Which equation is true?

A.
3
4
=
9
16
B.
6
8
=
4
3
C.
3
5
=
8
10
D.
12
16
=
36
48

Using trigonometric function the value of x is 51.3°.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here Let us take the given right triangle as ABC.

∠A = x , ∠B = 90° and AB = 25 , AC= 40

Now using Cosine ratio then

Cos  A = [tex]\frac{adjacent}{hypotenuse}[/tex]

=> cos x = [tex]\frac{25}{40}[/tex]

=> cos x = [tex]\frac{5}{8}[/tex]

=> x = [tex]cos^{-1}\frac{5}{8}[/tex]

=> x = 51.3°

Hence the value of x is 51.3°.

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Answer:

More fish were caught per person on Day 2

Step-by-step explanation:

Day 1:

3 people caught 1 fish = 3 fish

6 people caught 2 fish = 12

6 caught 3 = 18

6 caught 4 = 24

6 caught 5 = 30

3 caught 6 = 18

Total fish caught =  105

That's 105/30 = 3.5 fish per person

Day 2:

3 people caught 1 fish = 3 fish

3 caught 2 = 6

4 caught 3 = 12

6 caught 4 = 24

7 caught 5 = 35

7 caught 6 = 42

Total fish caught = 122

122/30 = 4 fish per person

If the respective sides are proportional and the corresponding angles are congruent, two triangles are said to be similar.

Triangles with the same form but different sizes are referred to as comparable triangles. Examples of related objects are all equilateral triangles and squares with any side length. In other words, two similar triangles have similar sides that are proportionately equal and similar angles that are congruent.

If two triangles have an equal number of corresponding sides and corresponding angles, they can be compared. Similar figures are objects that have the same shape but various sizes, like two or more figures.

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The systems have a unique solution if k ≠ 6.

The given equations are:

kx+ 2y=5

3x + y =1

Concept used:

If [tex]\frac{a_{1} }{a_{2} }[/tex] ≠  [tex]\frac{b_{1} }{b_{2} }[/tex] , then the system of equations [tex]a_{1}x + b_{1}y + c_{1} = 0[/tex]  [tex]a_{2}x + b_{2}y + c_{2} = 0[/tex] has a unique solution.

Calculation,

kx+ 2y-5=0

[tex]a_{1}=k, b_{1}=2 , c_{1} = -5[/tex]

3x + y -1=0

[tex]a_{2}=3, b_{2}=1 , c_{2} = -1[/tex]

according to the question,

[tex]\frac{a_{1} }{a_{2} }[/tex] ≠ [tex]\frac{b_{1} }{b_{2} }[/tex]

⇒[tex](\frac{k}{3})[/tex] ≠ [tex](\frac{2}{1} )[/tex]

⇒ k ≠ 6

∴ The systems have a unique solution if k ≠ 6.

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The point that is a solution to the system of linear equations is O (1,0).

Putting the value O (1,0) in both equations we get that this point satisfies both equations.

putting x = 1 and y = 0

y = -x+ 1

y = -1+1 = 0

also, 3x -y = 3

3 ×1 -0 = 3

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The intensity of earthquake shaking at any location is determined by the magnitude of the earthquake and its distance.

The most noticeable result of the earthquake is, first and foremost, the shaking of the ground. Along with shaking, earth rupture also happens. Infrastructure facilities suffer serious damage as a result of this. The size and distance from the epicentre of the earthquake affect how severe it is.

The local geographic circumstances have an impact on the severity as well. The visible cracking of the Earth's surface is referred to as ground rupture. Earthquake has killed more humans in past 100 years.

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An angle is 270 degrees when it is a reflex angle .

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.

An angle that is greater than 180 degrees and less than 360 degrees is referred to as a reflex angle. Reflex angles include, for instance, 270 degrees. There are several sorts of angles in geometry, including acute, obtuse, and right angles—angles that are less than 180 degrees.

A reflex angle equals the summation of 180 degrees and any of the primary angles (acute, right and obtuse angles). Therefore,

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27m^3-64 = (3m)^3 - (4)^3

= (3m-4)((3m)^2 + (3m)(4) + (4)^2)

= (3m-4)(9m^2 + 12m + 16)

The factored form of 27m^3-64 is (3m-4)(9m^2 + 12m + 16)

Answer:

(3m−4)(9m2+12m+16)

Step-by-step explanation:

this is difference of cubes (3m)^3 - (4)^3

now, apply difference of cubes formula

a^3−b^3 = (a−b)(a2+ab+b2)

where a=3m and b=4

(3m−4) ( (3)^2×(m)^2 + 4×3m + (4)^2)

(simplify)

(3m−4)(9m2+12m+16)

Answer:

f(-2) = -6

Step-by-step explanation:

f(x)=2x^2+7x        f(-2)

We put -2 in for x and solve

f(-2) = 2(-2)^2 + 7(-2)

f(-2) = 2(4) - 14

f(-2) = 8 - 14

f(-2) = -6

The new points after a rotation of 180 degrees are

M' = (-3,1)

N' = (-8,4)

0' = (-6,6)

P' = (-7,1)

Quadrilateral MNOP has vertices M(3,-1), N(8,-4),O(6. -6), and P(1,-7).

Given a point (x, y) and we rotate by 180 degrees, the new point will be (-x, -y).

Given the coordinate points  M(3,-1), N(8,-4), O(6. -6), and P(1,-7), if these coordinates are rotated 180 degrees, the corresponding coordinate of the pre-image will be at M'(-3,1), N' (-8,4),0'(-6,6) and P'(-7,1).

So, the resulting coordinates will be M'(-3,1), N' (-8,4),0'(-6,6), and P'(-7,1).

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The future value is $7,689,500.

The worth of a current asset at a future date based on an estimated rate of growth is known as future value (FV). Investors and financial planners care about future value because it helps them predict how much an investment made now will be worth in the future.

The future value formula assumes a constant rate of growth and a single up-front payment left untouched for the duration of the investment.

Given that,

P = 3500

R = 12%

T = 3 years

Future value (FV) = [tex]I*(1+R)^{T}[/tex]

where:

I=Investment amount

R=Interest rate

T=Number of years

Substituting the values in the formula given:

FV = 3500*(1+12)³= 3500*2197 = 7689500

Thus, the future value is $7689500

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Rachel that swam 2 2⁄3rd mile then another 4 and one-half mile, did 5/12 miles more than Jason

Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.

To solve this problem we must perform the corresponding algebraic operations with mixed fraction.

Data of the problem:

A mixed operation is solved as follows:

For the denominator: the same denominator is placed.

For the numerator:

We transform the mixed fractions into improper fractions and we have:

3 1/2

= [(3*2) + 1)] /2

= [6+ 1] /2

7/2

3 1/4

= [(3*4) + 1)] /4

= [12+ 1] /4

13/4

2 2/3

= [(3*2) + 2)] /3

= [6+ 2] /3

8/3

4 1/2

= [(4*2) + 1)] /2

= [8+ 1] /2

9/2

Calculating how many miles Rachel did more than Jason we have:

Rachel miles more = Rachel - Jason

Rachel miles more = (8/3 + 9/2) - (7/2 + 13/4)

Rachel miles more = [(16 + 27)/6] - [(14 + 13)/4]

Rachel miles more = 43/6 - 27/4

Rachel miles more = (172 - 162)/24

Rachel miles more = 10/24

Simplifying we have:

Rachel miles more = 5/12

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The number 48.050 has five significant figures.

What do you mean by an Significant figures?

Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures. Determine how many significant digits there are given a range of numbers.

Significant figures, also known as significant digits, are the digits in a measurement or a number that carry meaning contributing to its precision. In this case, the number 48.050 has four non-zero digits (4,8,0,5) and one zero (0) between two non-zero digits, which are significant figures.

The trailing zero after the decimal point does not affect the significant figures, it is simply a placeholder to indicate the number is less than one and has a magnitude of 0.050.

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Answer:

42 tiles

Step-by-step explanation:

Area of rectangular region= 70 X 36 = 2520 cm2

Area of 1 tile= 5 X 12 = 60 cm2

The number of tiles needed = Area of the rectangular region / Area of one tile = 2520/60 = 42

The four quadrants in a plane are Q1, Q2, Q3, Q4.

Quadrant one (QI), the top right quadrant of the coordinate plane, only contains positive coordinates. Quadrant two refers to the top left-fourth of the coordinate plane (QII). Quadrant three is on the bottom left corner (QIII). Quadrant Four is the bottom right fourth (QIV). In quadrant I, both the x- and y-coordinates are positive. In quadrant II, the x-coordinate is negative while the y-coordinate is positive. In quadrant III, the x- and y-coordinates are positive. In quadrant IV, the x-coordinate is positive while the y-coordinate is negative. In a coordinate system, a quadrant is the area formed by the x and y axes. The quadrants are created when the x- and y-axes connect at a 90-degree angle. These areas include coordinates, or the positive and negative values of the x- and y-axes.

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The slope is calculated by the formula : [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

The slope is defined as the ratio of the change in the y-axis to the change in the x-axis.

The slope of a straight line will define the line’s angle of steepness from the horizontal whether it rises or falls. When the line neither rises nor falls, then its slope will be zero.

This is the case with a horizontal line where it extends infinitely to its left or right but without any sign of rise or fall.

In a coordinate system, points are represented by a pair of coordinate values. This pair is having y to values x-value and y-value.

For example (x,y) will represent a point on the geometrical plane. Also, (0,0) will represent the origin point.

Let (x₁,y₁)and(x₂,y₂)  x₁, x₂ are the coordinates of x-axis and y₁,y₂ are the coordinates of y-axis

The formula to calculate slope is defined as given below,

m= y2−y1x2−x1

Where m is the slope of the line.

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Answer:

D' is (16,20)

Step-by-step explanation:

A translation is the movement of the graphed line, either vertically or horizontally. The two given points are A and D:

A (2,11)

D (10,9)

When the line is translated, point A becomes A' (8,22).

Pint A is moved to the right by 6, and up by 11. Lets do the same for point D to make it D'

D' = (10+6, 9+11)

D' = (16,20)

See the attached graph.

There are 11 trees that are more than 6m tall but not more than 12m tall.

What is the Range?

In mathematics, a range is the set of all output values, or results, of a function. In statistics, a range is a measure of dispersion, which is used to describe the distribution of a set of data.

The table provided gives the frequency of trees at different height ranges. The range for the trees more than 6m tall but not more than 12m tall is 6<h<=9, and the frequency for this range is 11. This means that there are 11 trees in the park that are taller than 6 meters but not taller than 12 meters.

Hence, There are 11 trees that are more than 6m tall but not more than 12m tall.

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Since we are going to check the similarity of the triangles and we have given two sides and angle we have to check the Side-Angle-Side option of the similarity. We have equal angles.

Since we are going to check the similarity of the triangles and we have given two sides and angle we have to check the Side-Angle-Side option of the similarity. We have equal angles. Then, we have to check the proportionality of the sides. If these triangles are equal, then VT/QR=UT/RS. If we calculate it, 28/7=44/11=4. This last number is the similarity ratio and since we have proportionality, ΔQRS ~ ΔVTU.

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The number that should be added to the expression x²+4x to change it into a perfect square trinomial is 4.

The general form of a perfect square trinomial is (x + y)^2, where x and y are the roots of the trinomial. To check if a trinomial is a perfect square, we can try to factor it into the square of a binomial. We can also complete the square method, which involves adding and subtracting the square of half of the x-coefficient of the linear term and then grouping the resulting terms.

It is important to note that for a trinomial to be a perfect square trinomial, the constant term must be a square of an integer and the linear term must be an even number.

Perfect square trinomials are used in solving quadratic equations and understanding their solutions, they also have applications in algebra, geometry, and trigonometry. Factoring them is a fundamental skill in algebra and is used in solving different types of mathematical problems.

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Complete Question: –

What will make the expression x²+4x a perfect square trinomial?

The simplified rational expression of the square root of 16y^7 is given as follows:

[tex]4y^3\sqrt{y}[/tex]

The rational expression for this problem is defined as follows:

[tex]\sqrt{16y^7} = (16y^7)^\frac{1}{2}[/tex]

The power of power rule states that when an exponential expression is elevated to a power, the powers are multiplied.

4 is the square root of 16, hence:

16 = 4².

Meaning that the expression is of:

(4²y^7)^0.5.

Then the simplified radicals are of:

Then the simplified expression is given as follows:

[tex]4y^3\sqrt{y}[/tex]

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Answer: 14.31

Step-by-step explanation:

Using Law of Sines, we know that

[tex]\frac{16}{sin(72)} =\frac{PR}{sin(90)}[/tex]

Thus, [tex]PR=16.8233955878[/tex]

Then, using [tex]\frac{\alpha }{sin(\alpha)} =2R[/tex],

we know that [tex]\frac{16.8233955878}{sin(s)} =\frac{16.8233955878}{sin(36)} =28.621670112 = 2R[/tex]

Therefore, [tex]R = 14.310735056[/tex]

Answer:

0.18 cents

Step-by-step explanation:

They are simply asking for the difference between the gas at the street and at the gas station which is 2.57 - 2.39 = 0.18

The numbers are 2 and 4.

Difference in math is the result of one of the important mathematical operations, which is obtained by subtracting two numbers. It tells us by how much a number differs from the other.

Addition is a way of combining things and counting them together as one large group. Addition in math is a process of combining two or more numbers.

Here we have,

The difference in two numbers is 2.

2 and 4 are two numbers away from each other.

The sum of the same two numbers is 6.

2+4=6

Hence, In least to greatest order they would be written 2, 4.

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For x^2 * 5x to end in 5, x must be an odd number.

The last digit of a number is determined by its units digit. For example, the last digit of 123 is 3, the last digit of 789 is 9, and so on.

When you multiply two numbers, the last digit of the product is determined by the last digit of each factor. For example, the last digit of 3 * 4 is 2, the last digit of 6 * 7 is 2, and so on.

In this case, x^2 * 5x is a product of two numbers, x^2 and 5x. To find the units digit of x^2, we can square the units digit of x. The units digit of 5x is the units digit of x.

So, since we want x^2 * 5x to end in 5 , the last digit of x^2 * 5x has to be 5. The last digit of x^2 is the square of the last digit of x, and the last digit of 5x is 5 if x is odd and 0 if x is even.

--The question is not readable, answering to the question below--

"For what value of (x^2) * 5x ends in 5?"

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Answer:36/(x+3)^2*(x-3)^2

Step-by-step explanation:

Step 1: Perform the horizontal line test as the first step. Move a horizontal line from the graph's bottom to its top to accomplish this. The graph fails the horizontal line test and does not have an inverse if the horizontal line touches two or more points on the graph at any given time. Continue to Step 2 if the graph passes the horizontal line test.

Step 2: Determine the given function's domain and range in step two.

Step 3: A square root function is the inverse of a quadratic function. We switch the domain and range in order to graph the inverse. The graph has the same structure but has been rotated to have the original function's domain and range switched.

A quadratic function is the inverse of a square root function. We switch the domain and range of the original function to get the graph of the inverse. In other words, the range of the inverse quadratic function is the domain of the square root function. The domain of the inverse quadratic function is the range of the square root function. The graph's geometry is the same, but it has been rotated to give it the right domain and range.

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One of the most important considerations when designing or evaluating a function is its convexity. A function is said to be convex if it is possible to represent its shape in a single, continuous surface.

However, it is not always straightforward to determine if a particular function is convex or not. There are various criteria that can be used to determine whether a given function is convex or nonconvex. These include the "vertex test" and the "region test." The vertex test is a simple and intuitive way to determine whether or not a function is convex. It can be performed as follows: First, identify any critical points of the function using the first derivative. Then, draw a graph of these functions and identify the point at which the graphs of these functions intersect. The point where this intersection occurs is the vertex of the function. If the graph of the function does not intersect at any point, then it cannot be concave and can therefore be considered to be convex.

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A polynomial function's sum is the result of adding all of its terms together. Simply add the coefficients of each phrase together, followed by the exponents of each term, to obtain the sum.

Take the polynomial function, for instance:

f(x) = 2x² + 4x + 3

The function's sum is  2x² + 4x + 3 = 9

Determine the highest exponent before attempting to get the sum of a polynomial with many terms. Next, sum up each term's coefficients that has that exponent. Add the exponents of each phrase to the total of the coefficients after the coefficients have been added. The polynomial function's sum is the final total.

Take the polynomial function, for instance:

f(x) = 2x³ + 4x² + 3x + 5

The function's sum is 2x³ + 4x² + 3x + 5 = 14

In conclusion, you put the coefficients of each term together to determine the total of a polynomial function, and then you add the exponents of each term to the sum of the coefficients. The polynomial function's sum is the final total.

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Answer:

A) [tex]\displaystyle -2\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{9}{10}\div\biggr(-\frac{2}{5}\biggr)=\frac{9}{10}*\biggr(-\frac{5}{2}\biggr)=\frac{9(-5)}{10(2)}=\frac{-45}{20}=\frac{-9}{4}=-2\frac{1}{4}[/tex]