Solve this system of equations for x using the addition method. (Must show steps of addition method to get credit. Do not solve using the substitution method. )

The surface area of the figure is 549.5 square ft

Given that

The composite figure comprises of a cone and a cylinder of the following dimensions

Cone: Radius = 5 ft and Height = 12 ft

Cylinder: Radius = 5 ft and Height = 6 ft

The surface area of the figure is calculated as

Surface area = Cone + Cylinder -  Circle

So, we have

Surface area = πr(r + √[h² + r²]) + 2πr(r + h) - πr²

Substitute the known values in the above equation, so, we have the following representation

Surface area = 3.14 * 5 * (5 + √[12² + 5²]) + 2 * 3.14 * 5 * (5 + 6) - 3.14 * 5²

Evaluate

Surface area = 549.5

Hence, the surface area is 549.5

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By answering the above question, we may state that Debra would thus function need to travel 150 miles for the price of the two plans to be the same.

Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.

The starting charge and the cost per mile would be added together for the first plan's total cost:

Costs for plan 1 total 47.96 plus 0.19x.

The first charge and the cost per mile would be added together for the second plan's total cost:

Plan 2's overall cost is 53.96 plus 0.15x.

Set the two total cost expressions equal to one another and solve for x to get how many miles Debra would need to go for the two plans to be the same in price:

47.96 + 0.19x = 53.96 + 0.15x

0.04x = 6

x = 150

Debra would thus need to travel 150 miles for the price of the two plans to be the same.

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The probability of getting sum of 6 is C)5/36.

What is probability?

Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

We know that,

Probability of event = number of favorable outcome/ Total outcome

When a 6 sided dice die twice then

Total number of outcome = 6*6=36

Favorable outcome is a sum of 6, Ways of obtaining a sum of 6

(1,5), (5,1), (2,4),(4,2) and (3,3). Thus, there are 5 ways in which 6 can be obtained using  rolling dice twice, Then

=> P(sum of 6 )=5/36

Hence the correct option is C)5/36.

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Answer:

c. The numbers must have a sum of 12.

Step-by-step explanation:

Given a polynomial [tex]x^2+cx+d[/tex], in its factored form, [tex](x+a)(x+b)[/tex], the following must be true:

[tex]a + b = c[/tex]

[tex]a \cdot b = d[/tex]

In the given polynomial, we can assign the following values:

[tex]c = -12[/tex]

[tex]d=20[/tex]

Using these values, we can go through the answer choices:

Remember: we are finding the statement that is NOT true.

a) "the numbers must have a product of 20"

If we look at the equation [tex]ab = d[/tex], we can see that this statement is correct; therefore, we should not check it.

b) "the numbers must both be negative"

This is not necessarily true, as a positive plus a negative can still result in a negative; however, in this case, it is true (if we factor, we get a = -2, b = -10).

c) "the numbers must have a sum of 12"

This is false, since c = -12. The numbers (a and b) must add to negative 12, not positive 12; therefore c) is the correct answer.

A rectangle has 2 lines of symmetry.

What is a line of symmetry?

A line of symmetry is a line that divides a shape into two mirror-image halves. When a shape is divided by a line of symmetry, each half of the shape is a reflection of the other half, and they are said to be symmetric or mirror images of each other. In other words, if you were to fold the shape along its line of symmetry, the two halves would match up perfectly. The presence or absence of lines of symmetry is an important characteristic of shapes and can be used to identify and classify them.

Calculate the line of symmetry of a rectangle -

A rectangle has two lines of symmetry: one line that runs vertically down the center of the rectangle, and another line that runs horizontally across the center of the rectangle.

To understand why a rectangle has two lines of symmetry, consider that any line that runs down the center of a rectangle will divide it into two halves that are mirror images of each other. This is true for lines that run vertically or horizontally through the center of the rectangle.

In contrast, a rectangle does not have diagonal lines of symmetry. That is, there is no line that can be drawn from one corner of the rectangle to another corner that will divide it into two mirror-image halves.

Overall, a rectangle has two lines of symmetry, and these lines are important to its geometry and properties.

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This can be resolved with d = 25 miles by multiplying equation both sides by

If Jen has driven 15 miles, and this is 3/5 of the total distance, we can use the following equation to find the total distance d:

15 = (3/5) * d

To solve for d, we need to isolate it on one side of the equation. We can start by dividing both sides of the equation by 3/5, which is the same as multiplying by its reciprocal, 5/3:

15 * (5/3) = d

Simplifying the expression on the left side, we get:

25 = d

Therefore, the total distance Jen needs to travel to get to the mall is 25 miles.

In summary, the equation that can be used to find the total distance d, given that Jen has driven 15 miles and this is 3/5 of the total distance, is:

15 = (3/5) * d

Which can be solved for d by multiplying both sides by 5/3, giving:

d = 25 miles

In conclusion, assuming that Jen has driven 15 miles, which is 3/5 of the entire trip, the equation that can be used to determine the whole distance d is:

15 = (3/5) * d

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The surface area of the shape is 110 square units.

The area of a two-dimensional figure is the area enclosed by its perimeter. The area of a closed figure is the number of unit squares that cover its surface. Area is measured in square units such as cm2 and m2. The area of a shape is measured in two dimensions.

The rectangle's surface area is:

Area = 10 × 9 = 90 unit square

The area of the triangle is:

Area = 0.5 × 10 × 4 = 20 unit square

The figure's area is as follows:

Total = 90 + 20

Total = 110 unit square

Hence, the shape's area is 110 unit square.

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Answer:

7pts=4.20332

i think

Step-by-step explanation:

[tex]\cfrac{1}{6}+\cfrac{3}{4}-\cfrac{2}{3}\implies \cfrac{(2)1~~ + ~~(3)3~~ - ~~(4)2}{\underset{\textit{using this LCD}}{12}}\implies \cfrac{2+9-8}{12}\implies \cfrac{3}{12}\implies \cfrac{1}{4}[/tex]

Answer: 8 5/7

Step-by-step explanation:

Well, first you make the common denominator between the two, which would be 46/14 and 76/14. Now you add 46 and 76 and receive 122/14. You can simplify that and get 61/7, and now you turn it into a mixed number:

8 5/7

Answer:

The given polynomial already has two terms that can be factored out:

9x^2y^6 - 25x^4y^8 = (3xy^3)^2 - (5x^2y^4)^2

Now we have a difference of squares:

= (3xy^3 - 5x^2y^4)(3xy^3 + 5x^2y^4)

Therefore, 9x^2y^6 - 25x^4y^8 can be rewritten as the product of (3xy^3 - 5x^2y^4) and (3xy^3 + 5x^2y^4).

Answer: The answer would be   (3xy^3-5x^2y^4)(3xy^3+5^2y^4)

(C)

Step-by-step explanation: Cant explain how to but for a quick answer it is C, and you can check the image for proof.

The expression cos(a-b) is equivalent to cos(a)cos(b) + sin(a)sin(b), while the expression cos(a)cos(b) - sin(a)sin(b) is equivalent to cos(a+b).

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It focuses on the study of the properties of trigonometric functions such as sine, cosine, and tangent, which are used to calculate the angles and sides of triangles.

in the given question,

The expression cos(a-b) is equivalent to cos(a)cos(b) + sin(a)sin(b), while the expression cos(a)cos(b) - sin(a)sin(b) is equivalent to cos(a+b).

Therefore, we can rewrite the expression cos(a-b) as cos(a)cos(b) + sin(a)sin(b) and then compare it to the expression cos(a)cos(b) - sin(a)sin(b) by changing the sign of the second term in the first expression:

By comparing these two expressions, we can see that they are very similar, except that the sign of the second term is different. Specifically, we have:

So, we can say that the values of cos(a-b) and cos(a)cos(b) - sin(a)sin(b) are related by the sign of the sin(a)sin(b) term. If the sign is positive in the first expression, then it is negative in the second expression and vice versa.

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The mean of the sampling distribution is 606060 and the standard deviation is 871.78.

As long as the sample size is sufficient (usually, n 30), the central limit theorem implies that if we repeatedly take random samples from a population, the sampling distribution of the sample means will resemble a normal distribution, regardless of the form of the population distribution. This indicates that given the sample mean and standard deviation, we may utilise the normal distribution to draw conclusions about the population mean. Because it enables us to estimate population parameters even when we don't know the population distribution, the central limit theorem is significant.

Given that,

n = 757575

p = 80% = 0.8

q = 1 - 0.8 = 0.2

The mean of the binomial distribution is given as:

Mean: μ = np = (757575)(0.8) = 606060

The standard deviation of the binomial distribution is given as:

σ = √(npq) = √((757575)(0.8)(0.2)) = 871.78

Hence, the mean of the sampling distribution is 606060 and the standard deviation is 871.78.

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The piecewise function graphed is given as follows:

A piece-wise function is a function that has different definitions, based on the input x of the function.

For this problem, the intervals are given as follows:

For the first interval, the interval is open due to the open circle, and the quadratic function is a translation up 4 units of y = x², hence^:

y = x² + 4, x < 2.

For the second interval, which is the closed interval, we have a decaying line with slope of -1 and x-intercept of 4, hence:

y = -x + b

0 = -4 + b

b = 4.

Hence:

y = -x + 4, x ≥ 2.

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Answer:

6 units to the right

Step-by-step explanation:

Z(3,4) → Z'(9,4)

d = √(9-3)² + (4-4)² = √6²+0² = 6   to the right

The translation of point Z of triangle XYZ from (3, 4) to Z′(9, 4) is a move of 6 units to the right.

In Mathematics, particularly geometry, the translation of a point is the process of moving the point a specific number of units either up, down, left or right. In the case of your triangle XYZ, the original position of point Z is at (3, 4) and Z′ is positioned at (9, 4). The y-coordinate hasn't changed; it remains at 4. This tells us that the translation is not up or down. However, if we observe the x-coordinate, you’ll see that it went from 3 to 9. Changing the x-coordinate moves the point horizontally, so we know our translation is left or right. Lastly, the difference between 3 and 9 is 6. We can therefore determine that the point moved 6 units to the right.

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Answer:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Step-by-step explanation:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

The required solutions of the equation |3x| = 9 are x = 3 and x = -3.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.

Here,

We can solve the given equation by isolating the absolute value on one side and simplifying it.

|3x| = 9
| x | = 3

Now, we need to solve two separate equations for x:

When x is positive:
|x| = 3
=> x = 3 (since x is positive)

When x is negative:
|x| = 3
-x = 3 (since x is negative)
x = -3

Therefore, the solutions of the equation |3x| = 9 are x = 3 and x = -3.

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Answer:

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, we can consider the distance from home to Best Buy as the hypotenuse, and the distance traveled west and south as the other two sides.

Let's call the distance from home to Best Buy "x". Then, using the Pythagorean theorem:

x^2 = (distance south)^2 + (distance west)^2

We know that the distance west is 5 miles, and the distance home is 25 miles. We don't know the distance south, so let's call that "y".

Then we have:

x^2 = y^2 + 5^2

25^2 = y^2 + 5^2

Solving for y, we get:

y^2 = 25^2 - 5^2

y^2 = 600

y = sqrt(600)

y = 24.49 (rounded to two decimal places)

Now we can plug in y to find x:

x^2 = y^2 + 5^2

x^2 = 24.49^2 + 5^2

x^2 = 625.12

x = sqrt(625.12)

x = 25.00 (rounded to two decimal places)

Therefore, the distance from home to Best Buy is approximately 25 miles.

Step-by-step explanation:

Answer:

Bases

Step-by-step explanation:

Answer: -5

Step-by-step explanation:

from slope-intercept form, y=mx + b, where b is (-2), and the slope/m is (-5).

hope this helps, and please respond if I'm wrong

M = -5

That’s the answer

Answer:

each of the other sides is 2√2 = 2.8284

Step-by-step explanation:

A 45°- 45°-90° triangle is also known as a right isosceles triangle because two of the legs are the same as two of the angles are the same at 45°

If a is the length of one of the legs then the hypotenuse, h,  which is the longest side is given by the equation

[tex]h = \sqrt{a^2 + a^2}\\\\h = \sqrt{2a^2}\\\\h = a \sqrt{2}[/tex]

Or, dividing by √2 on both sides,

[tex]\dfrac{h}{\sqrt{2} }= a[/tex]

Given h = 4

[tex]a =\dfrac{ 4}{\sqrt{2}} = \dfrac{2\cdot2}{\sqrt{2}} = 2\sqrt{2} \quad\quad\quad(since $\dfrac{2}{\sqrt{2}}$ = \sqrt{2}})[/tex]

a = 2√2 = 2.8284

So each of the other sides is 2√2 = 2.8284

Answer:

Step-by-step explanation:

Using the remainder theorem we get:

[tex]f(-2)=-5[/tex],  [tex]f(1)=4[/tex], and [tex]f(-1)=0[/tex]

So we get

[tex]f(-2)=(-8)(p-1)+4p-2q+r=-5[/tex]

                 [tex]-8p+8+4p-2q+r=-5[/tex]

                              [tex]-4p-2q+r=-13[/tex]  [tex](a)[/tex]

[tex]f(1)=(p-1)+p+q+r=4[/tex]

                       [tex]2p+q+r=5[/tex]               [tex](b)[/tex]

[tex]f(-1)=-(p-1)+p-q+r=0[/tex]

                                 [tex]-q+r=-1[/tex]    [tex](c)[/tex]

We need to solve (a), (b) and (c) simultaneously to find p,q, and r.

from [tex](c)[/tex]  [tex]r=q-1[/tex]. Sub this into (a) and (b):

[tex]-4p-2q+(q-1)=-13 \rightarrow -4p-q=-12[/tex]    [tex](d)[/tex]

      [tex]2p+q+(q-1)=5 \rightarrow q=3-p[/tex]              [tex](e)[/tex]

Sub (e) into (d) we get

[tex]-4p-(3-p)=-12 \rightarrow p=3[/tex]

Sub [tex]p=3[/tex] into [tex](e) \rightarrow q=0[/tex]

Sub  [tex]p=3,q=0[/tex] into [tex](c) \rightarrow r=-1[/tex]

SOLUTION: [tex]p=3,q=0,r=-1[/tex]    

So [tex]f(x)=2x^3+3x^2-1[/tex]

by dividing (x+1) into f(x) we get  (I am not showing working for this division)

[tex]f(x)=(x+1)(2x^2+x-1)[/tex]

[tex]\rightarrow f(x)=(x+1)(2x-1)(x+1)[/tex]

The principal amount of the loan is $1,200,000.

What is simple interest?

Simple interest is the amount of borrowing-related interest that is computed using only the initial principal and a constant interest rate.

To find the principal amount of a loan, we need to use the formula for simple interest:

I = Prt

Where I is the interest, P is the principal, r is the interest rate as a decimal, and t is the time in years.

In this case, we know that the interest is $3,150 and the interest rate is 10.5%. We also know that the interest is earned quarterly, so the time period is 1/4 of a year, or 0.25 years.

Substituting these values into the formula, we get:

3150 = P * 0.105 * 0.25

Solving for P, we get:

P = 3150 / (0.105 * 0.25) = $1,200,000

Therefore, the principal amount of the loan is $1,200,000.

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Answer:

Step-by-step explanation:

y=4x + 10

y=3x + 15

Therefore, if a population of 150 mice triples in size every four months, there will be approximately 2,952,450 mice in the neighbourhood in 3 years.

Mathematicians use the unitary method to answer proportional relationship problems involving two or more quantities. It entails calculating the worth of one unit of one quantity in relation to another. For instance, let's say we are aware that 3 pencils cost $6. The following is how we can calculate the price of a solitary pen using the unitary method: The value of a single entity of the quantity "pen cost" in terms of the quantity "number of pens" was determined in this case. Once we are aware of a unit's worth, we can use that knowledge to determine the value of any other quantity that is related to it.

given

The population triples, or grows three times, in number, after four months. As a result, if we commence with 150 mice, the population will look like this after 4 months:

150 × 3 = 450 mice

The populace will triple once more after another 4 months (or 8 months from the beginning), becoming:

450 × 3 = 1350 mice

The populace will triple once more after another 4 months (or 12 months from the beginning), becoming:

1350 × 3 = 4050 mice

There is a pattern here: every four months, the populace triples. Therefore, we can determine how many times the population triples after three years (or 36 months) have passed:

36 months divided by 4 months per triple equals 9 triples.

the following group will exist after three years:

2,952,450 mice are equal to 150 × 39 (150 x 19,683).

Therefore, if a population of 150 mice triples in size every four months, there will be approximately 2,952,450 mice in the neighbourhood in 3 years.

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Answer:

True

Step-by-step explanation:

To compare the two speeds, we can calculate the speed of each in miles per hour (mph) and then compare them.

22 miles in 20 minutes = (22/20) miles per minute = 1.1 miles per minute

To convert to mph, we can multiply by 60 to get:

1.1 x 60 = 66 mph

38 miles in 30 minutes = (38/30) miles per minute = 1.27 miles per minute

To convert to mph, we can multiply by 60 to get:

1.27 x 60 = 76.2 mph

Therefore, 38 miles in 30 minutes is faster than 22 miles in 20 minutes, as 76.2 mph is greater than 66 mph.

In other words, the statement "22 miles in 20 minutes is less than 38 miles in 30 minutes" is true.

We know that 50% of the data falls between the minimum value and the median (i.e., between 5 and 35). So the answer is: 50%.

The median is a useful measure of central tendency in datasets that are skewed or have outliers, as it is less sensitive to extreme values than the mean. It is also useful in datasets with non-numeric values, such as rankings or survey responses. In addition to the median, other measures of central tendency include the mean and mode. Each measure has its own strengths and weaknesses, and the appropriate measure to use depends on the nature of the dataset and the research question being asked.

To answer this question, we need to determine the position of the lower whisker and the vertical bar relative to the range of the data.

The lower whisker extends to 5, which is the minimum value in the dataset. The vertical bar inside the box is located at 35, which represents the median of the dataset.

Therefore, we know that 50% of the data falls between the minimum value and the median (i.e., between 5 and 35).

So the answer is: 50%.

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