STATE THE DOMAIN OF EACH OF THE FOLLOWING RELATIONS.

1.7) {(x, y): x = root y}
Domain ………

1.8) {(r, s): s = (2r -5)/13r }
Domain ………

1.9) {(a, b): ab = 12}
Domain ………​

Answer:

see explanation

Step-by-step explanation:

Where the graph crosses the x- axis the y- coordinate is zero.

Let y = 0 in the equation and solve for x

- 4(0) = 15 - 5x, that is

15 - 5x = 0 ( subtract 15 from both sides )

- 5x = - 15 ( divide both sides by - 5 )

x = 3 ← x- intercept ⇒ (3, 0 )

Where the graph crosses the y- axis the x- coordinate is zero.

Let x = 0 in the equation and solve for y

- 4y = 15 - 5(0), that is

- 4y = 15 ( divide both sides by - 4 )

y = - [tex]\frac{15}{4}[/tex] ← y- intercept ⇒ (0, - [tex]\frac{15}{4}[/tex])

Answer:

45

Step-by-step explanation:

(6 + 3i)(6 − 3i) =6 (6 − 3i)+ 3i(6 − 3i)

= 36 -18i +18i-9[tex]i^{2}[/tex]

if [tex]i^{2} =-1[/tex]

36 -18i +18i-9[tex]i^{2}[/tex] = 36-9(-1)

=36+9

=45

=36-9i^2

=6^2 - (3i)^2

Answer:

[tex]\displaystyle 45[/tex]

Step-by-step explanation:

[tex]\displaystyle (6 + 3i)(6 - 3i) = 36 - 9i^2 = 36 - 9[-1] = 36 + 9 = 45[/tex]

Extended Information on the Complex Number System

[tex]\displaystyle \sqrt{-1} = i \\ -1 = i^2 \\ -i = i^3 \\ 1 = 4\:[Any\:multiple\:of\:four][/tex]

I am joyous to assist you anytime.

Answer:

2^6

Step-by-step explanation:

2 is being multiplied 6 times meaning it would be 2 to the 6th power.

Answer:

x² - 8x + 12 = 0

(x - 6)(x - 2) = 0

x = 2, 6

f(4) = -4

Plot (0, 12), (2, 0), (4, -4), (6, 0), and (8, 12) on the graph. Then draw a smooth curve that goes through these points.

Answer:

4^5x-5

Step-by-step explanation:

4^5x-7/4^-2

=4^5x-5

The expression 4⁵ × 4⁻⁷ divided by 4⁻² simplifies to 1 by using the properties of exponents. First, add the exponents in the numerator, then subtract the exponents for division, resulting in 4⁰, which equals 1.

We need to simplify the expression:

4⁵ times 4⁻₇ ext{ divided by } 4⁻²

To simplify, let's first combine the powers of 4 in the numerator:

= 4⁵ times 4⁻⁷

= 4⁽⁵⁺⁽⁻⁷⁾⁾

= 4⁻²

= 4⁻² ext{ divided by } 4⁻²

= 4⁽⁻²⁻⁽⁻²⁾⁾

= 4⁽⁻²⁺²⁾

= 4⁰

4⁰ = 1

Therefore, the given expression simplifies to 1.

it will surely look like an angle on a straight line. which adds up.to 180,so the answer is horizontal angle at 180degrees

Final answer:

The correct answer is A. Straight angle at 180°, describing the angle formed when a laptop screen is moved from a 90° position to lying flat against the desk.

Explanation:

The question asks about the angle formed when a laptop screen is opened from a right angle (90°) to lying flat against the desk, covering a full range from vertical to horizontal. This describes a straight angle, which measures 180°. Initially, the laptop screen at a 90° angle to the keyboard represents a right angle. Pushing the screen down to lie flat transitions this to a straight angle, where the angle between the keyboard and the back of the screen spans a flat, straight line. Therefore, the correct answer is A. Straight angle at 180°.

Answer:

[tex]\large\boxed{y-3=-(x+4)}\\or\\\boxed{y+4=-(x-3)}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

The formula of a slope:

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

We have two points (-4, 3) and (3, -4).

Substitute:

[tex]m=\dfrac{-4-3}{3-(-4)}=\dfrac{-7}{7}=-1[/tex]

Put the value of a slope and the coordiantes of the point (-4, 3) or (3, -4) to the equation of a line:

for (-4, 3)

[tex]y-3=-1(x-(-4))\\\\y-3=-(x+4)[/tex]

for (3, -4)

[tex]y-(-4)=-1(x-3)\\\\y+4=-(x-3)[/tex]

Answer:

[tex]x^{2} =1, then\ x=1[/tex] is NOT true.

Step-by-step explanation:

1.

[tex]If\ x=1, then\ x^{2} =1[/tex] ......True

( 1 )² = 1

2.

If [tex]x^{2} =1, then\ x=1[/tex] ........ NOT True

∴ x =± 1     .........this is correct

3.

[tex]If\ x=-1, then\ x^{2} =1[/tex] ......True

( -1 )² = 1

4.

x2 = 1 if and only if x = 1 or x = -1. .........True

( 1 )²  = 1

( -1 )² = 1

Answer:

never

Step-by-step explanation:

In a right triangle, every angle has an opposite side and an adjacent side. And there's always a hypotenuse.

The sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.

The tangent ratio of an angle is the opposite side over adjacent side, it is not the sine ratio of a triangle.

For example, ABC is a right angled triangle having length of the sides are a,b,c.

So

[tex]sine\ C=\frac{a}{c}[/tex]

The sine ratio of an angle sometimes is the opposite side over the adjacent side.

The question pertains to the definition of the sine ratio in trigonometry. The sine ratio of an angle is not defined as the opposite side over the adjacent side; rather, it is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse of a right-angled triangle.

Therefore, the correct statement is the sine ratio of an angle sometimes is the opposite side over the adjacent side, specifically in the case of a 45°-45°-90° triangle where the sides are equal, but this is not generally true for all angles in trigonometry.

Answer:

5/63

Step-by-step explanation:

8/9(5/7)(1/8)=

8/9(5/7)=

40/63(1/8)=

5/63

by the way 8/9 x 5/7 x 1/8

is also the same as (8/9)(5/7)(1/8)

To find the product of 8/9, 5/7, and 1/8, multiply the numerators and denominators to get 40/504 and simplify it to 5/63.

To solve the multiplication of fractions, we need to multiply the numerators together and the denominators together. For the expression 8/9 times 5/7 times 1/8, we multiply the numerators 8, 5, and 1 to get 40, and the denominators 9, 7, and 8 to get 504. Simplifying the fraction 40/504 involves finding the greatest common divisor, which is 8 for both numerator and denominator, and dividing them by this number.

Doing so, we get 40 ÷ 8 = 5 and 504 ÷ 8 = 63. Hence, the solution simplified is 5/63.

Answer:

1.5

Step-by-step explanation:

12 divided by 8 = 1.5

1.5 x 8 = 12

Answer:

for #4 x=-7

Step-by-step explanation:

a negative times a negative is a positive and 8 times 7 = 56

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]8z\leq 16[/tex]

Solve for z

Divide by 8 both sides

[tex]z\leq 16/8[/tex]

[tex]z\leq 2[/tex]

The solution for z is the interval ----> (-∞,2]

All real numbers less than or equal to 2

In a number line the solution  is the shaded area at left of z=2 (closed circle)

using a graphing tool

see the attached figure

Answer:

399.409

Step-by-step explanation:

Add both numbers to get your answer.

Answer:

The answer is

399. 409

Answer:

Step-by-step explanation:

96:24

96 divide by 24 = 4

so it would be 4 cars to 1 truck

so 4:1

Answer:

4:1                                                                                                               Explanation: because of how when you divide the two its 4 and there's one truck left

Answer:

x = 7

Step-by-step explanation:

x + 7 = 14

Subtract 7 from both sides

x = 14 - 7 = 7

Answer: the answer is 7

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

Answer:

I am not sure but i think 2

Answer:

False.

Step-by-step explanation:

Because we have to isolate y and subtracting 2 will not put y alone on one side.

We have to subtract 2x in order to solve for y.

Answer:

False

Step-by-step explanation:

To solve this equation 2x + y = 5, you need another pair equation with the same variables, or one of the variables (x or y) need to be known to solve this equation.

Or you need to subtract 2x from both side to make y subject of formula.

Answer:

a = 108° and b = 144°

Step-by-step explanation:

The opposite angles of a rhombus are the same and the sum of all the angles of the rhombus is 360°.

So, from the given diagram of the rhombus we can write  

2b + 2× 36 = 360

⇒ 2b = 360 - 72 = 288

⇒ b = 144° (Answer)

Again, the each angles of a pentagon is given to be a.

Hence, we can write 3a + 36 = 360

⇒ 3a = 324

⇒ a = 108° (Answer)

Answer:

B and E repeat infinitely.

Step-by-step explanation:

A) 6/4  = 1.5 (ends)

B) 4/11  ≈ 0.36363636...  (repeats 36 forever)

C) 9/8  = 1.125 (ends)

D) 5/7  ≈ 0.7143  (does not repeat)

E) 8/9  ≈ 0.88888888...  (repeats 8 forever)

F) 7/8 = 0.875  (ends)

Answer: 10(x+2)

Step-by-step explanation:

Answer:

(x+2) + 10

Step-by-step explanation:

(x+2) is his current age, then you add the 10 years to get your answer.

Answer:

[tex]SA=502.4\ ft^2[/tex]

Step-by-step explanation:

we know that

The surface area of a cone is equal to

[tex]SA=\pi r^{2}+\pi rl[/tex]

we have

[tex]r=8\ ft\\l=12\ ft\\\pi=3.14[/tex]

substitute the given values

[tex]SA=(3.14)(8^{2})+(3.14)(8)(12)[/tex]

[tex]SA=200.96+301.44=502.4\ ft^2[/tex]

Answer:

p=ak^t

p1=491272*k^0

p2=782341*k^10

782341/491272 = k^10

k=1.047629

growth rate is 4.7629%

2012: predicted population is 491272*1.047629^12=858,642 people

1245863=491272*1.047629^t

1.047629^k=2.5363599

ln both sides is k ln 1.0476=ln 2.5363

t=20.000 years.

Rule of 72 would say 72/4.76 or 15.12 years for doubling

14.90 years

2017 predicted is 491272*1.0476^17 or 1083552, or more than actual, so the rate of growth is slowing down.

The required exponential growth rate, k is 4.7629%

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

The exponential function will be as

p=a[tex]k^t[/tex]

p₁=491272*k⁰

p₂=782341*k¹⁰

782341/491272 = k¹⁰

k = 1.047629

So, the growth rate is 4.7629%

2012: the predicted population is 491272 × 1.047629¹² =858,642 people

1245863=491272 × [tex]1.047629^t[/tex]

[tex]1.047629^k[/tex] = 2.5363599

ln both sides is k ln 1.0476 = ln 2.5363

t = 20.000 years.

Rule of 72 would say 72/4.76 or 15.12 years for doubling

14.90 years

2017 predicted is 491272 × 1.0476¹⁷ or 1083552, or greater than the real rate of increase, hence the rate of growth is decreasing.

Learn more about exponential function here:

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Answer:

Your answer is B: F(x)=(x-1)(x-1)(x-1)(x+1)

Answer:

The answer is 41/4.

Step-by-step explanation:

Given:

-41/4 to get the additive inverse.

Now, the additive inverse of any number is a number that, when added to the number the result is zero.

Here, 41/4 is the additive inverse.

Because when it is added to -41/4 the result is 0.

Therefore, the answer is 41/4.

Answer:

-216

Step-by-step explanation:

Negative times positive is negative.

27 * 8 = 216

Answer is negative, so

-27 * 8 = -216

Answer:

-216

Step-by-step explanation:

Write the problem as a mathematical expression. ( − 27 ) ⋅ ( 8 )

multiply -27 by 8

About 2% chance.

There are ten numbers and you want to choose a number less than three. There are only two numbers less than three; 1 & 2. Because there are only 2 numbers less than three and 10 to choose from, it becomes a 2% chance.

Answer: 20%

Step-by-step explanation:

[tex]\text{Hey there!}[/tex]

[tex]\text{The \bf{product}}\text{ of 8 and 12 is [blank]}[/tex]

[tex]\text{Whenever you see the word \bf{product}}\text{ in mathematics, it usually means}\\\text{multiply}[/tex]

[tex]\text{\bf{The PRODUCT of 8 and 12 is 96 because 8 times 12 equal 96}}[/tex]

[tex]\boxed{\boxed{\huge{\text{\bf{Answer: 96}}}}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Step-by-step explanation:

Hello!

Product means to multiply.

Which means it’s x added by itself y times.

For this problem it means 8 added by itself 12 times.

You can do:

8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8, which equals 96.

Or, 8 x 12.

Which is 96.

It still represents 8 + 8, etc.

But your doing it faster.

Therefore, your Product is 96.

Answer:

B

Step-by-step explanation:

Each box of cookies is $3 since 4 x 3 =12, 6 x 3 = 18, and 9 x 3 = 27. So we want to multiply the number of boxes, b, by 3 to get the cost, c. The correct equation is c = 3b.

An equation that models this situation is c = 3b. The correct option is B.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given the data is,

b     c

4     12

6     16

9     27

c = kb

12 = k x 4

k = 12 / 4 = 3

c = 3b

Therefore, the equation that models this situation is c = 3b. The correct option is B.

To know more about an expression follow

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