If the ratio of teachers to students on a field
trip is 3:40. How many teachers are on the field
trip if there are 160 students present?

Answer:

y = -(5/2)x + 3 is a line perpendicular to y = (2/5)x + 2. This line is also perpendicular to y = (2/5)x + 9 because it has the same slope.

Step-by-step explanation:

A) So the line you are given is written in slope intercept form y = mx + b meaning that the slope of the line is  m = 2/5 and the intercept  b = 9 (so the line hits the y axis at 0,9). A line that is parallel has to have the same  slope so we know our m is the same. So we have y = (2/5)x + b. We need b. It passes (0, 2) since the x coordinate is 0 you know the y intercept is 2 but you can verify this using the point slope formula:

y - y1 = m(x - x1) plug in values

y - 2 = (2/5)(x - 0) now simplify

y - 2 = (2.5)x  last solve

y = (2/5)x + 2 see how when the x coordinate is 0 you can automatically use the point slope intercept formula? Neato!

B) Now we want a line perpendicular to y = (2/5)x + 2 and that passes through 0,3. What are the properties of a line perpendicular to a line of the form y = mx + b and passes through (0, 3)?  We know that the slope of this new line will be the reciprocal and have the opposite sign of m. So the new slope we will call it mnew = -(1/m) so plug in for m and you get mnew = -(1/[2/5]) if you simplify you get that the mnew = -(5/2). So we have half of our equation for the perpendicular: y = -(5/2)x + b. If you look at (0, 3) you see that the y intercept is 3 so b = 3. So:

The equation of the line that passes through given point and is parallel to the line with the given is y = 2x-1

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, we need to find the equation of a line passing through the point (3, 5) and is parallel to y = 2x-6,

Comparing the given equation with the general equation of line y = mx+c

m = 2 (the slope)

We know that the two parallel lines have equal slope.

Therefore, the required equation is =

y = 2x+c

To find the value of c, put x = 3 and y = 5,

5 = 2(3) + c

c = -1

Therefore,

The required equation is =

y = 2x-1

Hence, the equation of the line that passes through given point and is parallel to the line with the given is y = 2x-1

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Answer:

yufcyiciygciykgc, nbhgcv

Step-by-step explanation:

98yfgouyfuchkgcbvkhgcihdiytdiytditdytdiytdityghvhgcxdfsrtyuhkjbhcgfdxzsaewrsdxfhgyujkhjmnb cvngfjkhji

Answer:

2/3 x 12 = 8/x

8x

Answer:

[tex]x=\frac{20}{3} =6.67[/tex]

Step-by-step explanation:

[tex]x=15*\frac{4}{9}=\frac{20}{3} =6.67[/tex]

Answer:

6 2/3 or 20/3 or 6.6667

Step-by-step explanation:

Since the figures are similar, you can find x through comparing ratios. To get from 9 to 4, multiply 9 by 4/9. To find x, you must then multiply 15 by 4/9.

15 x 4/9 = 6 2/3 or 20/3 or 6.6667

Answer:

x can be 14 or more

Step-by-step explanation:

Answer:

x>13! I hope I helped? :')

Steps for answer!

1. Subtract 11 from both sides.

24−11<x

2. Simplify  24-11 to 13.

13<x

3. Switch sides.

x>13

Answer:

20

Step-by-step explanation:

Answer:

1/5=20%

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

☺

Answer:

Step-by-step explanation:

To solve this you need the Law of sines

a, b, c are the sides opposite to angles A, B and C respectively

Applied to the given triangle we have one side given, the opposite angle to be found.

Answer:3Y+6=12

3(2)+6=12

Step-by-step explanation:Because 3 + 3 is 6 So That means that you repeat the pattern 4 times 3 Times 4 equals 12

Answer:

♥️♥️♥️

3434

Step-by-step explanation:

sana makatulong

Givn : OK = 3, OJ = 30, KN = 1, JM = 3

ON=OK+KN=3+1=4

OM=OJ+JM=30+10=40

In triangles OKJ & ONM,

OKOJ=330=110

ONOM=440=110

Angle O is common in both the triangles.

Two sides are in same proportion and the included angle is common (SAS) . Hence both the triangles are similar.

That means KJNM=110 or the two sides are parallel.

Hence ˆK=ˆN,ˆJ=ˆM corresponding angles.

Two sides in each triangle that are proportional to each other, and a corresponding included angle in both triangles that are congruent, both triangles are similar.

Recall:

Two triangles can be proven to be similar by the SAS Similarity Theorem, if they both have two pairs of corresponding side lengths that are proportional to each other and also have a corresponding included angle that is congruent to each other.

Using the image given, let's determine if two of the given side lengths of each triangle are proportional to each other.

Given:

[tex]\frac{OM}{OJ} = \frac{ON}{OK}[/tex]

[tex]\frac{40}{30} = \frac{4}{3}[/tex] (proportional)

Also, <NOM and <KOJ are congruent to each other (included angles).

Therefore, since we have two sides in each triangle that are proportional to each other, and a corresponding included angle in both triangles that are congruent, both triangles are similar.

The similarity statement is: [tex]\triangle NOM \sim \triangle KOJ[/tex]

Theorem: Side-Angle-Side Similarity Theorem (SAS)

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Answer:

6 < 2n = 4

Step-by-step explanation:

ig

Answer:

a) [tex]\frac{10}{21}[/tex]

b) [tex]\frac{1}{2}[/tex]

c) [tex]\frac{16}{25}[/tex]

d) [tex]\frac{10}{27}[/tex]

e) [tex]\frac{80}{209}[/tex]

f) [tex]\frac{29}{50}[/tex]

Step-by-step explanation:

Ratio means to divide in simple terms, therefore you divide each value by the other.

Answer:

Sum of all angles of a triangle is 180

so we can have our equation as-

65+65+x=180

x=180-130

x=50

Hope it helps

Answer:

15

Step-by-step explanation:

The first thing we have to do is find angle A

I will assume that you know SOH CAH TOA (if not ,ask)

We will use TOA

Tan(angle)=5/10

angle= 26.565

Now that we know angle A we will look at these two triangles as one big one

We know that side CA=30 and that anglea=26.56 so we can use TOA again

Tan(26.565)=x/30

30tan(26.565)=x

x=15

Answer:

the answer is 15

Step-by-step explanation:

Answer: d

Step-by-step explanation:

Answer:

The answer is 3

Step-by-step explanation:

3/4x4 =3

4 x 3/4 = 3

All you are doing is reducing the numbers with the greatest common factor which is the number 4.

Answer:

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Answer: 213 2/3 miles

Step-by-step explanation:

first we need to set up an equation to solve

let your equation be in y=mx+b form since we are using a rate

Since this is a word problem, dissect it and match each part with a variable in the slope-intercept equation

y = Budget

m = rate

x = how many miles she can go -- the unknown variable

b = the initial fee

Your equation should be: 50 = 0.15x + 17.95

We want to soIve for x now so first get rid of the coefficient not attached to it

To do this, you do the inverse function of addition, which is subtraction

Subtract 17.95 from both sides

Your new equation will be: 32.05 = 0.15x

0.15 is still attached to x, so we want to do the inverse function of multiplication, which is division

divide both sides by 0.15

Your final answer: 213 2/3 miles

Answer:

[tex]10n \le 30[/tex]

[tex]n \le 3[/tex]

Step-by-step explanation:

Given

[tex]Total = \$30[/tex]

[tex]Cost (each) = \$10[/tex]

Required

Determine the inequality

Assume she wants to buy n CDs.

If 1 CD costs $10, then n CDs costs 10n.

So, the inequality is:

[tex]10n \le 30[/tex]

We used [tex]\le[/tex] because the amount she wants to spend cannot exceed 30

Divide both sides by 10, to solve for n

[tex]n \le 3[/tex]

Answer:

Y = negative x + 9

Step-by-step explanation:

Find the equation of the line for side S-

m= 4-1/1-4 = 3/-3 = -1

The Gradient is -1

Since parallel lines share the same gradient, it should be either of the first two options.

We can see side Q shares the same gradient: 3-6/6-3= -1

Find the equation of the line of side Q-

y-y1= m(x-x1)

y-6= -1(x-3)

y-6=-x+3

y= -x+9

Answer:

a

Step-by-step explanation:

Answer: No

Step-by-step explanation:

4.8%

=> 4.8 / 100

=> 4.8 = 0.048

Answer:

given :

y= 3x,

-3x-y = -24.

now just substitute the values

since y = 3x,

-3x-3x = -24

Answer:

  D.  8/2 +(-10)² = 104

Step-by-step explanation:

To find which statements are true, evaluate the expression for the given variable values. You do this by putting the numbers in place of the respective variables, then doing the arithmetic.

The respective expression values are ...

  A 83 ≠ 37 . . . . (4/2) +9² = 2 +81 = 83

  B 31 ≠ 61

  C 52 ≠ 61

  D 104 =104 . . . . true statement

__

I find it less tedious to write a function into a calculator or spreadsheet and let it do the repetitive math. Examples of the calculation are shown above.

Answer:

a. You are looking for an annuity that will give $41,000 in 5 years with a quarterly compounding rate of 4.25%.

Convert periods and interest to quarterly rate.

Period = 5 * 4 = 20 quarters

Interest = 4.25 / 4 = 1.0625‬%

41,000 = Annuity * ( [ 1  +  i ] ^n - 1 )/i

41,000 = Annuity * ( [ 1 + 1.0625%]²⁰ - 1) / 1.0625%

41,000 = Annuity * 22.1534596596

Annuity = 41,000 / 22.1534596596

= $1,851

b. There were 20 payments of $1,851 made which totals:

= 1,851 * 20

Cash from deposits = $‭37,020‬

Cash from interest = 41,000 - ‭37,020‬ = $3,980

Answer:

7x * 14

Step-by-step explanation:

hope this helps :)

4x - 14= -3

hope this helps! (:

Answer:

14 - 4x = -3

Step-by-step explanation:

Hope this helps. B)

Answer:

it is a distributive property