Simplify the equation

Answer:

[tex]5y^3-2x^2+2[/tex]

Step-by-step explanation:

I like to start off by rearranging the like terms next to each other, going from the greatest power to the least, so that they are more clear.

So in this case it would be: [tex]2y^3+3y^3+x^2-3x^2+1+5-4[/tex]

Now you can add them together. Remember you can only add/subtract coefficient or variable with the same base and power.

And with that in mind, the final result should be,
[tex]5y^3-2x^2+2[/tex]

Hope this helps!

Answer:

Let's call the total amount of the lottery winnings x.

If Kelly took one half of the earnings, then she took 1/2x and Toey took 1/2x as well.

Toey spent 1/4 of his earnings, so he spent 1/4*(1/2x) = 1/8x

So Joey spent 1/8 of the total lottery winnings.

When the number of blue frogs increased by 60% and the number of green frogs decreased by 60%, the percentage of the overall increase is solved to be 60%

Assuming the number of blue frogs and the number of green frogs are equal and = y

Then the total number of frogs = y + y = 2y

Increasing the percentage of each by 60%, the factor for percentage increase by 60% is 1.6

hence 1.6y + 1.6y = 3.2y

percentage change

= change in price / original price * 100

= (3.2y - 2y) / 2y * 100

= 1.2y / 2y * 100

= 0.6 * 100

= 60

hence the percentage change is 60%

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Answer:

Not sure what you meant and could of used some specifics but I got this with my experience in algebra and geometry.

9906513923.77

98765 times triangle A 32598765÷325

The x-intercept of the equation y=-13x+234 is (18,0).

The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.

The equation of the point slope form is: (y - y₁) = m(x - x₁)

where, (x, y) is a random point on the line and m is the slope of the line.

1) From the give table, we have (18, 0) and (15, 39).

Here, slope(m) = (39-0)/(15-18)

m= -13

2) Substitute m= -13 and (x₁, y₁)=(18, 0) in point slope form, we get

(y-0)= -13(x-18)

y=-13x+234

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (18,0)

y-intercept(s): (0,234)

Therefore, the x-intercept of the equation y=-13x+234 is (18,0).

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The following are the values for the length of each rectangles:

(a) L = 37.5 m

(b) L = 26.2 cm

(c) L = 25.5 km

(d) L = 20 m

In calculating for the area of rectangle, the breadth is multiplied by the length of the rectangle.

We shall evaluate for the Lengths of the rectangles as follows:

Length = 375 m²/ 10 m

Length = 37.5 m

Length = 393 cm²/ 15 cm

Length = 26.2 cm

Length = 280.5 km²/ 11 km

Length = 25.5 km

Length = 340 m²/ 17 m

Length = 20 m

Hence, 37.5 m, 26.2 cm, 25.5 km, and 20 m are the respective values for the length of rectangles with area 375 m², 393 cm², 280.5 km², and 340 m².

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Answer:

A

Step-by-step explanation:

-3 x 4 = -12

[tex]10^{3}[/tex] x [tex]10^{6}[/tex] = [tex]10^{9}[/tex]  You add the exponents when you are multiplying powers with the same bases.

Answer:

Pythagorean theorem:

[tex]a ^{2} + b ^{2} = c^{2} [/tex]

[tex]2 ^{2} + 11 ^{2} = c^{2} [/tex]

2×2=4 11×11=121

4+121=125

[tex]c = \sqrt{125} [/tex]

Using circle theorems, the value of x in the cyclic quadrilateral is 6 units

A cyclic quadrilateral is a four-sided shape whose vertices all lie on the same circle. This means that all four angles of the quadrilateral are equal to one another.

This is further explained by circle theorem which is a branch of mathematics that deals with the properties of circles and their relationships with other shapes. It is based on the fact that all points on a circle are equidistant from the center of the circle. Circle theorem has many applications, such as finding the area of a circle, calculating the circumference of a circle, and even determining the angles of a triangle formed by three points on a circle.

In this given problem, to find the value of x, we have to use proportions or ratios of the sides given.

This becomes;

(x + 6) / x = 12 / x

when the denominators cancel out;

x + 6 = 12

Collect like terms

x = 12 - 6

x = 6

The value of x is 6

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Answer:

Graph is attached below

Step-by-step explanation:

To start off, let's find the y-intercept, which is when x=0

So, when x=0,

[tex]y=\frac{3}{4}(0)+5[/tex], which is y=5.

So we can put a point on (0, 5)

From there, since the slope is 3/4. We can go up 3 and right 4 to plot a point there, you can also do down 3 and down 4 from the y-intercept point, then keep going either, up 3 and right 4 or down 3 and left 4, which should give you a diagonal line that looks something like;

a) X is a binomial random variable because there is a fixed number of trials, for each trial, the probability of winning is the same, and for each trial there are only two possible outcomes, winning and losing.

b) The mean and the standard deviation of X are given as follows:

This means that out of nine friends, the expected number of those who area expected to win a prize is of 1.125, varying around 0.99.

c) At least 3 friends winning a prize is not unusual, as 3 is less than 2.5 standard deviations above the mean.

The binomial distribution represents the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

The change of winning is of one in eight, hence the parameter p is obtained as follows:

p = 1/8 = 0.125.

There are nine friends, hence the parameter n is given as follows:

n = 9.

Then the mean is of:

E(X) = 9 x 0.125 = 1.125.

The standard deviation is of:

[tex]\sqrt{V(X)} = \sqrt{9 \times 0.125 \times 0.875} = 0.99[/tex]

A measure is considered unusual if it is more than 2.5 standard deviations above the mean, hence the upper bound is given as follows:

More than 1.125 + 2.5 x 0.99 = 3.6 friends.

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Answer:

To calculate the tip, we first need to find 24% of the total bill. To do this, we can multiply the bill amount by 24% (expressed as a decimal).

Tip = 0.24 * 73.25

= 17.58

Therefore, the tip should be $17.58 in dollars.

Answer:

12 students

Step-by-step explanation:

The number of students surveyed: 53 + 46 = 99 students
The number of student having both: 99 - 87 = 12 students

The arithmetic sequence's fifth term is therefore 84.

An arithmetic sequence's nth term is determined by a = a + (n - 1)d. So, enter the values a = 2 and d = 3 into the formula to determine the nth term.

The formula to determine the nth term of an arithmetic series is a = a1 + (n - 1)d if a1 is the first term and d is the common difference.

In the mathematical sequence, 84 is the fifth term.

The process for calculating value

An arithmetic sequence's nth term can be calculated using the following formula:

Tn = a + (n -1)d

Where;

First term is a.

N words are present.

d is the typical difference

We must substitute nas 5's value in order to find the fifth term.

T5 = 4 + (5-1) 20

T5 = 4 + 4(20) (20)

the bracket be expanded

T5 = 4 + 80

T5 = 84

The arithmetic sequence's fifth term is therefore 84.

The complete question is,

4 is the initial term and 20 is the constant difference in an arithmetic series. Discover the sequence's sixth phrase.

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Beginning at the y-intercept (0,35),Line is solid, slopes down one and over one, and is shaded beneath.

Choose your variables first.

If x is the amount of hours spent mowing lawns,

Let y equal the number of hours worked at the clothes business.

A minimum of $400 must be earned from both employment (400 or more)

15x + 10y ≥ 400

In order to graph y = -15/10x +35, get y.

10 hours minimum every day in the store.

35 hours maximum per week

x + y ≤ 35

To graph y = -x + 35, find y.

Making the graph: 0 to 35 for the x and y axes.

First equation: y = -15/10x + 35 y-intercept = 35 slope: solid line on the y-axis starting at 35, going down 12, over 10 Shade above solid line

Second formula: y 10

At y=10, draw a solid horizontal line; more than should be shaded above the line.

Third formula: y = -x + 35

beginning at the y-intercept (0,35)

Line is solid, slopes down one and over one, and is shaded beneath.

The overlapping region on the graph will appear as a little triangle with its points under the line from the third equation, above the horizontal line, and above the line from the first equation.

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The value of the tangent of angle B where the tangent of angle A is 1/2 and ∠A and ∠B are the non-right angles in the right triangle is; tan B = 2

A right triangle is a triangle that has the measure of one of the interior angles as 90°.

The angles in the right triangle that are not right angles = A and B

tan(A) = 1/2

The value tan B

Angle ∠A and angle ∠B are complementary angles

Therefore; m∠A + m∠B = 90°

The tangent trigonometric ratio indicates that the tangent of a non-right angle in a right triangle is; (The length of the opposite side)/(The length of the adjacent side)

Let a represent the length of the side opposite to angle ∠A, and let b represent the length of the side opposite to the angle ∠B, we get;

tan(A) = a/b

tan (B) = b/a

Therefore, if tan(A) = 1/2, tan(B) = The inverse of tan(A) = 1/(1/2) = 2

tan B = 2

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To graph the system of equations 3x - 2y = 4 and 3x + 2y = 8, we first need to solve for the value of x and y.

To solve for x and y, we can use the first equation 3x - 2y = 4,

3x - 2y = 4

y = (3x/2) - 2

we can substitute this value of y into the second equation 3x + 2y = 8

3x + 2(3x/2 - 2) = 8

3x + 3x - 4 = 8

6x = 12

x = 2

Now we can substitute the value of x into the first equation to find the value of y

3(2) - 2y = 4

6 - 2y = 4

-2y = -2

y = 1

so the point of intersection is (2,1)

In order to graph the system of equations, we can plot the point of intersection (2,1) and then use the slope-intercept form of the equations to graph the lines.

The slope-intercept form of the first equation is y = (3/2)x - 2

The slope-intercept form of the second equation is y = (1/2)x + 4

So, the lines have a slope of 3/2 and 1/2 respectively.

We can now plot these lines on the coordinate plane, with the point of intersection (2,1) being the point where the lines cross.

The graph of the system of equations is the two lines crossing at the point (2,1)

The shape of the ABCD is a rhombus. The diagonals are not equal to each other.

What is the 2-dimensional shape?

A two-dimensional shape with horizontal and vertical axes is known as a 2d shape (x-axis and y-axis). Two-dimensional shapes have only length and width. There is no thickness or height to these shapes.

Given the vertices of ABCD are  A(-3,0), B (1,5), C(-3,10) and D(-7,5).

The formula distance between points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].

The distance between A and B is √[(1 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4

The distance between B and C is √[(-3 - 1)²+(10 - 5)²] = √(4²+5²) = 6.4

The distance between C and D is √[(-7 - (-3))²+(5 - 10)²] = √(4²+5²) = 6.4

The distance between A and D is √[(-7 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4

The distance between A and C is √[(-3 - (-3))²+(10 - 0)²] = √(10²) = 10

The distance between B and D is √[(-7 - 1)²+(5 - 5)²] = √(8²) = 8

The slope of a line passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).

The slope of AB is (5-0)/(1-(-3))=5/4

The slope of BC is (10-5)/(-3-1)=-5/4

The slope of CD is (5-10)/(-7-(-3))=5/4

The slope of AD is (5-0)/(-7-(-3))=-5/4

The number of vertices of the quadrilateral is 4.

Thus it is either a square or rectangle or rhombus or parallelogram.

Since the length of all sides is equal thus it is either a square or rhombus.

Since the diagonals are not equal it is a rhombus.

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Answer: 150 percent.

Step-by-step explanation:

The problem asks for the percent increase in the annual student fees from 2000 to 2014.

First, we need to know how to find a percent increase.

The percentage change formula is

(Increase in amount) / (Original amount) * 100

Using this formula, we can solve this problem.

Since the fee in 2000 was $6000 and the fee in 2014 was $15000, we can find the increase in fees.

Increase in fees = 15000-6000 == 9000

Next, let's use the formula to find the answer.

Percentage Increase = (Increase in fees) / (Original amount) * 100

= 9000 / 6000 * 100

= 150

Therefore, the answer is 150 percent.

Answer:

39

Step-by-step explanation:

x+x+1+x+2=120

3 consecutive numbers leading to x=39 !

The time needed to travel the entire distance is given as follows:

1.27 minutes.

Before obtaining the time, we need to obtain the entire distance.

The distance is the perimeter of the rectangle, which is the sum of all the outer side lengths of the right triangle.

The sides of the right triangle are given as follows:

40 yards and 70 yards.

Applying the Pythagorean Theorem, the length of the hypotenuse is given as follows:

h² = 40² + 70²

[tex]\sqrt{40^2 + 70^2}[/tex]

h = 80.6 yards.

Then the total distance is given as follows:

40 + 70 + 80.6 = 190.6 yards.

The time is given by the division of the distance by the velocity of 150 yards per minute, hence:

t = 190.6/150

t = 1.27 minutes.

The problem is given by the image presented at the end of the answer.

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Using substitution method, the values of a and b in the system of linear equations are 6.3 and 3.65

A system of linear equations is a set of two or more linear equations that contain two or more variables. The goal of solving a system of linear equations is to find the values of the variables that satisfy all of the equations in the system simultaneously. Linear equations are equations that can be written in the form of ax + b = y, where a, b, and x are constants and x is the variable.

To solve this problem, we have to solve the equations simultaneously using either substitution or elimination method.

0.95a + 1.1b = 10 ...eq(i)

a + b = 9.95 ...eq(ii)

From equation (ii)

a + b = 9.95

a = 9.95 - b ...eq(iii)

Put eq(iii) into eq(i)

0.95(9.95 - b) + 1.1b = 10

b = 3.65

put b = 3.65 into eq(ii)

a + 3.65 = 9.95

a = 6.3

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Answer:

10 cupcakes

Step-by-step explanation:

6 cupcakes have mint icing. This means there are 24 cupcakes left. 7/12 of these, or 14 cupcakes, have chocolate frosting. This means that there are 10 vanilla frosted cupcakes.

A worker's starting wage at this job is $13.5.

$31.70 per hour can be expected after 7 years of experience.

What is the system of equations?

System of equations, also known as simultaneous equations, Two or more equations to be solved together in algebra (i.e., the solution must satisfy all the equations in the system). The number of equations must equal the number of unknowns for a system to have a unique solution.

Given that a worker earns $16.10 per hour with 1 year of experience.

The other worker earns $21.30 per hour with 3 years of experience.

The model that represents the wages of a worker is

y = ax + b

Where x is the number of years of experience, and y is total wages.

Now putting x =1 and y = 16.10 in y = ax + b:

16.10 = a + b .....(i)

Now putting x =3 and y = 21.30 in y = ax + b:

21.30 = 3a + b .....(ii)

Subtract equation (ii) from equation (i)

3a + b =21.30

a + b = 16.10

(-)  (-)    (-)

__________

2a = 5.2

a = 2.6

Putting a = 2.6 in equation (i)

16.10 = 2.6 + b

b = 16.10 - 2.60

b = 13.5

The model is y = 2.6x + 13.5

A worker's starting wage is $13.5 at this job.

Putting x = 7  in y = 2.6x + 13.5:

y = 2.6×7 + 13.5

y = $31.70

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The value of the expression P(x) in the function for the weight of a thin water layer between heights x and Δx, P(x)·Δx, is;  P(x) = 47040·x N/m

A function is a rule that defines the relationship between a set of input and outputs variables, such that each input variable is mapped to only one output variable.

The parameters of the right prism are presented as follows;

Height of the isosceles triangular face = 5 meters

Width of the triangle = 4 meters

The length of the right prism = 6 meters

The function for the weight of a thin water layer between height x and height x + Δx = P(x)·Δx

Weight = Density × Volume × Gravity

Volume = Cross sectional area × Height

Cross sectional area = Width × Length = Width × 6

Using similar triangles, we get;

Width, W = (4/5)×x

Therefore; Cross sectional area = (4/5)×x × 6

Weight = Density × Cross sectional area × Gravity × Height

The height of the section = Δx, therefore;

Weight = Density × Cross sectional area × Gravity × Δx = P(x) × Δx

Therefore; Density × Cross sectional area × Gravity = P(x)

P(x) = ρ × (4/5) × x × 6 × g

The density of water, ρ = 1000 kg/m³

g = 9.8 m/s²

P(x) = 1000 kg/m³ × (4/5) × x × 6 m × 9.8 m/s² = 47040·x N/m

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Using the concept of proportions and ratio, the building of 6ft casts a shadow of 3.33ft

Proportions are a way of comparing two or more quantities by expressing them as fractions or ratios. They are used to describe the relationship between parts of a whole.

A proportion can be written in different ways. For example, the proportion of red apples to total apples can be written as "3 out of 5", "3:5", or "3/5". In this case, 3 is the number of red apples, 5 is the total number of apples and 3/5 is the proportion of red apples.

Data;

Setting up a proportions or two ratios for this.

36 / 20 = 6 / x

cross multiply both sides and solve for x

36 * x = 20 * 6

36x = 120

x = 3.33

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Answer:

Step-by-step explanation:

24²=24×24

Which is 576

The simplified form of the given expression is 3(i-2)

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms. For example, in the expression 4x + y, the two terms are 4x and y.

Given is an expression, (−8+i)+(2+2i)

Simplifying the expression,

(−8+i)+(2+2i)

= -8 + i + 2 + 2i

= -8+2+2i+i

= -6+31i

= 3(i-2)

Hence, the simplified expression is 3(i-2)

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