1080 sec: 6 min: 1080 sec simplified

Answer:

See below

Step-by-step explanation:

Point slope form

y - - 8 = (-1)(x -3)      re-arrange

y + 8 = -x+3

y = -x - 5

The vertices of the path of the comet E are; (-12,0) and (+12,0) as it is moving an elliptical path.

Comet 'E' is modeled by

((y + 16)²)/400 + (x²)/144 = 1

This is an equation of an ellipse. So, the path traveled by Comet E will be an elliptic path.

Comparing with the equation of ellipse;

((y - k)²)/(b²)+ ((x - h) ²)/(a ²) = 1

whose; Centre is (h,k) and Vertex is (h±a, 0)

On Comparing Centre (h, k), h= 0 and k = -16,

a²=144

a = 12

b²=400

b=20

So, Centre (0, -16),

The Vertex (-12,0) and (+12,0)

So, the vertices of the path of the comet E are; (-12,0) and (+12,0).

Part B: The path of Comet H has been modeled as; a horizontal hyperbola.

Thus, The Comet H travels closer to the sun.

Part C: The sun represents the one of the foci of both the Comet E and Comet H.

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The polynomial is x³ + 2x

If the zeros or roots of the polynomial are given, then the standard form of the polynomial can be found.

That is, a, b and c are roots of the polynomial, then  the polynomial will be of degree 3 since 3 zeros are there and the factors of the polynomial will be , x-a, x-b and x- c.

Then the polynomial is, (x-a)(x-b)(x- c) = x³-(a+b+c)x-abc

Here the zeros of the polynomial are x = 0, x = i√2 and x = -i√2.

So the factors of the polynomial are (x-0), (x - i√2) and (x +i√2).

Hence the polynomial is , (x-0) (x - i√2)(x +i√2) = x(x²+2) = x³ + 2x

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Answer:

y=x^2+3x-10

Step-by-step explanation:

.........

Algebraic equations are mathematical equations that consist of unknown variables. These unknown variables can be represented with any letter of the alphabet.

The cost of 2 pounds(lb) of the first type of candy is $8

Note that: x represents the cost per pound (lb) of the first type of candy

The Algebraic equation for the above statement is given as:

2lb × $x + 3 Ib × $1.50 = $2.50(2lb + 3lb)

2x + 4.5 = 12.5

Collect like terms

2x = 12.5 - 4.5

2x = 8

Divide both sides by 2

2x/2 = 8/2

x = 4

The cost of the 1 pound of first type of candy is $4

The cost of 2 pounds(lb) of the first type of candy is calculated as:

2 x $4

= $8

hope it will be helpful

well, the midpoint of segment AB is the center of the circle, so

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 -2}{2}~~~ ,~~~ \cfrac{ 9 +1}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ 10 }{2} \right)\implies \stackrel{center}{(2~~,~~5)}[/tex]

now since we know AB is the diameter, so half that distance AB is its radius, so

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}[/tex]

[tex]AB=\sqrt{(~~6 - (-2)~~)^2 + (~~9 - 1~~)^2} \implies AB=\sqrt{(6 +2)^2 + (9 -1)^2} \\\\\\ AB=\sqrt{( 8 )^2 + ( 8 )^2} \implies AB=\sqrt{ 64 + 64 } \implies AB=\sqrt{ 128 } \\\\\\ AB=8\sqrt{2}\hspace{5em}\stackrel{\textit{half that is the radius}}{\cfrac{8\sqrt{2}}{2}\implies 4\sqrt{2}\implies \sqrt{32}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{2}{h}~~,~~\underset{5}{k})}\qquad \stackrel{radius}{\underset{\sqrt{32}}{r}} \\\\\\ (x-2)^2~~ + ~~(y-5)^2~~ = ~~(\sqrt{32})^2\implies {\large \begin{array}{llll} (x-2)^2~ + ~(y-5)^2~ = ~32 \end{array}}[/tex]

The new hourly rate using compatible numbers is $21.

Given,

The earnings of Mrs. Gomez = $19.50 per hour

She gets a raise of 5%

We have to estimate her new hourly rate by using compatible numbers.

Compatible numbers:

Compatibility in mathematics refers to the mental ease with which a number can be added, subtracted, multiplied, or divided. Compatibility refers to the proximity of the compatible numbers to the real numbers, which facilitates estimation of the solution and simplifies problem-solving.

So,

Compatible number of 19.50 is 20.

The amount raised = 20 × 5/100 = 5/5 = $1

Now, the new hourly rate = 20 + 1 = $21.

That is, the new hourly rate using compatible numbers is $21.

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Answer:

5+8=x

step by step explanation

The constant of proportionality when the restaurant is placing an order for paper towels is 12.

It should be noted that the constant of proportionality simply means the ratio that is important to show the proportional relationship between the two given values.

This will be illustrated as:

y = kx

y = Number of paper roll

x = Number of cases ordered

From the table, this will be:

y = kx

12 = k × 1

k = 12

Therefore, the constant of proportionality is 12.

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Answer:

176 yd

Step-by-step explanation:

UNSHADED REGION (white rhombus): A=(s1+s2)/2 * H

s1=7

s2=1+7=8

H=6

A=(7+8)/2*6=45

SHADED + UNSHADED REGION (big parallelogram): area of parallelogram A=B*H

B=17

H=7+6 = 13

A=17*13=221

SHADED REGION: big parallelogram area - rhombus area

221 - 45 =176 yd

The number sentence that is true is 1/3 x (-2/5)=-2/15 . Option A

A fraction is simply defined as the subset of a whole set or the part of a whole element.

The several types of fractions includes;

Examples of simple fractions: 1/2, 1/8

Examples of proper fractions: 3/4, 8/10

Examples of mixed fractions: 3 1/6, 2 1/8

Examples of improper fractions: 7/4, 8/5

Given the fraction;

a. 1/3 x (-2/5)

The product of the fraction is = - 2/15

b. -1/3 x 2/5 = 2/15

The product is = -2/15

c. -1/3 x (-2/5)

The product is 2/15

d. 1/3 x 2/3

The product is 2/9

Hence, the sentence is option A

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Answer:

You've gotta be kidding me...It's easy come on

-2 is the answer

Step-by-step explanation:

f(x)= -x-1        JUST SUBSTITUTE 1 FOR X

f(1)= -(1)-1

f(1)= -2

The solution for the given inequality is p < -2.2. The graph that represents the solution is attached below.

From the question, we are to determine the graph for the solution set for the given inequality

The given inequality is p - 3.6 < -5.8

First, we will solve the inequality

Solving the inequality

p - 3.6 < -5.8

Add 3.6 to both sides

p - 3.6 + 3.6 < -5.8 + 3.6

p < -2.2

The solution is p < -2.2

The graph of the inequality is shown below

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Answer: number line with an open circle on point negative 2.2 and arrow shaded to the left

Step-by-step explanation:

If this guy is correct

The required value of the function at x = 4 and 3 is f(4) = -12 and f(3) = -7.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given function ,

f(x) = 8 - 5x
put x = 4
f(4) = 8 - 5(4)
f(4) = 8 - 20
f(4) = -12

Again,
put x = 3
f(3) = 8 - 5(3)
f(3) = 8 - 15
f(3) = -7

Thus, the required value of the function at x = 4 and 3 is f(4) = -12 and f(3) = -7.

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Answer:

5 7/10

Step-by-step explanation:

first you multiply five by the three, then add the eleven. so now you have a improper fraction, 26/5 plus 1/2. find the Least common denominator which is 10, and whatever you do to the denominator you do to the numerator which makes 57/10 simplify and you'll get 5 7/10

Answer:

Step-by-step explanation:

1. Find the lcm(least common denominator)

(5 x 2 = 10)

2. Multiply the numerators by the same number as the denominator(you multiplied 5 by 2 to get 10 so you multiply 311 by 2. You multiplied 2 by 5 to get 10 so you multiply 1 by 5.)

311 x 2 = 622

1 x 5 = 5

3. Add

622/10 + 5/10 = 627/10

4. Simplify

627 ÷ 10 = 62 [tex]\frac{7}{10}[/tex] (it can also be written as: 62.7)

Answer:

x = 60

Step-by-step explanation:

(2x + 15)° and 135° are corresponding angles and are congruent , then

2x + 15 = 135 ( subtract 15 from both sides )

2x = 120 ( divide both sides by 2 )

x = 60

Answer:

x = 60

Step-by-step explanation:

The two angles are corresponding. This means that both of the angles are congruent (same). So, you set both of them equal to each other. That means to do 2x + 15 = 135. You do basic algebra and then you get 60 for x. Hope this helps!

Answer:

y - intercept is (0,2)

x - intercept is (3,0)

Step-by-step explanation:

This is standard form.  

Let x  = 0

2x + 3y = 6

2(0) + 3y = 6

3y = 6   Divide both sides of the equation by 3

y  = 2

The y intercepts is (0,2)

Let y = 0

2x + 3(0) = 6

2x = 6  Divide both sides of the equation by 2

x = 3

The x intercept is (3,0)

Answer:

x-intercept (3, 0)

y-intercept (0, -2)

Step-by-step explanation:

        At x-intercept the y = 0. The line passes the x-axis.

             2x  -0 = 6

                   2x = 6

                     x = 6 ÷ 2

                     x = 3

x-intercept (3, 0)

At y-intercept, x = 0 . The line passes y-axis.

      0 - 3y = 6

        -3y  =  6

           y =  6 ÷ (-3)

           y = (-2)

y-intercept (0 , -2)

Plot these two points in the graph and join the points.

Answer: The cost of her phone is $1,820.

45*12=540 per year

540*3=1,820 every 3 years.

She would have had the phone between 2 and 3 years if she had spent 1,500.

The coordinates of A"B"C" are as follows :

A = 1 1/2,3

B = 1 1/2,0

C = -4 1/2, 3.

Using one or more numbers, or coordinates, a coordinate system in geometry establishes a unique way to locate points or other geometrical objects on a manifold, such Euclidean space. a group of numbers representing a precise place. On graphs, there are typically two numbers: the first one indicates the length along, and the second one indicates the length up or down. For instance, the value of the point (12,5) is 12 units. In general, alphanumeric characters are used to express GPS coordinates, which are a distinctive identifier of a certain geographic location on the globe. Points of intersection in a grid system are referred to as coordinates in this context. Typically, the latitude and longitude coordinates are used to represent GPS coordinates.

Five units up and along.

90degrees clockwise is x, y, y, -x.

A = 1,2

B = 1,0

C = -3, 2.

Times everything by 3/2 now.

A = 1 1/2,3

B = 1 1/2,0

C = -4 1/2, 3.

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In accordance with analytic geometry, the equation that represents the line is y = - (1 / 4) · x - 6.

Herein we find the representation of a line set on a Cartesian plane. According to analytic geometry, line are represented by equations of the form y = m · x + b, where m, b are the slope and the y-intercept, respectively.

Both the values of the slope and the y-intercept can be found by knowing the location of two points lying on the line. If we know that (x₁, y₁) = (0, - 6) and (x₂, y₂) = (4, - 7), then we find the following system of linear equations:

b = - 6                                    (1)

4 · m + b = - 7                        (2)

By (1) in (2):

4 · m - 6 = - 7

4 · m = - 1

m = - 1 / 4

The equation that represents the line is y = - (1 / 4) · x - 6.

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Answer:

-4/15 - 17

negative 4 over 15 plus negative 17

Step-by-step explanation:

2/3g - 5 - 11/15g - (1/5g +12)

Your wording is extremely confusing but I tried :]

-4/15 - 17

is the correct answer (I think)

:]

The required simplified value of the given expression is -4/15 - 17.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
2 over 3 times g minus 5 minus 11 over 15 times g minus the expression one over 5 times g plus 12 is given as

= 2/3g - 5 - 11/15g - (1/5g +12)

Adding the alike terms,
= 2/3g -11/15g -1/5g -5 -12
= [10 - 11 -3] /15 g - 17
= -4g/15 -17

Thus, the required simplified value of the given expression is -4/15 - 17.

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Answer: 45%

Step-by-step explanation: 45% of 1,900 is 855

Answer: x = 65

Step-by-step explanation:

1) First find the mini triangles, left and right angles

We will be calling the left one A and the right one B.

2) Next use triangle sum to find B.

62 + 50 + b = 180

b = 68

3) Use triangle sum again to find A.

53 + 80 + a = 180

a = 47

4) Use triangle sum to find the top mini angle.

47 + 68 + c = 180

c = 65

5) Since x is in the vertical angle of c, they are equal

c = x

65 = x

The probability of choosing a painting random and it is British is 0.50.

Given,

The total number of paintings = 30

Then,

T = Painting from 20th century

B = British paintings

We have to find the probability of choosing a painting random and it is British.

Here,

Probability = British/ Its from 20th century

Probability = n (B and T) / n(T)

                  = x / (x + x(x-2))

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

                  = 3 / (3 + 9 - 6)

                  = 3 / 6 = 1/2 = 0.5

Here, the probability of choosing a painting random and it is British is 0.50.

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The variable y is shown with no exponent. Any term with no exponent is understood to have an exponent of 1, so y has an exponent of 1.