What are the ordered pairs of the solutions for this system of equations?

[tex]f(x)=3x^2+3\hspace{5em}\displaystyle \lim_{h\to 0}~\cfrac{f(2+h)~~ - ~~f(2)}{h} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{f(2+h)~~ - ~~f(2)}{h}\implies \cfrac{[3(2+h)^2+3]~~ - ~~[3(2)^2+3]}{h} \\\\\\ \cfrac{[3(4+4h+h^2)+3]~~ - ~~[3(4)+3]}{h}\implies \cfrac{[(12+12h+3h^2)+3]~~ - ~~[15]}{h} \\\\\\ \cfrac{[12h+3h^2+15]~ - ~~[15]}{h}\implies \cfrac{12h+3h^2}{h}\implies \cfrac{h(12+3h)}{h}\implies 12+3h \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{h\to 0}~\cfrac{f(2+h)~~ - ~~f(2)}{h}\implies \lim_{h\to 0}~12 + 3h\implies 12+3(0)\implies \text{\LARGE 12}[/tex]

The value of x in the equation x = [a^2 + a^2]/[ab + 1] is [2a^2]/[ab + 1]

Equations are mathematical expressions that are represented by the equal to or equality sign i.e =

Examples of equations are:

a + b = c

y = mx + c

Ax + By = C

y = ax^2 + bx + c

y =  x

The equation is given as

x = [a^2 + a^2]/[ab + 1]

To start with, we evaluate the like terms i.e. we add a^2 and a^2

This is represented as

a^2 + a^2 = 2a^2

Substitute 2a^2 for a^2 + a^2 in the given equation

So, we have

x = [2a^2]/[ab + 1]

The above equation cannot be further simplified

Hence, the value of x in the equation x = [a^2 + a^2]/[ab + 1] is [2a^2]/[ab + 1]

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the slope is represented by m

the x coordinate of the ordered pair is x1

the y coordinate of the preferred pair is y1

y-y1=m(x-x1)

Step-by-step explanation:

no calculator at hand ?

f(-3.5) means that we have to replace every x in the function expression by -3.5 and then calculate.

f(-3.5) = (-3.5)² - 5(-3.5) + 6 = 12.25 + 17.5 + 6 = 35.75

The value of integral ₀∫¹ ( eˣ - 2 )² dx is 8 + ( e² - 1) / 2 - 4e.

When infinitesimal data are combined, notions such as displacement, area, and volume can be created. An integral assigns numbers to functions in a way that describes these concepts. Integration is the action of locating integrals.

Consider the integral expression,

₀∫¹ ( eˣ - 2 )² dx

Using ( a + b )² = a² + b² + 2ab

[tex]\int_0^{1}( e^{x} - 2 )^{2} dx = \int_0^{1}(e^{2x}+4-2e^{x})dx[/tex]

[tex]\int_0^{1}( e^{x} - 2 )^{2} dx = \int^0_{1}e^{2x} dx +\int_0^{1}4 dx - \int_0^{1}4e^{x} dx[/tex]

Now, integration of eˣ is eˣ + c where c is constant.

Therefore,

[tex]\int_{0}^{1} ( e^{x} - 2 )^{2} dx = [ \frac{e^{2x}}{2} ]_0^{1} + [ 4x ]_0^{1} - [ 4e^{x}]_0^{1}[/tex]

₀∫¹ ( eˣ - 2 )² dx = ( e² / 2 - e⁰/2 ) + ( 4 - 0 ) - ( 4e¹ - 4e⁰ )

₀∫¹ ( eˣ - 2 )² dx =  e² / 2 - 1/2 + 4 - 4e + 4

₀∫¹ ( eˣ - 2 )² dx = e² / 2 - 4e + 8 - 1/2

₀∫¹ ( eˣ - 2 )² dx =  = 8 + ( e² - 1) / 2 - 4e

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Answer:

the answer would be x=8

Step-by-step explanation:

6×4=24

24/3=8

Answer:

Step-by-step explanation:

-6+2y=10

2y=10+6

2y=16

2y/2=16/2

y=8

so the final answer of first question is y=8

The next one is

6x-2y=-10

as we got from the first question y=8 so

6x-2(8)=-10

6x-16=-10

6x=-10+16

6x/6=6/6

so the final answer is 1

The dimensions of the rectangle are; length 63 inches and width is 20 inches.

Let 'L' be the length of the rectangle.

Let 'W' be the breadth of the rectangle.

As, the length of a rectangle is three more than triple the width.

Thus,

L = 3 + 3W

The formula for the perimeter is;

Perimeter = 2 (L+W)  

The value of perimeter is 166 inches.

Thus,

166 = 2(3 + 3W +W)

166 = 2(3 + 4W)

166 = 6 + 8W

166 - 6 = 8W

W = 20

W = width = 20 inches

L = 3 + 3W

L = 3 + 3(20)

L = 3 + 60

L = 63 inches.

Thus, the dimensions of the rectangle are; length 63 inches and width is 20 inches.

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Answer:

3 heartbeats per sec.

Step-by-step explanation:

Number of heartbeats / Total time will give the rate or number of heartbeats per sec.

Answer:

x = 0

Step-by-step explanation:

Let's solve the problem,

→ (x/9) + 8 = 8

→ x/9 = 8 - 8

→ x = 0 × 9

→ [ x = 0 ]

Thus, the value of x is 0.

The width of the rectangle = 15 yd

The length of the rectangle = 60 yd.

Perimeter of a rectangle = 2(length + width).

Given the following:

Width of the rectangle = w

Length of the rectangle = 4w

Perimeter of the rectangle = 150 yd.

Therefore:

2(4w + w) = 150

2(5w) = 150

10w = 150

10w/10 = 150/10

w = 15

Width of the rectangle = w = 15 yd

Length of the rectangle = 4w = 4(15) = 60 yd.

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Answer:

3.7517%

Step-by-step explanation:

take 3.7 and divide it by 4 to get 0.925

then apply 0.925% to x 4 times to find out the compounded rate

1. 1/2

2. 3/10

3. 2 and 3/5

4. 1 and 7/12

5. 1 and 1/3

The amount when 500 invested at 9% interest compounded monthly be worth after 4 years will be $715.7.

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

We know that the compound interest is given as

[tex]\rm A = P \left ( 1 + \dfrac{r}{n} \right ) ^{nt}[/tex]

Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of years.

For interest compounded monthly, the value of n is 12.

The amount when 500 invested at 9% interest compounded monthly be worth after 4 years will be

[tex]\rm A = 500 \left ( 1 + \dfrac{0.09}{12} \right ) ^{12 \times 4}[/tex]

Simplify the equation, then we have

A = 500 (1.0075)⁴⁸

A = 500 x 1.4314

A = $715.70

The amount when 500 invested at 9% interest compounded monthly be worth after 4 years will be $715.7.

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The domain and range of the function is -3 ≤ x < 7 and -7 ≤ x < 6 respectively.

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

For domain :-

Since, the domain is the set of all allowed x inputs of a function.

The smallest x can get is x = -3 as shown by the left-most point.

The largest x can get is x = 7, though we can't actually reach this value due to the open hole at the right-most point.

The interval of all possible x values is -3 ≤ x < 7  which converts to the interval notation [-3, 7)

We use a square bracket to include the endpoint and a parenthesis to exclude the endpoint.

We can say "x is any number between -3 and 2, including -3 but excluding 2".

For range :-

Since, the range is the set of all allowed y inputs of a function.

The smallest x can get is x = -7 as shown by the left-most point.

The largest x can get is x = 6, though we can't actually reach this value due to the open hole at the right-most point.

The interval of all possible x values is -7 ≤ x < 6  which converts to the interval notation [-7, 6)

We use a square bracket to include the endpoint and a parenthesis to exclude the endpoint.

Hence, the domain and range of the function is -3 ≤ x < 7 and -7 ≤ x < 6 respectively.

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The distance between the school and the hospital on the map  is 8 cm

Here, we want to find the distance between the school and the hospital on the map

The scale is that 4cm to 5km

So ;

if 4 cm = 5km

Then x cm = 10km

x * 5 = 4 * 10

5x = 40

x = 40/5

x = 8 cm

Therefore the distance between the school and the hospital on the map  is 8 cm

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The value of y' according to the given equation in the task content is; 1.

According to the task content, it follows that the equation given is; 2x³y - 3x² = 4y'.

On this note, the value of y' can be determined by substituting the given values of x and y as follows;

2(2)³×1 - 3(2)² = 4y'

16 - 12 = 4y'

y' = 4/4

y' = 1.

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Answer:

Wish i could help

Step-by-step explanation:

Answer:

5/8 of pizza left

Step-by-step explanation:

The condition that will create a biased estimator of a population parameter is D. The expected value of the estimator is not equal to the population parameter.

It should be noted that a parameter is a descriptive measure applied to a whole population. There are numerous population parameters exist. For instance, the population size (N) is one parameter.

For T(x) to be an unbiased estimator of population parameter, it is necessary that the expected value of the estimator is equal to population parameter.

Therefore, the condition that will create a biased estimator of a population parameter is that the expected value of the estimator is not equal to the population parameter.

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Answer:

[tex]7x + 5y \leqslant 30[/tex]

Answer:

$600

Step-by-step explanation:

450 = 3/4 (because 75%=3/4)

450/3=150. 150 = 1/4, or 25%. Now it's just as simple as multiplying 150 4 times to get 100%, or the original cost, 150 times 4 equals 600. Therefore the notebooks original price is $600

Answer:

x = -36

Step-by-step explanation:

Subtract 9 from 3.2(x−6)=14⋅−6

Multiply 14 by −6.2(x−6)=−84

Divide each term

Simplify the left side.

Move all terms not containing x to the right side of the equation.

x = -42 + 6

Add -42 & 6

x = -36

The amount of bacteria after 12 hours would be 8 grams

Rate can be defined as  the ratio between two quantities that are related in size but may be in different units.

It is also known as the ratio of comparison between quantities of different units.

From the information given, we have that;

To determine the amount of bacteria after 12 hours, we have;

= 12 × 15/ 100

multiply and find quotient

= 1. 8

In 12 hours, the amount of bacteria is ;

= 6 + 1. 8

= 7. 8 grams

= 8 grams

Thus, the amount of bacteria after 12 hours would be 8 grams

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The number of minutes of each medium should be used to minimize costs if television costs $900/minute and radio costs $200/minute is 45 minutes and 3.33 minutes respectively.

x ≥ 0

y ≥ 0

x + y ≤ 80

0.09x + 0.006y ≤ 2.16

From (1)

x ≤ 80 - y

0.09x + 0.006y ≤ 2.16

0.09(80 - y) + 0.006y ≤ 2.16

7.2 - 0.09y + 0.006y ≤ 2.16

7.2 - 0.084y ≤ 2.16

-0.084y ≤ 2.16 - 7.2

-0.084y ≤ -5.04

y ≤ -5.04 / -0.084

y ≤ 60

x + y ≤ 80

x + 60 ≤ 80

x ≤ 80 - 60

x ≤ 20

The number of minutes of each medium should be used to minimize costs if television costs $900/minute and radio costs $200/minute is

Television = $900 / 20

= 45 minutes

Radio = $200/60

= 3.33 minutes

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Answer: 105 degrees

Step-by-step explanation:

two sides of a trapezoid add up to 180 degrees

180 - 75 = 105

Answer:

Step-by-step explanation:

21 divided by 7 is 3 so 3 minus 10 is negative 7

The solution is : 7 when subtract the quotient of 21 and 7 from 10.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

given that,

the quotient of 21 and 7

i.e. we have to divide 21 by 7

i.e. 21/7 = 3

so, we get,

the quotient of 21 and 7 is 3

now, we have to Subtract 3 from 10

i.e. 10 - 3

= 7

so, we get,

21 divided by 7 is 3 so 10 minus 3 is  7.

Hence, The solution is : 7 when subtract the quotient of 21 and 7 from 10.

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Based on the packaging of the cookies, the number of ways you can buy 36 cookies is 12 ways.

The ways you can buy the cookies include:

In conclusion, there are 12 ways to buy the cookies.

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