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Answer:

parallel line: y = 8x - 26

perpendicular line: y = -1/8 x - 13/8

Step-by-step explanation:

1.

Lines are parallel, so slopes are equal, and y-intercepts are different.

Given line:

y = 8x - 2

New line:

y = 8x + b

Use point (3, -2) and solve for b.

-2 = 8(3) + b

-2 = 24 + b

b = -26

Equation: y = 8x - 26

2.

Lines are perpendicular, so slopes are negative reciprocals.

Given line:

y = 8x - 2

New line:

m = -1/8

y = -1/8 x + b

Use point (3, -2) and solve for b.

-2 = -1/8 × 3 + b

-2 = -3/8 + b

b = -16/8 + 3/8

b = -13/8

Equation: y = -1/8 x - 13/8

Therefore , the solution of the given problem of triangle comes out to be the distance of  the drone from the start point is  13feet.

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It is a fundamental geometric figure. Triangle ABC is the term used to refer to a triangle containing the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

Here,

Given : Height of drone  = 5 feet

and  distance of drone covered is 12 feet

Thus ,

to calculate the distance of  the drone from the start point

distance can be represented as H

Since it forms right triangle.

By using pythagoras theorem,

=> 5² + 12² = H²

=> H² = 169

=> H = √169

=> H = 13

Therefore , the solution of the given problem comes out to be the distance of  the drone from the start point is  13feet.

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Answer:

[tex]\frac{6}{10}, \frac{7}{10}, \frac{8}{10},\frac{9}{10}[/tex] (in general, the numerator has to be greater than half the denominator)

Step-by-step explanation:

There are an infinite number of fractions greater than 1/2, but we can generally form a rule to figure out whether a fraction is greater than 1/2, which will help us find those fractions!

Let's first just express a fraction in the form: [tex]\frac{a}{b}[/tex], and we have to ask our self, what determines whether this is 1/2? Well we know if we have 1/2, and multiply it by two, then we have a whole, or one, but the only case where we have a whole, or one, in fraction form, is where the numerator and denominator are equal.

This means, multiplying the numerator "a" by 2, will result in it being equal to the denominator "b". From here, it can be determined that for the fraction: [tex]\frac{a}{b}[/tex], to be 1/2, then the numerator "a" has to be half the denominator "b". But this is just telling us what "a" and "b" need to be, for the fraction to be equal to 1/2, not greater than 1/2. This is still useful, since in general the following is true: [tex]\frac{a+1}{b}[/tex], if we add one to the numerator, the fraction becomes bigger. So if we want the fraction to be bigger than 1/2, the numerator "a" just needs to be bigger or larger than the half the denominator "b".

Let's select a denominator, and from there find numerators that make the fraction bigger than 1/2. For this example let's just select "9". In this case, for a fraction to be 1/2, the numerator just has to be larger than 9/2 or 4.5, but since we can't have decimals in fractions, or at least proper fractions, we just need the numerator to be greater than or equal to 5 (5 is included, since it's still bigger than 4.5)

[tex]\frac{4}{5}[/tex] is actually the only proper fraction, since 5/5 would just simplify to one.

Let's do another example, in this case let the denominator be 10. For the fraction to be considered greater than 1/2, the numerator, has to be greater than half the denominator, 10/2 = 5.

[tex]\frac{6}{10}, \frac{7}{10}, \frac{8}{10},\frac{9}{10}[/tex] would all be valid answers (although some do simplify further). But all of them represent fractions which have a greater value than 1/2

When the cross-section of a wall is 7/16 of an inch thick and the drywall is 1/4 inches thick, the thickness of the texturing on wall is A. 3/16

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

From the information, the cross-section of a wall is 7/16 of an inch thick. If the drywall is 1/4 inches thick. The thickness of the texturing on the wall is the total thickness of the wall minus the thickness of the drywall. The total thickness of the wall is 7/16 inches, and the thickness of the drywall is 1/4 inches, so the thickness of the texturing is:

= 7/16 inches - 1/4 inches

= 3/16 inches.

Therefore, the answer is A. 3/16 inches.

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There are 3,024 different ways 1,214 can be shown.

Basically A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.

Given 1,214

since there are 4 places in the digit,

so 4 values less than 10 can be solved by

9, 8, 7, and 6

so by permutation to find ⁹P₄ = 9!/(9 - 4)!

= (9 x 8 x 7 x 6 x5!)/5!

⁹P₄  = 3,024

Hence there are 3,024 different ways.

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Answer:

it is undefined

Step-by-step explanation:

Slope of the line x=-24 is undefined. We'll compare the line x = -24, with x = h. So this line is a vertical line that is parallel to the y-axis. We know that the slope of the y-axis is undefined. Since x=-24 and y-axis are parallel, so x=-24 will have the same slope, that is undefined.

Answer:

undefined slope

Step-by-step explanation:

When you have the line x=-24, you have a vertical line, where the x-value is constant, given in the equation, but the y-value varies between negative infinity and positive infinity. If we were to plug two points into the slope formula, we would get: [tex]\frac{y_2-y_1}{-24-(-24)}\to\frac{y_2-y_1}{0}[/tex], because there is no change in x, the x values are the same. Thus it is said that the slope is undefined.

Answer:

  $202.30

Step-by-step explanation:

You want to know the value of a 20% tip on a bill of $1011.50.

The tip amount can be found by multiplying the bill amount by the tip percentage:

  20% · $1011.50 = $202.30

Lucas tipped the server $202.30.

__

Additional comment

You know that 10% of the amount can be found by moving the decimal point one place: $101.15.

20% of the amount will be double this value: $202.30. You can do this math mentally.

The amount of syrup she needs is 3/4 cups of syrup. Option A

A fraction can be described as the part of a whole variable, element or number.

The several types of fractions are;

Also, proportion can be defined as a mathematical comparison between two numbers

From the information given, we have that;

6 cups of soap = 1 /4 cup of syrup

Then 18 cups of soap = x cups of syrup

cross multiply, we get;

6x = 18(1/4)

multiply the values

6x = 18/ 4

Divide both sides by the coefficient of x , we get;

x = 18/ 4 × 1/6

x = 3/ 4 cup of syrup

Hence, the value is 3/4

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Answer:

Step-by-step explanation:

Answer:

Domain: All real numbers

Range: All real numbers greater than or equal to -1

Answer:

27

Step-by-step explanation:

To find 45% of 60, you can multiply 60 by 0.45

60 x 0.45 = 27
45% of 60 is 27.

Answer:

sorry needed points so sorry

Step-by-step explanation:

Answer: To find the expected amount of money the radio caller should win, you can multiply the prize amount by the probability of winning that prize, and add those products for each prize. The expected value is also known as the mean value.

$500 * 1/8 = $62.50

$750 * 1/8 = $93.75

$1,250 * 1/8 = $156.25

$2,500 * 1/8 = $312.50

$5,000 * 1/8 = $625.00

$10,000 * 1/8 = $1250.00

$25,000 * 1/8 = $3,125.00

Total expected value = $62.50 + $93.75 + $156.25 + $312.50 + $625.00 + $1250.00 + $3,125.00 = $5,050.00

So, the expected amount of money the radio caller should win if the caller gets to spin the wheel once is $5,050.

It's worth to mention that the probability for each prize is the same, but the prizes are not the same so each prize win will be different according to the prize amount.

The expected value doesn't assure that the prize will be won, but it's a good approximation of the prize the caller could win.

Step-by-step explanation:

On solving the provided question, we can say that - the percentage value of 12 % of 90 = 10.8

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

12% of 90 = 12/100 X 90

= 0.12 X 90 = 10.8

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The probability that the next customer will pay cash or a credit card is 56%, since 3 customers paid cash and 53 customers used a credit card out of a total of 81 customers.

Customers are individuals or organizations who purchase goods and services from a business. They play an important role in a company's success as they provide the revenue needed to sustain and grow the business. Customers become loyal to a business when they are provided with quality products, excellent customer service, and competitive prices. Companies that focus on customer satisfaction often develop long-term relationships with their customers, as they understand the importance of customer loyalty. Companies must strive to continually meet the changing needs of their customers in order to remain successful in the long term.

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The solution of the system of equations:

y = 3x - 4

y = (-1/2)*x + 3

Is (2, 2).

Here we have the following system of equations:

y = 3x - 4

y = (-1/2)*x + 3

To solve this graphically, we just need to graph both equations on the same coordinate axis, and find a point where these two graphs intercept.

Below you can see the graph of the system, and there you can see that the lines intercept at the point (2, 2), so that is the solution of the system.

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Answer:

r=3

Step-by-step explanation:

use slope formula : y2-y1 / x2-x1

-5-3 / r-5

the numerator is -8 which means the denominator has to be -2 in order to have the slope be 4

so r-5 = -2

3-5 = -2

Answer:

A.  x ≥ 21[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

81 - 1[tex]\frac{1}{5}[/tex] x ≤ 55

-1[tex]\frac{1}{5}[/tex] x ≤ 55-81

-[tex]\frac{6}{5 }[/tex] x ≤ -26

x ≥ -26(-[tex]\frac{5}{6}[/tex])       **flip the inequality when you divide by a negative number

x ≥ 21[tex]\frac{2}{3}[/tex]

Answer:

The set A is defined as the set containing the elements c, d, e, f, and g.

The set B is defined as the set of odd numbers greater than 5 and less than 13. This set includes the elements 7, 9, and 11.

Step-by-step explanation:

1.  you are asked to find how many weeks it would take Alex to work 51 hours.

2. Alex  works  [tex]3\frac{1}{7}[/tex] weeks.

3. It makes sense in fractional from.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction.

Alex works 3 hours a day and 4 days a week.

Alex works in a week = ( 3×4) hour = 12 hour

Alex  works = 51 hours = 48 hours + 3 hours = (48/12) weeks + 1 day

= 3 weeks and 1 day.

= [tex]3\frac{1}{7}[/tex] weeks.

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Therefore ,option 3 is hence the appropriate choices. By the Side-Angle-Side Triangle Congruence Theorem, these triangles are congruent.

Any three points in a plane can be connected to create triangles, which have three sides and three angles. They were one of the very first geometric shapes to be studied. They are particularly important because any polygon, whether it has four, five, six, or n sides, may be split into a triangle.

Here,

From the provided figure, it is clear that there are two triangles.

ABC and EFG are the triangles.

AB = EF

AC = FG

BC = EG

As a result, the triangles ABC and EFG are congruent according to the triangle's SSS theorem, and angle A is equal to angle D.

Therefore ,D and E are hence the appropriate choices. By the Side-Angle-Side Triangle Congruence Theorem, these triangles are congruent.

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By drawing the line x + y = 2, one of the solution to the given system of equations is (0, 2).

Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²  

Where:

From the information provided, we have the following system of equations:

x² + y² = 9             ......equation 1.

x + y = 2              .............equation 2.

Next, we would use an online graphing calculator to plot the given system of equations and then highlight (read) the point of intersection, which is the ordered pair (0, 2).

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Answer:

It is 6.4*10^-2.

this is your answer

The siblings met at the point (4,7). This can be determined by looking at the graph and seeing that the point (4,7) is the only point with an x-coordinate of 4 and a y-coordinate of 7.

Coordinate refers to the pair of numbers used to identify the position of a particular point on a graph, map, or other two-dimensional plane. Each coordinate consists of an x-coordinate and a y-coordinate that indicate the horizontal and vertical position of the point, respectively. Coordinates can be used to plot points, draw shapes, and determine distances between points. For example, the coordinates (4, 7) would tell you that the point is located four units to the right and seven units up from the origin point. Coordinates can also be used to describe the location of a point in three-dimensional space, with the addition of a z-coordinate.

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On solving the provided question, we can say that  on matching the expressions are 100X 14 = 1400 and 14(10) = 140 and 361 . 100 = 36100 and 100(361) = 36100

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

so, on matching the expressions are

100X 14 = 1400

14(10) = 140

361 . 100 = 36100

100(361) = 36100

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Answer: To replace the three steps with a ramp, the height of the ramp must be equal to the total height of the steps. Since each step is 10 cm high, the total height of the three steps is 3 * 10 = 30 cm.

The length of the ramp must be equal to the length of the steps, since the ramp is replacing them. Since each step is 35 cm long, the total length of the three steps is 3 * 35 = 105 cm.

So the length of the ramp to replace the three steps leading to the front door is 105 cm, correct to one decimal place.

Step-by-step explanation: