simplify the following: 4(y + 2)

The area outside of the doghouse in which the dog can play is 16π m².

Thus, option (B) is correct.

Given:

The leash is 4 m long.

The doghouse is a 2 m × 2 m square.

First, the area of a square is given by side length squared

So, the area of the doghouse is:

Area of the doghouse = side length² = 2²

                                                             = 4 m².

Next, the area of the circle with a radius of 4 m.

The area of a circle is given by the formula A = πr²,

So, Area of the circle = π(4²) = 16π m².

Therefore, the area is 16π m².

Thus, option (B) is correct.

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Answer:

6b+16n=178

n=b+7

Step-by-step explanation:

Let b=the number of bracelets made

Let n=the number of necklaces made

​

System of Equations:

​

6b+16n=178

n=b+7

Answer:

Angle HFG = 24 degrees

Step-by-step explanation:

From the diagram, we have the following;

Angle EFH and angle HFG are complementary (they add up to be 90 degrees)

angle EFH + angle HFG = 90

Angle HFG = 90-66

Angle HFG = 24 degrees

Well there are no choices listed so it's going to be hard to say which; we'll write an expression for all of them and then give a few instances.

A parabola with a minimum forms a CUP, concave-up positive, meaning the coefficient a on x² must be positive, a>0.  

The general form with vertex (p,q) is

y = a(x-p)² + q

So for us, all our parabolas are of the form

y = a(x- -3)² + 9

y = a(x² + 6x + 9) + 9

y = ax² + 6ax + 9(a+1)

That's the general form for a parabola with vertex (-3,9); a>0 assure the parabola has a minimum at the vertex.

Some instances:

a=1 gives

Answer: y = x²+6x+18

a=4 gives

y = 4x² + 24x + 45

Other positive as give other possible answers; without the choices it's impossible to know which one they're seeking.

Answer:

x = - 11

Step-by-step explanation:

u and v are parallel if you  have equal alternate interior angles .

that is ,

x + 111 = 100

x = 100 - 111

x = - 11

Answer:

15

Step-by-step explanation:

Given :

StartAbsoluteValue 8 EndAbsoluteValue + StartAbsoluteValue Negative 7 EndAbsoluteValue

THE ABSOLUTE value of any given number is the positive equivalent of that number ; hence ;

|8| = 8 ;

|-7| = 7

Hence,

|8| + |-7| = 8 + 7 = 15

Answer:

15

Step-by-step explanation:

Answer:

Hi, your answer is y=[tex]-\frac{1}{2} x[/tex]-3

Step-by-step explanation:

We will use the slope-intercept formula which is

[tex]\frac{y2-y1}{x2-x1}[/tex]

We will use two points in this case I'll use

(-2,-2) and (-8,1)

[tex]\frac{1-(-2)}{-8-(-2)}[/tex]=[tex]-\frac{3}{6}[/tex] which can be simplified as [tex]-\frac{1}{2}[/tex]

Your Y will be -3

which your final answer will be y=-1/2x-3

Hope this helps :)

Answer:

y=4

Step-by-step explanation:

3 x 2=6

6 - 2= 4

Answer:

y = 4

Step-by-step explanation:

Equation: y = 3x - 2

Plug in x = 2

New equation: y = 3(2) - 2

Simplify: y = 6 - 2 --> y = 4

Answer: y = 4

Answer:

-22

Step-by-step explanation:

if a = 4, then it will be

-4 + 3(-6)

-4 - 18

which will be equal -22

4 + 3 × -6 = -22

Your welcome! :)

Answer:

2400 seconds

Step-by-step explanation:

Answer:

40 min = 2400 sec

Step-by-step explanation:

Answer:

The answer is 2(23x+4).

Answer:

16.6 units

Step-by-step explanation:

Hi there!

We can use the Pythagorean theorem to help us solve this problem: [tex]a^2+b^2=c^2[/tex] where c is the longest side of a right triangle (the hypotenuse) and a and b are the other two sides

It's safe to assume that x is the longest side in this triangle, making it the c value. Plug 14 and 9 into the equation as a and b and solve for x:

[tex]14^2+9^2=x^2\\196+81=x^2\\277=x^2\\x=16.6[/tex]

Therefore, the value of x is 16.6 units when rounded to the nearest tenth.

I hope this helps!

Answer:

Each brace uses 2.[tex]\overline 6[/tex] inches of wood

Step-by-step explanation:

The given parameters are;

The length of the board from which he cuts the wood = 8 feet

The length of the wood he cuts from the board = 4 feet

The number of corners on the braces of equal sizes he makes with the wood he has left = 18 corner brace

We have;

The length of the wood he has left = (The length of the board) - (The length of the wood he cuts from the board)

∴ The length of the wood he has left = 8 feet - 4 feet = 4 feet

The length of each brace the man can cuts from the wood he has left = (The length of the wood he has left)/(The number of corner braces he cuts)

∴ The length of each brace = (4 feet)/(18 braces) = (48/18) inches/(braces) = (8/3) inches/brace = 2.[tex]\overline 6[/tex] inches of wood per brace

Answer

X=25

Step-by-step explanation:

Answer:

Proportion of chocolate in biscuit tin = 5:7

Step-by-step explanation:

Given:

Number of chocolate in biscuit tin = 10

Number of shortbread biscuits in biscuit tin = 4

Find:

Proportion of chocolate in biscuit tin

Computation:

Proportion of chocolate in biscuit tin = Number of chocolate in biscuit tin / Total product in biscuit tin

Proportion of chocolate in biscuit tin = 10 / [10 + 4]

Proportion of chocolate in biscuit tin = 10 / 14

Proportion of chocolate in biscuit tin = 5:7

Answer:

Step-by-step explanation:

area of semi circle=πr^2/2

=3.14*(2.4)^2/2

=3.14*5.76/2

=18.0864/2

=9.0432 cm^2

Answer:

72/25 [tex]\pi[/tex] cm² or 9.047786842... cm²

Step-by-step explanation:

Area of whole circle is [tex]\pi r^{2}[/tex]

[tex]\pi[/tex]×2.4² = 144/25[tex]\pi[/tex] cm² or 18.09557368... cm²

Since it is a semi-circle, divide this value by 2 (or multiply by 0.5, either way, your halving it):

144/25[tex]\pi[/tex] ÷ 2 = 72/25 [tex]\pi[/tex] cm² or 9.047786842... cm²

Given:

[tex]f(1)=7[/tex]

[tex]f(n)=3f(n-1)+3[/tex]

To find:

The value of f(3).

Solution:

We have,

[tex]f(n)=3f(n-1)+3[/tex]               ...(i)

Substituting [tex]n=2[/tex] in (i), we get

[tex]f(2)=3f(2-1)+3[/tex]

[tex]f(2)=3f(1)+3[/tex]

Substituting [tex]f(1)=7[/tex] in the above equation, we get

[tex]f(2)=3(7)+3[/tex]

[tex]f(2)=21+3[/tex]

[tex]f(2)=24[/tex]

Now, substituting [tex]n=3[/tex] in (i), we get

[tex]f(3)=3f(3-1)+3[/tex]

[tex]f(3)=3f(2)+3[/tex]

Substituting [tex]f(2)=24[/tex] in the above equation, we get

[tex]f(3)=3(24)+3[/tex]

[tex]f(3)=72+3[/tex]

[tex]f(3)=75[/tex]

Therefore, the value of f(3) is 75.

Answer:

x = 1

Step-by-step explanation:

-3 (7x + 7) = -38 - 4x

-3(7x)-3(7) = -38 - 4x

-21x - 21 = -38 - 4x

-21x+4x = -38+21

-17x = -17

x = -17/-17

x = 1

Answer:

x = 1.

Step-by-step explanation:

-3(7x + 7) = -38 - 4x

Use distributive property to get:

-21x - 21 = -38 - 4x

Add 4x to both sides to get:

- 17x - 21 = -38

Add 21 to both sides to get:

- 17x = -17

x = 1.

I hope this helps, have a nice day.

Answer:

80miles

Step-by-step explanation:

Area of a square grid = L²

L is the side length of the grid

Given that Area of the square = 400mi square

400 = L²

L =√400

L = 20miles

To get the number of miles travelled, we will find its perimeter

P = 4L

P = 4(20)

P = 80miles

Hence Jacob's family travels 80miles

The polynomial function of degree 7 with the given zeros and multiplicities is: f(x) = x³(x + 2)³(x - 2)

To find a polynomial function with the specified zeros and multiplicities, we can construct it using the factors that correspond to each zero and multiplicity.

Since -2 has a multiplicity of 3, it means it appears three times as a zero. Similarly, 0 has a multiplicity of 3, and 2 has a multiplicity of 1.

A polynomial function with these zeros and multiplicities can be written as:

f(x) = (x + 2)³ × x³ × (x - 2)

To make it a polynomial of degree 7, we can multiply it by an additional linear factor:

f(x) = (x + 2)³ × x³ × (x - 2) × (x - r)

Where "r" is a constant representing the last factor. This factor ensures the degree of the polynomial is 7.

Now, we need to find the value of "r" to complete the polynomial. Since we already have three factors with multiplicity 3 and one factor with multiplicity 1, the polynomial has already reached its degree of 7.

Therefore, we don't need to include the "x - r" factor, and the final polynomial is:

f(x) = (x + 2)³ × x³ × (x - 2)

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The polynomial function of degree 7 with -2 as a zero of multiplicity 3, 0 as a zero of multiplicity 3, and 2 as a zero of multiplicity 1 is f(x) = x^7 + 4x^6 - 12x^5 + 20x^4 - 16x^2.

To find a polynomial function of degree 7 with the given zeros and multiplicities, we can start by constructing the factors of the polynomial.

Since -2 is a zero of multiplicity 3, we have the factor (x + 2)^3. Similarly, since 0 is a zero of multiplicity 3, we have the factor x^3. Lastly, since 2 is a zero of multiplicity 1, we have the factor (x - 2).

Multiplying these factors together, we obtain:

(x + 2)^3 * x^3 * (x - 2)

Expanding this expression, we get:

(x^3 + 6x^2 + 12x + 8) * x^3 * (x - 2)

To simplify further, we multiply the terms:

(x^6 + 6x^5 + 12x^4 + 8x^3) * (x - 2)

Expanding again, we obtain:

x^7 - 2x^6 + 6x^6 - 12x^5 + 12x^4 - 24x^3 + 8x^3 - 16x^2

Combining like terms, we get:

x^7 + 4x^6 - 12x^5 + 20x^4 - 16x^2

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Answer:

-1

Step-by-step explanation:

y2-y1/x2-x1

-4-5/5- -4

-9/9

-1

Answer:

x=2

Step-by-step explanation:

i would set up a system of equation using the pythagorean theorem:

1^2+x^2=z^2

4^2+x^2=y^2

Add up these equations to get:

17+2x^2=y^2+z^2

But notice that

y^2+z^2=5^2

So you can substitute

17+2x^2=25

2x^2=8

x^2=4

x=2

:)

The coach can select 3 people to swim in the relay in 120 ways.

'In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter.'

According to the given problem,

Number of players = 10

Number of people to be selected = 3

We know,

[tex]^{n}C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex] where, n = Total number of players

                                 r = Number of players to be selected

Number of ways to select 3 people out of 10 = [tex]^{10} C_{3}[/tex]

                                                                           = [tex]\frac{10!}{3!*7!}[/tex]

                                                                            = 120 ways

Hence, we can conclude, the coach can select 3 people out of 10 in 120 ways.

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Answer:

b) tan 26° = 18/x

Step-by-step explanation:

tan is opposite/adjacent

Answer:

Answer B

Step-by-step explanation:

You have the angle, the opposite and are looking for the adjacent

The only solutions is using tan

tan = opposite / adjacent

Answer: pretty sure it is 201 tiles

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A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. The given statement is True.

A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.

The given statement is true and can be observed in the given image below.

Hence, the given statement is True.

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Answer:

Your answer is 82

Step-by-step explanation:

15+25+13+13+8+8=82

Answer: c

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{12p^{5}r}{-10pq} = \frac{-6p^{5-1}r}{5q}\\\\=\frac{-6p^{4}r}{5q}[/tex]

[tex]\frac{a^{m}}{a^{n}}=a^{m-n}[/tex]