(ii) If p = 5 and 9 a) If x = (a + 7) and y = (a - 7), show that a? = xy + 49 ​

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

336 ways

Explanation:

The number of ways n objects can be arranged in r slots is given by

There are 3 medals and we have 8 candidates.

Therefore, the number of different ways the medials can be awarded is

which is our answer!

Answer:

40 shirts

Step-by-step explanation:

if half of her shirts are short sleeved, then double that amount is the total shirts

Answer:

24.997

Step-by-step explanation:

Let's start with the easy parts of the perimeter...the flat parts...7 + 7 = 14. We'll add that to the arch shortly.

We need to find the circumference of the whole circle, then divide by 4 to get 1/4 of a circle. (There might be a faster way, but this gets the job done.)

circumference = (2)(pi)(r)

= 2(3.142)(7) = 43.988

Now divide that by 4 for the distance of the arch.

43.988/4 = 10.997

Add that to the flat parts

10.997 + 14 = 24.997

Please let me know if you have any questions.

Answer:

acute i think??

Step-by-step explanation:

Answer:43.3

Step-by-step explanation:

Answer:

a straight line can still be used to approximate the relationship if a general linear trend can be discerned.

Step-by-step explanation:

The correct option is - A straight line can still be used to approximate the relationship if a general linear trend can be discerned.

Reason -

If a scatter graph contains points that do not fall in a perfect line, then a straight line can still be used to approximate the relationship if a general linear trend can be discerned.

Answer:

A: x < 3

Step-by-step explanation:

Answer: x < 3

Step-by-step explanation:

We start by subtracting 6 from both sides -

x + 6 - 6 < 9 - 6

Then, we get this -

x < 3

Which is the answer

One gallon is equivalent to 128 fluid ounces

3 gallons is equivalent to 3*128 fluid ounces

= 384 fluid ounces

One plastic cup can hold 12 guide ounces

So cups needed will be 384/12

32 cups

Mr. Cruz can completely fill 32 plastic cups with the water from the cooler.

In mathematics, divides left-hand operands into right-hand operands in the division operation.

The 3-gallon water cooler contains 3 x 128 = 384 fluid ounces of water.

We can divide the total amount of water in the cooler by the amount of water each plastic cup can hold to find out how many cups can be completely filled:

384 fluid ounces / 12 fluid ounces/cup = 32 cups

Therefore, he can completely fill 32 plastic cups with the water from the cooler.

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Answer:

Divided into five equal parts

Angle BCF = 38 degrees

Angle BED = 79 degrees

Angle BDE = 63 degrees

Angle B = 79 degrees

Angle C = 79 degrees

Angle ACF = 38 degrees

Angle F = 104 degrees.

We have,

As ED//BC,

We can say that angle EDB = angle BCF = 38 degrees.

Also, in rhombus ABCF, angles BCF and CAF are equal,

So CAF = 38 degrees.

In triangle BED,

We have angle BED = 79 degrees and angle EDB = 38 degrees.

Angle BDE = 180 - (79 + 38) = 63 degrees.

In triangle BDE,

We also has angle B = angle EBD = 180 - (63 + 38) = 79 degrees.

In trapezium BCDE,

Angles B and C are equal, so angle C = 79 degrees.

Finally, in rhombus ABCF, angles CAF and ACF are equal,

So ACF = 38 degrees.

Therefore,

Angles A and C of triangle ACF equal 38 degrees each, and angle F is:

= 180 - (38 + 38)

= 104 degrees.

Thus,

angle BCF = 38 degrees

angle BED = 79 degrees

angle BDE = 63 degrees

angle B = 79 degrees

angle C = 79 degrees

angle ACF = 38 degrees

angle F = 104 degrees.

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The complete question.

In the figure, ABCF is a rhombus and BCDE is a trapezium. ED//BC, BCF=38 degrees, and BED= 79 degrees.

Find the following:

Angle BCF

Angle BED

Angle BDE

Angle B

Angle C

Angle ACF

Angle F

Answer:

\(\huge\boxed{\bf\: \frac{93}{20}=4.65}\)

Step-by-step explanation:

\(3 \frac { 1 } { 4 } + 1 \frac { 2 } { 5 }\)

Now,

\(3 \frac { 1 } { 4 } \\= \frac{4 * 3+1}{4}\\= \frac{13}{4}\)

Then,

\(1 \frac { 2 } { 5 }\\= \frac{1* 5+2}{5} \\= \frac{7}{5}\)

So,

\(3 \frac { 1 } { 4 } + 1 \frac { 2 } { 5 }\\= \frac{13}{4}+\frac{7}{5}\\ \\\mathrm{LCM = 20}\\\\= \frac{65}{20}+\frac{28}{20} \\=\boxed{\bf\: \frac{93}{20}=4.65}\)

\(\rule{150pt}{2pt}\)

Answer:

$ 4.75

Step-by-step explanation:

You have to divide 19 by 4 which is 4.75. Since it's asking how many dollars, the answer might be a decimal. You can check the answer by multiplying 4.75 by 4. Showed my work below.

The value of m∠1 is 158° as the two line x and y are parallel.

Two lines are said to be parallel if they do not meet at any point and the perpendicular distance between them is always the same.

In the given figure it is given that x║y and m∠2 = 22°.

Now let us use the above principles to solve the value of the other angles.

m∠2+m∠1 = 180°(linear pair)

or, m∠1= 180°-22°

or, m∠1=158°

m∠2+m∠3 = 180°(co-interior angles are supplementary)

or,m∠3=158°

m∠2=m∠4(Corresponding angles are equal)

or, m∠4=22°

m∠2=m∠5 (vertically opposite angles are equal)

or, m∠5=22°

m∠6=m∠1 (vertically opposite angles are equal)

or, m∠6=158°

m∠2=m∠7(alternate angles are equal)

or, m∠7=22°

m∠3=m∠8 (vertically opposite angles are equal)

or, m∠8=158°

Hence all the above angles are calculated using the properties of parallel lines.

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Answer:

1 hour  =    50/4= $12.5

4 hours = $50

\(5\frac{1}{2}\) can be written as 11/2 or 5.5

Let's take x to be the salary for working 5.5 hours.

4                      50

5.5                   x

Using cross-multiplication, you will get the equation:

4x = 275

x = 68.75

THEREFORE, HE EARNS $68.75 IN \(5\frac{1}{2}\) hours.

Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

The answer is B, which is to find the common denominator.

In solving a rational equation, the first step is usually to find a common denominator for all the fractions in the equation. This allows us to combine the fractions into a single fraction and simplify the equation.

To find the common denominator, we need to identify the factors of the denominators and determine the least common multiple (LCM) of these factors. Then, we multiply each fraction by the appropriate factor(s) to get the common denominator. For example, if we have the equation:

(3/x) + (4/2x) = 1/4

The denominators are x and 2x, which have factors of x and 2. The LCM of these factors is 2x, so we need to multiply the first fraction by 2 and the second fraction by 1 to get:

(6/2x) + (4/2x) = 1/4

Then we can combine the fractions and simplify the equation to get:

(10/2x) = 1/4

From here, we can continue to solve for x by cross multiplying and manipulating the equation.

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The expression "x - y + z" can be simplified and rearranged using the associative property and commutative property of addition. Let's break it down step by step:

1. x - y + z

According to the associative property of addition, the grouping of terms does not affect the result when only addition and subtraction are involved. Therefore, we can choose to group "y" and "z" together:

2. x + (-y + z)

Next, using the commutative property of addition, we can rearrange the terms "-y + z" as "z + (-y)":

3. x + (z + (-y))

Now, we have the expression "x + (z + (-y))". According to the associative property of addition, we can group "x" and "z + (-y)" together:

4. (x + z) + (-y)

Finally, we can rewrite the expression as "(x + z) - y", which is equivalent to "(x - y) + z":

5. (x + z) + (-y) = (x - y) + z

Therefore, "x - y + z" is indeed the same as both "x - (y + z)" and "(x - y) + z" due to the associative and commutative properties of addition.

Answer:

Inches of fence Sam built each day = 108 inches per day

Step-by-step explanation:

Sam built a fence that was 54 feet long. She built the same length of fence each day for 6 days.

How many inches of fence did Sam build each day?

Total length of fence Sam built = 54 feet

How many inches of fence did Sam build each day?

Number of days = 6

Convert 54 feet to inches

1 feet = 12 inches

54 feet = 648 inches

Inches of fence Sam built each day = Total inches of fence built / number of days

= 648 inches / 6 days

= 108 inches per day

Inches of fence Sam built each day = 108 inches per day

The MMPI-2 test is used for the assessment of psychopathology and personality of patients.

It includes 567 true-false questions, resulting in 10 clinical scales, among which one is the anxiety subscale.

A score of 30 or less is usually considered very low.

The questions are answered by the patient, usually in a clinical or research setting.

A one-sample t-test is conducted in the problem, whereby a sample of 18 participants in a yoga group is tested for anxiety scores.

The following are the parameters of the one-sample t-test:Groups:

18 participants

Null hypothesis: The anxiety scores of Felipe's yoga group are statistically equal to 30." value: 30

Type of test: One-tailed test

Alternative hypothesis: The anxiety scores of Felipe's yoga group are greater than 30.

Degrees of freedom: n - 1 = 17T-observed value: (35.2 - 30) / (10.4 / sqrt(18)) = 2.41T-critical value: 1.734

Reject or retain null hypothesis: Since the t-observed value (2.41) is greater than the t-critical value (1.734), Felipe should reject the null hypothesis, which implies that his yoga group's scores are greater than 30.P-value: 0.014Cohen’s d value: (35.2 - 30) / 10.4 = 0.5

If the " value were reduced to 0.01, Felipe would still reject the null hypothesis, since the p-value (0.014) is lower than the alpha level (0.01).

For the sample mean: 35.2CI for 42%: 35.2 ± 0.58CI for 79%: 35.2 ± 1.16CI for 95%: 35.2 ± 2.13

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Answer:

C  \(y=-\frac{3}{4}x-3\)

Step-by-step explanation:

Based on how the line slopes, it is negative. The best way I can remember how to tell if a function is negative or positive is to read it like a book. If the left-most point of the line is above the right-most point, it is negative, such as is the case here. If the left-most point is below the right-most point, then it is positive.

Having determined that it is negative, A is eliminated. It also intersects the y-axis at -3, which eliminates D. To figure out how much it slopes, figure a point where the line cleanly goes through a point on the graph, such as (0,-3).

Using (0,-3) as a starting point, count how many points, or squares, on the graph, it takes to get to the next intersected point along the x-axis. Once you have that x-axis point, do the same thing along the y-axis.

In this example, you would go to the right (positive) 3 points, then down (negative) 4. The negative makes the m variable in the function \(y=mx+b\) a negative. This function is also a fraction due to how for every 3 points moved to the right, it goes down by 4 if that makes any sense.

Anything that goes right and up is positive, while anything left and down is negative.

C

�

=

−

3

4

�

−

3

y=−

4

3

x−3

Step-by-step explanation:

Based on how the line slopes, it is negative. The best way I can remember how to tell if a function is negative or positive is to read it like a book. If the left-most point of the line is above the right-most point, it is negative, such as is the case here. If the left-most point is below the right-most point, then it is positive.

Having determined that it is negative, A is eliminated. It also intersects the y-axis at -3, which eliminates D. To figure out how much it slopes, figure a point where the line cleanly goes through a point on the graph, such as (0,-3).

Using (0,-3) as a starting point, count how many points, or squares, on the graph, it takes to get to the next intersected point along the x-axis. Once you have that x-axis point, do the same thing along the y-axis.

In this example, you would go to the right (positive) 3 points, then down (negative) 4. The negative makes the m variable in the function

�

=

�

�

+

�

y=mx+b a negative. This function is also a fraction due to how for every 3 points moved to the right, it goes down by 4 if that makes any sense.

Answer:

For the table:

Angle 1 and Angle 8 are equal you could say?

Angle 3 and 5 are supplementary (add up to 180 degrees).

Angle 4 and 8 are equal (again, no idea what the answer choices are).

For the selecting thing in image 3:

Angles 5 and 6 are supplementary.

Angles 1 and 7 are supplementary.

Angles 8 and 2 are supplementary.

Angles 5 and 2 are supplementary.

Hope this is helpful?

Answer:

  A: alternate; same-side; corresponding

  B: (5, 6), (1, 7), (8, 2), (5, 2)

Step-by-step explanation:

These are a matter of definition. It is usually a good idea to acquaint yourself with the vocabulary of math and geometry, so you can understand the relationships and what the questions are.

  ∠1 and ∠8 -- alternate exterior angles

  ∠3 and ∠5 -- same-side interior angles

  ∠4 and ∠8 -- corresponding angles

__

Angle pairs that are both acute or both obtuse are not supplementary. A supplementary pair will consist of one acute and one obtuse angle.

  ∠5 and ∠6

  ∠1 and ∠7

  ∠8 and ∠2

  ∠5 and ∠2

Answer:

28x^2

Step-by-step explanation:

5+5+9+9 = 28

Answer: independent=t. dependent=v

Step-by-step explanation:

Answer:

373737373746372838484883848r

The final answer is (1 + 21√2)/(21√2). The process of rationalization involves changing the form of an expression to eliminate radicals from its Denominator, or to eliminate denominators from a radical expression.

To rationalize the denominator 1/7 + 3√2,

A rational number is a number that can be expressed as a ratio of two integers, with the denominator not equal to zero. The fraction 4/5, for example, is a rational number since it can be expressed as 4 divided by 5.

Step-by-Step SolutionTo rationalizes the denominator 1/7 + 3√2, we'll need to follow these steps.

Step 1: First, we need to create a common denominator for the two terms. The common denominator is 7. Thus, we can convert the expression to the following form:(1/7) + (3√2 × 7)/(7 × 3√2).

Step 2: Simplify the denominator to 7. (1/7) + (21√2)/(21 × 3√2).

Step 3: The numerator and denominator can now be simplified. (1 + 21√2)/(7 × 3√2).Step 4: Simplify further. (1 + 21√2)/(21√2).We have successfully rationalized the denominator!

The final answer is (1 + 21√2)/(21√2).

The final answer is (1 + 21√2)/(21√2). The process of rationalization involves changing the form of an expression to eliminate radicals from its denominator, or to eliminate denominators from a radical expression.

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To find the value of the integral ∫[0 to 1] (f(x) - g(x)) dx, we can use the given information and properties of integrals. We are given that ∫[0 to 1] (f(x) - 2g(x)) dx = 6 and ∫[0 to 1] (2f(x) + 2g(x)) dx = 9. From these equations, we can derive the value of the desired integral.

Let's start by manipulating the second equation:

∫[0 to 1] (2f(x) + 2g(x)) dx = 9

2∫[0 to 1] (f(x) + g(x)) dx = 9

∫[0 to 1] (f(x) + g(x)) dx = 9/2

Now, let's subtract the first equation from the above equation:

∫[0 to 1] (f(x) + g(x)) dx - ∫[0 to 1] (f(x) - 2g(x)) dx = 9/2 - 6

∫[0 to 1] 3g(x) dx = -3/2

Since we want to find ∫[0 to 1] (f(x) - g(x)) dx, we can rewrite the equation as:

∫[0 to 1] (f(x) + g(x)) dx - 2∫[0 to 1] g(x) dx = -3/2

Substituting the value of ∫[0 to 1] (f(x) + g(x)) dx from the second equation, we get:

9/2 - 2∫[0 to 1] g(x) dx = -3/2

Simplifying the equation, we find:

∫[0 to 1] g(x) dx = 6

Therefore, the value of ∫[0 to 1] (f(x) - g(x)) dx is 6.

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Answer:

4.8-46c+13x

Step-by-step explanation:

The expected number of games it will take to win on a slot machine game with a probability of winning of 0.152 is approximately 6.579 games.

The expected number of games can be calculated using the formula for the expected value of a geometric distribution. In this case, the probability of winning on each game is 0.152.

The expected number of games is calculated as the reciprocal of the probability of winning. Therefore, the expected number of games is 1 divided by 0.152, which is approximately 6.579.

This means that on average, it is expected to take approximately 6.579 games to win on the slot machine. However, it's important to note that this is an average value and individual experiences may vary. Some players may win on their first few games, while others may take more games to win. Nonetheless, on average, it is expected to take approximately 6.579 games to achieve a win.

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Step-by-step explanation: