Use the graph of the function to find its domain and range. Write the domain and range in interval notation

The area of a trapezium with base 8 top 6 height 4 is 28 cm².

Given that, base of trapezium (b)=8 cm, top of trapezium (a)=6 cm and height of trapezium = 4 cm.

What is the area of a trapezium?

The trapezium is a quadrilateral with pair of sides parallel. The area of a trapezium is the area enclosed within its four sides.

We know that area of a trapezium [tex]=\frac{1}{2}(a+b) \times h[/tex]

Where a and b are parallel sides of a trapezium.

Now, the area of a given trapezium [tex]=\frac{1}{2}(6+8) \times 4[/tex] cm²

=14×2=28 cm²

Therefore, the area of a trapezium with base 8 top 6 height 4 is 28 cm².

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The Graph B  best represents a parabola , Option D has the correct data points and so is the right answer.

A function is a mathematical way of representing relation between two variables.

The function given is

y = 2x²

For x = - 2, y = -2(- 2)² = -8

For x = - 1, y = -2(- 1)² = -2

For x = 0, y = -2(0)² = 0

For x = 1, y = -2(1)² = -2

For x = 2, y = -2(2)² = -8

the  table of x-y will be:

x  - 2    - 1    0    1    2

y    -8     -2   0  -2   -8

The graph is attached with the answer.

The parabola opens downward and has the data points as mentioned above .

Therefore Option D is the correct answer.

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Answer:

Step-by-step explanation:

Complete the following table using the equation: y = 2 x squared

x

-2

-1

0

1

2

y

Plot the points on a graph and determine which graph best represents the equation.

Graph A

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

Graph B

On a coordinate plane, a parabola opens down and goes through (negative 1, negative 2), has a vertex at (0, 0), and goes through (1, negative 2).

a.

8, 2, 0, 2, 8; Graph A

b.

-8, -2, 0, -2, -8; Graph A

c.

8, 2, 0, 2, 8; Graph B

d.

-8, -2, 0, -2, -8; Graph B

Please select the best answer from the choices provided

A

B

C

D

   answer is '' a '  got it right

Example:

[tex](f+g)(x)=f(x)+g(x)[/tex]

To add this, we can substitute in the functions and combine like terms.

We're given:

Add k to k:

[tex](k+k)(x) = k(x)+k(x)\\(k+k)(x) = 5x-6+5x-6\\(k+k)(x) = 10x-12[/tex]

Input x as 4:

[tex](k+k)(4) = 10x-12\\(k+k)(4) = 10(4)-12\\(k+k)(4) = 40-12\\(k+k)(4) = 28[/tex]

[tex](k+k)(4)=28[/tex]

(k+k)(4) is equivalent to 28.

If we have two non-empty sets X & Y, then each element of X is relative to at least one element of Y. This relation between elements of two sets is called function.

Addition of two functions : If f(x) & g(x) be two functions, then

(f+g)(x) = f(x)+g(x)

Given, k(x) = 5x-6

Now, Adding function k with k we get,

(k+k)(x) = k(x)+k(x)

           = (5x-6)+(5x-6)

           = 5x-6+5x-6

           = 10x-12

We have to find, (k+k)(4)

∴  (k+k)(4) = (10×4)-12

                = 40-12

                = 28

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Answer:

y=5x+13

Step-by-step explanation:

when x=-3, y=-2, and when x=-2,  y=3. we know that every time x increases by 1, y also increases by 5. This means that the slope is 5. to find the y-intercept, we need x to be 0. to find that, increase x by 2. if x increases by 2, then y would also increase by 10. add 10 to 3 and add 2 to -2 to get x=0 and y=13. the coordinates would be (0,13). the y-intercept is 13. now that we have enough information, we can conclude that y=5x+13. To check your answer, plug in the values for x.

Step-by-step explanation:

[tex] \frac{5 {}^{ - 4x + 7} }{125 {}^{x} } [/tex]

[tex] \frac{5 {}^{ - 4x + 7} }{5 {}^{3x} } [/tex]

[tex]5 {}^{ - 4x + 7 - 3x} [/tex]

[tex]5 {}^{ - 7x + 7} [/tex]

Answer:

The domain is-3<x<3. It can also be (-∞,-3) U (-3,3) U (3, ∞).

Step-by-step explanation:

The U stands for Union. The second  answer usually used only for college algebra.

Answer:

  -5

Step-by-step explanation:

Substituting x=4 into the equation gives a 2-step linear equation in y. It is solved by isolating the variable and making its coefficient be 1.

__

When x=4, the equation becomes ...

  -3x +9y = -57

  -3(4) +9y = -57

  -12 +9y = -57

The first step is to "isolate" the variable term (9y) by adding the opposite of the constant that is on the same side of the equation. The result is that the variable term is by itself on one side of the equal sign.

  -12 +12 +9y = -57 +12 . . . . . add the opposite of -12

  9y = -45 . . . . . . . . . . . . . . simplify

The second step is to make the coefficient of y be 1. We do that by multiplying by its inverse, 1/9. Equivalently, we divide by 9.

  (1/9)(9y) = (1/9)(-45) . . . . multiply by the inverse of 9

  y = -5 . . . . . . simplify

Step-by-step explanation:

Anything which has a decimal point is not a whole number

6830 is

66 is

717.59 is not

808 is

42.3 is not

1/10 = 0.1 ergo is not

Answer: It rounds to 28 km

Explanation:

The units or ones digit is "7". The next digit over (9) is five or larger. This means we bump the 27 up to 28. Everything after the 7 is ignored.

So we could have something like 27.999871212512 and we still follow the same idea of focusing on the 27, bumping it up to 28, and everything else gets ignored.

The reason for this is because 27.9 is much closer to 28 than it is to 27. Draw out a number line to help see this. Split the region from 27 to 28 into 10 equal pieces. The 9th little piece represents 27 & 9/10 aka 27.9

Refer to the number line diagram below.

Answer:

D.

Step-by-step explanation:

Answer:

1000 pencils = $ 20.

10 pencils = ?

10 * 20 / 1000

200/1000

2/10

1/5

0.5.$

Answer:

$0.20

Step-by-step explanation:

If 1000 pencils cost $20, then we must first find the unit rate.

20/1000 = 0.02, so it costs $0.02 for each pencil. To find out what ten pencils cost, we multlipy 0.02 by 10.

0.02 * 10 = 0.2, or $0.20.

Brainliest, please :)

Answer:

that makes no sence at all i read it over 3 times and still font understand a word of it

sorry :(

We can rewrite the equation of the given line to be in slope-intercept form as follows.

[tex]x-y=7\\x=y+7\\y=x-7[/tex]

Thus, the slope of the given line is 1.

Since parallel lines have equivalent slopes, the slope of the line we want to find is also 1.

Substituting into point-slope form,

[tex]y-0=1(x-1)\\\\\boxed{y=x-1}[/tex]

Answer:

1)  x + 96 = 90°

2)  x + 89 = 80°

Step-by-step explanation:

Consecutive Interior Angles Theorem

When a transversal line intersects two parallel lines, it forms two pairs of consecutive angles on either side of the transversal line.  Each pair of consecutive interior angles are supplementary (sum to 180°).

To find the measure of the angle circled on the diagram, find the value of x by using the Consecutive Interior Angle Theorem:

⇒ (x + 96)° + (x + 96)° = 180°

⇒ x + 96 + x + 96 = 180

⇒ 2x + 192 = 180

⇒ 2x + 192 - 192 = 180 - 192

⇒ 2x = -12

⇒ 2x ÷ 2 = -12 ÷ 2

⇒ x = -6

Substitute the found value of x into the expression to find the measure of the angle circled on the diagram:

⇒ x + 96 = -6 + 96 = 90°

⇒ x + 96 = 90°

To find the measure of the angle circled on the diagram, find the value of x by using the Consecutive Interior Angle Theorem:

⇒ (x + 109)° + (x + 89)° = 180°

⇒ x + 109 + x + 89 = 180

⇒ 2x + 198 = 180

⇒ 2x + 198 - 198 = 180 - 198

⇒ 2x = -18

⇒ 2x ÷ 2 = -18 ÷ 2

⇒ x = -9

Substitute the found value of x into the expression to find the measure of the angle circled on the diagram:

⇒ x + 89 = -9 + 89

⇒ x + 89 = 80°

Answer:

[tex]\boxed {1) 90^{o}}\\\boxed {2) 80^{o}}[/tex]

Step-by-step explanation:

Part 1 :

Part 2 :

Answer:

Step-by-step explanation:

Givens

r = 14 miles / hour

Problem

Convert to feet per second.

Solution

Later on, you will learn how to solve these kinds of conversion problems using a method called Unit Analysis. Since you likely have not been taught this method, will just use proportions.

1 mile = 5280 feet

14 miles = x                          Cross multiply

x = 14 * 5280                       Simplify

x = 73920 feet

1 hour = 3600 seconds

Answer

r = 73920 feet / 3600 seconds

r = 20.533 feet  / secpmd

Answer:

Step-by-step explanation:

The area of the rectangular garden given the length and width is 16 1/2 square feet

Area of a rectangular garden = length × width

= 5 1/2 feet × 3 feet

= 11/2 × 3

= 33/2

= 16 1/2 square feet

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Answer:

[tex]3^2=x+5[/tex]

Step-by-step explanation:

Given equation:

[tex]\log_3(x+5)=2[/tex]

Method 1

[tex]\textsf{Using the Log law:} \quad \log_ab=c \:\: \Longleftrightarrow \:\: a^c=b[/tex]

[tex]\implies \log_3(x+5)=2[/tex]

[tex]\implies 3^2=x+5[/tex]

Method 2

Make both sides of the equation the index to base 3:

[tex]\implies \log_3(x+5)=2[/tex]

[tex]\implies 3^{\log_3(x+5)}=3^2[/tex]

Apply the log law [tex]a^{\log_ax}=x[/tex] :

[tex]\implies x+5=3^2[/tex]

Swap sides:

[tex]\implies 3^2=x+5[/tex]

Solve for x

Although the question hasn't asked to solve for x, here is the solution:

[tex]\implies 3^2=x+5[/tex]

[tex]\implies 9=x+5[/tex]

[tex]\implies x=9-5[/tex]

[tex]\implies x=4[/tex]

Check

Substitute the found value of x into the original equation:

[tex]x=4 \implies \log_3(4+5)=\log_39=2 \quad \leftarrow\textsf{correct}[/tex]

[tex]\\ \rm\Rrightarrow log_3(x+5)=2[/tex]

[tex]\\ \rm\Rrightarrow x+5=3^2[/tex]

[tex]\\ \rm\Rrightarrow x+5=9[/tex]

[tex]\\ \rm\Rrightarrow x=9-5[/tex]

[tex]\\ \rm\Rrightarrow x=4[/tex]

Work Shown:

|x+2| + 7 > 10

|x+2| > 10-7

|x+2| > 3

x+2 > 3 or x+2 < -3

x > 3-2 or x < -3-2

x > 1 or x < -5

The graph for x > 1 has an open circle at 1 and shading to the right.

The graph for x < -5 has an open circle at -5 and shading to the left

Both of these facts combine to describe Choice C

In other words, we have open circles at -5 and 1, with nearly everything shaded except for the region between the open circles.

The open circles are used to exclude those x values mentioned.

The function g(x) is derived by translating the function by the three units, according to the graph.The equation for the red graph will be,g(x) = x²+3

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

From the graph, it is obtained that the function g(x) is obtained by translating the function by the three units.

Hence,the equation for the red graph will be,g(x) = x²+3

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Answer:

1/7

Step-by-step explanation:

Alternative Form: 0.142857, 7^-1

Answer:

1

Step-by-step explanation:

49 is divisible by 7, 1, 49. 25 is divisible by 5, 1, 25. they are exclusively prime so the highest factor is 1 and the only

Answer:

Step-by-step explanation:

[tex]25x^4-49y^2=(5x^2)^2-(7y)^2\\=(5x^2+7y)(5x^2-7y)\\=(5x^2+7y)[(\sqrt{5} x)^2-(\sqrt{7y} )^2]\\=(5x^2+7y)(\sqrt{5} x+\sqrt{7y} )(\sqrt{5} x-\sqrt{7y} )[/tex]

The equivalent expression to ∑n(n+1) is ∑n²+∑n.

Equivalent expressions are defined as algebraic expressions which give the same resulting expression. An algebraic expression (or) a variable expression is defined as a combination of terms by the operations such as addition, subtraction, multiplication, division.

Here, given expression;

       ∑(n(n+1))

     = ∑ (n² + n)

     = ∑n²+∑n

Thus, the equivalent expression to ∑n(n+1) is ∑n²+∑n.

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Yes, by using the factor theorem and synthetic division method, x + 3 is a factor of -x³ + 4x - 15.

According to the factor theorem, a given polynomial of f(x) has a factor if and only if f=0.

From the given information:

Using the synthetic division method:

[tex]\mathbf{= \dfrac{-x^3+4x - 5}{x+3} }[/tex]

[tex]\mathbf{\implies \dfrac{-(x+3) (x^2-3x + 5)}{x+3} }[/tex]

Cancel out the common factors, we have:

[tex]\mathbf{\implies - (x^2-3x + 5)}[/tex]

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Answer:

Its A

Step-by-step explanation:

I said so

Answer:

445

Step-by-step explanation:

I think it is 445 because each term is +1 and time is the number of terms you want to find.

So

(2+1) time 2 = 6

(6+1) time 3 = 7

(88+1)  time 5 = 445

Answer:

$21.25

Step-by-step explanation:

The cost of the 2 adult tickets before the discount is $8 * 2 = $16

The cost of the 2 child tickets before the discount is $5 * 2 = $10

The total cost before the discount is $16 + $10 = $26

The total cost after the discount is

$26 * (1 - 0.15) =

$26 * 0.85 =

$21.25

The long leg and the hypotenuse of the isosceles right triangle will be 7.07 units.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The short leg of a 90-45-45 triangle is 5.

The right triangle is an isosceles right triangle. Then the two side will be same.

Then the long leg and the hypotenuse will be

H² = 5² + 5²

H² = 25 + 25

H² = 50

H = 7.07 units

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Answer: Yes.

Step-by-step explanation: However, charging your battery to high voltages except for the first time can significantly decrease your battery's lifespan. According to some studies charging a battery to only 85% to 90% can improve its discharge cycle from 300 to even an extra 1000 recharges.