When looking at a rational function f(x) = (x+3)(x-2)(x+5) ——————— (x-3)(x+2)(x-5), Charles and Bobby have two different thoughts. Charles says that the function is defined at x = - 2, x = 3, and x = 5. Bobby says that the function is undefined at those x values. Who is correct? Justify your reasoning.

Therefore, the measure of angle ∠Y to the nearest tenth of a degree is approximately 103.2 degrees.

To find the measure of angle ∠Y, we need to use the law of cosines, which relates the lengths of the sides of a triangle to the cosine of its angles.

The formula for the law of cosines is:

\(c^2 = a^2 + b^2 - 2ab cos(C)\)

Where a, b, and c are the lengths of the sides of the triangle, and C is the angle opposite to side c.

In our case, we know the lengths of the sides w, x, and y, and we want to find the angle ∠Y, which is opposite to side y. So, we can use the formula as follows:

\(y^2 = w^2 + x^2 - 2wx cos(Y)\)

Substituting the values, we have:

\(630^2 = 170^2 + 590^2 - 2(170)(590) cos(Y)\)

Simplifying and solving for cos(Y):

\(cos(Y) = (170^2 + 590^2 - 630^2) / (2170590)\)

cos(Y) ≈ -0.236

Note that the cosine of an angle is negative if the angle is between 90 and 180 degrees, which is the case for angle ∠Y in this triangle. Therefore, we need to use the inverse cosine function to find the measure of angle ∠Y:

Y ≈ 103.2 degrees

Rounding to the nearest tenth of a degree, we get:

Y ≈ 103.2°

Therefore, the measure of angle ∠Y to the nearest tenth of a degree is approximately 103.2 degrees.

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Answer:1244

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use the formula for calculating compound interest PN=P0(1+rk)Nk where N is the unknown, PN=2250, k=1, N=15, and r=0.028. Substitute the values into the formula and simplify.

2250=P(1+0.0281)1⋅15

2250=P(1.028)15

2250=P(1.5132...)

1486.91=P

Rounded to the nearest dollar, Lucy's initial deposit was $1487.

The rewritten expression of y = x + 8/3x using the distributive property is y = x(1 + 8/3)

From the question, we have the following parameters that can be used in our computation:

Y can represent the distance Frog B hopped as y=x+ 8/3 x.

This means that

y = x + 8/3x

Factor out x from the equation

So, we have

y = x(1 + 8/3)

The above equation has been rewritten using the distributive property.

Hence, the rewritten expression using the distributive property is y = x(1 + 8/3)

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Answer:

None of the sides can be a triangle.

Step-by-step explanation:

Answer:

parallelogram

Step-by-step explanation:

That's the answer....

\(\huge\blue{\fbox{\tt{Solution:}}}\)

We can simplify the expression using trigonometric identities.

First, we can use the double angle formula for sine to write sin(2x) = 2sin(x)cos(x).

Next, we can use the double angle formula for cosine to write cos(2x) = cos^2(x) - sin^2(x) = 1 - 2sin^2(x). Rearranging this equation gives 2sin^2(x) - 2cos^2(x) = -cos(2x) + 1.

Substituting these identities into the original expression gives:

tan(x-1) ( sin2x-2cos2x) = tan(x-1) [2sin(x)cos(x) - 2(1 - 2sin^2(x))]

= 2tan(x-1)sin(x)cos(x) - 2tan(x-1) + 4tan(x-1)sin^2(x)

We can use the identity tan(x) = sin(x)/cos(x) to simplify this expression further:

2tan(x-1)sin(x)cos(x) - 2tan(x-1) + 4tan(x-1)sin^2(x)

= 2sin(x)cos(x)/(cos(x-1)) - 2sin(x)/(cos(x-1)) + 4sin^2(x)/(cos(x-1))

Multiplying both sides of the equation by cos(x-1) gives:

2sin(x)cos(x) - 2sin(x) + 4sin^2(x)cos(x-1) = 2(1-2sin(x)cos(x))

Expanding the left-hand side of the equation gives:

2sin(x)cos(x) - 2sin(x) + 4sin^2(x)cos(x) - 4sin^2(x) = 2 - 4sin(x)cos(x)

Simplifying this equation gives:

4sin^2(x) - 2sin(x) - 2 = 0

This is a quadratic equation in sin(x), which can be solved using the quadratic formula.

Answer:

f(4)= 36

f(4) = 7n-7

Step-by-step explanation:

f(4)= 9(4)

36= f(4)

f(4) = - 2(4)(n-1)-1

8(n-1) - 1

7 (n-1)

7n-7 = f(4)

Answer:

x=7

Step-by-step explanation:

9x-9=5x+19

Combine like terms

9x-5x=19+9

4x=19+9

4x=28

x=7

The equation of the line that passes through the points (1,6) and (2,7) is y = x + 5.

We can use the point-slope version of the equation, which is: to determine the equation of a line passing through two specified points.

y - y₁ = m(x - x₁)

where (x₁, y₁) are the coordinates of one of the points, m is the slope of the line, and (x, y) are the coordinates of any other point on the line.

Use the points (1,6) and (2,7) to find the equation of the line:

Using (x₁, y₁) = (1,6):

y - 6 = m(x - 1)

Now, substitute the coordinates (2,7) into the equation:

7 - 6 = m(2 - 1)

1 = m

So, the slope of the line is m = 1.

Substitute this value into the equation:

y - 6 = 1(x - 1)

y - 6 = x - 1

y = x + 5

Therefore, the equation of the line that passes through the points (1,6) and (2,7) is y = x + 5.

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Answer:aw dawd

Step-by-step explanation:awd awdkakwd

Answer:

1. Constant multiplicative.

2. 1.05.

Step-by-step explanation:

Their savings increase by 1.05x every year.

I'm not sure why m is chosen as the slope, but you can think of the phrase "mountains have a slope" to help remember m is involved.

The b is the y intercept.

For example, y = 2x+5 has a slope of 2 and y intercept of 5.

The Richter scale is logarithmic, which means that for every one-unit increase in magnitude, the energy released by the earthquake increases by a factor of 10.

To calculate how many times more intense earthquake A was than earthquake B, we need to find the difference in their magnitudes and then raise 10 to that power.

The difference in magnitudes is:

8.2 - 4.6 = 3.6

To find how many times more intense earthquake A was than earthquake B, we need to raise 10 to the power of 3.6:

10^3.6 = 3981.07

Therefore, earthquake A was approximately 3981.07 times more intense than earthquake B. Rounded to two decimal places, the answer is 3981.07.

\(\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{2}{ h},\stackrel{-4}{ k})\qquad \qquad radius=\stackrel{4}{ r} \\\\\\\ [x-2]^2~~ + ~~[y-(-4)]^2~~ = ~~4^2\implies (x-2)^2~~ + ~~(y+4)^2~~ = ~~16\)

Answer:

4/3

Step-by-step explanation:

\( \frac{8}{9} \div \frac{6}{9} \\ \\ \implies \: \frac{8}{9} \times \frac{9}{6} \\ \\ \implies \: \frac{8}{1} \times \frac{1}{6} \\ \\ \implies \: {\boxed {\purple{\frac{4}{3} }}}\)

Step-by-step explanation:

CFB reads as twenty five degrees

complementary angle  will add to it to sum 90 degrees  = sixty five degrees

   angle CFD is sixty five degrees

Given:

The given points are A(-3,-1) and B(5,3).

Required:

We need to find the set of all points that are the same distance from the points A(-3,-1) and B(5,3).

Explanation:

Recall that the set of points that are the same distance from the point A(-3,-1) and (5,3) is the perpendicular bisector of the line segment AB.

Consider the slope formula.

We get the slope of the line segment AB is 1/2.

The slope of the perpendicular is the negative reciprocal of the slope of the line segment AB.

The perpendicular line is passing through the midpoint of A(-3,-1) and B(5,3).

Consider the midpoint formula.

Consider the general form of the line equation.

Substitute m=-2, x=1, and y=1 in the line equation to find b.

Add 2 to both sides of the equation.

Substitute m=-2 and b=3 in the line equation.

We get the perbenticular bisector y =-2x+3.

Final answer:

Answer:

Step-by-step explanation:

You want to identify the given shapes as a regular or irregular polygon, or neither.

A regular polygon is one that has all sides congruent, and all interior angles congruent. Polygon E is marked as having congruent sides and congruent angles.

Polygon E is a regular polygon.

A polygon is a closed figure formed by line segments connected end-to-end. A simple polygon is one that has no intersecting line segments. A convex polygon is one that has all interior angles measuring 180° or less.

Any simple polygon that is not a regular polygon is an irregular polygon.

Polygons A, B, D are irregular polygons.

A circle is not a polygon. Figure C is neither a regular polygon nor an irregular polygon.

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Kala spun the spinner 1000 times and got the following results:

- Yellow: 400 times

- Red: 300 times

- Blue: 300 times

1. Calculate the amount of sales tax:

  - The item costs $350 before tax.

  - The sales tax rate is 14%.

  - To find the sales tax amount, multiply the cost of the item by the tax rate:

    Sales tax = $350 * 0.14 = $49.

2. Determine the total cost of the item including tax:

  - Add the sales tax amount to the original cost of the item:

    Total cost = $350 + $49 = $399.

3. Analyze the spinner results:

  - The spinner has 10 equal-sized slices.

  - There are 4 yellow slices, 3 red slices, and 3 blue slices.

  - Kala spun the dial 1000 times.

4. Calculate the frequency of each color:

  - Yellow: Kala got 400 yellow results out of 1000 spins.

  - Red: Kala got 300 red results out of 1000 spins.

  - Blue: Kala got 300 blue results out of 1000 spins.

5. Calculate the probability of landing on each color:

  - Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.

  - Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.

  - Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.

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Answer:

54 students

Step-by-step explanation:

45% of 120 is 54

Answer:

The minimum value is 0

Step-by-step explanation:

If there is a negative sign in front of the x^2 it is always a maximum (-x^2 goes downwards)

If the x^2 is positive it always a minimum.

You have the correct ordered pair, the minimum value is equal to the y value.

Answer:A unique line is defined by any two distinct (not identical) points. You have two distinct, which means you have a line. To find the equation for the line, we start with the slope-intercept equation for a line. This is only a template for a generic line, so we will have to find the specific values of m (slope) and b (y-intercept) that define your line.

The template: y = mx + b

b is the y-intercept, which, if you look at (0,–2), you will see is –2; it is where the line crosses the y-axis. Fill that value of b into our template to get:

y = mx – 2

Now, we only need the value of m, which is the slope. If you have two points on a line, you can calculate the slope of that line. The slope is the change (difference) of y over the change in x (difference) of x for two given points on the line. It's a fraction or ratio though sometimes it can be reduced to an integer.

So, taking your two points, you calculate the slope, m, in the following way:

(x1,y1) = (0,–2)

(x2,y2) = (5,1)

        y2 – y1                   1 – (–2)                1 + 2               3

m = ________   =     ________    =     ________  =    ____

       x2 – x1                      5 — 0            

Step-by-step explanation:

There is no day when the Number of cupcakes sold at Location 1 is equal to the number of cupcakes sold at Location 2. on Day 5, Location 2 sold 850 cupcakes.

(a) To determine the number of cupcakes sold at each location on Day 5, we substitute x = 5 into the equations:

For Location 1:

y = 150x + 200

y = 150(5) + 200

y = 750 + 200

y = 950

Therefore, on Day 5, Location 1 sold 950 cupcakes.

For Location 2:

y = 150x + 100

y = 150(5) + 100

y = 750 + 100

y = 850

Therefore, on Day 5, Location 2 sold 850 cupcakes.

(b) To find the day when the number of cupcakes sold at Location 1 is equal to the number of cupcakes sold at Location 2, we set the two equations equal to each other:

150x + 200 = 150x + 100

We can see that the variable x cancels out, which means the value of x doesn't matter in this case. The equation simplifies to:

200 = 100

However, this equation is not true. It implies that the number of cupcakes sold at Location 1 can never be equal to the number of cupcakes sold at Location 2.

Therefore, there is no day when the number of cupcakes sold at Location 1 is equal to the number of cupcakes sold at Location 2.

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Note the full question may be :

A local bakery keeps track of the number of cupcakes sold each day at two different locations. At Location 1, the number of cupcakes sold is represented by the equation y = 150x + 200, where x represents the number of days and y represents the number of cupcakes sold. At Location 2, the number of cupcakes sold is represented by the equation y = 150x + 100.

(a) Determine the number of cupcakes sold at each location on Day 5.

(b) On which day will the number of cupcakes sold at Location 1 be equal to the number of cupcakes sold at Location 2?            

Answer:

The answer is 49.! :)

Step-by-step explanation:

If you look at the table, it shows 3;7. If you look at the 21 in the 2 row, and look under it in the other orange row its 49. So the answer would be 49! :)

Answer:

49

Step-by-step explanation:

To calculate the final account balance after 7 years with a 5% interest rate compounded 12 times per year, we can use the formula:

A = P(1 + r/n)^(nt)

where:

A = the final account balance

P = the initial principal (the amount Heather invested), which is $4,625 in this case

r = the annual interest rate, which is 5%

n = the number of times the interest is compounded per year, which is 12 in this case

t = the number of years the money is invested, which is 7 in this case

Substituting these values into the formula, we get:

A = $4,625(1 + 0.05/12)^(12*7)

A = $4,625(1.0041667)^84

A = $4,625(1.480244)

A = $6,849.46

Therefore, Heather’s account balance will be $6,849.46 after 7 years if the interest is compounded 12 times each year.

Answer:

Cant see the picture

Step-by-step explanation:

Cant see the picture

Answer: 110 - 33 equals 77.

Step-by-step explanation:

Dude, just subtract- (if I get this wrong I’m sorry)

Answer:

24

Step-by-step explanation:

Answer:

y=2x^2+16x+11

Step-by-step explanation:

Standard form is y=ax^2+bx+c.

In order to write this polynomial in standard form, we need to simplify and then arrange the terms in decreasing order.

Rewrite (x+4)^2 as (x+4)(x+4) and then expand using FOIL.

y=2(x⋅x+x⋅4+4x+4⋅4)−21

Simplify.

y=2(x^2+8x+16)−21

Apply the distributive property and simplify.

y=2x^2+2(8x)+2⋅16−21

y=2x^2+16x+32−21

y=2x^2+16x+11

Therefore,

y=2x^2+16x+11