Convert the polar equation to rectangular form and identify the graph. Support your answer by sketching the graph. Show and explain your work.

Answer:

[tex]x^{6}[/tex]

Step-by-step explanation:

To simply exponents in a fraction, subtract the exponent for each variable in the denominator from the exponent in the numerator.

Answer:

[tex]x^6[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{x^{10}}{x^4}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \dfrac{x^{10}}{x^4}=x^{(10-4)}=x^6[/tex]

The value of x is 12.

Given that the angles are m∠DBC=(12X-18) and m∠ABD=(8x+30).

An angle is made when two rays are joined together at any common point.

We will find the value of x by equating both the given angles as

m∠DBC=m∠ABD

Now, we will substitute the values of angles as

12x-18=8x+30

Further, we will subtract 18 from both sides and simplify it as

12x-18+18=8x+30+18

12x=8x+48

Now, we will subtract 8x from both sides and simplify as

12x-8x=8x+48-8x

4x=48

Now, we will divide both sides by 4, we get

4x/4=48/4

x=12

Hence, the value of x when m∠DBC=(12x-18) and m∠ABD=(8x+30) is 12.

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Answer: g(x)=2x-3

Step-by-step explanation:

f(x)=2x-9

g(x)=2x-9+6 ==> Translate 6 units up

g(x)=2x-3

Answer:

the line runs that aligns with the y-intercept

Step-by-step explanation:

Ok so I was very confused on this too. Not even going to lie to ya, I struggled with this for a long time. However once you get the hang of it, it's actually rather simple.

So, lets try a problem. What is 0.04 as a fraction?

Well, we know that 0.04 is 4%. And you can do [tex]\frac{4}{100}[/tex] which is 0.04, or 4%

Does that make sense? If not let me explain it a little more.

Well basically all you have to do is put that number over 100.

Here are some examples of decimals to percentage to fraction:

0.5 = 50% = [tex]\frac{50}{100}[/tex] or in simplest form [tex]\frac{1}{2}[/tex]

0.11 = 11% = [tex]\frac{11}{100}[/tex]

0.03 = 3% = [tex]\frac{3}{100}[/tex]

I really hope this helped you!!!

If not let me know how i can explain it and what doesn't make sense!

Answer: To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, [tex]\frac{6}{10}[/tex]. If needed, simplify the fraction.

Step-by-step explanation:

1) (c) The range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ –11}.

2) (d) The x-intercepts of the graph of the function f(x) = x² + 4x - 12 are ( - 6, 0) and ( 2, 0 ).

1). A parabola opens upward and it passes through ( - 3, 0) and ( 1, 0), and has vertex at ( - 1, - 11 ).

We have the function for the parabola f(x) = 3x² + 6x - 8.

Vertex and the coefficient of the quadratic term are two features of a parabola that aid in determining its range.

Therefore, the critique point of the range and a portion of the constraint is the vertex's vertical coordinate. The next step is to determine if the parabola is concave up or down. The parabola is concave up in this issue if the coefficient of the quadratic terms is positive. As a result of the parabola's concave upward shape, all real numbers greater than - 11 fall into the function's permissible range.

Hence, the range of the function is {y|y ≥ –11}.

2). The graph of the function with the equation f(x) = x² + 4x - 12 is a parabola that opens upward, passes between the points ( - 6, 0) and ( 2, 0), and its vertex is at ( - 6, 0). ( - 2, - 16). It is the y-intercept ( 0, - 12).

The x-intercepts are the locations where the graph and x-axis meet. The y-coordinate of these points is always zero. A parabola can only have two x-intercepts at most. As we can see, the parabola passes through the points ( - 6, 0) and ( 2, 0), and have y coordinates 0, hence the x-intercepts are ( - 6, 0) and ( 2, 0).

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The complete question is mentioned below:

1. On a coordinate plane, a parabola opens up. It goes through (negative 3, 0), has a vertex at (negative 1, negative 11), and goes through (1, 0).

What is the range of the function f(x) = 3x² + 6x – 8?

(a) {y|y ≥ –1}

(b) {y|y ≤ –1}

(c) {y|y ≥ –11}

(d) {y|y ≤ –11}

2. On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 2, negative 16), has a y-intercept at (0, negative 12), and goes through (2, 0).

What are the x-intercepts of the graph of the function f(x) = x² + 4x – 12?

(a) (-6, 0), (2,0)

(b) (-2, -16), (0, -12)

(c) (- 6, 0), ( - 2, - 16),

(d) ( 2, 0) (0, -12),

(e) ( - 6, 0), (2, 0)

Answer: -5/2

Step-by-step explanation:

4y−10∣=20

Combine like terms and use the properties of equality to get the variable on one side of the equal sign and the numbers on the other side. ∣4y−10∣=20 Use the definition of absolute value.

4y−10=20

4y−10=−20

Add 10 to both sides of the equation. 4y=30 which then equals  4y=−10

Divide both sides by 4 to get y = 15 over 2 converted to y = negative 5 over 2

(hope this is helpful)

Answer:

8.3x10^1

Step-by-step explanation:

you don't even need to do any math for this question. just look for the number between 1 and 10

The value of x from the given parallel lines, using corresponding angles concept, we get 32°.

Given that, straight line m parallel to straight line n and t is the transversal.

The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.

Here, x°=32°

Therefore, the value of x from the given parallel lines is 32°.

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Answer:

No

Step-by-step explanation:

A function has to pass the vertical line test, meaning that if you put a vertical line anywhere on the graph then the line will only intecert the funtion once. Buy in this graph it intercests twice.

The equations that have the same solution as 3x - 12 = 24 include:

Given data

3x - 12 = 24

3x - 12 = 24

3x = 24 + 12

3x = 36

x = 36 / 3

x = 12

substituting the value of x in the equations to get to check if the value is same for the given question

a. 15x - 60 = 120

15 * 12 - 60 = 120

180 - 60 = 120

120 = 120 correct

b. 3x=12

3 * 12 = 12

36 ≠ 12 incorrect

C. 3x = 36

3 * 12 = 36

36 = 36 correct

d. x - 4=  8

12 - 4 = 8

8 = 8 correct

e. 12x - 12 = 24

12 * 12 - 12 = 24

144 - 12 = 24

132 ≠ 24 incorrect

Hence we can say that the equations that have same solution as the given equation are options A, C, and D

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complete question

The complete question is attached

Answer: The answer for question 48. is -9, The answer for question 49. is 1/2, the answer for question 50. is -2.25, and for question 51 it's 4/5

Step-by-step explanation:

How to solve question 48

1/2(-12-6)-3(5-3)

-6+3-15+9

-3-6

-9

How to solve question 49

(20/2)+10/(-10+20+30)

10+10/40

20/40

1/2

How to solve question 50.

3/4(-15+4)+(8+7)/(-3)

-45/4+3+15/-3

-11.25+3+15/-3

6.75/-3

-2.25

How to solve question 51

5(7)-(3+4)/-2^2-2^2+3^2

35-7/4+4+27

28/35

4/5

Hope this helped owo

Answer:

Step-by-step explanation:

11x+90=15x

The computation shows that Michael will take 22.5 hours to paint a similar sized house working

Based on the information given, the appropriate equation to use will be:

= 1/15 + 1/18 + 1/Michael = 1/6

Add the two fractions on the left

11/90 + 1/Michael = 1/6

1/Michael = 1/6 - 11/90

Take the reciprocal

Michael = 45/2

Michael= 22.5

Michael will take 22.5 hours.

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Answer:

rr

Step-by-step explanation:

xd

ddddd

Answer:

the answer would be A

Answer:

h(t) decreases by a factor of 1.95

Step-by-step explanation:

- 1.95

h(t) decreases by a factor of 1.95

We need to know about a composite bar chart to solve the question. The answer for (a) is Tim received 8 texts on Monday, (b) Tim received 4 emails on Thursday and (c) 0.52 of the messages were emails.

A composite bar chart is used when there are two sets of data that are connected and their frequencies are combined.In this question there are two sets of data emails and texts but both of them belong to the same category which is messages. For question (a) we can easily say from the diagram that the number of texts Tim received on Monday is 8.

For question (b) we need to find out the number of emails Tim received on Thursday, for this we have to look at the bar for Thursday and subtract the number of texts received from total number of messages to get the number of emails received that means, 15-11=4, so Tim received 4 emails on Thursday.

For question (c) we need to find the total number of messages received by Tim for five days, total number of emails received and then calculate the fraction of emails out of messages.

Total number of messages=14+16+14+15+14=73

Total number of emails=6+10+10+4+8=38

Fraction of emails over messages=[tex]\frac{38}{73}[/tex]=0.52

Thus 0.52 of the messages were emails.

We analysed the composite bar chart to find out the answers of the three questions, Tim received 8 texts on Monday,4 emails on Thursday and 0.52 of the messages were emails.

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Answer:

a= 5

b= 7

c=

Step-by-step explanation:

Answer:

8*z^2-3

Step-by-step explanation:

The number in the equation is -10.

Given,

The sum of a number and three is ​tripled the result is one less than twice the number.

We can take the number as x.

Then,

3(x + 3) = (2x - 1)

Equate the above equation and find x.

3x + 9 = 2x - 1

Add -2x to both sides:

That is,

3x - 2x + 9 = 2x - 2x - 1

x + 9 = -1

Add -9 to both sides:

We get,

x + 9 - 9 = -1 - 9

x = -10.

That is, the number in the equation is -10.

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Answer:

Marvin

Step-by-step explanation:

Kelly works four hours a day on tickets and solves on average 38 tickets per day.

38 tickets / 4 hours = 9.5 tickers per hour

_____________________

Brian works five hours per day and solves 45 tickets per hour.

45 tickets / 5 hours = 9 tickers per hour

_____________________________

Marvin works six hours a day on tickets and solves on average 59 tickets per day.

59 tickets / 6 hours = 9.83333 tickers per hour

______________________

Linda works five and a half hours a day on tickets and solves 53 tickets per day.

53 tickets / 5.5 hours = 9.6363637 tickers per hour

Who solves the most tickets per hour? Marvin at 9.833 tickets an hour

30,000 9,000 4 this it the answer to your question

Option C) is correct which is Adam started the construction at the wrong place. He should have started at point R and drawn an arc across both rays.

According to the question we can see that Adam first draws an arc on a line and draws the bisector, which gives him the error.

We know that when we construct an angle bisector, first we put the compass on the point of the angle and make an arc and from that arc we make two arcs that intersect at a point. Then we draw a ray from the point of angle to that intersecting point which gives us the angle bisector.

Here Adam didn't draw the arc from point R.

Thus, Adam started the construction at the wrong place. He should have started at point R and drawn an arc across both rays.

Hence option C) is the correct option.

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Answer:

11

m/1= 100, m/2 = 80, m/3 = 100

12

m/1 = 47, m/2= 133, m/3=47

Step-by-step explanation:

Number 11 uses Cointerior angle rule

Number 12 uses Cointerior angle rule and Corresponding angle rules

The equation that models the data will be y = 3 + x and for x = 12, y will be 15.

We are given the equation:

y = a + b x

Also, we have some points of the equation as:

X         2         3         4         5         6           8

Y         5         6         8         9         10         12​

For the point ( 2 , 5 ), we have the equation as:

5 = a + b ( 2 )

5 = a + 2 b

a = 5 - 2 b   …(1)

For the point (3 , 6), we have the equation as:

6 = a + b (3)

6 = a + 3 b

a = 6 - 3 b   …(2)

From (1) and (2), we get that:

5 - 2 b = 6 - 3 b

3 b - 2 b = 6 - 5

b = 1

a = 5 - 2

a = 3

So, the equation will become:

y = 3  +  x

For x = 12, we get the value of y as:

y = 3 + 12

y = 15

Therefore, we get that, the equation that models the data will be y = 3 + x and for x = 12, y will be 15.

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Answer:

  70

Step-by-step explanation:

You want the number of paths from corner to corner on a 5×5 grid with no backtracking.

The geometry of the problem matches that of Pascal's triangle, attached.

In the attached figure, the value at each node is the sum of the values above and to the left. This matches the counting process for paths that can be used to get to any particular point on the grid: the total number of ways to get there is the sum of the ways it can be approached from above and the ways it can be approached from the left.

The given grid has some numbers filled in. If we continue to assign values to nodes that are the sum of the values above and to the left, we find the node values match the upper left 5×5 array of values in the attachment.

The value at the lower right corner of that array is 70. That is, ...

there are 70 ways to get from A to B.

__

Alternate solution

The path taken will always have 8 steps. Of those, 4 must be to the right, and 4 must be down. The number of ways we can choose 4 of those 8 steps to be steps to the right is "8 choose 4" ...

  C(8,4) = 8!/(4!(8-4)!) = (8·7·6·5)/(4·3·2·1) = 70

Of course, using Pascal's triangle is simply another way to find the value of C(n,k).

The number of minutes that it will take for the two drones be at the same altitude is 17 minutes.

It should be noted that ablack drone is currently at an altitude of 1,170 feet and is dropping at a rate of 64 feet per minute. The expression will be:

1170 - 64m

The white drone is at an altitude of 966 feet and is dropping at a rate of 52 feet per minute. This will be 966 - 52m where m = number of minute

Therefore, we will equate both equations. This will be:

1170 - 64m = 966 - 52m

Collect like terms

-64m + 52m = 966 - 1170

12m = 204

Divide

m = 204 / 12

m = 17

Therefore, the number of minutes that it will take for the two drones be at the same altitude is 17 minutes.

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