Find the value of x

The two points with an x-coordinate of 2 and a distance of 5 from (-2, -4) are: (2, -4 + 2√13) and (2, -4 - 2√13)

What is distance formula?

Distance is a measurement of how far away two things or locations are, either numerically or occasionally qualitatively.

Distance formula: [tex]distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]

We can solve this problem using the distance formula, which gives us the distance between two points in a plane:

[tex]distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]

Let (x, y) be a point with an x-coordinate of 2. Then we can write the distance from (-2, -4) to (x, y) as:

[tex]distance = \sqrt{((x - (-2))^2 + (y - (-4))^2)}[/tex]

Simplifying this expression, we get:

[tex]distance = \sqrt{((x + 2)^2 + (y + 4)^2)}[/tex]

We know that the distance between (-2, -4) and (x, y) is 5. Therefore, we can write:

[tex]\sqrt{((x + 2)^2 + (y + 4)^2)} = 5[/tex]

Squaring both sides, we get:

[tex](x + 2)^2 + (y + 4)^2 = 25[/tex]

Expanding the left side, we get:

[tex]x^2 + 4x + 4 + y^2 + 8y + 16 = 25[/tex]

Simplifying this expression, we get:

[tex]x^2 + 4x + y^2 + 8y - 5 = 0[/tex]

To find all points with an x-coordinate of 2 that satisfy this equation, we can substitute x = 2 and simplify the resulting equation:

[tex]2^2 + 4(2) + y^2 + 8y - 5 = 0[/tex]

Simplifying this equation, we get:

[tex]y^2 + 8y + 3 = 0[/tex]

We can solve this quadratic equation using the quadratic formula:

y = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 8, and c = 3.

Plugging in these values, we get:

y = (-8 ± sqrt(8^2 - 4(1)(3))) / 2(1)

Simplifying this expression, we get:

y = (-8 ± √52) / 2

y = (-8 ± 2√13) / 2

y = -4 ± √13

Therefore, the two points with an x-coordinate of 2 and a distance of 5 from (-2, -4) are: (2, -4 + 2√13) and (2, -4 - 2√13)

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Answer:

The inequality that represents the given statement is:

12 + w ≥ 45

Step-by-step explanation:

If the bacteria in a dish that contains 2 bacteria quadruple every 16 minutes can be represented by the expression 2×4t/16, an equivalent expression for the number of bacteria in the dish for any time, t, in minutes is B. 8t/16.

An equivalent expression depicts two algebraic expressions that have the same value when the values for the variables are plugged in.

An algebraic expression is the combination of variables, values, constants, and numbers using mathematical operands without the equal symbol (=).

2×4t/16 = 8t/16

2×4t/16 ≠ 4t8

2×4t/16 ≠ 2×2t8

2×4t/16 ≠ 4×2t16

Thus, 2×4t/16 = 8t/16 as equivalent expressions.

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The required values of exponent a, b, and c are 6, 8, and 9 respectively.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
Given expression,
[tex][x^{24}y^{32}]^{1/4} \times (x^{-3}z^{27})^{1/5} = x^ay^bz^c[/tex]

We have to determine the value of a, b, and c in the exponents, so in order to get the solution we have to simplify the given expression.

[tex][x^{7}y^{8}] \times (x^{-1}z^{9}) = x^ay^bz^c\\x^{7 -1}y^8z^9 = x^ay^bz^c\\x^{6}y^8z^9 = x^ay^bz^c[/tex]

Comparing the exponent across the equal sign we get,
a = 6
b = 8
z = 9

Thus, the required value of exponent a, b, and c are 6, 8, and 9 respectively.

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Answer:

The team was penalized 10 yards on each play.

Answer:

A

Step-by-step explanation:

step by step you will learn

Based on the information provided, the statement "Ricardo is half as likely to spin a 2 or 4 than an odd number" is false.

To better understand if this is a valid statement, let's calculate the probability in each case.

Probability to get a 2 or 4:

1/ 8=  0.125 or 12.5% ( 0.125 x 100 = 12.5%)

Probability to get an odd number:

4/8 = 0.5 or 50% (0.5 x 100 = 50%)

This shows that the probability of getting a 2 or a 4 is 12.5%, while the probability of getting an odd number is 50%, which makes the statement false.

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Answer:

There is a direct relationship, in which the value of the division of the circumference by the diameter is a constant. This constant is know as Pi.

Answer:

26

Step-by-step explanation:

10(2) -2(-3)=20+6=26

Answer:

Step-by-step explanation:

[tex]\tt 10a-2b[/tex]

[tex]\tt a=2[/tex]

[tex]\tt b=-3[/tex]

______

Simplify: 10×2 = 20

Simplify: 2×-3= -6

Simplify:-

_____________________

Hope this helps! :)

Answer:

B

Step-by-step explanation:

The answer is 21 because the pattern is multiplying by 3!

Answer:

Step-by-step explanation:

Here are the step-by-step instructions to find the number of ear cleanings that the groomer gave:

Start with the given number of nail trims, which is 15.

Divide the number of nail trims by 5 to find out how many groups of 5 nail trims there are. This gives us: 15 ÷ 5 = 3.

Multiply the number of groups of 5 nail trims by the corresponding ratio of ear cleanings per 5 nail trims, which is 3. This gives us: 3 × 3 = 9.

This means that for every 5 nail trims, the groomer gave 3 ear cleanings, and since the groomer gave 15 nail trims, they gave 9 ear cleanings in total.

So, the pet groomer gave 9 ear cleanings in total.

Answer:

We can start by setting up a ratio of the number of fruit skewers made to the number of liters of milkshake made:

fruit skewers : milkshake = 202020 : 444

Simplifying this ratio by dividing both sides by 444, we get:

fruit skewers : milkshake = 455 : 1

This means that for every 1 liter of milkshake made, Atilio makes 455 fruit skewers. Therefore, if Atilio makes 202020 liters of milkshake, they would make:

202020 x 455 = 91919100

So, Atilio would make 91919100 fruit skewers for the party.

Step-by-step explanation:

Answer:

Let's denote the speed of the second car as x (in miles per hour). Then the speed of the first car is 12 miles per hour faster, which is x + 12.

We know that both cars traveled the same amount of time, so we can use the formula:

distance = speed × time

For the first car, we have:

234 = (x + 12) × time

For the second car, we have:

180 = x × time

We want to find the speeds of both cars, so we need to solve for x and x + 12. We can start by solving for time in both equations:

time = 234 / (x + 12)

time = 180 / x

Since both expressions are equal to time, we can set them equal to each other:

234 / (x + 12) = 180 / x

To solve for x, we can cross-multiply and simplify:

234x = 180(x + 12)

234x = 180x + 2160

54x = 2160

x = 40

Therefore, the speed of the second car is 40 miles per hour, and the speed of the first car is x + 12 = 52 miles per hour.

Step-by-step explanation:

Answer:

Let x = speed of first car x + 12 = speed of second

Step-by-step explanation:

Answer:

The heaviest piece of chocolate weighed 2.94 ounces.

Step-by-step explanation:

Answer:

300.20

Step-by-step explanation:

because it was a nice guesss

$7,008 is the future value of a 2-year investment of $6,525 into a simple interest rate account with an annual interest rate of 3.7%.

percentage, a relative value indicating hundredth parts of any quantity.

The formula to calculate the future value of an investment with simple interest is:

FV = P(1 + rt)

where FV is the future value, P is the principal amount, r is the annual interest rate expressed as a decimal, and t is the time period in years.

P = $6,525

r = 0.037

t = 2 years

Plugging these values into the formula, we get:

FV = $6,525(1 + 0.037×2)

FV = $6,525(1.074)

FV = $7,008.

Therefore, the future value of a 2-year investment of $6,525 into a simple interest rate account with an annual interest rate of 3.7% is $7,008.

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The probability of getting tens depends on the context. If you are referring to a regular deck of cards, there are four tens out of 52 cards, so the probability is 4/52 or 1/13. If you are referring to rolling a regular six-sided die, there is only one ten, so the probability is 1/6.

The probability of getting tens depends on the context. If you are referring to a regular deck of cards, there are four tens (10 of hearts, diamonds, clubs, and spades) out of a total of 52 cards. So the probability of drawing a ten is 4/52 or 1/13. If you are referring to rolling a regular six-sided die, there is only one ten (the number 10 itself) out of a total of six possible outcomes. So the probability of rolling a ten is 1/6.

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Answer:

onomatopoeia

Step-by-step explanation:

onomatopoeia are words that are sounds

Answer:

Onomatopoeia

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

We are asked for the diameter, radius, and area of a circle.

We are given the Circumference.

We should know that;

[tex]Circumference = (diameter)\pi[/tex]

[tex]Circumference = 24\pi[/tex] (Exact)

This means that the Diameter is 24.

The Radius is [tex]\frac{1}{2}[/tex] of the Diameter.

This means that the Radius is 12.

The area of a circle is represented as;

[tex]Area = \pi(radius)^2[/tex]

We have the requirements to find the area, with the value of the radius.

Solve for the area;

[tex]Area = \pi(12)^2[/tex]

[tex]Area = 144 \pi[/tex] (Exact)

[tex]Area = about \ 452.39.[/tex] (Approx.)

Answer:

Step-by-step explanation:

The simple interest can be calculated using the formula:

I = P * r * t

where:

P = principal amount = $575

r = annual interest rate = 6.5% = 0.065

t = time period = 10 years

I = 575 * 0.065 * 10

I = $373.75

The new balance can be found by adding the interest to the principal:

New balance = Principal + Interest

New balance = $575 + $373.75

New balance = $948.75

Rounded to the nearest cent, the new balance is $948.75.

The value of sin (x/2) is -√(26/27).

The value of cos (x/2) is -√(2/27)

The value of tan (x/2) is 1/12.

We know that sin(x) = -2/27 in Quadrant 3, which means that x lies between 180 degrees and 270 degrees.

a. To find sin(x/2), we can use the half-angle formula:

sin(x/2) = ±√[(1-cos(x))/2]

Since x lies in Quadrant 3, we know that cos(x) is negative. To find cos(x), we can use the Pythagorean identity:

sin²(x) + cos²(x) = 1

(-2/27)² + cos²(x) = 1

cos²(x) = 1 - (-2/27)²

cos(x) = -√(1 - (-2/27)²)

cos(x) = -25/27

Now we can substitute cos(x) into the half-angle formula:

sin(x/2) = ±√[(1-(-25/27))/2]

sin(x/2) = ±√[(27/27 + 25/27)/2]

sin(x/2) = ±√[52/54]

sin(x/2) = ±√(26/27)

Since x is in Quadrant 3, sin(x/2) is negative.

Therefore;

sin(x/2) = -√(26/27)

b. To find cos(x/2), we can use the half-angle formula:

cos(x/2) = ±√[(1+cos(x))/2]

Again, we know that cos(x) is negative, so we can use the value we found earlier:

cos(x/2) = ±√[(1-25/27)/2]

cos(x/2) = ±√[2/27]

Since x is in Quadrant 3, cos(x/2) is also negative.

Therefore;

cos(x/2) = -√(2/27)

c. Finally, to find tan(x/2), we can use the identity:

tan(x/2) = sin(x)/(1+cos(x))

We already know sin(x) and cos(x), so we can substitute them in:

tan(x/2) = (-2/27)/(1-25/27)

tan(x/2) = (-2/27)/(-24/27)

tan(x/2) = 1/12

Therefore,

tan(x/2) = 1/12

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Answer:

x^2+8x+8/2x+4

Step-by-step explanation:

Please help me with my question that I posted.  I really need help.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can use the distributive property and basic algebraic operations to multiply the given expression:

(2x+3)(x^2 - 6x - 2)

= 2x(x^2 - 6x - 2) + 3(x^2 - 6x - 2) // Distribute 2x and 3

= 2x^3 - 12x^2 - 4x + 3x^2 - 18x - 6 // Multiply each term

= 2x^3 - 9x^2 - 22x - 6 // Combine like terms

Therefore, (2x+3)(x^2 - 6x - 2) simplifies to 2x^3 - 9x^2 - 22x - 6.

slope = 3-1/9-3 = 2/6 = 1/3

y = 1/3x + b

1 = 1/3(3) + b

1 = 1 + b

b = 0

equation: y = -1/3x + 0

Answer:

When the ball hits the ground, its height will be 0 meters. Therefore, we need to solve the equation:

h(t) = 0

8t - 5t^2 + 4 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula, but in this case, it's easier to use factoring:

(5t - 4)(t - 1) = 0

From this equation, we can see that either 5t - 4 = 0 or t - 1 = 0. Solving for t in each case, we get:

5t - 4 = 0 ==> t = 0.8 seconds

t - 1 = 0 ==> t = 1 second

Therefore, the ball will reach the ground after either 0.8 seconds or 1 second, depending on the initial height of the ball.

240 more residents have an occupation in industry than have an occupation in government. The solution has been obtained by using arithmetic operations.

It is believed that the four fundamental operations, often referred to as "arithmetic operations", can describe all real numbers. The four mathematical operations that produce the quotient, product, sum, and difference are divide, multiply, add, and subtract.

We are given a graph determining the types of occupations of the 1,200 residents of a town.

Percentage of residents having occupation in government is:

100% - 25% - 15% - 25% - 30% = 5%

Number of residents having occupation in industry is as follows:

25% of 1200 = 300

Similarly, number of residents having occupation in government is:

5% of 1200 = 60

Number of more residents that have occupation in industry than have an occupation in government is:

300 - 60 = 240

Hence, 240 more residents have an occupation in industry than have an occupation in government.

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The circle graph was missing in the question which has been attached below.

The probability that exactly three plants don't grow is given as follows:

0.0054 = 0.54%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The parameter values for this problem are given as follows:

The probability that exactly three don't grow is P(X = 3), hence:

P(X = 3) = C(8,3) x (0.05)^3 x (0.95)^5 = 0.0054.

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The domain and the range of h(n) consist of all possible sets of whole numbers.

Other answers are listed below

How to determine the domain and the range of h(n)

From the question, we know that:

h(n) is the number of houses

n and h(n) can only take whole numbers as its values

So, we have

Thus, the domain and range consist of all possible sets of whole numbers.

How to determine h(5) and h(11)

From the figure, we can see that

The number of houses is the same as the figure number

This means that

h(5) = 5 and h(11) = 11

How to represent the explicit function of h(n)

By the computations above, we have the formula of h(n) to be:

h(n) = n

The values of s(4) and s(7)

Here, we have

s(n) is the number of segments

From the figure, we can see that

The number of segments is twice the the figure number

So, we have

s(4) = 8

s(7) = 14

The growth pattern of s(n)

Recall that:

The number of segments is twice the the figure number

This means that

The growth pattern of s(n) is linear, with a constant rate of change

The explicit function of s(n)

Above, we have

The number of segments is twice the the figure number

Mathematically, this can be expressed as

s(n) = 2n

How to complete the table for f(5) and f(7)

From the table, we can see that

The division of a term by 2 gives the next term

So, we have

f(5) = 2/2 = 1

f(7) = 1/2/2 = 1/4

How to determine the domain of f(n)

The possible values of n are real numbers

Thus, the domain consist of all possible sets of real numbers.

The observation of the function

Above, we have

The division of a term by 2 gives the next term

This represents the observation

How to determine the value of g(4)

From the question, we have

This means that

g(n) = 2(9)^n-1

So, we have

g(4) = 2(9)^3

g(4) = 1458

How to complete the statements

The function is a doubling function

So, we have

g(n) = g(n - 1) * 2, g(n) = g(n - 2) * 4 and  g(n) = g(n - 3) * 8

How to determine the value of g(24)/g(21)

Recall that

g(n) = 2(9)^n-1

So, we have

g(24) = 2(9)^23

g(21) = 2(9)^20

When the equations are divided, we have

g(24)/g(21) = 2(9)^23/2(9)^20

Evaluate

g(24)/g(21) = 729

Hence, the value is 729

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The mean oil-change time for which there is a 10% chance of being at or below is approximately 15.92 minutes.

We can start by using the Central Limit Theorem.

Data given:

The population mean is μ = 16.9 minutes

population standard deviation is σ = 4.7 minutes

sample size of n = 40 oil changes performed between 10 A.M. and 12 P.M.

The standard error of the mean (SE) is given by:

SE = σ / √n

SE = 4.7 / √40

SE = 0.743

To find the mean oil-change time for which there is a 10% chance of being at or below, we need to find the z-score associated with the 10th percentile of the standard normal distribution, which is -1.28 (using a standard normal distribution table or calculator).

We can use the formula for a z-score:

z = (x - μ) / SE

where x is the desired mean oil-change time.

Substituting the known values and solving for x, we get:

-1.28 = (x - 16.9) / 0.743

x = -1.28 * 0.743 + 16.9

x = 15.92

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The total cost of Joeli's purchases is $45.35.

What is the addition?

Addition is a mathematical operation that combines two or more numbers or quantities to produce a sum. It is one of the four basic arithmetic operations, along with subtraction, multiplication, and division. In addition, the numbers being combined are called addends, and the result is called the sum. The addition operator is represented by the symbol "+".

To find the total cost of Joeli's purchases, we need to add the cost of the helmet to the cost of the elbow pads:

Total cost = helmet cost + elbow pads cost

Total cost = $27.57 + $17.78

Total cost = $45.35

Therefore, the total cost of Joeli's purchases is $45.35.

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By answering the above question, we may infer that Due to the fact that equation we are multiplying a unit of money by a unit of time, the units for this product are dollars.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

$9/hour multiplied by 8 hours results in:

$8 × $9/hour = $72

Due to the fact that we are multiplying a unit of money by a unit of time, the units for this product are dollars.

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