In the image below, lines n and mare parallel. What is the measure of angle 4?

a.98
b.82
c.164
d.122
help me asap pls

Answer:

[tex]sin\theta =\pm\dfrac{4}{5}\\tan\theta =\pm\dfrac{3}{4}[/tex]

Step-by-step explanation:

Kindly refer to the attached image of a right angled [tex]\triangle ABC[/tex].

Let [tex]\angle C = \theta[/tex]

Sides BC = a

AB = c and

AC = b respectively.

To prove:

[tex]sin^2\theta+cos^2\theta =1[/tex]

Proof:

Using Sine and Cosine values:

[tex]sin\theta =\dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin\theta =\dfrac{AB}{AC} = \dfrac{c}{b }[/tex]

[tex]cos\theta =\dfrac{Base}{Hypotenuse}\\\Rightarrow cos\theta =\dfrac{BC}{AC} = \dfrac{a}{b}[/tex]

As per Pythagorean theorem:

[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow b^{2} = a^{2} + c^{2} .......... (1)[/tex]

Considering the LHS of [tex]sin^2\theta+cos^2\theta =1[/tex]:

[tex](\frac{c}{b})^2+(\frac{a}{b})^2\\\Rightarrow \frac{c^2+a^2}{b^2}[/tex]

Now, using equation (1):

[tex]\Rightarrow \dfrac{b^2}{b^2} = 1 = RHS[/tex]

Hence, proved that : [tex]sin^2\theta+cos^2\theta =1[/tex]

Now, we are given that:

[tex]cos\theta =\frac{4}{5}[/tex]

To find, sine and cosine values of the angle i.e. [tex]sin\theta = ?[/tex] and [tex]tan\theta = ?[/tex]

Using [tex]sin^2\theta+cos^2\theta =1[/tex]:

[tex]sin^2\theta+(\dfrac{4}{5})^2 =1\\\Rightarrow sin^2\theta = \dfrac{9}{25}\\\Rightarrow sin\theta = \pm \dfrac{3}{5}[/tex]

We know that:

[tex]tan\theta =\dfrac{sin\theta}{cos\theta}\\\Rightarrow tan\theta =\pm \dfrac{\dfrac{3}{5}}{\dfrac{4}{5}}\\\Rightarrow \bold{tan\theta =\pm \dfrac{3}{4}}[/tex]

Answer:

If we stipulate that a baby is premature if the length of pregnancy is in the lowest 4%, find the length that separates premature babies from those who are not premature. The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.

hope it helps :)

please mark it the brainliest!

Answer:

2

Step-by-step explanation:

area of a parallelogram : b x h (base x height)

since there are no measurements, we are looking at the squares

im assuming that the squares are 1x1 squares

hence, for the base of the parallelogram, we are counting the squares

i added the halves together and got the answer 2

then we need to take the height

which im also assuming is 1

b x h = 1 x 2

a = 2

sorry if this is wrong but the angle that it was taken at, is not very clear ; (

Answer:

  $125

Step-by-step explanation:

With a 20% off coupon, the price you pay is 80% of the marked price. If that amount is $100, you have ...

  $100 = 0.80p

  p = $100/0.80 = $125

The maximum price of the shoes you can buy is $125.

_____

Check

20% of $125 is -.20×$125 = $25. When that is subtracted, the price you pay is ...

  $125 -25 = $100

Answer:

$125

Step-by-step explanation:

let the maximum price be 'x'

[tex]x -( \frac{20}{100} \times x) = 100[/tex]

[tex]x - ( \frac{x}{5} ) = 100[/tex]

[tex] \frac{4x}{5} = 100[/tex]

[tex]4x = 500[/tex]

[tex]x = 125[/tex]

Answer:

domain is (0, 30)

Range is (1900, 2500)

Step-by-step explanation:

We are told that Jessica plans to decrease her calorie intake by 40 calories every 2 days for the next 30 days.

This means that the domain of this period is between 0 days to 30 days.

Thus, the domain is (0, 30)

Now,she plans decrease of 40 calories every 2 days. This amounts to an average of 20 calories a day.

Which means that in a month of 30 days, she would have decreased her daily calorie intake by; 20 × 30 = 600 calories.

Since she is currently on 2500 calories per day, it means that the new targeted daily intake is; 2500 - 600 = 1900 calories.

Thus, the range for this situation would be between 1900 calories and 2500 calories.

Range = (1900, 2500)

Answer:

3, -2, -1, 0, 1, 2, 3

Step-by-step explanation:

Given the inequality expression |x| < 4 where x is unknown. To her the possible values of x, we must undeterstand that the absolute value of a number returns both positive and negative value.

Hence |x| can either return +x or -x

If x is positive, the inequality expression will be x<4.

If the value of x is negative, then -x<4

From -x<4

Multiply both sides by minus sign will change the sense of the inequality sign.

-(-x) > -4

x>-4

If x is greater than -4, then -4<x.

Combining both inequality will give;

-4 < x and x<4

-4<x<4

Hence the possible values of Javier's number are integers between -4 and 4.

The values are -3, -2, -1, 0, 1, 2, 3.

Answer:

11565 km

Step-by-step explanation:

The computation is shown below:

But before reaching the final solution first we need to do the following calculations

The angle lies between the Galapagos  and  Nauru is

= 90° + 166.50°

= 256.5°

Since the sum of angle is 360 degrees

So the major arc and the minor arc is

= 360° -  256.5°

= 103.50°

Now the angles lies between galapagos islands is

= 180°  - 90°

= 90°

And, between the naura island is

= 180°  - 166.50°

= 13.5°

Now the total of this two island is

= 90°  + 13.5°

= 103.5°

The length is

[tex]= \frac{\pi r }{180^{\circ}} \times \theta\\\\ = \frac{6,400\pi}{180^{\circ}} \times 103.5^{\circ}[/tex]

= 11565 km

Answer:

B) 1820

Step-by-step explanation:

10% = 2600 ÷ 10 = 260

30% = 260 x 3 = 780

2600 - 780 = 1820

Hope this helps! :D

Answer:

The intercepts of a graph are points at which the graph crosses the axes. The x-intercept is the point at which the graph crosses the x-axis. At this point, the y-coordinate is zero. Yes it also matter because x axis go sideways and the y axis goes up and down. Hope this helps

Answer:

The intercepts of a graph are points at which the graph crosses the axes. The x-intercept is the point at which the graph crosses the x-axis. At this point, the y-coordinate is zero.

Step-by-step explanation:

Answer:

[tex]y = 0.01092395604x^3[/tex]

Step-by-step explanation:

Given:

[tex]y = 0.000304x^3[/tex]

Where y is in pounds and x is in inches

Required

Represent y in kilogram and x in centimetre

[tex]y = 0.000304x^3[/tex]

The expression can be rewritten as

[tex](y\ pound) = 0.000304(x\ inch)^3[/tex]

------------------------------------------------------------------------------------------------

If [tex]0.394\ inch= 1\ cm[/tex]

Divide both by 0.394

[tex]\frac{0.394\ inch}{0.394}= \frac{1\ cm}{0.394}[/tex]

[tex]1\ inch= \frac{1\ cm}{0.394}[/tex]

[tex]1\ inch = 2.538\ cm[/tex] (Approximated)

Multiply both sides by x

[tex]x * 1\ inch = 2.538\ cm * x[/tex]

[tex]x \ inch = 2.538x\ cm[/tex]

------------------------------------------------------------------------------------------------

If [tex]2.20\ pound = 1\ kg[/tex]

Divide both by 2.20

[tex]\frac{2.20\ pound}{2.20} = \frac{1\ kg}{2.20}[/tex]

[tex]1\ pound = \frac{1\ kg}{2.20}[/tex]

[tex]1\ pound = 0.455\ kg[/tex] (Approximated)

Multiply both sides by y

[tex]y * 1\ pound = 0.454\ kg * y[/tex]

[tex]y \ pound = 0.454y\ kg[/tex]

------------------------------------------------------------------------------------------------

Substitute 0.455y kg for y pound and 2.538x cm for x inch in [tex](y\ pound) = 0.000304(x\ inch)^3[/tex]

[tex]0.454y = 0.000304(2.538x)^3[/tex]

[tex]0.454y = 0.000304(16.35x^3)[/tex]  Approximated

[tex]0.454y = 0.0049704x^3[/tex]

Divide both sides by 0.455

[tex]\frac{0.455y}{0.455} = \frac{0.0049704x^3}{0.455}[/tex]

[tex]y = \frac{0.0049704x^3}{0.455}[/tex]

[tex]y = 0.01092395604x^3[/tex]

Answer:

T = 100I/PR

Step-by-step explanation:

1) Original: I = PRT/100

2) Multiply both sides by 100: 100I = PRT

3) Divide both sides by PR: 100I/PR = T

Answer:

gr uf

Step-by-step explanation:

Answer:

[tex]M(-\dfrac{3}{2}, -2)[/tex]

Step-by-step explanation:

[tex]M(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2})[/tex]

[tex]M(\dfrac{-3 + 0}{2}, \dfrac{3 + (-7)}{2}) =[/tex]

[tex]= M(\dfrac{-3}{2}, \dfrac{-4}{2})[/tex]

[tex]= M(-\dfrac{3}{2}, -2)[/tex]

Answer:

1,000 because it's in the thousands place

Step-by-step explanation:

Answer:

Step-by-step explanation:

From Thales' theorem:

                                        [tex]\dfrac y7\ =\ \dfrac45\\\\y=\dfrac45\cdot7\\\\y = \dfrac{28}5\\\\y = 5.6[/tex]

Points are very important in geometry.

In fact, a point is the most basic figure in geometry.

A point has no size, only position.

Although it's basic, it's used all the time in geometry and it creates things.

For example, two points creates line segments.

Line segments are used in postulates and theorems.

The 325.623 round to the nearest 10 is 325.6.

Rounding a number of means simplifying it while retaining its value close to what it was. The end output is less accurate but more usable. For instance, 73 rounded to the closest ten is 70, because 73 is closer to 70 than 80.

The tens' digit is the rule for rounding to the closest a hundred. If the number is five or more, round up. If the number is four or less, round down. Consider the number formed by the digits in the tens and one's columns when rounding to the nearest hundred.

To round to the next thousand, write down the multiple of 1000 closest to our number. The thousands' digit will either remain unchanged or rise by one.

Therefore, the nearest 10 is 325.6.

To learn more about round figures, refer to the link:

https://brainly.com/question/12342753

#SPJ2

Answer:

10

Step-by-step explanation:

answer 10 10x10= 100 100/10=10

Answer:

875 ft³

Step-by-step explanation:

First, let's break it down into three different sections.

Starting with the cube on the bottom and then the rest of the Rectangular Prism.

The formula for Volume Cube  V = a³

The formula for Volume of Rectangular Prism:  V = lwh

From the picture we can see that the bottom is a cube with a lenght of 5 ft thus V = 5³ = 125 ft³

The second Rectangular Prism in the middle has a lenght of 20 ft (15 + 5), a width of 5 ft and a height of 5 ft. Use the formula above 20x5x5 = 500 ft³

The top  Rectangular Prism has a lenght & with of 5 ft and a height of 10 ft.

So again 5x5x10 = 250 ft³

Now all we need is to add them all together:

125 + 500 + 250 = 875 ft³

Answer:

e

Step-by-step explanation:

The line crosses (1/2,0) and (0,4/7)

Let m be the slope of this line

● m = [0-(4/7)]/[(1/2)-0)]

● m = (-4/7)/(1/2)

● m = (-4×2)/7

● m = -8/7

So the slope of this line is -8/7

Answer:

b. 8a-35s

Step-by-step explanation:

Answer:

t-5 = Ned's age

Step-by-step explanation:

t = teds age

Ted is 5 years older than Ned

t = Ned +5

Subtract 5 from each side

t-5 = Ned

t-5 = Ned's age

ted = 5 tears older than Ned.

ted = t years.

→ t = Ned's age + 5

→ Ned's age + 5 = t

→ Ned's age = t - 5

So,

Then, t - 5 = Ned's age.

Answer: $1,500

Step-by-step explanation:

Let x represent the total income.

20% of the total amount = 300   -->  0.20x =  300

                                                          ÷0.20     ÷0.20

                                                                   x = 1500

Answer:

The total income is $1,500.

Step-by-step explanation:

$300 / 20% = $15       [ budget percent x 15 = budget amount in dollars]

Housing:            10 x 15 = $150

Food:                  30 x 15 = $450

Fuel:                    15 x 15 = $225

Clothing:            20 x 15 = $300

Health:                15 x 15 = $225

Miscellaneous:   10 x 15 = $150

Total Income:   150+450+225+300+225+150 = $1500

Answer: The answer is y=9 i did the math twice to make sure.

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

The equation is in the form:

Ax + By =C

3x + 2y = 18

y-intercept = C/B = 18/2 = 9

Answer:

GK = 10x+1

GH = 16.4

HK = 20.6

Step-by-step explanation:

Given the expressions 4x+2=GH, 6x-1=HK and GK = 37, according to vector addition GH + HK = GK

Substituting the functions into the formula we will have:

GK = 4x+2 + 6x-1

collect like terms

GK = 4x+6x +2-1

GK = 10x+1

The algebraic expression that represents GK is 10x+1.

To get the value of x, since GK = 37

10x+1 = 37

10x = 37-1

10x = 36

x = 36/10

x = 3.6

Since GH =4x+2, substitute x = 3.6 into the function

GH = 4(3.6)+2

GH = 14.4+2

GH = 16.4

Also HK = 6x-1

HK = 6(3.6)-1

HK = 21.6-1

HK = 20.6

Hence the algebraic expression that represents GK is 10x + 1 and the value GH is 16.4, HK is 20.6

Answer:

b = sqrt(161)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

8^2 + b^2 = 15^2

64 + b^2 = 225

Subtract 64 from each side

b^2 = 225-64

b^2 =161

Take the square root of each side

sqrt(b^2) = sqrt(161)

b = sqrt(161)

Answer:

C.  The number 5/11 is a rational number because it is a repeating decimal.

Step-by-step explanation:

The importance of this question is to distinguish a rational number from an irrational number.

A rational number can be written as a ratio or a set of repeating decimals.

An irrational number cannot be written as a ratio and cannot be represented by repeating decimals.

So out of the four options you have, the first two, A and B, are false, C is true, and D is false since rationality doesn't have anything to do with signs.

Cheers.

Answer:

Step-by-step explanation:

When you divide it through diagonals, you will get two congruent triangles ( Side Side Side congruent - SSS)

Answer: [tex]w=\dfrac{V}{lh}[/tex]

Step-by-step explanation:

Given: The formula for the volume V of a rectangular prism is V = ℓwh, where ℓ represents the length, w represents the width, and h represents the height.

We rearrange this formula by dividing  ℓh both sides of the formula to get the new formula for the width of the rectangular prism, we get'

[tex]w=\dfrac{V}{lh}[/tex]

Hence, the new formula for the width of the rectangular prism. :

[tex]w=\dfrac{V}{lh}[/tex]

Answer:

26.6°

Step-by-step explanation:

The area of a triangle is given by (1/2) * (base) * (height). The two triangles share the same height, so in order for the shaded triangle to have twice the area, its base must be twice that of the non-shaded triangle.

The non-shaded triangle is a right triangle with two 45° angles, so it's an isoceles right triangle with a base equal to its height.

This means that the height of the shaded triangle is 1/2 of its base. Knowing that we can get the angle of ACB with:

tan⁻¹(1/2) ≈ 0.4636476 (in radians)

Convert to decimal angle:

0.4636476 * (180/π) ≈ 26.6°