I need help with number 11 - 16

We can show that x² + 5x = 3 given the dimensions of the rectangle that has an area of 9 cm² as explained below.

To find the area of a rectangle, use the formula given below:

Area of a rectangle = (length)(width).

Given the parameters:

To show that x² + 5x = 3, plug in the values into the formula for the area of a rectangle:

(x + 3)(x + 2) = 9

Apply the distributive property of equality

x(x + 2) + 3(x + 2) = 9

x² + 2x + 3x + 6 = 9

Combine like terms:

x² + 5x + 6 = 9

Add -6 to both sides of the equation

x² + 5x + 6 - 6 = 9 - 6 [subtraction property of equality]

x² + 5x = 3

Thus, if the area of the rectangle with the given dimensions is 9 cm², then we can show that, x² + 5x = 3 as explained above.

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Answer:

05/20 is not an equivalent fraction

Step-by-step explanation:

1) Write each fraction in its simplest form. To do this divide the numerator by the denominator.

04/12 becomes 1/3

07/21 becomes 1/3

05/20 becomes 1/4

09/27 becomes 1/3

2) all the fractions simplify to the same number except 05/20. So, we can conclude that 05/20 is not an equivalent fraction

Answer:

Greater.

Step-by-step explanation:

The in the function , the square root term has to give a real number if is to be real. This can only happen if because if then will give a complex number and therefore will not be real.

Thus, the domain for f(x) is all real numbers greater than or equal to 2.

Answer:

The domain for f(x) is all real numbers greater than or equal to 2.

Step-by-step explanation:

Given function:

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

The domain of a function is the set of all possible input values (x-values).

As the square root of a negative number cannot be taken:

[tex]\implies x-2\geq 0[/tex]

Therefore:

[tex]\implies x-2+2\geq 0+2[/tex]

[tex]\implies x\geq 2[/tex]

Therefore, the domain of the given function is greater than or equal to 2.

_

Average of given n numbers X1,X2,.........,Xn is x= £xi/n

Let the my number be x

Given:- The average of 3,15,x is 40

£xi/n =40

3+15+x/3=40

Multiplying 3 both side

18+x=120

x=120-18

x=102

Hence, my number is 102

The solution for the expression x² = 12 will be x = ±2√3.

The expression is given in the form of square of a variable x which is equal to 12. This expression does not form a perfect square as the constant term is not a perfect square number. A perfect square is a number which is expressed as the square of whole number, or a number multiplied by itself twice. Here, we are given that x² = 12. We take square root of the expression on both the sides then,

√x² = √12

x = √(2×2×3)

x = ±2√3

We use the sign '±' because any number which when expressed in variable form comes out of the square root then it can be positive or negative,

Thus, the value of x is ±2√3.

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Answer:

Below in bold.

Step-by-step explanation:

10% = 0.10 as a decimal fraction.

After t years:

Amount = 6000(1 + 0.10)^t

Answer:

True???

Step-by-step explanation:

Is this a true or false question?

P+12=even number

Examples...

12+12=24

16+12=28

66+12=78

Answer:

YES

Step-by-step explanation:

even + even = even

always and forever

The order of the rotational pentagon is 6.

The amount of times a form may be turned in a full circle without losing its appearance is known as its order of rotational symmetry. The only time the triangle appears the same after being rotated a full 360 degrees is when it returns to its original beginning position. It only has one rotational symmetry order, which is the initial position. A form can only have one rotational symmetry order.

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The probability that the first applicant with advanced training in programming is found on the third interview is  0.0469

Let X denote the number interviewed until 1 has advanced training and follows a geometric distribution with parameter 75%, so

Geometric distribution is: (1-75%)

                                        =0.75

The density function of geometric distribution is,

[tex]P(X=x)=p(1-p)^{x-1}[/tex], for all x = 1,2,3,....

Now, we calculate the probability that the first applicant with advanced training in programming is found on the third interview:

P(X=3) =[tex]0.75(1-0.75)^{3-1}[/tex]

          =[tex]0.75(1-0.75)^{2}[/tex]

          =0.75×0.0625

          =0.0469

Hence, the required probability is 0.0469

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Answer:

x = 15

Step-by-step explanation:

Let's start by copying down the equation.

6 + 4x + 3 = 6x - 21

Let's simplify this equation and we get,

4x + 9 = 6x - 21

Now, we can add 21 to both sides to isolate 6x on one side. Then, we get...

4x + 30 = 6x

Now, we minus 4x from both sides to get rid of it.

Then we get...

2x = 30

Thus, x = 15

6 + 4x + 3 = 6x - 21

We minus (4x+3) on both side.

6 + 4x + 3 - (4x+3) = 6x - 21 - (4x + 3)

6 = 2x - 24
2x = 30
x = 15.

Recheck : 6 + 60 + 3 = 90 - 21
69 = 69 (nice.)

Answer:

90

Step-by-step explanation:

4 x 23 = 92
2 x (-1) = -2
1 x 0 = 0

92 + (-2) + 0 = 90

Answer:

x= x1.5  y = x1.5

E' = E dilated by 1.5

Step-by-step explanation:

-1 x 1.5 =-1.5  -3 x 1.5 = -4.5  (-1.5,-4.5)

0 x 1.5 =0  1 x 1.5 = 1.5  (0,1.5)

3 x 1.5 = 4.5   -2 x 1.5 =-2  (4.5.-3)

The system of Inequality for the given graph is;

2x + 3y ≥ 12

3x - 5y ≥ 15

Inequalities that use < or > symbols are always plotted with a dashed line while Inequalities that use ≤ or ≥ symbols are always plotted with a solid line.

Now, if the shaded portion is above a dashed line, the the symbol is > but if it is shaded above a solid  line, then the symbol is ≥. In this question, a solid line is used for both equations and shaded above the lines and so we will use ≥.

Equation of Line 1;

x-intercept = 6

y intercept = 4

Slope = -2/3

Thus, using the general equation of slope of line, the equation of this inequality is; 2x + 3y ≥ 12

Similarly, the equation of the second line will be;

3x - 5y ≥ 15

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Ellie needs 1.5 gallon of milk (that is 24 cups).

we are given 2 cup = 1 pint

we have 24 cup which will be equal to 24/2 i.e. 12 pint.

we are given 2 pint = 1 quart

we have 12 pint which will be equal to 12/2 i.e. 6 quart

we are given 4 quart = 1 gallon

we have 6 quart which will be equal to 6/4 i.e. 1.5 gallon.

Hence, we know 24 cups of milk is equivalent to 1.5 gallon of milk

what are conversions in maths?

By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. When a conversion is required, the right conversion factor to an equivalent value must be applied. For instance, 12 inches equals 1 foot when converting between inches and feet.

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Answer:

[tex]-98y^2+70y[/tex]

Step-by-step explanation:

Expand the equation [tex]-14y(7y-5)[/tex], we get

[tex](-14y*7)-(-14y*5)[/tex]

Which is equal t0:o

[tex]-98y^2+70y[/tex]

The product of given monomial by binomial is -98y²+70y.

Given that, -14y(7y - 5).

To multiply two polynomials: multiply each term in one polynomial by each term in the other polynomial. Add those answers together, and simplify if needed.

Using distributive property, multiply given monomial by binomial. That is,

-14y(7y - 5)=-14y×7y - (-14y)(5)

= -98y²+70y

Therefore, the product of given monomial by binomial is -98y²+70y.

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From the given linear equation graph, we can tell that the equation of the line in slope intercept form is; y = 1.2x + 3

The general form of equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

From the given graph, we see that;

y - intercept = 3

x - intercept = -2.5

Now, we can find the slope by taking two coordinates;

(-2.5, 0) and (0, 3)

Slope = (3 - 0)/(0 - (-2.5))

Slope = 3/2.5

Slope = 1.2

Thus, the equation of the line is;

y = 1.2x + 3

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Answer:

6 levels

Step-by-step explanation:

60 - 5 (to set up the character)

55 total minutes

8(l) = 55

L = 55/8

L = 6.875

.˙. they can finish 6 levels

Answer:

Non-linear

Step-by-step explanation:

Because the line is not straight.

The rational equivalent to 0.86 can be written as 43/50.

A rational number may be defined as the number which can be expressed in the form of p/q where p and q are integers, and the term q cannot be equal to zero. It can be either positive or negative or both. We can also say that any fraction which does not have zero in the denominator is called a rational number. Zero can also be regarded as a rational number as it can also be represented as a fraction. For example, 0/2, 0/5.  In order to write 0.86 as a rational number, we have to convert it in fraction form. In fraction form it can be written as

0.86 = 86/100

This is also a rational number, but we simplify it further and we get

86/100 = 43/50 which is a rational number.

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Answer:

That means the sum of the first 99 positive integers is 49(100) + 50 = 4900 + 50 = 4950. 2.

answer step by step:

hope this helps

Answer: (5.50-2.50)/4 = 0.75. each bag of apples is $0.75

Step-by-step explanation:

first, you subtract $5.50 by $2.50 to get $3, the cost of the 4 bags of apples altogether ($5.50 - $2.50 = $3)

then you divide $3 by 4 to get the cost of each bag of apples. (3/4 = 75)

so each bag of apples is $0.75

i hope this helps!

Answer:

d^2=(x2-x1)^2+(y2-y1)^2

d^2=[3-(-2)]^2+(9-4)^2

d^2=(5)^2+(5)^2

d^2=25+25

d^2=50

d= [tex]\sqrt{50}[/tex]

d=7.07 units

Given that each term has a common difference, this is an arithmetic sequence as per the explicit formula that generates this sequence.

In this instance, the next word in the sequence is obtained by adding 2 to the previous term. To put it another way, a n = a 1 + d (n – 1) This is the arithmetic sequence’s formula.

Firstly, we have to find the initial phrase in a given series. Thereafter we have to find the shared difference between the following phrases in the sequence. For an explicit rule, replace the general form with the first term and common difference.

The distance between succeeding terms in an arithmetic series is always the same.

The difference between consecutive terms in the sequence 3, 5, 7, 9…, for instance, is an example of an arithmetic sequence.

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Given the shown figure

since

The Central Angle Is Twice The Inscribed Angle

where

a= mACB

2a = mAPB=56

then

a= mACB=28

Correct answer

option b

28

Answer:

y = (1/2)x + -3

Step-by-step explanation:

Point 1: (0, -3); Point 2: (6, 0)

            (x₁, y₁)                (x₂, y₂)

       y₂ - y₁           0 - (-3)      0 + 3         3           1

m = ------------- = ------------ = ---------- = -------- = --------

        x₂ - x₁            6 - 0           6            6           2

y - y₁ = m(x - x₁)

y - (-3) = (1/2)(x - 0)

y + 3 = (1/2)x

   - 3              -3

----------------------------------

y = (1/2)x - 3

I hope this helps!

Answer: y=0.5x-3

Step-by-step explanation:

[tex]\displaystyle\\(0,-3)\ \ \ \ (6,0)\\ \frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} \\\\x_1=0\ \ \ \ x_2=6\ \ \ \ \ y_1=-3\ \ \ \ \ y_2=0\\\\\frac{x-0}{6-0} =\frac{y-(-3)}{0-(-3)}\\\\\frac{x}{6} =\frac{y+3}{0+3} \\\\\frac{x}{6} =\frac{y+3}{3}[/tex]

Multiply both parts of the equation by 3:

[tex]\displaystyle\\\frac{x}{2} =y+3\\\\0.5x=y+3\\\\0.5x-3=y+3-3\\\\0,5x-3=y\\\\Thus,\ y=0.5x-3[/tex]

The equation for the line parallel to given line containing C:

y = 8/9x + 64 / 9

What is Parallel line ?

Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.

Given that a line's equation is,

y = 8 / 9x - 7

If we contrast this equation with a line's slope-intercept,

this line's slope = 8/9

Since every line parallel to this one will have a same slope,

The parallel line's slope is equal to

The symbol for the line with the slope 'm' and the coordinates (x', y') is

y - y' = m(x - x')

As a result, the equation of the line through (-1, 8) with a slope will be,

y - 8 = 8/9 (x-1)

y =8/9x - 8/9 - 8

y = 8/9x + 64 / 9

Hence, The equation for the line parallel to given line containing C is

y = 8/9x + 64 / 9

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The plant are growing at the same rate per day is given by equation 1[tex]y=\frac{3}{2}x +\frac{3}{2}[/tex] and equation 4 [tex]y = \frac{3}{2}x+1[/tex] i.e because they have same slope(rate of change )

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.

The plant are growing at the same rate per day is given by equation 1[tex]y=\frac{3}{2}x +\frac{3}{2}[/tex] and equation 4 i.e [tex]y = \frac{3}{2}x+1[/tex]

because they have same slope(rate of change )

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