(12)+24=120+24=144

We know that ∠A=144°.

Step-by-step explanation:

e.g. 452 and 397

but also e.g. 448 and 429

An individual will want small remote valve and a large valve close to the cylinder in order to build the pressure.

It should be noted that pressure simply means the measure of the force that's applied over a unit area.

In this case, an individual will want small remote valve and a large valve close to the cylinder in order to build the pressure between each valve and also create more pressure for the cylinder.

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Answer:

Step-by-step explanation:

What is 6 divided by 3/56 ÷ 3 5. The trick to working out 6 divided by 3/5 is similar to the method we use to work out dividing a fraction by a whole number. ... 6 x 5 3 = 30 3. So, the answer to the question "what is 6 divided by 3/5?" ... 30 3. ... 10 1. ... 10 1 = 10.

Answer:

The numbers in 6 divided by 3/5 are labeled below:

6 = whole number

3 = numerator

5 = denominator

To make it a fraction form answer, you multiply the whole number by the denominator and make the result the new numerator. The old numerator becomes the new denominator:

6 x 5

3

 =  

30

3

Thus, the answer to 6 divided by 3/5 in fraction form is:

30

3

To make the answer to 6 divided by 3/5 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:

30 / 3 = 10

The answer is rounded to the nearest two decimal points if necessary.

30/3 can be simplified to 10/1.

10/1 is an improper fraction and should be written as 10.Step-by-step explanation:

Answer:

c

Step-by-step explanation:

40 cubic units

divide the shape into 2 pieces first.

4 × 4 ×2 = 32

4×2 = 8

32 + 8 = 40

the idea being that, each cube in the stack, is a 1x1x1 = 1 unit³, now if that's so, then, Check the picture below.

The equation which John solve to find w, the greatest width in centimeters he can use for the mosaic, is w(w + 2) = 48.

Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,

[tex]A=a\times b[/tex]

Here, (a)is the length of the rectangle and (b) is the width of the rectangle

The area of the tile is 48 square cm. John wants to make the mosaic with this tile having the length 2 cm longer than the width.

Let suppose the width of the rectangle mosaic is w cm. Thus the length of it is,

[tex]l=w+2[/tex]

As the area of a rectangle is the product of its length and width and Tte area of the tile is 48 square cm. Thus,

[tex]48=(w+2)\times w\\48=(w+2)w\\[/tex]

The equation which John solve to find w, the greatest width in centimeters he can use for the mosaic is

[tex]w(w + 2) = 48[/tex]

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Answer:

B. w(w + 2) = 48

Step-by-step explanation:

I just took the quiz.

Have the day you deserve :)

8x^5 y^8 z^9 ur welcome

Answer:

[tex]64x^6y^{12}z^{14}[/tex]

Step-by-step explanation:

[tex]\left(8x^3y^6z^7\right)^2[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n[/tex]

[tex]\left(8x^3y^6z^7\right)^2=8^2\left(x^3\right)^2\left(y^6\right)^2\left(z^7\right)^2[/tex]

[tex]=8^2\left(x^3\right)^2\left(y^6\right)^2\left(z^7\right)^2[/tex]

[tex]8^2=64[/tex]

[tex]=64\left(x^3\right)^2\left(y^6\right)^2\left(z^7\right)^2[/tex]

[tex]=64x^6\left(y^6\right)^2\left(z^7\right)^2[/tex]

[tex]=64x^6y^{12}\left(z^7\right)^2[/tex]

[tex]=64x^6y^{12}z^{14}[/tex]

~lenvy~

The tax revenue Australia would generate each year is $96,054,697,991.

The percentage is the value per hundred.

Working population of Australia =  11,565,470 people

Annual average salary = $26,450

Income tax rate = 31.4%

Tax revenue generated by each resident = 26450*(31.4/100)

Tax revenue generated by each resident =$8305.3

So, Tax revenue generated by 11,565,470 residents =  11,565,470*8305.3

Tax revenue generated by 11,565,470 residents = $96,054,697,991

Therefore, the tax revenue Australia would generate each year is $96,054,697,991.

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Answer:

find the product of (4m-n) and (3m-2n)