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[tex]~~~~\dfrac{12}{x^2 -49} \cdot \dfrac{x^2+9x+14}{9}\\\\\\=\dfrac{4}{x^2 -7^2}\cdot \dfrac{x^2 + 7x +2x +14}{3}\\\\\\=\dfrac{4}{(x+7)(x-7)} \cdot \dfrac{x(x+7)+2(x+7)}{3}\\\\\\=\dfrac{4}{(x+7)(x-7)}\cdot \dfrac{(x+7)(x+2)}{3}\\\\\\=\dfrac{4(x+2)}{3(x-7)}[/tex]

Answer:

[tex]\frac{4(x + 2)}{3(x - 7)}[/tex]

Step-by-step explanation:

Hello!

We can simplify this by factoring, and cross reducing.

The final simplified form is [tex]\frac{4(x + 2)}{3(x - 7)}[/tex]

Answer:because it’s like a quarter

Step-by-step explanation:

A quarter is 25c, 25•3=75

The probability of drawing three queens from a standard deck of cards is 0.000162.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Total cards = 54

No. queens in a deck = 4

Probability of drawing a queen card = 4/54

Now that 1 queen has been taken, the no. of cards becomes = 53

and

no. of queens = 3

Probability of getting a queen again = (3/53)(4/54)

Two queens have already been removed.

No. of cards in the deck = 52

No. of queens in the deck = 2

Probability of drawing three queens

= (2/52)(3/53)(4/54)

= 0.000162 approximately

The probability of drawing three queens from a standard deck of cards is 0.000162.

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Answer:

[tex]x = - \frac{7}{4} \: \frac{1}{2} [/tex]

Step-by-step explanation:

[tex]8 {x}^{2} + 14x - 4x - 7 = 0 \\ 2x(4x + 7) - (4x + 7) = 0 \\ (4x + 7)(2x - 1) = 0[/tex]

Answer:

[tex]\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}[/tex]

Step-by-step explanation:

Given: 8x² + 10x - 7 = 0

When factoring trinomials of the form ax² + bx + c:

1. Split the middle term:

⇒ 8 × -7 = -56 [multiply the leading coefficient and the last term]

⇒ 14, -4 [find the product factors that add to the middle term's coefficient]

⇒ 8x² + 14x - 4x - 7 = 0 [rewrite with those factors replacing the middle term.]

2. Factor by grouping:

⇒ 8x² + 14x - 4x - 7 = 0 [factor out 2x]

⇒ 2x(4x + 7) - 4x - 7 = 0 [factor out -1 or the negative sign]

⇒ 2x(4x + 7) -1(4x + 7) = 0 [factor out 4x + 7]

⟹ (4x + 7)(2x - 1) = 0

3. Separate into 2 cases:

Case 1:

⇒ 4x + 7 = 0 [subtract 7 from both sides]

⇒ 4x + 7 - 7 = 0 - 7

⇒ 4x = -7 [divide both sides by 4]

⇒ 4x ÷ 4 = -7 ÷ 4

⟹ x = [tex]\bold{-\dfrac{7}{4}}[/tex]

Case 2:

⇒ 2x - 1 = 0 [subtract 1 from both sides]

⇒ 2x - 1 + 1 = 0 + 1

⇒ 2x = 1 [divide both sides by 2]

⇒ 2x ÷ 2 = 1 ÷ 2

⟹ x = [tex]\bold{\dfrac{1}{2}}[/tex]

Solutions:

[tex]\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}[/tex]

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Answer:

3/4

Step-by-step explanation:

Scale factor is the ratio between two different triangles. They can be scaled if they are similar triangles, which they are (in this case). Since we know that these two triangles are similar, we want to match all the sides up in a way where they all have the same ratio.
NK=3 and AH = 4, so NK/AH = 3/4.
GK=6 and LH = 8, so GK/LH = 6/8 = 3/4.
GN = 15 and LA = 20, so GN/LA = 15/20 = 3/4.
We found the matching ratios, so the answer is 3/4.

Answer:

i think its 4.7

Step-by-step explanation:

Answer:

AC is an enlargement of AE

scale factor = 11.7 ÷ 5.2 = 2.25

CD is an enlargement of AB

10.5 ÷ 2.25 = 4.666666...

= 4.7 (rounded to nearest tenth)

Answer:

3 < x < 6

Step-by-step explanation:

1) Subtract 2 from the whole equation.

- 13 - 2 > -5x > -28 - 2

2) Simplify.

-15 > -5x > -30

3) Divide the whole equation by -5.

-15/-5 < x < -30/-5

4) Simplify.

3 < x < 6

Step-by-step explanation:

1. So first you have to cross multiple the two terms

2.Solve the algebraic equation

By dividing with 12 on both sides

(Note :That's a 32 in the picture sometimes i really write bad)

Answer:

Jan is not correct

Step-by-step explanation:

Rhombus and parallelogram both have their opposite angles to be equal and the opposite sides to be parallel but Rhombus has all its sides to be equal like the square while the parallelogram has only the opposite sides to be equal like the rectangle

This are function used to determine the term of a sequence. The second and the third term of the sequence is 6 and 18

This are function used to determine the term of a sequence. Given the following functions

an+1 = 3an

Given that a1 = 2

a2 = 3a1

a2 = 3(2)

a2 = 6

For the third term a3

a3 =3a2

a3 = 3(6)

a3 = 18

Hence the second and the third term of the sequence is 6 and 18

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The balloon's vertical distance above the ground is 430 feet.

You look straight parallel to the ground. But when you have to watch something down, then you take your sight down by moving your head up.

The angle from horizontal to the point where you stopped your head is called the angle of depression.

From a hot-air balloon, Brody measures a 39° angle of depression to a landmark that's 532 feet away, measuring horizontally.

The angle of depression = 39°

The base = 532

We need to find the vertical distance consider perpendicular.

[tex]\rm Tan \theta = \dfrac{perpendicular}{base } \\\\\rm Tan 39 = \dfrac{perpendicular}{532} \\\\\rm Tan 39 \times 532 =perpendicular\\\\0.80 \times 532\\\\P = 430.80[/tex]

Therefore, the balloon's vertical distance above the ground is 430.80 feet.

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Answer:

430.81

Step-by-step explanation:

hard way

Answer:

[tex]the \: probability \: is \: \frac{5}{60} \\ when \: simplified \: becomes \: \frac{1}{12} [/tex]

Step-by-step explanation:

The solution is in the image

If the hockey team scores 9 goals in their next game, it means that; the mean would be the most affected.

We are given the data set as;

3, 6, 2, 1, 2, 3, 0, 4, 5, 1, 5, 4.

Let us rearrange in ascending order to get;

0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6.

The mean = (0 + 1 + 1 + 2 + 2 + 3 + 3 + 4 + 4 + 5 + 5 + 6)/12 = 3

Median = (3 + 3)/2 = 3

Mode = 1, 2, 3, 3, 5

Now, if they score 9 goals in their next game, it means that;

Mean = 45/13 = 3.46

Median = 3

Mode remains the same

Thus, mean will be the most affected.

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Answer:

3

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

substitute b = 7 into the expression

2(10 - b)

= 2(10 - 7)

= 2(3)

= 6

Answer:

all you have to do is substitute

B. 6

Step-by-step explanation:

2(10-7)

2(3)

6

The correct answer is A. y - 3 = -6(x + 1) of the  linear equation in point-slope form for the line that goes through (-1,3) and (1, -9).

To write the linear equation in point-slope form, we need to use the formula:

[tex]y - y_1 = m(x - x_1),[/tex]

where [tex](x_1, y_1)[/tex] represents one of the given points, and m represents the slope of the line.

Step 1: Find the slope (m):

[tex]m = \frac {(y_2 - y_1) }{(x_2 - x_1)}\\= \frac {(-9 - 3)} { (1 - (-1))}\=\frac {-12 } {2}= -6.[/tex]

Step 2: Choose one of the given points (-1, 3), and substitute its coordinates into the point-slope form:

[tex]y - 3 = -6(x - (-1)).[/tex]

Step 3: Simplify and rearrange the equation:

[tex]y - 3 = -6(x + 1)\\y - 3 = -6x - 6.[/tex]

Therefore, the correct equation is A. y - 3 = -6(x + 1).

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Since the limit of f(x) is non-zero, the limit distributes over the quotient and

[tex]\displaystyle \lim_{x\to c} \frac{g(x)}{f(x)} = \frac{\displaystyle \lim_{x\to c}g(x)}{\displaystyle \lim_{x\to c}f(x)} = \frac{\dfrac15}{-4} = \boxed{-\frac1{20}}[/tex]

Answer:

Mean: 123

Median: 28

Mode: 23

Step-by-step explanation:

give brainliest

Answer:

Mean = 123, Median = 28 , Mode = 23

Step-by-step explanation:

Mean is the average of all the numbers.

Mean = [tex]\frac{3+721+23+63+27+29+95+23}{8} \\= \frac{984}{8} \\= 123[/tex]

Median is the middle most value of the numbers when arranged in ascending order. (Average of the 2 middlemost numbers if there are even number of values.)

Arranged Values: 3,23,23,27,29,63,95,721

Median = [tex]\frac{27+29}{2} \\= \frac{56}{2} \\= 28[/tex]

Mode is the value that occurs the most in the numbers.

Mode =  23

Answer:

Step-by-step explanation:

You save 25% on a $199 television. How much do you save?

25% = 1/4

so

199 : 4 = 49.75$

Answer:

You save $49.75

Answer:

  (smallest, largest) = (B, C), (D, E), (G, J)

Step-by-step explanation:

Side lengths of a triangle are proportional to the sine of the opposite angle. In a triangle, a larger angle will always have a larger sine. That means the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side.

__

The shortest side is 5 units, opposite angle B. The longest side is 7 units, opposite angle C.

The shortest side is 3 units, opposite angle D. The longest side is 5 units, opposite angle E.

The shortest side is 5 units, opposite angle G. The longest side is 5.1 units, opposite angle J.

_____

Additional comment

Angles in a triangle may exceed 90°. The sine function actually is decreasing for angles above 90°. However, since the total of angles of a triangle must be exactly 180°, there cannot be two angles in a triangle such that the smaller angle has the larger sine.

Answer:

x is 92 degrees

The lines x and a are parallel and congruent, meaning they are evenly proportioned and have the same length.

Answer:

  (4, -8)

Step-by-step explanation:

The components of a vector are found by subtracting the tail from the head.

__

  Head - Tail = (1, -6) -(-3, 2) = (1 -(-3), -6 -2) = (4, -8)

⇒ The component form is (4, -8), or maybe 4i -8j.

_____

Additional comment

There are many ways that the components of vectors can be described. The particular format you are expected to use will likely be found in your curriculum materials.

(4,-8) is the answer

Answer:

Below in bold.

Step-by-step explanation:

Petra uses the expression distance = time * speed

which is (4 + h)55    where 4 + h = total time for the 2 days.

Sierra uses the same expression but for each individual day and adds them:

4*55 + 55h

= 220 + 55h.

The amount paid for the computer including sales tax is 0.918p

The price paid is given as:

Price = p

A 15% off means that he pays 85%.

So, we have:

Amount = 85% * p = 0.85p

A sales tax of 8% means:

Total = 0.85p * (1 + 8%)

Evaluate the product

Total = 0.918p

Hence, the amount paid is 0.918p

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The correct interval notation for the continuous set of all numbers between 5 and 6, including 5, but not including 6 is [5, 6) option (C) is correct.

It is defined as the representation of a set of values that satisfy a relation or a function. It can be represented as open brackets and close bracket the close the brackets means the value is at the close bracket also included, and open bracket means the value at the open bracket does not include.

We have:

Continuous set of all numbers between 5 and 6, including 5, but not including 6.

From the above statement we can represent the number in the interval notation:

The numbers are between 5 and 6.

(5, 6)

As it is mentioned that 5 is included and 6 is not included, then:

[5, 6)

Thus, the correct interval notation for the continuous set of all numbers between 5 and 6, including 5, but not including 6 is [5, 6) option (C) is correct.

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Answer:

84.8

Step-by-step explanation:

Begin by finding the total area of the circle. You have been given the radius.

A = πr²

A = π(6)²

A = 36π

A = 113

If there is only 3/4 of the circle, then multiply the entire area by 3/4 to find the final answer.

113 x 3/4 = 84.8