What is the equation of the graph below?

Answer:

162 kg

Step-by-step explanation:

135 + .2(135) = is the elephant's weight now

135 + 27 = 162 kg

Answer:

20% of 135 is 27 so you just add that to the original weight and you would get 162kg!

Step-by-step explanation:

Hope it helps! =D

Answer: A $14 dollar meal with a 20% tip would be $16.80. The tip would be $2.80.

Step-by-step explanation:

People generally tip 15-20% of the bill. To calculate the tip multiply the total check by 1 plus the decimal percentage tip you'd like to leave. If you wanted to leave a 20% tip, you would add 1 to 0.20 to get 1.20. Multiply 14 by 1.20 to get the total amount you'd leave including the tip which would be $16.80.

Hope this helps!

For item a, the linear functions are given as follows:

1. y = 1.5x.

2. y = 0.5x - 1.

3. y = -0.5x + 1.

4. y = -1.5x - 1.

For item B, we have that:

1. The functions are:

a. y = 2x + 3.

b. y = 0.5x - 1.

2. The unit rates(slopes) are:

a. 2

b. 0.5.

A linear function is modeled by:

y = mx + b

In which:

In graph 1, the function goes through (0,0), hence b = 0, and through point (2,3), hence the slope is:

m = (3 - 0)/(2 - 0) = 3/2 = 1.5.

Hence the function is:

y = 1.5x.

In graph 2, the function goes through (0,-1), hence b = -1, and through point (2,0), hence the slope is:

m = (0 - (-1))/(2 - 0) = 1/2 = 0.5.

Hence the function is:

y = 0.5x - 1.

In graph 3, the function goes through (0,1), hence b = 1, and through point (2,0), hence the slope is:

m = (0 - 1)/(2 - 0) = -1/2 = -0.5.

Hence the function is:

y = -0.5x + 1.

In graph 4, the function goes through (0,-1), hence b = -1, and through point (2,-4), hence the slope is:

m = (-1 - (-4))/(0 - 2) = -3/2 = -1.5.

Hence the function is:

y = -1.5x - 1.

In table a, the function goes through (0,3), hence b = 3, and through point (1,5), hence the slope is:

m = (5 - 3)/(1 - 0) = 2.

Hence:

y = 2x + 3.

The unit rate, which is the slope, is of 2.

For table b, the function goes through (2,0) and (6,2), hence the slope is:

m = (2 - 0)/(6 - 2) = 1/2 = 0.5.

Hence:

y = 0.5x + b.

When x = 2, y = 0, hence we can find b as follows.

0 = 0.5(2) + b

b = -1.

Thus:

y = 0.5x - 1.

The unit rate is of 0.5.

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If the variation is direct, then the value of y decreases with a decrease in x and increases when x increases.

On the other hand side, if we are following inverse variation then the value of y will decrease if x increases and increase if x decreases.

If there is a constant k that is nonzero and such that y = kx, then the variable y fluctuates directly as x. The expression y = kx is referred to as a direct variation equation, and the variable constant is denoted by the number k.

A function with the following equation as its definition is known as an inverse variation: xy = k , where k is a constant real integer that is not zero. There are several instances when one quantity changes as another does so indirectly.

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Answer:

y1=-4/3, y2=1/2

Step-by-step explanation:

The value of the expression when a = 6 and b = -4 is -1

The expression is given as

2a/3b

The values are given as

a = 6 and b = -4

Substitute a = 6 and b = -4 in the expression 2a/3b

2a/3b = 2 * 6/3 * --4

Evaluate the products

2a/3b = 12/-12

Evaluate the quotient

2a/3b = -1

Hence, the value of the expression when a = 6 and b = -4 is -1

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Complete question

What is the value of the expression when a = 6 and b = -4? 2a/3b

The given function → f(x) = x⁵ - 3x³ is odd in nature.

A function f(x) is even if f(−x) = f(x) and is odd if f(−x) = − f(x).

Given is the function -

f(x) = x⁵ - 3x³

In order to find f(-x), replace 'x' by '-x' in f(x) -

f(x) = x⁵ - 3x³

f(-x) = (-x)⁵ - 3(-x)³

f(-x) =  - x⁵ + 3x³

f(-x) =  3x³ -  x⁵

Now -

f(-x) ≠ f(x)

So, it is not a even function.

In order to find '-f(x)', multiply f(x) by '-1' -

f(x) = x⁵ - 3x³

- f(x) = - (x⁵ - 3x³) = - x⁵ + 3x³ = 3x³ - x⁵

Now -

f(-x) = -f(x)

So, it is a odd function.

Therefore, the given function → f(x) = x⁵ - 3x³ is odd in nature.

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The error Jacy made was that the hypothesis or if part and the conclusion part was not appropriate . The correct conditional statement is  "If water is below 0°C then water freezes."

Conditional statement is a statement which contain both hypothesis and conclusion . Thus there are two parts in conditional statement, first is the hypothesis part or the if part then the second part is the conclusion part or then part.

According to the question the conditional statement is

  " Water freezes if it is below 0°C."

Which is not correct as the error is that the first part should be hypothesis part or if part and the second part should be the conclusion of the hypothesis.

Hence the correct conditional statement is :

      "If water is below 0°C then water freezes."

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Answer:

A) Vertical angles are congruent

B) 40 and b are vertical angles and c and a are vertical angles.

C) <a = 40

<b = 140

<c = 140

Step-by-step explanation:

A straight angle is a straight line.  It is 180°

The simplified form of given number is 16

We are given the number 64 with exponent ²/₃

Now, as per the known fact, cube of 4 is equal to 64. As, 4 multiplied with 4 gives 16. Further multiplying 16 and 4 gives 64. So, rewriting the number using 4 as follows -

Number = [tex]4^{3(2/3) }[/tex]

Cancelling 3 from exponent as it is present in both numerator and denominator. Rewriting the number with remaining exponent to find the simplified form of the number-

Number =  4²  

Taking square of the number to find the simplified form of the number given in question

Number = 16

Hence, the simplified form of the number is 16

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The inverse of the function f (x) = 15 - 3 x is f ⁻¹ (x) = 5 - x/3 which is also a function.

We are given the function:

f (x) = 15 - 3 x

Now, we need to find the inverse of the function.

For this, first we write the function as:

y = 15 - 3 x

Now, we will find the function in terms of x

3 x + y = 15

3 x = 15 - y

x = 5 - y/3

So, the inverse will become:

f ⁻¹ (x) = 5 - x/3

g (x) = 5 - x/3

Now, for one one function:

g (x₁) = g (x₂)

5 - x₁/3 = 5 - x₂/3

- x₁ / 3  = - x₂ / 3

x₁ = x₂

So, it is one - one.

So, the inverse is also a function as every element of x only has one image in y.

Therefore, the inverse of the function f (x) = 15 - 3 x is f ⁻¹ (x) = 5 - x/3 which is also a function.

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Answer:

Step-by-step explanation:

[tex]\sqrt{25+9}[/tex] =

[tex]\sqrt{34}[/tex] =

≈5,83095    (5,8309518948453)

The image of point Q under the translation at (x,y) -> (x+1,y+2) is (-3,6)

To plot the image of point Q under the translation we need given information.

The translation is given as:

(x,y) -> (x+1,y+2)

The point Q is located at

(-4,4)

So, the image would be:

(x,y) -> (-4+1,4+2)

Evaluate

(x,y) -> (-3,6)

Hence, the image of point Q under the translation at (x,y) -> (x+1,y+2) is (-3,6)

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The lifetime cost of Ellen's dishwater is $1,030.44

What is Number system?

A system of writing to express the number is called number system.

Given that;

Cost of dishwasher before sales tax 9.22% is = $315

And, Sales tax = 9.22%

Hence, Total cost = 315 *( 1 + 0.0922) = 315 * 1.0922 = 344.043

And, Average of 10 times per week for the next 6 years before replacing it.

Since, There are 52 weeks in a year.

So, Average uses is calculated as,

10  * 52  * 6 = 3120

Since, cost for water = $0.09

Cost for electricity = $0.13

Total cost per uses = $0.22

Hence, Cost of uses = 0.22 * 3120 = $686.40

Now, Purchase cost = $344.043

And, Cost of uses =  $686.40

Hence, Lifetime cost =  $344.043 + $686.40 = $1,030.443

So, The lifetime cost of Ellen's dishwater is $1,030.44.

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They travel at 30.64 miles per gallon of gas when they drove 143 miles and used 4 2/3 gallons of gas.

This is solved by unitary method.

Distance travelled by (4 and 2/3) or 14/3 gallons of gas = 143 miles.

So, we get that for 1 gallon of gas it will be given as:

Distance travelled by 1 gallon of gas = 143 miles × 3/14

= 30.64 miles

So, they travel at 30.64 miles per gallon of gas when they drove 143 miles and used 4 2/3 gallons of gas.

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Answer: -5/8

Step-by-step explanation:

we have constructed the given quadrilateral.

The dimensions of the quadrilateral are:

WX = 4 cm

XY = 3.5 cm

YZ = 5 cm
WZ = 5.5 cm

∠ x = 75°

First draw a line segment  WX = 4 cm.

Now from the point X, construct an angle of 75°.

Now, on the ray of that angle, mark an arc that is 3.5 came long and mark the intersection point as Y

Now, from point Y, draw an arc of 5 cm and from point W draw an arc of 5.5 cm.

Mark their intersecting point as Z

Join WZ and YZ

The quadrilateral is formed.

Therefore, we have constructed the given quadrilateral.

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The relationship a linear function and the equation is y = -3x + 24

The table of values is given as

Number of Clubs      Free Time (hours)

1                                         27

2                                         24

3                                          21

4                                           18

A linear relationship is any relationship with a constant rate

From the above table, we can see that as x increases by 1, y decreases by 3

This means that

Slope = Rate = -3

Hence, the relationship a linear function

In (a), we have

Slope = -3

Also, we have

Number of Clubs      Free Time (hours)

1                                         27

Reduce the above parameters by the constant rate

So, we have

Number of Clubs      Free Time (hours)

0                                      24

1                                         27

The above means that

y-intercept = 24

A linear equation is represented as

y = Slope * x + y-intercept

So, we have

y = -3x + 24

Hence, the equation is y = -3x + 24

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The correct answer to the given question is 5 .

If a mathematical equation has real roots, then its solutions or roots are real numbers. If an equation has distinct roots, we contend that all of its solutions or roots are not equal. A quadratic equation has real and distinct roots if its discriminant is bigger than.

In the case where the discriminant is positive or zero, a quadratic equation has real roots (not negative). This indicates that, in terms of algebra, b² >= 4ac. This indicates visually that the quadratic's parabola-shaped graph crosses the x axis at least once.

We have been given to evaluate √25 .

√25 = √(5 × 5)

= √5²

= 5

Therefore, the value of the given question is 5.

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No The extraneous solution of this equation

The given equation is

    [tex]\sqrt{3x + 13}[/tex] - 5 = x

    [tex]\sqrt{3x + 13 }[/tex] = x + 5

We have to find the value of x, so we need to square both sides of the equation

   [tex](\sqrt{3x + 13} )^{2}[/tex] = [tex](x + 5)^{2}[/tex]

  3x + 13 = [tex]x^{2}[/tex] + 10x + 25

  [tex]x^{2}[/tex] + 7x + 12 = 0

 [tex]x^{2}[/tex] +  4x + 3x + 12= 0

x( x + 4) + 3( x + 4) =0

(x + 4) ( x + 3 ) = 0

x = - 3, -4

To find the value of the extraneous solution we need to put both the value of x in the equation

x = -3

[tex]\sqrt{(3 * -3) + 13}[/tex] - 5 = -3

[tex]\sqrt{-9 + 13}[/tex] - 5 = -3

[tex]\sqrt{4}[/tex] - 5 = -3

2 - 5 = -3

-3 = -3

Now

x = -4

[tex]\sqrt{(3 * -4 ) + 13}[/tex] - 5= -4

[tex]\sqrt{-12 +13}[/tex] - 5 = -4

[tex]\sqrt{1}[/tex] - 5 = -4

-4 = -4

Hence we get that the value of x is the solution to the equation.

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Using the above exponent rule,  the value of t in the given equality [tex]5^3/ 5^9 = 5^t[/tex] will be t = -6.

The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.

Exponentiation(the process of raising some number to some power) have some basic rules as:

[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c\\\\a^b = a^b \implies b= c \: \text{ (if a, b and c are real numbers and } a \neq 1 \: and \: a \neq -1 )[/tex]

WE need to find the value of t in the given equality 5^3/ 5^9 = 5^t

Using the above exponent rule, we get

[tex]5^{3 -9 }= 5^t\\\\5^{-6}= 5^t[/tex]

Therefore, compairing both the side we get;

t = -6.

Hence the value of t in the given equality[tex]5^3/ 5^9 = 5^t[/tex]will be t = -6.

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The integers that will make the inequality false are integers greater than 3

The inequality expression is given as

5x + 6 ≤ 2x + 15

Collect the like terms.

So, we have

5x - 2x  ≤ -6 + 15

Evaluate the like terms.

So, we have

3x ≤ 9

Divide both sides of the expression by 3

So, we have

x ≤ 3

Hence, the integers that will make the inequality false are integers greater than 3

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Answer:

250%

Step-by-step explanation:

divide both sides by 0. 4 so A/0.4=B then rearrange so then its (1/0.4)xA=B then divide so its 2.5A=B and obviously 2.5= 250/100 so that makes the answer 250%

is that better?

It will take the reporter 7 minutes to type the document

The reporter can type 215 words in one minute

The reporter wants to type a document that is 1505 words long

The amount of time it will take the reporter to type a document that is 1505 long can be calculated as follows

215 = 1

1505 = x

cross multiply both sides to get the value of x

215x= 1505

divide both sides by the coefficient of x which is 215

215x/215 = 1505/215

x= 7

Hence the reporter will use 7 minutes to type out the 1505 word document

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Answer:

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

pizza has rotational symmetry of 60 degrees. Thus, the order of symmetry will be 6.

The number of chair being set up for a round table in a party is 6.

The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes is called as probability.

Given that,

Banquet table rentals are often suited for less formal gatherings as opposed to round tables for formal ones.

Banquet tables are typically 4 feet, 6 feet, or 8 feet long and 30 inches wide. 8-foot tables

The most widely utilized dimension for guest seats. 4 chairs are present.

Eight people can sit comfortably at an 8-foot table.

Although seating can be provided at 4 and 6 foot tables

These sizes are often employed for different objectives.

4 guests may fit comfortably at a 4 foot banquet table, and 6 guests can

Banquet table can comfortably sit 6.

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