The following points represent a relation where x represents the independent variable and y represents the dependent variable.


Does the relation represent a function? Explain.

Yes, because for each output there is exactly one input
Yes, because for each input there is exactly one output
No, because for each output there is not exactly one input
No, because for each input there is not exactly one output

Answer:

1

Step-by-step explanation:

12

Using trigonometric identity, the value of the expressions are (Cosx + Cos5x)/2 + Sin3x.Cosx, √3/2, √3/2 and -√3/2

To solve this problem, we need to apply trigonometric identity;

1.

Cos2x · Cos3x - Sinax. Sin3x:

Using the identity Cos(A - B) = CosA.CosB + SinA.SinB, we can write:

Cos2x · Cos3x = (Cos(2x - 3x) + Cos(2x + 3x))/2 = (Cos(-x) + Cos(5x))/2 = (Cosx + Cos5x)/2

So the expression becomes:

(Cosx + Cos5x)/2 - Sinax. Sin3x

Using the identity Sin(A - B) = SinA.CosB - CosA.SinB, we can write:

Sinax. Sin3x = (Sin(ax - 3x) - Sin(ax + 3x))/2 = (Sin(-2x) - Sin(4x))/2 = (-Sin2x - Sin4x)/2

So the expression becomes:

(Cosx + Cos5x)/2 + (Sin2x + Sin4x)/2

Using the identity SinA + SinB = 2.Sin((A+B)/2).Cos((A-B)/2), we get:

(Sin2x + Sin4x)/2 = Sin3x.Cosx

Therefore, the expression simplifies to:

(Cosx + Cos5x)/2 + Sin3x.Cosx

2.

Sinzx Cosx+Cosex Sinx:

Using the identity Sin(A + B) = SinA.CosB + CosA.SinB, we can write:

Sinzx Cosx+Cosex Sinx = Sin(x + z)

So the expression is equivalent to Sin(x + z).

3.

Sın 85° Cos25°- Cos 85°. Sin 25°:

We can use the identity Sin(A - B) = SinA.CosB - CosA.SinB:

Sin 85° Cos25°- Cos 85°. Sin 25° = Sin(85° - 25°) = Sin60° = √3/2

4.

Cos 160°. Cos10° + Sin160°. Sin10°:

We can use the identity Cos(A - B) = CosA.CosB + SinA.SinB:

Cos 160°. Cos10° + Sin160°. Sin10° = Cos(160° - 10°) = Cos150° = -√3/2

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Answer:

Step-by-step explanation:

If AB║DC,

∴∡BAC=∡ACD(ALTERNATE  aNGLES)

AB=DC

AC=AC (COMMON SIDE)

∡BAC=∡ACD (PROVED)

∴ ΔABC≡ΔACD(S.A.S)

∴EF=FG

An equation of the line that is perpendicular to y = 4x + 6 and passes through the point (8, -4) is y = -x/4 - 2

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

4 × m₂ = -1

m₂ = -1/4

At point (8, -4), an equation of the line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-4) = -1/4(x - 8)

y + 4 = -1/4(x - 8)

y = -x/4 + 2 - 4

y = -x/4 - 2

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Answer:

= 16.

Step-by-step explanation:

x= 2

y = -1

[tex] {(2xy)}^{2} \\ = {(2(2)( - 1)) \\ }^{2} \\ = {(2( - 2)) \\ }^{2} \\ = {( - 4)}^{2} \\ = - 4 \times - 4 \\ = 16[/tex]

The slope is 1/19.5 and it is positive slope.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

Given that, the cost of tickets to the amusement park is $19.50 for 1 ticket and $78 for 4 tickets.

Here, the coordinates are (19.50, 1) and (78, 4)

Now, the slope = (4-1)/(78-19.50)

= 3/58.5

= 1/19.5

Therefore, the slope is 1/19.5 and it is positive slope.

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Answer:

A , B and C

Step-by-step explanation:

182 is a rational number as it can be written in p/q form. (182/1)

182 is a positive integer.   {Integers:   ........ -4 , -3 , -2 , -1 , 0 , 1 , 2 , 3 .......}

182 is a whole number. {0, 1 , 2 , 3 ,...............}

The ages of Gregory and Janet are 10 and 16 years respectively.

Gregory is six years younger than Janet. 7 years ago, Janet was thrice as old as Gregory. Therefore, the ages of Gregory and Janet are as follows:

Let

x = age of Janet

Gregory age = x - 6

x - 7 = 3(x - 6 - 7)

Hence,

x - 7 = 3(x - 13)

x - 7 = 3x - 39

x - 3x = -39 + 7

-2x = -32

divide both sides by -2

x = -32 / -2

x = 16 years

Therefore,

Janet age = 16 years

Gregory's age = 16 - 6 = 10 years

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Janet's current age is 16 and Gregory's current age is 10

Let's start by using algebra to represent the information in the problem.

Let's assume that Janet's current age is "J" and Gregory's current age is "G".

From the first sentence, we know that:

G = J - 6

From the second sentence, we know that 7 years ago, Janet was thrice as old as Gregory.

J - 7 = 3(G - 7)

So, we have

J - 7 = 3(J - 6 - 7)

This gives

J - 7 = 3J - 39

So, we have

2J = 32

This gives

J = 16

This also means that

G = 16 - 6

G = 10

Hence, Gregory's age is 10

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Answer: DON'T COPY AND PASTE!! a-lot of people say they get a plagiarism charge so try to switch or add more words to this but i hope it helps!!!

Step-by-step explanation:

Claim - The volume of the bowl is 715.17

evidence - The hemisphere has a radius of 8

- so its volume is 2/3πr³        r = radius

= 2/3 × π × (8)³

she can fill = 2/3 × 2/3 × 22/7 × (8)³   cm³

= 715.17cm³

reasoning - Therefore according to my calculations The volume will be 715.17 cm³

Area of semicircle is (πr²)/2 and perimeter is  (πr) + 2r

The area and perimeter of a semicircle can be calculated using the formulas for the area and circumference of a full circle, and then dividing by 2.

The formula for the area of a full circle is A = πr², where r is the radius of the circle. So the area of a semicircle would be A = (πr²)/2.

The formula for the circumference of a full circle is C = 2πr, where r is the radius of the circle. The perimeter of a semicircle would be half of the circumference, plus the diameter (which is 2r). So the perimeter of a semicircle would be P = (πr) + 2r.

So, to find the area and perimeter of a semicircle, you would need to know the radius of the semicircle, and then plug it into the formulas above.

For example, if the radius of the semicircle is 4, the area would be A = (π(4²))/2 = 8π, and the perimeter would be P = (π(4)) + (2(4)) = 4π + 8.

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The corresponding values of y so that each ordered pair is a solution of the equation y = 0.2x – 2 is,

Input    (x)    -6        -1       1  

Output (y)     -3.2  -2.2   -1.8

Function rule is the rule of writing the relationship between the two variables, one is dependent and another is independent.

The table given in the problem is;

Input    (x)    -6        -1       1  

Output (y)

We have given the equation as;

y = 0.2x – 2

Complete the table using the above function rule;

At (x) equal to -6,

y = 0.2x – 2

y = 0.2(-6) – 2

y = -3.2

At (x) equal to -1,

y = 0.2x – 2

y = 0.2(-1) – 2

y = -2.2

At (x) equal to 1,

y = 0.2x – 2

y = 0.2(1) – 2

y = -1.8

Hence,

Input    (x)    -6        -1       1  

Output (y)     -3.2  -2.2   -1.8

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Answer:

Step-by-step explanation:

7A) The completion of the number line, based on the ratio of Dahlias to Sunflowers, is as follows:

Dahilas            0     4     8     12     16     10     24    28    32

Sunflowers      0     3     6      9     12     15      18    21     24

7B) When there are 33 sunflowers, there will be 44 Dahlias.

7C) The ratio of Dahlias to all flowers when there are 21 total flowers is 0.57:1 or 12:21.

7D) The ratio of Sunflowers to all flowers in a bouquet with 70 total flowers is 0.43:1 or 3:7.

The ratio is the relative size of one value compared to another.

The ratio is determined as the quotient or average of two relative values.

The number of Dahlias = 8

The number of Sunflowers = 6

Ratio of Dahlias to Sunflowers = 1.33:1 (8:6)

Ratio of Sunflowers to Dahlias = 0.75: 1 (6:8)

The sum of ratios = 14 (8 + 6)

B) When there are 33 sunflowers, there will be 44 Dahlias (33/0.75).

C) The ratio of Dahlias to all flowers:

The total flowers = 21

Dahlias = 12 (21 x 8/14)

The Ratio of Dahlias to all flowers = 12:21 = 0.57:1

The ratio of dahlias to Sunflowers = 12:9

D) The ratio of Sunflowers to all flowers:

The total flowers = 70

Sunflowers = 30 (70 x 6/14)

The ratio of Sunflowers to all flowers = 30:70 = 0.43:1

Ratio of sunflowers to dahlias = 30:40 = 3:4

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Answer:

x = 5

y = -4

Step-by-step explanation:

 3x + 4y = -1 -----------(I)

-2x - 5y = 10 -----(II)

Multiply equation (I) by 2 and equation (II) by 3 and then add. Doing so, x will be eliminated, and we can find the value of 'y'.

  (I) * 2           6x + 8y = -2

 (II)* 3            -6x - 15y = 30  {Now add}

                            -7y   = 28

Divide both sides by (-7),

                               y = 28 ÷ (-7)

                               [tex]\boxed{y=(-4)}[/tex]

Plugin y = (-4) in equation (I),

            3x + 4*(-4) = -1

              3x - 16 = -1

                    3x = -1 +16

                     3x = 15

                       x = 15÷3

                        [tex]\boxed{x=5}[/tex]

basically draw 1 linear line with domain constraints for the first two

y = 1/2x + 6 {7<x < 13}

y = 1/2x + 3 {x<7}

the values might have to be tweaked a little as the stars are not exactly on point

Answer:

It will take Ryan 59.6 years to break even on his purchase of 3 discount points (1% each) for a $520,000 loan with an APR of 4.15%. This break-even point was calculated by finding the difference in monthly payments between the loan with and without the discount points, and dividing the cost of the points by that difference.

The diagonal of the DVD cover art has a length of 8 inches. (Correct choice: A)

In this question we need to estimate the length of the diagonal of the DVD cover art, this can be used by means of scale factor relative to the width of the movie cover. Scales are an useful resource to represent systems at affordable dimensions. By assuming that both DVD cover art and movie cover have similar geometries, we can estimate the diagonal of the DVD cover art by proportion formula:

6 in / 72 in = x / [(8 ft) · (12 in / ft)]

x = (6 in / 72 in) × 96 in

x = 8 in

The length of the diagonal of the DVD cover art is equal to 8 inches.

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Answer:

The last choice

Step-by-step explanation:

Since 3/8 is smaller than 1/2(=4/8) and 1/4 is also smaller than 1/2(=2/4), she has enough water to make her snacks.

I hope this makes sense to you. I am generally good with following up with additional questions. Feel free to leave a comment if you have any questions or you can also message me as well!

Answer:

226.19 cubic units

Step-by-step explanation:

radius = r = 6 units

height = h = 6 units.

To find the volume of resulting solid, subtract the volume of cone from the volume of hemisphere.

Volume of the resulting solid = Volume of hemisphere - volume of cone

                                                [tex]\sf \bf = \dfrac{2}{3}\pi r^3 - \dfrac{1}{3}\pi r^2h\\\\\\=\dfrac{2}{3}*3.14*6*6*6 - \dfrac{1}{3}*3.14*6*6*6\\\\\\=(3.14*6*6*6)(\dfrac{2}{3}-\dfrac{1}{3})\\\\=3.14*6*6*6**\dfrac{1}{3}\\\\=3.14*6*6*2\\\\=226.19 \ cubic \ units[/tex]

Formula used to calculate the grades to a student is as follows:

F=G−((1−w)×C))/w.

You may determine the grade you need on the final exam to get your desired course grade if you know your present grade and the final test's weight.

The explanation for the given formula, F = Final exam grade

G = Grade you want for the class

w = Weight of the final exam, divided by 100 (put weight in decimal form vs. percentage form)

C = Your current grade.

Being able to keep track of your class grades is a really valuable ability. You may keep track of your progress and see whether you need to work more to achieve the grade you want. In order to figure out how much you need to raise your grade with a point system. Compare that number against the point count for the work you have not yet done. Thus this is the way to calculate grades.

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Answer:

The Prime Factors and Pair Factors of 2023 are 7 × 17 and (1, 2023), (7, 289), (17, 119) respectively.

Answer:

To determine how many times 7 is a factor in 2023:

1. Divide 2023 by 7 to obtain the quotient: 2023/7 = 288.571.

2. If the result of the division is a whole number, 7 is a factor in 2023.

3. Round down 288.571 to obtain the integer 288.

4. Since the result of the division is a whole number, 7 is a factor in 2023 and occurs 1 time.

The population in 2020 is 2,240,700

A population is the set of people concentrated in a particular area.

Given that, in 2010, the population of a city was 88,000, from 2010 to 2015, the population grew by 4%. From 2015 to 2020, it fell by 3%. We need to determine the population in 2020,

For population growing we will multiply the population is 104 and for population reducing we will multiply by 97,

Therefore, the population in 2020 =

88000 × 5(104/100) × 5(97/100)

= 88000 × 5.25 × 4.85

= 2,240,700

Hence, the population in 2020 is 2,240,700

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The minimum and maximum side lengths to complete a triangle with two side lengths of 18 cm and 21 cm are 3 cm and 39 cm, respectively.

A triangle is a closed two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is formed by connecting three non-collinear points. The three sides and three angles of a triangle are interconnected by various geometrical principles and formulas, such as the Pythagorean theorem, trigonometric ratios, and the Law of Cosines. Triangles are commonly classified based on their side lengths and angles, including equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles are also used in various real-life applications, such as in architecture, engineering, and physics.

To complete a triangle with side lengths 18 cm and 21 cm, the length of the third side must be such that it satisfies the triangle inequality. The triangle inequality states that the sum of any two sides of a triangle must be greater than the third side.

Let x be the length of the third side. Then we have:

18 + 21 > x

18 + x > 21

21 + x > 18

Simplifying each inequality, we get:

x < 39

x > 3

x > -3 (since length cannot be negative)

The minimum value of x is 3 cm (when the two sides form a degenerate triangle), and the maximum value of x is 39 cm (when the three sides form an equilateral triangle). Therefore, the minimum and maximum side lengths to complete a triangle with two side lengths of 18 cm and 21 cm are 3 cm and 39 cm, respectively.

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the length of BC is 11.9 cm.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given a right triangle ABC with hypotenuse AC and the foot angle of 58-degree.

Using the sine ratio in the right triangle

sin58° = (Opposite side)/(hypotenuse)

In our case,

opposite side = height

opposite side = BC

hypotenuse = AC

hypotenuse = 14(given)

So,

Multiply both sides by 14

14 × sin58° = BC, thus

BC ≈ 11.9 cm

Therefore, the height of the given right angle triangle will be 11.9 cm(Approx.).

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Complete question:

Answer: A sorry if i got it wrong

Step-by-step explanation:

The fraction is given as follows:

8.3/10.3.

The fraction is modeled as follows:

x/y.

In which:

From the features of the problem, a system of equations is built to identify the variables.

If the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2,the result is 4, hence the first equation is of:

4x/(y - 2) = 4.

Hence:

4x = 4(y - 2)

4x = 4y - 8

x = y - 2.

If the numerator of the fraction is increased by 15 and 2 subtracted from the double of the denominator, the result is 5/4, hence the second equation is of:

(x + 15)/(2y - 2) = 5/4.

We know that x = y - 2, hence the value of y is obtained as follows:

(y + 13)/(2y - 2) = 5/4.

5(2y - 2) = 4(y + 13)

10y - 10 = 4y + 52

6y = 62

y = 62/6

y = 10.3.

Then the value of x is of:

x = y - 2

x = 10.3 - 2

x = 8.3.

Hence the fraction is:

8.3/10.3.

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The solution for x in the circle is x = 12

Since the measure of angle EFG is m∠EFG = 9x-7 and the measure of arc GE is 17x-2

We can determine the value of x using the inscribed angle theorem.

Thus, we have:

m∠EFG = 1/2 (arc GE)

9x-7  = 1/2 * (17x-2)

2(9x-7) = 17x - 2

18x - 14 = 17x - 2

18x - 17x = -2 + 14

x = 12

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The cost per hour for this recreational activity in the scenario which is also the unit rate is $2.5 per hour.

Number of hours= 2 hours

Total cost to roller skate = $5

Cost per hour of recreational activity= Total cost to roller skate / Number of hours

= $5 / 2 hours

= $2.5 per hour

In conclusion, it costs $2.5 per hour to roller skate.

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If one object has twice as much mass as another object it also has twice as much Inertia.

Let the mass of object A= m₁

mass of object B = m₂

Given that m₁ = 2m₂

Speed, velocity and acceleration are subject to motion of the object. Given the insufficiency of information in the question, nothing can be said about these.

This is basically Newton's first law of motion, this law states that, every object continues in a state of rest of uniform motion in a straight line, unless acted upon by an external force

On the other hand, inertia is directly dependent on the mass. Hence, inertia of object A would be twice the inertia of object B.

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10 mL is equal to 2 teaspoons or 0.67 tablespoons. One teaspoon is equal to 5 mL, so to convert 10 mL to teaspoons, divide 10 by 5. One tablespoon is equal to 15 mL, so to convert 10 mL to tablespoons, divide 10 by 15.

10 mL is equal to 2 teaspoons (tsp) or 0.67 tablespoons (tbsp).

One teaspoon is equal to 5 mL, so to convert 10 mL to teaspoons, you can divide 10 by 5, which gives:

10 mL / 5 mL/tsp = 2 tsp

Therefore, 10 mL is equal to 2 teaspoons.

One tablespoon is equal to 15 mL, so to convert 10 mL to tablespoons, you can divide 10 by 15, which gives:

10 mL / 15 mL/tbsp = 0.67 tbsp

Therefore, 10 mL is equal to approximately 0.67 tablespoons.

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The missing reason is ∠ ABC ≅ ∠ DBE by vertically opposite angles postulate and Δ ABC ~ Δ  DBE by AA rule.

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. Vertically opposite angles are equal to each other. These are sometimes called vertical angles.

Given that, ∠ C ≅ ∠ E, and we need to find a reason to prove Δ ABC ~ Δ  DBE,

As we know that, to prove two triangles similar we can show two corresponding angles congruent in them, then they will be similar by AA rule,

Here, we already have, ∠ C ≅ ∠ E, we need one more,

If we see the figure, we get ∠ ABC and ∠ DBE are vertically opposite angles

We know that, Vertically opposite angles are equal to each other.

Therefore, ∠ ABC ≅ ∠ DBE

Hence, the missing reason is ∠ ABC ≅ ∠ DBE by vertically opposite angles postulate and Δ ABC ~ Δ  DBE by AA rule.

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