please help me with this

Answer:

Exact Distance = [tex]\frac{4\sqrt{10}}{5}[/tex]

Approximate Distance = 2.529822

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

Explanation:

This process is quite involved if you don't know the shortcut formula. I'll go over the long method first, and then show the shortcut in the next section.

First we'll need the equation of the line through points O and M. Use of the slope formula will show line OM has slope -1/3, which you are correct in stating.

Then use point slope form to determine the equation of line OM is y = (-1/3)x+11/3. This converts to the standard form x+3y = 11.

For anything in the form Ax+By = C, the equation perpendicular to this is of the form Bx-Ay = D. The A,B coefficients swap, and one item is negated. This helps form the negative reciprocal slope needed for the perpendicular line.

Compare x+3y = 11 to Ax+By = C. We see that A = 1 and B = 3.

So Bx-Ay = D turns into 3x-y = D. Then plug in the coordinates of H(-3,2) and compute to get

3x-y = 3(-3)-2 = -9-2 = -11. So D = -11

The equation 3x-y = D turns into 3x-y = -11 which is the equation of the line through point H and this line is perpendicular to line OM.

At this point, we have this system of equations

x+3y = 11

3x-y = -11

Solve that system however you wish. Substitution may be the best choice. Doing so leads to the intersection point (-2.2, 4.4)

The last step is to apply the distance formula between the points H(-3,2) and the intersection point (-2.2, 4.4)

The distance you should get is [tex]\frac{4\sqrt{10}}{5} \approx 2.529822[/tex]

I'm skipping steps because listing everything out would take up way too much space in my opinion.

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

The first section goes over a fairly lengthy process of finding the perpendicular distance. Luckily, there's a shortcut.

Consider an equation of the form Ax+By=C, aka standard form. Now consider a point P located at (m,n) that is not on the line Ax+By = C. We can find the distance from P to the line using this formula below

[tex]d = \frac{|Am+Bn-C|}{\sqrt{A^2+B^2}}[/tex]

In this case, A = 1, B = 3 and C = 11 found back in the previous section. So you'll still need to calculate the equation of line OM.

Also, we'll use (m,n) = (-3,2) which are the coordinates of point H

From here it's a fairly straightforward computation

[tex]d = \frac{|Am+Bn-C|}{\sqrt{A^2+B^2}}\\\\d = \frac{|1*(-3)+3*2-11|}{\sqrt{(1)^2+(3)^2}}\\\\d = \frac{|-8|}{\sqrt{1+9}}\\\\d = \frac{8}{\sqrt{10}}\\\\[/tex]

Optionally we can rationalize the denominator like so

[tex]d = \frac{8}{\sqrt{10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{10}\sqrt{10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{10*10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{100}}\\\\d = \frac{8\sqrt{10}}{10}\\\\d = \frac{2*4\sqrt{10}}{2*5}\\\\d = \frac{4\sqrt{10}}{5}\\\\d \approx 2.529822\\\\[/tex]

There are different ways to write down the answer, but they all represent the same number.

Answer:

y=1/2x-10

Step-by-step explanation:

X is the slope (1/2)

to find b=

-6=1/2(8)+b

-6=4+b. Subtract four from each side

-10=b

Answer:

x = -7

Step-by-step explanation:

-42=-7+5x

-42 + 7 = 5x

5x = - 35

x = -35/5

x = - 7

Hope it helps!

Answer:

x = -7

Step-by-step explanation:

Given equation:

[tex]-42 = -7 + 5x[/tex]

        [tex]-42 = 5x -7[/tex]

    2. Flip the equation.

        [tex]5x + 7 = -42[/tex]

    3. Add 7 to each side.

        [tex]5x - 7 + 7 = -42 + 7[/tex]

        [tex]5x = -35[/tex]

    4. Divide both sides by 5.

        [tex]\frac{5x}{5}[/tex] = [tex]\frac{-35}{5}[/tex]

    5. Divide the fraction.

        [tex]-35[/tex] ÷ [tex]5[/tex] = [tex]-7[/tex]

Answer:

x=11 I hope it helps you

Step-by-step explanation:

Answer:

4x - 3

Step-by-step explanation:

Givens

f(x) + g(x)

f(x) = 3x - 5

g(x) = x + 2

Equation

f(x) + g(x) = 3x - 5 + x + 2

Solution

f(x) + g(x) = 4x - 3 Collected like terms from the equation.

Remark

If you think of f(x) and g(x) as equal to different y values, it might help you to solve questions like this.

Answer:

7

Step-by-step explanation:

since a quartet consists of 4 people, it's basically asking how many groups of 4 can you make out of 30.

You can do this in your head or divide: 30 / 4 =7 r2

The given trigonometry proof is given below

(a)[tex]\frac{1}{1+\sin (\theta)}+\frac{1}{1-\sin (\theta)}=2 \sec ^2(\theta)[/tex]

Manipulating left side

[tex]$$\begin{aligned}&\frac{1}{1+\sin (\theta)}+\frac{1}{1-\sin (\theta)} \\&\text { Simplify } \frac{1}{1+\sin (\theta)}+\frac{1}{1-\sin (\theta)}: \frac{2}{(\sin (\theta)+1)(-\sin (\theta)+1)} \\&=\frac{2}{(1+\sin (\theta))(1-\sin (\theta))}\end{aligned}$$[/tex]

Rewrite using trig identities

[tex]=\frac{2}{\cos ^2(\theta)}[/tex]

Use the basic trigonometric identity: [tex]\frac{1}{\cos (x)}=\sec (x)[/tex]

[tex]$$=2 \sec ^2(\theta)$$[/tex]

(b)[tex]\frac{\cos (x)}{1+\sin (x)}=\sec (x)-\tan (x)[/tex]

Manipulating right side

[tex]$$\sec (x)-\tan (x)$$[/tex]

Express with sin, cos

[tex]=\frac{1-\sin (x)}{\cos (x)}[/tex]

Rewrite using trig identities

[tex]=\frac{\cos (x)}{1+\sin (x)}[/tex]

(c)Manipulating right side[tex]$\tan (x)-\cot (x)$[/tex]

Express with sin, [tex]$\cos$[/tex]

[tex]$$\begin{aligned}&=\frac{-\cos ^2(x)+\sin ^2(x)}{\cos (x) \sin (x)} \\&\sin ^2(x)=1-\cos ^2(x) \\&=\frac{1-\cos ^2(x)-\cos ^2(x)}{\cos (x) \sin (x)} \\&=\frac{1-2 \cos ^2(x)}{\sin (x) \cos (x)}\end{aligned}$$[/tex]

(d) [tex]\frac{\sin (x)}{1-\cot (x)}+\frac{\cos (x)}{1-\tan (x)}=\sin (x)+\cos (x)[/tex]

Manipulating left side

[tex]\frac{\sin (x)}{1-\cot (x)}+\frac{\cos (x)}{1-\tan (x)}[/tex]

Express with sin, cos

[tex]=\cos (x)+\sin (x)[/tex]

(e)Manipulating left side

[tex]\frac{2-\sec ^2(x)}{\sec ^2(x)+2 \tan (x)}[/tex]

Express with sin, cos

[tex]=\frac{-1+2 \cos ^2(x)}{1+2 \cos (x) \sin (x)}$$[/tex]

Rewrite using trig identities

[tex]=\frac{\cos (x)-\sin (x)}{\cos (x)+\sin (x)}$$[/tex]

(f)Manipulating left side [tex]$\cot ^2(x)-\cot ^2(y)$[/tex]

Express with sin, cos

[tex]=\frac{\cos ^2(x) \sin ^2(y)-\cos ^2(y) \sin ^2(x)}{\sin ^2(x) \sin ^2(y)}$$[/tex]

Rewrite using trig identities

[tex]=\frac{\cos ^2(x)-\cos ^2(y)}{\sin ^2(x) \sin ^2(y)}$$[/tex]

Trigonometry is the field of mathematics that deals with certain angles' functions and how to use such functions in computations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

The area of mathematics known as trigonometry examines the link between the ratios of a right-angled triangle's sides to its angles. Trigonometric ratios, such as sine, cosine, tangent, cotangent, secant, and cosecant, are employed to analyze this connection.

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Answer:

C. 8

Step-by-step explanation:

I almost thought this was going to be Pythagorean Theorem, but no.

Use Cosine Law:

cos θ =  [tex]\frac{10^2 + 21^2 - 17^2}{2(10)(21)}[/tex]

θ = cos−1(0.6)

θ = 53.130...

Now use the SOHCAHTOA ratio for sine ([tex]\frac{opposite}{hypotenuse}[/tex]) to find x now that you have one angle:

sin θ = [tex]\frac{x}{10}[/tex]

x = 10sinθ (θ isn't needed to be written out as it is shown in the equation above)

x = 8

Answer:

rise = -3

run = 4

rise/run = -3/4

Step-by-step explanation:

See figure for visual

The rise/run ratio gives the slope of the line

Take any two points on the line. I chose A(x1 = 2, y1 = 3) and B(x2 = 6, y2 = 0) as shown in the graph

For these two points the rise is (y2 - y1) = 0 - 3 = -3

The corresponding run is (x2 - x1) = 6 - 2 = 4

rise/run = -3/4 which is the slope of the line. This line has a negative slope - as x increases, y decreases

Not sure if that's what they are looking for.

Hope that helps

Answer:

$852

Step-by-step explanation:

From the given question, the following are given:

Present value, PV = $675

Rate, r = 6% = 0.06

Number of years, n = 2 years

Number of times per year, m = 2

The balance in his account is the future value (FV), so that;

Future value = PV[tex](1+r)^{nm}[/tex]

                     = 675[tex](1+0.06)^{(2*2)}[/tex]

                     = 675 x 1.26248

                     = 852.174

Future value = $852

Thus, the balance in Alex's account would be $852.

Answer:

x = ½

y = 3

Step-by-step explanation:

0,8 –4x = –0,4y ==> –4x + 0,4y = –0,8

6x + 0,4y = 4,2 ==> 6x + 0,4y = 4,2

______________–

–10x = –5,0

x = –5/–10

x = 1/2

–4x + 0,4y = –0,8

–4(½) + 0,4y = –0,8

–2 + 0,4y = –0,8

0,4y = –0,8 + 2

y = 1,2/0,4

y = 3

x = ½

y = 3

Follow my account^^

Order we can find the median is 56.

What is the mathematical mode?

A) 65 + 50+ 44+ 86 + 90 + 50+ 35 + 110 + 70 + 50 + 35 + 60+ 56/13

= 61.62

B) Arrange the number from small to large

35, 3,44,50,50,50,56,60,65,70,86,90,110

from this order we can find the median is 56.

c) we found that 50 was the most frequent acurrrence .

So, mode is 50.

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Answer:

A

Step-by-step explanation:

If you have s number of stools and c number of chairs, the price can be expressed as 50s + 65c. Since the question says you cannot spend more than 3000, you could spend less than or equal to 3000. So the inequality is 50s + 65c ≤ 3000.

Answer:

35 times 3= 105 times 4

Step-by-step explanation:

Answer:

$33.28

Step-by-step explanation:

Find the cost of 1 pound of peach by divind by 3 then times that cost by 8.

Answer:

The square root of a perfect square will always be a whole positive or negative number

Step-by-step explanation:

Answer:Hello! Here we have a cube, with a mass of 10g and a side length of 2.5cm.

First we want to determine the volume.

The volume of a cube, is equal to his cubic side length, where  L is the side length:

So  

So the volume of the cube is 15.625 cubic centimeters.

Now we want to calculate te density of the material, as you know:

This means that the density is 0.64 grams per cubic centimeter.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

1. Determine the value: V=L^3

so, (1.7)^3= 4.913

2. Calculate the density: mass divided by volume

10 divided by 4.913= 2.0

Answer: 2

Answer:

1/2

Step-by-step explanation:

1/2*1*1= 1/2

No, 4.379 is not a whole number, it is a decimal number.

Answer: No it is not a whole number.

Step-by-step explanation: Whole numbers are a set of numbers including all natural numbers and 0. They are a part of real numbers that do not include fractions, decimals, or negative numbers.

Answer:

y=4x+3 The slope is 4 and the y-intercept is 3

Step-by-step explanation:

Answer:

slope = 4, y- intercept = 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x + 3 ← is in slope- intercept form

with slope m = 4 and y- intercept c = 3

Answer:

12π

Step-by-step explanation:

The formula for arc length is given as:

[tex] s = \frac{\theta}{360\degree} \times 2\pi r[/tex]

Plug r = 24 and θ=π/2 in the above formula, we fi d:

[tex] s = \frac{\frac{\pi}{2}}{360\degree} \times 2\pi \times 24\\\\

s = \frac{\frac{\pi}{2}}{2 \pi} \times 48\pi\\\\

s = \frac{\pi}{2\times 2 \pi} \times 48\pi \\\\

s = \frac{\pi}{4\pi} \times 48\pi \\\\

\huge \purple {\boxed{s = 12\pi}} \\

[/tex]

Step-by-step explanation:

ghjkkknn. bjkkmn. bhcddfkkkk answer in image

Answer:

0.492 is the answer

Step-by-step explanation:

The probability that the two students are the same sex is 0.49.

Since the class contain 32 (18+14) children out of which  18 girls and 14 boys.

First step

Using general multiplication rule

P(Two girls)=P(First girls)×P(Second girl; First girl)

P(Two girls)=18/32×17/31

P(Two girls)=18×17/32×31

P(Two girls)=306/992

P(Two boys)=P(First boys)×P(Second boys; First boys)

P(Two girls)=14/32×13/31

P(Two girls)=14×13/32×31

P(Two girls)=182/992

Second step

Use addition rule for mutually exclusive events

P(Same sex)=P(Two girls)×P(Two boys)

P(Same sex)=306/992×182/992

P(Same sex)=306+182/992

P(Same sex)=488/992

P(Same sex)=61/124

P(Same sex)=0.49

Inconclusion the probability that the two students are the same sex is 0.49.

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Answer:

Figure 1: 98, 82

Figure 2: 64

Figure 3: 157, 23

Step-by-step explanation:

Figure 1: complementary angles theorem, coordinating angles theorem

Figure 2: vertical angles theorem

Figure 3: alternate interior angles theorem, complementary angles theorem

Let me know if this helped!

**please mark brainliest!!!

Answer:

no solution

Step-by-step explanation:

solve the equation

3x - 8 = 3(x-4) + 1    

3x - 8 = 3x - 11

3x + 3 = 3x

x + 3 = x

A number x plus 3 cannot equal a number x.        

the given equation has no solutions.

The equation 3x - 8 = 3(x - 4) + 1 is a linear equation. To determine the number of solutions, we can simplify and analyze the equation.

Expanding the right side of the equation, we have 3x - 8 = 3x - 12 + 1.

Simplifying further, we get 3x - 8 = 3x - 11.

By subtracting 3x from both sides, we have -8 = -11.

However, this leads to a contradiction. -8 is not equal to -11.

Since the equation leads to a contradiction, there is no solution to the equation.

In conclusion, the given equation has no solutions.

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Answer:

t-5=12

Step-by-step explanation:

Answer:

He pays taxes on the amount after the discount. So 10% of $40.50 versus $45.

Step-by-step explanation:

10% on $40.50 = $4.05

10% on $45.00 = $4.50

when you take 10% of $45, you're left with $40.50 because you'd do 40*10/100. when you go to add the 10% tax, you are no longer taxing $45, you're taxing $40.50 which is $4.05. 40.50+4.05=44.55