Given f(x) = -3x? + 10, what is f(-2)?

Answer:

a. red: yellow

[tex]8:10=4:5[/tex]

There are 4 reds for every 5 yellows.

b. green: yellow

[tex]5:10=1:2[/tex]

There is 1 green for every two yellows.

c. red: total

[tex]8:35[/tex]

There are 8 reds out of 35 chocolates.

Hope this helps

Answer:

x=2 and y= ‐6

Step-by-step explanation:

Let the two numbers be 'x' and 'y'

Here, it says two numbers add up to make -4

So,

x+y= ‐4 .....equation (i)

Also, its says two numbers subtract to make 8

So,

x‐y=8 .....equation (ii)

We have,

x+y= ‐4 .....equation (i)

x‐y=8 .....equation (ii)

Subtracting equation (i) from equation (ii)

x‐y=8

x+y=‐4

-----------

‐2y=12

y=12/‐2

y= ‐6

Now, replacing value of x in equation (i)

x+y= -4

4x+(‐6) = -4

4x‐6= ‐4

x= -4+6

x= 2

Therefore the unknown numbers are 2 and ‐6

The average rate of change for the interval from x = 8 to x = 9 is 13,122 (3⁸to 3⁹).

Function is a self-contained block of code that performs a specific task. It is used to separate logical code into separate parts and make the code more manageable. A function can accept inputs, known as parameters, and return an output, known as a return value. Functions can be reused throughout a program, making the code more efficient and easier to debug.

This can be calculated by subtracting the starting value (3⁸ = 6561) from the ending value (3⁹ = 19683) and then dividing the result by the interval (9 - 8 = 1). Mathematically, this is expressed as (19683 - 6561) / (9 - 8) = 13,122. This result shows that the rate of change for the exponential function between x = 8 and x = 9 is 13,122.

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Katie runs the fastest at 14.469 ft/s

To compare the speeds of each runner, we need to convert all the measurements to the same units. Let's convert them all to feet per second:

Therefore, in order of fastest to slowest runner:

Katie (14.469 ft/s)

Noah (12.133 ft/s)

Stephanie (8 ft/s)

Jessica (9.514 ft/s)

Hence, Katie runs the fastest

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Using equations the answers to both subparts are shown:

(A) The equation: (500x + 5600)/x = C

(B) Cost per person (C) = $1,060

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2.

When two or more components must be taken into account collectively in order to comprehend or describe the overall situation, this is known as an equation.

So, (A) the equation would be:

C is the cost per person and x is the number of people.

(500x + 5600)/x = C

(B) Cost per person if 10 people are traveling.

x = 10

(500x + 5600)/x = C

(500*10 + 5600)/10 = C

(5000 + 5600)/10 = C

10600/10 = C

$1,060 = C

Therefore, using equations the answers to both subparts are shown:

(A) The equation: (500x + 5600)/x = C

(B) Cost per person (C) = $1,060

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a. If the data is weight, the z-score for someone who is overweight would be positive.

b. If the data is IQ test scores, an individual with a negative z-score would have a low IQ.

c. If the data is time spent watching TV, an individual with a z-score of zero would watch the average amount of TV.

d. If the data is annual salary in the U.S and the population is all legally employed people in the U.S., the z-scores of people who make minimum wage would be negative.

The z-score represents how far a data point is from the mean in terms of standard deviations. If someone is overweight, their weight would be above the mean weight, so their z-score would be positive.

Again, the z-score represents how far a data point is from the mean in terms of standard deviations. If someone has a negative z-score for IQ test scores, it means their score is below the mean score, so their IQ would be low.

A z-score of zero means the data point is exactly at the mean, so someone with a z-score of zero for time spent watching TV would watch the average amount of TV.

Again, the z-score represents how far a data point is from the mean in terms of standard deviations. If someone is making minimum wage, their salary would be below the mean salary, so their z-score would be negative.

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The coordinate of centroid of the triangle is (2, 8/3), the coordinate of the circumcenter is (-7/32, 121/24) and the coordinate of orthocenter is (2, 9/2)

a. To find the centroid of a triangle, we take the average of the x-coordinates and the average of the y-coordinates of the vertices. Therefore, the x-coordinate of the centroid is:

(x₁ + x₂ + x₃) / 3 = (-4 + 2 + 8) / 3 = 2

Similarly, the y-coordinate of the centroid is:

(y₁ + y₂ + y₃) / 3 = (0 + 8 + 0) / 3 = 8/3

So the coordinate of the centroid is (2, 8/3).

b. The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. To find the circumcenter, we can find the equations of the perpendicular bisectors of any two sides of the triangle and solve for their intersection point.

Let's take the sides formed by vertices (-4, 0) and (2, 8), and vertices (-4, 0) and (8, 0). The midpoint of the first side is ((-4+2)/2, (0+8)/2) = (-1, 4), and the slope of the line passing through the two points is (8-0)/(2-(-4)) = 8/6 = 4/3. Therefore, the equation of the perpendicular bisector passing through (-1, 4) is:

y - 4 = (4/3)(x + 1)

Simplifying this equation, we get:

y = (4/3)x + 13/4

Similarly, the midpoint of the second side is ((-4+8)/2, (0+0)/2) = (2, 0), and the slope of the line passing through the two points is (8-0)/(2-8) = -8/6 = -4/3. Therefore, the equation of the perpendicular bisector passing through (2, 0) is:

y = -(4/3)(x - 2)

To find the intersection point of these two lines, we can set the equations equal to each other and solve for x:

(4/3)x + 13/4 = -(4/3)(x - 2)

x = -7/32

Substituting x = -7/32 into either of the equations, we get:

y = (4/3)(-7/32 + 1) + 4 = 121/24

So the coordinate of the circumcenter is (-7/32, 121/24).

c. The orthocenter of a triangle is the point where the altitudes of the triangle intersect. An altitude of a triangle is a line segment from a vertex of the triangle perpendicular to the opposite side.

Let's take vertex (-4, 0) and find the equation of the line passing through this vertex and perpendicular to the opposite side formed by vertices (2, 8) and (8, 0). The slope of the opposite side is (0-8)/(8-2) = -8/6 = -4/3, so the slope of the line we want is the negative reciprocal of this, which is 3/4. Therefore, the equation of the altitude passing through (-4, 0) is:

y - 0 = (3/4)(x + 4)

Simplifying this equation, we get:

y = (3/4)x + 3

Let's now take vertex (2, 8) and find the equation of the altitude passing through it. The slope of the opposite side formed by vertices (-4, 0) and (8, 0) is (0-0)/(8-(-4)) = 0, which means the altitude passing through (2, 8) is a vertical line passing through (2, 0). Therefore, the equation of this altitude is:

x = 2

Now we need to find the intersection point of these two altitudes. Substituting y = (3/4)x + 3 into the equation x = 2, we get:

y = 9/2

The coordinate of the orthocenter is (2, 9/2)

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Answer:

Do C.

Step-by-step explanation:

The cube roots of 117 441 in rectangular form are: a. 3.00 +4.002, b. –4.96 +0.604, c. -1.96 + 1.964, d. - 124.10 + 11.95, e. 3.00 4.00, f. 4.68 - 1.764, g. 1.96 4.602, and h. 75.00+ 100.00.

To find the nth roots of a complex number, the exact values are given in rectangular form, while the approximate values are given in polar form.

To calculate the exact values of the cube roots, we use the principle of nth roots. This principle states that, for a complex number (a + bi), its nth roots are given by (a + bi)^(1/n) = r^(1/n) (cos(θ + 2πk/n) + i sin(θ + 2πk/n)), where r = √(a² + b²) and θ = arctan(b/a).

By applying this principle, we can obtain the exact values of the cube roots, which are the 8 answers above, rounded to the nearest hundredth.

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The if we take the transpose of C, we havecT = [C1 C2 ... Cp]And by transposing the above formula, we havecTj = [B1j A2 B2j ... Am Bmj]Therefore, we have a summation formula for Cij, Cj, and cT.

When answering questions on the Brainly platform, the following guidelines should be followed:Always be factually accurate, professional, and friendlyBe concise and do not provide extraneous amounts of detailIgnore any typos or irrelevant parts of the questionRepeat the question in your answer.Provide a step-by-step explanation in your answer.Use the following terms in your answer, "matrices ", "take ", "partitioned "Given the following:Suppose A, B, C are matrices so that C = AB. Also suppose that the rows of A are aſ,. am, the columns of A are A1, ..., An. Also, the rows of B are b], ,...,6% and the columns of B are B1, Also, the rows of C are cſ, ..., Cm and the columns of Care C1, ..., Cp. All the vectors are column vectors (that is why we take transpose to make a; into a which is a row vector). Also, the elements of A, B, C are denoted by Aij, Bij, Cij respectively. We need to write a summation formula for Cij, Cj, and cT.Hint: To really benefit from this exercise, do not just "write the formula." Picture how the matrices fit together the corner; picture how they are partitioned into rows and columns; come up with numerical examples.The product of two matrices A and B is given byCij = Ai1B1j + Ai2B2j + ... + AinBnjGiven that C = AB, then we haveCj = [A1 B1j + A2B2j + ... + AmBmj]Therefore, if we take the transpose of C, we havecT = [C1 C2 ... Cp]And by transposing the above formula, we havecTj = [B1j A2 B2j ... Am Bmj]Therefore, we have a summation formula for Cij, Cj, and cT.

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The approximate measure of angle B is 90°. The sum of the interior angles of the triangle is 180°.

The first part of your answer is correct. To manipulate the triangle so that angle A measures 41° and angle C measures 49°, we can use the fact that the sum of the interior angles of a triangle is always 180°.

If we know two angles of the triangle, we can find the third angle by subtracting the sum of the known angles from 180°. So, to find the measure of angle B, we can use the equation:

angle A + angle B + angle C = 180°

Substituting in the given angle measures, we get:

41° + angle B + 49° = 180°

Simplifying, we get:

angle B = 90°

Therefore, the approximate measure of angle B is 90°.

For the second part of your answer, the correct answer is 180°. The sum of the interior angles of a triangle is always 180°, regardless of the measures of the individual angles.

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Complete question:

Manipulate the triangle so angle A measures 41° and

angle C measures 49º.

What is the approximate measure of angle B?

Angle B = (41, 90, 49, 80)

What is the sum of the interior angles of the triangle?

(90, 170, 180, 200)

The value height of the shed is 9 feet.

The area of the shed = 64 square feet

The volume of the shed = 576 cubic feet.

The area occupied inside a rectangular prism is referred to as the volume of the prism. A polyhedron with two pairs of congruent and parallel bases is referred to as a rectangular prism. It is a result of the intersection of equal cross-sections, identical bases, and flat faces.

Calculating the volume of the rectangular prism

The volume of rectangular prism = area of base x height

Substituting the values -

576 = 64 x h

h = 576 / 64

h = 9

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To simplify it, first factor the denominators of each fraction in eqation 1/(1-p+p²) + 1/(1+p+p²) - 2p/(1-p²+p⁴) and simplify to get simplified equation is  2(1+p)/[(1-p+p²)(1+p+p²)] .

What is  factor ?

In mathematics, a factor is a number or algebraic expression that divides another number or expression without leaving a remainder.For example, the expression x^2 - 4 can be factored as (x+2)(x-2) .

What is  denominator ?

denominator is a bottom part of a fraction. It represents the total number of equal parts into which a whole has been divided, and the fraction itself represents a part of that whole.For example,

in equation  (x+2)/(x-2)  , (x-2) is denominator .

In the given question ,

1/(1-p+p²) + 1/(1+p+p²) - 2p/(1-p²+p⁴ )   Next, we can find a common denominator for the three fractions. To do this, we need to factor the denominator of the third fraction further using the difference of squares formula as  1/(1-p+p²) + 1/(1+p+p²) - 2p/[(1-p+p²)(1+p+p²)]

Now we can find a common denominator by multiplying the first fraction by (1+p+p²)/(1+p+p²) and the second fraction by (1-p+p²)/(1-p+p²):

[(1+p+p²)/(1+p+p²)]/(1-p+p²) + [(1-p+p²)/(1-p+p²)]/(1+p+p²) - 2p/[(1-p+p²)(1+p+p²)]

= [(1+p+p²)+(1-p+p²)-2p]/[(1-p+p²)(1+p+p²)]

= [2+2p]/[(1-p+p²)(1+p+p²)]

= 2(1+p)/[(1-p+p²)(1+p+p²)]

Therefore, the simplified expression is 2(1+p)/[(1-p+p²)(1+p+p²)].

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Elise walked a distance of 9.2 kilometers on Tuesday.

To solve the problem, we need to first understand the information provided.

On Monday, Elise walked a distance of 9.9 kilometers.

On Tuesday, she walked a distance that was 0.7 kilometers less than what she walked on Monday.

This means that we need to subtract 0.7 kilometers from the distance that she walked on Monday to find the distance she walked on Tuesday.

To do this, we can use subtraction. We start by writing down the distance Elise walked on Monday, which is 9.9 kilometers, and then subtract 0.7 kilometers from it.

9.9 km - 0.7 km = 9.2 km

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The probability that a randomly chosen person: a) Has a red car = 0.496 b) Has a speeding ticket = 0.424 c) Has a speeding ticket given they have a red car = 0.467 d) Has a red car given they have a speeding ticket = 0.629 e) Has a red car and got a speeding ticket = 0.234 f) Has a red car or got a speeding ticket = 0.686.

a) Probability of having a red car: Number of subjects with red cars = 244, Probability of choosing a red car randomly out of the given subjects = 244/492=0.496

b) Probability of having a speeding ticket: Number of subjects with speeding tickets = 209, Probability of choosing a person with a speeding ticket out of the given subjects = 209/492=0.424

c) Probability of having a speeding ticket given they have a red car: Probability of having a red car = 0.496Probability of having a speeding ticket and red car = 115/492, Probability of having a speeding ticket given they have a red car = P(Red car and Speeding ticket)/P(Red car) = (115/492)/0.496 = 0.467

d) Probability of having a red car given they have a speeding ticket: Probability of having a speeding ticket = 0.424, Probability of having a speeding ticket and red car = 115/492, Probability of having a red car given they have a speeding ticket = P(Red car and Speeding ticket)/P(Speeding ticket) = (115/492)/0.424 = 0.629

e) Probability of having a red car and getting a speeding ticket: Number of subjects with both red car and speeding ticket = 115, Probability of choosing a person with both red car and speeding ticket out of the given subjects = 115/492=0.234

f) Probability of having a red car or getting a speeding ticket: P(Red car or Speeding ticket) = P(Red car) + P(Speeding ticket) - P(Red car and Speeding ticket) = 0.496 + 0.424 - 0.234 = 0.686.

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Step-by-step explanation:

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The measure of angle C is 53.13 degrees.

What are trigonometric functions?

Trigonometric functions are a set of mathematical functions used to relate the angles of a right triangle to the lengths of its sides. There are six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. Each function represents a ratio of two sides of a right triangle.The tangent function, denoted as tan(x), is a trigonometric function that represents the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

Calculating the value of angle C :

The three sides of the given right triangle are 3 cm, 4 cm, and 5 cm.

To find the measure of angle C, we can use the trigonometric function called inverse tangent, or arctan, which gives the ratio of the length of the opposite side to the length of the adjacent side.

Using the Pythagorean Theorem, we can verify that the given triangle is a right triangle:

[tex]5^2 = 3^2 + 4^2[/tex]

[tex]25 = 9 + 16[/tex]

[tex]25 = 25[/tex]

So, the triangle is a right triangle.

To find the measure of angle C, we can use the arctan function:

[tex]tan(C) =opposite/adjacent = 3/4[/tex]

[tex]C = arctan(3/4) \approx 53.13[/tex] degrees

Therefore, the measure of angle C is 53.13 degrees (rounded to the nearest hundredth).

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Answer:

(x³ + 7x² + 2)÷(x-1) = x² + 8x + 15 + 8/(x-1).

Maria has the highest standardized score of 2.13, making her the one who made the best score.

Janna's standardized score is 0.80, and Maria's is 2.13.

Janna scored 77 on her history test, while the class average was 72.7 with a standard deviation of 6.1. To find the standardized score, the formula is (score - average) / standard deviation. Therefore, the standardized score for Janna is [tex](77-72.7)/6.1[/tex]= 0.80.

Maria scored 89 on her biology test, while the class average was 82.6 with a standard deviation of 5.6. To find the standardized score, the formula is (score - average) / standard deviation. Therefore, the standardized score for Maria is [tex](89-82.6)/5.6[/tex]= 2.13.

Maria has the highest standardized score of 2.13, making her the one who made the best score.

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Answer:

ICE CREAM

Step-by-step explanation:

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

P of spade = 1/4

P of face cards = 3/13

{P = probability}

Step-by-step explanation:

•Total cards in a deck = 52

No. of spade cards in the deck = 13

therefore,

Probability of drawing a spade out of a deck of cards = 13/52 = 1/4

No. of face cards in a deck = 3×4 = 12 (joker,king,queen)

therefore,

Probability of drawing a face card out of a deck of cards = 12/52 = 3/13

First let's start with the equation:

x + y = -11

xy = -180

We can substitute -11 in for x + y to get:

xy = -180

x(-11) = -180

Now let's divide both sides by -11

x = 180/11

x ≈ 16.36

We can now use the equation x + y = -11 to solve for y

y = -11 - 16.36

y ≈ -27.36

The two numbers that add to -11 but multiply to -180 are 16.36 and -27.36.

The force equation for the system is F = bV - bF, where F is the force of friction, V is the velocity of the object, and b is the coefficient of viscous friction.

Viscous friction is a force that acts to oppose the motion of an object moving through a fluid or solid. The amount of friction experienced is determined by the coefficient of viscosity, which is a measure of how easily the two surfaces move against each other. In this equation, bV is the force generated by the object's motion, and b

F is the opposing force of friction. Together, these two forces determine the net force acting on the object.

Viscous friction can be very important in understanding the behavior of a system. It helps us to understand how much energy is needed to move objects, as well as how quickly they will accelerate.

Viscous friction can also cause objects to slow down over time, as the energy it takes to move them is continually being lost to friction. Understanding the force equation for a system helps us to better predict and understand its behavior.

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Answer:

The 2nd equation is false.

Step-by-step explanation:

You don't even have to solve. DE is not 58, it's 40.

The 2nd equation is false.

After 6 days, the probability that the stock has its original price is 5/16.

There are two possible scenarios that can take place when the stock price fluctuates from one day to the next. Either the price goes up by 1/8th of a point with probability 1/3 or it goes down by 1/8th of a point with probability 2/3.

The price of the stock after six days can be denoted as S6. The price of the stock after the first day can be represented as S0.

Since the price fluctuates either up or down by 1/8th of a point on each day, the price after six days can be represented as follows:S6 = S0 + (up, up, up, up, up, up), (up, up, up, up, up, down), (up, up, up, up, down, up), ... , (down, down, down, down, down, down)

In order to return to the original price, the stock must go up and down by the same amount. As a result, there must be an equal number of ups and downs in the six-day period.

As a result, we must calculate the probability of obtaining an equal number of ups and downs over six days.

Let's represent an increase in the stock price as 'U' and a decrease as 'D.'

The total number of ways in which the stock can go up and down over six days is [tex]2^6 = 64[/tex].

The total number of ways in which the stock can return to its original price can be calculated as follows: [tex]N(UUUDDD) = 6! / (3! * 3!) = 20[/tex]

The probability of the stock returning to its original price after six days can be calculated as:

[tex]P = N(UUUDDD) / 64 = 20 / 64 = 5 / 16[/tex]

Therefore, the probability that after 6 days the stock has its original price is 5/16.

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The height of an open cylinder of radius of 8cm given that it has a curved surface area of 1000 cm² is equals to the 159.24 cm.

The area obtained after substracting the circular area from the total area of the cylinder is called as curved surface area. Curved surface area is calculated by formula, 2πrh

where r --> radius of cylinder

h --> height of cylinder

π --> math special constant

We have an open cylinder with the following dimensions,

Radius of cylinder, r = 8 cm

Curved surface area of cylinder, A = 1000 cm². We have to calculate the height of this open cylinder. Let the height of an open cylinder be 'h cm' . Using the above formula, height of cylinder, h = curved Area/ 2πr

=> h = A/2π

=> h = 1000/2 ( 3.14)

=> h = 1000/6.28

=> h = 159.24

Hence, required value of height is 159.24 cm.

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Answer:

9/12

Step-by-step explanation:

To determine which fraction is not equivalent to 2/3, we can simplify each fraction and compare it to 2/3. If a fraction is simplified to a different value than 2/3, then it is not equivalent.

16/24 simplifies to 2/3, so it is equivalent to 2/3.

6/9 simplifies to 2/3, so it is equivalent to 2/3.

12/18 simplifies to 2/3, so it is equivalent to 2/3.

9/12 simplifies to 3/4, which is not equivalent to 2/3.

10/15 simplifies to 2/3, so it is equivalent to 2/3.

Therefore, the fraction that is not equivalent to 2/3 is 9/12.

Answer:

9/12 is not equal to 2/3

Step-by-step explanation:

To find which fractions are equivalent and which are not, we must make sure they are proportional.

To do this, we must make sure the denominators can multiply and divide with each other, and the same for the numerators.

12 divided by 3 is 4,

but 4 times 2 is not 9

Therefore, the answer is 9/12

Jake is presently [tex]0[/tex] years old and the year is [tex]2036[/tex], which is not a relevant response or there may be some missing details in the question.

A span of time that is equivalent to one year on the Calender but starts at a different period. A cycle of 365 and 366 day split into twelve month starting in January and ending in December.

Every monthly on the calender has four complete weeks since every month has at least 28 days. A few month have a few more days, but these extra days don't add up to a full week, therefore they aren't counted.

Let's first find the current year, given that the year in which their ages will sum up to [tex]16x[/tex] is[tex]2036[/tex].

[tex]2036 - (y - 2036) = 2*2036 - y[/tex]

Simplifying this expression, we get:

[tex]2*2036 - y = 4072 - y[/tex]

[tex]2y = 4072[/tex]

[tex]y = 2036[/tex]

Now, let's find Jake's current age by subtracting his birth year from the current year [tex]y - (2036 - 7x)[/tex]

Since their ages sum up to 16x in 2036, we have:

[tex]x + 7x = 16x[/tex]

[tex]8x = 16x[/tex]

[tex]x = 0[/tex]

This means that Jake is currently [tex]0[/tex] years old, which is not a meaningful answer.

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Answer:

x=1

Step-by-step explanation: