Find the missing side length of the triangle.

When the completing the square is applied, the rewritten function is (x + 2)^2 = 4

The equation is given as:

x^2 + 4x = 0

The above equation is a quadratic equation and the coefficient of x in the above equation is 4.

So, we have:

k = 4

Divide the variable k by 2

k/2 = 4/2

k/2 = 2

Square the above result

(k/2)^2 = 4

Next, we add 4 to both sides of x^2 + 4x = 0

x^2 + 4x + 4 = 4

Expand the equation by expressing 4x as 2x + 2x

This gives

x^2 + 2x + 2x + 4 = 4

Factorize the above equation

x(x + 2) + 2(x + 2) = 4

Factor out x + 2 from the above equation

(x + 2)(x + 2) = 4

Rewrite the equation as a perfect square of (x + 2)

(x + 2)^2 = 4

Hence, the rewritten function after completing the square is (x + 2)^2 = 4

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The volume of the rectangular prism is 8 1 / 8 units³

volume of a rectangular prism = lwh

where

Therefore,

volume of a rectangular prism = base area × height

volume of a rectangular prism = 16 1 / 4 × 1 / 2

volume of a rectangular prism = 65 / 4 × 1 / 2

volume of a rectangular prism =  65 / 8

volume of a rectangular prism =  8 1 / 8 units³

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Answer:

[tex]y^6[/tex]

Step-by-step explanation:

So there is an exponent identity that states: [tex](x^b)^a = x^{a*b}[/tex] which means this question becomes: [tex](y^2)^3 = y^{2*3} = y^6[/tex].

Just so you completely understand why this works, it might help to express y^2, as what it truly represents: [tex]y^2=y*y[/tex]. So using this definition we can substitute it into the equation so it becomes: [tex](y*y)^3[/tex]. Now let's use the definition of exponents like we just did with the y, to redefine this in terms of multiplication: [tex](y*y)^3 = (y * y) * (y * y) * (y * y)[/tex]. We can just multiply all these out, and we get: [tex]y * y * y * y * y * y =y^6[/tex].

To make it a bit more general when we have the exponent: [tex]x^b[/tex] it can be expressed as: [tex](x*x*x...\text{ b amount of times})[/tex] now when we raise it to the power of a. we get: [tex](x * x * x...\text{ b amount of times})^a[/tex] which can further be rewritten using the definition of an exponent to become the equation: [tex](x*x*x\text... \text{ b amount of times}) * (x * x * x...\text{ b amount of times})...\text{ a amount of times}[/tex] which just simplifies to: [tex]x*x*x*x...\text{ a times b amount of times}[/tex]. Hopefully this makes the identity a bit more understandable

Answer:

1. a = 32, c = 24

Step-by-step explanation:

a = c+8

a-20 = 3(c-20)

(c+8)-20 = 3c-60

c = 24

a = 24+8

a = 32

2. t = 15, j = 9

t-3 = 2(j-3)

t-3 = 2j-6

t = 2j-3

t + 2 + j + 2 = 28

(2j-3)+ 2 + j + 2 = 28

3j + 1 = 28

3j = 27

j = 9

t-3 = 2(9-3)

t-3 = 2(6)

t-3=12

t = 15

3. b=36, s=31

b = s + 5

b+s = 67

(s+5)+s = 67

2s+5 = 67

2s = 62

s = 31

b = 31+5

b = 36

4. 231

h + t + u = 6

(with h=hundreds digit, t=tens digit, u=units digit)

h = 2u

t = h+u

t = (2u) + u

(2u) + (2u +u) + u = 6

6u = 6

u = 1

h = 2

t = 3

the number is 231

5. 48

u = 2t

the 2-digit number is 10t+u

2(10t+u) = 10u+t+12

2(10t + 2t) = 10(2t) + t + 12

20t + 4t = 20t + t + 12

24t = 21t + 12

3t = 12

t = 4

u = 2*4

u = 8

the number is 48

Answer:

3/8

Step-by-step explanation:

There are 8 equal slices so each slice is 1/8th of the whole pizza

1/8+1/8=2/8 he ate right away

2/8+1/8 for what he ate before going to sleep

2/8+1/8=3/8

The p-value from the hypothesis test is 0.142 i.e., greater than the given significance level of 0.05. So, the null hypothesis is not rejected. The z-score for the given sample is 1.471.

The decision rule based on p-value states,

Since it is given that the valve would produce a mean pressure of 5.4 pounds/square inch. I.e., μ = 5.4 p/si

So, Defining the hypothesis:

Null hypothesis H0: μ = 5.4

Alternative hypothesis Ha: μ ≠ 5.4

It is given that,

The valve was tested on 24 engines. I.e., Sample size n = 24

The sample mean X = 5.7

Standard deviation σ = 1.0 and

The significance level = 0.05

Since the population distribution is approximately normal,

the test statistic is calculated as follows:

z = (X - μ)/(σ/[tex]\sqrt{n}[/tex])

On substituting the value,

z = (5.7 - 5.4)/(1.0/[tex]\sqrt{24}[/tex])

  = (0.3)/0.204

  = 1.471

Fron this z-score, the p-value is calculated as 0.142.

Since, the value of p > 0.05 (significance level), the null hypothesis is not rejected.

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Answer:

16x-2

Step-by-step explanation:

Perimeter is 2w+2l

so we plug it in

2(3x+1) + 2(5x-2)

now we distribute

6x+2 + 10x -4

now we add like terms

6x+10x+2-4

16x-2

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

To find an unknown side of a right angled triangle we use a theorum called pythagorus theorum..

(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

(h)^2 = (p)^2 + (b)^2

(a) hypotenuse = x cm, base = √30 cm, perpendicular = √12 cm.

→ h^2 = p^2 + b^2

→ (x)^2 = (√12)^2 + (√30)^2

→ x^2 = 12 + 30

→ x^2 = 42

→ x = √42

→ x = 6.480...

→ x = 6.5 cm. (approx)

(b) hypotenuse = √300 cm, base = √200 cm,perpendicular = x cm.

→ h^2 = p^2 + b^2

→ (√300)^2 = (x)^2 + (√200)^2

→ 300 = x^2 + 200

→ x^2 = 300 – 200

→ x^2 = 100

→ x = √100

→ x= 10 cm.

(c) hypotenuse = √66 cm, base = √17 cm,perpendicular = x cm.

→ h^2 = p^2 + b^2

→ (√66)^2 = (x)^2 + (√17)^2

→ 66 = x^2 + 17

→ x^2 = 66 – 17

→ x^2 = 49

→ x = √49

→ x = 7 cm.

(d) hypotenuse = x cm, base = 5√12 cm,perpendicular = 2√3 cm.

→ h^2 = p^2 + b^2

→ (x)^2 = (2√3)^2 + (5√12)^2

→ x^2 = 12 + 50

→ x^2 = 62

→ x = √62

→ x = 7.874...

→ x = 7.9 cm. (approx)

The correct answer is  8.5 in.

we know that

The formula of area of triangle is equal to

             [tex]A = \frac{1}{2} (b) (h)[/tex]

We have

b = BC = 6 in

h = AD = x in

substitute

[tex]A = \frac{1}{2} (6) (x)[/tex]

[tex]A = 3x^{2} in^{2} ..................(1)[/tex]

Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.  

Let  a,b,c be the lengths of the sides of a triangle.  

The area is given by:-

[tex]A = \sqrt{p(p-a) (p-b) (p-c)}[/tex]                     where p is half the perimeter

[tex]p = \frac{a +b+ c}{2}[/tex]

a = 9 in , b= 9 in, c = 6 in

[tex]p = \frac{9 + 9 + 6}{2} = 12 in[/tex]

Find the area

[tex]A = \sqrt{12( 12 - 9) (12-9) (12 - 6)}[/tex]

[tex]A = \sqrt{12 (3)(3)(6)}[/tex]

[tex]A = \sqrt{648}[/tex]

[tex]A = 25.46 in^{2}[/tex]

Substitute the value of the area in the equation 1 and solve for x

[tex]A = 3x in^{2}[/tex]

25.46 = 3x

x = 25.46/3

x = 8.5 in

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The complete question is -

HELP PLEASE! Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.

A. 8 in.

B. 11.3 in.

C. 8.5 in.

D. 6.2 in.

The correct probability that Juan's bus is going to be late every week next week is 20 percent.

We have the total number in the stimulation on to be from 0 to 9

On the fact that it would be late, the number ranges from 2 to 9

Hence the fact that it would be late would be

2/10

= 0.2

0.2 is also the same as 20 percent.

Juan rides the bus to school each day. He always arrives at his bus stop on time, but his bus is late 80% of the time. Juan runs a simulation to model this using a random number generator. He assigns these digits to the possible outcomes for each day of the week:

• Let 0 and 1 = bus is on time

• Let 2, 3, 4, 5, 6, 7, 8, and 9 = bus is late

The table shows the results of the simulation.

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Using addition or multiplication, Teresa has twice a number of wood as Samuel.  

According to the question,

Teresa needs twice as many feet of wood as Samuel  in order to find the number of pieces of wood Teresa need only if we add the number Teresa has by itself or multiply it by 2.

Hence, we need to do only multiply it by 2

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Answer: 0.1

Step-by-step explanation:

The smaller the absolute value of the correlation coefficient, the weaker the correlation.

The value of 8√6 as a square root is √384

Surd are written as the square root of prime numbers. Given the expression below;

8√6

This is can be written as;

8√6 = √(8 * 8 * 6)

8√6 = √64 * 6

8√6 = √384

Therefore the value of 8√6 as a square root is √384

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Answer:

A. (-1, 3) (3, 2) (-2, 1)

B. [tex]\sqrt{17}[/tex]   [tex]\sqrt{5}[/tex]  [tex]\sqrt{26}[/tex]  

Step-by-step explanation:

The formula for finding the midpoints is [tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex].

MIDPOINTS

[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{4-6}2,\frac{4+2 }2} )[/tex] = (-1, 3)

[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{4+2}2,\frac{4+0 }2} )[/tex] = (3, 2)

[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{-6+2}2,\frac{2+0 }2} )[/tex] = (-2, 1)

Next, we will use the distance formula, [tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex].

DISTANCE

[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(-1-3)^{2} + (3-2)^{2} }[/tex] = [tex]\sqrt{17}[/tex]

[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(-1+2)^{2} + (3-1)^{2} }[/tex] = [tex]\sqrt{5}[/tex]

[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(3+2)^{2} + (2-1)^{2} }[/tex] = [tex]\sqrt{26}[/tex]  

a. To find the coordinates of endpoints we must add two x values and divide by 2 and then add 2 y- values and divide by 2.

(4-6)/2=-1  (4+2)/2=3

Repeat for other sides.

(2-6)/2=-2 (2+0)/2=1

(2+4)/2=3  (4+0)/2=2

Coordinates of midpoints are (-1,3), (-2,1), (3,2)

b. Now we use the distance formula for each midpoint to find the length of the inner- triangle.

sqrt((-1+2)^2 + (3-1)^2)

Sqrt(5)

Repeat.

Sqrt(17)

Sqrt(26)

The lengths of the inner triangle are as follows:

(-1,3), (-2,1) = Sqrt(5)

(-1,3), (3,2) = Sqrt(17)

(-2,1), (3,2) = Sqrt(26)

Step-by-step explanation:

Therefore,the answer is [tex] \cfrac{3}{y} - x[/tex].

Answer:

[tex]\frac{32\pi }{9}[/tex] or [tex]11.17[/tex]

Step-by-step explanation:

[tex]2\pi 8(\frac{80}{360} )[/tex]

[tex]=16\pi (\frac{80}{360} )[/tex]

[tex]=16\pi (\frac{2}{9})[/tex]

[tex]=\frac{32\pi }{9}[/tex]

Answer:

Step-by-step explanation:

The domain of a function is the set of x-values for which it is defined. The range of a function is the set of y-values the function produces.

The domain is the horizontal extent of the graph. This graph extends from x=0 toward x→∞. The domain is x ≥ 0. In interval notation, it is written [0, ∞).

The range is the vertical extent of the graph. This graph extends from y=0 toward y→∞. The range is y ≥ 0. In interval notation, it is written [0, ∞).

Answer:

95 - 20[tex]\sqrt{15}[/tex]

Step-by-step explanation:

(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )²

= (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )

each term in the second factor is multiplied by each term in the first factor, that is

5[tex]\sqrt{3}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) - 2[tex]\sqrt{5}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) ← distribute parenthesis

= 75 - 10[tex]\sqrt{15}[/tex] - 10[tex]\sqrt{15}[/tex] + 20 ← collect like terms

= 95 - 20[tex]\sqrt{15}[/tex]

Answer:

95 - 20√15

Step-by-step explanation:

I assume the expression is (5√3 − 2√5)^2 (?).

(5√3 − 2√5)*(5√3 − 2√5)

25√3^2 - 20√15 + 4√5^2

25*3 - 20√15 +4*5

75 - 20√15 +20

95 - 20√15

The x-intercepts of the function y = 2x^2 -x - 120 are (-7.5, 0) and (8, 0)

The function is given as:

y = 2x^2 - x - 120

Set the function to 0

2x^2 - x - 120 = 0

Factor out 2

2(x^2 - 0.5x - 60) = 0

Divide by 2

x^2 - 0.5x - 60 = 0

Expand the function

x^2 + 7.5x - 8x - 60 = 0

Factorize the function

(x + 7.5)(x - 8) = 0

Split

x + 7.5 = 0 and x - 8 = 0

Solve for x

x = -7.5 and x = 8

Hence, the x-intercepts of the function y = 2x^2 -x - 120 are (-7.5, 0) and (8, 0)

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Answer:

4 : 9

Step-by-step explanation:

ratio of corresponding sides and ratio of perimeter are equal

then ratio of perimeter = 4 : 9

False, Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.

What animals evolved during Cambrian period?

When did animals evolve in the Cambrian?

What long lived group of arthropods went extinct at the end of the Permian?

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The complete question is -

True or false . Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.

The solution of the recurrence relation is [tex]a_n=3.2^n[/tex]

For given question,

We have been given a recurrence relation [tex]a_n = 2a_{n-1}[/tex] for n ≥ 1

and an initial condition [tex]a_0=3[/tex]

Let [tex]a_n[/tex] = m², [tex]a_{n-1}[/tex] = m and [tex]a_{n-2}[/tex] = 1

So from given recurrence relation we get an characteristic equation,

⇒ m² = 2m

⇒ m² - 2m = 0                     .........( Subtract 2m from each side)

⇒ m(m - 2) = 0                     .........(Factorize)

⇒ m = 0    or  m - 2 = 0

⇒ m = 0   or   m = 2

We know that the solution of the recurrence relation is then of the form

[tex]a_n=\alpha_1 {m_1}^n + \alpha_2 {m_2}^n[/tex]  where [tex]m_1,m_2[/tex] are the roots of the characteristic equation.

Let, [tex]m_1[/tex] = 0   and [tex]m_2[/tex] = 2

From above roots,

[tex]\Rightarrow a_n=\alpha_1 {0}^n + \alpha_2 {2}^n\\\\\Rightarrow a_n=0+\alpha_2 {2}^n\\\\\Rightarrow a_n=\alpha_2 {2}^n[/tex]

For n = 0,

[tex]\Rightarrow a_0=\alpha_2 {2}^0\\\\\Rightarrow a_0=\alpha_2 \times 1\\\\\Rightarrow a_0=\alpha_2[/tex]

But  [tex]a_0=3[/tex]

This means [tex]\alpha_2=3[/tex]

so, the solution of the recurrence relation would be [tex]a_n=3.2^n[/tex]

Therefore, the solution of the recurrence relation is [tex]a_n=3.2^n[/tex]

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Answer:

x=15

Step-by-step explanation:

Use the Pythagorean Theorem: a^2+b^2=c^2

1. a = 20, b = x, c = 25

2. 20^2+b^2= 25^2

3. Expand: 400+b^2= 625

4. Subtract + Simplify: b^2= 625-400

5. Fully Solve: b^2 = 225 -> Square root of b^2 = Square root of 225

6. Last Step: Simplify: b = 15.

Here is a similar problem for you to solve, put your answer in the comments.

a= 12, b=5, c=?

Solve for c using the Pythagorean theorem.

Answer:

40%

Step-by-step explanation:

Percent must be equal to 100, so if 60 are girls, then 40% must be boys.

Option D. The triangle inequality theorem is verified by by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side.

From the given picture we can see the length of the sides. These are 7, 4 and 15.

The length of the two sides cannot join due to the fact that they are less than 15.

4 + 7 < 15

11< 15

Hence the answer is D.

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by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side