How can you tell if the rule you have written for a set of points is correct?

Answers

Answer 1

Hey there!

In order to do that, you take both of the x values and plug them back in to see if you got the desired y value. If you do, it's correct.

For example:

If you had the equation:

y = 2x + 5

and had the points (5,15) and (3,1)

We would check the first coordinates by plugging in the x value:

y = 2(5) + 5
y = 15

Since 15 is our y value, we're correct.

For our next, we can do the same thing, and plug in the x value:

y = 2(3) + 5
y = 6 + 5
y = 11

Since we don't have our desired value, we know we're wrong.

Hope this helps!

Related Questions

The area of circular garden is 530.66 feet2. What is the circumference of the garden? (Use 3.14 for .

Answers

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2\quad \begin{cases} r=radius\\ ------\\ A=530.66 \end{cases}\implies 530.66=\pi r^2 \\\\\\ \cfrac{530.66}{\pi }=r^2\implies \sqrt{\cfrac{530.66}{\pi }}=r \\\\\\ \textit{circumference of a circle}\\\\ C=2\pi r\qquad \implies C=2\pi \left( \sqrt{\cfrac{530.66}{\pi }} \right)[/tex]

what is the sum of the rational expressions below? 2x-1/7x + x/x-2
a. 9x^2-5x+2/7x^2-2
b. 9x^2-5x+2/7x^2-14x
c. 3x-1/8x-2
d. 2x^2-5x+2/7x^2-14x

Answers

x-4/2x=3x/2x-1 (invert the bottom and then multiply)
x-4 (2x+3x/2x-1) ( the 2x's cancel)
x-4 (3x/-1)
x-4 (-3x) (expand)
-3x^2 + 12x=0
-3x^2= -12x (bring 12x to other side making it negative)
-3x^2/3x= -12x/-3x (divide both sides by -3x)
x=4
Hope that helps

[tex] \frac{2x-1}{x} + \frac{x}{x -2} = \frac{(2x-1)(x-2) +(x)(7x)}{(7x)(x-2)}[/tex]

You know the first term of the numerator wil be 2x^2 +7x^2 = 9x^2, and the last term of the denominator will be 7x(-2) = -14x.

This is sufficient work to identify selection B as the correct choice.

Solve 12 = x/4 algebraically. Then, check your answer.

Answers

x= 48
this is found by simplifying both sides of the equation , then isolating the variable

what is the square root of 64 multiplied by 72 divided by the sum of 43 plus 0

Answers

Parentheses are useful for identifying the operands of the various operations. Without them we assume you have
.. (√64)*72/(43 +0) = 8*72/43
.. = 576/43
.. = 13 17/43
.. ≈ 13.395

Write a number sentence that compares 3/5 and 5/6

Answers

To compare 3/5 and 5/6th we need to convert them to a common denominator so if we multiply their denominators we get 5x6 = 30 but we must multlply the numerator by the same number so 3/5 = 18/30th and 5/6 = 25/30 so we see that 25/30 is greater than 18/30th or then 5/6 is greater than 3/5.

find the volume of the cylinder 13mm and 16mm answer choices

A. 16,990
B. 8,491
C. 4,247
D. 2,369

Answers

The volume of the cylinder of a radius of 13mm and a height of 16mm

is, B. 8491 mm³.

What is a cylindrical shape?

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

Given, The cylinder has a radius of 13mm and a height of 16mm.

Therefore, The volume of this cylinder is,

= π×(13)²×16 mm³.

= 8,490.56 mm³.

Q. find the volume of the cylinder having a radius of 13mm and a height of 16mm answer choices.

A. 16,990

B. 8,491

C. 4,247

D. 2,369

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A hurricane has a large eye of about 80 miles. How many kilometers wide is the eye?

Answers

It is given that a hurricane has a large eye of about 80 miles.

We have to determine about how many kilometers wide is the eye.

Since 1 mile = 1.6 kilometers (approximately)

To convert the unit 'mile' into 'kilometer' ,

we have to multiply the given number by '1.6'.

So, 80 miles = [tex] 80 \times 1.6 = 128 [/tex] kilometers.

So, the hurricane eye is about 128 kilometers wide.

Final answer:

To convert 80 miles to kilometers, multiply by the conversion factor of 1.60934, resulting in an eye of the hurricane that is approximately 128.75 kilometers wide.

Explanation:

To convert the size of a hurricane's eye from miles to kilometers, we use the conversion factor that 1 mile is approximately equal to 1.60934 kilometers. If a hurricane has an eye that is about 80 miles wide, we need to multiply this distance by the conversion factor to obtain the width in kilometers.

Step-by-step Conversion:

Identify the width of the hurricane's eye in miles: 80 miles.

Use the conversion factor: 1 mile = 1.60934 kilometers.

Multiply the width in miles by the conversion factor to get the width in kilometers: 80 miles * 1.60934 km/mile = 128.7472 kilometers.

Therefore, the eye of the hurricane is approximately 128.75 kilometers wide.

The system of equations is graphed on the coordinate plane. y=−12x−1y=14x−4 A graph with a blue line passing through coordinates (0, -4) and (4, -3) and a red line passing through coordinates (0, -1) and (4, -3). Enter the coordinates of the solution to the system of equations in the boxes. ( , )

Answers

we have that

case 1)
system of equations is
y=−12x−1
y=14x−4

using a graph tool
see the attached figure

the solution of the system is the point (0.115,-2.385)

case 2)
system of equations is
blue line passing through coordinates A (0, -4) and B (4, -3)
red line passing through coordinates C(0, -1) and D (4, -3)

using a graph tool
see the attached figure

the solution of the system is the point (4,-3)

A tree on a hillside casts a shadow c = 235 ft down the hill. if the angle of inclination of the hillside is b = 16° to the horizontal and the angle of elevation of the sun is a = 46°, find the height of the tree. (round your answer to the nearest foot.)

Answers

Final answer:

By using the tangent function with the effective angle formed by the difference between the sun's elevation and the hill's incline, and the length of the shadow, we calculate the height of the tree to be approximately 136 feet.

Explanation:

To find the height of a tree on a hillside, we utilize the given angles and the length of the shadow it casts. The shadow is cast down the hill (c = 235 ft) with the hill inclining at an angle of 16° to the horizontal (b) and the sun's angle of elevation at 46° (a). To solve this, we can use trigonometry, specifically the concept of similar triangles and the tangent function, which relates the angle to the ratio of the opposite side over the adjacent side in a right triangle.

First, we find the effective angle Θ the sun's rays make with the hillside, which is the difference between the sun's elevation angle and the hill's inclination angle: Θ = 46° - 16° = 30°. Then, using the tangent function which involves the height of the tree (h) and the length of the shadow (c), we set up the equation tan(Θ) = h / c. Substituting the values gives tan(30°) = h / 235 ft.

Next, we solve for h: h = 235 ft x tan(30°). Calculating this, we find h is approximately 135.7 ft. Therefore, rounding to the nearest foot, the height of the tree is 136 feet.

which of the following values of x makes the rational expression below undefined? x-25/x+13
a. 13
b. 0
c. 25
d. -13

Answers

x-25 / x + 13
For this case what you should know is that an indefinite expression are those in which mathematically no numerical value can be obtained.
We have then that a division between zero causes an expression to be undefined.
For x = -13 we have:
(-13-25) / (- 13 + 13) = - 38/0 (undefined)
Answer:
x = -13
d. -13

Answer:

Option D

Step-by-step explanation:

We will check each option for the given expression (x-25)/(x+13)

(A). for x = 13

[tex](\frac{x-25}{x+13})=\frac{13-25}{13+13} =\frac{-12}{26}[/tex]

So expression is defined.

(B). for x = 0

[tex]\frac{x-25}{x+13}=\frac{0-25}{0+13} =(\frac{-25}{13})[/tex]

So expression is defined.

(C). For x = 25

[tex](\frac{x-25}{x+13})=\frac{25-25}{25+13} =0[/tex]

So expression is defined

(D). For x = -13

[tex]\frac{x-25}{x+13}=\frac{-13-25}{-13+13}=( \frac{-38}{0})[/tex]

Function is not defined.

Option D is the answer.

what is the greatest common factor of 30 and 18

Answers

the answer should be 2*3

Hello there! :)

The GCF of 30 and 18 is 6.

STEPS:

List all the factors of 30 and 18:

18: 1, 2, 3, 6, 9, 18

30: 1, 2, 3, 5, 6, 10, 15, 30.

So the GCF is 6.

Hope this helps you!

~Just a felicitous girlie

#HaveAnAwesomeDay

[tex]SilentNature :)[/tex]

Can someone please help me with this ?

Answers

Answer:

E. 2i√5

Step-by-step explanation:

√-20 = (√-1)(√20) = i·(2√5) = 2i√5

The set of points (2, 3), (9, 3), (9, –2), and (2, –2) identifies the vertices of a quadrilateral. Which is the most specific description to tell which figure the points form?
A parallelogram
B square
C rectangle
D trapezoid

Answers

a sorry if I get it wrong

Answer:

C rectangle

Step-by-step explanation:

All the coordinates of the setpoint are (x,y) so, you need to draw the axis and you'll found a rectangle (attached)

It is not a square because its side and height are not equal.

It is not a parallelogram because there are no diagonals.

It is not a trapezoid because it has parallels sides.

It's a rectangle because it has two pairs or parallels, one longer than the other.

For what interval is the function f(x) = (20 + \sqrt{x}) / (\sqrt{20 + x}) continuous?

Answers

Try this solution:
1. according to the condition
[tex] \left \{ {{x \geq 0} \atop {20+x\ \textgreater \ 0}} \right. \ =\ \textgreater \ \ x \geq 0.[/tex]
2. for more details see the attached graph.

Answer: [0;+oo)

A cake recipe suggests a cooking temperature of 325 °F if the batter is less than one inch thick and 350 °F if the batter is more than one inch thick. If the cake batter has a volume of 110 in3 and your cake pan is 9 inches by 11 inches, what does the oven need to be set at if the oven temperature settings are in degrees Celsius? (round to nearest whole number) A) 140 °C B) 163 °C C) 177 °C D) 190 °C

Answers

its C because i got the same question

Answer C

the shape of cake pan is usually cuboid

volume of cuboid = length * breadth * height

110 = 9 *11 * height

height = 10/9 = 1.11 inches

so, the batter is more than 1 inch thick,

the temperature required is 350 degree F or 177 degree C

3.1 Q15
An athlete whose event is the shot put releases a shot. When the shot whose path is shown by the graph to the right is released at an angle of 70°, it's height, f(x), in feet, can be modeled by:
[tex]f(x)=-0.06x^2 + 2.7x + 5.9[/tex]
where x is the shot's horizontal distance, in feet, from its point of release.

What is the maximum height of the shot and how far from it's point of release does this occur?

Answers

The maximum height of the shot is represented by the y-coordinate of the vertex, and the horizontal distance when the maximum height occurs is represented by the x-coordinate of the vertex.

Find x-coordinate of the vertex (horizontal distance)
The function above is in standard form of ax² + bx + c = 0
In standard form of ax² + bx + c = 0, we could find the x-coordinate of the vertex by the formula of
[tex]x= -\cfrac{b}{2a} [/tex]

Extract the information of a and b from the function f(x) = -0.06x² + 2.7x + 5.9
a = -0.06
b = 2.7

Input the value of a and b to the formula of x-coordinate of the vertex
x = [tex]-\dfrac{b}{2a} [/tex]
x = [tex]- \dfrac{2.7}{2 \times (-0.06) \\} [/tex]
x = [tex]- \dfrac{2.7}{-0.12} [/tex]
x = [tex] \dfrac{2.7}{0.12} [/tex]
x = 22.5
The x-coordinate represents the horizontal distance. So the maximum height occurs when the distance is 22.5 feet far from its point of release.

Find y-coordinate of the vertex (the maximum height)
To find the maximum height, input the value of x-coordinate of the vertex to the function.
f(x) = -0.06x² + 2.7x + 5.9
f(22.5) = -0.06(22.5)² + 2.7(22.5) + 5.9
f(22.5) = -0.06(506.25) + 60.75 + 5.9
f(22.5) = -30.375 + 60.75 + 5.9
f(22.5) = 36.275
The maximum height is 36.275 feet

Final answer:

The maximum height reached by the shot is 36.375 feet. This occurs at a horizontal distance of 22.5 feet from its point of release.

Explanation:

This is a question about the maximum height of a shot put. The equation presented here is a quadratic function, and it has the form of a parabola. The maximum value of a parabola that opens downwards (as in this case, where the coefficient of x2 is negative) is given at its vertex.

To find the 'x' coordinate of the vertex, use the formula -b/2a, where 'a' is the coefficient of x2 and 'b' is the coefficient of 'x'. In this case, 'a' is -0.06, and 'b' is 2.7. -b/2a = -(2.7)/(2*-0.06) equals 22.5 feet. This is the horizontal distance from the point of release where the shot reaches the maximum height. To find the maximum height, substitute the value of 'x' into the equation, f(22.5) = -0.06*(22.5)2 + 2.7*22.5 + 5.9. This gives the maximum height as 36.375 feet.

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please translate 2 minus the product of a number and 9 is 20.

Answers

Hey there! :D

2 minus the product of a number and 9 is 20.

2-9n=20 <== equation

number=n minus= - (9 and n are next to each other, so that means they are being multiplied) It is equal to 20.

I hope this helps!
~kaikers

The statement '2 minus the product of a number and 9 is 20' translates to the equation 2 - 9x = 20. Solving for x, we find the solution x = -2, meaning the number in question is -2.

The student is asking to translate the phrase '2 minus the product of a number and 9 is 20' into a mathematical equation. The 'product of a number and 9' can be represented as '9x' where 'x' is the unknown number. Therefore, translating the entire phrase, we end up with the equation: 2 - 9x = 20.

To solve for 'x', we first bring '9x' to the other side of the equation by adding '9x' to both sides, resulting in 2 = 9x + 20. Subsequently, we subtract 20 from both sides, yielding -18 = 9x, and then we divide both sides by 9 to find the value of 'x'. So, x = -18 / 9, which simplifies to x = -2.

The solution for the equation is x = -2, which means the number we were looking for is -2.

solve 3y − 7 = y + 5 and explain each step please so i understand

Answers

3y − 7 = y + 5

So first, make sure you have a variable on one side only. Just subtract y from both sides.

2y - 7 = 5

Now, isolate the variable by adding 7 on both sides (inverse operations) to cancel the negative 7.

2y = 12

Finally, divide by the coefficient of the variable, in this case, 2.

y = 6

That's your answer (y = 6)! Hope this helped!

What you must do for this case is the clearance of the unknown y.
We have then:
Step 1:
(3y - 7) - y = (y + 5) - y
Step 2:
2y-7 = 5
Step 3:
(2y-7) + 7 = (5) +7
Step 4:
2y = 12
Step 5:
y = 12/2
y = 6
Answer:
y = 6

find the values of x and y in the following equation. (x + yi) + (4 + 9) = 9 -4i

Answers

we have that

if the expression is (x + yi) + (4 + 9) = 9 -4i
x+13=9-----------> x=9-13-------------> x=-4
yi=-4i----------- > y=-4

the solution is
x=-4
y=-4

if the expression has a typing error and it is really (x + yi) + (4 + 9i) = 9 -4i
then
x+4=9------------> x=9-4-------< x=5
y+9=-4-------------> y=-4-9 ------------> y=-13
the solution is
x=5
y=-13

Final answer:

In this question we solve the given complex number equation. By comparing real and complex components on both sides of the equation, we find the values satisfying the equation are x = 5 and y=-13.

Explanation:

In this complex number equation, we must solve for x and y: (x + yi) + (4 + 9) = 9 -4i. Begin by simplifying the left side of the equation, to give (x + 4 + yi +9i) = 9 - 4i. This further simplifies to (x + 4) + (y + 9)i = 9 -4i.

Now we can see that the real component of the equation (x + 4) must equal the real component on the other side of the equation (9), and the complex component of the equation (y + 9)i must equal the complex component -4i. Setting these equal gives x + 4 = 9 and y + 9 = -4.

Solving these gives x = 5 and y = -13, which are the values for x and y satisfying the equation.

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64 is 4 times the difference between Sarah's age a and 44 assume Sarah is older than 44 write an equation to determine Sarah's age a

Answers

Let s represent Sarah's age.
.. 64 = 4(s -44)

___
Sarah is 60.

Answer:

Sarah's age is 60.

Step-by-step explanation:

We have that Sarah's age is a.

The problem states that 64 is 4 times the difference between Sarah's age a and 44.

[tex]a - 44 = \frac{64}{4}[/tex]

[tex]a - 44 = 16[/tex]

[tex]a = 44 + 16[/tex]

[tex]a = 60[/tex].

Sarah's age is 60.

what ia 10 + 10 -10 x 5932

Answers

Hello,

The answer is "59,320"

Reason:

First write the equation:

10+10-10*5932

10+10=20

20-10=10

10*5392=53,920

=59,320

If you need anymore help feel free to ask me!

Hope this helps!

~Nonportrit

Answer:

The answer would be 59,320

Step-by-step explanation:

10+10 is 20

20-10 is 10

10x5,932 is 59,320

Sara wrote 524 words in her journal. Then she crossed out 56 words and added 95 new words. How many words are written in her journal now?

Answers

you have 524 words then subtract by 56 bc she crossed them out and then she added 95 by writing them so therefor the answer is 563

Olive wants to invite friends over for some ice cream. She has a total of 8 pints of ice cream in her freezer. If she splits each pint into 1/2 pint servings, how many servings of ice cream will olive have?

Answers

we know that
Olive has a total of 8 pints of ice cream
If she splits each pint into 1/2 pint servings----------> 8/(1/2)-----> 8*2=16

the answer is 16 servings of ice cream

gabriel made 4 small meatloaves. he cut each meatloaf into fourths. how many 1/4 size pieces of meatloaf does gabriel have

Answers

He would have sixteen pieces.

Melissa bought a cake that cost $75. the sales-tax rate is 10 percent. what is the total amount she paid for the cake

Answers

Answer:

The total amount that Melissa paid for the cake is $82.5

Step-by-step explanation:

we know that

The total amount that Melissa paid for the cake is equal to the cost of the cake plus the sales tax

we have that

the cost is equal to $75

Find the sales tax

The sales tax is 10%, therefore find the 10% of the cost of the cake

10%=10/100=0.10

(0.10)*$75=$7.5

Adds the cost and the sales tax

$75+$7.5=$82.5

Match each area to its corresponding radius or diameter of the circle.(All areas are approximate.) Tiles area: 221.5584 square units area: 78.5 square units area: 452.16 square units area: 36.2984 square units area: 314 square units area: 886.2336 square units Pairs radius: 12 units arrowBoth diameter: 16.8 units arrowBoth radius: 3.4 units arrowBoth diameter: 10 units arrowBoth

Answers

we know that
Area circle=pi*r²--------------> r=√(A/pi)

case 1) 221.5584 square units area -------------> r=√(221.5584/pi)=8.398 units
Diameter=2r-----> 2*8.4=16.8 units

case 2) 78.5 square units area-------------> r=√(78.5/pi)=5 units
Diameter=2r-----> 2*5=10 units

case 3) 452.16 square units area -------------> r=√(452.16/pi)=12 units
Diameter=2r-----> 2*12=24 units

case 4) 36.2984 square units area -------------> r=√(36.2984/pi)=3.4 units
Diameter=2r-----> 2*3.4=6.8 units

case 5) 314 square units area -------------> r=√(314/pi)=10 units
Diameter=2r-----> 2*10=20 units

case 6) 886.2336 square units -------------> r=√(886.2336/pi)=16.8 units
Diameter=2r-----> 2*16.8=33.6 units

5x−4y=−10
−4x+5y=8
Solve System of equations

Answers

5y = 4x + 8 and y = 4x/5 + 8/5

{5x−4y=−10 ⇒ 5x = 4y-10 ⇒ x=(4y-10)/5 ⇒ x = 0.8y - 2
{-4x+5y=8

-4(0.8y-2) + 5y = 8
-3.2y + 8 + 5y = 8
1.8y = 8 - 8
1.8y = 0
y = 0

5x−4·0=−10
5x = -10
x = -10/5
x = -2

Your answer is (-2, 0)

How do you check your answer for volume of a cylinder? Desperate need of answering

Answers

1. Make sure you're using the correct formula for the dimensions given. The usual formula gives volume in terms of radius and height. If you are given the diameter, the formula will be different, or you need to compute the radius before you use the formula.

2. Make sure you're using the appropriate value for π. Many calculators have the value built-in. Many problems posted on Brainly require the use of 3.14, which will give different answers. (One recent problem required the use of 3.) If your calculator doesn't have π built in, a reasonable value is 355/113, which is good to 7 significant figures.

3. Make sure the units you are using are compatible (generally, all the same). If your height is in one unit (say inches) and your diameter is in another unit (say centimeters), you need to do units conversion before you put the numbers in the formula. The result of putting your units in the formula with your numbers should be that you end up with units cubed. For example, for a radius of 2 cm and a height of 3 cm, the volume will be
.. V = π(2cm)^2*(3 cm) = 12π cm^3.

4. Compare the dimensions and the volume to things you know. You know the approximate size of a gallon jug, a 2 liter pop bottle, a 5-gallon bucket. Check your answer for reasonableness.

5. Make an estimate based on the dimensions. Round to 1 or 2 significant figures and make a guess as to the approximate result you should get. For this, you can use 3 for π, as you just want to be "somewhere in the ballpark" as opposed to being off by a factor of 10 or more. This requires a certain amount of number sense and knowledge of multiplication tables.

6. Make certain your calculator is being used correctly. If parentheses are involved, make sure you enter the closing parentheses--as opposed to letting the calculator put them in according to its own rules. If division or fractions are involved, make sure you have parentheses around the denominator in every case. 1/2*3 ≠ 1/(2*3) It can be helpful to use a calculator that shows you what it did. (The Google calculator does that, for example.)

7. Sometimes, it helps just to do the calculation twice (possibly in a different order). Inadvertent error can creep in even when you think you're paying attention.

8. If you're doing the math by hand, make use of all available techniques for checking your arithmetic.

convert 3(3.14)/8 radians to degrees

Answers

67.5 degrees

3pi/8 * 180/pi = 67.5

A newborn child receives a $9,000 gift toward a college education from her grandparents. How much will the $9,000 be worth in 18 years if it is invested at 7.6% compounded quarterly? Round to the nearest cent.

Answers

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$9000\\ r=rate\to 7.6\%\to \frac{7.6}{100}\to &0.076\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\to &4\\ t=years\to &18 \end{cases} \\\\\\ A=9000\left(1+\frac{0.076}{4}\right)^{4\cdot 18}\implies A=9000(1.019)^{72}[/tex]

Other Questions

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