Are lines A and B parallel? Why?

Answer:

For 1 year Jeff pays $1200.

For 6 years he pays 7200 / 6 = 1200 per year.

For 9 years he pays 10800 / 9 = 1200 per year.

Jeff's unit rate is $1,200 per year.

Daniel pays $1,150 per year.

150 is less than 1200, so the answer would be:

A.  Daniel's unit rate is lower. It is $1,150 per year

Answer:

constant is - 19

Step-by-step explanation:

the constant is the term in an expression with no variable attached to it.

12r + \(\frac{r}{2}\) - 19

the only term without the variable r attached to it is - 19

then the constant term is - 19

The correct solution set for the given graph include the following: D. {infinite set of points on the line}.

In Mathematics, a quadrant can be defined as the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.

This ultimately implies that, there are four (4) major quadrants in any graph and these include the following:

Generally speaking, the solution set of a graph simply refers to all of the points that lie on its line. By critically observing the graph of lines a and b, we can reasonably infer and logically deduce that they both have the same slope, solution set, as well as increasing and decreasing infinitely.

In this context, the correct solution set lies in both Quadrant II and Quadrant III because both lines move towards negative and positive infinity i.e [-∞, ∞].

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Answer:

15 is the answer to the question

Answer:

15, which for some reason does not seem to be an option.

Step-by-step explanation:

Product means to multiply to numbers, items etc.

5 times 3, as you should know, is 15.

Hope this helps.

Given:

Volume = 80 cubic centimeters

The square root of 76.8 is 8.76.

Square root of 76.8 is 8.746.

Given,

\(\sqrt{76.8}\)

Now,

Simplifying the square root :

If square root of x is to be calculated then,

\(\sqrt{x}\) = \(x^{1/2}\)

Similarly,

\(\sqrt{76.8}\) = \(76.8^{1/2}\)

= 8.746

Thus the square root of 76.8 is 8.746.

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Answer:

d. you just have to multiply everything

Answer:

Point C

Step-by-step explanation:

Each of the lines are counted by 5 and if counting carefully, C would be 0.75, or, 3/4

Point C on the number line below represents a value of 0.75.

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

To find point on the number line which represents a value of 0.75..

Now, We get;

Point A = 0.3

Point B = 0.55

Point C = 0.75

Thus, Point C on the number line below represents a value of 0.75.

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700 + 30

= 730

Hope it's help you!

Answer:

730

Step-by-step explanation:

So you have 700 ok then you are adding 30 to that so in 700 there are no tens or one's so you can just slide that 30 right in there and make 730.

Hope this helps have a great day:)

Answer:

Step-by-step explanation:

The next is to simplify

The required length of the segments are found as :

AB = 3.16

AC = 5.1

BC = 5.66

Perimeter = 13.92

A perimeter is  described as a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

We make use of the distance formula:

Distance = √ ((x2 - x1)² + (y2 - y1)²

segment AB:

x1 = 1, y1 = 5

x2 = 4, y2 = 4

= √ ((4 - 1)² + (4 - 5)²

= √ (9 + 1)

= √ (10)

= 3.16

Segment AC:

x1 = 1, y1 = 5

x2 = 0, y2 = 0

= √ ((0 - 1)^2 + (0 - 5)^2)

= √ ((-1)^2 + (-5)^2)

= √ (1+ 25)

=√ (26)

= 5.1

Segment BC:

x1 = 4, y1 = 4

x2 = 0, y2 = 0

= √ ((0 - 4)² + (0 - 4)²

=√ ((-4)² + (-4)²

= √ (16 + 16)

= (32)

= 4 x √(2)

= 5.66

Perimeter = segment AB + segment  AC + segment  BC

Perimeter =  13.92

Perimeter =  13.92

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the complete question is attached in the image:

The class of the equation and the cross section equation are;

The equation is a hyperboloid of two sheets

The cross sections are;

Equation at z = 0 is; y²/8 - x²/8 = 1

Equation at y = -4 is; x²/8 + z² = 1

Equation at y = 0 is; x²/8 + z² = -1

Equation at y = 4 is; x²/8 + z² = 1

Equation at x = 0 is; y²/8 - z² = 1

An equation is a mathematical statement which indicates the equivalence two expressions by joining them with the '=' sign.

The equation can be presented as follows;

y² = x² + 8·z² + 8

y² - x² - 8·z² = 8

y²/8 - x²/8 - z² = 1

The above equation is the equation of an hyperboloid of two sheets, where;

a² = 8, b² = 1, and c² = 8

Please find attached the diagram of the surface, created with an online 3D graphing tool.

The equation for the cross section at z = 0, can be obtained by plugging in z = 0, into the equation as follows;

y²/8 - x²/8 - 0 = 1

y²/8 - x²/8 = 1

The above equation is the equation of an hyperbola in the xy plane

The equation for the cross section at y = -4, can be obtained by plugging in y = -4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 4²/8 = -1

- x²/8 - z² = -1

x²/8 + z² = 1

The above is an equation of an ellipse in the xz plane

The equation for the cross section at y = 0, can be obtained by plugging in y = 0, into the equation as follows;

0²/8 - x²/8 - z² = 1

- x²/8 - z² = 1

Therefore; x²/8 + z² = -1

The equation for the cross section at y = 4, can be obtained by plugging in y = 4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 2 = -1

x²/8 + z² = 1

The above equation is the equation of an ellipse in the xz plane

The equation for the cross section at x = 0, can be obtained by plugging in x = 0, into the equation as follows;

y²/8 - 0²/8 - z² = 1

y²/8 - z² = 1

The equation is the equation of an hyperbola in the yz plane

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Answer:

1,2,-5,-1,3

Step-by-step explanation:

the coefficients are the numbers before the variables (x and y)

if there is nothing infront of the variable then the coefficient is 1

if there is only a negative sign infront of the variable then the coefficient is -1

Value of an exterior angle of a triangle is equal to the sum of values of two opposite interior angles of a triangle.

\(\qquad\displaystyle \tt \dashrightarrow \: 5x + 10 = 40 + 70\)

\(\qquad\displaystyle \tt \dashrightarrow \: 5x = 110 - 10\)

\(\qquad\displaystyle \tt \dashrightarrow \: 5x = 100\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 100 \div 5\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 20\)

Value of x = 20°

Hey! there . Thanks for your question :)

Answer:

Step-by-step explanation:

In this question we are given with two interior angles of the triangle that are 40° and 70° , also we are given an exterior angle that is (5x + 10)°. And we are asked to find the value of angle x.

Solution :-

For finding the value of angle x , we have to use exterior angle property of triangle which states that sum of opposite interior angles of triangle is equal to the given exterior angle. So :

Step 1: Making equation :

\( \longmapsto \: \sf{40 {}^{°} + 70 {}^{°} = (5x + 10) {}^{°} }\)

Solving :

\( \longmapsto \: \sf{110 {}{°} = (5x) {}^{°} +10 {}^{°} }\)

Step 2: Subtracting 10 on both sides :

\( \longmapsto \sf{ 110 {}^{°} - 10 {}^{°} = 5x + \cancel{10 {}^{°}} - \cancel{10 {}^{°} } }\)

We get ,

\( \longmapsto \sf{(5x ){}^{°} = 100 {}^{°} }\)

Step 3: Dividing both sides by 5 :

\( \longmapsto \dfrac{ \cancel{5}x {}^{°} }{ \cancel{5}} = \dfrac{ \: \: \: \: \cancel{ 100} {°}^{} }{ \cancel{5} }\)

On cancelling , we get :

\( \longmapsto \underline{\boxed{\red{\sf{ \bold{ x = 20 {}^{°} }}}}} \: \: \bigstar\)

Verification :-

For verifying sum of both the interior angles is equal to given exterior angles. As we get the value of x as 20 we need to substitute it's value in place x and then L.H.S must be equal to R.H.S :

Therefore , our answer is correct .

Answer:

f(x) = -3/2 x - 2

Step-by-step explanation:

The line rises to the left so the slope is negative, also:

the slope of the line is -3/2 and the y-intercept is at (0, -2)

Answer:p=0.72 a=0.77

Step-by-step explanation:

By using system of equations we get cost per apple is 0.75 and cost per pear is 0.8.

A system of equations is a collection of two or more equations with a same set of unknowns.

By given data we construct system of equations

3a+2p=3.85...(1)

4a+p=3.80...(2)

We have to solve the above equations ,

Multiply with 2 in second equation.

8a+2p=7.6

So Now subtract from 1

3a+2p-8a-2p=3.85-7.6

3a-8a=-3.75

-5a=-3.75

a=3.75/5

a=0.75

Now substitute value of a in 3a+2p=3.85

3(0.75)+2p=3.85

2.25+2p=3.85

2p=1.6

p=0.8

Therefore cost per apple is 0.75 and cost per pear is 0.8.

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The extremas of the function f(x) = x³ - 7x² + 10x are given as follows:

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Answer:

Step-by-step explanation:

The area of a parallelogram of width W and length L is A = W*L.

The area of a trapezoid of width W and different side lengths L1 and L2 is

A = W(L1 + L2)/2.  

To find the area of the trapezoid, take the average of the lengths L1 and L2 of the two parallel sides and call the result L.  Then apply the formula for the area of a parallelogram, given above).

Answer:

23.75

Step-by-step explanation:

Answer:

the answer is 23.75  because my teacher told me it was the answer

Step-by-step explanation:

Step-by-step explanation:

s1 = 5

s2 = s1 × -2 = 5×-2 = -10

s3 = s2 × -2 = -10 × -2 = 20

...

now, we could do all that manually.

but there is also a formula for geometric sequence.

in fact, there are 2 - one for finite and one for infinite sequences.

and I was not completely honest, each of these 2 had some sub-forms depending on the size of the multiplier or ratio.

since we need the sum of the first 5 terms, which of the 2 do you think we need ?

of course, finite, because 5 is a normal number we can "touch". it is not infinity.

so, the formulas for finite sums of geometric sequences are :

if |r| < 1, Sn = a(1 - r^n)/(1 - r)

if |r| > 1, Sn = a(r^n - 1)/(r - 1)

if r = 1, Sn = na

if r = -1, then Sn = a or 0 depending on if n is odd or even.

the sequence is in general

s1 = a

sn = sn-1 × r

in our case a = 5, r = -2.

so, what form of the formula do we need ?

|-2| = 2, and 2 > 1, so ...

S5 = 5(-2^5 ‐ 1)/(-2 - 1) = 5(-32 - 1)/-3 = 5×-33/-3 =

= 5 × 11 = 55

quick check, as the 5 terms are

5

-10

20

-40

80

and their sum is : 55

correct !

the area of the region of points satisfying the inequalities x ≤ 0, y ≤ 0, and y ≥ |x + 4| − 5 is 12.5 square units.

Answer:

To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:

8x = x + 9

Solving for x, we get:

x = 1.5

Therefore, AB = 8x = 8(1.5) = 12.

To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:

AB^2 + BD^2 = AD^2

Substituting the values, we get:

12^2 + BD^2 = (1.5 + 9)^2

Simplifying, we get:

BD^2 = 56.25

Taking the square root of both sides, we get:

BD = 7.5

Hence, the length of AB is 12 and the length of BD is 7.5.

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Answer:

You just gave the answer...

5/4 = 1a

5/4 = a

Answer:

Step-by-step explanation:

To make a box plot of the data, we first need to find the five-number summary, which consists of the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum.

The data in ascending order is:

29, 36, 39, 41, 45, 48, 57

The minimum is 29, the maximum is 57, and the median is the middle value, which is 41.

To find Q1 and Q3, we need to find the medians of the lower and upper halves of the data, respectively. The lower half is:

29, 36, 39, 41

The median of this half is (36 + 39) / 2 = 37.5. So Q1 = 37.5.

The upper half is:

45, 48, 57

The median of this half is (48 + 57) / 2 = 52.5. So Q3 = 52.5.

Now we can draw the box plot. Here's how it looks:

          |                 ___

 29     |                |       |

          |                |       |

 36     |                |       |

          |                |        |

 39    |                |       |___

         |                |       |      |

 41    |                |       |       |

        |                |       |       |

        |__|_____|___|___|__

                   37.5 41 52.5

The line in the box represents the median, the box goes from Q1 to Q3, and the whiskers extend to the minimum and maximum values. Any data points beyond the whiskers are considered outliers.

Answer:

  a) 30 kangaroos in 2030

  b) decreasing 8% per year

  c) large t results in fractional kangaroos: P(100) ≈ 1/55 kangaroo

Step-by-step explanation:

We assume your equation is supposed to be ...

  P(t) = 76(0.92^t)

__

a) P(10) = 76(0.92^10) = 76(0.4344) = 30.01 ≈ 30

In the year 2030, the population of kangaroos in the province is modeled to be 30.

__

b) The population is decreasing. The base 0.92 of the exponent t is the cause. The population is changing by 0.92 -1 = -0.08 = -8% each year.

The population is decreasing by 8% each year.

__

c) The model loses its value once the population drops below 1/2 kangaroo. For large values of t, it predicts only fractional kangaroos, hence is not realistic.

  P(100) = 75(0.92^100) = 76(0.0002392)

  P(100) ≈ 0.0182, about 1/55th of a kangaroo