Solve the following system of equations. Show all work and solutions.


y = 2x^2 + 6x + 1

y = −4x^2 + 1

Answer:

  54 chickens

Step-by-step explanation:

This problem requires you find the area of Thomas's field, then use that area to find the number of chickens he can keep. The irregularly-shaped field can be considered as composed of shapes that you know how to find the area of.

__

There are many ways the area can be divided. One of them is shown in the attachment. That shows the area to be the sum of the areas of a triangle and a trapezoid.

The triangle has a base of 20 m and a height of 7 m, so an area of ...

  A = 1/2bh

  A = 1/2(20 m)(7 m) = 70 m²

The trapezoid has bases of 11 m and 18 m, and a height of 14 m. Its area is ...

  A = 1/2(b1 +b2)h

  A = 1/2(11 m +18 m)(14 m) = 1/2(29 m)(14 m) = 203 m²

The area of the field is the sum of these areas:

  field area = triangle area + trapezoid area

  field area = 70 m² +203 m² = 273 m²

__

Each chicken requires an area of 5 m², so the total area for n chickens is ...

  area for n chickens = 5n . . . . square meters

This area cannot exceed the area of the field, so an inequality can be written:

  area for n chickens ≤ field area

  5n ≤ 273

  n ≤ 54.6 . . . . . . divide by 5

Thomas can keep a maximum of 54 chickens in the field.

When the metronome was created out of a piece of solid wood, the minimum amount of solid wood that was used from the pyramid will be C. 540 centimeters cubed.

From the information given, the metronome ticks at adjustable intervals to help keep time when playing music.

In rhis case, when the metronome was created out of a piece of solid wood, the minimum amount of solid wood that was used from the pyramid will be:

= 20 × 9 × ✓9

= 20 × 9 × 3

= 540

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Answer:

540

Step-by-step explanation:

C

Answer:

what environmental ethics

Answer:

-2/35

Step-by-step explanation:

Slope y-intercept form : y = mx + b

Here m is the slope and b is the y-intercept

Write the given equation in slope y-intercept form.

   [tex]\sf \dfrac{2}{7}x + 5y = 15\\\\[/tex]

           [tex]\sf 5y = \dfrac{-2}{7}x + 15\\\\ y =\dfrac{-2}{7*5}x + \dfrac{15}{5}\\\\ y = \dfrac{-2}{35}x + 3\\\\ \boxed{\bf Slope = \dfrac{-2}{35}}[/tex]

Answer:

Step-by-step explanation:

Answer:

122.5 degrees

Step-by-step explanation:

A six sided polygon's interior angles sum to

  (n-2)(180) =  (6-2) (180) = 720 degrees

then   x + x + x +     x+10    + 130   + 90 = 720

                          4x = 490        so x = 122.5 degrees

For this exercise, the graph of a logarithmic function is shown in the image attached below.

A logarithmic function is a type of function that graphically represents the inverse of an exponential function. Mathematically, a standard logarithmic function is written as [tex]y = log_nx[/tex].

In Mathematics, the domain of any logarithmic function is from (x > 0) to infinity (+∞). Thus, its graph moves to the right on the vertical axis and it increases to infinity (+∞) as the value of x increases.

In this scenario, an image of all the graphs wasn't provided, so, I would proceed to add an attachment to illustrate the graph of a logarithmic function.

Note: The graph (u-shaped) shown in the image attached above is that of a parabolic function.

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Ann and Bob's age is 21 years  and 28 years respectively and after 14 years the ratio will be 5:6.

What is Ratio ?

The comparison of one quantity to other is called a ratio and when two ratios are equal they are said to be in proportion.

It is given in the question that

The ratio of Ann's age to bob's age is 3:4

in 7 years time this ratio will be 4:5

their ages now = ?

Let the age of Ann and Bob is x and y

x:y = 3:4

x =(3/4)y

After seven years

(x+7):(y+7) = 4 :5

(x+7)/(y+7) = 4/5

((3/4)y +7)/(y+7) = 4/5

(3y +28)/(y+7) = 16/5

5*(3y+28)= 16(y+7)

15y +140 = 16y+112

y = 140-112

y =28 years

x = 21 years.

After x years suppose the ratio is 5 :6

(21+x)/(28+x) = 5:6

126 +6x = 140 + 5x

x = 14 years.

Therefore after 14 years the ratio will be 5:6.

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The title of the work introduced is Rechnung nach der lenge/auff den Linien und Feder.

In mathematics, an operation is a function that takes zero or more input values to a well-defined output value.

Adam Riese developed the signs + and - as mathematical operations and the title of the work introduced is Rechnung nach der lenge/auff den Linien und Feder.

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Answer:

27 units

Step-by-step explanation:

6 (base) × 9 (height) = 54

54 × 1/2 = 27

Answer:

Given, an isosceles right triangle has area 8 cm². We have to find the length of its hypotenuse. We know that in an isosceles triangle two sides are of equal length. Therefore, the length of the hypotenuse is √32 cm.

After calculation the value is 4.62 * 10⁴ in Scientific Notation.

It is a way of presenting very large and small number in simpler and more understandable form.

It is given that

Calculate 3.1 x 10⁸ divided by 6.7 x 10³

[tex]\rm \dfrac{3.1*10^8}{6.7*10^3}\\\\By \;the \;exponent\; theorem\\\\\dfrac{a^m}{a^n} = a ^{m-n}[/tex]

Therefore

0.462 * 10⁵

4.62 * 10⁴

Therefore the answer after calculation is 4.62 * 10⁴ .

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The x-intercept and y-intercept of the equation: 3x - y = -9 is -3 and 9 respectively.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have equation:

3x - y = -9

The above equation represents a linear equation;

The equation can be written as:

y = 3x + 9

To find the x-intercept plug y = 0

x = -3

To find the y-intercept plug x = 0

y = 9

Thus, the x-intercept and y-intercept of the equation: 3x - y = -9 is -3 and 9 respectively.

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If the degree of the polynomial is 3. Then the value of m will be 2. Then the correct option is B.

The complete question is attached below.

Let the polynomial is given below.

axⁿ + bxⁿ⁻¹ + .... + kx¹ + lx⁰

Then the highest power of the polynomial is known as the degree of the polynomial.

The polynomial is given as

[tex]\rm 10x^2 + 2x^my-4y[/tex]

The degree of the polynomial is 3. Then the value of m will be

m + 1 = 3

    m = 2

Then the correct option is B.

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The probability of winning when betting on two lines that touch each other on the table is 6/38

The sample size is given as:

n = 38

The numbers on the range 1-2-3-4-5-6 is:

Range = 6

So, the probability is calculated as:

P = Range/n

This gives

P = 6/38

Hence, the probability of winning is 6/38

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k(2)=

Option C is true

k(3)

D is true

k(4)

k(5)

k(6)

E is not true

k(1)

So

B is false

Similarly

-1 is not in domain even though

A is false

Answer:

[tex]k(2) = 2[/tex]

[tex]k(3) = 0[/tex]

Step-by-step explanation:

Given:

[tex]\begin{cases}k(1)=4\\k(n)=k(n-1)-2\end{cases}[/tex]

The function [tex]k(n)[/tex] tells us that each term is 2 less than the preceding term.

Therefore:

[tex]\implies k(1)=4[/tex]

[tex]\implies k(2)=k(1)-2=4-2=2[/tex]

[tex]\implies k(3)=k(2)-2=2-2=0[/tex]

[tex]\implies k(4)=k(3)-2=0-2=-2[/tex]

[tex]\implies k(5)=k(4)-2=-2-2=-4[/tex]

[tex]\implies k(6)=k(5)-2=-4-2=-6[/tex]

Rearranging the formula to make the preceding term the subject:

[tex]\begin{aligned} k(n) & = k(n-1) - 2\\\implies k(n)+2 & = k(n-1)\\k(n-1) & =k(n)+2\end{aligned}[/tex]

Therefore:

[tex]\implies k(1)=4[/tex]

[tex]\implies k(0)=k(1)+2=4+2=6[/tex]

[tex]\implies k(-1)=k(0)+2=6+2=8[/tex]

Conclusion

Therefore, the correct answers from the answer options are:

[tex]k(2) = 2[/tex]   and   [tex]k(3) = 0[/tex]

Answer: a1=6

               An = An-1 - 4

Step-by-step explanation:

N represent what number in the sequence you choose. So in the equation n-1 would be the umber in the equation subtracting 1 then subtracting the difference. The factor you are multiplying by in this sequence is -4. You find the difference by taking any number in the sequence and dividing it by the previous number in the sequence.

Answer:

The third option.

Step-by-step explanation:

It is the third option because it is subtracting by 2 each time.

Hope this helps!

If not, I am sorry.

Answer:

388848y2

Step-by-step explanation:

yup yup

Answer:

(0, -5)

Step-by-step explanation:

the y-intercept of the parabola is when x = 0 (crossing the y axis)

The multiplication of the matrix [tex]\left[\begin{array}{ccc}4\\9\\7\end{array}\right] \left[\begin{array}{ccc}1&-2&1\end{array}\right][/tex]will be [tex]\left[\begin{array}{ccc}4&-8&4\\9&-18&9\\7&-14&7\end{array}\right][/tex].

A matrix is a representation of the rectangular arrangement of numbers into rows and columns.

Matrix multiplication refers to the product of two matrices.

The condition of matrix multiplication is that the number of columns of the 1st matrix must equal the number of rows of the 2nd one.

The given matrix are

[tex]\left[\begin{array}{ccc}4\\9\\7\end{array}\right] \left[\begin{array}{ccc}1&-2&1\end{array}\right][/tex]

The multiplication of the matrix will be

[tex]\left[\begin{array}{ccc}4&-8&4\\9&-18&9\\7&-14&7\end{array}\right][/tex]

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The simplification of the indices can be seen in the explanation below.

[tex]\mathbf{= \dfrac{1^3}{32r^5y^3}}[/tex]

The simplification of indices entails simplifying the indices to the simplest form possible by using the laws of indices.

From the information given, we have:

1.

[tex]\mathbf{= \dfrac{1^3}{32r^5y^3}}[/tex]

2.

[tex]\mathbf{= \dfrac{214}{2ry^3}}\\[/tex]

[tex]\mathbf{=\dfrac{ 107}{ry^3}}[/tex]

3.

= 2×4 √4xy³

= 8 √4xy³

= 8 × 2√xy³

= 16√xy³

4.

= 2rty 4ry³

= 2tr²y⁴

5

= 413/21²y³

= 413/441 y³

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Answer:

1.

2.

3.

= 2×4 √4xy³

= 8 √4xy³

= 8 × 2√xy³

= 16√xy³

4.

= 2rty 4ry³

= 2tr²y⁴

5

= 413/21²y³

= 413/441 y³

Step-by-step explanation:

Answer:

3.82362

rounded: 3.82

Step-by-step explanation:

An example of a exponential function with growth rate of 5 is given as y = 2(5)^4

These are functions that increases geometrically. The standard exponential function is given as;

y = ab^x

where

An example of a exponential function with growth rate of 5 is given as y = 2(5)^4

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Answer:

Blue Rectangle: 135 mm²

Blue Triangle: 45 mm²

Not sure if you need this but the Total Square: 225 mm²

Step-by-step explanation:

Area of a rectangle: length x width

Area of a triangle: [tex]\frac{1}{2}[/tex] x base x height

First find the area of the blue rectangle.

Length = 15 mm

Width = 9 mm

Area = 135 mm²

Now find the area of the blue triangle:

Base = 6 mm (because the bottom is 15 total and you subtract the 9)

Height = 15 mm

Area = 45 mm²

Hope it helps!

Answer:

1 and 1/4 pounds

Step-by-step explanation:

Answer:

(-7, -10)

Step-by-step explanation:

Solve for x and y in double variable equation

y = 2x + 4

y = x - 3

y = x - 3, plug in to first equation

x - 3 = 2x + 4

x = -7

y = -7 - 3

y = -10

(-7, -10)

Answer: y = -12

Equation's:

Solve them simultaneously:

4x - 28 = 1.5x - 18

4x - 1.5x = -18 + 28

2.5x = 10

x = 10/2.5 = 4

Now find the value of y:

y = 4x - 28

insert x = 4

y = 4(4) - 28

y = 16 - 28 = -12

Answer:

[tex]y=-12[/tex]

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}y = 4x - 28\\y = 1.5x - 18\end{cases}[/tex]

Use the method of substitution to solve for x:

[tex]\begin{aligned}y & = y\\\implies 4x-28 & = 1.5x - 18\\4x-1.5x & = -18+28\\2.5x & = 10\\x & = 10 \div 2.5\\x & = 4\end{aligned}[/tex]

Substitute the found value of x into one of the equations and solve for y:

[tex]\begin{aligned} y & = 4x-28\\\implies y & =4(4)-28\\y & = 16-28\\y & = -12\end{aligned}[/tex]