provide two more examples of relationship patterns found in mathematics and describe the pattern in each case​

Answer:

66 chairs

Step-by-step explanation:

Total number of chairs = 594

Total number of rows = 9

Number of chairs per row

= 594/9

= 66 chairs

__________

Hope it helps ⚜

Simple As you can see 12 cookies are there and 3 children are there so

1 children will have = 12 ÷ 3

= 4

like this each kid will have 4 cookies where 4>2

A triangle is a three-edged polygon with three vertices. The height of the triangle can be written as h = (2A)/b.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

The complete question is:
Given the equation of the area of a triangle. how did you find the height of the triangle? A=(1/2)b x (h)

(Hint: Solve the equation for h)

Given the equation of the area of the triangle. Therefore, the height of the triangle can be written as,

A=(1/2)b x (h)

2A = b x h

h = (2A)/b

where h is the height of the triangle and b is the length of the base of the triangle.

Hence, the height of the triangle can be written as h = (2A)/b.

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Hello and Good Morning/Afternoon!

Let's take this problem step-by-step:

What the problem asks for:

  ⇒ to rationalize the denominator

      ⇒ rationalize means that you multiply the numerator and

          demonimator by the denominator

Let's put that into action:

    [tex]\frac{\sqrt{a +1}-2 }{\sqrt{a+1}+2 } * \frac{\sqrt{a +1}+2 }{\sqrt{a+1}+2 }\\=\frac{a +1-4 }{a+1+4\sqrt{a+1}+4 } \\=\frac{a-3}{a+4\sqrt{a+1}+5 }[/tex]<== Answer

Hopefully that helps!

Using the Fundamental Counting Theorem, there are 65,536 outcomes possible for the season record.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For this problem, the parameters are given as follows:

[tex]n_1 = n_2 = \cdots = n_{16} = 2[/tex]

Then the number of ways is:

[tex]N = 2^{16} = 65,536[/tex].

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Answer:

x = -8/3

Step-by-step explanation:

-5(-3x+1)=-45

⇔ 15x - 5 = -45  (left side of the equation expanded)

⇔ 15x = -45 + 5 (add 5 to both sides)

⇔ 15x = -40

⇔ x = -40/15    (Divide both sides by 15)

⇔ x = -8/3  (simplify)

The exponential function that gives the relationship between y and t is:

[tex]y = 370000(1.06)^t[/tex].

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

In this problem, the parameters are given as follows:

A(0) = 370000, r = 0.06.

Hence the equation is:

[tex]y = A(0)(1 + r)^t[/tex]

[tex]y = 370000(1 + 0.06)^t[/tex]

[tex]y = 370000(1 .06)^t[/tex]

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Answer:

[tex]\frac{-D}{4a}[/tex]

Step-by-step explanation:

y-coordinate is [tex]\frac{-D}{4a}[/tex] where a is coefficient of quadratic polynomial (ax^2+bx+c) and D is discriminant of the quadratic equation when you equate it to zero.

Answer:

The ac product of [tex]35x^2+41x+12[/tex] is 420.

The factors of the ac product that add to 41 are 20 and 21.

[tex]35x^2+41x+12 =[/tex] [tex](7x+4)(5x+3)[/tex]

Step-by-step explanation:

1) The general form of a quadratic is [tex]ax^2 + bx + c[/tex]. Hence, multiplying 35 by 12 gives you the product of ac, which is 420.

2) We need to find two numbers that multiply to 420 and add up to 41 simultaneously. If we pull out the factors of 420, two of them will be 20 and 21, which multiply to 420 as well as add up to 41.

3) Write [tex]41x[/tex] as a sum.

[tex]35x^2+20x+21x+12[/tex]

Now, we can factor them out by grouping.

[tex]35x^2+20x+21x+12\\5x(7x+4)+3(7x+4)[/tex]

Since, [tex]7x +4[/tex] is common in both of the factors, we only take one of the [tex]7x+4[/tex] along with [tex]5x[/tex] and [tex]3[/tex].

[tex](7x+4)(5x+3)[/tex]

Answer:

[tex]\text{The ac product of }\: 35x^2+41x+12 \text{ is }\boxed{420}\:.[/tex]

[tex]\text{The factors of the ac product that add to 41 are }\:\boxed{20} \: \text{ and }\: \boxed{21}\:.[/tex]

[tex]35x^2+41x+12=\left( \: \boxed{5}\:x+\:\boxed{3}\:\right)\left(\: \boxed{7}\:x+\boxed{4}\:\right)[/tex]

Step-by-step explanation:

Given quadratic:

[tex]35x^2+41x+12[/tex]

Factoring quadratics by grouping

To factor a quadratic in the form [tex]ax^2+bx+c[/tex],  find two numbers that multiply to ac and sum to b.

[tex]\implies ac=35 \cdot 12 = 420[/tex]

[tex]\implies b = 41[/tex]

Therefore, the two numbers that multiply to 420 and sum to 41 are:
20 and 21

Rewrite b as the sum of these two numbers:

[tex]\implies 35x^2+20x+21x+12[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies 5x(7x+4)+3(7x+4)[/tex]

Factor out the common term [tex](7x+4)[/tex] :

[tex]\implies (5x+3)(7x+4)[/tex]

Conclusion

[tex]\text{The ac product of }\: 35x^2+41x+12 \text{ is }\boxed{420}\:.[/tex]

[tex]\text{The factors of the ac product that add to 41 are }\:\boxed{20} \: \text{ and }\: \boxed{21}\:.[/tex]

[tex]35x^2+41x+12=\left( \: \boxed{5}\:x+\:\boxed{3}\:\right)\left(\: \boxed{7}\:x+\boxed{4}\:\right)[/tex]

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At the end of the third day, the new reading on the odometer will be 12,578 mi

The initial odometer reading is 12,386 miles.

Then, the driver takes drives to and from work, such that each trip is 32 miles. Then each day he drives 2*2mi = 64 miles.

And he does this for 3 days, then the total distance driven is:

3*64mi = 192 miles.

At the end of the third day, the new reading on the odometer will be:

R = 12,386 mi + 192mi = 12,578 mi

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Answer:

if the red line is included it is a. if the red line is excluded it is C. I believe.

Answer:

A

Step-by-step explanation:

the equation of the line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 3 ) and (x₂, y₂ ) = (0, 1) ← 2 points on the line

m = [tex]\frac{1-3}{0-(-3)}[/tex] = [tex]\frac{-2}{0+3}[/tex] = - [tex]\frac{2}{3}[/tex]

the line crosses the y- axis at (0, 1 ) ⇒ c = 1

y = - [tex]\frac{2}{3}[/tex] x + 1 ← equation of line

the solutions to the inequality lie above the line, including the line, in the shaded area , then

y ≥ - [tex]\frac{2}{3}[/tex] x + 1 → A

Answer:

{(-3, 16),(0, 15),(3, 14)}

Step-by-step explanation:

just plug in the points for x and y and solve to see if 15 is the answer you get for all of them which would give you B as your answer

numbers like 0 and 1 and 3 (because it would cancel 1/3x) are good numbers to do quick math with

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If the height of prism is 6 inches and the volume is 144 cubic inches then the lengths of the diagonals of the rhombus will be 6 by 8 inches.

Given right prism has a rhombus as a base. Height of prism is 6 inches and the volume of prism is 144 cubic inches.

A right prism is a prism in which the edges and faces are perpendicular to the base faces.

Volume is the amount of substance a container can hold in its capacity.

Volume of right prism=area of base* height

=[tex]1/2 * d_{1}* d_{2} *6[/tex]

144=(144*2)/6 * [tex]d_{1} d_{2}[/tex]

(144*2)/6=[tex]d_{1} *d_{2}[/tex]

By options we get that the lengths of diagonals could be 6 inches by 8 inches.

Hence the length of diagonals be 6 inches and 8 inches.

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Answer: Hence the length of diagonals be 6 inches and 8 inches.

Step-by-step explanation:

(edg) got it right on test

The system of equations that is represented in the graph is:,y = -2.x-2y =6..Option B is correct.

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

Two lines may be seen on the graph:

y = -2

The lines pass through (-3) and  (6, 0). We use the slope-intercept form to get the second line's equation: y=mx+c

m = 0-(-3)/(6-0)

m=3/6

m=1/2

Substitute the values as;

[tex]\rm y = \frac{1}{2}x+c[/tex]

For the point x = 0 and y = -3

[tex]\rm y = \frac{1}{2}x-3[/tex]

The equation can be written as;

x - 2y = 6

The system of equations that is represented in the graph is:,y = -2.x-2y =6..

Hence, option B is correct.

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Answer:

61.75

Step-by-step explanation:

1900x0.03x1.08333333=61.75

Answer:

1.08 meters

Step-by-step explanation:

Divide by 100 to find this out. 108/100 = 1.08

You can remember this by knowing that the "centi-" prefix means 100 (technically, 100ths). Just like you probably already know 100 cents in a dollar (USD) or 100 years in a century. Even the "cent" in percent means per hundred. There are 100 centimeters in a meter. A centimeter is about as wide as your little finger. A meter is close to a yard.

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

Answer:  [tex]\textsf{0.108 meters}[/tex]

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

Given:  [tex]\textsf{108 centimeters}[/tex]

Find:  [tex]\textsf{Covert to meters}[/tex]

Solution:  In order to convert centimeters to meters we need to divide the amount of centimeters by 100 since there are 100 centimeters in one meter.  After doing 108/100 we get 1.08 meters.

Answer:

The sum of three consecutive even integers is 96

31+32+33=96

The dependent and the independent variable in the relationship y=60x are y and x respectively.

The Independent variables are variables whose value does not depend on any other variable. And it causes the change in other variables.

The dependent variable is those variables whose value is not independent and change in this variable is dependent on the change of the independent variable.

Given that you did 60 brush strokes in 1 minute. Therefore, the rate can be written as,

Rate = 60 strokes per minute

Now, the number of stokes in x minutes can be written as,

y = 60x

where y is the number of stokes,

x is the number of minutes

In the above relation, y is the dependent variable because its numerical value depends on time, while x is the independent variable.

Hence, The dependent and the independent variable in the relationship y=60x are y and x respectively.

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Answer:

x = - 11

Step-by-step explanation:

y = 15 is a horizontal line parallel to the x- axis

a perpendicular line must therefore be a vertical line parallel to the y- axis with equation

x = c

where c is the value of the x- coordinates the line passes through.

the line passes through (- 11, - 1 ) with x- coordinate of - 11 , then

x = - 11 ← equation of perpendicular line

Answer:

x = -11

Step-by-step explanation:

The line y = 15 is a horizontal line to the x-axis passing which passes through x = 0, y = 15

The line perpendicular to y = 15 passing through (-11, -1) is a vertical line where x = -11 for all values of y including -1

So the equation is x = -11

See attached graph

The line with slope = 2 will be closer to the y-axis than the line with slope = 1/2

The slopes are given as:

Slope = 2

Slope = 1/2

The greater the absolute value of the slope of a linear equation.

The closer the function is to the y-axis

This means that the line with slope = 2 will be closer to the y-axis than the line with slope = 1/2

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Using the profit concept, we have that:

Profit is given by revenue subtracted by costs.

In this problem, we have that:

Hence the expression for the profit is given as follows:

P(x) = R(x) - C(x)

P(x) = 90x - 0.5x² - 50x - 300

P(x) = -0.5x² + 40x - 300.

A profit of $300 is found when P(x) = 300, hence:

300 = -0.5x² + 40x - 300

0.5x² - 40x + 600 = 0.

x² - 80x + 1200 = 0.

(x - 60)(x - 20) = 0.

Hence the values are:

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The equivalent expression of -2x + 5 is 5 - 2x

The expression is given as:

-2x + 5

The symmetry rule of expression states that:

a + b = b + 1

So, we have:

-2x + 5 = 5 - 2x

Hence, the equivalent expression of -2x + 5 is 5 - 2x

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Answer:

I don't know if you have any questions or need any further information please contact me your Telugu movie review poster

Answer:

[tex]1 \frac{125001}{200000}[/tex] or 1.625005

Step-by-step explanation:

To find a number between two numbers, if you're allowed to pick any number you want between those two numbers, one natural choice is the midpoint... the point that is exactly halfway between the two numbers.

Finding a midpoint

To find the midpoint of two numbers, divide their sum by 2:

[tex]\text{midpoint}=\dfrac{\text{first number}+\text{second number}}{2}[/tex]

It is convenient to have both numbers in decimal form or both numbers in fraction form for adding and dividing by 2.

Fraction form:

To convert 1.62501 to a fraction, we note that the last decimal digit is in the hundred-thousandths place, so we'll need a fraction with 100,000 in the denominator.

[tex]1.62501=1\frac{62501}{100000}[/tex]

Using our midpoint formula:

[tex]\text{midpoint} = \dfrac{ 1 \frac{5}{8} + 1 \frac{62501}{100000} } {2}[/tex]

find a common denominator...

[tex]\text{midpoint} = \dfrac{ 1 +(\frac{5}{8})*\frac{12500}{12500} + 1 +\frac{62501}{100000} } {2}[/tex]

[tex]\text{midpoint} = \dfrac{ 1 + \frac{62500}{100000} + 1 +\frac{62501}{100000} } {2}[/tex]

combining like terms...

[tex]\text{midpoint} = \dfrac{ 2 +\frac{125001}{100000} } {2}[/tex]

rewriting the division as multiplication of a reciprocal....

[tex]\text{midpoint} = \left(2 +\frac{125001}{100000} \right) *\dfrac{1}{2}[/tex]

distributing...

[tex]\text{midpoint} = \left(2 *\dfrac{1}{2} +\frac{125001}{100000} *\dfrac{1}{2}\right)[/tex]

[tex]\text{midpoint} = 1 +\frac{125001}{200000}[/tex]

[tex]\text{midpoint} = 1 \frac{125001}{200000}[/tex]

So, [tex]1 \frac{125001}{200000}[/tex] is the midpoint of the two numbers, and is a number that is between them.

Decimal form:

To convert [tex]1 \frac{5}{8}[/tex]  to a decimal, we divide 5 by 8.  5 divided by 8 is 0.625.

So, [tex]1 \frac{5}{8}=1.625[/tex]

To find a midpoint of 1.625 and 1.62501, we use our midpoint formula:

Using our midpoint formula:

[tex]\text{midpoint} = \dfrac{ 1.625 + 1.62501} {2}[/tex]

[tex]\text{midpoint} = \dfrac{ 3.25001} {2}[/tex]

[tex]\text{midpoint} =1.625005[/tex]

So, 1.625005 is midpoint of the two numbers, and is a number that is between them.

Extension with decimals:

Knowing the decimal form of the two numbers, 1.625 and 1.62501, we can include trailing zeros at the end of these numbers (since it is to the right of the decimal point), so that 1.625 is equivalent to 1.625000, and 1.62501 is equivalent to 1.625010.

Note that the last two digits are in the millionths place, and that changing the digit in the millionths place for the first number (while leaving all other digits as they are) will also be a number between the two numbers (all 9 of the numbers with a star written below):

1.625000

1.625001*

1.625002*

1.625003*

1.625004*

1.625005*

1.625006*

1.625007*

1.625008*

1.625009*

1.625010

(a) The side length of the square is 8 m, so its area is 64 square m.

(b) The radius of the circle is 4 m, so its area is [tex](\pi)(4^{2})=16\pi[/tex] square m.

(c) Subtracting areas, we get the area of the shaded region is [tex]64-16\pi[/tex] square m.

Answer:

is the a. Perpendicular lines form 90° angles.

The given vertices combine with the fourth vertex as follows;

a) Coordinates; (-4, 5)

Lengths of the sides; 4 and 5

b) Coordinates; (4, 5)

Lengths of the sides; 4 and √41

c) Coordinates; (-4, -5)

Lengths of the sides; 5 and √41

The given vertices are;

(0, 0): The origin

(-4, 0): 4 units to the left of the origin along the abscissa

(0, 5): 5 units above the origin, along the ordinate

a) The point that forms a rectangle is above the point (-4, 0) and to the left of the point (0, 5), which gives;

The coordinates of the point that forms a rectangle is the point (-4, 5)

The lengths of the sides are;

0 - (-4) = 4

5 - 0 = 5

b) The first parallelogram is formed by moving an equal distance of the point (-4, 0) from the origin from the point (0, 5), which gives;

The lengths of the sides are;

c) The second parallelogram is formed by the moving an equal distance of the point (0, 5) from the origin from the point (-4, 0), which gives;

The lengths of the sides are;

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Answer:

(h + k) (2) = 5

Step-by-step explanation:

[tex]h(x) = x{^2} + 1 \space\ \space\ \space\ \space\ \space\ \space\ \space\ k(x) = x -2\\\\[/tex]

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

               = x² + 1  +  x - 2

               = x² + x -1

∴ (h + k) (2) = (2)² + 2 -1

                  = 5