Which equation represents the circle shown?
A. (x − 3)2 + (y − 3)2 = 4
B. (x − 3)2 + (y − 3)2 = 16
C. (x + 3)2 + (y + 3)2 = 4
D. (x + 3)2 + (y + 3)2 = 16
E. (x + 4)2 + (y + 4)2 = 3

Answer:

x < -3 or x > 2

Step-by-step explanation:

x² + x - 6 > 0

Convert the inequality to an equation.

x² + x - 6 = 0

Factor using the AC method and get:

(x - 2) (x + 3) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x - 2 = 0

x = 2

x + 3 = 0

x = -3

So, the solution is x < -3 or x > 2

Answer:

0.8413 = 84.13% probability that a bolt has a length greater than 2.96 cm.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 3 cm and a standard deviation of 0.04 cm.

This means that \(\mu = 3, \sigma = 0.04\)

What is the probability that a bolt has a length greater than 2.96 cm?

This is 1 subtracted by the p-value of Z when X = 2.96. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{2.96 - 3}{0.04}\)

\(Z = -1\)

\(Z = -1\) has a p-value of 0.1587.

1 - 0.1587 = 0.8413

0.8413 = 84.13% probability that a bolt has a length greater than 2.96 cm.

Answer:

All you have to do is write how you feel about this it's simple :|

Step-by-step explanation:

To solve for x in the equation log(16x) = 3/2, we need to use the definition of logarithms, which states that log base b of a is equal to c if and only if b raised to the power of c equals a.

In this case, we have:

log(16x) = 3/2

Rewriting this in exponential form, we get:

10^(3/2) = 16x

We can simplify 10^(3/2) as follows:

10^(3/2) = 10^(1/2) * 10^1 * 10^(1/2) = (sqrt(10))^2 * 10^(1/2) = 10 * sqrt(10)

Therefore, we have:

16x = 10 * sqrt(10)

Dividing both sides by 16, we get:

x = (10 * sqrt(10)) / 16

Simplifying this expression, we get:

x = (5 * sqrt(10)) / 8

So the solution to the equation log(16x) = 3/2 is x = (5 * sqrt(10)) / 8.

Answer:

\(\Huge \boxed{\boxed{ x = 1}}\)

Step-by-step explanation:

Isolate the variable on one side of the equation before trying to solve it. It means that you should only have constants (numbers) on the other side of the equal sign and the variable alone on the one side.

To do this, you can add, subtract, multiply, divide, or use any other operation to both sides of the equation as long as you do the same thing on both sides.

Your final step depends on the equation and how you've simplified it. In general, you want to figure out how you arrived at the final equation by working backwards from it. You'll isolate the variable in the last action you took.

-------------------------------------------------------------------------------------------------------------

Step1: Subtract \(\bold{2x}\) from both sides

Step 2: Subtract 3 from both sides

Step 3: Divide both sides of the equation by 6

So the solution to the equation \(\bold{8x + 3 = 2x + 9}\) is \(\bold{x = 1}\).

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Answer:

Step-by-step explanation:

First Choice

Answer:

we see it in our left side of the road

The expression with the correct coefficients in each block is given as follows:

20x³ + 0x² - 7x.

The functions in the context of this problem are defined as follows:

The operation is given as follows:

f(x)g(x) + h(x).

Hence, to obtain the resultant function, we apply the definitions into the operation and the simplify, applying the distributive property and combining the like terms, as follows:

4x(5x² - 4) + 9x = 20x³ - 16x + 9x = 20x³ - 7x.

As there is no x² term, the coefficient of zero multiplies the term x².

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The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

62 steps per minute

Explanation:

Let the number of steps he climbed per minute be x.

If Robert climbed 775 steps in 12 and 1/2 minutes, let's go ahead and determine many steps he took per minute by setting up the question as a proportion;

Answer:

21.142

Step-by-step explanation:

not sure it's correct

Answer:

A and D

Step-by-step explanation:

-14 is less than -8 because is further away from 0

Use the property of similarity of triangles =》the corresponding sides of a triangle should be in the same ratio.

Take the missing side as 'x'.

The corresponding sides here are,

■ 7 & 14 ft

■ 5 & x ft

7/14 = 5/x

7x = 5 × 14 (cross multiplication)

7x = 70

x = 70/7

x = 10 ft

Height of the tree = 10 ft.

_____

Hope it helps ⚜

there woldbe 96 volume

Step-by-step explanation:

to find the volume you have to multiply width x lenghth x height

so set up your equation like this -

3 x 2 x 2

the times everything by 2 so it will now look like this -

6 x 4 x 4

then solve and get the answer 96

Answer:

25) -4, -1

Equation: -4x-1

27) 4, 4

Equation: 4x+4

29) 5/2,0

Equation: 5/2x

Step-by-step explanation:

Y=mx+b

Answer:

Step-by-step explanation:

1/3:4=n

1/3*1/4=n

n=1/12

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check

1/3:4=1/12

1/3*1/4=1/12

1/12=1/12

The answer is good

Answer:

26w

Step-by-step explanation:

you can start by dividing the total length of the road by the distance that can be repaired per week:

13 km ÷ 3 1/2 km/week = 3.71 weeks

Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:

A.  h'(2) = 5

B.  m'(2) = -24

C.  y = 8x - 31

D.  j'(2) = 3/25 = 0.12

Step-by-step explanation:

When differentiating composite functions, use the chain rule.

\(\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\$\left[f\left(g(x)\right)\right]'=f'\left(g(x)\right) \cdot g'(x)$\\\end{minipage}}\)

Chain Rule: The derivative of a composite function is the product of the derivative of the outer function evaluated at the inner function and the derivative of the inner function.

Using the chain rule, if h(x) = g(f(x)) then h'(x) = g'(f(x)) ⋅ f'(x).

To find h'(2), substitute x = 2 into the differentiated equation:

\(\begin{aligned}h'(x)& = g'(f(x)) \cdot f'(x)\\\\\implies h'(2)& = g'(f(2)) \cdot f'(2)\\& = g'(5) \cdot 1\\& = 5 \cdot 1\\&=5\end{aligned}\)

Therefore, h'(2) = 5.

Using the chain rule, if m(x) = f(x²) then m'(x) = f'(x²) ⋅ 2x.

To find m'(2), substitute x = 2 into the differentiated equation:

\(\begin{aligned}m'(x) &= f'(x^2) \cdot 2x\\\\\implies m'(2) &= f'(2^2) \cdot 2(2)\\&=f'(4) \cdot 4\\&=-6 \cdot 4\\&=-24\end{aligned}\)

Therefore, m'(2) = -24.

To find the slope of the tangent line to the graph of k at x = 4, substitute x = 4 into the derivative of k(x).

If k(x) = f(g(x)) then k'(x) = f'(g(x)) ⋅ g'(x).

Therefore, the slope of the tangent line is:

\(\begin{aligned}k'(x) &= f'(g(x)) \cdot g'(x)\\\\\implies k'(4) &= f'(g(4)) \cdot g'(4)\\&= f'(5) \cdot 4\\&= 2 \cdot 4\\&= 8\end{aligned}\)

Now calculate k(x) when x = 4:

\(\begin{aligned}k(x)&=f(g(x))\\\\\implies k(4) &= f(g(4))\\&=f(5)\\&=1\end{aligned}\)

To write the equation of the tangent line, substitute the found slope m = 8 and point (4, 1) into the point-slope equation:

\(\begin{aligned}y-y_1&=m(x-x_1)\\y-1&=8(x-4)\\y-1&=8x-32\\y&=8x-31\end{aligned}\)

Therefore, an equation for the line tangent to the graph of k at x = 4 is:

To find the derivative of j(x) use the quotient rule.

\(\textsf{If\;\;$j(x)=\dfrac{g(x)}{f(x)}$\;\;then:}\\\\\\j'(x)=\dfrac{f(x)g'(x)-g(x)f'(x)}{(f(x))^2}\)

To calculate j'(2), substitute x = 2 into the equation:

\(\begin{aligned} \implies j'(2)&=\dfrac{f(2)g'(2)-g(2)f'(2)}{(f(2))^2}\\\\&=\dfrac{5 \cdot 1-2 \cdot 1}{(5)^2}\\\\&=\dfrac{5-2}{25}\\\\&=\dfrac{3}{25}\\\\&=0.12\end{aligned}\)

Therefore, j'(2) = 3/25 = 0.12.

Answer:

give me more instructions so i can actually help

Step-by-step explanation:

We can see that the correct equation that can depict the problem is 3(d+17.20) = 782.07. Option D

We have to look at the problem that we have here. In the case of the question that we have been asked, we can see that for the problem that has been given here, it is clear that; Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to park her car.

If it is known that Each night, the hotel charged d dollars and $17.20 for parking. We can say that let the amount that is charged for the lodging be d and we have the equation as; 3(d+17.20) = 782.07.

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By finding all the four slopes, we can see that the word is ECHA.

We know that the general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

We know that if the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:

s = (y₂ - y₁)/(x₂ - x₁)

With that formula we can get the slopes.

1) Using the points (0, 3) and (2, 4).

m = (4 - 3)/(2 - 0) = 1/2, so the letter is E.

2)Using (-1, -12) and (1, -8)

m = (-8 + 12)/(1 + 1) = 4/2 = 2, so the letter is C.

3) We have (2, -6) and (-4, -3) so:

m = (-3 + 6)/(-4 - 2) = 3/-6 = -1/2, so the letter is H

4)we can use the points (0, 3) and (1, 1), so:

m = (1 - 3)/(1 - 0) = -2, so the letter is A

Then the word is ECHA

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The change in temperature is just the difference of the temperature

So, the temperature has changed 15 degrees Celsius during the day.

Answer:

900 square meters

Step-by-step explanation:

The property is in the shape of a square.

The perimeter of a square is given as:

P = 4L

where L = length of its side

Therefore, the length of the property is:

120 = 4 * L

L = 120 / 4 = 30 meters

The area of a square is given as:

A = L * L

Therefore, the area of the property is:

A = 30 * 30 = 900 square meters

The loss in percentage is 25%.

Given that,

Cost price of an article      = $28

Selling price of the article = $21

We know that,

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Now  loss can be calculated by subtracting selling price from  cost price,

Therefore,

28 - 21 = 7

Hence there are loss of $7 in business,

Now to calculate percentage loss,

Divide loss by cost price then multiply with 100,

Then,

⇒ (7/28)x100

⇒ 25%

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Answer:It is The first one.

Step-by-step explanation: