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Point (5,5) lies on the graph of f(x) = log2(x + 3) + 2

Given,

g(x) = log2x

Here,

The point (8,3) lies on the graph of g(x).

If we compare g(x) with f(x) we can see that, f(x) is obtained from g(x) after following translations:

a) Adding 3 to x.

Addition of 3 to x means horizontal shift towards left. So this means the point will also be shifted 3 units to left

f(x) = log2(x + 3)

b) Addition of 2 to the function value

This indicates a vertical shift upwards by 2 units. So this means the point will also be shifted 2 units up.

f(x) = log2(x + 3) + 2

This is the required function.

Moving (8,3) 3 units to left at x axis it will be (5,3).

Then moving it 2 units up at y axis it will be (5,5)

Therefore option B is correct .

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the curve length of C over the interval 0 ≤ t ≤ π/2 is (3π/2) units.

What is Parametric curve?

To find the curve length of the curve C defined by the parametric equations x = cos(3t) and y = sin(3t), where t ranges from 0 to π/2, we can use the arc length formula for parametric curves.

The arc length formula for a parametric curve defined by x = f(t) and y = g(t), where a ≤ t ≤ b, is given by:

\(L = ∫[a, b] √[ (dx/dt)^2 + (dy/dt)^2 ] dt\)

Let's calculate the arc length for the given curve C:

x = cos(3t)

y = sin(3t)

First, we need to find the derivatives dx/dt and dy/dt:

dx/dt = -3sin(3t)

dy/dt = 3cos(3t)

Now, let's substitute these derivatives into the arc length formula:

\(L = ∫[0, π/2] √[ (-3sin(3t))^2 + (3cos(3t))^2 ] dt\)

\(L = ∫[0, π/2] √[ 9sin^2(3t) + 9cos^2(3t) ] dtL = ∫[0, π/2] 3 √[ sin^2(3t) + cos^2(3t) ] dtL = ∫[0, π/2] 3 dtL = 3[t] from 0 to π/2L = 3(π/2 - 0)L = 3π/2\)

Therefore, the curve length of C over the interval 0 ≤ t ≤ π/2 is (3π/2) units.

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Answer:

B

Step-by-step explanation:

We know that AB has endpoints at A(4, -3) and B(3, 7).

To find Line D, which is the perpendicular bisector of AB, we first need to find the slope of AB and its midpoint.

So, let's find the slope of AB using the slope formula:

Let (4, -3) be (x₁, y₁) and let (3, 7) be (x₂, y₂). Substitute them into the slope formula:

So, the slope of AB is -10.

Remember that the slopes of perpendicular lines are negative reciprocals of each other.

Therefore, the slope of our Line D is the negative reciprocal of -10. Which is -10 flipped and multiplied by a negative.

So, Line D has a slope of 1/10.

Now, since Line D is also the perpendicular bisector of AB, we need to find the midpoint of AB since Line D must pass through this point.

To find the midpoint, we can use the midpoint formula:

We can again let (4, -3) be (x₁, y₁) and let (3, 7) be (x₂, y₂). Substitute them into the midpoint formula to obtain:

Evaluate. So, the midpoint is:

Now, we can find the equation of our Line D. We know that its slope is 1/10, and that it must pass through (3.5, 2). So, we can use the point-slope form:

Where m is the slope. Let's let (3.5, 2) be (x₁, y₁) and substitute 1/10 for m. This yields:

This is the same as choice C. So, choice C is indeed an equation of Line D.

We can distribute the right to obtain:

Add 2 to both sides to acquire:

This is the same as choice D. So, choice D is indeed an equation of Line D.

Moreover, we can put this into standard form by multiply everything by 10, which gives:

Subtracting x from both sides yields:

This is the same as A. So, choice A is also an equation of Line D.

There is no way to acquire choice B. So, B is not an equation of Line D.

Therefore, our answer is B.

And we're done!

Answer:

16

Step-by-step explanation:

from what I can tell the numbers are being cut by 1/2 every time meaning that half of 32 is 16 thus it is the most logical answer

Answer:

I am not sure, but my answer is n= –2,(54).

Step-by-step explanation:

2 − 18n = 4n + 58

–4n − 18n = (–2) + 58

–22n=56 |:(–22)

n= –2,(54)

Answer:

None

Step-by-step explanation:

This type of equation is a tautology, it will always be true

We want to see how many solutions does the given equation has.

We will see that the equation has infinite solutions.

The given equation is:

2(x + 4) = 2x + 8

To find how many solutions it has, we need to solve it, we first can distribute the product at the left to get:

2(x + 4) = 2x + 8

2x + 2*4 = 2x + 8

2x + 8 = 2x + 8

Note that we have the exact same thing in both sides, so the value of x can be any real number, and the equation will still be true.

This means that there are infinite solutions for the given equation.

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Step-by-step explanation:

Answer:

-20x

Step-by-step explanation:

Answer: is it 208 or not i'm doing the same test

Step-by-step explanation:

Answer:

\(\frac{m^{3}n+5 }{m^{2}n^{2} }\)

Explanation :

is down below in the picture

Please give me brainiest!!

P(A and B) expressed in the simplest form is (B) 2/21.

To express P(A and B) in the simplest form:

Therefore, P(A and B) expressed in the simplest form is (B) 2/21.

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The complete question is given below:

A bag contains 4 black tiles, 5 white tiles, and 6 blue tiles. Event A is defined as drawing a black tile from the bag on the first draw, and event B is defined as drawing a white tile on the second draw.

If two tiles are drawn from the bag, one after the other without replacement, what is P(A and B) expressed in the simplest form?

A. 4/45

B. 2/21

C. 4/15

D. 5/14

The 21st digit in the decimal expansion of 1/7 is 2 and the 5280th digit in the decimal expansion of 5/17 is 5.

a. To find the 21st digit in the decimal expansion of 1/7 we need to find the decimal expansion. The decimal expansion of 1/7 is a repeating decimal

= 1/7 = 0.142857142857142857…

The sequences 142857 repeat indefinitely. To find the 21st digit, we can divide 21 by the length of the repeating sequence,

= 21 / 6 = 3

Therefore, the third digit in the repeating sequence is 2

b.To find the 5280th digit in the decimal expansion of 5/17 we need to find the decimal expansion. The decimal expansion of 5/17 is a repeating decimal is

=  5/17 = 0.2941176470588235294117647…

The repeating sequences are 2941176470588235

The 5280th digit = 5280 / length of the repeating sequence,

5280 / 16 = 0

Therefore, the 5280th digit is the last digit in the repeating sequence, which is 5.

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a) The Name of the angle of elevation is ∠c = 83.3°

b) The Name of the Hypotenuse side is AC

c) The Name of the Opposite side is AB

The angle formed between the line of sight and the horizontal is known as the angle of elevation. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.

We can use the tangent ratio to determine the angle of elevation:

tan(angle of elevation) = opposite/adjacent

tan(angle of elevation) = 29.25/4.75

tan(angle of elevation) = 6.157

The inverse tangent (tan⁻¹) both sides, we obtain:

angle of elevation = tan⁻¹(6.157)

Using a calculator, we get:

angle of elevation ≈ 81.3 degrees (rounded to the nearest tenth)

The elevation angle is roughly 81.3 degrees.

d) The Name of the Adjacent side is BC

e) The Trig Ratio I will be using is Tan θ = Sin θ/Cos θ because we are  

   given the side Opposite Side & Adjacent Side

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The probability P(X=2, Y+Z ≤ 3) is 13. Random variables are variables in probability theory that represent the outcomes of a random experiment or event.

To find the probability P(X=2, Y+Z ≤ 3), we need to sum up the joint probabilities of all possible combinations of X=2, Y, and Z that satisfy the condition Y+Z ≤ 3.

Step 1: List all the possible combinations of X=2, Y, and Z that satisfy Y+Z ≤ 3:

X=2, Y=1, Z=1

X=2, Y=1, Z=2

X=2, Y=2, Z=1

Step 2: Calculate the joint probability for each combination:

For X=2, Y=1, Z=1:

f(2, 1, 1) = (2+1) * 1 = 3

For X=2, Y=1, Z=2:

f(2, 1, 2) = (2+1) * 2 = 6

For X=2, Y=2, Z=1:

f(2, 2, 1) = (2+2) * 1 = 4

Step 3: Sum up the joint probabilities:

P(X=2, Y+Z ≤ 3) = f(2, 1, 1) + f(2, 1, 2) + f(2, 2, 1) = 3 + 6 + 4 = 13

They assign numerical values to the possible outcomes of an experiment, allowing us to analyze and quantify the probabilities associated with different outcomes.

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A deck has a total of 52 cards.

The probability of getting a black 4 is then:

Integrate (ax)2 − b2 3/2 with respect to x. The result is (2/5)ax5/2 − (b2/5)x3/2 + c, where c is the constant of integration.

Integrate (ax)2 − b2 3/2 with respect to x.

First, use the power rule to rewrite the integrand as

(2/5)ax5/2 − (b2/5)x3/2.

Next, use the integration by parts formula to integrate the expression:

∫(2/5)ax5/2 − (b2/5)x3/2 dx

= (2/5)ax5/2 − (b2/5)x3/2 + c,

where c is the constant of integration.

Integrating (ax)2 − b2 3/2 with respect to x involves using the power rule and the integration by parts formula. The power rule states that when integrating a function to the nth power, the exponent is reduced by one and the coefficient is multiplied by the original exponent divided by the reduced exponent. Therefore, the integrand is rewritten as (2/5)ax5/2 − (b2/5)x3/2. The integration by parts formula is then used to integrate the expression, resulting in (2/5)ax5/2 − (b2/5)x3/2 + c, where c is the constant of integration.

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Answer:

Jared

Step-by-step explanation:

4/25 is larger than 3/25

Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

Answer:

The steak per pound : 2/4 = $1/2=$0.5/ pound

Is it 1 dollar for 2 pound  :   It's correct

Step-by-step explanation:

It will cost $8,783.69 to complete this prank.

To get number of balls needed, we will calculate volume of the room and divide it by the volume of a single ball.

Volume of the room = Length * Width * Height

Volume of the room = 10ft * 10ft × 3ft

Volume of the room = 300 cubic feet

Radius = diameter / 2

Radius = 3in / 2

Radius = 1.5in

Radius = 1.5/12ft

Radius = 0.125ft

Volume of a single ball = (4/3) * π * (radius)^3

Volume of a single ball = (4/3) * π * (0.125ft)^3

Volume of a single ball ≈ 0.013 cubic feet

Number of balls needed = Volume of the room / Volume of a single ball

Number of balls needed = 300 cubic feet / 0.013 cubic feet

Number of balls needed =  23,077 balls

Since a 100 pack is purchased for $37.99:

Number of packs needed = Number of balls needed / 100

Number of packs needed ≈ 23,077 balls / 100 balls per pack

Number of packs needed ≈ 231 packs

Total cost = Number of packs needed × Cost per pack

Total cost ≈ 231 packs × $37.99 per pack

Total cost = $8,783.69

Full question:

Bri is doing her schoolwork in a room that is 10ft by 10ft. Since it’s the end of the year we’ve decided to fill this room with 3” diameter plastic balls to a depth of 3ft. Estimate the number of balls needed to fill her office space. To keep things consistent round the volumes of the plastic ball to the nearest thousandths.

A 100 pack of multi colored 3in plastic balls can be purchased at Walmart for 37.99. How much would it cost us to complete this prank.

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We can find the rate of change of cereal sold to amount spent.

From given information,

Increase in boxes of cereal sold is 200,000 - 100,000 = 100,000

Increase in money spent is 60,000 - 40,000 = 20,000

The rate of change of boxes of celear sold to amount spent is:

100,000/20,000 = 5

If we were to write a linear equation of the form y = mx + b, this rate of change would be m.

Thus,

y = 5x + b

Keep in mind, x is amount spent and y is boxes of cereal sold

We need to find b, so we can easily put the point x = 40,000 and y = 100,000 to find b. Shown below:

y = 5x + b

100,000 = 5(40,000) + b

100,000 = 200,000 + b

b = -100,000

Final Equation of the Line:

We need amount of money needed (x) for 1,000,000 boxes of cereal sold (y).

We can substitute and find the answer:

The third answer choice is correct.

$220,000

The direction of the resulting force upon the piling is approximately 298.85 degrees

We can use vector addition to find the direction of the resulting force. Let's call the force exerted by the first bulldozer F1, and the force exerted by the second bulldozer F2. We can represent each force as a vector with a magnitude and direction.

F1 has a magnitude of 1850 pounds and points in a westerly direction. We can represent it as a vector (-1850, 0).

F2 has a magnitude of 3250 pounds and points in a northerly direction. We can represent it as a vector (0, 3250).

To find the resulting force, we need to add these two vectors. We can do this by adding the x-components and the y-components separately.

The x-component of the resulting force is -1850 (from F1) plus 0 (from F2), which is -1850.

The y-component of the resulting force is 0 (from F1) plus 3250 (from F2), which is 3250.

So the resulting force is a vector with components (-1850, 3250). We can find the direction of this vector by taking the inverse tangent of the ratio of the y-component to the x-component.

tan(theta) = (3250) / (-1850)

theta = -61.15 degrees

The negative sign indicates that the resulting force points to the southwest. To get the angle in the range of 0 to 360 degrees, we can add 360 degrees to the angle if it is negative.

theta = 360 - 61.15

theta = 298.85 degrees

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The equivalent operation is: b = (a < 5) ? 12 : (d = 30);

The original if/else statement is:

if (a < 5)

   b = 12;

else

   d = 30;

In this statement, the condition (a < 5) is evaluated. If the condition is true (i.e., if the value of a is less than 5), then the statement b = 12; is executed. Otherwise, if the condition is false (i.e., if the value of a is greater than or equal to 5), then the statement d = 30; is executed.

The equivalent operation using the conditional (ternary) operator is:

b = (a < 5) ? 12 : d = 30;

In this statement, the condition (a < 5) is evaluated. If the condition is true, the value 12 is assigned to b. This is indicated by ? in the statement. The : separates the true and false cases.

If the condition is false (i.e., if the value of a is greater than or equal to 5), the value 30 is assigned to d. This is the value assigned after the : in the statement.

The ternary operator statement (a < 5) ? 12 : d = 30; achieves the same outcome as the original if/else statement, providing an alternative way to write the logic based on the condition a < 5.

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In summary, there are 6 ways to distribute 9 identical balls into 3 identical boxes. This can be determined by finding the number of ways to write 9 as a sum of 3 integers.

To explain further, let's consider the problem of writing 9 as a sum of 3 integers. We can think of this as distributing 9 identical balls into 3 identical boxes, where each box represents one of the integers. Since the boxes are identical, we only need to consider the number of balls in each box.

To find the number of ways to distribute the balls, we can use a concept called "stars and bars." Imagine 9 stars representing the 9 balls, and we need to place 2 bars to separate them into 3 boxes. The positions of the bars determine the number of balls in each box.

For example, if we place the first bar after the 3rd star and the second bar after the 6th star, we have 3 balls in the first box, 3 balls in the second box, and 3 balls in the third box. This corresponds to one way of writing 9 as a sum of 3 integers (3+3+3).

By using stars and bars, we can determine that there are 6 different arrangements of bars among the 9 stars, resulting in 6 ways to distribute the 9 identical balls into the 3 identical boxes.

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Answer:

First add all the equations like (11y-32)+(3x-16)+(6x+7)=180

Step-by-step explanation:

You would first combine all the like terms so put all the variables on one side and the numbers on the other. After you have done that, you would just solve.

From the given symmetry the given figure has point and rotational symmetry.

As given in the question,

Figure is attached.

The attached figure is having two arrows clockwise and anticlockwise.

So the given figure has point symmetry.

Given figure does not have line symmetry.

So the given figure has rotational symmetry.

Therefore, the given figure has point and rotational symmetry.

The above question is incomplete, the complete question is:

Determine whether the figure has line, point, and/or rotational symmetry. Check all that apply. (1 point)

Line

Point

Rotational

None

Figure is attached.

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Answer:

not a monomial

Step-by-step explanation:

monomial

Prefix mono- means 1 so, monomial means one term

This has more than one term so it’s not a monomial

Hopes this helps please mark brainliest

Answer:

(1,4)

Step-by-step explanation:

take 2 minus 1 then nine minus 5

the formal definition of the definite integral: ∫()=lim→∞[∑=1(∗)Δ]  is the formula in terms of i and n for the gernal left endpoint x i-1

What is the formula for left endpoint approximation?

Rule: Left-Endpoint Approximation

On each subinterval [xi−1,xi] (for i=1,2,3,…,n), construct a rectangle with width Δx and height equal to f(xi−1), which is the function value at the left endpoint of the subinterval. Then the area of this rectangle is f(xi−1)Δx

In this problem you will calculate ∫302+4 by using the formal definition of the definite integral: ∫()=lim→∞[∑=1(∗)Δ].

(a) The interval [0,3] is divided into equal subintervals of length Δ. What is Δ (in terms of )? Δ

(b) The right-hand endpoint of the th subinterval is denoted ∗. What is ∗ (in terms of and )

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