Which set of equations could be parametric equations?
y= x and y= 3x
y= x + 1 and y= 3x2
x= t and y=3t
x= 3y and y= x+1

Answer:

This is only if you are looking to find the Arch AED        11pi/4

Step-by-step explanation:

See photo

Arc length AED of a given circle with a radius of 3 units is 11π/4.

According to the given diagram,

The angle subtended by arc AED or central angle = 360°-120°-45°-30° = 165°

The radius of the circle = 3 units

Arc length = Central angle(in radians) * Radius

So, arc length AED = 165 *π/180 * 3

Arc length AED = 11π/12 * 3 = 11π/4

Therefore, the Arc length AED of a given circle with a radius of 3 units is 11π/4.

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Answer:

Step-by-step explanation:

2x + 4 = -42         subtract 4 from both sides

2x + 4 - 4 = -42 - 4

2x = -46         divide both sides by 2

2x/2 = -46/2

x = -23

Steps To Solve:

2x + 4 = -42.

2x + 4 - 4 = -42 - 4

2x = -46

2x/2 = -46/2

x = -23 (Answer)

______

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Answer:

37 and  29

Step-by-step explanation:

x + y = 66

x - y = 8

*******************************************

solve second equation for x

x = y + 8

substitute for x in first equation

y+8 +y = 66

2y = 58

y = 29

*******************************************

x - 29 = 8

x = 37

******************************************

x = 37 and y = 29

Final answer:

To solve for the two numbers, set up equations based on the sum and difference provided. By solving these equations, we find that the numbers are 52 and 14.

Explanation:

The sum of two numbers is 66, and their difference is 38. This problem can be solved using a system of equations. Let's denote the two numbers as x and y.

According to the information given:

Now, we can solve these equations simultaneously.

The two numbers that satisfy the conditions of the problem are 52 and 14.

Answer:

θ = π n + π/2 for n element Z

Step-by-step explanation:

Solve for θ:

1 + 2 cos(2 θ) + cos^2(2 θ) = 0

Write the left hand side as a square:

(cos(2 θ) + 1)^2 = 0

Take the square root of both sides:

cos(2 θ) + 1 = 0

Subtract 1 from both sides:

cos(2 θ) = -1

Take the inverse cosine of both sides:

2 θ = 2 π n + π for n element Z

Divide both sides by 2:

Answer:  θ = π n + π/2 for n element Z

Answer:

The second option

Step-by-step explanation:

The second option because it is the one in which if you multiply f4 to the values of x, you would get y.

And that is why it is the second option.

Answer:The greater value is 600 x 10⁻⁸. And the lesser value is 2 x 10⁻⁸. The number 600 x 10⁻⁸ is 300 times greater number 2 x 10⁻⁸.

Step-by-step explanation:⇒ 6 x 10⁻⁶ and 2 x 10⁻⁸⇒ 600 x 10⁻⁸ and 2 x 10⁻⁸The number  600 x 10⁻⁸ times greater than the number 2 x 10⁻⁸ will be ⇒ 600 x 10⁻⁸ / 2 x 10⁻⁸⇒ 300

Final answer:

The circumference of Saturn is not greater than that of Earth; Earth's circumference is greater. Saturn's circumference at 40,100 km is approximately 0.11 times that of Earth. Also, 0.037854921 rounded to the nearest hundredth is 0.04, and 6 x 10⁻⁶ is larger than 2 x 10⁻⁸.

Explanation:

To answer how many times greater the circumference of Saturn is than the circumference of Earth, we need to compare the two given circumferences. The circumference of Earth is 365,882 km, and the circumference of Saturn is given as 4.01 x 10⁴ km.

First, we convert Saturn's circumference to a standard numerical form: 4.01 x 10⁴ is 40,100 km. Now, we can divide the circumference of Saturn by the circumference of Earth: 40,100 km / 365,882 km which roughly equals 0.11. This means that Saturn's circumference is about 0.11 times the circumference of Earth, which indicates that Earth's circumference is actually greater, not Saturn's.

For the second part, estimating 0.037854921 to the nearest hundredth would result in 0.04 because the third digit after the decimal is 7, which rounds the second digit up to 4.

Comparing the numbers 6 x 10⁻⁶ and 2 x 10⁻⁸, 6 x 10⁻⁶ is larger because it is only 10⁻⁶ compared to 2 x 10⁻⁸ which is much smaller being 10⁻⁸.

Answer:

8/12

Step-by-step explanation:

2/3 x 4= 8/12

Answer:

4/6

The drawing will help

Answer:

a = 14

Step-by-step explanation:

Given

9 + a = 23 ( subtract 9 from both sides )

a = 14

Answer:

9+14=23

Step-by-step explanation:

you subtract 9 from 23 and you get 14 so there for the answer is 9+14=23

Answer:

measure of each base angle =  80 each angle

measure of vertex angle = 20

Step-by-step explanation:

x=base angle    

2x+ x/4= 180

Multiply everything by 4 to eliminate the fraction

8x+x = 720

9x=720

x=80

80/4=12

Final answer:

In an isosceles triangle where the vertex angle is one-fourth the measure of a base angle, using the properties of a triangle and the Triangle Angle Sum Theorem, we find each base angle measures 80 degrees and the vertex angle measures 20 degrees.

Explanation:

Given an isosceles triangle, where the vertex angle is one-fourth the measure of a base angle, we can find the measures of the angles using the properties of a triangle. From the Triangle Angle Sum Theorem, we know that the sum of the angles in any triangle is 180 degrees.

Let's denote the measure of the base angle as 'b'. Since the triangle is isosceles, both base angles are equal, so we have 2b for the sum of the base angles. The vertex angle, being one-fourth of a single base angle, is ¼×b = b/4. According to the Triangle Angle Sum Theorem, we can write:

2b + (b/4) = 180

Multiplying through by 4 to clear the fraction gives us:

8b + b = 720

Combining like terms:

9b = 720

Dividing both sides by 9 gives us:

b = 80

Now that we have the measure of the base angle, we can find the measure of the vertex angle:

measure of vertex angle = b/4

Substitute b = 80 into the equation:

measure of vertex angle = 80/4

measure of vertex angle = 20

So, the measure of each base angle is 80 degrees, and the measure of the vertex angle is 20 degrees.

Answer:

See explanation

Step-by-step explanation:

Which display is more useful for approximating the minimum distance?

More useful is box-and-whisker plot (second display) because there you can exactly see that the minimum distance is 10 km (left point at the plot).

Which display can be used to find that there were 23 vehicles at Nam’s Used Car Lot?

More useful is first display, because you see the following information:

Distance           Number of vehicles

0 - 50                              3

50 - 100                          4

100 - 150                         5

150 - 200                        6

200 - 250                       3

250 - 300                       2

Total number of vehicles = 3 + 4 + 5 + 6 + 3 + 2 = 23

Answer:

23 vehicles

I'm on khan academy right now and its 23

Answer:

Part 1: Less.

Part 2: Greater.

Part 3: Greater.

Part 4: Less.

Part 5: Equal.

Step-by-step explanation:

Part 1: Assume that the value is x initially.

So, 55% decrease of value of x will give [tex]x(1 - \frac{55}{100}) = 0.45x[/tex].

Again, 25% increase of the value obtained will give [tex]0.45x(1 + \frac{25}{100}) = 0.45 \times 1.25 \times x = 0.5625x[/tex]

So, it is less than x. (Answer)

Part 2: Assume that the value is x initially.

So, 75% increase followed by [tex]33\dfrac{1}{3}  = 33.33[/tex]% decrease will give [tex]x \times (1 + 0.75) \times (1 - 0.333) = x \times 1.75 \times 0.667 = 1.167x[/tex]

So, it is greater than x.

Part 3: Assume that the value is x initially.

So, 20% decrease followed by 40% increase will give [tex]x \times (1 - 0.2) \times (1 + 0.4) = x \times 0.8 \times 1.4 = 1.12x[/tex]

So, it is greater than x.

Part 4: Assume that the value is x initially.

So, 30% increase followed by 30% decrease will give [tex]x \times (1 + 0.3) \times (1 - 0.3) = x \times 1.3 \times 0.7 = 0.91x[/tex]

Hence, it is less than x.

Part 5: Assume that the value is x initially.

So, 100% increase followed by 50% decrease will give [tex]x\times (1 + 1) \times (1 - 0.5) =x \times 2 \times 0.5 = x[/tex]

Hence, the final value is same as x. (Answer)

Answer:

the pictures uppppppppp

Answer: -9

Step-by-step explanation: When your adding and subtracting positives and negatives, it's a good idea to use a number line to visualize what's going on.

When you're simplifying a problem like (+4) + (-13) we start at zero and +4 moves us 4 units to the right along our number line.

From there, -13 then moves us 13 units back to the left so we end up at -9.

Image provided.

Therefore, (+1) + (-13) = -9

The equation of a circle if the ends of the diameter are (18,-13) and (4,-3)​ is [tex](x-11)^{2}+(y+8)^{2}=74[/tex]

Given that ends of diameter are (18, -13) and (4, -3)

To find the equation of circle, let us first find the center (h, k) of the circle

We know that the center of the circle lies in the center of the diameter also. In order to find the center, get the average of both x and y

[tex]\mathrm{c}=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]

[tex]\begin{array}{l}{c=\frac{18+4}{2}, \frac{-13-3}{2}} \\\\ {c=\frac{22}{2}, \frac{-16}{2}} \\\\ {\mathrm{c}=(11,-8)}\end{array}[/tex]

These are the coordinates of the center of the circle

Now we need to find the radius, we need the center (h, k) and one of the given points (4, -3):

The equation of circle is given as:

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

[tex]\begin{array}{l}{(4-11)^{2}+(-3-(-8))^{2}=r^{2}} \\\\ {(-7)^{2}+(-3+8)^{2}=r^{2}} \\\\ {(-7)^{2}+(5)^{2}=r^{2}} \\\\ {49+25=r^{2}} \\\\ {r=\sqrt{74}}\end{array}[/tex]

So the equation of the circle is:

[tex]\begin{array}{l}{(x-11)^{2}+(y-(-8))^{2}=(\sqrt{74})^{2}} \\\\ {(x-11)^{2}+(y+8)^{2}=74}\end{array}[/tex]

Answer:

A.) -9

Step-by-step explanation:

it is observed that triangles ABL and KML are similar triangles

hence the following ratios are valid:

LA / LK = LB/LM = AB/KM

we can see that LA/LK = LB/LM = 1/2

hence the above ratio becomes

1/2 = AB/KM  (rearranging)

KM = 2AB

We are given that KM = (x + 21) and AB = (x + 15)

hence

KM = 2AB

(x + 21) = 2 (x + 15)

x + 21 = 2x + 30

x - 2x = 30 - 21

-x = 9

x = -9

Answer:

Option B is the correct choice.

Step-by-step explanation:

The graph is attached below.

We have to find the [tex]x[/tex] intercept meaning the value of the point on[tex]x-axis[/tex] when [tex]y=0[/tex]

So we will put the value of zero [tex](0)[/tex] instead of [tex]y[/tex] in our given equation.

So here we have solved it algebraically.

[tex]y=\frac{3}{4}x-3[/tex]

Putting [tex]y=0[/tex]

[tex]0=\frac{3}{4}x-3[/tex]

[tex]0=\frac{3x-12}{4}[/tex]

Multiplying [tex]4[/tex] both sides.

[tex]0=3x-12[/tex]

Adding [tex]12[/tex]both sides.

[tex]12=3x[/tex]

Dividing with [tex]3[/tex] both sides.

[tex]x=\frac{12}{3}=4[/tex]

So the x-intercept of the given equation is [tex]4[/tex] which can be written as [tex](4,0)[/tex] in terms of coordinates.

Option B [tex](4,0)[/tex] is the correct choice.

Answer:

16 servings

Step-by-step explanation:

To calculate the servings of chicken, we need two pieces of information. We need to know how much money the food bank has and how many ounces of chicken is available. This information is given. Therefore, we can work out the servings of chicken by dividing the ounces of by the amount of money.

[tex]=1774.4/110.9=16[/tex]

So 16 servings of chicken can be provided for 110.9 pounds.

Assuming first number is (2^3)(3^2), second number is (2^2)(3^1).

First number:         2 * 2 * 2 * 3 * 3

Second number:   2 * 2 * 3

Both numbers have at least two factors for 2 and one factor for 3.

Their greatest common factor is (2^2)(3).

To solve this, subtract 2 from both sides, and you end up with x = 8. :)

Answer:

the first diagram (circled one in the attached figure)

Step-by-step explanation:

number of pickle slices in each burger = [tex]\frac{78}{26} = 3[/tex] (I hope you know how to find this)

The diagram is nothing but expressing fraction diagrammatically.

The fraction is 78 divided by 26. So assume bar of size 78. Now divide it into 26 equal parts. The same is shown in the diagram.

For example: [tex]\frac{1}{4}[/tex] of a chocolate bar is nothing but one piece when you divide the chocolate bar into four equal parts.

Answer:

The perimeter is 37

Step-by-step explanation:

there you go

The perimeter of the triangle is 37 units.

Perimeter is given by the sum of all the sides of any figure.

Given that, ABC, DE is a midsegment of Δ ABC, DE = 7, AB = 10, and BC = 13.

According to the midpoint theorem states that “The line segment in a triangle joining the midpoint of any two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

Therefore, AC = 2DE

AC = 14

Therefore, perimeter = sum of all sides,

= 10+13+14

= 37

Hence. the perimeter of the triangle is 37 units.

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Answer:

slope = [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ )= (3, 4) ← 2 points on the line

m = [tex]\frac{4-0}{3+2}[/tex] = [tex]\frac{4}{5}[/tex]

Answer: s = 1.44

Step-by-step explanation:

11 - 18*s = -15

-18*s = -15 - 11

-18*s = -26

18*s = 26

s = 26/18

s = 13/9

s = 1.44

If the measure of the supplement of an angle is 60 degrees less than four times the measure of the complement of the angle, the required angle will be 40degrees.

Let the measure of the required angle be x

Supplement of the angle = 180 - x ....................1

Complement of the angle = 90 - x

four times the measure of the complement of the angle = 4(90-x)

60 degrees less than four times the measure of the complement of the angle = 4(90-x) - 60 ................................ 2

Equate 1 and 2 to get the unknown value 'x'

180 - x = 4(90-x) - 60

180 - x = 360-4x-60

180 - x = 300 - 4x

Collect the like terms

-x + 4x = 300 - 180

3x = 120

Divide both sides by 3

3x/3 = 120/3

x = 40

Hence the measure of the required angle is 40 degrees

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The measure of the angle is found to be 40 degrees. This was determined by setting up and solving the equation based on the given relationships between the angle's supplement and complement. Therefore, the angle measures 40 degrees.

To find the measure of the angle, let's denote the angle as x. We know the following:

According to the problem, the supplement of the angle is 60 degrees less than four times the complement of the angle. Therefore, we have the equation:

(180 - x) = 4(90 - x) - 60

First, expand and simplify the right-hand side:

180 - x = 360 - 4x - 60

Combining like terms, we get:

180 - x = 300 - 4x

Next, add 4x to both sides to start isolating x:

180 + 3x = 300

Then, subtract 180 from both sides:

3x = 120

Finally, divide both sides by 3:

x = 40

Thus, the measure of the angle is 40 degrees.

Answer:

Length of new radius 4 cm.

Step-by-step explanation:

Given radius of circle = 16 cm

Circle is dilated with scale factor 1/4

We need to find the new radius

To calculate New radius we need  to multiply radius of the circle with the dilated factor.

Hence new radius = [tex]16 \times \frac{1}{4}= 4\cm[/tex]

Hence Length of new radius is 4 cm.  

1. Positive but not perfect: Figure 4

2. Correlation coefficient equal to 1:

3. Strongest linear relationship: Figure 2

Step-by-step explanation:

"Correlation is the link between two quantities"

The relationship is said to be positive if both are increasing and said to be negative if both are opposite i.e. one is increasing and one is decreasing.

In the Given figures

1. Positive but not perfect linear relationship:

The perfect positive relationship is when both the quantities are increasing and the scatter points are in a line that grows linearly. Here, The data set in figure 4  has positive correlation but as the points are scattered around a line so the correlation is positive but not perfect.

2. Correlation equal to 1

The correlation in figure 1 is the perfect correlation as the data points follow a straight line and both the quantities are increasing.

3. Strongest linear relationship:

The relationship in figure 2 has the strongest in figure 2 as the data points are more close to the best fit line

Keywords: Correlation, Scatter Plot

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The equation of line parallel to y = -5x + 6 and passes through the point (-4, -1) is y = -5x -21

Given that, a line passes through (-4, -1) and it is parallel to y = -5x + 6

We have to find the line equation of that line.

Now, as we can see given line equation is in slope intercept form y = mx + c

where "m" is the slope of line and "c" is the y-intercept

So, by comparison, slope of that line is m = -5

We know that slopes of two parallel lines are equal

And as the required line is parallel to given line, it will also have the same slope.

Then, slope of our line = -5

And let us find the line equation point slope form

y – a = m(x - b) where (b, a) is a point on the line

So, line equation is y – (-1) = -5(x – (-4))

y + 1 = -5(x + 4)  

y + 1 = -5x – 20  

y = -5x -20 – 1

y = -5x -21

Thus the equation of required line is y = -5x -21  

The equation of the line parallel to y = -5x + 6 and passing through (-4, -1) is y = -5x - 21, which is determined using the point-slope form of a line with the given point and the parallel line's slope.

To find an equation of a line that is parallel to the given line y = -5x + 6 and passes through a specific point (-4, -1), we need to use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Since parallel lines have the same slope, the line we are looking for will also have a slope of -5. Using the point (-4, -1) and the slope -5, we can substitute these values into the point-slope form:

y - (-1) = -5(x - (-4))
y + 1 = -5(x + 4)
y = -5x - 20 - 1
y = -5x - 21

Thus, the equation of the line is y = -5x - 21.

He has been withdrawing money for 69 days.

Step-by-step explanation:

Amount of credit card = $5000

Let,

x be the number of days

Amount after withdrawing $45 each day for x days = $1895

Amount left = Total amount - Withdrawal amount per day * number of days

1895 = 5000 - 45*x

[tex]1895=5000-45x[/tex]

Solving for x;

[tex]1895-5000=-45x\\-3105=-45x\\-45x=-3105[/tex]

Dividing both sides by -45

[tex]\frac{-45x}{-45}=\frac{-3105}{-45}\\x=69[/tex]

He has been withdrawing money for 69 days.

Keywords: subtraction, division

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Answer:

The graph will show what the line is.

Step-by-step explanation:

y-3 = -5/6(x+3)

Distribute first:

y-3= -5/6x - 15/6

-15/6 is negative because when disributing, -5/6, the negative sign will follow it.

Single out the y:

this means to make the y alone! by doing this, just add 3 to the other side

y-3= -5/6x - 15/6

+3             +3

______________

y= -5/6x + 3/6

Simplify:

y= -5/6 +1/2

-> 3/6 can be simplified to 1/2

Find the Y-intercept on the graph

1/2 on the graph is between 0 and 1

Graph the slope:

from the Y-intercept, go down 5 units, and to the right 6 units.

Then you have your graph!

Answer:

(-1, 5)

(0, 3)

(2, -1)

Step-by-step explanation:

we have

[tex]f(x)=3-2x[/tex]

Remember that

If a ordered pair is a solution of the given function, then the ordered pair must satisfy the given function

Verify each case

case a) (-2, -1)

substitute the value of x and the value of y in the given function and compare the result

[tex]-1=3-2(-2)[/tex]

[tex]-1=7[/tex] ---> is not true

therefore

Is not a ordered pair of the given function

case b) (-1, 5)

substitute the value of x and the value of y in the given function and compare the result

[tex]5=3-2(-1)[/tex]

[tex]5=5[/tex] ---> is true

therefore

Is a ordered pair of the given function

case c) (0, 3)

substitute the value of x and the value of y in the given function and compare the result

[tex]3=3-2(0)[/tex]

[tex]3=3[/tex] ---> is  true

therefore

Is a ordered pair of the given function

case d) (1,0)

substitute the value of x and the value of y in the given function and compare the result

[tex]0=3-2(1)[/tex]

[tex]0=1[/tex] ---> is not true

therefore

Is not a ordered pair of the given function

case e) (2, -1)

substitute the value of x and the value of y in the given function and compare the result

[tex]-1=3-2(2)[/tex]

[tex]-1=-1[/tex] ---> is true

therefore

Is a ordered pair of the given function