Jonah has read 1/4 of his mystery book. He has 36 pages. How many pages are in the mystery book

Note that in the above sketch, ΔABC ≇ ΔDCA. That is they are NOT congruent. The proof is that ∠ADC which is supposed to be = ∠BAC are not equal. Thus, line AC which is supposed to be equal to Line BC are not equal.

When two triangles are congruent, it means they are exactly the same in terms of their shape and size, so all corresponding sides and angles are equal.

In ΔABC,

Line AB = 8ft
Line BC = 11ft

Line AC = 13.6ft

∠ABC = 90°

∠BAC = 53.97°
∠ACB = 36.03°


As you can see,

Where as, ∠ADC = 62° - given

∠BAC = 53.97°

Also

Where as:

AC (The Hypotenuse ΔABC which is also the Adjacent Side of ΔACD) = 13.6ft

BC (The adjacent side of ΔABC) = 11ft.

Note that in order to prove congruence, at least two angles and one side from both Triangles must be equal (Angle Angle Side Theorem). Or

Two sides and one angle from both Triangles must be equal (Side - Angle - Side).

Or All three angles (Angle - Angle - Angle);
Or All three Sides (Side - Side Side).

In this case, only one side from both Triangles AC is common to both Triangles.

On the basis of the above, therefore, ΔABC ≇ ΔDCA.


The calculations showing how we arrived at the missing sides and angles are given below:


ΔABC:

AC = √(AB² + BC²)
AC = √(8² + 11²)
AC = √(64 + 121)
AC = √(185)
AC = 13.6014705087

AC [tex]\approx[/tex] 13.60

∠ ACB = arcsin (AB/AC)
∠ ACB = arcsin (8/13.6014705087)
= arcsin(0.58817169767505)
∠ ACB = 0.6288 rad converted to degrees

∠ ACB  = 36.03°

Thus, since the sum of Angles in a Triangle is 180°
∠BAC = 180-36.03° -90°
∠BAC = 53.97°


ΔACD


y (AD) = AC / sin(β)
y (AD) =  13.6/ sin(62°)
y (AD)  = 13.6/0.88294759285

AD = 15.40°

CD = √(AD² - AC²)

CD = √(15.4029526893712 - 13.62)

CD = √52.290951550999

CD = 7.23

The outstanding angle in ΔACD is ∠CAD

Since the sum of Angles in a Triangle is 180°

∠CAD = 180 - 90 - 62
∠CAD = 28°

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Full Question:

Although part of your question is missing, you might be referring to this full question: See attached Image.

We can start by converting the mass of the bag of dog food from kilograms to grams:

8 kilograms = 8,000 grams

Then, we can divide the total mass of the bag of food by the daily amount given to the dog:

8,000 grams ÷ 100 grams/day = 80 days

Therefore, the bag of dog food will last for 80 days.

The measure of angle 1 would be equal to 59 degrees.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

We have been given the angles as 31 degrees and 90 degree

We know that the sum of angle of triangle is 180 then the angle 1 will be;

31 + 90 + m∠1 = 180

m∠1 = 180 - 90 - 31

m∠1 = 59

Hence, m∠1 = 59

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The logarithmic equation that is equivalent to the given exponential equation

The logarithmic equation that is equivalent to the exponential equation [tex]((1)/(3))^-4=81 (is)  log(1/3) 81 = -4[/tex]

To rewrite an exponential equation as a logarithmic equation,

we can use the following formula:

bx = y → logb y = x

In this case, b = (1/3), x = -4, and y = 81. So, we can plug these values into the formula to get the logarithmic equation:

[tex]log(1/3) 81 = -4[/tex]

This is the logarithmic equation that is equivalent to the given exponential equation.

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The volume of the silo is approximately 9,685.73 cubic feet.

What is volume of a cylinder?

The volume of a cylinder can be calculated using the formula:

[tex]V = \pi r^2h[/tex]  where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.

We are given that the diameter of the silo is 17 feet. The radius, which is half the diameter, is therefore:

r = 17/2 = 8.5 feet

We are also given that the height of the silo is 42 feet.

Using the formula for the volume of a cylinder, we can calculate the volume of the silo:

[tex]V = \pi r^2h[/tex]

[tex]= \pi(8.5)^2(42)[/tex]

≈ 9,685.73 cubic feet

Therefore, the volume of the silo is approximately 9,685.73 cubic feet.

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Pythagorean theorem: Show that ⟨x, y⟩ = 0

Let V be an Euclidean space and let x, y ∈ V.(a) If ∥x + y∥ = ∥x − y∥ then determine ⟨x, y⟩.We know that ∥x + y∥² = ⟨x + y, x + y⟩ = ⟨x, x⟩ + ⟨x, y⟩ + ⟨y, x⟩ + ⟨y, y⟩ = ∥x∥² + 2⟨x, y⟩ + ∥y∥²And ∥x − y∥² = ⟨x − y, x − y⟩ = ⟨x, x⟩ − ⟨x, y⟩ − ⟨y, x⟩ + ⟨y, y⟩ = ∥x∥² − 2⟨x, y⟩ + ∥y∥²Since ∥x + y∥ = ∥x − y∥, we have ∥x∥² + 2⟨x, y⟩ + ∥y∥² = ∥x∥² − 2⟨x, y⟩ + ∥y∥²⟨x, y⟩ = 0(b) Show that 2⟨x, y⟩ ≤ ∥x∥² + ∥y∥².We know that ∥x + y∥² = ∥x∥² + 2⟨x, y⟩ + ∥y∥²And ∥x + y∥² ≥ 0So ∥x∥² + 2⟨x, y⟩ + ∥y∥² ≥ 0⟨x, y⟩ ≤ (∥x∥² + ∥y∥²)/2(c) If (z, y) = 0 for all z ∈ V then show that y = 0.Let z = y, then (y, y) = 0⟨y, y⟩ = ∥y∥² = 0∥y∥ = 0So y = 0(d) If ∥x∥ = ∥y∥ for some x, y ∈ V then ⟨x + y, x − y⟩ = 0.We know that ∥x + y∥² = ∥x∥² + 2⟨x, y⟩ + ∥y∥²And ∥x − y∥² = ∥x∥² − 2⟨x, y⟩ + ∥y∥²Since ∥x∥ = ∥y∥, we have ∥x∥² = ∥y∥²So ∥x + y∥² − ∥x − y∥² = 4⟨x, y⟩ = 0⟨x, y⟩ = 0(e) Pythagorean theorem: Show that ⟨x, y⟩ = 0 if and only if ∥x + y∥² = ∥x∥² + ∥y∥².We know that ∥x + y∥² = ∥x∥² + 2⟨x, y⟩ + ∥y∥²If ⟨x, y⟩ = 0, then ∥x + y∥² = ∥x∥² + ∥y∥²If ∥x + y∥² = ∥x∥² + ∥y∥², then 2⟨x, y⟩ = 0⟨x, y⟩ = 0

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The lengths in the left side are proportional to the ones in the right side, with that we know that x = 10.

The lengths in the left side and the ones in the right side are proportional, such that the scale is k.

Then we can write:

21*k = 27

(x - 3)*k = (x - 1)

With the first equation, we can find the value of k, then we will get.

k = 27/21

Replacing that in the second equation we will get:

(x - 3)*27/21 = (x - 1)

Now we can solve this.

(x - 3)*27 = 21*(x - 1)

Now we can solve this for x.

27x - 81 = 21x - 21

27x - 21x = 81 - 21

6x = 60

x = 60/6 = 10

x = 10

That is the value of x.

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Answer:

First, we need to find the radius of the pipe by dividing the diameter by 2:

radius = 3ft / 2 = 1.5ft

Next, we can use the formula for the volume of a cylinder:

V = πr²h

where V is volume, π (pi) is approximately 3.14, r is the radius, and h is the height (or length) of the cylinder.

Plugging in the values we have:

V = 3.14 x (1.5ft)² x 17ft

V = 3.14 x 2.25ft² x 17ft

V = 3.14 x 38.25ft³

V ≈ 120ft³

Rounding to the nearest whole number and including the unit:

The volume of the pipe is about 120 cubic feet.

[tex]\bold{Work \ Shown:}[/tex]

[tex]d = 3 = diameter[/tex]

[tex]r = d\div2 = 3\div2 = 1.5 = radius[/tex]

[tex]h = 17 = height \ or\ length \ of \ the\ pipe[/tex]

[tex]\pi = 3.14\ approximately[/tex]

[tex]V = volume \ of \ the \ cylinder \ pipe[/tex]

[tex]V = \pi \times r^2 \times h[/tex]

[tex]V = 3.14 \times (1.5)^2\times 17[/tex]

[tex]V = 120.105[/tex]

[tex]V=120[/tex]

The cylindrical pipe's volume is about 120 cubic feet.

the actual distance the Patel family will travel by the time they reach Clarksville is 72 miles.

What is the distance in math?

As its name implies, any distance formula outputs the distance (the length of the line segment). In coordinate geometry, there is a number of formulas for finding distances, such as the separation between two points, the separation between two parallel lines, the separation between two parallel planes, etc.

Smithville to Jonesville distance in map = 3(3/4) inches = (15/4) inches .

given that,

(1/2) inch = 4 miles .

1 inch = 8 miles .

Distance from Smithville to Jonesville = (15/4) * 8 = 30 miles .

similarly,

Jonesville to Clarksville distance in map = 5(1/4) = (21/4) inches .

Distance from Jonesville to Clarksville = (21/4) * 8 = 42 miles .

The actual distance the Patel family will travel by the time they reach Clarksville = 30 + 42 = 72 miles

Hence, the actual distance the Patel family will travel by the time they reach Clarksville is 72 miles.

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The volume of the cone is  1004.8 cm³.

Let's calculate the volume of the cone with radius 8 cm and the slant height is 17 cm. Therefore, let's find the volume of the cone as follows:

volume of a cone = 1 / 3 πr²h

where

Therefore,

h² = 17² - 8²

h = √289 - 64

h = √225

h = 15 cm

Therefore,

volume of a cone = 1 / 3 × 3.14 × 8² × 15

volume of a cone = 1 / 3 × 3.14 × 64 × 15

volume of a cone = 3014.4 / 3

volume of a cone = 1004.8 cm³

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[tex] \mathbb{ANSWER:}[/tex]

The slope is -2 while the y-intercept is -1.

[tex] \mathbb{EXPLANATION:}[/tex]

The slope and the intersection with the y-axis of the graph or the y-intercept is already given if you will just simply look at the equation. An equation written in y = mx + b is in slope-intercept form, where m is the slope and b is the y-intercept. So, the number being multiplied to x or the coefficient of x is the slope while the constant is the y-intercept.

The solution is: population in 2015 will be 40,115,896

The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents.

But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

calculate the average percent change in population in California from 2000-2009.

Add all the percentage than divide by 9 since there is 9 year

1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93/9 = 1.3567%

The number of periods from 2009 to 2015 is 6:

Future: 37,000,000•(1+0.013567)^6 = 40,115,896.06

Hence, the solution is: population in 2015 will be 40,115,896

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Answer:

Step-by-step explanation:

d^2

When dividing subtract indices OR

dxdxdxdxd /dxdxd

d's cancel out leaving dxd=d^s

The surface area of the cone is 578.1 square feet.

We know that for a cone of radius R and slant height H the surface area is given by the formula:

S = pi*R^2 + pi*R*(H)

with pi = 3.14

On the diagram we can see that H = 19.3ft, and the diameter of the base is 14 ft, then the radius is:

R = 14ft/2 = 7ft

REplacing these values in the formula above we will get:

S = 3.14*(7ft)^2 + 3.14*7ft*(19.3ft) = 578.1 ft²

So the correct option is the second one.

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According to the information we can infer that the volume of the prism would be 63cm³

To find the volume of the prism we must perform the following mathematical operation:

First of all we must find the cube root of each of the options.
[tex]\sqrt[3]{84} = 4,3795191398878892657\\\sqrt[3]{63} = 3,9790572078963918596\\\sqrt[3]{42} = 3,4760266448864497867\\\sqrt[3]{7} = 1,9129311827723891012[/tex]

Once we find these values we must check them with the formula for the volume of a pyramid. In this case, it would be the area of the base times the height. Then we must take into account that the cube root of these numbers would be the equivalent to the side length of the figures.

In the case of 63, the procedure would be as follows:

Then we can establish that this value corresponds to the length of the sides and the height of the pyramid because as a result it gives us the volume of the pyramid. So to find the volume of the prism we must do the following operation:

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The value of y is -3. The equation formed from the question is 4x + y = 65 and 5x -3y = 94.

First, we will solve for x

Multiplying the 4x + y = 65 equation by 3 we get

12x +3y =195

Now solving both the equation

The variable y gets cancelled because of having the same value

∴ 17x = 289

x= 17

Now putting the value of x in equation 4x + y = 65 to get the value of y

4*17 +y =65

68 +y = 65

y= -3

Now putting the value of x in equation 5x -3y = 94  to get the value of y

5*17 -3y =94

85 -3y =94

-3y = 94-85

y= -3

Therefore, the value of y is -3

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Answer:

I think it is 0.68. Try that. If not sorry.

To create a multi-dimensional visualization of (a+b)^5, we can use a Pascal's Triangle, which shows the coefficients of each term in the expansion. Each row of the triangle corresponds to a power of (a+b), and the numbers in each row are the coefficients of the terms in the expansion. Here is a visualization of the first six rows of Pascal's Triangle:

```
           1
         1   1
       1   2   1
     1   3   3   1
   1   4   6   4   1
 1   5  10  10   5   1
```

The sixth row corresponds to the expansion of (a+b)^5, and the numbers in this row are the coefficients of the terms in the expansion: 1, 5, 10, 10, 5, 1. We can use these coefficients to create a multi-dimensional visualization of (a+b)^5:

```
            a^5
         5a^4b
      10a^3b^2
    10a^2b^3
  5ab^4
b^5
```

Each term in the expansion is represented by a different level in the visualization, with the coefficient of each term shown at the beginning of the level. This multi-dimensional visualization allows us to see the relationship between the coefficients and the terms in the expansion of (a+b)^5.

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If 2x-1 is a factor of 24x⁴ - 2x² +2x +f , the value of f is  1 - 2x.

Synthetic division is a method of polynomial division used to divide a polynomial by a linear expression of the form x - a, where a is a constant. It is a shorthand way of performing long division for polynomials and is particularly useful when the divisor is of the form x - a, as it eliminates the need for writing out the full divisor in each step of the division process.

Since 2x-1 is a factor of the given polynomial, we know that it will divide exactly into the polynomial, leaving no remainder. Therefore, we can use polynomial long division to find the quotient when 24x⁴ - 2x² + 2x + f is divided by 2x-1:

           12x³ + 5x² - 3x - f/2 + 1/4

      ____________________________________

2x - 1 |   24x⁴ + 0x³ - 2x² + 2x + f

         - (24x⁴- 12x³)

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

12x^3

- (12x³ - 6x^2)

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

5x^2

- (5x² - 2.5x)

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

2.5x

- (2.5x - f/4)

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

f/4 + 2x/4 - 1/4

Since there is no remainder, the last term in the quotient must be zero. Therefore:

f/4 + 2x/4 - 1/4 = 0

Simplifying and solving for f, we get:

f/4 = 1/4 - 2x/4

f = 1 - 2x

Therefore, f = 1 - 2x.

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(a) Revenue function: R = 13x
Cost function: C = 2x + 1540
(b) Break-even point: 2x + 1540 = 13x
x = 1540/11
x = 140 units

(c) Break-even point as a percent of capacity: 140/2500 x 100% = 5.6%
(d) Break-even point in sales dollars: 13 x 140 = $1820
(a) The revenue function is R(x) = 13x, where x is the number of units sold. The cost function is C(x) = 2x + 1540, where x is the number of units sold.
(b) To find the break-even point, we set R(x) = C(x):
13x = 2x + 1540
11x = 1540
x = 140
So the firm needs to sell 140 units to break even.
(c) The break-even point as a percent of capacity is 140/2500 = 0.056 or 5.6%.
(d) The break-even point in sales dollars is 140 units * $13/unit = $1820.

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Option D i.e. number line with closed circle on point negative 7 over 22 and arrow shaded to the left represents the solution to the inequality.

A comparison between two or more mathematical expressions is known as an inequality.

We are given an inequality as one seventh m is less than or equal to negative one twenty second.

So, from the above information, we get the inequality as

m/7 ≤ −1/22

Now, on solving the above inequality, we get the following

⇒m/7 ≤ −1/22

⇒m ≤ −7/22

Hence, Option D i.e. number line with closed circle on point negative 7 over 22 and arrow shaded to the left represents the solution to the inequality.

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The comparison between the distance he biked and swam is 3 : 1.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

From the given information the comparison of the distance he swam to the distance he biked can be represented in the form of ratios.

Given, He rode his bike 3/4 miles and swam for 1/4 mile.

Therefore, The ratio of biking : swimming = 3/4 : 1/4.

Now, Multiplying by 4 to get rid of the denominator we have,

Biking : Swimming = 3 : 1.

As the days in both comparisons increase in the same manner the ratio will remain the same.

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Answer:

$4.8

Step-by-step explanation:

5 for $3

So $3 ÷ 5 to get the price of one

Answer is 60c or $0.6

Then you multiply $0.6 with 8 to get the price of 8 oranges

So $0.6 x 8 = $4.8

Answer:

the cost of 8 oranges is 4.8$

step by step explanation

using ratio amd proportion

let x be the unknown amount

[tex]5 = 3 \\ 8 = x \\ cross \: multiply \\ 5x = 24 \\ divide \: \: both \: sides \: by \: 5 \\ \frac{5x}{5} = \frac{24}{5} \\ x = \frac{24}{5} \\ x = 4.8[/tex]

therefore the answer is 4.8 dollars will buy 8 oranges

thank you

The process to find the scale factor of a shape and the concept of sequence of transformations is explained below.

In order to find the scale factor of a shape, we need to compare the corresponding side lengths of the original shape to the corresponding side lengths of the new shape after a dilation.

The scale factor is the ratio of any two corresponding side lengths.

The sequence of transformations is defined as the order in which different transformations are applied to a shape.

For example, if we have a triangle and we first translate it, then rotate it, and then dilate it, the sequence of transformations would be : translate → rotate → dilate.

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The given question is incomplete, the complete question is

How do you find the scale factor of a shape? And What is the sequence of transformations?

As a result, Jamie could rewrite the equation as (1+sin theta)/cos² theta by multiplying both the denominator and the numerator by (1+sin theta), and then replacing 1-sin² theta with cos² theta.

A ²is part of a whole. The number is expressed mathematically as a quotient, which divides the denominator and the numerator. Both are integers in a simple fraction. A complicated fraction contains a fraction in the numerator or denominator. The denominator of a correct fraction is greater than the numerator

Jamie can double the numerator and write 1/(1-sin theta) to ensure that the fraction's denominator is cos² theta. Neither 1-cos theta nor any other option, but the numerator by (1+sin theta):

1/(1-sin theta) × (1+sin theta)/(1+sin theta) = (1+sin theta)/(1-sin² theta)

We may replace cos² theta for 1-sin² theta using the identity sin² theta + cos² theta = 1:

(1+sin theta)/cos² theta

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Debra's two area baking plates are 17 square inches different in size.

The area surrounding a shape forms its perimeter. Area is a unit of measurement for interior space. Surface area is a measurement of a solid shape's exposed surface, whereas area is a two-dimensional measurement of the size of a flat surface (three-dimensional).

The square baking dish has the following surface area with an 8-inch side length:

Area of first square = (side length)² = 8² = 64 square inches

Similarly, the surface area of a square baking dish with 9-inch sides is:

Area of second square = (side length)² = 9² = 81 square inches

Difference in area = |Area of second square - Area of first square|

Difference in area = |81 - 64|

Difference in area = 17 square inches

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Answer:

Degree: The degree of the function is 3.

X-Intercepts with multiplicity greater than 1: x = -2 and x = 0

How many distinct x-intercepts?: There are two distinct x-intercepts.

How many zeros are there?: There are three zeros, one at x = -2 and two at x = 0 (with a multiplicity of 2).

Shaun ordered 7 tacos and 8 burritos, for a total of 160160 calories from tacos and 320320 calories from burritos.

To solve this problem, we need to use a system of equations. Let's call the number of tacos Shaun ordered x and the number of burritos he ordered y. We can then write the following equations:

160x + 320y = 3680 (the total number of calories consumed)
x + y = 15 (the total number of items ordered)

We can rearrange the second equation to get y = 15 - x and then substitute that into the first equation to solve for x:
160x + 320(15 - x) = 3680
160x + 4800 - 320x = 3680
-160x = -1120
x = 7

Now that we know x, we can plug it back into the second equation to solve for y:
7 + y = 15
y = 8

So, Shaun ordered and ate 7 tacos and 8 burritos.

Tacos eaten (x) : 7
Burritos eaten (y) : 8

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So the slope-intercept form of the equation of the line passing through the two given points is:

y = -5x + 26

If an equation is expressed in the form y=mx+b, where m denotes the slope and b the y-intercept, it is said to be linear.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

To find the slope of the line passing through the two given points (5,1) and (2,16), we can use the formula:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) = (5,1) and (x2, y2) = (2,16)

m = (16 - 1)/(2 - 5) = -5

So the slope of the line is -5.

To find the y-intercept b, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

Using the point (5,1) and the slope m = -5, we get:

y - 1 = -5(x - 5)

Simplifying this equation, we get:

y = -5x + 26

So the slope-intercept form of the equation of the line passing through the two given points is:

y = -5x + 26

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