What is the value of a?
5 units
5 1/3
6 2/3
7 units​

The slope of the line passing through the points (-6, 1) and (8, -7) is -4/7.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given the data in the question;

Point A: ( -6,1 )

x₁ = -6

y₁ = 1

Point B: ( 8,-7 )

x₂ = 8

y₂ = -7

Now, plug the given x and y values into the slope formula above and simplify:

[tex]Slope\ m = \frac{y_2 - y_1}{x_2 - x_1} \\\\Slope\ m = \frac{-7 - 1}{8 - (-6)} \\\\Slope\ m = \frac{-7 - 1}{8 + 6} \\\\Slope\ m = \frac{-8}{14} \\\\Slope\ m = -\frac{4}{7}[/tex]

Therefore, the slope of the line is -4/7.

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The function that describes the table of values is y = 1/2x + 2

From the question, we have the following parameters that can be used in our computation:

x= (-8) (-4) (4) (8)

y= (-2) (0) (4) (6)

From the table, we can see that

As x increases by 4

The y values increase by 2

So, we have

m = Slope = 2/4 = 1/2

The equation is calculated as

y = mx + c

So, we have

y = 1/2x + c

Using the other points, we have

1/2 * -4 + c = 0

So, we have

c = 2

This gives

y = 1/2x + 2

Hence, the function that describes the table of values is y = 1/2x + 2

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Answer:

It takes 135 of the 1/3 unit cubes to fill the prism.

Step-by-Step Explanation:

The volume of the prism is 5 cubic units. This means the prism can be filled with five 1×1×1 unit cubes

How many cubes with 1/3 unit side lengths can fit in a cube with 1-unit side lengths?

There are 27 cubes with 1/3 unit side lengths in 1 cubic unit.

Since the rectangular prism is made up of 5 cubic units, we would have 5×27 total cubes with 1/3 unit side lengths.

It takes 135 of the 1/3 unit cubes to fill the prism.

Solving a system of equations we can see that each pound of trail mix costs $3.50, and each pound of jelly beans costs $1.50

Let's define the variables:

Then we can write a system of equations so we will get:

5x + 3y = 22

2x + 12y = 25

To solve this, we can subtract 4 times the first equation fom the second one:

2x + 12y - 4(5x + 3y) = 25 - 4*22

2x + 12y - 20x - 12y = -63

-18x = -63

x = -63/-18

x = 3.5

That is the cost of each pound of trail mix, and replacing that in one of the equations:

2*3.5 + 12y = 25

y = (25 - 2*3.5)/12

y = 1.5

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Lucio is 64 meters from the starting point.

The square has four sides of equal length, so Lucio has walked half the length of one side.

To return to the starting point, he needs to walk the other half of the side, which is 64 meters.

The angle Lucio turns is irrelevant, as long as he turns 180 degrees in total.

With this in mind, it can be seen that based on the parameters and the conditions, Lucio is 64 meters from the starting point because the angle to which he turns is irrelevant.

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The question in English:

In a square Lucio walks in straight sections, starting from the flagpole, at one point he changes direction turning 150º to his left, advances 64 meters and stops. To return to the pole you have to turn 75º to the left. How far are you from the starting point?

The  best measure of center for the data shown is the median, and its value is 17.

The median is the best measure of center for the given data set. To find the median, we arrange the numbers in ascending order:

10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24

Since the data set has an odd number of values, the median is the middle value, which in this case is 17.

Therefore, the best measure of center for the data shown is the median, and its value is 17.

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Option 2 is the correct graph for the function f(x) = [tex]4[(1/2)^{x}][/tex] .

Given ,

f(x) = [tex]4[(1/2)^{x}][/tex]

Mathematically the graph will of exponential in nature.

So,

Let us assume few values to understand the nature of graph.

Firstly,

Let x= 1

f(x) = [tex]4[(1/2)^{1}][/tex]

f(x) = 2

Let x = 2

f(x) = [tex]4[(1/2)^{2}][/tex]

f(x) = 1

Let x = 3

f(x) = [tex]4[(1/2)^{3}][/tex]

f(x) = 0.5

Thus from these values of f(x) corresponding to the values of x second graph will be correct .

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Answer:

See explanation

Step-by-step explanation:

Depends on what you consider a holiday. The federal government says that there are 12 holidays: New Year's Day, Martin Luther King Jr. Day, Inauguration Day (every four years: not considered), Presidents Day, Memorial Day, Juneteenth, Independence Day, Labor Day, Columbus Day, Veterans Day, Thanksgiving, and Christmas.
If new year's Day is on a Sunday:

Sunday: New Year's Day,

Saturday: Veteran's Day,

Monday: MLK, Presidents Day, Memorial Day, Labor Day, Columbus Day, Christmas.

Tuesday: Independence Day,

Wednesday:

Thursday: Thanksgiving,

Friday: Juneteenth
so all of the days MUST have a holiday except Wednesday. So there is a 6/7 chance that a Monday will have a holiday.

The measure of central angle DBC is 68 degree.

Hence, option C is correct.

In the given figure,

Measure of intercepted arc = 68 degree,

We have to find the measure of central angle DBC

We know that,

When two circle radii intersect in the center of a circle, they produce a vertex. These circle arms may begin at two distinct positions along the arc of such a circle. The two radii cross to produce a central angle, which serves to divide a circle into separate sectors.

A central angle is generated in the center of a circle when two radii within the circle overlap. As previously stated, a central angle in geometry is one whose vertex forms at the canter of the circle and whose arms cross the circle at two separate positions.

By connecting these two locations, an arc on the circle is formed. As a result, a central angle is the angle formed by an arc in the center of a circle.

Thus by property of central angles,

central angle = measure of intercepted arc

Hence,

⇒ m ∠DBC = 68 degree.

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Answer:

Step-by-step explanation this is a tough one but i know everything the answer is 69

The value of x is 94 degree.

we know that

The inscribed angle measures half that of the arc comprising

So, <K = 1/2 (80+92)

<K = 1/2 x 172

<K = 86 degree

Now, inscribed quadrilateral, the opposite angles are supplementary

So, <K + x= 180

86 + x = 180

x = 180- 86

x= 94 degree

Thus, the value of x is 94 degree.

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In a case whereby boat is spotted in the water with an angle of depression of 20° from the top of a lighthouse that is 89 feet tall. To the nearest foot,  the distance away  the boat from the base of the lighthouse is [tex]191 feet[/tex]

The angle of depression is the angle formed by the horizontal line and the horizontal line's observation of the item.

The bottom of the lighthouse bears a triangle with a 90 degree angle. That implies that we can calculate the distance between a boat and the bottom of a lighthouse using trigonometry.

[tex]tan(25) = \frac{89}{x}[/tex]

[tex]x = \frac{89}{tan(25)}[/tex]

[tex]x = 190.86[/tex]

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The sides of each triangle from shortest to greatest:

AB < AC < BC

EG < FG = EF

XY < XZ < YZ

XY = XZ = YZ

We have,

The sides opposite to the angles can be considered as the length measurement.

So,

9)

∠A = 80

∠B = 66

∠C = 180 - (80 + 66) = 180 - 146 = 34

So,

∠C < ∠B < ∠A

This means,

AB < AC < BC

10)

∠E = 65

∠F = 50

∠G = 65

So,

∠F < ∠E = ∠G

EG < FG = EF

11)

∠X = 94

∠Y = 53

∠Z = 33

So,

∠Z < ∠Y < ∠X

XY < XZ < YZ

12)

∠P = 60

∠Q = 60

∠Z = 60

So,

∠P = ∠Q = ∠Z

XY = XZ = YZ

Thus,

The sides of each triangle from shortest to greatest:

AB < AC < BC

EG < FG = EF

XY < XZ < YZ

XY = XZ = YZ

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The points on the scatter plot show the different predictions. The straight line drawn is called the line of regression.

Errors in prediction for each point can be determined by drawing a vertical line from the point to the line of regression. As seen in the image, all of the prediction points are found on the line except for points (14,25) and (16,25). Therefore, these points contain errors in prediction.

The graph that represent this data using the points is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The x and y values

Where

x = stars

y = price

To determine the graph that represent the data, we enter the x and y values in a graphing tool to create the graph

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Answer: 48

Step-by-step explanation:

This isn't college

J=2S

J+S=72

3S=72

S=24

24*2=48

Juan has 48

The number of Cheetos you can buy in the supermarket is 7.

You have $16 and a coupon for a five dollar discount at a local

supermarket . One bag of hot Cheetos cost 3 dollars. Therefore, the

number  of bag of Cheetos you can buy can be calculated as follows:

Therefore, altogether he has 16 + 5(coupon discount)  = 21 dollars to spend

in the super market.

Therefore,

number of Cheetos worth 3 dollars one can buy = 21 / 3

number of Cheetos worth 3 dollars one can buy = 7

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Angle 4 is equal to the sum of the measures of the two nonadjacent interior angles because of the corresponding angles theorem for parallel lines and a transversal.

Angle 4 can be considered as the sum of two nonadjacent interior angles because of the properties of parallel lines and a transversal line. When a transversal line intersects two parallel lines, it creates several pairs of corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles.

In this case, we have two parallel lines and a transversal line that intersects them.

Angle 4 is formed by the intersection of the transversal line with one of the parallel lines.

The two nonadjacent interior angles that we are interested in can be identified as the adjacent angles on the other parallel line, corresponding to the same transversal line.

According to the corresponding angles theorem, when two parallel lines are cut by a transversal line, the corresponding angles formed are congruent.

Therefore, the two nonadjacent interior angles that correspond to angle 4 are congruent.

Since congruent angles have the same measure, we can conclude that the measure of angle 4 is equal to the sum of the measures of the two nonadjacent interior angles.

This property holds true for any pair of parallel lines intersected by a transversal line.

It is a fundamental concept in geometry that helps us understand the relationships between angles formed by parallel lines and transversals, and it is useful in solving various geometric problems and proofs.

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As per the given image, the surface area of the composite figure is 1996 square meters.

Calculating the surface areas of the rectangular prism and the prism at the top separately and adding them together will yield the surface area of the composite figure.

The rectangular prism's surface area is as follows:

Surface Area = 2(length x width + length x height + width x height)

Surface Area of rectangular prism = 2(15m x 10m + 15m x 25m + 10m x 25m)

= 2(150m² + 375m² + 250m²)

= 2(775m²)

= 1550m²

Surface Area = 2(length x width) + perimeter of base x height

Surface Area of prism = 2(8m x 6m) + (8m + 6m) x 25m

= 2(48m²) + 14m x 25m

= 96m² + 350m²

= 446m²

Total surface area = Surface Area of rectangular prism + Surface Area of prism

= 1550m² + 446m²

= 1996m²

Thus, the answer is 1996m².

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The unit rate in pounds per person is 0.1875 pounds.

To find the unit rate in pounds per person, we need to divide the total pounds of candy by the number of people.

Given that Lucy split 3/4 pounds of candy among 4 people, we can calculate the unit rate as follows:

Unit rate = (3/4) pounds / 4 people

= 3/4 x 1/4

= 0.75 /4

To find the unit rate, we divide the numerator (0.75 pounds) by the denominator (4 people):

Unit rate = 0.75 pounds / 4 people

≈ 0.1875 pounds per person

Therefore, the unit rate in pounds per person is 0.1875 pounds.

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The value of the given expression is:

2⁴ + 2³ = 24

Remember that a power (exponent actually) tells us how many times we need to multiply the base by itself, so:

2 to the power of 4 is 2⁴ = 2*2*2*2 = 4*4 = 16

Similarly, for the other case we have:

2 to the power of 3 is 2³ = 2*2*2 = 4*2 = 8

Then we will get:

2 to the power of 4 + 2 to the power of 3

2⁴ + 2³

16 + 8 = 24

That is the value of the expression.

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While one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

In a race between two runners, one of them had a personal best time, while the other runner neither trained nor had a personal best time.

The runner who had a personal best time implies that they had trained and put in effort to improve their performance. A personal best time suggests that they have achieved their highest level of performance in a race. This indicates that the runner has dedicated time and effort to their training regimen, focusing on improving their speed and endurance.

On the other hand, the runner who neither trained nor had a personal best time implies that they did not invest effort in training or actively seek to improve their performance. They may have participated in the race casually or without specific training goals in mind. As a result, they did not achieve a personal best time, indicating that they did not put in the necessary effort to reach their full potential.

In summary, while one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

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The polar coordinates (r, θ) for the given rectangular coordinates are

(10, π/3)

To convert rectangular coordinates (5, 5√3) to polar coordinates (r, θ), we can use the following formulas:

r = √(x² + y²)

θ = arc tan (y/x)

Given the rectangular coordinates (5, 5√3), we have:

x = 5

y = 5√3

let's calculate the values

r = √(5² + (5√3)²

= √(25 + 75)

= √100

= 10

θ = arctan(5√3/5)

= arctan (√3)

= π/3 (since θ is in the interval [0,2π))

Therefore, the polar coordinates (r, θ) for the given rectangular coordinates are (10, π/3).

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The Probability that the randomly chosen coin is gold, given that it is small, is 4/5 or 0.8 when expressed as a decimal.

To find the probability that the randomly chosen coin is gold, given that it is small, we need to determine the number of small gold coins and the total number of small coins.

From the given information, Marco has 12 small gold coins and 3 small silver coins, making a total of 12 + 3 = 15 small coins.

The probability that the coin is gold, given that it is small, can be calculated as the ratio of the number of small gold coins to the total number of small coins:

P(Gold|Small) = Number of Small Gold Coins / Total Number of Small Coins

P(Gold|Small) = 12 / 15

Simplifying the fraction, we have:

P(Gold|Small) = 4 / 5

Therefore, the probability that the randomly chosen coin is gold, given that it is small, is 4/5 or 0.8 when expressed as a decimal.

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Using the distributive property, the boxes would be filled as follows;

(4 × 3 ) + (4 × 7 )

Mathematicians use the distributive property to explain how multiplication distributes across addition or subtraction. It offers a rule for expanding terms and condensing expressions.

With the help of the distributive property, we can factor polynomials, simplify expressions, and solve equations more quickly in algebra and arithmetic.

We know that;

4 × (3 + 7) =(4 × 3 ) + (4 × 7 )

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The required answer are :

a. Odds in favor of drawing a spade: 13:39 or simplified as 1:3.

b.the odds against drawing a five are:

Favorable outcomes: 4 Unfavorable outcomes: 48

Odds against drawing a five: 48:4 or simplified as 12:1.

Given that, suppose one card is drawn at random from a standard deck.

To find the odds in favor of drawing a spade, we need to determine the number of favorable outcomes (spades) and the number of unfavorable outcomes (non-spades).

In a standard deck of 52 cards, there are 13 spades (A♠, 2♠, 3♠, ..., 10♠, J♠, Q♠, K♠) and 39 non-spades (all other cards).

The odds in favor of drawing a spade can be expressed as the ratio of favorable outcomes to unfavorable outcomes. Therefore, the odds in favor of drawing a spade are:

Favorable outcomes: 13 Unfavorable outcomes: 39

Odds in favor of drawing a spade: 13:39 or simplified as 1:3.

(b) To find the odds against drawing a five, we need to determine the number of favorable outcomes (non-fives) and the number of unfavorable outcomes (fives).

In a standard deck of 52 cards, there are 48 non-fives (all cards except 5♠, 5♥, 5♦, and 5♣) and 4 fives (5♠, 5♥, 5♦, and 5♣).

The odds against drawing a five can be expressed as the ratio of unfavorable outcomes to favorable outcomes.

Therefore, the odds against drawing a five are:

Favorable outcomes: 4 Unfavorable outcomes: 48

Odds against drawing a five: 48:4 or simplified as 12:1.

Hence, the answer are:

a. Odds in favor of drawing a spade: 13:39 or simplified as 1:3.

b.the odds against drawing a five are:

Favorable outcomes: 4 Unfavorable outcomes: 48

Odds against drawing a five: 48:4 or simplified as 12:1.

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Answer:

The value of y in the equation (3 - 2√5) * (-y) = 25 - 9√5 is given by y = -25 + 9√5.

Step-by-step explanation:

La respuesta: 20-(-40)=60. 50-(-50)=100.

Para 20-___=60, tienes que restar 60 de 20. 20-60=-40

Para 50-___=100. tienes que restar 100 de 50. 50-100=-50.

Un negativo menos un negativo es igual a un positivo.

The required answer is ±12.316.

Given that 170cos(β) = -15

To solve the equation 170cos(β) + 15 = 0, we can isolate the cosine term:

170cos(β) = -15

Divide both sides of the equation by 170:

cos(β) = -15/170 cos(β) = -3/34

To find the value of sin(β), by using the Pythagorean identity:

sin^2(β) + cos^2(β) = 1

sin^2(β) = 1 - cos^2(β)

sin^2(β) = 1 - (-3/34)^2

sin^2(β) = 1 - 9/1156

sin^2(β) = (1156 - 9)/1156

sin^2(β) = 1147/1156

Taking the square root of both sides:

sin(β) = ±√(1147/1156) sin(β) ≈ ±0.996

Finally, to find tan(β), we can use the identity:

tan(β) = sin(β) / cos(β)

tan(β) ≈ (±0.996) / (-3/34)

tan(β) ≈ (±0.996) * (-34/3)

tan(β) ≈ ±11.32.

sin β + tan β =±12.316

Therefore, the required answer is ±12.316

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