Parallel lines p and q are intersected by transversal r, as show.

The LCD of the rational equation [tex]-\frac{3}{x + 2} + \frac{5x}{x - 1} = \frac{x + 2}{x^2 -3x + 2}[/tex] is (x + 2) (x -1)(x - 2)

The rational equation is given as:

[tex]-\frac{3}{x + 2} + \frac{5x}{x - 1} = \frac{x + 2}{x^2 -3x + 2}[/tex]

Factorize the quadratic denominator

[tex]-\frac{3}{x + 2} + \frac{5x}{x - 1} = \frac{x + 2}{(x -1)(x - 2)}[/tex]

Write out the denominators

(x + 2), (x - 1) and (x -1)(x - 2)

Remove the repetition

(x + 2) (x -1)(x - 2)

Hence, the LCD of the rational equation is (x + 2) (x -1)(x - 2)

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Answer:

pi

Step-by-step explanation:

First solve the integral

[tex]\int\ {(1+ cos x} )\, dx[/tex]

[tex]\int\ {1} \, dx +\int\ {cos x} \, dx[/tex]

[tex]\int\ {1} \, dx = x[/tex] and [tex]\int\ {cos x} \, dx = sin x[/tex]

x + sin x

Now consider the limit from 0 to π

[tex]\lim_{0 \to \\pi } (x+sin x)[/tex]

(π +sin π) -(0 +sin 0)

sin π = 0 and sin 0 = 0

π-0

π

Answer:

[tex]\displaystyle \int\limits^\pi_0 {(1+\cos x)} \, dx=\pi[/tex]

Step-by-step explanation:

[tex]\displaystyle \int\limits^\pi_0 {(1+\cos x)} \, dx\\\\=x+\sin x\biggr|^{\pi}_0\\\\=[\pi+\sin\pi]-[0+\sin0]\\\\=\pi[/tex]

Remember your antiderivatives!

Using a calculator, it is found that the correlation coefficient for this data is given by:

B. -0.901.

To find the coefficient, which has symbol r², we input in a calculator the values of x and the values of y, hence:

r² = -0.901.

Which means that option B is correct.

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All real numbers

1. f(x) = 2x

2. g(x) = 2x

Substitute g(x) to the 2x in the first statement.

You'll get: f(x) = g(x)

Therefore, x ∈ all real numbers (any value of x would make it a true statement)

Answer:

A. How are GH and GI related?

B. Write an equation to solve for x.

C. Let's solve the equation...

GH : 2x

GI : x + 12

D. Now, that we solve for x, let's find the length of GH....

GH = 2x where, x = 12

Therefore, the length of GH is 24.

Answer:

Hence, a fair dice has a probability of 16 to land on any predetermined number 1 through 6. Therefore, to land on 3 the probability is 16

Step-by-step explanation:

The smallest possible number that is divisible by 45 when the blanked place of the number is filled is 345285.

The divisible rule of 9 and 5 are:

Two digits of the 6-digit number are missing.

[tex]X = 345 * 8*[/tex]

The smallest possible number from this is divisible by 45. The factors of 45 are 9 and 5.

[tex]45=9\times5[/tex]

Thus, the 6-digit number which is divisible by 45, must be divisible by 9 and 5.  

To be divisible with 5, the number has 0 or 5 in last. So the numbers can be,

[tex]X = 345 * 85\\X=345 * 80[/tex]

For first number, when the blank is filled with number 2 to make sum 9 and for second the blank number should be 7. Thus, the numbers,

[tex]X = 345 285\\X=3457 80[/tex]

Thus, the smallest possible number that is divisible by 45 when the blanked place of the number is filled is 345285.

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Using geometric sequence concepts, it is found that:

a) The rule is: [tex]P_n = 750000(0.5)^{n-1}[/tex].

b) An exponential relationship exists between the two variables.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

A geometric sequence represents an exponential relationship between the variables.

In this problem, considering that the first-place finisher wins half of $1.500.000 in total prize money, and each finisher earns half of the one who finished above, the first term and the common ratio are given by:

[tex]a_1 = 750000, q = 0.5[/tex].

Hence the nth term of the sequence is given by:

[tex]P_n = 750000(0.5)^{n-1}[/tex]

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The equation of the line that passes through the points (7, 450) and (14, 401) is y + 7x = 499

The equation of a line  can be represented as follows:

y - y₁ = m(x - x₁)

where

Therefore, (7, 450)(14, 401)

m = 401 - 450 / 14 - 7 = -49 / 7 = -7

Therefore, using (7, 450)

y - 450 = -7(x - 7)

y - 450 = -7x + 49

y + 7x = 49 + 450

y + 7x = 499

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Answer:

Step-by-step explanation:

perimeter of a rectangle P= 2(L+W)

L= length

W= width

48=2(L+W)---------------(1)

twice the length= 2×L= 3L

decreased by three= 2L-3

three times the width= 3×W= 3W

twice the length decreased by three is equal to three times the width

2L-3= 3W-------------------(2)

solving equation one and two simultaneously

from equation (2)

3W= 2L-3

W=2L/3-3/3

W= 2L/3 - 1----------(3)

substitute equation (3) into equation (1)

48=2(L+2L/3-1)

48=2L+4L/3-2

48×3=6L+4L-6

144=10L-6

10L=144+6

10L=150

dividing bothsides by 10

L= 15

substitute L= 15 into equation (2)

2L-3=3W

2(15)-3=3W

30-3 = 3W

27= 3W

3W= 27

dividing bothsides sides 3

3W=27/3

W=9

Answer:

175000

Step-by-step explanation:

If the 1 is centimeters, then you would take 7 centimeters and multiply it by 25000 to get 175000.

Put u=17

Answer:

59.5.

Step-by-step explanation:

h = 3.5u

When u = 17,

h = 3.5*17

= 59.5

Answer:

in fractions

16/18 = 8/9

4/18 = 2/9

Answer:

8/9 and 2/9

Step-by-step explanation:

for 16/18

divide the numerator and denominator by 2 to option it's simplest form

16/18÷2/2 = 8/9

for 4/18

also divide the numerator and denominator by 2 to get the simplest form.

4/18 ÷2/2= 2/9

Answer:

Step-by-step explanation:

Answer:

A = 8 and B = 6

Step-by-step explanation:

Since (B = A - 2), we can substitute (A - 2) in for the "B" variable in the first equation to isolate "A".

(A - 5)² + (B - 3)² = 18                                 ----->  Original equation

(A - 5)² + ((A - 2) - 3)² = 18                         ----->  Plug in B = A - 2

(A - 5)² + (A - 5)² = 18                                ----->  Subtract

(A² - 10A + 25) + (A² - 10A + 25) = 18       ----->  Expand parentheses

2A² - 20A + 50 = 18                                 ------>  Add like terms

2A² - 20A + 32 = 0                                   ----->   Subtract 18 from both sides

2(A² - 10A + 16) = 0                                   -----> Remove common factor

2(A - 2)(A - 8) = 0                                      -----> Factor within parentheses

A = 2                                                         -----> Find A - 2 = 0

A = 8                                                        -----> Find A - 8 = 0

Since "A" gave two possible values, we need to plug them into both equations to see which value gives reasonable "B" values.

When A = 2:

B = A - 2                           -----> Original equation

B = 2 - 2                           -----> Plug in A = 2

B = 0                               -----> Subtract

(A - 5)² + (B - 3)² = 18       -----> Original equation

(2 - 5)² + (B - 3)² = 18       ------>  Plug in A = 2

(-3)² + (B - 3)² = 18           -----> Subtract within first parentheses

9 + (B - 3)² = 18               -----> Square value within first parentheses

(B - 3)² = 9                      ----->  Subtract 9 from both sides

B - 3 = 3                          ----->  Take square root of both sides

B = 6                               ----->  Add 3 to both sides

When A = 8:

B = A - 2                         -----> Original equation

B = 8 - 2                         -----> Plug in A = 8

B = 6                             -----> Subtract

(A - 5)² + (B - 3)² = 18       -----> Original equation

(8 - 5)² + (B - 3)² = 18       ------>  Plug in A = 8

(3)² + (B - 3)² = 18            -----> Subtract within first parentheses

9 + (B - 3)² = 18               -----> Square value within first parentheses

(B - 3)² = 9                      ----->  Subtract 9 from both sides

B - 3 = 3                          ----->  Take square root of both sides

B = 6                               ----->  Add 3 to both sides

As you can see, when A = 2, there are two possible values of "B" depending on the equation. However, when A = 8, both equations give a "B" value of B = 6. Therefore, A = 8 and B = 6 are the answers.

Answer:

We are given the dimension of the side being 5 inches and it states that we need to determine the surface area.  The first step that we must do is find the area of one side and then we multiply it by 6 because we have 6 same sides.

[tex]A = s^2[/tex]

[tex]A = (5\ in)^2[/tex]

[tex]A = 25\ in^2[/tex]

Now that we have the area of one side we can multiply it by 6 to get the total surface area.

[tex]A = 25\ in^2 * 6[/tex]

[tex]A = 150\ in^2[/tex]

Therefore, our final answer is that the surface area is 150 inches squared

Hope this helps!

Answer:

150 square inches

Step-by-step explanation:

find the area of 1 square face

5*5=25

multiply by 6 faces

25*6=150

The experimental probability that a coin toss results in two heads showing is 3/14

The sample space of two coins is:

S = {HH, HT, TH, TT}

In the above sample space, we have:

The theoretical probability of two heads is calculated as:

P = n(HH)/Total

This gives

P = 1/4

Hence, the theoretical probability of two heads is 1/4

To do this, we make use of the table in the question

The table is given as:

Result                                  Frequency

Two heads (HH)                     30

Two tails  (TT)                        40

One head, one tail (HT)        70

Total                                     140

The experimental probability of two heads is calculated as:

P = n(HH)/Total

This gives

P = 30/140

Simplify

P = 3/14

Hence, the experimental probability of two heads is 3/14

Using the sample space in (a), we have:

The theoretical probability of two tails is calculated as:

P = n(TT)/Total

This gives

P = 1/4

Hence, the theoretical probability of two tails is 1/4

From the table in the question, we have:

Two tails  (TT)  =40

Total = 140

The experimental probability of two tails is calculated as:

P = n(TT)/Total

This gives

P = 40/140

Simplify

P = 2/7

Hence, the experimental probability of two tails is 2/7

Using the sample space in (a), we have:

The theoretical probability of one head and one tail is calculated as:

P = n(HT)/Total

This gives

P = 2/4

Simplify

P = 1/2

Hence, the theoretical probability of one head and one tail is 1/2

From the table in the question, we have:

One head one tail  (HT)  = 70

Total = 140

The experimental probability of one head one tail is calculated as:

P = n(HT)/Total

This gives

P = 70/140

Simplify

P = 1/2

Hence, the experimental probability of one head one tail is 1/2

The reason for the difference between the probability types is because one is as a result of an actual experiment, while the other is an estimate of the experiment.

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In this question, we are presented with two triangles are required to find he missing sides in them. the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively

In the first triangle, we need to use trigonometric ratio to find the missing side in the triangle

Data;

To find the adjacent side, we need to use cosine rule on this problem.

[tex]cos\theta = \frac{adjacent}{hypothenuse} \\cos45 = \frac{x}{8\sqrt{2} } \\x = 8[/tex]

The adjacent side is equal to 8 units

In the second triangle, we also need to use trigonometric ratio, but let's write down our data

We can use both cosine and sine rule here or use one and use Pythagoras's theorem to find the other side.

[tex]cos \theta = \frac{adjacent}{hypothenuse} \\cos 30 = \frac{x}{10} \\x = 8.660[/tex]

The adjacent side is equal to 8.660, let's find the opposite side using sine rule

[tex]sin\theta = \frac{opposite}{hypothenuse} \\sin 30 = \frac{y}{10} \\y = 5[/tex]

And lastly, the value of the other angle is

[tex]90 + 30 + z = 180\\z = 180 - 120\\\\z = 60[/tex]

From the calculations above, the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively

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Answer:

2

Step-by-step explanation:

-3 log₂ (-n + 10) = -16+7

-3 log₂ (-n + 10) = -9

log₂ (-n + 10) = -9/-3

log₂ (-n + 10) = 3

-n + 10 = 2^3

-n + 10 = 8

n=2

To solve this problem, we have to understand and establish some basic mathematical facts on a cone.

The answer to this question are option b and c only.

This is a solid figure that has the base of a circle and the top is made up round triangle.

The formula of volume of a cone is given as

[tex]v = \frac{1}{3}\pi r^2 h[/tex]

where;

In the given question, the first fact given is if the radius doubles the diameter and that false.

[tex]diameter = 2 * radius[/tex]

If we have the value of the the radius, we can calculated the base area using area of a circle

[tex]area = \pi r^2[/tex]

The volume of a cone is actually one-third the volume of a cylinder

we can only calculate the volume of the cone is we have the value of the height of the cone.

The answer to this question are option b and c only.

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Answer:

B, C, D, E

Step-by-step explanation:

Got it wrong the first time.

Answer:

x = 3.255 cm

Step-by-step explanation:

Given:

⇒ y = 10cm

⇒ θ = 19

To find:

⇒ Value of "n"

Solution

⇒ By Pythagoras theorem

⇒ Δ Sin θ = n/y

⇒ sin 19° = n/10

⇒ 0.3255 = n/10

⇒ n = 0.3255 × 10

⇒ n = 3.255 cm

Hence, the answer is = n = 3.255 cm.

Answer:

1/5

Step-by-step explanation:

solution [ calculation of probability ]

P= (3/3+6) × (6/3+6-1)

=3/9×6/10

=1/5

Answer:

0.91 g/cm³

Step-by-step explanation:

Density Formula

Solving

An estimate of the percentage of defective items in the population if 5 of 200 items were defective is 2.5%.

The percentage of a defective item out of a total item can be calculated as follows:

% defective item = no of defective item/total no of items × 100

According to this question, in a random sample of 200 items, 5 items were defective.

% defective item = 5/200 × 100

% defective item = 2.5%

Therefore, an estimate of the percentage of defective items in the population if 5 of 200 items were defective is 2.5%.

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Answer:

5/8

Step-by-step explanation:

There are 8 sections, and 4 sections that are 1, and 1 pink section. So adding these up, we get 5/8.

Hope this helped! :)