Select the correct answer
Which statement is true about the slope of the graphed line?

A the slope is negative B the slope is positive. C the slope is negative D the slope is undefined

Answer:

This is an obtuse scalene triangle with the length of E measuring around 749 cm.

<D = 54.754° ≈ 55°

<E = 114°

<F = 11.246° ≈ 11°

Side D = 670 cm

Side E = 749.46937 cm ≈ 749 cm

Side F = 160 cm

Explanation:

When given two sides, and an angle, we can use trigonometry to find the missing angles, and sides.

Given the triangle ∆DEF with side D measuring 670 cm, side F measuring 160 cm, and angle E measuring 117°, we can apply the law of sines to identify the missing information. A & a chronologically refers to the first angle, and side. B & b chronologically refers to the second angle, and side. And C & c chronologically refers to the third angle, and side.

a / Sin (A) = b / Sin (B) = c / Sin (C)

[side 1]. [side 2]. [side 3].

↓ ↓ ↓

sideD/sin(<D) SideE/sin(<E) SideF/sin(<F)

______________________________

670cm / Sin(D) = E cm / Sin(114) = 160 / sin(F).

Since we are only given two sides with an angle measure, we can refer to the law of cosines to figure this one out.

It states that A = arccos(b²+c²-a²/2bc) → cos(A) = b²+c²-a²/2bc

B = arccos(a²+c²-b²/2ac) → cos(B) = a²+c²-b²/2ac

and C = arccos(a²+b²-c²/2ab) → cos(C) = a²+b²-c²/2ab

capital A, B, and C are angles A, B, and C.

lowercase a, b, and c are sides a, b, and c.

Therefore c² = a² + b² − 2ab cos(C),

b² = a² + c² - 2ac cos (B), and a² = b²+c² - 2bc.

SOH CAH TOA.

Since we know this, we can solve for pretty much everything as long as we are given at least 3 variables. Chronologically, because we are solving for side e, we must use b² = a² + c² - 2ac cos (B), because the rest are only variables we are given, making it easy to solve. So b² = 670² + 160² - 2(670 × 160) × cos(114°) = 561704.3362754.

Now take the square root of that to get b by itself, so √561704.3362754.... = 749.4693698046.... ≈ 749

Answer:749

Step-by-step explanation:

S.A.S law or Cosines

e=561704.33628= 749.469= 749

Answer:

23

Step-by-step explanation:

15% of 20 = 3  then add the 3 to the 20 to get 23

23Answer:

Step-by-step explanation:

15/100*20 = 3

20+3 = 23

Answer:

$6.18 per hour

Step-by-step explanation:

You can get this number by multiplying 0.03 by 6

Answer:

x = 20

Step-by-step explanation:

Assuming you require the value of x

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

7x - 15 is an exterior angle of the triangle, thus

7x - 15 = x + 28 + 4x - 3 , that is

7x - 15 = 5x + 25 ( subtract 5x from both sides )

2x - 15 = 25 ( add 15 to both sides )

2x = 40 ( divide both sides by 2 )

x = 20

Answer:

80%

Step-by-step explanation:

300/3=100

60/3=20

100-20=80

Answer:

[tex]S : T = 5 : 8[/tex]

Step-by-step explanation:

Represent the first half with F and the second with S

We have that:

[tex]F = 9[/tex] --- From the first statement

[tex]S = 2F - 3[/tex] --- From the next statement

Required

Determine the ratio of S to the total point

First, we need to determine the value of S

Substitute 9 for F in [tex]S = 2F - 3[/tex]

[tex]S = 2 * 9 - 3[/tex]

[tex]S = 18 - 3[/tex]

[tex]S = 15[/tex]

Next, we determine the total points

[tex]Total = F + S[/tex]

[tex]Total = 9 + 15[/tex]

[tex]Total = 24[/tex]

The ratio of S to total is: (Represent total with T)

[tex]S : T = 15 : 24[/tex]

Divide both ration by 3

[tex]S : T = 15/3 : 24/3[/tex]

[tex]S : T = 5 : 8[/tex]

Hence, the ratio is 5 to 8

Answer:

holy,  thats hard, I will try to do it for you

Step-by-step explanation:

Answer:

The mother is wrong

Step-by-step explanation:

What we do here will be to add the fractions of the cakes that we have

Mathematically, that will be;

14/12 + 5/6 = 24/12 = 2

This means that the mother is wrong and the cakes can actually be made into 2

Answer:

[tex]\sqrt{3}:3\\1:\sqrt{3}[/tex]

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios. There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant, and cotangent.

The longest side of the triangle is called the hypotenuse and the other two sides are the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.

The tangent ratio is defined as:

[tex]\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]

The cotangent ratio is defined as:

[tex]\displaystyle \cot\theta=\frac{\text{adjacent leg}}{\text{opposite leg}}[/tex]

As shown above, the tangent and the cotangent are the ratios of the two legs in any possible order.

If the triangle has angles of 30°, 60°, and 90°, then we can take one of the acute angles and find the tangent and cotangent to know the required ratios:

Let's take for example the 30° angle:

[tex]\displaystyle \text{ratio of legs: }\tan 30^\circ=\frac{\sqrt{3}}{3}[/tex]

[tex]\displaystyle \text{ratio of legs: }\cot 30^\circ=\sqrt{3}[/tex]

Thus the possible ratios from the list are:

[tex]\sqrt{3}:3\\1:\sqrt{3}[/tex]

The reciprocals of those ratios are also applicable

Answer:

g ∈ ∅

Step-by-step explanation:

Expand the expression

30 g + 12 = 30  

Cancel out the 30g on both sides

12 = 0

Decide whether the statement is true or false

g ∈ ∅

Answer:

6.5%

Step-by-step explanation:

2,015/31,000 = .065

Answer: 120

Step-by-step explanation:

From the question, we are informed that there are 10 people in a math club and that three people will be chosen for the Pi Day committee.

The number of different ways that the club members can structure the committee goes thus:

This can be solved by:

nCr = n! / r! (n - r)!

where n = 10

r = 3

= n! / r! (n - r)!

= 10! / 3! (10 - 3)!

= (10 × 9 × 8) / (3 × 2)

=120

Answer:

ANSWERS ARE B, C, AND D.

Step-by-step explanation:

I found the unit rate of 350 and 5, because we can use a calculator (as stated on top) I just punched in 350 divided by 5 and got 70. Now i know this may not sound that "professional", but nothing needs to always be professional as long as its efficient and most importantly gets you the right answer. I then took the time to multiply each number, (the ones on the left : 3, 3.5, 6, 7.25, and 8) by 70. If the answer you got on the calculator match up to the number on the right, (240, 420, 507.50, and 490) its correct, if it doesn't match up, you can tell that its most likely not the answer. You should end up with three answers that all end up having the unit rate of 70. Hope this helps anyone who needed it.

ANSWERS ARE B, C, AND D.

Answer:

The answer is B,C, And D

Step-by-step explanation:

I just saw it on Khan and got it right.

Answer:

Its A

Step-by-step explanation:

Trust me

Answer:

a

Step-by-step explanation:

Answer:

16 hours

because in 16 hours 2 inches per hour it will overflow

Answer:

The answer is D.

Step-by-step explanation:

Answer:

X ≥ 12, (Or A)

Step-by-step explanation:

First, you would do two step equation.

3-2x     ≥   -17

+3        |     +3

----------|------------------

-2x      ≥       -14

Then you divide each side by -2

And you get, X≥12

Which, does not represent any of the graphs.

Answer:

C is correct

Step-by-step explanation:

3+6=9

2 sides on a triangle must be greater than the other side

Answer:

the answer is A. $32.23

Step-by-step explanation:

Answer:

$32.00

Step-by-step explanation:

To find the sales tax always multiply the sales tax to to the cost of you item.

Being your sales tax is 4%  you will Multiply 30.99 x .04 (not just 4)

30.99 x .04 = 1.2396  ( round to the nearest tenth) since the number after the 3 is 5 or above ,,,,round it off to 24...Making it $1.24 (tax)  Now add that to your cost of the shoes

$30.99 + $1.24 = $32,23

For future :  if the tax is 10, 20, 35%... You will multiply the cost of item by .10, .20, .35 (put the point in front of it .

Answer:

D

Step-by-step explanation:

I'm not entirely sure if I'm correct but from what I gathered I'm pretty sure it's D.

Answer:

The answer is 3

Hope this helps!

Answer:

The influence is there is none

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

C) A car can travel 80 miles on 2 gallons of gasoline.

Step-by-step explanation:

They gave us the unit rate which is 40 mile/1 gallon of gasoline. With the unit rate, we can then simplify each answer choice.

Simplified version of answer a: 1 mile/40 gallon of gasoline (we know it is wrong because it doesn't match with the unit rate.)

Simplified version of answer b: 41 mile/ 1 gallon of gasoline (we know it is wrong because it doesn't match with the unit rate.)

Simplified version of answer c: 40 miles/1 gallon of gasoline (this one is the correct answer since it matched the unit rate.

Simplified version of answer d: 40 miles/ 20 gallon of gasoline  (we know it is wrong because it doesn't match with the unit rate.)

Hope this helped you : )

Answer:

Quotient/Answer = 402

Hence the first digit is 4 and it's place value = hundreds

Step-by-step explanation:

Quotient = Dividend ÷ Divisor

Dividend = 3216

Divisor = 8

Quotient = 3216 ÷ 8

= 402

We are asked to find the place value of the first digit

Hence the first digit is 4 and it's place value = hundreds

Answer:

the answer is 56

Step-by-step explanation:

Answer:

The measure to angle 2 is 44.

Step-by-step explanation:

The segment towards the bottom is a straight line meaning it should equal 180°. 180 - 68 = 112. A triangle should equal 180° as well... so you add 112 to 24, then subtract that value from 180: 180 - 136 = 44

Answer:

Step-by-step explanation:

4 boxes with 7 pencils each

26

4*7 = 28

He has 28 pencils in total.

Number of extra pencils

= 28 - 26 = 2

Hope this helped,

Kavitha Banarjee

Answer:

<6 and <8

<1 and <7

Step-by-step explanation:

Supplementary are angles that add up to 180 degrees. (A straight line)

Answer:

Multiply both terms of the numbers

hense you would do: 2(9a + 12) = 18a + 24

It doesn't have to be 2 however. If can be any number you want it to be

Step-by-step explanation:

Answer:

12+9a is equivelent to 9a+12 :-)

Step-by-step explanation: