The circle given by : x^2 + y^2 - 6y - 12 = 0 can be written as:
x^2 + (y - k)^2 = 21.
What is the value of k in this equation?

Answers

Answer 1

Step-by-step explanation:

Given equation of circle is,

[tex] {x}^{2} + {y}^{2} - 6y - 12 = 0 \\ by \: compairing \: it \: with \: \\ {x}^{2} + {y}^{2} + 2gx + 2fy = 0 \: we \: get \\2 g = 0 \: or \: g = 0 \\ 2f= - 6 \\ or \: f= - 3 \\ c = - 12[/tex]

again the another form of circle is,

[tex] {x}^{2} + {(y - k)}^{2} = 21 \\ or \: {x}^{2} + {y}^{2} - 2ky + {k}^{2} - 21 = 0 \\ by \: compairing \:it \: with \: \\ {x}^{2} + {y}^{2} + 2gx + 2fy = 0 \: we \: get \\ g = 0 \\f = - k \\ c = {k}^{2} - 21[/tex]

now equating the values of f in both equations,

-k=-3

i.e. k=3

therefore k=3


Related Questions

PLZZZZZZZZZZZZZ HELP I NEED TO PASS THIS TEST I WILL GIVE BRAINLIST ANSWER TO WHO ANSWERS IT RIGHT

A statue has the shape of a square pyramid. The side length of the square base is 20 feet. The slant height of the monument is 16 feet. What is the height of the monument? Enter your answer, rounded to the nearest tenth of a foot, in the box.

____

|___| ft

Answers

Answer:

[tex]b=12.5[/tex] ft

Step-by-step explanation:

From this description we can draw this diagram

Now we can use the Pythagorean theorem to find the height.

[tex]10^2+b^2=16^2\\\\b^2=256-100\\\\b=\sqrt{156}[/tex]

This square root is equal to

[tex]b=12.489[/tex]

Which rounds to

[tex]b=12.5[/tex] ft

Help with number four plz!!!!!!

Answers

Answer:

Yes

Step-by-step explanation:

First we'll find the number of total bars of soap.

8 + 8 + 11 = 27

Is 27 divisible by 27?

Yes because 27 / 3 = 9

So you could rearrange the soaps to have 9 bars in each basket.

What is the slope if the line x+3y = 10

Answers

Answer:

the slope is -1/3

the Y intercept is 10/3

Step-by-step explanation:

Answer:

-1/3

Step-by-step explanation:

We want to get the equation in slope intercept form (y=mx+b)  where m is the slope and b is the y intercept

x+3y = 10

Subtract x from each side

x-x+3y = -x+10

3y = -x+10

Divide each side by 3

3y/3 = -1/3x +10/3

y = -1/3x +10/3

The slope is -1/3 and the y intercept is 10/3

Identify the equation that represents the line of best fit on this scatter plot.
30 POINTS

Answers

[tex]y=\frac{5}{7} x+2[/tex]

How?

The way you find it is easy. +2 means go up 2y. 5 is y too, so you do 2+5=7. Now go 7 positive x. The answer is this.

Hope this helped:)

Answer:

C. [tex]y=\frac{5}{7}x+2[/tex].

Step-by-step explanation:

We have been given a scatter plot. We are asked to find the equation of line of best fit.

First of all, we will find slope of line of best fit using points [tex](0,2)[/tex] and [tex](7,7)[/tex].

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{7-2}{7-0}[/tex]

[tex]m=\frac{5}{7}[/tex]

We can see that y-intercept of line of best fit is 2.

We will write our equation in slope intercept form [tex]y=mx+b[/tex], where,

m = Slope,

b = The y-intercept.

Upon substituting [tex]m=\frac{5}{7}[/tex] and [tex]b=2[/tex] in slope-intercept form, we will get:

[tex]y=\frac{5}{7}x+2[/tex]

Therefore, the equation of line of best fit for given scatter plot is [tex]y=\frac{5}{7}x+2[/tex] and option C is the correct choice.

Help me find the which statements are true!!!!

Answers

Answer:

C.

Step-by-step explanation:

[tex]\text{A. The absolute value of the slope of the line is equal to}\ \dfrac{HJ}{FG}\\\bold{FALSE}\\\text{because the slope of the line is equal to}\ \dfrac{HJ}{KJ}\\------------------------------\\\text{B. The absolute value of the slope of the line is equal to}\ \dfrac{FG}{JK}\\\bold{FALSE}\\\text{because the slope of the line is equal to}\ \dfrac{FG}{FK}\\------------------------------[/tex]

[tex]\text{C. Because triangles FGH and HJK are similar, the slope is the same}\\\text{between any two distinct points on the line.}\\\bold{TRUE}\\------------------------------\\\text{D. Because triangles FGH and HJK are not similar, the slope is found}\\\text{by using two distinct points on one of the triangles}\\\bold{FALSE}\\\text{because triangles FGH and HJK are similar (AAA)}[/tex]

find the solution to the system

y=x^2+8x+2
y=7x+4

A(-2,-10) and (1,11)
B(2,10) and (-1,-11)
C(-2,-34) and (1,11)
D no solution

Answers

Answer:

A

Step-by-step explanation:

Given the 2 equations

y = x² + 8x + 2 → (1)

y = 7x + 4 → (2)

Substitute y = x² + 8x + 2 into (2)

x² + 8x + 2 = 7x + 4 ( subtract 7x + 4 from both sides )

x² + x - 2 = 0 ← in standard form

(x + 2)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 1 = 0 ⇒ x = 1

Substitute these values into (2) for the corresponding values of y

x = - 2 : y = - 14 + 4 = - 10 ⇒ (- 2, - 10)

x = 1 : y = 7 + 4 = 11 ⇒ (1, 11)

The solutions are (- 2, - 10) and (1, 11) → A

a number is chosen at random from 1 to 50 find the probability of selecting factors of 36​

Answers

Answer:

9/50 or 18%

Step-by-step explanation:

The factors of 36 are-

123469121836

That's 9 factors. 1-50 means that it is a 9 out of 50 chance, or 80%.

When a number is chosen at random from 1 to 50 the probability of selecting factors of 36 is 2/50​.

What is probability?

Probability is the ratio that shows us how likely an event will occur from a given set of events.

We can find the required probability below:

The factors of 36 are:

36 = 2*2*3*3

Therefore the factors of 36 are 2 and 3.

Total number of factors = 2

Total number of numbers from 1 to 50 = 50

The probability of selecting factors of 36​ = P(selecting factors of 36)

= 2/50

The probability of getting a factor of 36 when a number is chosen at random is 2/50.

Therefore, we have found that when a number is chosen at random from 1 to 50 the probability of selecting factors of 36​ is 2/50.

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A sculptor creates an arch in the shape of a parabola. When sketched onto a coordinate grid, the function f(x) = –2(x)(x – 8) represents the height of the arch, in inches, as a function of the distance from the left side of the arch, x. What is the height of the arch, measured 3 inches from the left side of the arch?

Answers

The correct answer is:  D) 30 inches

Explanation:

We know that x represents the distance in inches from the left side of the arch. Using 3 for x, we have:

f(3) = -2(3)(3-8)

f(3) = -2(3)(-5)

f(3) = -6(-5)

f(3) = 30

Therefore, the correct answer is 30 inches! Thank you for your inquiry, your welcome for the answer and explanation!

The correct answer is:  D) The height of the arch, measured 3 inches from the left side of the arch 30 inches

What is the height?

In math, height can be defined the vertical distance from the top to the base of the object. It is measured in cm, inches, meters, etc.

We know that x represents the distance in inches from the left side of the arch. Using 3 for x, we have:

f(3) = -2(3)(3-8)

f(3) = -2(3)(-5)

f(3) = -6(-5)

f(3) = 30

Therefore, the correct answer is 30 inches

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What is the measure of Angle F, to the nearest degree?

Answers

Do you have a picture to go along with this question?

Calculate electric force a 0.020kg balloon is charged by rubbing and then stuck to the ceiling

Answers

Answer:

Step-by-step explanation:

therefore, force F = m*g  

= 0.02 kg * 9.8 m/s^2  

= 0.196 Newton Force in the MKS system of units is measured in NEWTONS and results from a product of mass in Kg and acceler. the formula is  s o the force=mass x acceleration. and the answer is .02x9.8^2= 1.6928ation in meters/sec^2

Final answer:

The electric force of a charged balloon sticking to the ceiling is due to the interaction between the balloon and the induced positive charge in the ceiling. This force is related to the principle of electrostatics and can theoretically be calculated using Coulomb's Law, but would require more details. However, for the balloon to remain stuck to the ceiling, this electrostatic force must be greater than the weight of the balloon.

Explanation:

To calculate the electric force of a charged balloon sticking to the ceiling, you first need to consider the scenario as an interaction between the charged balloon and the induced charge in the ceiling. This scenario is related to the principle of electrostatics, where like charges repel and different charges attract. It is the electrostatic force that is making the balloon stick to the ceiling.

The balloon gets charged by picking up extra electrons (negative charge) when rubbed. When brought near the ceiling, these extra electrons in the balloon repel the electrons in the ceiling, causing the area of the ceiling near the balloon to be positively charged. This induced positive charge in the ceiling then attracts the negatively charged balloon. The force between the balloon and the ceiling can be caluclated using Coulomb's Law, which states that the force between two charges is directly proportional to the product of their charges, and inversely proportional to the square of the distance between them. However, to accurately calculate this force using Coulomb's law, we need more information such as the amount of charge on the balloon and the distance from the balloon to the ceiling.

Finally, for a balloon to stick to the ceiling, the electrostatic force must be greater than the weight of the balloon. The weight of the balloon can be calculated using the formula Weight = mass x gravity. In this case, the mass of the balloon is 0.020kg and the gravitational force is approximately 9.8 m/s². Therefore, the weight is 0.020kg x 9.8 m/s² = 0.196N. So for the balloon to stick to the ceiling, the electrostatic force must be greater than 0.196 N.

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How do I find the measure of angle A?

Answers

Final answer:

The measure of angle A can be calculated using trigonometry and the components of a known vector. The relationship of the components forms a right triangle, the properties of which can be used to find the measure of angle A.

Explanation:

The measure of angle A can be calculated using trigonometry if we know the distances from the problem. By knowing the scalar components Ax and Ay of vector A, we can find its magnitude and direction angle. In this case, the direction is the angle the vector forms with the positive direction on the x-axis, measured in the counterclockwise direction. The lengths A, Ax, and Ay form a right triangle, related by the Pythagorean theorem.

If the vector A is known, then its magnitude A and its angle are known. To find Ax and Ay, we use the following relationships for a right triangle: Ax = Acose. If the vector lies in the first or the fourth quadrant, where component Ax is positive, angle A is identical to the direction angle. Conversely, when the vector lies in the second or third quadrant, where component Ax is negative, the direction angle is A = 0 + 180°.

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The measure of angle A in the given figure is equal to 20 degrees.

To solve this question we can use the property of a triangle that the sum of all angles in a triangle is equal to 180 degrees.

We have been given three different angles in this figure which are: 90 degrees, 71x-1, and 20x.

Let us find the value of x before finding the value of angle A

71x-1 + 20x + 90 = 180

71x + 20x = 180 - 90 + 1

91x = 91

x = 1

Now we can calculate the value of angle A as:

20x

= 20 (1)

= 20 degrees

The measure of angle A is 20 degrees.

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A small pie factory needs to ship 360 pies a day to stay profitable. 180 pies are baked every 3 hours. Of the baked pies, 20% go directly to freezer storage and 80% are loaded on a truck for delivery. Find the constant of proportionality for the number of pies baked and loaded on a truck for delivery. A.48 B. 60 C. 96 D. 144

Answers

Answer:

Constant of proportionality should be 48.

Step-by-step explanation:

Given that a small pie factory needs to ship 360 pies a day to stay profitable. 180 pies are baked every 3 hours. Of the baked pies, 20% go directly to freezer storage and 80% are loaded on a truck for delivery.

Now we need to find about what is the constant of proportionality for the number of pies baked and loaded on a truck for delivery.

Number of baked pies = 180

Number of pies loaded on truck for delivery = 80% of baked pies

= 0.80(180)= 144 in 3 hours.

So number of pies loaded per hour = 144/3= 48

Hence constant of proportionality should be 48.

The points (4, 1) and (x, -6) lie on the same line. If the slope of the line is 1 what is the value of x?

A -3
b 3
c 9
d 11

Answers

Answer:

x=9

Step-by-step explanation:

The Slope is given by the following equation

m= (y2-y1) / (x2-x1)

Where x2=4, x1=x, y2=1, y1=-6, m=1 by requirements of this problem

Developing the equation we have this:

[tex]1=\frac{1-(-6)}{4-x}[/tex]

Which leaves to the following equation

[tex]5=4-x[/tex]

Resulting that x=9

7x+(2x+7)=9x+7 show work

Answers

it is true 9x=9x

7x+(2x+7)=9x+7

7x+2x+7=9x+7

-7. -7

7x+2x=9x

9x=9x

the class kept track of rainy and sunny days. During the 54 days, classified rainy or sunny, the ratio of rainy days is 7 to 14. How many sunny days were there?

Answers

There are 36 sunny days

1:2

1 + 2 = 3

54/3 = 18

1 • 18 = 18

2 • 18 = 36

There are 36 sunny days.

Hope this helps!

If it does then I would appreciate it if you could make me brainliest.

The 2 ft side length of the scale drawing corresponds to a side length of 120 feet for the actual skate park. What is the scale factor?

Answers

Answer:

The scale factor is [tex]\frac{1}{60}[/tex]

Step-by-step explanation:

we know that

The scale factor is equal to the ratio between the side length of the scale drawing to the corresponding side length in the actual

so

[tex]\frac{2}{120}=\frac{1}{60}[/tex]

Answer:

1/60

Divide

Step-by-step explanation:

What is 2000x27895 equals

Answers

Answer:

55790000  :p :)

 

Answer: it would be 55,709,000

Step-by-step explanation:

What is the value of h when the function h(x)=x^2−8x+14 is converted to vertex form?

Answers

Answer:

h=4

Step-by-step explanation:

The given function is

[tex]h(x)=x^2-8x+14[/tex]

We add and subtract the square of half the coefficient of x.

[tex]h(x)=x^2-8x+(\frac{-8}{2})^2-(\frac{-8}{2})^2+14[/tex]

[tex]h(x)=x^2-8x+(-4)^2-(-4)^2+14[/tex]

The first three terms forms a perfect square trinomial

[tex]h(x)=(x-4)^2-16+14[/tex]

[tex]h(x)=(x-4)^2-2[/tex]

We now compare to the vertex form;

[tex]h(x)=a(x-h)^2+k[/tex]

We have h=4


l dont know what to do?​

Answers

1. Multiply the amount of iced tea mix by 1/3 to get the amount of water.

Explanation:

As seen in the graph, for every 1 cup of water, 3 tablespoons of the mix are needed.

3 * X = 1

X= 1/3

2. Use the equation y=3x

X=18 , y=cups of water needed

Y= 3*18

Y= 54 cups of water are needed

All the dimensions of a triangle were multiple by the same factor. If the base of the triangle went from 1 centimeter to 3 centimeters, the area of the triangle was multiple by what?
6
3
9
12

Answers

Answer:

the area is multiplied by 9.

Step by Step Explanation:

Let x be the base

Let y be the height

Since all dimensions were multiplied by the same number, 3,

Original area,

1/2 × x × y = (1/2)xy

New area,

1/2 × 3x × 3y = (1/2)(9)xy

Hence, area is multiplied 9 times.

If the half-life of K-40 is 1.3 billion years and if a sample rock found on an island is estimated to be 1 billion years old, what percentage of the original parent K-40 would be present in the rock? Round your numerical values to the hundredths decimal place.

Answer Choices

(A) 76.92%
(B) 1.3%
(C) 58.67%
(D) 99.99%

Answers

For this case, we must make a rule of three, to find the percentage of the k-40 found in the sample found.

1.3 ----------> 100%

1 -------------> x

Where "x" represents the percentage of k-40 present in the sample found.

[tex]x = \frac {1 * 100} {1.3}\\x = 76.9230[/tex]

Rounding off we have:

76.92%

ANswer:

Option A

The percentage of parent K-40 remaining in the rock is calculated as 76.92% of the original K-40.

Percentage of parent K-40 remaining in the rock:

Calculate the number of half-lives: 1 billion years / 1.3 billion years = 0.7692 or about 0.77 half-lives.

Use the formula[tex](1/2)^n[/tex] where n is the number of half-lives to find the percentage remaining: [tex](1/2)^0.77[/tex]  ≈ 0.76.

Convert to a percentage for the original K-40 remaining in the rock: 0.76 * 100% ≈ 76.92%.

Can some body help me with number 12 it’s due tomorrow.

Answers

Answer:

Mean = 51.375

Mode = 55,44

Step-by-step explanation:

add all the numbers up and divide by 8

find the most repeating numbers.

Answer:

Mean: 51.375

Median: 51.5

Mode: 44, 55

Hope This Helps!  Have A Nice Day!!

The figures are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number.

The area of the smaller trapezoid is 771 m2.
a.
4,096 m2
b.
4,028 m2
c.
784 m2
d.
21 m2

Answers

Answer:  Option b.

Step-by-step explanation:

First, you need to calculate the ratio of the area. This is:

[tex]ratio=(\frac{64}{28})^2\\\\ratio=\frac{256}{49}[/tex]

You know that the area of the smaller trapezoid is 771 m², then you can set up the following proportion, where "x" is the area of the larger trapezoid. Then you have:

[tex]\frac{256}{49}=\frac{x}{771}[/tex]

Now you must solve for "x". Therefore, you get that the area of the larger trapezoid is:

 [tex]x=(771)(\frac{256}{49})\\\\x=4,028m^2[/tex]

To the nearest whole number, the area of the other similar figure is: b. 4,028 m².

What is the Area of Similar Figures?

The ratio of the areas of two similar figures equals the ratio of the square of their corresponding sides.

Thus:

Let x represent the area of the other figure.

Therefore:

771/x = (28²)/(64²)

771/x = 784/4,096

x = (771 × 4,096)/784

x = 4,028

Therefore, to the nearest whole number, the area of the other similar figure is: b. 4,028 m².

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Make q the subject of the formula 2(q+p) = 1+5q. Give your answer in the form ap-b/c where a,b and c are all positive integers

Answers

Answer:

[tex]\frac{2p-1}{3}[/tex]

Step-by-step explanation:

Since you want to get q only and q appears in both side of the equation. Try to isolate q to one side.

1) Expand 2(q+p)

2q + 2p = 1 + 5q

2) Move all q terms to one side

5q - 2q = 2p - 1

3q = 2p - 1

3) Divide 3 on both side (to isolate q)

q = [tex]\frac{2p-1}{3}[/tex]

After making q the subject of the formula in the equation 2(q + p) = 1 + 5q, the resulting solution is:

[tex]q = \frac{2p - 1}{3}[/tex]

The given equation is:

2(q + p) = 1 +5q

To make q the subject of the formula, follow the steps below

Expand the expression using the distributive rule

2q + 2p = 1 + 5q

Collect like terms by subtracting 2q from both sides of the equation

2q - 2q + 2p = 1 + 5q - 2q

2p = 1 + 3q

Subtract 1 from both sides of the equation

2p - 1 = 1 + 3q - 1

2p - 1 = 3q

Divide through by 3

[tex] \frac{2p - 1}{3} = q[/tex]

Therefore after making q the subject if the formula in the equation 2(q + p) = 1 + 5q, the resulting solution is:

[tex] q = \frac{2p - 1}{3}[/tex]

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Find the fifth roots of 32(cos 280° + i sin 280°)

Answers

Answer:

The fifth root is 2[cos(56°) + i sin(56°)]

Step-by-step explanation:

* To solve this problem we must revise De Moiver's rule

- In the complex number with polar form

∵ z = r(cosФ + i sinФ)

∴ z^n = r^n(cos(nФ) + i sin(nФ))

* In the problem

- The fifth root means z^(1/5)

- We can put 32 as a form a^n

∵ 32 = 2 × 2 × 2 × 2 × 2 = 2^5

∴ z = 2^5[cos(280°) + i sin(280°)]

* Lets find z^(1/5)

[tex]*z^{\frac{1}{5}}=[2^{5}]^{\frac{1}{5} } (cos(\frac{1}{5})(280)+isin(\frac{1}{5})(280)[/tex]

[tex]*(2^{5})^{\frac{1}{5}}=2^{5.\frac{1}{5}}=2[/tex]

∴ z^(1/5) = 2[cos(56) + i sin(56)]

* The fifth root of 32[cos(280°) + i sin(280°)] is 2[cos(56°) + i sin(56°)]

 

Suppose f(x) = x^2 and g(x) = (3x)^2 which statement best compares with he graph of g(x) with the graph of f(x)

Answers

Answer:

Step-by-step explanation:

f(x) = x^2 and g(x) = (3x)^2.  g(x) can be rewritten as 9x^2.

The graph of g(x) is similar to that of f(x), except that the graph of g(x) is the result of vertical stretching of the graph of f(x) by a factor of 9.

Answer: The graph of g(x) is horizontally compressed by a factor of 3.

Step-by-step explanation:

Got this answer right on apex

Bob's bill for dinner at surefire steak house was $45. In addition he piad 5°\° of the bill in tax and he left a tip for 15°\° of the bill how much did Bob spend for tax and tip combined how much did Bob spend in all?

Answers

Answer:

$54

Step-by-step explanation:

First

45 times .05= 2.25

Second

45 plus 2.25

Third

45 times .15= 6.75

Fourth

45+2.25+6.75

Answer:

$54

Step-by-step explanation:

Okay. if the bill in tax was 5% and the tip is 15% just add them up to make it easier. Now, you have 20%, and you have to now find 20% of 45, make 20% into .20, do .20x45 which equals 9 which represents $9. Finally, add $9 (from tip and tax) to $45 (how much the food cost) = $54

No problem!

can someone help me with this?​

Answers

V=ABh

S=a +b+c

————-

2

=83.5

HELP IM ‍♀️ CONFUSED WILL GIVE BRAINLIEST AND 10 points CAN SOMEONE HELP WITH MY HOMEWORK QUESTIONS

Answers

Answer:

1 3/4

Step-by-step explanation:

8.25-6.5

Answer:

I believe it is B

Lowest- 6 1/2 inches

Tallest- 8 1/4 inches

6 1/2-8 1/4= 1 3/4

I am sorry if this is wrong.

Can someone help ASAP I really need help 15 points

Answers

Answer:A=85 E=73 S=37 L=66.5 (or 65) T=82 P=53 D=10 O=89 C=17

Step-by-step explanation:

I am very good at Pythagorean theorem I did it this year.

To do this it is actually like the easiest thing to do in math. The formula is A²+B²=C². To do this it is easier with a scientific calculator. If you don't have one you can use this online calculator: desmos.com/scientific

Step 1. get the two number and square (²) them ( multiply that number by it) For Example 30 multiplied by 30. Or on the calculator I gave you just do 30²+40²

Step 2. After that you will get 2500. Then on the calculator get this symbol √ and but the number 2500 in front of it. it should look like this. √2500.

Step 3. After that you will get 50 which is your answer. And that is how you do Pythagorean theorem.

I hope that helped you. If you don't have a scientific calculator you can use the link I provided above. If you can't use it I reccomend buying one.

Answer: It is a cold place
Other Questions
Which tasks would be performed by someone in an Administration and Information Support career? A) Analyzing information to predict future sales and supervising others B) Answering telephone calls and filing paperwork C) Training employees and administering employee benefits D) Hiring and firing employees and approving budgets Alex is outgoing, therefore; he makes friends easily.I usually like green vegetables; but the broccoli I ate today was terrible.It was an emergency; otherwise, I would not have called you so early in the morning. Ms. Scully is a great teacher; because she has been working at the school for decades. which is punctuated correctly? Explain the difference between addiction and tolerance. Find the value of b in the graph of y=3x+b if it is known that the graph goes through the point:O(3,8) What is the term for visual representation of data A.extrapolationB.graph C.interpolation D.Correlation Believing that heinz should not steal the drug because stealing is wrong and heinz will get caught and go to jail is representative of which type of moral thinking? What statement best describes slave trade in the United States in the beginning of the 1800s?Slavery was not an issue at this time.Slavery was abolished in all states.Slave trade was outlawed, but it still continued illegally.Slavery was illegal, but the government did nothing about it. Read the text and review the chart.The standard plank test is an easy way to measure the strength and endurance of your core muscles. You can perform the test at home. All you need is a stopwatch and a partner.To perform the standard plank test:Move into the plank position, positioning feet and hands on the floor as if doing a push-up.Hold this "up position as long as possible, being careful to keep your back straight and flat.Have a partner time how long you can hold the pose. The timer should be stopped when your hips begin to sag or rise.How does the performance chart included in this document help clarify the standard plank test procedure?It illustrates the main purpose of the test for test takers.It provides test takers with tips for improving endurance.It shows test takers how test results should be recorded.It helps test takers interpret and evaluate their test results. when you count by 1's from any integer what are you counting? Please help!ThanksBRIANLIEST OF 2 PPL ANSWER Write a paragraph to explain how profits, incentives, and competition motivate households and businesses. 20 Points! Please Help.Taxes upon the money people earn from jobs or investments are called:A. Property taxesB. Income taxesC. Sales taxesD. Excise taxes Jacob is tasked with the duty of selecting one name from a list of all employees in his company to award him or her and his or her family an all-expenses-paid trip to Canada. After selecting a name from a drum with all employee names in it, the lucky winner is Sally from recruiting. What kind of sampling is this? Stratified random sampling Systematic sampling Simple random sampling Convenience sampling While traveling to and from a certain destination, you realized increasing your speed by 10 mph saved 1 hours on your return. If the total distance of the roundtrip was 600 miles, find the speed driven while returning. What was the name of the gelatinous form of gasoline that burns the skin of anyone exposed to it, which was dropped by american airplanes on enemy positions during the vietnam war? Find the measure of CD.Round to the nearest tenth.PLEASE NEED HELP!!! WILL GIVE BRAINLIESTgreenhouse gases trap _____.a. carbon dioxideb. infrared radiationc. uv radiationd. visible spectrum radiation the answer is not carbon dioxide in gradpoint Julia bought 300 pounds of grain for herhorses. When a rainstorm flooded thestorage shed, 30% of the grain rotted andhad to be thrown out. How many poundsof grain will Julia be able to use? What do z R mean for math as an answer to a inequality What is the measure of a