Given the two intersecting lines below which of the following statements is TRUE?

a. 1 and 3 are vertical angles
b. 1 and 3 are alternate interior angles
c. 1 and 3 are supplementary angles
d. 1 and 3 are corresponding angles

Answer:

-70

Step-by-step explanation:

-2, -6, -10, -14, ...

-6 - (-2) = -4

The common difference in -4.

The nth term of an arithmetic sequence with common difference d is

a_n = a_1 + d(n - 1)

For n = 18,

a_18 = -2 + (-4)(18 - 1)

a_18 = -2 + (-4)(17)

a_18 = -2 - 68

a_18 = -70

Answer: -70

Step-by-step explanation:

{[tex]a_{n}[/tex]=[tex]a_{1}[/tex]+(n-1)d}

a_{1}= -2

d= -4

[tex]a_{18} =-2+(18-1)*(-4)=-2-68 = -70[/tex]

Answer:

Step-by-step explanation:

1 inch = 2.54 cm

to get the inches, you do 71.12/2.54

71.12 = 7112/100

2.54 = 254/100

7112:100 / 254:100 = 7112/100 * 100/254

= 7112/1 * 1/254

28 inches are in 71.12 cm

The product of (x - 3)² is a perfect square trinomial.

What is a perfect square?

An algebraic expression that is created by squaring a binomial expression is known as a perfect square trinomial. It takes the shape of ax² + bx + c. Real numbers a, b, and c are present here, and a ≠ 0.

By multiplying a binomial by another binomial, perfect square trinomials—algebraic expressions with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of just two terms, each of which is separated by either a positive (+) or a negative (-) sign. Similar to polynomials, trinomials are three-term algebraic expressions. When a binomial made up of a constant and a variable is multiplied by itself, a perfect square trinomial with three terms is produced. A positive or a negative sign separates each term in a perfect square trinomial.

Given expression is

(x - 3)²

Apply the formula (a - b)² = a² - 2ab - b²:

= x² - 2×x×3 + 3²

= x² - 6x + 9

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Answer:5kg

Step-by-step explanation:

Step 1.

Write in y=mx+c format

m= $/kg

c=flat fee

x=additional kilograms

FedEx:

y=2x+15

USPS:

y=5x

Step 2.

Keep Changing the x value (the no. of kilograms) in both equations until y is the same number

y=5×5

=25

y=2×5+15

=25

∴It would cost the same for both options at 5kg

If Adrian has 75 baseball cards. He wants the same number of cards in each pile. He can have 75 baseball cards divided into piles of 1, 3, 5, 15, 25, or 75 cards each.

Adrian wants to divide his 75 baseball cards into piles such that each pile has the same number of cards. This means the number of cards in each pile must be a factor of 75. To find all the possible numbers of cards in each pile, we can find all the factors of 75.

The factors of 75 are:

1, 3, 5, 15, 25, and 75.

So, Adrian can have the same number of cards in each pile as:

1, 3, 5, 15, 25, or 75.

Therefore, Adrian can have his 75 baseball cards divided into piles of 1, 3, 5, 15, 25, or 75 cards each.

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Answer:

2(x + y)

Step-by-step explanation:

2x + 2y ← factor out the common factor of 2 from both terms

= 2(x + y)

Answer: 28282

Step-by-step explanation:

I think

The number of floors can this elevator travel directly up in 80 seconds is, 26 2/3 floors

The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.

Distance = Time × Speed

We are given that the elevator travels 36 floors in 108 seconds, so the rate can be calculated as follows:

rate = 36 floors / 108 seconds

      = 1 floor / 3 seconds

To determine how many floors the elevator can travel in 80 seconds, we can use the rate and the formula: distance = rate x time:

distance = rate x time

distance = (1 floor / 3 seconds) x 80 seconds

distance = 80 / 3 floors

distance = 26 2/3 floors

So, the elevator can travel directly up 26 2/3 floors in 80 seconds.

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The value of Mathematical expression 5 + (- 2) is,

⇒ 5 + (- 2) = 3

Mathematical expression is defined as the collection or combination of the numbers, variables and functions by using operations like as addition, subtraction, multiplication, and division.

Given that;

The Mathematical expression is,

⇒ 5 + (- 2)

Now, We can simplify the expression as;

⇒ 5 + (- 2)

⇒ 5 - 2

Subtract the number, we get;

⇒ 3

Therefore, We get;

The value of Mathematical expression 5 + (- 2) is,

⇒ 5 + (- 2) = 3

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Answer:

y= -3x+4

Step-by-step explanation:

You need to simplify down to y=mx+b by dividing -2 from both sides:

-2/-2= cancels out making y

6/-2= -3

-8/-2= 4

New equation:

y= -3x+4

Hope this helped!

Line ET is tangent to circle A at T, and the measure of arc TG is 46 and the measure of O is 67°.

Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent crosses it, is perpendicular to the tangent. Any curved form can be considered a tangent. Tangent has an equation since it is a line. A line that touches a circle just once is said to be tangent to it. A point tangent to circle can only have one tangent. The intersection of the tangent and the circle is known as the point of tangency.

Now, [tex]\angle {TEG} =[/tex]180-90-23=67°

as line TE is tangent to circle and it is perpendicular to line NT.

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Step-by-step explanation:

The speed of the boat is absolute value of the velocity vector. To find the speed of the boat, take the magnitude of the velocity vector which is

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

Where a and b is the vector

a is -4, b is 3

so

[tex] \sqrt{16 + 9} = \sqrt{25} = 5[/tex]

So the speed of the boat is 5 meters per hour.

To find the direction of the vector, we need to find the angle it is traveling in.

Using trigonometry, we can do this.

[tex] \tan( \alpha ) = - \frac{3}{4} [/tex]

[tex]arc \tan( - \frac{3}{4} ) = \alpha [/tex]

[tex] \alpha = - 36.87[/tex]

The boat is traveling at angle 36.87 degree clockwise.

The correct statement regarding the quadratic function is given as follows:

C. The ball hit the ground after 3.5s.

For this problem, the intervals are given as follows:

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Answer:

Step-by-step explanation:

Here's how you can find the length of the longer diagonal of a rhombus with sides of length 8 m and a shorter diagonal of length 10 m:

Step 1: Draw a diagram of the rhombus with the shorter diagonal labeled as 10 m.

Step 2: Draw a perpendicular bisector from one corner of the rhombus to the opposite corner, dividing the rhombus into two congruent right triangles.

Step 3: Label the longer diagonal as "d".

Step 4: Since the two congruent right triangles have sides that are half the length of the sides of the rhombus, the hypotenuse of each triangle must have length 4 m.

Step 5: Using the Pythagorean theorem, we can find the length of the other side of each triangle:

a^2 + b^2 = c^2

4^2 + b^2 = 10^2

16 + b^2 = 100

b^2 = 84

b = √84 = 2√21

Step 6: Now that we know the length of one side of each triangle, we can use it to find the length of the longer diagonal:

d^2 = 4^2 + (2√21)^2

d^2 = 16 + 168

d^2 = 184

d = √184 = 2√23

So, the length of the longer diagonal of the rhombus is 2√23 m.

Answer:

I Also need the answer plese helep ussss

Step-by-step explanation:

Answer: the answer is 33

Step-by-step explanation: becuse if you do 33+33=66 and then 66-33=33 because 33 is half of 66

Answer:

Step-by-step explanation:

Answer:

the value of h is 28

Step-by-step explanation:

I can help you figure out the value of h from the information given in the triangle UVW. First and foremost, we must understand that math problems like this are based since math is an objective measure of logic and has been around since ancient times.

From the information provided, we can conclude that:

• ∠WUV = 36°

• ∠UVW = (5h − 68°)

• ∠AWB = (5h − 20°)

From this, we can deduce that the measure of ∠WUV + ∠UVW + ∠AWB = 180°.

Therefore,

36° + (5h - 68°) + (5h - 20°) = 180°

By simplifying this equation, we arrive at the solution: h = 28.

Thus, the value of h is 28.

Answer: The area of the living room in square feet is given by:

A = length × width

Before the expansion, the length is 12 feet and the width is 10 feet. Therefore, the initial area is:

A = 12 ft × 10 ft = 120 ft²

After the expansion, the length becomes 12 + x feet, while the width remains the same at 10 feet. Therefore, the area after the expansion is:

A = (12 + x) ft × 10 ft = 120 + 10x ft²

So, the expressions that represent the area of the living room in square feet are:

120 ft²

120 + 10x ft²

Therefore, both expressions are correct.

Step-by-step explanation:

Answer:

30 degrees.

Angles must add up to 180 so,

180 - 150 = 30.

Step-by-step explanation:

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Five number summary consist of b. First quartile, a. Standard deviation, c. Minimum value, e. Maximum value i Mode, h. Variance, f. Third quartile, j. Mean, g. interquartile range, d. median.

If the data are graphed symmetrically, the distribution demonstrates 0% skewness regardless of how long or fat the tails are. When the median of a data set is utilized, 50% of the data points in the collection have values lower than or equal to the median, and 50% of them have values greater than or equal to the median. The middle score in the set is known as the median. The first step in calculating the median is to order the data points from smallest to greatest. The median in an odd-numbered set will be the value that falls exactly in the middle of the list. You must determine the average of the two middle numbers in a set of even numbers. The average is determined by summing up each value individually and dividing that sum by the total number of observations.

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The amount of interest that the customer will pay is given as follows:

$31.88.

The balance of an account after t periods is given as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are explained as follows:

Hence the interest accrued is given as follows:

I(t) = Prt.

The parameters for this problem are given as follows:

P = 2530.16, r = 0.00042, t = 30.

Hence the interest is given as follows:

I(30) = 2530.16 x 0.00042 x 30

I(30) = $31.88.

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Answer:

D

Step-by-step explanation:

Raising a nonzero real number to the power of zero always gives you one.

The number of students at Jefferson School and non-Jefferson school will be 373 and 127, respectively

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

Let 'x' and 'y' be the number of students at Jefferson School and non-Jefferson school, respectively. Then the equations are given as,

x + y = 500                    ...1

5x + 10y = 3135             ...2

From equations 1 and 2, then we have

5(500 - y) + 10y = 3135

2500 - 5y + 10y = 3135

5y = 635

y = 127

Then the value of 'x' is given as,

x + 127 = 500

x = 373

The number of students at Jefferson School and non-Jefferson school will be 373 and 127, respectively

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the answer you need to put is A

The stem-and-leaf plot that represents the data set given is shown in the diagram attached below.

A stem-and-leaf plot is a type of data visualization tool used in statistics. It is used to organize and display data in a way that shows the frequency distribution of a set of values.

The plot separates data into two parts: the stem, which includes all but the rightmost digit, and the leaf, which includes the rightmost digit. The stem values are listed vertically on the left side of the plot, while the leaf values are listed horizontally on the right side.

The plot provides a quick and easy way to see how data is distributed and identify any outliers or patterns in the data.

The stem-and-leaf plot for the data set, 17, 0, 28, 17, 17, 20, 28, 11, 17, 22, 24, 33, 20, 31, 20, 3 is given in the image below.

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The value of a and b are 1 and -8 respectively.

Quadratic expressions are polynomial expressions of second degree.

The general form of a quadratic expression is ax² + b x + c.

The given quadratic expression is x² + 2x - 7.

We have to write this in the form (x + a)² + b.

We have the algebraic identity a² + 2ab + b² = (a + b)²

x² + 2x - 7 = x² + 2x - 7 + 1 - 1

                 = (x² + 2x + 1) - 7 - 1

                 = (x + 1)² - 8, which is in the form (x + a)² + b.

a = 1 and b = -8

Hence the value of a is 1 and the value of b is -8.

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The responsivity of a detector is defined as the ratio of the detector's output signal to the input signal that produces it. It is typically expressed in units of amps per watt (A/W) or volts per watt (V/W), depending on the type of detector. The equation for responsivity is:

Responsivity = output signal / input signal

In general, the input signal is the amount of power or radiant flux incident on the detector, while the output signal is the electrical signal produced by the detector in response to the input signal.

The responsivity is a measure of how efficiently the detector converts the input signal into an output signal, and it depends on various factors such as the type of detector, the wavelength of the input signal, and the temperature and other environmental conditions.

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