What's the correct letter name for this below?

Consider the upper triangle

if we want to find b side, consider the following trigonometric identity:

in this case, we have:

solve for b:

then, we can conclude that

Now, for a-side, consider the following trigonometric identity:

in this case, we have:

solve for a:

then, we can conclude that

Now, for the c-side, consider the greater triangle :

if we denote the hypotenuse by h, then by Pythagorean theorem we have:

but h = a + c, then, replacing this in the previous equation we have

but, we know that a is

then we have:

now, taking the square root of both sides of the equation we obtain:

solve for c:

then we can conclude that :

and

Given that Angelo's kayak travels 10km/h in still water, and the river's current flows at a rate of 4km/h.

Travelling downstream means Angelo is travelling with the current, that is the current of the water will add to Angelo's speed.

Their combined speed will be;

To travel 35 km downstream;

Recall that;

substituting the given values;

Therefore, it'll take 2.5 hours

The angle relationships which are correct are:

∠4 and ∠6 are same side interior angles.

∠3 and ∠6 are alternate interior angles.

Side interior angles

Two angles that are on the same side of the transversal and written the same side of the transversal when two lines are intersected by a third line are called side angles.

Alternate interior angles

Alternate interior angles are the angles formed on the opposite sides of the transversal.

Hence the correct relationship are ∠4 and ∠6 are same side interior angles and ∠3 and ∠6 are alternate interior angles.

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1365 batting orders  are possible for the game.

Given,

In the question:

In a cricket match, you have a squad of 15 players and you need to select 11 for a game.

To find the how many batting orders are possible for the game?

Let's Know:

What are combination?

Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects.

Combination formula

ⁿCr = n! / ((n – r)! r!

n = the number of items.

r = how many items are taken at a time.

Substitute the values in above formula :

15! / 11! (15 - 11)!

= 15! / 11! 4!

= 15 × 14 × 13 × 12 / 4 × 3 × 2

= 1365 orders

Hence, 1365 batting orders  are possible for the game.

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The distance between point (6,-3) and (4,3) is 3.162 units using the point formula for distance that is √((x2-x1)²+(y2-y1)²) units.

Since it only represents a dot, a point is a dimensionless shape, whereas a line is one dimension. Both points are lines that can be used to depict various sizes and shapes in a plane.

Coordinates are numerical distances or angles that uniquely identify points on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). Mathematicians, scientists, and engineers frequently use a variety of coordinate systems.

Here,

distance between point (6,-3) and (4,3)

=√((x2-x1)²+(y2-y1)²)

=√((4-6)²+(3+3)²)

=√((-2)²+(6)²)

=√(4+36)

=√(40)

=2√(10)

=3.162

According to the point formula for distance, which is √((x2-x1)²+(y2-y1)²) units, the distance between point (6,-3) and point (4,3) is 3.162 units.

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The sum of the first four terms of the arithmetic sequence is 24.

From the information illustrated, the arithmetic sequence is given by 2n + 1.

The first term will be:

= 2n + 1

= 2(1) + 1 = 3

The second term will be:

= 2n + 1

= 2(2) + 1 = 5

The third term will be:

= 2n + 1

= 2(3) + 1

= 7

The fourth term will be:

= 2n + 1

= 2(4) + 1

= 9

The sum of the first four terms will be:

= 3 + 5 + 7 + 9

= 24

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An arithmetic sequence is given by 2n + 1. What is the sum of the first 4 terms of that arithmetic sequence?

The equation of this line is y =4.

From the given graph we can infer that line A is a horizontal line

It can be expressed in the form y = constant

Hence the equation of this line is y = 4

Similarly, from the given graph we can infer that line B is a vertical line

It can be expressed in the form x = constant

Hence the equation of this line is x = 8

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In a proportional relationship, the ratio between the two variables are equaivalent.

We can also say that one variable is a constant times the second variable in a proportional relationship.

Therefore, the situation that does not represent a proportional relationship from the given choices is:

C. The weight in x weeks of a puppy that gains 2 pounds per week it is starting weight is 5 pounds.

This is because there is an initial value of 5 pounds here

By using 3 factors 2, 3, and 7, if we create a product game board with the numbers 4 6 9 14 49 then the missing product is 21.

To solve this problem we have to follow a few steps. First, we should know about factors.

What are the factors?

Factors of a number are such numbers as they can divide the whole number without remaining.

Example: The factors of 24 are 1, 2, 3, 4, 6, 8, and 12.

Now we have to analyze the given numbers,

4 = 2× 2

6 = 2× 3

9 = 3× 3

14 = 2× 7

49 = 7× 7

The factors are 2, 3, and 7. Therefore, the missing product is, 3× 7= 21

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The image of point (-3,-1) under a reflection in the origin( 3 , 1 )

Point (x, y) is reflected over the line y = x, and the reflection is (y, x)

Find the point of a reflection on a point by what method?

The x-coordinate and y-coordinate of a point change positions when it is reflected across the line y = x. The x- and y-coordinates shift positions and are negated when a point is mirrored across the line y = -x. Therefore, Point (x, y) is reflected over the line y = x, and the reflection is (y, x)

following a reflection, a 3-1 picture Reason: A(3,1) becomes A'(3,3+3(1)), or A', when it is reflected over y=3 (3,7)

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Answer: [tex](x-5)^2 +(y+4)^2 =25[/tex]

Step-by-step explanation:

The equation of a circle with center [tex](h, k)[/tex] and radius [tex]r[/tex] is [tex](x-h)^2 +(y-k)^2 =r^2[/tex].

So, the equation is [tex](x-5)^2 +(y+4)^2 =25[/tex].

The equation of the circle in the figure is (x-5)²+(y+4)²=25

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

From the figure the circle has a center at (5, -4) and radius 5

The standard form equation of the circle is (x-h)²+(y-k)²=r²

(h, k) is the center of the circle and r is the radius of circle

Plug in the values of center and r

(x-5)²+(y-(-4))²=5²

(x-5)²+(y+4)²=25

Hence, the equation of the circle in the figure is (x-5)²+(y+4)²=25

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The function that gives f(x) = 2x² - 7

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f (14) = 2(14)²−7

Now, here the changing value is 14 according to which the resultant values changes.

so, every time it depends on the function value which can be any number.

Then, let us consider that number is x.

Thus, the function that gives f(x) = 2x² - 7

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If a test requires that you answer either part A or part B. Part A consists of 6 true-false questions, and part B consists of 6 multiple-choice questions with one correct answer out of six. 46720 different completed answer sheets are possible.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items.

A test requires that you answer either part A or part B.

Part A consists of 6 true-false questions.

i.e.  there are 2 choices to answer each question

Now, the number of ways to answer Part A :  2⁶=64   (1)

Part B consists of 6 multiple-choice questions with one correct answer out of five.

i.e.  there are 6 choices to answer each question.

Now, the number of ways to answer Part B : 6⁶=46656

Now, the number of  different ways to completed answer sheets are possible= 46656+64

=46720

Hence 46720 different completed answer sheets are possible.

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The value of the indices given will be

[tex](\sqrt{5}) (\sqrt[3]{5})[/tex] simplifies to give [tex]5^{\frac{5}{6} }[/tex] or [tex]\sqrt[6]{3125}[/tex][tex]\sqrt[6]{3125}[/tex]

The indices concept can be used for this simplification. An index is the small number which tells us how many times a term had been multiplied by itself.

[tex](\sqrt{5}) (\sqrt[3]{5}) = 5^{\frac{1}{2} } . 5^{\frac{1}{3} }\\\\(\sqrt{5}) (\sqrt[3]{5}) =5^{\frac{1}{2} +\frac{1}{3} }\\\\(\sqrt{5}) (\sqrt[3]{5}) =5^{\frac{2+3}{6}[/tex]

[tex](\sqrt{5}) (\sqrt[3]{5}) = 5^{\frac{5}{6}} = \sqrt[6]{5^{5} } = \sqrt[6]{3125}[/tex]

Therefore, the result of the simplification is [tex]5^{\frac{5}{6} }[/tex] or [tex]\sqrt[6]{3125}[/tex]

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Answer: -20%

Step-by-step explanation:

new-old divided by old

68-85=-17

-17/85=-0.2

-0.2x100=-20

-20%

Answer:

112

Step-by-step explanation:

448/4=112

The solution to the questions are

The given parameters are:

Every item is on sales for half the original price, plus 3 dollars.

In this case, the function g(x) is half the original price

Let the original price be x

So, we have the following equation

Price = 1/2x

Express as a function

g(x) = 1/2x

The given parameters are:

Every item is on sales for half the original price, plus 3 dollars.

In this case, the function f(x) is the 3 dollars added

Let the original price be x

So, we have the following equation

Price = x + 3

Express as a function

f(x) = x + 3

In (A) and (B), we have

g(x) = 1/2x

f(x) = x + 3

The function (f o g)(x) is calculated as

(f o g)(x) = f(g(x))

So, we have

(f o g)(x) = g(x) + 3

Substitute g(x) = 1/2x

(f o g)(x) = 1/2x + 3

Here, we have

(f o g)(x) = 1/2x + 3

This means that x = 60

So, we have

(f o g)(60) = 1/2 x 60 + 3

Evaluate

(f o g)(60) = 33

Hence, the value of the shirt is $33

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To make 4 batches of lemon cookie, Ronald will need 13.3 cups of sugar.

Firstly converting mixed fraction to fraction, thus getting the amount of cups of sugar required for 1 batch.

Number of cups of sugar required for 1 batch = (3×3 + 1)/3

Performing multiplication and addition in numerator

Number of cups of sugar required for 1 batch = 10/3

Number of cups of sugar required for 4 batches = 10/3 × 4

Performing multiplication to find the number of cups of sugar required

Number of cups of sugar required for 4 batches = 40/3

Performing division to find the number of cups in decimal

Number of cups of sugar required for 4 batches = 13.3

Thus, 13.3 cups of sugar will be needed by Ronald.

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The probability that the student scores an 85 or better and he receive an A in the score is 0.45.

In the question it is given that the professor tells that the student has 90% chance of getting A, if he gets 85 or better in mid term exam.

The student is 50% sure that he will get 85 or better in the examination.

To get the probability of the student scores an 85 or better and he receives an A grade, we use multiplication rule.

P( student getting A grade and 85 or better)= P(getting A) x P(getting 85 or better)

P(getting A)=0.9

P(getting 85 or better)=0.5

= 0.9x0.5

P( student getting A grade and 85 or better)=0.45

Therefore, probability that the student scores an 85 or better and getting A is 0.45.

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Answer: nonlinear function

Step-by-step explanation:

The rate at which y increases is not constant with respect to x.

Given data:

First find f( -1 ) and g( -1 ),

Therefore, we have

The Radius is 15.27 cm and the the Diameter is 30.55 cm

Given

Circumference = 96cm

Circumference is the total arc length of a circle or it is simply the perimeter of a circle.

The formula for circumference is 2πr

where π = Ratio of circumference to the diameter of a circle

π = 3.14

r = Radius of the circle

Substituting the value in the formula we get

2πr = 96 cm

πr = 48 cm

r = 15.27 cm

Diameter (d)  = 2 × r

hence        d = 2 × 15.27 cm

                 d = 30.55 cm

Hence the radius = 15.7cm

Diameter = 30.55 cm

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Answer:

84

Step-by-step explanation:

5*6=30

14*6=84

If you need further explanation just tell me!

Work Shown:

(14 children)/(5 teachers) = (x children)/(30 teachers)

14/5 = x/30

14*30 = 5*x

420 = 5x

5x = 420

x = 420/5

x = 84

So:

f(x) = 2x + 10

To solve for x, we are going to subtract 10 on both sides of the equation:

f(x) - 10 = 2x + 10 - 10

f(x) - 10 = 2x

Then, dividing by 2, we get:

Answer:

To find the greatest common factor (GCM) for monomials, as you have in this case, you can write the complete factorization of each monomial and find the common factors. Then:

As you can see, all of these terms have x*x*x*x in common, and this is equal to x^4.

Thus, the GCF for this list of terms is:

To find the initial population, we evaluate

at t=0:

Therefore, the initial population was 160 individuals.

To find the population after 10 years, we evaluate the given function at t=10:

Therefore, the population after 10 years is 678 individuals.

Answer:

The initial population was 160 individuals.

The population after 10 years is 678 individuals.

Answer:

  a. $9,090.91

  b. $10,526.32

Step-by-step explanation:

You want to know the value of your $10,000 savings when the price level (a) increases by 10%, and (b) decreases by 5%.

As the price level goes up, the number of items that can be purchased with a given dollar amount goes down in inverse proportion.

When the price level increases by 10%, it is multiplied by 1 +10% = 1.10. The effective purchasing power of the savings will be inversely proportional to that:

  $10,000/1.10 = $9,090.91 . . . "real value" of savings

When the price level decreases by 5%, it is multiplied by 1 -5% = 0.95. The effective purchasing power of the savings will be inversely proportional, so will be ...

  $10,000/0.95 = $10,526.32 . . . "real value" of savings

__

Additional comment

The price level index is usually normalized to a value of 100 at some specified point in time. An increase of 10% in price level would be reflected in an index value of 100×1.10 = 110. Effectively, this means that what did cost $100 at the reference time now costs $110.

With $10,000, you could have purchased 100 of those items, but now you can purchase only 90.91 of those items. Your purchasing power has changed in inverse proportion to the price level.

For the entire year, $9091 will be spent if prices rise by 10%.

In the event that prices drop by 5% for the entire year, $10,526.32

Integers include zero, a positive natural number, and a negative integer represented by a minus sign. The negative numbers are the inverse additions of the comparable positive numbers.

Given,

If the price index is 100, savings equal $10,000.

a) If prices increase by 10% annually, the following formula will be used to calculate the true value of the savings:

Real Value = Nominal Value x Prior Year CPI / Current Year CPI

According to the CPI:

= 100 + (100 x 10/100)

For the current year, = 110%.

The resultant value will be

= $10000 x 100/110

= $9090.90

b) If prices decline by 5% annually, the following formula will be used to calculate the true value of the savings:

Real Value = Nominal Value x Prior Year CPI / Current Year CPI

According to the CPI:

= 100 - (100 x 5/100)

for the current year, = 95%

Consequently, the true value will be:

= $10000 x 100/95

=$10,526.32

As a result, your savings would actually be worth $9090.90 if prices rose by 10% annually.

Alternatively, if prices fall by 5% over the course of the year, the actual worth of your savings is $10,526.32.

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Answer:

Option 1

Step-by-step explanation:

[tex]40+20=60 \\ \\

5(8+20)=5(28)=140 \\ \\ 2(20+10)=2(30)=60 \\ \\ 5(8+4)=5(12)=60 \\ \\ 10(4+2)=10(6)=60[/tex]