(1 point) For each trigonometric expression A,B,C,D, E, choose the expression from 1,2,3,4,5 that completes a fundamental identity. Enter the appropriate letter (A,B,C,D, or E) in each blank.

Answer:

[tex]6 \sqrt{6} [/tex]

Step-by-step explanation:

The square value of hypotenuse is equal to the square value of sum of the two legs:

[tex] {15}^{2} + {x}^{2} = {21}^{2} [/tex]

225 + x^2 = 441 subtract 225 from both sides

x^2 = 216 find the root of both sides

x = 6√(6)

Answer:

$5304.25.

Explanation:

The simple interest formula is given by

where

A = future value

P = princple amount

r = interest rate /100

t = time interval.

Now in our case

A = unknown

P = $4900

r = 5.5 / 100

t = 18 / 12 ( we are converting months to years. 18 months = 18 /12 years )

Putting the above values into the simple interest rate formula gives

which simplifies to give

Hence, the future value is $5304.25.

We have 305 cakes. As we know

We have to find the solution for the equation:

The equation has no solution, becuase there is no value of x that satisfy the equation.

Given in the question:

a.) There are four Defenders on a soccer team.

b.) This represents 20% of the players on the team.

Given

a: angle

a = 60

r: radius

r = 3

Procedure

The length of an arc depends on the radius of a circle and the central angle θ

The answer would be s = pi

Answer:

12-3X=X-3=5

Step-by-step explanation:

The value of h by solving the given relationship we get, h = 9

In the above question, a word problem is given with the following relations which are as

First we'll express the given word problem statements into mathematical equation expressions

Therefore, The difference of twice of h and 5 is as much as the sum of h and 4

It can be written as in mathematical equation form as

2h - 5 = h + 4

Now, we need to find the value of h by solving the above mathematical equation formed put of the given relationship

Here,

2h - 5 = h + 4

2h - h = 5 + 4

h = 9

Hence, The value of h by solving the given relationship we get, h = 9

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Step-by-step explanation:

Plot the point ​(3​,​3):

this means where x = 3 and y = 3

Answer:

From the given quadilaterals, let's determine the specific name for each based on the property marked.

• 1a. ,All four sides are marked equal.

Since all four sides are equal, we can say the specific name for the quadilateral is a Square.

A square is a quadilateral with four equal sides.

• 1b. In this quadilateral, we have one pair of parallel sides.

Given that the quadilateral is NOT drawn to scale, the quadilatral here can be said to be a Trapezoid.

A trapezoid is a quadilateral with one pair of parallel side.

• 1c. In this quadilateral, all four angles are marked as right angles.

Given that all four angles are right angles, the specific name for the quadilateral is a Rectangle.

A rectangle is a quadilateral with four interior right angles.

ANSWER:

• 1a. Square

• 1b. Trapezoid

• 1c. Rectangle.

Given the equation:

First, we open the brackets

Next, we collect like terms. (Bring terms containing x to the left-hand side)

Finally, we divide both sides by -6 (negative 6) to obtain x.

The value of x is 2.

System of equations:

To solve the system by graphing, we have to remember that the point in which both graphs meet is the solution of the system.

• Graph of both equations:

As we can see, there is no point in which both meet. Then, this system has no solution.

Answer: none

using the parabola formula:

y = a(x-h)² + k²

vertex = (h, k)

We are given a parebola equation of: y = x²+9

comparing both equations to get the vertex:

y = y

a = 1

(x-h)² = x²

x² = (x + 0)²

(x-h)² = (x + 0)²

h = 0

+k = +9

k = 9

The vertex of the parabola as (x, y): (0, 9)

Given that f(x)=x2-4/3, f(a)=7, and f(11)=b, a+b can only be a multiple of prime numbers is 5

This calculator for finding the prime factors and the factor tree of an integer is available for use.

How is a prime factor discovered?

The simplest method for determining a number's prime factors is to keep dividing the starting number by prime factors until the result equals 1. When we divide the number 30 by its prime factors, we obtain 30/2 = 15, 15/3 = 5, and 5/5 = 1. We received the balance, thus it cannot be factored any further.

Example: 36 can be written as the product of two prime factors, 22 and 32. The prime factorization of 36 is stated to equal the equation 22 32.

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EXPLANATION:

We must replace in the equation given the altitude in the variable x ; the exercise is as follows:

Given:

The objective is to divide the 4921÷ 63​ using compatible numbers.

Explanation:

First, the compatible numbers are,

To calculate division:

Now, the division can be performed as,

Hence, the value of the division is 82.

The reflection over the x-axis is given by:

And the reflection over the y-axis is given by:

Thus, a function that is equivalent to the reflection of ABCD across both axis would be:

Answer:

[tex]y-9=-\dfrac{8}{3}(x-7)[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]

Define the given points:

Substitute the defined points into the slope formula:

[tex]\implies \textsf{slope}\:(m)=\dfrac{1-9}{10-7}=-\dfrac{8}{3}[/tex]

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope and one of the points into the point-slope formula:

[tex]\implies y-9=-\dfrac{8}{3}(x-7)[/tex]

It's important to know that a rational number can be expressed as fractions, but also when they are expressed as decimals, the decimal part repeats infinitely, that is, it has a pattern or finite decimal digits.

Answer:

Colin bought 7 7/8 boxes

Step-by-step explanation:

Let R represent  the number of boxes bought by Ryan and A represent the number of boxes bought by Allan

R = 3 1/2

Convert to improper fraction:
3 1/2 = (3 x 2 + 1)/2 = 7/2

Allan bought 1 3/4 more boxes than Ryan

A = R + 1 3/4

Convert 1 3/4 to improper fraction:
1 3/4  7/4

So A = 7/2 + 7/4 = 14/4 + 7/4 = 21/4

Colin bought 1 1/2 times as many boxes as Allan
C = 1 1/2 x A

Convert 1 1/2 to improper fraction:

1 1/2 = 3/2

So C = 3/2 x 21/4

= 63/8 = 7 7/8 boxes

we have that

The surface area of the pyramid is equal to the area of its square base plus the area of its four triangular faces

step 1

Find out the area of the square base

A=15^2

A=225 ft2

step 2

Find out the area of one triangular face

the area of a triangle is equal to

A=(1/2)(b)(h)

we have

b=15 ft

h ----> is the slant height

To find out the slant height, apply the Pythagorean Theorem

h^2=10^2+(15/2)^2

h^2=100+56.25

h=12.5 ft

therefore

A=(1/2)(15)(12.5)

A=93.75 ft2

step 3

The surface area is equal to

SA=225+4(93.75)

By definition, the commutative property of addition says that changing the order of addends does not change the sum, which is precisely what the equation is trying to show by changing the order of the sum, therefore, the property illustrated is the commutative property of addition.

It is given that the exchange rate is $3 per Dinar. It is required to find how many Dinars you will get if $54 is exchanged.

Since 1 Dinar is equivalent to $3, it follows that the number of Dinars equivalent to $54 is:

The answer is 18 Dinar.

A car can travel 28 miles per gallon of gas. How far can the car travel on 8 gallons of gas?

Applying proportion

28/1=x/8

solve for x

x=(28)*8

x=224 miles

The required domain and the range of the given function is (0, ∞) and (-8, -2) respectively.

Given that,
A graph of the function is shown we have to determine the domain and range of the function with the help of the graph.

The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.

Here,
As of the graph,
The graph describes as only the positive real number because the graph only consists of the positive x-axis, so the domain of the function is all positive real numbers. While the ordinate of the graph is describe for -8 to -2 on the negative y-axis thus the rang of the given function lies between -8 to -2.

Thus, the required domain and the range of the given function is (0, ∞) and (-8, -2) respectively.

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In order to find possible dimensions for the scaled rectangle, the proportion between the dimensions of the rectangles must be the same.

So first let's find this proportion for rectangle R:

Now, let's find the proportion of the possible options of rectangle S:

So the correct options are the first, second and fourth options.

Answer:

From the solution the largest possible integer value of x is;

Explanation:

Given the inequality;

To solve, let's add 1 to both sides of the inequality;

then let us divide both sides of the inequaty by -1.

Note: since we are dividing by a negative number the inequality sign will change.

Therefore, From the solution the largest possible integer value of x is;

ANSWER and EXPLANATION

We have that the 1 - 5th terms of the sequence are:

2/3, 1, 3/2, 9/4 and 27/8

To plot the graph of this sequence, we have:

=> on the x axis, the term number (i.e. n = 1, 2, 3, 4, 5)

=> on the y axis, the term(i.e. a(n) 2/3, 1, 3/2, 9/4, 27/8)

We will plot the graph of n versus a(n).

That is:

That is the graph.

Answer:

To find the volume of the given cuboid.

Length of the cuboid = 6.8 yd

Breadth of the cuboid = 4.5 yd

Height of the cuboid = 3.4 yd

We get,

Volume of a cuboid is,

where l,b and h are the length, breadth and height respectively.

Substitute the values we get,

Answer is: Volume of the cuboid is 104.04 cubic yards.

We have the next given equation:

Now, we can solve for x using the exponent's properties:

Add both sides ln:

With the ln we can take down the exponent and simplify ln*e = 1.

Hence,

Hence, the correct answer is option B.