Solve 6(x-3) + 7 = -5.
OA. X = 2
OB. x= 3
OC. X= 4
O D. x = 1

Using the Law of Cosines and the Law of Sines, we can find the remaining parts of the triangle with sides of lengths a = 9, b = 8, and c = 15. The angles of the triangle are approximately 32.5°, 57.0°, and 90.5°.

Let's start by using the Law of Cosines to find one of the angles. The Law of Cosines states that for any triangle with sides of lengths a, b, and c, and an angle opposite to side c, the following equation holds:

c² = a² + b² - 2ab*cos(C)

Plugging in the given values, we have:

15² = 9² + 8² - 2 * 9 * 8 * cos(C)

Simplifying this equation gives us:

225 = 81 + 64 - 144 * cos(C)

144 * cos(C) = 225 - 81 - 64

144 * cos(C) = 80

cos(C) = 80 / 144

cos(C) ≈ 0.5556

To find the angle C, we can take the inverse cosine (cos⁻¹) of 0.5556:

C ≈ cos⁻¹(0.5556)

C ≈ 57.0°

Now that we have one angle, we can use the Law of Sines to find the other angles. The Law of Sines states that for any triangle with sides of lengths a, b, and c, and angles A, B, and C (opposite to sides a, b, and c, respectively), the following equation holds:

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

Plugging in the values we know, we have:

sin(A) / 9 = sin(57.0°) / 15

Cross-multiplying and solving for sin(A) gives us:

sin(A) = 9 * sin(57.0°) / 15

sin(A) ≈ 0.5373

Taking the inverse sine (sin⁻¹) of 0.5373 gives us:

A ≈ sin⁻¹(0.5373)

A ≈ 32.5°

Finally, we can find the remaining angle B by using the fact that the sum of angles in a triangle is 180°:

B = 180° - A - C

B ≈ 180° - 32.5° - 57.0°

B ≈ 90.5°

Therefore, the angles of the triangle are approximately 32.5°, 57.0°, and 90.5°.

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The hypotenuse is 5 of a right triangle with legs of length3 and4

The Pythagoras theorem goes as follows:

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

a²+b²=c²

'A' and 'B' are the other two legs, and '=' is the hypotenuse of the right triangle. As a result, the Pythagoras equation can be used for any triangle that has one angle that is exactly 90 degrees to create a Pythagoras triangle.

Here: a=3,b=4

32+42=c²

9+16=c²

25=c²

=√25=5

So, the hypotenuse is 5

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Answer:

y=x+6; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6.

Step-by-step explanation:

Answer:

Its D

Step-by-step explanation:

y=x+6; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6.

Answer: B

Step-by-step explanation: 61 - (f x 14) would give us the number of french fries he had left over

Answer:

No

Step-by-step explanation:

See take 0.2 for example

In fraction it is 2/100 which can be easily reduced and should be reduced depending on the type of question.

1/50 would be the answer for my example.

Answer:

Im pretty sure its 5

Step-by-step explanation:

5:1 due to 20/4 would be 5. I can give you more of an explaination if needed.

Answer:

5 triangles to 4 circles.

Answer:

A ) x < 48

B ) X less than or equal to 8

C ) 4/5

Step-by-step explanation:

I hope this helps you out!

Answer:

you got it kinda just take away the shaded part for the angle <edf

Step-by-step explanation:

Answer:

The image has the area outlined that you should shade.

Step-by-step explanation:

Hope it helps and is correct!

385 sets of three teams { a , b , c } were there in which a beat b , b beat c , and c beat a.

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Given.

Assume that each team played 40 times, winning 20 games and losing 20 games. We can see that each side must have beaten each other once and won against each other once.

Combinations are:

As a result, if we choose any three teams, there will be just one set of games in which A defeats B, B defeats C, and C defeats A. As a result, we simply need to choose three teams from the available 21 options. (Remember that order is irrelevant to set notation.)

Thus

²¹C₃

= 21*20*19/3!

= 7*10*19

= 1330.

However, this is based on 40 games for each side. They actually only participated in 20 games, thus we divided this total by two (665) to arrive at the actual answer.

20 games were played by each side. There must be 21 teams because they cannot compete against one another.

Three-team groups can be chosen.

21!/3!18! = 1330 ways

During the round robin, each will have played the other.

For instance, AB, BC, and CA.

There are two typical results.

The other two players can be defeated by one person. Another winner and loser will result from those two players competing. A team will so win two games, lose two games, and win one game.

Alternatively, each side could have a win and a loss. The question is how many of those three-person groupings are there.

One team wins twice in the first scenario mentioned above. That means two of that team's victories. The games in the group have been chosen. This is achievable.

45 ways divided by 21 players from 10!/2!8! =

945 ways

Therefore, there must be 385 methods left over to represent the scenario in the question after deducting 945 from 1330.

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Answer: (a) 64°

(b) Yes, it is safe

Step-by-step explanation:

A fireman needs to get water to a second-floor fire. His ladder is 30 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.

(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest whole number and show all your work.

We solve the above question using the trigonometric function of Sine

sin θ = Opposite side/Hypotenuse sides

θ = Angle formed with the ground = ?

Opposite side = 27 ft

Hypotenuse side = 30 ft

Hence,

sin θ = 27 ft/30 ft

sin θ = 9/10 = 0.9

θ = arc sin (0.9)

θ = 64.158067237°

Approximately to the nearest whole number = 64°

(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 70°.Will the ladder be safe the way it is positioned?

From the above calculation, the angle the ladder makes with the ground is 64° and now we want that angle to be 70°

Hence:

64° < 70°

Therefore, the ladder will be safe the way it is positioned.

Answer:

A = 5 ;  B = 6

B = 7 ; C = 8

C = 9 ; D = 10

convert C:D where C is equals to C in B:C

C = 144 ; D = 160    

convert B:C where B is equals to B in B:C

C = 144 B = 126

convert A:B where B is equals to B in B:C

B = 126 A = 30

A = 30, B = 126, C = 144, D = 160

ratio

Step-by-step explanation:

The required answer to the subtraction problem 83,456 - 728.88 is, 82,727.12

Subtraction is mathematical terminology that helps and elaborates the decrease in the original value by some value.

Here,
To perform the subtraction, you line up the decimal points and subtract the digits in each place value starting from the right. In this case, you subtract 8 from 6, which requires borrowing 1 from the digit to the left, giving you 16 - 8 = 8 in the one's place. You then subtract 2 from 5, giving you 3 in the tenth place. Continuing this process, you get the result of 82,727.12.

Thus, the answer to the subtraction problem 83,456 - 728.88 is, 82,727.12

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Answer:

You did not provide the answer, so I did some research into this question.

Your possible answer is 700.

2,598,960 many different hands consisting of four queens and one king.

What is combination?

A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components

To choose 4 kings, there is only one way, and to choose a queen, there are four.

Thus, there are 4 different methods to draw the 5 cards as instructed.

The probability of drawing cards is taken into account while calculating the number of ways to draw 5 cards from a typical 52-card deck.

= 52!/(47!)(5!) = 2,598,960.

Hence,  2,598,960 many different hands consisting of four queens and one king.

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The 98% confidence interval for the true mean noise level is approximately (55.9, 57.1).

To find the 98% confidence interval for the true mean noise level, we can use the formula:

CI = mean ± Z * (σ / sqrt(n))

Where:

CI is the confidence interval,

mean is the sample mean,

Z is the z-score corresponding to the desired confidence level,

σ is the population standard deviation,

n is the sample size.

In this case, we have:

mean = 56.5 (sample mean)

σ = 3.5 (population standard deviation)

n = 180 (sample size)

Confidence level = 98%

First, we need to find the z-score corresponding to a 98% confidence level. The remaining 2% is split equally between the two tails of the distribution, so we have 1% in each tail. We can find the z-score using a standard normal distribution table or a graphing calculator. For a 98% confidence level, the z-score is approximately 2.33.

Now we can calculate the confidence interval:

CI = 56.5 ± 2.33 * (3.5 / sqrt(180))

CI = 56.5 ± 2.33 * (3.5 / 13.416)

CI = 56.5 ± 2.33 * 0.261

CI = 56.5 ± 0.607

CI ≈ (55.9, 57.1)

Therefore, the 98% confidence interval for the true mean noise level is approximately (55.9, 57.1).

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Answer:

the answer is A

hope this helsp

._.

Answer:

1111...................... ................

Answer:

c

ccccccccccccccccccccccccccccccccccccccccccccccccc

Answer:

0.06

Step-by-step explanation:

Answer:

8.4 cm

Step-by-step explanation:

Given that:

A right angled triangle, let \(\triangle ABD\). Right angled at \(\angle A\).

Altitude AC to the hypotenuse BD.

Length of side BC = 5 cm

Length of side CD = 11 cm

We have to find the value of shorter leg of triangle. i.e. side AB = ?

Using the concept of similarity, we can say the following:

\(\dfrac{AB}{BC} = \dfrac{BD}{AB}\\\Rightarrow AB^2=BC.BD\\\Rightarrow AB^2=5\times (5+11)\\\Rightarrow AB^2=5\times 16\\\Rightarrow AB^2=80\\\Rightarrow AB=\sqrt{80}\\\Rightarrow \bold{AB\approx 8.4\ cm}\)

The length of shorter leg of the triangle = 8.4 cm

Answer:

Region B & C

Step-by-step explanation:

Usually, in inequality graphs, the solutions are usually located in the shaded region of the graph.

Also, we make the boundary line thick if the points on that line also contain solutions to the inequality.

In this question, the boundary line of function g(x) is thick and the shaded region is B and C.

To find the Jacobian of the transformation, we need to calculate the partial derivatives of the new variables (x and y) with respect to the original variables (u and v). The Jacobian matrix is given by:

J = [ ∂x/∂u ∂x/∂v ]

[ ∂y/∂u ∂y/∂v ]

Let's calculate the partial derivatives:

∂x/∂u = 2 (since x = 2u)

∂x/∂v = 3v (since x = 3uv)

∂y/∂u = 0 (since y does not contain u)

∂y/∂v = 3u (since y = 3uv)

Therefore, the Jacobian matrix is:

J = [ 2 3v ]

[ 0 3u ]

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The expression for the volume of marble removed is (2t³/3).

The given information is as follows:

A sculptor cuts a pyramid from a marble cube with volume t^3 ft^3

The pyramid is t ft tall

The area of the base is t^2 ft^2

The formula to calculate the volume of a pyramid is,V = 1/3 × B × h

Where, B is the area of the base

h is the height of the pyramid

In the given scenario, the base of the pyramid is a square with the length of each side equal to t ft.

Thus, the area of the base is t² ft².

Hence, the expression for the volume of marble removed is given by the difference between the volume of the marble cube and the volume of the pyramid.

V = t³ - (1/3 × t² × t)V

   = t³ - (t³/3)V

    = (3t³/3) - (t³/3)V

   = (2t³/3)

Therefore, the expression for the volume of marble removed is (2t³/3).

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Answer:

Step-by-step explanation:

(

−

)

(

−

2

+

)

The approximate percent of the price increase is 8.5%.

A subwoofer box for sound costs $260.40 after a price increase. The cost before the price increase was $240.00. What was the approximate percent of the price increase?To calculate the percent increase, you can use the formula:percent increase = (new value - old value) / old value * 100In this case, the old value is $240.00 and the new value is $260.40. Therefore,percent increase = (260.40 - 240.00) / 240.00 * 100 ≈ 8.5%So, the approximate percent of the price increase is approximately 8.5%.Explanation:This is a problem involving percent increase.

The formula to calculate percent increase is:percent increase = (new value - old value) / old value * 100Let's plug in the given values. The old value is $240.00 and the new value is $260.40.percent increase = (260.40 - 240.00) / 240.00 * 100percent increase = 20.40 / 240.00 * 100percent increase ≈ 0.0850 or 8.5%Therefore, the approximate percent of the price increase is 8.5%.

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Answer:

Should be the first one. You have $5 flat fee and an additional 10 cents per text. Then you have a $10 flat fee and an additional 5 cents per text. so the first equation would be 0.1x + 5 and the second one would be 0.05x + 10

Answer:

V = 3 x 14 x 6 1/4 = 3 x 14 x 25/4 = 1050/4 = 525/2 = 262 1/2 ft

=> Option D is correct

Hope this helps!

:)

Answer:

\( 262 \frac{1}{2} \: {ft}^{3}\)

Step-by-step explanation:

\(l = 14 \: ft \: \: \\b = 6 \frac{1}{4} \: ft = \frac{25}{4} \: ft \: \: \\h = 3 \: ft \\ \\ V_{rectangular \: prism} = lbh \\ = 14 \times \frac{25}{4} \times 3 \\ = \frac{1050}{4} \\ = 262 \frac{1}{2} \: {ft}^{3} \)

An ounce unit will best represent each scenario.

The average weight of an elephant is around 3000-4000 kg.

The average weight of a mouse = 15-20 grams

The average weight of a puppy = 25-30kg

It is given that

Weight of the elephant = \(1.5 * 10^5\) units ≈150000 units

Weight of the mouse = \(6.3*10^2\) units ≈630 units

Weight of the puppy = \(1.2*10^3\) units ≈1200 units

1 ounce = 0.0253495 kg

150000 ounces = 3800kg, near to actual value

630 ounces = 16kg, near to actual value

1200 ounces = 30kg, near to actual value

Therefore, an ounce unit will best represent each scenario.

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Answer:

the answer should be 10