Solve 8 sin² (x) - 2 sin(x) - 3 = 0 for all solutions 0 < x < 2π

Answer:

7.5

Step-by-step explanation:

A trapezoid is a quadrilateral where the bases are parallel, but the legs are not parallel.

Given vertices of trapezoid STUV:

The parallel bases of the trapezoid are TU and SV.

Find the lengths of TU and SV using the distance formula.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

[tex]\begin{aligned}TU&=\sqrt{(x_U-x_T)^2+(y_U-y_T)^2}\\&=\sqrt{(6-2)^2+(10-7)^2}\\&=\sqrt{(4)^2+(3)^2}\\&=\sqrt{16+9}\\&=\sqrt{25}\\&=5\end{aligned}[/tex]

[tex]\begin{aligned}SV&=\sqrt{(x_V-x_S)^2+(y_V-y_S)^2}\\&=\sqrt{(8-0)^2+(6-0)^2}\\&=\sqrt{(8)^2+(6)^2}\\&=\sqrt{64+36}\\&=\sqrt{100}\\&=10\end{aligned}[/tex]

The midsegment of a trapezoid is the segment parallel to the bases that connects the midpoints of the legs.

[tex]\boxed{\begin{minipage}{6.5cm}\underline{Midsegment of a Trapezoid}\\\\$M=\dfrac{b_1+b_2}{2}$\\\\where:\\ \phantom{ww}$\bullet$ $M$ is the length of the midsegment. \\\phantom{ww}$\bullet$ $b_1$ and $b_2$ are the parallel bases. \\\end{minipage}}[/tex]

Substitute the found lengths of the bases into the midsegment formula:

[tex]\implies M=\dfrac{5+10}{2}[/tex]

[tex]\implies M=\dfrac{15}{2}[/tex]

[tex]\implies M=7.5[/tex]

The length of the midsegment is 7.5.

The algebraic expression that represents the number of beads per necklace is given as follows:

250/8.

The algebraic expression representing the number of beads per necklace is obtained applying the proportion in the context of the problem.

The proportion is given by the division of the total number of beads by the total number of necklaces, as follows:

Beads per necklace = Number of beads / Number of necklaces.

The parameters for this problem are given as follows:

Hence the algebraic expression that represents the number of beads per necklace is given as follows:

250/8.

(dividing the number of beads by the number of necklaces given in this problem).

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ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased.

There are several methods to define a formula. A mathematical statement that establishes the equivalence of two mathematical expressions is the definition of an equation in algebra. This is best shown by the formula 3x + 5 = 14. In this instance, the word equal comes between the phrases 3x + 5 and 14. Even the most basic algebraic equations include the usage of mathematical variables.

X now has 300 mg of sodium in it.

[tex]x = 300[/tex]

Y also has 450 mg of sodium in it.

[tex]y = 450[/tex]

Samuel reportedly buys five more frozen dinners than soup cans, and they all have a combined salt content of 6000 mg.

Let the number of frozen dinners be "b," and the number of soup cans be "a."

ax + by = 6000

a(300) + b(450) = 6000 .

Samuel bought 5 more frozen dinners than soup cans, according to the inquiry, which results in equation

[tex]a + 5 = b \\a(300) + (a + 5)(450) = 6000\\300a + 450a = 6000 - 2250\\ 750a = 3750\\ a = 3750/750\\ a = 5\\5 + 5 = b\\ b = 10[/tex]

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The number of cards that featured rookie players is given as follows:

11 cards.

The number of cards with rookie players is obtained applying the proportion, which is a fraction of the total amount in the context of a problem.

To find the desired amount, the proportion is multiplied by the total number of cards, hence obtaining the number of cards with rookie players.

The parameters for this problem are given as follows:

Hence the number of cards featuring rookie players is calculated as follows:

3/4 x 15 = 45/4 = 11.25 cards.

Rounding to the nearest integer, 11 cards.

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A graph of the solution to this inequality (x < 5) is shown on the number line in the image attached below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for the comparison of two (2) or more numerical data, numerals, and variables that are contained in an algebraic equation, especially based on the following inequality symbols:

Generally speaking, a number line is a type of chart which primarily decreases in numerical value towards the right from zero (0) and increases in numerical value towards the left from zero (0).

Next, we would solve the given inequality by adding eight to both sides as follows;

−8 + x < −3

−8 + x + 8 < −3 + 8

x < 5

Therefore, the solution is x is less than five.

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The value of the diagram represented by 4/5 divided by 2/3 is 6/5

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

A numerical number that designates a portion of a whole is used to represent fractions. A fraction is a component or segment taken from a whole, which can be any number, a certain amount, or an object. Let's use an illustration to better comprehend this idea. The pizza in the accompanying image has been sliced into 8 equally sized pieces. Now, if we wish to refer to a single portion of the pizza, we can do so by using the notation 1/8, which indicates that we are talking about one portion out of 8 equally sized portions.

The fractions are 4/5 and 2/3

Now 4/5 divided by 2/3 is given by

[tex]\frac{\frac{4}{5} }{\frac{2}{3} }[/tex] = [tex]\frac{4}{5}*\frac{3}{2} = \frac{6}{5}[/tex]

The value of the diagram represented by 4/5 divided by 2/3 is 6/5

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On solving the provided question we cans ay that - the area of the rectangle will A = 121 cm sq.

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

So we have been provided with,

L = 11 cm and B = 11 cm

so, A  = L X B = 11 X 11 = 121 cm sq.

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The area of the sum of all the center triangles in the sequence of figure can not be determined; since the series has an indefinite number of terms, the series does not have a sum. Option D

The area of a given triangle is the space that it occupies on a 2 dimensional plane. So that the major formula that can be used to determine the area of a triangle is;

Area of a triangle = 1/2 * base * height

The sum of area of given triangles implies the mathematical addition of the values of area for each of the triangles.

In the given question, it was given that the pattern continues indefinitely. Thus it is impossible to determine the area of the sum of all center triangles in the sequence of figure.

Therefore the appropriate answer is option D. Since the series has an indefinite number of terms, the series does not have a sum.

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Line a is parallel to line b and goes through the point (1,2). Line b goes through the point (3,1) and is perpendicular to line c whose equation is y = -2x+3.The y-intercept of line a is -7

given that

Line a is parallel to line b and goes through the point (1,2)

Line b goes through the point (3,1) and is perpendicular to line c

equation of line c is y = -2x+3

To find y-intercept of line a.

we need to find the slope of the equation

slope(m) = [tex]\frac{y2 - y1}{x2 - x1}[/tex]  =[tex]\frac{1 - (-3)}{2 - 1}[/tex] = [tex]\frac{4}{1}[/tex] = 4

now , we need to write equation in slope intercept form

y = mx + b

1 = (4)2 + b

1 = 8 + b

b  = -7

The y-intercept of line a is -7

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All the ordered pairs that represent points on the graph of this equation include the following:

A. (-4, 4).

C. (-2, 1)

E. (2, -5)

F. (0, -2)

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

In order to determine the ordered pairs that represent points on the graph of the given function, we would plot its equation by using an online graphing calculator and then read all the ordered pairs that lie on the line.

By critically observing the graph of the given function (see attachment), the solutions are include following;

Ordered pair = (-4, 4).

Ordered pair = (-2, 1).

Ordered pair = (2, -5).

Ordered pair = (0, -2).

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Complete Question:

Which ordered pairs represent points on the graph of this equation? Select all that apply.

2y= –3x–4

(-4, 4)

(7, 6)

(-2, 1)

(0, 7)

(2, -5)

(0, -2)

Answer:

1.66

Step-by-step explanation:

1x1.66=1.66

The distance that is covered is  98.3 m.

We know that in this case now, we would need to obtain the distance that has been traveled as it has been shown. We can see from the diagram, that  the angle of inclination of the kite from Zainab's sight is 35⁰ and the distance between Zainab's eyes and the kite is 120 meters.

Using the trigonometric ratios for the right angled triangles we have;

Cos θ = adjacent /hypotenuse

adjacent = d

hypotenuse = 120 m

cos 35 = d/120

d = 120 cos 35

d = 98.3 m

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Answer:

q=40

Step-by-step explanation:

q/10+71=75

       -71.  -71

q/10=4

 x10 x10

q=40

hopes this helps

Answer:

What the guy above me says!

Step-by-step explanation:

Therefore , the solution of the given problem of sequence comes out to be T =  5832.

The phrase "sequence" refers to a grouping of numbers, or "terms." 2, 5, and 8 are examples of terms. By making advantage of a specific pattern some sequences follow, it is possible to make some sequences infinitely long. To continue the sequence, use the sample of 2,5,8, and then add 3. There are equations that show where to seek for words in a list of words. In mathematics, a sequence is a group of items that are all in some kind of order .  The length of the series is the total number of ordered objects, which may be limit . arranging two or more things in a sensible order. Chronological.

Here,

Given :

to determine the nth term norm for the members of the cube in order.

1, 8, 27, 64, and... are

the cube numbers.

The 18th term

=> T(18) = 183

=> T(18) = n³

=>T(n) =  n³ = 5832

Therefore , the solution of the given problem of sequence comes out to be T =  5832.

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Answer:

okay now I really think that doing or solving any question like this will start first by solving out Earth I mean x okay by solving it out and after solving it and I'm really sorry cuz I'm using a voice note that's why I'm having all this misinterpretation so when you sort out x you begin to sort out all the questions nowhere for them to settle number the certain number will be x know where the four times a number will be no where the 903 will be and I really think that is it

Answer:

142 degrees

Step-by-step explanation:

they are vertical angles!

Answer:

$19.55

Step-by-step explanation:

$23-15%=$19.55

The average change in height of the rainwater each day is 1.35 inches.

The rate at which one value in a function changes in proportion to another is known as the average rate of change. The slope of a graphed function is typically calculated using the average rate of change.

Given, Gualberto has a barrel that collects rainwater. As the rainwater evaporates, the height of the rainwater changes from 24.83 in. to 18.08 in.

Thus,

The change of height in 5 days = 24.83 - 18.08

The change of height in 5 days = 6.75

Hence,

The Average change of height in 5 days = 6.75 / 5

The Average change of height in 5 days =  1.35

Therefore, Every day, the rainwater's height changes by 1.35 inches on average.

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The y-coordinate matched with the given x-coordinate:

x = 100  → y = 3

x = 1/10   → y = 0

x = 10  → y = 2

x = 1   → y = 1

x = 1/100  → y = -1

The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.

Given:

Logarithmic function,

y = log(10x).

(1).

x = 100

So,

y = log{(10)(100)}.

y =  log(1000)

y = 3

(2).

x = 1/10

So,

y = log{(10)(1/10)}.

y = log(1)

y = 0

(3).

x = 10

So,

y = log{(10)(10)}.

y = log(100)

y = 2

(4).

x = 1

So,

y = log{(10)(1)}.

y = log(10)

y = 1

(5).

x = 1/100

So,

y = log{(10)(1/100)}.

y = log(1/10)

y = -1

Therefore,  the y-coordinate matched with the given x-coordinate

x = 100  → y = 3

x = 1/10   → y = 0

x = 10  → y = 2

x = 1   → y = 1

x = 1/100  → y = -1

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The quantity of gravel in tons which the truck can carry when the road bans are in effect as required to be determined is; 11.475 tons.

It follows from the task content that the quantity of gravel which the truck in discuss can carry when road bans are in effect be determined.

First, since the truck normally carries 10 cubic yards of gravel and each cubic yard weighs 1.35 tons.

Therefore, the truck can carry; 10 × 1.35 = 13.5 tons of gravel.

On this note, since the truck can only be loaded 85 percent of normal capacity when road bans are in effect.

The quantity which the truck can carry when road blocks are in effect is therefore; ( 85 / 100 ) × 13.5 = 11.475 tons of gravel.

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The total cost of the vegetables to the nearest cent is $3.44

The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.

Two quantities are compared to form a ratio. An equality of two ratios is a percentage. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.

Angela bought 2 pounds of yellow squash and 1 pound of zucchini. The yellow squash and the zucchini were both on sale for $1.146 per pound.

To find the total cost of the yellow squash, we can multiply 2 pounds by $1.146 per pound:

2 pounds * $1.146/pound = $2.292

To find the total cost of the zucchini, we can multiply 1 pound by $1.146 per pound:

1 pound * $1.146/pound = $1.146

To find the total cost of the vegetables, we can add the cost of the yellow squash and the zucchini:

$2.292 + $1.146 = $3.438

The total cost of the vegetables to the nearest cent is $3.44

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Answer:b a

Step-by-step explanation:

Answer:

3 batches of meatloaf requires 6 pounds of beef

and 3 cups of bread crumbs.

Step-by-step explanation:

For pounds of beef

1 batch meatloaf = 2 pounds of beef

3 batches of meatloaf = x

Cross Multiply

x = 3 x 2 pounds of beef

x = 6 pounds of beef

3 batches of meatloaf requires 6 pounds of beef

For bread crumbs

1 batch meatloaf = 1 cup of bread crumbs

3 batches of meatloaf = x

Cross Multiply

x = 3 × 1 cup of bread crumbs

x = 3 cups of bread crumbs

3 batches of meatloaf requires 3 cups of bread crumbs.

Therefore, 3 batches of meatloaf requires 6 pounds of beef and 3 cups of bread crumbs.

Answer:

13, 15 17

Step-by-step explanation:

Let x = 1st number

Let x + 2 = 2nd number

Let x + 4 = 3rd number

x + x + 2 + x + 4 = 45  Combine like terms

3x + 6 = 45  Subtract 6 from both sides

3x + 6 - 6 = 45 - 6

3x = 39  Divide both sides by 3

[tex]\frac{3x}{3}[/tex] = [tex]\frac{39}{3}[/tex]

x = 13

Check:

13 + 15 + 17 = 45

Answer:3

Step-by-step explanation:

44.8 times 0.22 is 9.856 so 3 numbers will fall after the decimal point. You can also determine the answer by simply adding the number of decimal places in the numbers multiplied.

The right triangle drawings are used to model the shadow scenarios. Each side length of the triangle represents a different part of the scenario.

The hypotenuse represents the distance from the sun to the object casting the shadow, the side adjacent to the hypotenuse represents the length of the shadow, and the side opposite the hypotenuse represents the height of the object casting the shadow. In the real world, the hypotenuse is used to calculate the angle of the sun relative to the object casting the shadow.

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Therefore, using the supplied numbers, we may convert this data into a bar graph.

A graph is what?

A graph is a non-linear data structure made up of nodes, or vertices, and edges. In a graph, the nodes, also known as vertices, are joined together by any two edges. This graph's edges (E) are 1, 2, 1, 3, 2, 4, 2, 5, and 4, 50, while its vertices (V) are 1, 2, 3, 5, and 1.

given

[tex]P(A) = 0.70\\P(C|A) = 0.30\[/tex]

So we are to find

[tex]P(C|A) = P(A|C) * P( C) / P(A)\\[/tex]

As here as we are to find conditional probability .

As a result, option a) is accurate since p (c vertical line a) equals fraction numerator p (a vertical line c)p (a)over denominator p (c)end fraction.

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The solution of the system of equations:

y = 6x + 11

2x-  3y = 7

is (-5/2, -4).

Here we want to solve the following system of equations:

y = 6x + 11

2x-  3y = 7

We can see that y is already isolated on the first equation, so we can substitute this on the second equation.

We will get:

2x - 3*(6x + 11) = 7

2x - 18x - 33 = 7

Now we can solve that equation for x:

2x - 18x - 33 = 7

-16x - 33 = 7

-16x = 7 + 33

-16x = 40

x = 40/-16 = -10/4 = -5/2

And the value of y is what we get if we evaluate one of the functions in x = -5/2.

I will use the first one.

y = 6x + 11

y = 6*(-5/2) + 11

y = -15 + 11

y = -4

So the solution of the system of equations is (-5/2, -4).

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The measure of JK from the given similar quadrilaterals is 30 units.

Similar figures mean when two figures are of the same shape but are of different sizes. In other words, two figures are called similar when they both have a lot of the same properties but still may not be identical.

Given that, JKLM and PQRS are similar figures.

MJ=21, JK=4y-2, KL=6x+3, LM=36, PQ=10, QR=11, and RS=12.

Since, given quadrilaterals are similar, we get

JK/PQ =LM/RS

4y-2/10 =36/12

4y-2/10=3

4y-2=30

4y=32

y=8

So, JK=4y-2

JK=30 units

Therefore, the measure of JK is 30 units.

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