6/17
2
The equation F = 9/5 C + 32 is used to convert Celsius temperature to Fahrenheit
temperatures. C is the temperature in degrees Celsius. What is the temperature in
degrees Fahrenheit when the temperature in 35 in Celsius?
76
59
67
95

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:

Step-by-step explanation:

As all edges of a cube are expanding at a rate of 2 centimeters per second.

i.e ds/dt = 2 cm/s

The formula of volume of cube: V = s³

Differentiating the volume:

dv/dt = 3s²

Write ds/dt following derivative of volume

dv/dt = 3s² ds/dt

plug in the value: ds/dt = 2 cm/s

dv/dt = (3s²) (2)

dv/dt = 6s²

Given the edge is 2cm.

so plug in the value: s=2

dv/dt = 6s²

          = 6(2)²=6(4)=24 cm³/per second

SIMILARLY,

When the edge is 14cm

dv/dt = 6s²

plug in the value: s=14

dv/dt = 6s²

         = 6(14)²=6(196)=1176 cm³/per second

Thus,

The volume will be:

(a) 24 cm³

(b) 1176 cm³

Given:

Expanding rate,

Let,

(a)

When,

then,

→ [tex]\frac{dx}{dt} = 2 \ cm/sec[/tex]

Let,

→ [tex]V = x^3[/tex]

→ [tex]\frac{dV}{dt} = 3x^2 \frac{dx}{dt}[/tex]

        [tex]= 3\times 2^2\times 2[/tex]

        [tex]= 3\times 4\times 2[/tex]

        [tex]= 24 \ cm^3[/tex]

(b)

When,

then,

→ [tex]\frac{dx}{dt} = 2 \ cm/sec[/tex]

Let,

→ [tex]V = x^3[/tex]

→ [tex]\frac{dV}{dt} = 3x^2 \frac{dx}{dt}[/tex]

        [tex]=3\times 14^2\times 2[/tex]

        [tex]= 1176 \ cm^3[/tex]

Thus the above answer is correct.

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Answer:

x=11 I hope it helps you

Step-by-step explanation:

Answer:

C.) 120 or Option C is incorrect.

The answer is B.) 110

Step-by-step explanation:

See screenshot below

Hope this helps!

- ❤ 7272033Alt ❤

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:

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: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

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:

$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^^

Answer:

94

Step-by-step explanation:

Answer:

T<5,-2>

Step-by-step explanation:

It goes to the the right 5 and down 2 but it is put in a proper format

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:

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:

$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:

it has to be whole numbers

Step-by-step explanation:

because all of them are whole number no matter if there negative or positive

Answer:

D

Step-by-step explanation:

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:

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:

(-4,-3)

Step-by-step explanation:

Answer: D) No; If x is 5, the expression on the left simplifies to 8, making the inequality false.

In other words, if x = 5, then x+3 becomes 5+3 which ultimately becomes 8, but this is not greater than 8 on the right side.

Your steps could look like this

x+3 > 8

5+3 > 8 ... replace x with 5

8 > 8 ... this is a false inequality

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

Answer:

C. Graph B

Step-by-step explanation:

y ≥ 2x + 3

y ≤ -2x - 4

To find which side of the line the answer is, we can set y and x to 0 and see if the equation is true or false (this only works if the cordance of (0,0) does not lie on the line)

0 ≥ 2(0) + 3

0 ≥ 3 FALSE (the side of the line that should be shaded is the one that does not include the cordance of (0,0))

0 ≤ -2(0) - 4

0 ≤ - 4 FALSE (the side of the line that should be shaded is the one that does not include the cordance of (0,0))