Select the correct graph of the function y = 1∕4(x + 4)^2 + 3 below.

Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.

Remember: SOH-CAH-TOA

Looking from angle I, we know the opposite side and the hypotenuse. Therefore, we should use sine.

sin(I) = [tex]\frac{\sqrt{39}}{\sqrt{51}}[/tex]

To solve, you can use your calculator and the inverse sine function (sin^-1).

I = sin^-1([tex]\frac{\sqrt{39}}{\sqrt{51}}[/tex])

I = 61 degrees

Hope this helps!

Answer:

100 in²

Step-by-step explanation:

4 triangles, each of them has area = 10*5/2

so total area = (10*5/2)*4

= (10*5*2)

= 100 in²

Answered by GAUTHMATH

The lateral surface area of the pyramid is 100 in²

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

The pyramid has four triangular faces and one rectangular base we need to calculate the lateral surface area so we will calculate the area of the four triangles and sum up all the triangles.

4 triangles, each of them has an area = 10 x ( 5/2 )

So total area = (10 x 5/2) x 4

Total area = (10 x 5 x 2)

Total area = 100 in²

Therefore the lateral surface area of the pyramid is 100 in²

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Answer:

0=70!!!!!!!!!!!!!!!!!!!!!!

Answer:

-25/4 = u

Step-by-step explanation:

-3u-17=(u+8)

Add 3u to each side

-3u+3u-17=(u+3u+8)

-17 = 4u +8

Subtract 8 from each side

-17-8 = 4u+8-8

-25 = 4u

Divide by 4

-25/4 = 4u/4

-25/4 = u

===========================================

Explanation:

There are 3 ways to select the single math book and 4*3/2 = 12/2 = 6 ways to pick the two other books that are either physics or history (order doesn't matter). This is effectively because we have 3+1 = 4 books that are either physics or history, and we're using the nCr combination formula.

Overall, there are 3*6 = 18 ways to select the three books such that one is math, and the other two are either physics or history.

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

There are 3+3+1 = 7 books total. Since we're selecting 3 of them, we use the nCr formula again and you should get 35.

Or you could note how (7*6*5)/(3*2*1) = 210/6 = 35

This says there are 35 ways to select any three books where we can tell the difference between any subject (ie we can tell the difference between the math books for instance).

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

We found there are 18 ways to get what we want out of 35 ways to do the three selections. Therefore, the answer as a fraction is 18/35

Answer:

7/20 mile farther

Step-by-step explanation:

Subtracting 2/5 mile from 3/4 mile results in the distance you still have to walk:

3/4 - 2/5 = ?

Here the LCD is 20.  Thus, 3/4 becomes 15/20 and 2/5 becomes 8/20.

Then 3/4  - 2/5 = 15/20 - 8/20, or 7/20.

You still have 7/20 mile to walk to get home.

The function f has a an exponent which is the variable ( the letter x) therefore it is an exponential function.

The base is the number being raised by the exponent ( -1/4)

Answer:

f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.

Step-by-step explanation:

The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.

* if x>1, then x-1>0.

* Also since the parabola opens up, then y>5.

So let's solve y=(x-1)^2+5 for x.

Subtract 5 on both sides:

y-5=(x-1)^2

Take square root of both sides:

Plus/minus sqrt(y-5)=x-1

We want x-1>0:

Sqrt(y-5)=x-1

Add 1 on both sides:

Sqrt(y-5)+1=x

Swap x and y:

Sqrt(x-5)+1=y

x>5

y>1

Answer:

Multiply the product of 16,544 x 7 by 10 as it id the same as multiplying 16,544 x 70.

Answer:

There are 30 tens in 3 hundred.

Step-by-step explanation:

there are thirty tens in 3 hundred

minus sign ironically makes it go to the right

because the function crosses the y axis at -13

It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The equation y = x - 13 represents a transformation of the graph of y = x. To find the type of  transformation, we have to compare the two equations and look for changes.

In the equation y = x - 13, we subtract 13 from the value of x.

This means that the graph of y = x is shifted 13 units downwards,

since every point on the graph has 13 subtracted from its y-coordinate.

Hence,  It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.

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Answer:

0.6472 = 64.72% probability that a randomly selected page does not need to be retyped.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Poisson distribution with an average of three errors per page

This means that [tex]\mu = 3[/tex]

What is the probability that a randomly selected page does not need to be retyped?

Probability of at most 3 errors, so:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]

[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]

[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]

[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]

Then

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0498 + 0.1494 + 0.2240 + 0.2240 = 0.6472[/tex]

0.6472 = 64.72% probability that a randomly selected page does not need to be retyped.

Answer:

y = 3

Step-by-step explanation:

6sin(30) = 3

Answer:

Obtuse Scalene Triangle

Step-by-step explanation:

Sum of the squares of the smaller 2 sides < longest side squared = Obtuse Scalene Triangle

where's the diagram?

Answer:

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Using the cosine addition formula

cos(A ± B ) = cosAcosB ∓ sinAsinB

Then considering the left side

cos²(45 + A) + cos²(45 - A)

= [ cos45cosA - sin45sinA ]² + [cos45cosA + sin45sinA]]²

= [ [tex]\frac{1}{\sqrt{2} }[/tex] cosA - [tex]\frac{1}{\sqrt{2} }[/tex] sinA ]² + [ [tex]\frac{1}{\sqrt{2} }[/tex] cosA + [tex]\frac{1}{\sqrt{2} }[/tex] sinA ]²

= [tex]\frac{1}{2}[/tex]cos²A - sinAcosA + [tex]\frac{1}{2}[/tex] sin²A + [tex]\frac{1}{2}[/tex] cos²A + sinAcosA + [tex]\frac{1}{2}[/tex] sin²A

= cos²A + sin²A

= 1

= right side , then proven

Answer:

Step-by-step explanation:

cos 2x=cos²x-sin²x=cos²x-(1-cos²x)=cos²x-1+cos²x=2cos²x-1

2cos²x=1+cos2x

[tex]cos^2x=\frac{1}{2}(1+cos2x)[/tex]

cos²(45+A)+cos²(45-A)

[tex]=\frac{1}{2}(1+cos(90+2A))+\frac{1}{2}(1+cos(90-2A))\\=\frac{1}{2} (1-sin2A)+\frac{1}{2} (1+sin 2A)\\=\frac{1}{2} (1-sin2A+1+sin 2A)\\=\frac{1}{2} \times2\\=1[/tex]

cos (90-x)=sin x

cos (90+x)=-sin x

Answer:

(0,1) and (3,4)

Step-by-step explanation:

It's the points where they meets, judging the graph, it's x = 0, y = 1 and x = 3, y = 4

put them in the equation and you'll see the the values satisfies the equation

Answered by GAUTHMATH

Answer:

39-13=26

Step-by-step explanation:

plus(minus)=minus

10% of 360 is 18 more than 5% of 360.

The percentage is defined as ratio expressed as a fraction of 100.

What are Arithmetic operations?

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

Given data as :

10% of 360

5% of 360

Firstly, we have to determine 10% of 360,

⇒ 10% of 360

⇒ (10/100)360

⇒ (0.10)360

So, 10% of 360 is 36.

⇒ 5% of 360

⇒ (5/100)360

⇒ (0.05)360

So, 5% of 360 is 18.

Since 10% of 360 is more than 5% of 360

So, substract 18 from 36, and

⇒ 36 - 18

⇒ 18

Hence, 10% of 360 is 18 more than 5% of 360.

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Answer:

Step-by-step explanation:

3x²=15-4x

divide by 3 on both sides

x²=5-[tex]\frac{4}{3}[/tex]x ​ ​

move everything to one side

x²+[tex]\frac{4}{3}[/tex]x ​-5 = 0

add the square of 1/2 the middle term of [tex]\frac{4}{3}[/tex]  but also subtract it too

x²+[tex]\frac{4}{3}[/tex]x +[tex]( \frac{2}{3} )^{2}[/tex]​-5-[tex]( \frac{2}{3} )^{2}[/tex]​ = 0

now use the property of a perfect square to rewrite

[tex](x+\frac{2}{3}) ^{2}[/tex] -5 -[tex]\frac{4}{9}[/tex] = 0

rewrite 5 as a fraction

[tex](x+\frac{2}{3}) ^{2}[/tex] - [tex]\frac{45}{9}[/tex]- [tex]\frac{4}{9}[/tex] = 0

add up the fractions

[tex](x+\frac{2}{3}) ^{2}[/tex] - [tex]\frac{49}{9}[/tex] = 0

move to the other side

[tex](x+\frac{2}{3}) ^{2}[/tex] = [tex]\frac{49}{9}[/tex]

take the square root of both sides :P

[tex]\sqrt{((x+\frac{2}{3}) ^{2} }[/tex]  = [tex]\sqrt{\frac{49}{9} }[/tex]

much easier looking now, just use algebra to solve for x

x + [tex]\frac{2}{3}[/tex] = [tex]\frac{7}{3}[/tex]

subtract  [tex]\frac{2}{3}[/tex]  from both sides

x + [tex]\frac{2}{3}[/tex] -  [tex]\frac{2}{3}[/tex] = [tex]\frac{7}{3}[/tex] - [tex]\frac{2}{3}[/tex]

x = [tex]\frac{5}{3}[/tex]

:)  

​

Answer:

x = - 3, x = [tex]\frac{5}{3}[/tex]

Step-by-step explanation:

Given

3x² =15 - 4x ( add 4x to both sides )

3x² + 4x = 15 ← factor out 3 from each term on the left side

3(x² + [tex]\frac{4}{3}[/tex] x) = 15

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² + [tex]\frac{4}{3}[/tex] x

3(x² + 2([tex]\frac{2}{3}[/tex] )x + [tex]\frac{4}{9}[/tex] - [tex]\frac{4}{9}[/tex] ) = 15

3(x + [tex]\frac{2}{3}[/tex] )² - [tex]\frac{4}{3}[/tex] = 15 ( add [tex]\frac{4}{3}[/tex] to both sides )

3(x + [tex]\frac{2}{3}[/tex] )² = 15 + [tex]\frac{4}{3}[/tex] = [tex]\frac{49}{3}[/tex] ( divide both sides by 3 )

(x + [tex]\frac{2}{3}[/tex] )² = [tex]\frac{49}{9}[/tex] ( take the square root of both sides )

x + [tex]\frac{2}{3}[/tex] = ± [tex]\sqrt{\frac{49}{9} }[/tex] = ± [tex]\frac{7}{3}[/tex] ( subtract [tex]\frac{2}{3}[/tex] from both sides )

x = - [tex]\frac{2}{3}[/tex] ± [tex]\frac{7}{3}[/tex], then

x = - [tex]\frac{2}{3}[/tex] - [tex]\frac{7}{3}[/tex] = - 3

x = - [tex]\frac{2}{3}[/tex] + [tex]\frac{7}{3}[/tex] = [tex]\frac{5}{3}[/tex]

Answer:

B

Step-by-step explanation:

Subtracting second equation from first, term by term , gives

(8x - 4x) + (3y - 3y) = (14 - 8) , that is

4x + 0 = 6, so

4x = 6 → B

Answer:

In 24 years.

Step-by-step explanation:

Let the sum of money be 100 which amounts to 200 ( doubles itself ) in 6 years time. Interest on 100rs. Is 100. Putting the following in simple interest formula. You get :

[tex]100=\dfrac{100\times R\times 6}{100}\\\\R=\dfrac{100}{6}[/tex]

Now when 100 will become 5 times i.e 500 the interest will be 400rs.

Putting in simple interest formula:

[tex]400=\dfrac{\dfrac{100\times 100}{6T}}{100}\\\\T=\dfrac{2400}{100}\\\\=24\ yrs[/tex]

So, in 24 years, it will become 5 times.

Answer:

A. y + 1 = -5(x - 2)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

Step-by-step explanation:

Step 1: Define

Identify

Slope m = -5

Point (2, -1)

Step 2: Find Equation

Answer:

Given E(t)=1100(100-t)+580(100-t)^2

Put t = 99.5, we get

E(99.5)=1100(100-99.5)+580(100-99.5)^2

E(99.5)=1100(0.5)+580(0.5)^2

E(99.5)=1100(0.5)+580(0.25)

E(99.5)=550+145

E(99.5)=695m

Step-by-step explanation:

It can be concluded that -

E(99.5) = 695

E(100) = 0

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the function as follows -

E(t) = 1100(100 - t) + 580(100 - t)²

The given function is -

E(t) = 1100(100 - t) + 580(100 - t)²

At → E(99.5)

E(99.5) = 1100(100 - t) + 580(100 - t)²

E(99.5) = 1100(100 - 99.5) + 580(100 - 99.5)²

E(99.5) = 1100(0.5) + 580(0.5)²

E(99.5) = 550 + 145

E(99.5) = 695

At → E(100)

E(100) = 1100(100 - t) + 580(100 - t)²

E(100) = 1100(100 - 100) + 580(100 - 100)²

E(100) = 0

Therefore, it can be concluded that -

E(99.5) = 695

E(100) = 0

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Answer:

56+35=180 then solve it thanks

Answer:

Step-by-step explanation:

we have a two right triangle, with one side 115

lets say that the other side of the big right triangle is y

-in the big triangle find the third angle

180 -90 -35 = 55, because the sum of all interior angles in a triangle is 180

tan 55 = opp. /adj= y / 115

y = 115 * tan 55

-in the small right triangle

tan 56 = opp./ adj. = 115 / y-x

y-x = 115/ tan 56 , subtract y from both sides

- x=  -y +( 115/tan 56), multiply by -1 both sides

x= y -(115/tan56), substitute y for 115 * tan 55

x= (115*tan 55)- (115/tan56)

x≅86.6685

Answer:

[tex]3x^2 + 9x +9[/tex]

Step-by-step explanation:

Given

[tex](7x + 8 + 2x^2) + (2x + 1 + x^2)[/tex]

Required

The result in standard form

We have:

[tex](7x + 8 + 2x^2) + (2x + 1 + x^2)[/tex]

Remove brackets

[tex]7x + 8 + 2x^2 + 2x + 1 + x^2[/tex]

Collect like terms

[tex]7x+ 2x + 8 + 1 + 2x^2+ x^2[/tex]

[tex]9x + 9+ 3x^2[/tex]

The standard form of a quadratic equation is:

[tex]ax^2 + bx + c[/tex]

So, we have:

[tex]9x + 9+ 3x^2[/tex]

[tex]3x^2 + 9x +9[/tex]