Factor completely. 486 +108 x + 6 x^2=

Answer:

<2= 23°

Step-by-step explanation:

180°- 95°= 85°

(95° is on a straight line, angles on a straight line adds up to 180° so 95° is being subtracted from 180°. Therefore the next angle in the triangle will be 85°)

To find <2

180- (85°+ 72°)

(Angles on a triangle adds up to 180°)

180- 157

= 23

Answer:

D

Step-by-step explanation:

We are given that:

[tex]\displaystyle \cos x = -\frac{1}{3}\text{ where } \pi /2 \leq x \leq \pi[/tex]

And we want to find the value of tan(2x).

Note that since x is between π/2 and π, it is in QII.

In QII, cosine and tangent are negative and only sine is positive.

We can rewrite our expression as:

[tex]\displaystyle \tan(2x)=\frac{\sin(2x)}{\cos(2x)}[/tex]

Using double angle identities:

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

Since cosine relates the ratio of the adjacent side to the hypotenuse and we are given that cos(x) = -1/3, this means that our adjacent side is one and our hypotenuse is three (we can ignore the negative). Using this information, find the opposite side:

[tex]\displaystyle o=\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}[/tex]

So, our adjacent side is 1, our opposite side is 2√2, and our hypotenuse is 3.

From the above information, substitute in appropriate values. And since x is in QII, cosine and tangent will be negative while sine will be positive. Hence:

Simplify:

[tex]\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{(1/9)-(8/9)}[/tex]

Evaluate:

[tex]\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{-7/9} = \frac{4\sqrt{2}}{7}[/tex]

The final answer is positive, so we can eliminate A and B.

We can simplify D to:

[tex]\displaystyle \frac{2\sqrt{8}}{7}=\frac{2(2\sqrt{2}}{7}=\frac{4\sqrt{2}}{7}[/tex]

So, our answer is D.

Answer:

$65

Step-by-step explanation:

Collin gets 4x dollars which equals 52, so 4x = 52

Dan gets 5x dollars which equals y (the answer). solve for x = 13. 5 • 13 = 65.

Answer:

35 metres

Step-by-step explanation:

The question states that A runs 25% faster than B. This means that, for every 1 second that B runs, A runs 1.25 second

Assuming that the total length of the race, that we're looking for, is D. Then we can say that B made a total distance of D-7 meters, and A runs D.

time taken by A = [tex]\frac{D}{1.25}[/tex]

time taken by B = [tex]\frac{D-7}{1}[/tex]

equating both together, we have

[tex]\frac{D}{1.25}[/tex] = [tex]\frac{D-7}{1}[/tex]

1.25D  - 8.75 = D

1.25D - D = 8.75

0.25D = 8.75

D = 8.75/0.25

D = 35

Answer:

740

Step-by-step explanation:

42% of 1761 = 0.42 * 1761 = 739.62

Answer: 740

Answer:

1

5

2

Step-by-step explanation:

4-3=1

8-3=5

5-3=2

Hope this helps! :)

Answer:

[tex]x=14[/tex]

Step-by-step explanation:

The given triangle is a right triangle, meaning it is a triangle with a right angle, this is indicated by the box around one of the angles. When given a right triangle, one can use the right triangle trigonometric ratios. These ratios describe the relationship between an angle in a right triangle, and the sides in a right triangle. Such ratios are as follows,

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]

Bear in mind that the way one names the sides, in the sense of (opposite or adjacent) will change based on the angle one uses to describe the triangle. However, the hypotenuse is the same no matter the angle, as the hypotenuse is the side opposite the right angle.

In this case, one is given one of the angles, and the side opposite the angle. One is asked to find the hypotenuse of the triangle. One can use the sine (sin) ratio to achieve this.

[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]

Substitute,

[tex]sin(30)=\frac{7}{x}[/tex]

Inverse operations,

[tex]x=\frac{7}{sin(30)}[/tex]

Simplify,

[tex]x=14[/tex]

Answer:

x = 121°

Step-by-step explanation:

∠ 1 + 115° = 180°

∠ 1 = 180 - 115

∠ 1 = 65°

∠ 2 + 304° = 360°

∠2 = 360 - 304

∠ 2 = 56°

∠ 1 + ∠ 2 + ∠ 3 = 180°

65° + 56 ° + ∠ 3 = 180°

∠3 = 180 - 65 - 56

∠ 3 = 59°

∠3 + x = 180°

59° + x = 180°

x = 180 - 59

x =  121 °

Answer:

Hi, there your answer is 13.592

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Given that a1 = 6

an =  3 + 2(an-1),

Substitute n = 2 into the formula

a2 = 3 + 2(a1)

a2 = 3 + 2(6)

a2 = 3+12

a2 = 15

Hence the second term of the sequence is 15

Answer:

6x-3

Step-by-step explanation:

that is the procedure above

Step-by-step explanation:

5+4X+2x-8

=6x-3

answer is third option

Answer:

190,000

190,000

190,000

Step-by-step explanation:

190,000

190,000

Answer:

below

Step-by-step explanation:

Rage =

highest value - lowest value

= 7 - 1

=6

Answer:

The list of these events from least likely to most likely is Blue-Blue -> Black-Blue -> Blue-Black -> Black-Black

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Possible outcomes:

Black - Black

Black - Blue

Blue - Black

Blue - Blue

Probability of each outcome:

Black-Black:

14 out of 20, and then 9 out of 12. So

[tex]P_{BkBk} = \frac{14}{20} \times {9}{12} = \frac{14*9}{20*12} = \frac{126}{240}[/tex]

Black-Blue:

14 out of 20, then 3 out of 12. So

[tex]P_{BkBl} = \frac{14}{20} \times {3}{12} = \frac{14*3}{20*12} = \frac{42}{240}[/tex]

Less likely than black-black.

Blue - Black:

6 out of 20, then 9 out of 12. SO

[tex]P_{BlBk} = \frac{6}{20} \times {9}{12} = \frac{6*9}{20*12} = \frac{54}{240}[/tex]

More likely than black-blue, less likely than black-black.

Blue - Blue

6 out of 20, then 3 out of 12

[tex]P_{BlBl} = \frac{6}{20} \times {3}{12} = \frac{6*3}{20*12} = \frac{18}{240}[/tex]

Least likely of the outcomes.

List these events from least likely to most likely:

The list of these events from least likely to most likely is Blue-Blue -> Black-Blue -> Blue-Black -> Black-Black

Answer:

6 and 4

Step-by-step explanation:

Answer:

Part A: 4 and x are factors of 4x

Part B: 6 and 4

Part C:  4

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

the figure shown is a parallelogram with a base length of 10 ft and a height of 7 ft

the area of a parallelogram can simply be calculated by multiplying the base length by the height

hence, area = 7 * 10 = 70

Answer: 10 times 7

Step-by-step explanation: 10 times 7

Answer:

ED = 6

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{ED}{BA}[/tex] = [tex]\frac{EF}{BC}[/tex] , substitute values

[tex]\frac{ED}{9}[/tex] = [tex]\frac{12}{18}[/tex] ( cross- multiply )

18 ED = 108 ( divide both sides by 18 )

ED = 6

Answer:

483.87yd^2

Step-by-step explanation:

Given data

Height= 4yd

Radius= 7yd

The expression for the surface area of a cylinder is given as

Surface area=  2πr (4+ 7)

Surface area= 2*π*7 (4 + 7)

Surface area = 14π (11)

Surface area= 154*3.142

Surface area= 483.87yd^2

Hence the surface area is 483.87yd^2

Answer:

x+14.  

Sum of a number and 14 is x+14.

Answer: 2) 15 square units

Step-by-step explanation:

The area of the triangle is 15 square units if the triangle ABC with altitude CD, given A (-3, -4), B (-6, 2), C (0, 0), and D (-4, -2) which is correct option (2)

The distance between two points is defined as the length of the line segment between two places represents their distance. Most significantly, segments that have the same length are referred to as congruent segments and the distance between two places is always positive.

The formula of distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by: d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².

Given that a triangle ABC with altitude CD.

The coordinates for the triangle are A (-3, -4), B (-6, 2), C (0, 0), and D (-4, -2)

Given that the distance between C and D will be the height of the triangle

Since, the distance between the points by using the distance formula:

= √ (x₂ – x₁)² + (y₂ – y₁) ².

height = √ (-4 – 0)² + (-2 – 0) ²

height = √20

base = √45

Area of triangle = (1/2)base x height

Area of triangle = (1/2)√20×√45

Area of triangle = (1/2)30

Area of triangle = 15 square units

Hence, the area of the triangle is 15 square units if the triangle ABC with altitude CD

Learn more about distance between two points here:

https://brainly.com/question/15958176

#SPJ2

Answer:

28cm

Step-by-step explanation:

Area of a parallelogram equals the base length, which is y cm, multiplied by the height, which is 18cm.

So

Area= 504cm

y cm (base) x 18 cm (height) = 504cm^2 (area)

y cm = 504cm^2 / 18cm

y cm = 28cm

Answer:

28 cm

Step-by-step explanation:

Just use some good ol' algebra:

18y = 504

y = 28 cm

A parallelogram is basically a wonky rectangle, so it uses the same formula for area.

C. -1

Hope this helps! :)

______________

Answer:

-1

Step-by-step explanation:

Simplify the real and imaginary parts of the expression. That’s probably as simple as i can get it.

Hope this helps! :)

Hey there!

ASSUMING….
-14.4 = -1.2m

-1.2m = -14.4

DIVIDE -1.2 to BOTH SIDES

-1.2m/-1.2 = -14.4/-1.2

SIMPLIFY IT!

m = -14.4/-1.2

m = 12

Therefore, the answer should be:

m = 12

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

13a + 6b

Step-by-step explanation:

Given

(a + 3b) + 3(4a + b) ← distribute parenthesis

= a + 3b + 12a + 3b ← collect like terms

= 13a + 6b

Answer: 13a+3b+18

Step-by-step explanation:

First distribute the 3 to 4a+b

Then you get 12a+18

Add 12a+18 with a+3b

Answer:

B

Step-by-step explanation:

I'm pretty confident that it is B

Answer:

sorry this question is confusing

Step-by-step explanation:

Answer:

a) -6

b) 3

c) Y = -6x + 3

Step-by-step explanation:

Pick two points and find rise/run = slope

rise y1 - y2 = 9 - 3 = 6

run x1 - x2 = -1 - 0 = -1

slope = 6 / -1 = -6

The y intercept is where x = 0 which is given in the table (0,3) so

y intercept = 3

Point slope form is y = mx + b , so

y = -6x + 3

Answer:

A minimum of 16 dollhouses

Step-by-step explanation:

profit on each dollhouse= sp-cp= 29-17= $12

if we divide 184 by 12 we get abt 15.33, which means, she has to sell more than 15 Dollhouses to make a profit.

so the minimum number of dollhouses to be sold are 16

number a is too low so we will work with c after all I put that and got it eight

Your answer is C. - 972

I found 3 by dividing 36 by 12. I hope the image is self- explanatory.