Work out
a) 5 - 21
b) 7/3/3 + 2/1/20

{(1, 4), (-2, 8), (2, 2), (4, 9)} it is a function as every input has a unique output. Therefore, option B is not a function.

The given coordinate points are {(1, 2), (-2, 2), (5, 2), (4, 2)}.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

A) {(1, 2), (-2, 2), (5, 2), (4, 2)}

It is a function as every input has a single output.

So, 1, -2, 5 and 4 are the elements of the domain of the given relation.

Here domain ={1, -2, 5, 4} and range ={2}

B) {(7, 8), (7, 9), (7, 10), (7, 11)}

Since the element 7 corresponds to four different images i.e., 8, 9, 10 and 11. So, this relation is not a function.

C) {(0,0)}

It is a function as every input has a single output.

So, 0 is the element of the domain of the given relation.

Here domain ={0} and range ={0}

D) {(1, 4), (-2, 8), (2, 2), (4, 9)}

It is a function as every input has a unique output.

So, 1, -2, 2 and 4 are the elements of the domain of the given relation.

Here domain ={1, -2, 2, 4} and range ={4, 8, 2, 9}

{(1, 4), (-2, 8), (2, 2), (4, 9)} it is a function as every input has a unique output. Therefore, option B is not a function.

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If  they were 70 more cheeseburgers sold than hamburgers. The number of hamburgers  that were sold on Tuesday​ is 225.

Total of 603 hamburgers and cheeseburgers = x+y= 520

70 more cheeseburgers than hamburgers = y=x+70

Hence,

x+y= 502

y=x+70

Substitution

x+(x+70)= 520

2x+70 = 520

  -70    -70

2x= 450

2    2

x=225 hamburgers

Number of cheeseburgers

Substitute  x in either equation.

y=x+ 70

y=225 +70

y=295 cheeseburgers

Therefore 225  hamburgers was sold.

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Explanation: Please give brainly if it's right!

First move all the x and y values on one side, and the constants on the other:

-x² + y = − 1

-x² - y = -7

Multiply -1 to the 2nd equation to change signs and then solve:

-x² + y = − 1

+x² + y = +7

2y = 6

y = 3

Plug in y to either equation (I plug into the first one)

-x² + 3 = − 1

-x² = -4

x = 2

Answer:

a) [tex]\displaystyle{\dfrac{dG}{dV_{\text out}}=\dfrac{20}{V_{\text out}\ln 10}}[/tex]

b) [tex]\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = -\dfrac{20}{V_\text{out}^2\ln 10}}[/tex]

Step-by-step explanation:

From the given equations to find, we are differentiating function G with respect to V out. Therefore, we will be only using the equation (6):

[tex]\displaystyle{G=20\log (10V_{\text out})}[/tex]

Here’s a fresh-up reminders for logarithmic differentiation formula:

[tex]\displaystyle{f(V)=a\log_b V \to f'(x)=\dfrac{a\cdot V'}{V\ln b}}[/tex]

Note that V' means to derive or differentiate the V-term

Therefore, in this scenario, our values of term are:

Therefore, we can apply differentiation formula:

[tex]\displaystyle{\dfrac{dG}{dV_{\text out}}=\dfrac{20\cdot \dfrac{d(10V_{\text out})}{dV_{\text out}}}{10V_{\text out}\ln 10}}[/tex]

Simplify:

[tex]\displaystyle{\dfrac{dG}{dV_{\text out}}=\dfrac{20\cdot 10}{10V_{\text out}\ln 10}}\\\\\displaystyle{\dfrac{dG}{dV_{\text out}}=\dfrac{20}{V_{\text out}\ln 10}}[/tex]

And we have finished the part a. On part b, we just differentiate the answer from part a again, the second part is to obtain the second derivative which is to derive the first derivative. Therefore:

[tex]\displaystyle{\dfrac{d^2G}{dV_{\text out}^2} = \dfrac{d\left(\dfrac{20}{V_{\text out}\ln 10}\right)}{dV_{\text out}}}[/tex]

First, separate the constant every time when you have to differentiate a function:

[tex]\displaystyle{\dfrac{20}{\ln 10}\cdot \dfrac{1}{V_{\text out}}}[/tex]

Differentiate 1/V out: recall the formula of fraction:

[tex]\displaystyle{f(V)=\dfrac{1}{V} =V^{-1} \to f'(x)=-V^{-2} = -\dfrac{1}{V^2}[/tex]

The formula above is derived from power rules formula where:

[tex]\displaystyle{f(V)=V^n = nV^{n-1}}[/tex]

Therefore, from the function of V out:

[tex]\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = \dfrac{20}{\ln 10} \cdot \left(\dfrac{1}{V_\text{out}}\right)'}\\\\\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = \dfrac{20}{\ln 10} \cdot (V_\text{out})^{-1}}\\\\\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = \dfrac{20}{\ln 10} \cdot (-V_\text{out})^{-2}}\\\\\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = \dfrac{20}{\ln 10} \cdot \left(-\dfrac{1}{V_\text{out}^2}\right)}[/tex]

Simplify to latest as we get:

[tex]\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = -\dfrac{20}{V_\text{out}^2\ln 10}}[/tex]

Please let me know if you have any questions!

The conditional relative frequency that a female prefers running is 0.36

Statistics is a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data

The specific number (females prefer cycling = 0.15) and the fitting total. There are 2 possibilities for that total :

all females

all people preferring cycling

the way it was phrased I would say the reference is all females.

the conditional relative frequency is then

0.15 / 0.46 = 0.326

Hence the conditional relative frequency that a female prefers running is 0.36

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Answer:

Step-by-step explanation:

Dont listen to the above the answer is acually 58

Answer:

the amount of birdseed leftover is 32

Step-by-step explanation:

The coordinates (4, 0) and (3, -1) represents the solution of the function f(x).

According to the question -

y = f(x) = x - 4

Case 1 : P(4, 0)

0 = 4 - 4 = 0

P (4, 0) represents a solution

Case 2: P (3, -1)

-1 = 3 - 4 = -1

P (3, -1) represents a solution

The new coordinate after the given composite translation (x,y) → (x-5,y+5) will be (x+3,y+12).

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

As per the given translation rule,

(x,y) → (x+8,y+7)

The next translation is (x,y) → (x-5,y+5)

The resultant translation will be,

(x,y) → (x+8,y+7) to (x+8-5,y+7+5)

⇒ (x+3,y+12)

Hence "The new coordinate after the given composite translation (x,y) → (x-5,y+5) will be (x+3,y+12)".

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The measure of one of its angle is 150°

A Polygon is a two-dimensional closed figure made up of line segments (not curves). Polygon is a combination of two words, poly (which means many) and gon (which means shape) (means sides). To create a closed figure, at least three line segments must be connected end to end.

Given that

12 sided regular polygon

We can use the following formula to calculate the total number of degrees in any shape:

(n−2)⋅180

[Where n = number of sides]

(12−2)⋅180

(10)⋅180

=1800

So a 12-sided polygon has 1800 degrees. To calculate the measure of one angle, divide the total number of degrees (1800) by the number of sides, n.

(1800/12) = 150°

Therefore the measure of one of its angle is 150°

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Answer: $350

Reason: 10% of $350 is $35.

The representation of equation y = 3x + 1 is as shown below.

The correct answer is option (D)

In this question, we have been given an equation y = 3x + 1

We need to find the correct representation  of given equation.

For x = 0,

y = 3(0) + 1

y = 1

For x = 2,

y = 3(2) + 1

y = 7

for x = -1,

y = 3(-1) + 1

y = -2

This means, the options A, B and C are incorrect.

Therefore, the representation of equation y = 3x + 1 is as shown below.

The correct answer is option (D)

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Answer:

900,000

Step-by-step explanation:

From the given table, we are told that the honeybee beats its wings at a rate of:

There are 60 seconds in a minute, and 60 minutes in an hour.

Therefore, there are:

To find how many times a honeybee can beat its wings in an hour, multiply the number of times it beats its wings per second by 3600:

⇒ 250 × 3600 = 900,000

Therefore, a honeybee beats its wings 900,000 beat per hour.

Answer:

 (a)

  [tex]\left[\begin{array}{cc}20&80\\32&3\end{array}\right][/tex]

Step-by-step explanation:

You want the product of the given 2×2 matrices.

The value at any given (row, column) of the result matrix is the dot product of the corresponding row of the first matrix with the corresponding column of the second matrix.

For example, row 2 column 1 of the result will be the dot product of row 2 of the left matrix with column 1 of the right matrix:

  [-2, 3]·[-4, 8] = (-2)(-4) +(3)(8) = 8 +24  = 32

This is sufficient to identify the first answer choice as the correct one.

__

Additional comment

A suitable calculator can compute the entire product for you, as in the attachment.

one example of terminating decimal and one repeating decimal between -1/2and -1/3

terminating decimal = -2/5

repeating decimal = -3/11

A decimal with an end digit is referred to as a terminating decimal. It is a decimal with a limited number of digits.

examples of terminating decimal are

When a number's digits are periodic and its indefinitely repeated portion is not zero, the representation of that number as a decimal is said to be repeating or recurring.

Examples of a repeating decimal are

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Answer:

statement 1 is true

statement 2 is true

statement 3 is false

statement 4 is false

statement 5 is also false cause parallelogram has 2 pair of congruent sides

Answer:

1) 112°

3) 55°

4) 51°, complementary angles

Step-by-step explanation (question one):

3x +10 +2x = 180

3x +10 +2x -10 = 180 -10

3x + 2x = 170

5x = 170

x = 34

3(x)+10 = angle ABD

3(34)+10 = angle ABD

102+10 = angle ABD

angle ABD = 112°

Step-by-step explanation (question two):

180 -70 = 2x

110 = 2x

55 = x

angle SQT = 55°

Step-by-step explanation (question three):

Since it's a right angle, we can simply subtract.

90 -39 = 51

angle b = 51°

I wish you luck on your homework!

A linear function in slope-intercept form that only corresponds with this table is y = 2x + 8.

Mathematically, the slope-intercept form of a straight line is given by;

y = mx + b

Where:

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided, we have the following parameters:

Point (x, y) = (-1, 6)

Point (x, y) =  (0, 8)

Substituting the given points into the formula, we have;

Slope, m = (8 - 6)/(0 - (-1))

Slope, m = (2)/(0 + 1)

Slope, m = 2/1

Slope, m = 2.

In Mathematics, the y-intercept of a graph occurs at the point where the x-value is equal to zero (0), which is 8 in the table shown above.

Therefore, the slope-intercept form is given by:

y = mx + b

y = 2x + 8

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An algebraic representation which best describes this transformation is: C. (x, y) → (5x/2, 5y/2).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

By critically observing the graph, we can logically deduce the following vertices:

In this scenario, the transformation rule is given by this algebraic representation:

Q (x, y)                      →               Q' (x, y)

Coordinate Q = (2, 0)   →  Coordinate Q' = ((5/2 × 2), (5/2 × 0)) = Coordinate Q' = (5, 0).

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From the given data, total number of hamburgers of (1/4) pounds each using 2 1/2 pounds of ground beef is equal to 10.

As given in the question,

Total pounds of hamburger need to be made = 1 / 4 pounds

Total pounds of ground beef is used to make hamburger = 2 1 / 2 pounds

Let us consider 'n' be the total number of hamburger to be made each of

1 / 4 pound .

Required equation to show the given relation is given by:

n × ( 1 / 4) = 2  1/ 2

Convert mixed fraction into proper fraction we get,

⇒ n × ( 1 / 4) = 5 /2

⇒ n = ( 5/ 2) × ( 4 /1)

⇒ n = 5 × 2

⇒ n = 10 hamburgers

Therefore, from the given data, total number of hamburgers of (1/4) pounds each using 2 1/2 pounds of ground beef is equal to 10.

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Answer:

24

Step-by-step explanation:

let the starting number be x

she sold 1/2 x and has 1/2 x remaining with her

she bought 13 and has 25 now

so, 1/2x + 13 = 25

1/2 x= 25-13 = 12

hence x= 24

Answer:

    24

Step-by-step explanation:

now Mei has 25 stamp collections after adding 13 more to what she remained with after selling; this means that after selling she was left with (25_13)=12

this is the half of what she had initially

this means that she initially had (12*2)=24

this gives means that she started with 24 as a stamp of her collection

Based on the calculations, the distance between points (-5, -5) and (-9, -2) on a coordinate plane is equal to: A. 5 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Given the following points:

Substituting the given points into the formula, we have;

Distance = √[(-2 - (-5))² + (-9 - (-5))²]

Distance = √[(-2 + 5)² + (-9 + 5)²]

Distance = √[3² + 4²]

Distance = √[9 + 16]

Distance = √25

Distance = 5 units.

In conclusion, we can logically deduce that the distance between the given points on a coordinate plane is 5 units.

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Complete Question:

What is the distance between (-5, -5) and (-9, -2?

Choose 1 answer:

A. 5

B. 7

C. √12

D. √29

Answer: $56.25

Step-by-step explanation:

First, I'm going to assume that she makes 25% profit on the selling price.

Set the cost of the shirt as x. Profit is calculated as selling price - cost. Profit is stated to be 25% or [tex]\frac{1}{4}[/tex], so an equation can be set up as:

[tex]\frac{1}{4} *75=75-cost\\\\cost = 75-\frac{1}{4} *75=56.25[/tex]

Answer:

Step-by-step explanation:

The amount of yogurt that Karolina used when making 800 ml of salad is 300 ml.

A salad dressing is made by mixing yoghurt and mayonnaise in the ratio

3:5. For 800 ml of salad:

Amount of yoghurt = (3 / (3 + 5)) * 800 ml = 300 ml

The amount of yoghurt that Karolina used when making 800 ml of salad is 300 ml.

Answer:y=mxb

Step-by-step explanation:

Answer:

The equation is: y = 5x - 268

Answer:the geometric mean is the product of all the numbers in a set, with the root of how many numbers there are.

here, there are two numbers, so a square root is used.

geometric mean of

3

and

12

:

√

3

⋅

12

3

⋅

12

=

36

√

36

=

6

the value of the geometric mean of

3

and

12

is

6

.

Step-by-step explanation:

For the given rectangular playpen, the perimeter of rectangular playpen is 150 feet and its area is at least 1000 square feet. then the length of the rectangular playpen is equal to at least 17.35 feet and at most 57.66 feet.

As given in the question,

For the given rectangular playpen,

Perimeter of rectangular playpen is equal to 150 feet .

Area of the rectangular playpen is equal to at least 1,000 squared feet .

Area = length × width

Let x be the length of the rectangular playpen .

Then its width is equal to 1000 / x.

Substitute the value of length and width in perimeter we get,

Perimeter of rectangular playpen = 2 ( length + width )

⇒ 150 = 2 [ x + (1,000/x)]

⇒ 150 / 2 = ( x² + 1,000 ) / x

⇒ x² + 1000 = 75x

⇒ x² -75x + 1,000 =0

Simplify quadratic equation using discriminant we get,

x = [ -( -75) ± √(-75)² - 4(1) (1,000) ] / 2(1)

⇒ x = (  75 ± √5625 - 4000) /2

⇒ x = (75 ± 40.31) / 2

⇒ x = 57.66 or 17.35

Therefore, for the given rectangular playpen, the perimeter of rectangular playpen is 150 feet and its area is at least 1000 square feet. then the length of the rectangular playpen is equal to at least 17.35 feet and at most 57.66 feet.

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Answer: Neither

Step-by-step explanation:

The slope is 6.25, it means that her day pay increases by $6.25 for each computer sold

A general linear equation in the point-slope form is written as:

y = a*x + b

Where y and x are the two variables, a is the slope, and b is the y-intercept.

In this case, the linear equation is:

P(x) = 6.25*x + 75

We know that P(x) represents her pay, and x represents the amount of computers she sold.

Here we can see that the slope is 6.25, it means says how much her pay increases per computer sold.

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