Simplify by writing the expression without absolute value bars |x+7| for x<-7

Answer:

-x - 27/ 9 this is it djdjdj

The simplest form of the expression \(\frac{5(x-3)-3(2x+4)}{9}\) is \(\frac{-x-27}{9}\) .

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

Given the expression

\(\frac{5(x-3)-3(2x+4)}{9}\)

⇒ (5x - 15 - 6x - 12) ÷ 9

⇒  (-x - 27)/9

⇒ \(\frac{-x-27}{9}\)

Hence "The simplest form of the expression  \(\frac{5(x-3)-3(2x+4)}{9}\) is \(\frac{-x-27}{9}\) .

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Answer:

The initial population size is 500 fish

Population size after 9 years: 1910 fish

Step-by-step explanation:

Mathematical Model

We usually represent real situations as mathematical functions or rules that express the dependency of one variable quantity P with another variable quantity t.

The population size of a species of fish P(x) is modeled by the following function:

\(\displaystyle P(t)=\frac{3000}{1+3e^{-0.34t}}\)

Where t is the number of years elapsed since the species was added to the lake.

The initial population size can be found by substituting t for 0:

\(\displaystyle P(0)=\frac{2000}{1+3e^{-0.34*0}}\)

\(\displaystyle P(0)=\frac{2000}{1+3*1}\)

\(\displaystyle P(0)=\frac{2000}{4}\)

P(0)=500

The initial population size is 500 fish

The population size after t=9 years is:

\(\displaystyle P(9)=\frac{2000}{1+3e^{-0.34*9}}\)

\(\displaystyle P(9)=\frac{2000}{1+3e^{-3.06}}\)

\(\displaystyle P(9)=\frac{2000}{1.047}\)

\(P(9)\approx 1910\)

Population size after 9 years: 1910 fish

The translated function can be written as:

y = √(x + 2)

Here we know that the parent square root function is:

f(x) = √x

It passes through the point (0, 0) and opens to the right side.

The transformed function is similar, but it starts at (-2, 0)

So we had a translation of 2 units to the left.

Remember that for any function y = f(x) an horizontal translation of N units to the left is written as:

y = f(x + N)

Here we will have:

y = f(x + 2) = √(x + 2)

y = √(x + 2)

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Answer:

A

Step-by-step explanation:

y=\(\sqrt{x+2\)

Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

Answer:

\(\boxed{\red{\frac{1}{5} }}\)

Step-by-step explanation:

\(400 {cm}^{3} = 400ml \\ 2l = 2000ml\)

So, now we have to write 400cm^3 as a fraction of 2l

\( \frac{400}{2000} = \frac{4}{20} = \frac{1}{5} \)

Answer:

y = sin(x + 90°)

Step-by-step explanation:

cos 0 = 1

Since the point (0, 1) is on the graph, this graph is y = cos x, but that is not a choice, so this must be the graph of the sine function with a horizontal translation.

sin 0 = 0

sin 90° = 1

The translation is 90°.

Answer: y = sin(x + 90°)

Answer:

65.3 km/hr

Step-by-step explanation:

49/45 x 60 = 65.3 km/hr

Answer:

★ The answer would be 0.02 MILES PER HOUR

Step-by-step explanation:

Hope you have a great day :)

Answer:

250

5:15

true

i already helped you

Answer:

9- 4 hours 30 minutes

10- 250

11- False

Answer:

I think its C

Step-by-step explanation:

Nina will spend $ 25.98

Explanation

number of fences= 4

the measure of each fence= 3 ft and 4 inch

Step 1

convert the inches into ft

to do that

remember

12 inches = 1 ft

so

therefore, the measure of each fence is

Step 2

if the cost is $6 per foot,

the total would be

therefore, the answer is

$ 25.98

x

Natalie is 2 meters taller than the statue.

Calculating the distance in height between Natalie's head and the statue's peak is necessary.

According to the information provided, Natalie is located 8 meters from the statue, and Natalie's head is 10 meters from the top of the monument.

With the aid of the comparable triangles idea, we can establish the ratio shown below:

(height of statue) / (distance to statue) = (height difference) / (distance to Natalie's head)

Let's denote the height of the statue as "H" and the height difference as "D." The proportion can be written as:

H / 8 = D / 10

To find the height difference (D), we can rearrange the equation:

D = (H / 8) * 10

Given that the distance between the top of the statue and Natalie's head is 10 meters, we can substitute this value into the equation:

10 = (H / 8) * 10

Dividing both sides by 10:

1 = H / 8

Multiplying both sides by 8:

H = 8

Therefore, the height of the statue is 8 meters.

We deduct Natalie's height (10 meters) from the statue's (8 meters) height to find the height gap between the two:

Height difference = Statue's height - Natalie's height

= 8 - 10

= -2

The negative value indicates that Natalie's height is 2 meters taller than the statue.

Therefore, Natalie is 2 meters taller than the statue.

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The given set is (3, 4, 5, ...} is infinite set.

A set with an infinite number of elements is one that cannot be numbered. A set that has no last element is said to be endless. A set that can be put into a one-to-one correspondence with a suitable subset of itself is said to be infinite. No issue with the in-class assignment.

The stars in the clear night sky, water droplets, and the billions of cells in the human body are just a few examples of endless sets of objects that surround us. A set of natural numbers, however, serves as the best illustration of an infinite set in mathematics. There is no limit to the amount of natural numbers.

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The quotient when 6+8i is divided by 2i is given by -3i+4.

We know that, complex number \(i^1=-1\).

Given the divisor is = 2i and dividend is = 6+8i

Dividing the dividend by divisor we get,

(6+8i)/2i = 6/2i + 8i/2i = 3/i + 4 \(=\frac{3i}{i^2}+4\) = 3i/(-1)+4 = -3i+4

Hence the quotient is = -3i+4.

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Answer:

2-4i/5

Step-by-step explanation:

\(\frac{2i}{i-2} *\frac{i+2}{i+2}\\=\frac{2i(i+2)}{i^2-4}\\= \frac{2i(i+2)}{-1-4}\\ =\frac{2i(i+2)}{-5} \\ = \frac{-2 + 4i}{-5}\\ =( 2 - 4i )/ 5\)

Answer:

\(\frac{2i}{i-2}=\frac{2-4i}{5}\)

Step-by-step explanation:

The  letters of the word "UNDERDOG" can be arranged in 144 ways.

There are only two letters that are the same which are D, then the remaining letters are 6 letters.

V, E, O are vowels

         N  R  G

The vowels are not joined together

For N, R, G  A³3

There are 4 openings A³4

Hence:

A³4· A³3=4×3×2×3×2×1

A³4· A³3=144

Therefore the  letters of the word "UNDERDOG" can be arranged in 144 ways.

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The gradient of the line that passes through the pairs of points (c/2, -d) and (c/4, d/2) is -6d/c

From the question, the points are given as

(c/2, -d) and (c/4, d/2)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (c/2, -d) and (c/4, d/2)

The gradient of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (c/2, -d) and (c/4, d/2)

Substitute the known values in the above equation

So, we have the following equation

Slope = (d/2 + d)/(c/4 - c/2)

Evaluate the differences

Slope = (3d/2)/(-c/4)

So, we have

Slope = -3d/2 * 4/c

This gives

Slope = -6d/c

Hence, the slope of the line is -6d/c

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The value of sec(A) is 2/√(13) in simplified form, in the standard position.

What is the point of intersection?

When the lines intersect, the point of intersection is the only point that the two graphs have in common, so the coordinates of that point are the solution for the two variables used in the equations.

The terminal ray of an angle in standard position passes through the point (x,y) in the coordinate plane, where x and y are the coordinates of the point of intersection of the terminal ray with the x-axis and y-axis respectively.

Given that the terminal ray of angle A passes through the point (-6,4)

The coordinates of the point of intersection of the terminal ray with the x-axis are (-6,0) and y-axis are (0,4)

Using the distance formula

The distance from the origin to the point (-6,4) is √((-6-0)^2 + (4-0)^2) = √(6^2 + 4^2) = √(36 + 16) = √(52) = 2*√(13)

Now we can use these coordinates to find the value of sec(A) which is defined as sec(A) = 1/cos(A) = distance of point from x-axis/distance from origin.

sec(A) = 4/2*√(13) = 2/√(13)

hence, the value of sec(A) is 2/√(13) in simplified form, in the standard position.

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The length of PQ is 3√5 and its slope is -2

The length of SR is 3√5 and its slope is -2

The length of SP is 5√2 and its slope is -7

The length of RQ is 5√2 and its slope is -1

So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of  side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.

To find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:

D = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)  

and the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

1. Length PQ:

Using the distance formula, the length PQ can be calculated as follows:

PQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((3 - 0)² + (-4 - 2)²)

  = √(3² + (-6)²)

  = √(9 + 36)

  = √45

  = 3√5

2. Length SR:

Using the distance formula, the length SR can be calculated as follows:

SR = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - (-2))² + (-5 - 1)²)

  = √((1 + 2)² + (-6)²)

  = √(3² + 36)

  = √(9 + 36)

  = √45

  = 3√5

3. Length SP:

Using the distance formula, the length SP can be calculated as follows:

SP = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - 0)² + (-5 - 2)²)

  = √(1² + (-7)²)

  = √(1 + 49)

  = √50

  = 5√2

4. Length RQ:

Using the distance formula, the length RQ can be calculated as follows:

RQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((-2 - 3)² + (1 - (-4))²)

  = √((-2 - 3)² + (1 + 4)²)

  = √((-5)² + 5²)

  = √(25 + 25)

  = √50

  = 5√2

Now, let's calculate the slopes of the sides:

1. Slope PQ:

The slope of PQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-4 - 2) / (3 - 0)

  = -6 / 3

  = -2

2. Slope SR:

The slope of SR can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 1) / (1 - (-2))

  = -6 / 3

  = -2

3. Slope SP:

The slope of SP can be calculated using the slope formula:

m =\(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 2) / (1 - 0)

  = -7 / 1

  = -7

4. Slope RQ:

The slope of RQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (1 - (-4)) / (-2 - 3)

  = 5 / (-5)

  = -1

Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:

Length PQ: 3√5

Length SR: 3√5

Length SP: 5√2

Length RQ: 5√2

Slope PQ: -2

Slope SR: -2

Slope SP: -7

Slope RQ: -1

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Answer:

The correct answer is Option 3: 12y

Step-by-step explanation:

A polynomial term is usually made of a variable and a co-efficient.

Like terms are those terms that have the same variables i.e. x and 44x are like terms.

Given expression is:

\(6y-2y+8y\)

All the terms have only y which means that all three terms are alike.

The coefficients of like terms are added or subtracted according to their sign.

\(6y-2y+8y\) = 12y

Hence,

The correct answer is Option 3: 12y

Answer:

6.3

Step-by-step explanation:

19/3=6.3 repeating so i just shortened it to 6.3.

final answer: 6.3

The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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The original price of iPhones if the prices are reduced by 35% is $2,041

Let

Sale price = Original price - (Percentage discount × Original price

714.35 = x - (35% of x)

714.35 = x - 0.35x

714.35 = 0.65x

divide both sides by 0.65

x = 714.35 / 0.65

x = $2,041

In conclusion, the original price of iPhones after the discount is $2,041

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The Circle Sector Area correct answer is: O n(30in)2

To calculate the area of the sector in the circle, you would typically use the formula:

Area = (θ/360) * π *\(r^2\)

where θ is the angle of the sector in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

From the options you provided, the correct choice would be:

O n(30in)2

This option represents the square of the radius (30in) squared, which gives you the value of \(r^2.\)

Therefore, the Circle Sector Area correct answer is: O n(30in)2

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Answer:

x=6

Step-by-step explanation:

2x-9=x-3

2x-x=9-3

x=6

The right response is 400%. In other words, Johnny moves at four times the pace of Jane.

We must compare the speeds of Johnny and Jane in relation to one another in order to get their ratio. According to the issue, Jane moves at a pace that is 1/4 that of Johnny. In other words, Jane moves at a speed that is one-fourth that of Johnny.

We may compare the speeds as a fraction to figure out the ratio:

Johnny's speed divided by Jane's speed equals 4/1.

This indicates that Johnny is moving at a speed that is four times that of Jane. We can express Johnny's speed as 400% of Jane's speed in percentage terms.

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(a) The conditional PMF P X∣B (x) of X given the event B={X<4} can be calculated using the formula

P(X=x|B) = P(X=x and B)/P(B).

Since the event B={X<4} includes the events X=1, X=2, and X=3, we can calculate P(B) as the sum of the probabilities of these events:

P(B) = P(X=1) + P(X=2) + P(X=3) = (1/4) + (3/4)(1/4) + (3/4)^2(1/4) = 13/16.

Therefore, the conditional PMF P X∣B (x) is given by:

P(X=1|B) = P(X=1 and B)/P(B) = (1/4)/(13/16) = 4/13
P(X=2|B) = P(X=2 and B)/P(B) = (3/4)(1/4)/(13/16) = 3/13
P(X=3|B) = P(X=3 and B)/P(B) = (3/4)^2(1/4)/(13/16) = 6/13

(b) The probability that your favourite character is eliminated in one of the first two episodes given the spoiler is P(X=1|B) + P(X=2|B) = 4/13 + 3/13 = 7/13.

(c) The expected value of X conditioned on the event B can be calculated using the formula E[X|B] = sum(x*P(X=x|B)) for all x in the support of X. Therefore, E[X|B] = 1*(4/13) + 2*(3/13) + 3*(6/13) = 20/13.

(d) The conditional PMF P X∣C (x) of X given the event C={X>2} can be calculated using the formula P(X=x|C) = P(X=x and C)/P(C). Since the event C={X>2} includes the events X=3, X=4, ..., we can calculate P(C) as the sum of the probabilities of these events: P(C) = P(X=3) + P(X=4) + ... = (3/4)^2(1/4) + (3/4)^3(1/4) + ... = (3/4)^2/(1-(3/4)) = 12/16. Therefore, the conditional PMF P X∣C (x) is given by:

P(X=3|C) = P(X=3 and C)/P(C) = (3/4)^2(1/4)/(12/16) = 1/3
P(X=4|C) = P(X=4 and C)/P(C) = (3/4)^3(1/4)/(12/16) = 1/4
...

(e) The conditional PMF P Y∣C (y) of Y given the event C={X>2} can be obtained by shifting the conditional PMF P X∣C (x) of X given the event C={X>2} by 2 units to the left. Therefore, P Y∣C (y) = P X∣C (y+2) for all y in support of Y. This conditional PMF belongs to the family of geometric random variables with parameter 1/4.

(f) The conditional mean E[X|C] can be calculated using the formula E[X|C] = sum(x*P(X=x|C)) for all x in the support of X. Since the conditional PMF P X∣C (x) is a geometric distribution with parameter 1/4 shifted by 2 units to the right, we can use the formula E[X|C] = 2 + 1/(1/4) = 6.

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Answer:

x intercept (-3,0)

y intercepy (0,-6/5)

Step-by-step explanation:

uh i used a calculator but please lmk if this is correct