Which relation is a function?

Functions can't have multiple y values have the same x value.

[(-5, 1), (-3, 2), (-1, 3) (1, 4), (3, 5)] ** No repeating x-values.

[(-2, 1), (-4, 2), (0,3), (4, 1), (-2,5)]

[(-1, 5), (-1,4), (-1, 3), (-1, 2) (-1, 1)]

[(-6, -4), (-4, -2), (0, 0), (-4, 2) (-6, 4)]

Answer:

[(-5, 1), (-3, 2), (-1, 3) (1, 4), (3, 5)]

Answer:

1 unit right and 1 unit down

Step-by-step explanation:

When you replace x with x - h, you translate the graph h units horizontally.

When you replace y with y - k, you translate the graph k units vertically.

y = |x - 1| - 1

y + 1 = |x - 1|

y - (-1) = |x - 1|

Compare the last equation above with y = |x|. x was replaced by x - 1, so h = 1, and the translation is 1 unit horizontally. Since 1 is positive, it is a 1 unit translation to the right. y was replaced by y - (-1), so k = -1, and the vertical translation is 1 unit down.

Answer:

1 unit right and one unit down

Step-by-step explanation:

Final answer:

To find the radius of a circle, use the formula A = πr² and solve for r by dividing the area by π and then taking the square root of the result.

Explanation:

The radius of a circle can be found using the formula for the area of a circle, A = πr².

Given A = 324π cm², substitute this value into the formula: 324π = πr².

Solve for r by dividing both sides by π: r² = 324, r = √324, r = 18 cm.

You seem to generally have the right idea, and you seem to be able to solve the equations you write. However, your choice of equations for the problem sometimes needs a little work.

∠DBC = ∠DBE + ∠EBC

(12x -3) = (5x +12) + (3x +13) . . . . . substitute given values

12x -3 = 8x +25 . . . . . . . . . collect terms

4x = 28 . . . . . . . . . . . . . . . add 3-8x

x = 7 . . . . . . . . . . . . . . . . . . divide by 4

3x +13 = 3·7 +13 = 34

∠EBC = 34°

__________

∠FBC = ∠CBE

10x -9 = 4x +15 . . . . . substitute given values

6x = 24 . . . . . . . . . . . .add 9-4x

x = 4 . . . . . . . . . . . . . . divide by 4

∠FBC = (10·4 -9)° = 31°

∠FBE = 2·∠FBC = 2·31°

∠FBE = 62°

__________

∠1 +∠2 = 90°

(7x -19) +(x +5) = 90 . . . . . . substitute the given values

8x -14 = 90 . . . . . . . . . . . . . collect terms

8x = 104 . . . . . . . . . . . . . . . add 14

x = 13 . . . . . . . . . . . . . . . . . . divide by 8

∠2 = (13 +5)°

∠2 = 18°

__________

∠1 = ∠4

6x +25 = 10x -11 . . . . substitute the given values

36 = 4x . . . . . . . . . . . add 11-6x

9 = x . . . . . . . . . . . . . .divide by 4

∠1 = (6·9 +25)°

∠1 = 79° . . . . . . matches your answer

Try this option (this is not the only way!):

1. the rule: if 'number_1' - 'number_2' > 0, then number_1>number_2. If 'number_1'-'number_2'<0, then number_2>number_1.

2. according to the rule above: 9.36-9.359=0.001. 0.001>0, it means, 9.36>9.359.

x | - 8 - 4 0 4 8

y | 28 16 4 - 8 - 20

to calculate the values of y, substitute the given values of x into the equation

x = - 8 : y = (- 3 × - 8 ) + 4 = 24 + 4 = 28

x = - 4 : y = (- 3 × - 4 )+ 4 = 12 + 4 = 16

x = 0 : y = (- 3 × 0 ) + 4

0 + 4 = 4

x = 4 : y = (- 3 × 4 ) + 4 = - 12 + 4 = - 8

x = 8 : y = (- 3 × 8 ) + 4 = - 24 + 4 = - 20

Answer:

She would have to work for 33 hours.

Step-by-step explanation:

239.25/7.25=33. Since we are going with hours, this would be 33.

[tex] a^2+16^2=20^2[/tex]

[tex] a^2+256=400[/tex]

Subtracting 256 from both sides

[tex] a^2=144[/tex]

Taking squareroot both sides

[tex] a= \sqrt144[/tex]

[tex] a = \sqrt2.2.3.2.2.3[/tex]

[tex] a=12[/tex]

Therefore length of missing leg is

[tex] a = 12 units[/tex]

a^2+16^2=20^2

a^2+256=400

Subtracting 256 from both sides

a^2=144

Taking squareroot both sides

a= \sqrt144

a = \sqrt2.2.3.2.2.3

 a=12

Therefore length of missing leg is  

a = 12 units

The obvious one is (310 beats)/(1 minute).

To have equal numbers of bowls and cups, Randy should buy 4 packs of bowls and 3 packs of cups, as the least common multiple of 6 (number of bowls per pack) and 8 (number of cups per pack) is 24.

If Randy needs an equal number of bowls and cups for his picnic and one pack consists of 6 bowls and another pack consists of 8 cups, the least common multiple (LCM) of 6 and 8 must be found to ensure an equal number of both items. The LCM of 6 and 8 is 24, because 24 is the smallest number that both 6 and 8 can divide evenly into. Therefore, Randy will need to buy 4 packs of bowls (4 packs × 6 bowls per pack = 24 bowls) and 3 packs of cups (3 packs × 8 cups per pack = 24 cups) to have an equal number of each for his picnic.

29°

Consider the right triangle between the plank and the ground

the angle can be found using tangent ratio

tanx° = [tex]\frac{opposite}{adjacent}[/tex]

where adjacent = 18 and opposite = 10

tanx° = [tex]\frac{10}{18}[/tex]

x = [tex]tan^{-1}[/tex]([tex]\frac{10}{18}[/tex]) = 29.0546 ≈ 29°

Answer:

29 degrees to nearest degree.

Step-by-step explanation:

This is the angle whose tangent is  10/18 or 5/9.

this = 29 degrees

The third side of a triangle must always be less than the sum of the other 2 sides

here 8 + 8 = 16 and 17 ( the third side ) 17 > 16

Hence this is not a valid triangle

15.0 ( to the nearest tenth )

calculate the distance (d) using the distance formula

d = √(x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (7, - 4 ) and (x₂, y₂ ) = (- 8, - 5 )

d = √(-8 - 7 )² + (- 5 + 4 )² = √(225 + 1 ) = √226 ≈ 15.0

Here, we need to write the length of the insect in scientific notation.

The given length of the insect is 0.0052 meter

Now, to write 0.0052 meter in scientific notation we need to follow this:

Scientific notation always start with non-zero digit followed by a decimal point.

Since in our number the decimal is needed to be moved three places to the right to get the first non-zero digit.

The exponent of the 10 is [tex]-3[/tex].

[tex]10^{-3}=\frac{1}{1000} =0.001[/tex]

Therefore, our number 0.0052 can be written as:

[tex]5.2 \times 10^{-3}[/tex]

Hence, the require scientific notation is [tex]5.2 \times 10^{-3}[/tex].

Step-by-step explanation:

A triangle can be of many types like right angled triangle, isosceles triangle, scalene triangle, obtuse, acute etc.

A right angle can be defined as the triangle in which one of the angle is 90 degrees.

An obtuse angle is that type of triangle in which the the angle is more than 90 degrees and less than 180 degrees.

An isosceles triangle is one in which two sides are equal.

An acute angle is the triangle in which the angle is less than 90 degrees.

The attached triangle is :

1. Right angle triangle

2. Isosceles triangle

∠1 and ∠2 are alternate exterior angles where transversal BE crosses parallel lines AC and DF, therefore they are equal. ∠2 and ∠3 are opposite angles of a parallelogram, therefore they are equal.

... ∠1 = ∠2

... 3x -5 = 2x +15 . . . . substitute the given values

... x = 20 . . . . . . . . . . . add 5-2x

The measures of angles 1, 2, and 3 are 2·20+15 = 55 . . . degrees.

Answer:

8 2/35 miles per hour

Step-by-step explanation:

We are given distance traveled and the time required. We can use those directly in the relation that gives speed:

speed = distance / time

... = (18 4/5 miles)/(2 1/3 hours)

... = (94/5 miles)/(7/3 hours) . . . . . . converte mixed numbers to improper fractions

... = (94/5×3/7) miles/hour . . . . . . . "invert and multiply"

.. = 282/35 miles/hour . . . . . . . . . . improper fraction result

... = 8 2/35 miles/hour . . . . . . . . . . as a mixed number

let Leo's speed = x mile/hr

so Ethan speed = (x + 6) miles per hour

Distance = Speed × Time

so distance traveled by Leo in 2 hours = x × 2 = 2x

and distance traveled by Ethan in 1.5 hours = 1.5( x + 6 ) = 1.5x + 9

since  they meet on the path , After Ethan has ridden 1.5 hours and Leo has ridden 2 hours , so together the have traveled on complete path that is 65 miles.

⇒  distance traveled by leo in 2 hours + distance traveled by Ethan in 1.5 hours = 65

⇒  2x + 1.5x + 9 = 65

⇒ 3.5x = 56

⇒ x = 16

Hence Leo's speed = x miles/hr = 16 miles/hour

and Ethan's speed = (x + 6) miles/hr = 16 +6 = 22 mile/hour

Answer:

Leo's Speed = 16

Ethan's Speed = 22

Step-by-step explanation:

The third angle of the triangle will be the supplement of the sum of the given angles. In order for the triangle to be isosceles, two of the three angles must have the same value.

a) 180 -40 -75 = 65 . . . not isosceles

b) 180 -30 -100 = 50 . . . not isosceles

c) 180 -35 -70 = 75 . . . not isosceles

d) 180 -50 -80 = 50 . . . matches one of the other angles. This triangle is isosceles.

The appropriate choice is ...

... 50 and 80

The first question probably has a drawing that is not included. Can you please include whatever drawing cam with it?

The Qeustion 2:

starting with writing the complementary angles:

The angles <a and <b being complementary means that

<b = 180 - <a

The angles <b and <c are complementary - that means

<c = 180 - <b

now plug in the first equation for <b to get:

<c = 180 - (180 - <a) = 180-180+<a= <a

so

<c = <a

which was to be proved!

Answer:

1) B. 88

2) C. If 60 students read four books, then 120 students read two books.

Step-by-step explanation:

1) Solution

Step 1: Let "x" be the 5th test score.

Scores upto the 4th tests = 4*78 = 312

Step 2: Mean of the five tests = 80

(x + 312)/5 = 80

x + 312 = 80*5

x + 312 = 400

Step 3: Now find the value of x.

x = 400 - 312

x = 88

Therefore, Jacob scored 88 in the 5th test.

2) Solution

Step 1: 60 students read four books.

Now find the number of students.

Percentage of students read four books = 12% = 0.12

Total number of students = 60/0.12 = 500

Percentage of students reads two books = 24% = 24/100 = 0.24

Number of students read two books = 0.24*500

= 120

Hope you will understand the concept.

Thank you.

Hello,

Please, see the attached files.

Thanks.

The equation would be 4y=5x       4(x+15)=5x             x+15=y

let x be the amount that Shelia deposits each time

let y represent the amount that Sherri deposits each time

4(x+15)=5x

4x+60=5x

-4x       -4x

60=x

Check:

x+15=y                  60+15=y                        y=75

4(75)=5(60)

300=300

Shelia deposits $60 each time.

DERIVAR :

(2x – 1) / √ x2 + 1

Try this option:

1) to difine the equations of the lines given in the picture. They are: y= -0.5x+2 (for the left line, see the attached picture) and y=2x-3 (for the right line).

2) according to the condition (dark area and type of the line) the 1st inequation is y≥ -0.5x+2, the 2d inequation is y>2x-3.

3) the required system is

[tex]\left \{ {{y>2x-3} \atop {y\geq -0.5x+2}} \right.[/tex]

[tex]x=0.\overline{37}\\\\100x=37.\overline{37}\\\\100x-x=37.\overline{37}-0.\overline{37}\\\\99x=37\\\\x=\dfrac{37}{99}[/tex]

Answer:

216

Step-by-step explanation:

9 * 6 = 54

54 * 8 = 432

432/2 = 216 is the answer

The volume of a triangular prism is the area of the base multiplied by the height. This can be represented as volume = base × height

Let's first identify our values:

9 m = height of the prism

6 m = base of the triangle

8 m = height of the triangle

First, we need to calculate the area of the triangle. To calculate the area of a triangle, the formula is base × height ÷ 2.

The base of the triangle is 6 and the height of the triangle is 8 so 6 multiplied by 8 will give us a product of 48. Next, we need to divide 48 by 2 and we will get a quotient of 24.

Finally, we need to multiply the area of the triangle by the height of the prism.

24 × 9 = 216

Therefore, the volume of the triangular prism is 216[tex]m^{3}[/tex]

Answer:

a = 4.762203156

Step-by-step explanation:

Given:

ab^4 = 12 and a^5b^5 = 7776

Making the equations a subject of a;

a = 12/b^4 and a^5 = 7776/b^5

Finding fifth root on both sides of equation two;

a = [tex]\sqrt[5]{7776}[/tex]/b

You will get a = 6/b

Equating the two equations;

12/b^4 = 6/b

Multiplying both sides by b^4 gives:

b = [tex]\sqrt[3]{2}[/tex] = 1.25992105

We had that a = 12/b^4 so;

a = 12/1.25992105^4 = 12/2.5198421 = 4.762203156

i think it will be c not really 100 percent sure

Answer:

C 767

Step-by-step explanation:

2031 ÷ 3 = 767

and took test

The open circle at 3.75 and the arrow pointing left represents the values of x that are less than 3.75.

To graph [tex]\(x < \frac{17}{5} + \frac{7}{20}\)[/tex] on a number line, we'll first simplify the expression:

[tex]\(\frac{17}{5} + \frac{7}{20}\)[/tex]

To add these fractions, find a common denominator, which in this case is 20:

[tex]\(\frac{17}{5} = \frac{17 \times 4}{5 \times 4} = \frac{68}{20}\)[/tex]

Now, add the fractions:

[tex]\(\frac{68}{20} + \frac{7}{20} = \frac{75}{20}\)[/tex]

So, the expression simplifies to [tex]\(x < \frac{75}{20}\)[/tex].

To simplify [tex]\(\frac{75}{20}\)[/tex]:

[tex]\(75 \div 20 = 3.75\)[/tex]

This means the inequality is [tex]\(x < 3.75\)[/tex].

Now, to graph this on a number line, mark a point at 3.75, but as it is "less than" <, make sure to have an open circle at 3.75, indicating that it does not include the value itself. Then, draw an arrow to the left, signifying all values less than 3.75.

```

0-------------------o-------------------3.75------------------->

```

Here, the open circle at 3.75 and the arrow pointing left represents the values of x that are less than 3.75.

Learn more about fractions here:
https://brainly.com/question/78672

#SPJ6

Moving from -2 to 4 is a gain of 6 in the x-direction and a drop of 8 in the y-direction.  Thus, the slope of this line is m = -8/6, or m = -4/3.

Then, using the point-slope formula, y - 0 = (-4/3)(x-4), or y = (-4/3)x + 16/3

y=-1 1/3x+5 1/3

I hope this helps

The student’s total percent of all successful quizzes for the entire year is 72%.

To determine the percent of all successful quizzes for the entire year, we need to follow these steps:

Calculate the number of quizzes passed so far: The student has passed 60% of 20 quizzes. This is calculated as follows:

0.60 x 20 = 12 quizzes passed.

Determine the number of quizzes remaining: The student needs to write 50 quizzes in total, so the remaining quizzes are 50 - 20 = 30 quizzes.

Calculate the number of additional quizzes passed: The student is expected to pass 80% of the remaining quizzes.

0.80 x 30 = 24 quizzes passed.

Calculate the total number of quizzes passed: Add the quizzes passed so far to the additional quizzes passed.

12 + 24 = 36 quizzes passed in total.

Determine the percentage of successful quizzes for the entire year: Divide the total number of successful quizzes by the total number of quizzes.

(36 / 50) x 100 = 72% successful quizzes.

Thus, the student’s total percent of all successful quizzes for the entire year is 72%.