Given sin theta =
4/5 and pi/2 < theta < pi find cos 2theta

The radical function that has a domain of (x ∈ R such that x <= -3) and range of (y ∈ R such that y >= 4) is y = √(-x - 3) + 4.

The domain of this function is (x ∈ R such that x <= -3) because the inside of the square root must be non-negative, and x + 3 is negative when x <= -3. The range of this function is (y ∈ R such that y >= 4) because the square root of a non-negative number plus 4 is always greater than or equal to 4.

The height of the cylinder is h = 11 yards.

What is volume?

A measurement of three-dimensional space is volume. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.

Volume is a three-dimensional measurement that's used to gauge a solid shape's capacity. It implies that the volume of a closed figure determines how much space it can occupy in three dimensions.

Given:

A cylinder with a diameter of 8 yards has a volume of 552.64 yd3.

We have to find the height of the cylinder.

Consider, the volume formula for cylinder

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

Here diameter = 8 yards

⇒ Radius = 4 yards

Plug V = 552.64,  r = 4,  π = 3.14 in the above formula.

⇒

[tex]552.64 = (3.14)(4^2)h\\h = \frac{552.64}{(3.14)(16)} \\h = 11[/tex]

Hence, the height of the cylinder is h = 11 yards.

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Answer:64π cm2

Step-by-step explanation:your welcome

Answer:

[tex]\boxed{a:b:c:d = 1: \dfrac{3}{2}:\dfrac{3}{5}:3}[/tex]

Step-by-step explanation:

Determine all the variables in terms of a single variable, a

Ratios are nothing but fractions

[tex]a:b = \dfrac{a}{b}[/tex]

We have

[tex]\dfrac{a}{b} = \dfrac{2}{3}\\\\\longrightarrow b = \dfrac{3}{2}a[/tex]

[tex]\dfrac{b}{c} = \dfrac{5}{2}\\\\\longrightarrow c = \dfrac{2}{5} b = \dfrac{2}{5}\cdot \dfrac{3}{2} a[/tex]

[tex]c = \dfrac{3}{5}a[/tex]

[tex]\dfrac{b}{d} = \dfrac{1}{2}[/tex]

[tex]\longrightarrow d = 2b = 2\cdot \dfrac{3}{2}a = 3a[/tex]

So a:b:c:d becomes

[tex]a : \dfrac{3}{2}a : \dfrac{3}{5}a : 3a[/tex]

Which is

[tex]1: \dfrac{3}{2}:\dfrac{3}{5}:3[/tex]

Answer:
[tex]\boxed{a:b:c:d = 1: \dfrac{3}{2}:\dfrac{3}{5}:3}[/tex]

Answer: hope this helps

The food truck operator should park her truck on the perpendicular bisector of the line connecting the two streets.

A perpendicular bisector is a line that bisects a line segment and is perpendicular to it. In this case, it would be a line that is equidistant from both streets and also perpendicular to the line connecting them. This is the best option for the food truck operator because it ensures that she is equidistant from both streets.

An angle bisector is a line that bisects an angle and divides it into two congruent angles. It is not appropriate in this case as it would not guarantee that the food truck is equidistant from both streets.

A median is a line that connects a vertex of a triangle to the midpoint of the opposite side. It is not appropriate in this case as the streets are not a triangle and it would not guarantee that the food truck is equidistant from both streets.

An altitude is a line that is perpendicular to the base of a triangle and goes from a vertex to the opposite side. It is not appropriate in this case as the streets are not a triangle and it would not guarantee that the food truck is equidistant from both streets.

Step-by-step explanation:

Answer:

Step-by-step explanation:126

Minutes it will take the tank to drain completely is 3.88

There is independent quantity, and a quantity which depends on it (dependent quantity). When independent quantity moves by a unit measurement (single unit increment), the increment in dependent quantity is called rate of increment of dependent quantity per unit increment in independent quantity.

To find out the rate divide the amount of water leaving the tank by the time the water takes to leave the tank.

Jada notices 9 gallons of water leave the tank in five minutes.  ( The two gallons was obtained from 16-7 = 9)

The rate at which the tank is being emptied is  9 gallons/5 minutes = 1.8 gallons per minute;

For the tank to be empty, it has to lose all 7 gallons of water it has;

1 minute 1.8 gallons are lost

x minutes 7 gallons are lost

By cross multiplying;

x = 7/1.8 = 3.88 minutes

Therefore, the time taken at the rate will be 3.88 minutes

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Answer:

Step-by-step explanation:

V = 2/3 * pi * r3 gives the volume of a hemisphere of radius r.

V = 1/3 * pi * r2 * h gives the volume of a cone with radius r and height h.

We may compute the volume of both forms using the hemisphere's radius and the cone's base radius of 7 cm:

Hemisphere Volume = 2/3 * pi * (7 cm)3 = (14/3) * pi * 343 cm3 = 615.75 cm3

Cone Volume = 1/3 * pi * (7 cm)2 * 13 cm = 49 * pi * cm3 = 153.94 cm3

To get the overall volume of the solid, sum the volumes of the hemisphere and cone:

Volume total = 615.75 cm3 + 153.94 cm3 = 769.69 cm3

As a result, the total volume of the solid is 769.69 cm3.

As per given data of Lexi and Brittany runs , the number of seconds and yards taken by Lexi to catch up Brittany is 6 seconds  and 30 yards respectively.

As given in the question,

Let us consider,

Time taken by Brittany be 't₁ '

Time taken by Lexi be 't₂'

Brittany runs at the speed of 5 yards per seconds

Lexi runs at the speed of 7 yards per seconds

Distance covered by Brittany be 'x' yards

Distance covered by Lexi be 'x + 12 ' yards

t₁ = x / 5

t₂ = ( x + 12 ) / 7

When Lexi catch up Brittany

t₁ = t₂

⇒ x / 5 = ( x+ 12 ) / 7

⇒ 7x = 5x + 60

⇒ 2x = 60

⇒ x = 30 yards

Number of seconds taken by Lexi

= ( 30 + 12 ) / 7

= 6 seconds

Therefore, the number of seconds after which Lexi catch up Brittany is 6 seconds and Lexi will catch up Brittany at 30 yards of run.

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Answer:

h(-2) = -13

Step-by-step explanation:

h(x) = 5x-3                            h(-2)

h(-2) = 5(-2) - 3

h(-2) = -10 - 3

h(-2) = -13

Answer:

11

Step-by-step explanation:

34 - (2b + 5) + 2

34 - (2*10 + 5) + 2

34 - (20 + 5) + 2

34 - 25 + 2

9 + 2

11

Answer:

34 - (2b + 5) + 2 = 11

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ 34 - (2b + 5) + 2

We have to use,

→ b = 10

Let's simplify the expression,

→ 34 - (2b + 5) + 2

→ 34 - 2b - 5 + 2

→ (-2b) + (34 - 5 + 2)

→ -2b + 31

→ -2(10) + 31

→ -20 + 31

→ 11 => {final answer}

Therefore, the answer is 11.

Answer:

Step-by-step explanation:

b

Answer:

b

Step-by-step explanation:

should be the answer. hope it helps

Answer:

О   XY

Step-by-step explanation:

The chord is a segment that joins two points of a circumference and differs from the diameter because it passes through the central point of the circle.  

Brand B is the better buy because it offers the most ounces for the lowest price.

To compare the prices of the three brands, we need to convert them to a common unit of measurement. Brand A is priced at $4.89 for 54 ounces, Brand B is priced at $3.91 for 16 ounces, and Brand C is priced at $3.10 for 910 grams. Since 16 ounces is equivalent to 1 pound and 1 pound is equivalent to 453.59 grams, we can convert the weight of Brand B and C to ounces. 910 grams is equivalent to 2.01 pounds, which is equivalent to 32.16 ounces.

A.

54oz, convert to lb

54/16=3.375lb

find per lb

4.89/3.375=$1.4488888 per lb

B.

2 and 3/4=2.75, 3.91/2.75=$1.42181 per lb

C. 910/453.59=2.00621lb

3.10/2.00621=$1.545 per lb

compare

A: $1.4488888 per lb

B: $1.42181 per lb

C: $1.545 per lb

It is observed from the above calculation that Brand B have lowest price per unit on ounce.

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Answer:

[tex]\frac{x+4}{3(x-1)}[/tex]

[tex]x^2/x-1/3x^2/x+4[/tex]

This can be written as a/b * d/c using the KCF method, which stands for keep, change, flip when dividing fractions. You keep the first fraction, change the sign from divide to multiply, and flip the last fraction.

For example:

4/5 / 6/7 =

4/5 * 7/6

28/30

14/15

[tex]\frac{x^2}{x-1} * \frac{x+4}{3x^2}[/tex]

Next, multiply top and bottom to combine the fractions.

[tex]\frac{x^3+4x^2}{3x^3-3x^2}[/tex]

Factor [tex]x^2[/tex] out of [tex]x^3 + 4x^2[/tex].

[tex]\frac{x^2(x+4)}{3x^3-3x^2}[/tex]

Factor  [tex]3x^2[/tex]  out of [tex]3x^3-3x^2[/tex].

[tex]\frac{x^2(x+4)}{3x^2(x-1)}[/tex]

Cancel out [tex]x^2[/tex] from top and bottom.

[tex]\frac{x+4}{3(x-1)}[/tex]

Answer:

29

Step-by-step explanation:

this sequence is an arthimetic sequence in which every second number is 8 more than the previous number.so the next number is 21+8=29

Answer:

H = 2

Step-by-step explanation:

Convert the number.  H + 2 1/4 = 4 2/8

Reduce. H + 9/4 = 34/8

Rearrange the terms. H + 9/4 = 17/4

Calculate. H = 14/4 - 9/4

Multiply the total acceleration by the sine of the acceleration angle to determine the vertical acceleration. The formula for vertical acceleration is: [tex]A_y=A_t\times\sin(a)[/tex].

Any object on which gravity is the only force is referred to as a projectile. Gravity causes projectiles to move in a parabolic trajectory. Projectiles are not subject to any horizontal forces, and as a result, they are not accelerated horizontally.

A projectile's horizontal velocity is constant. Gravity causes a downward vertical acceleration with a magnitude of 9.8 m/s/s. A projectile's vertical velocity varies by 9.8 m/s each second. A projectile's vertical motion is unrelated to its horizontal motion.

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In a direct relationship, Y increases when X increases. On a graph, a direct relationship always has a positive slope. Inverse relationship: An inverse relationship means that the variables change in opposite directions: one increases while the other decreases, and vice versa.

Now, According to the question:

Direct relationship:

A direct relationship means that both variables increase together or both decrease together.

In a direct relationship, Y increases when X increases.

On a graph, a direct relationship always has a positive slope.

Inverse relationship:

An inverse relationship means that the variables change in opposite directions: one increases while the other decreases, and vice versa.

In an inverse relationship, Y decreases when X increases.

On a graph, an inverse relationship always has a negative slope.

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a) By multiplication a river on the map being 14 cm long has the actual length of 1190 km.

b) By division the actual distance between two towns being 765 km has the distance of 9 cm on the map.

What is multiplication?

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the numbers that are multiplied are referred to as the factors.

The value of 1 cm on map is a = 85 km.

The measurement of the river on the map b = 14 cm.

The actual length of the river = x.

Use the arithmetic operation of multiplication -

x = a × b

x = 85 × 14

x = 1190

Therefore, the measurement of river is 1190 km.

The actual distance between two towns is c = 765 km.

The distance on the map = y.

Use the arithmetic operation of division -

y = c/a

y = 765/85

y = 9

Therefore, the distance of two towns is 9 cm.

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The Production Possibility Frontier (PPF) is often called the "Opportunity Cost Curve" because it illustrates the concept of opportunity cost.

Opportunity cost is the cost of one alternative in terms of the benefits forgone of the best alternative. In other words, it's the cost of one choice in terms of the best alternative choice.

As we move along the PPF, we can see that as we produce more of one good, we must give up some production of the other good. This trade-off is represented by the slope of the PPF, which is the opportunity cost of producing one good in terms of the other good. The PPF illustrates the relationship between production and opportunity cost by showing the trade-offs that must be made and the opportunity costs associated with different production choices.

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A number line showing the solution of -8 - (-6) is :  A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.

A number line is a straight line drawn horizontally where the numbers are placed at an equal intervals.

Given expression is -8 - (-6).

That is the number -6 is subtracted from the number -8.

So we have to first draw an arrow to the number -8.

Then we have to draw an arrow of length -6 units from the number -8.

Then the arrow will stop at -2, which is the solution.

Hence the solution of the expression is -2.

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The rule of the transformation that has been applied to the ordered pairs of triangle QRS to triangle Q'R'S' is a rotation of 90° about the origin in a counterclockwise (anticlockwise) direction.

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of triangle QRS (∆QRS), the coordinates of the vertices of the image (∆Q′R′S′) are as follows:

(x, y)                               →            (-y, x)

Ordered pair Q = (-4, 2) → Ordered pair Q' = (-2, -4)

Ordered pair R  = (-3, 5) → Ordered pair R' = (-5, -3)

Ordered pair S = (0, 1) → Ordered pair S' = (-1, 0)

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The solutions to the quadratic equation are:

[tex]$x=\frac{1+\sqrt{19}}{6}, x=\frac{1-\sqrt{19}}{6}$[/tex]

[tex]$$6 x^2-2 x-3=0$$[/tex]

Solve with the quadratic formula

[tex]$$x_{1,2}=\frac{-(-2) \pm \sqrt{(-2)^2-4 \cdot 6(-3)}}{2 \cdot 6}$$[/tex]

[tex]$$\sqrt{(-2)^2-4 \cdot 6(-3)}=2 \sqrt{19}$$[/tex]

[tex]$$x_{1,2}=\frac{-(-2) \pm 2 \sqrt{19}}{2 \cdot 6}$$[/tex]

Separate the solutions

[tex]$$x_1=\frac{-(-2)+2 \sqrt{19}}{2 \cdot 6}, x_2=\frac{-(-2)-2 \sqrt{19}}{2 \cdot 6}$$[/tex]

[tex]$\begin{aligned} & x=\frac{-(-2)+2 \sqrt{19}}{2 \cdot 6}: \quad \frac{1+\sqrt{19}}{6} \\ & x=\frac{-(-2)-2 \sqrt{19}}{2 \cdot 6}: \quad \frac{1-\sqrt{19}}{6}\end{aligned}$[/tex]

The solutions to the quadratic equation are:

[tex]$x=\frac{1+\sqrt{19}}{6}, x=\frac{1-\sqrt{19}}{6}$[/tex]

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The solutions to the equation are approximately x = 0.015 and x = -0.142.

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Answer:

x = 2

Step-by-step explanation:

у = 12 - 4x

5x - Зу = -2

Solve the system algebraically.

Substitute the first equation into the second equation.

5x - 3( 12 - 4x) =-2

Distribute.

5x - 36 + 12x = -2

Combine like terms.

17x -36 = -2

Add 36 to each side

17x -36+26 = -2+36

17x = 24

Divide by 17

17x/17 = 34/17

x = 2

Answer:

x = 2

y = 4

Step-by-step explanation:

y = 12 - 4x  ⇒  ( 1 )

5x - 3y = -2  ⇒  ( 2 )

Let us find the value of x.

For that, take equation (2) and replace y with ( 12 - 4x ).

5x - 3y = -2

5x - 3 ( 12 - 4x ) = -2

5x - 36 + 12x = -2

Combine like terms.

17x - 36 = -2

Add 36 to both sides.

17x = -2 + 36

17x = 34

Divide both sides by 17.

x = 2

Let us find the value of y.

To find the value of y let us take equation ( 1 ) and replace x with 2.

y = 12 - 4 × 2

y = 12 - 8

y = 4

Answer:

it should be eight

Step-by-step explanation:

if i am correct

The measure of angle A will be 60°

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given a triangle that has three angles such as: 6x, 4x, and 2x.

From the general property of Triangles:

Sum of all angles = 180°

6x + 4x + 2x = 180°

12x = 180°

x = 15

Since ∠A = 4x

Thus,

∠A = 15 *4

∠A = 60

therefore, The measure of angle A will be 60°

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Answer: Two quanties are said to have a proportional relationship if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio. ... inversely proportional: y is inversely proportional to x of y=k/x.

As a result, 3.90 represents the top's angle to Jada.

Trigonometric identities are equations involving trigonometric functions that hold true for each possible value of the variables.

The area of mathematics known as trigonometry deals with particular angles' mathematical functions and how to use them. A common angle in trigonometry has six different functions. Sine, cosine, tangent, cotangent, secant, and cosecant are their names, respectively, as well as their acronyms (csc).

Trigonometric Identities are equality statements involving trigonometry functions that hold true for all values of the input variables in the equation. The side length and angle of a triangle are both subject to a variety of distinctive trigonometric identities.

The height of the Empire State building exists 1466.85 ft.

Let the given information be

She is 100 feet away when she spots it.

The top, she has to look up at an angle of 86.1 degrees.

[tex]$$\begin{aligned}& =(\sin (86.10) \times 100) \div(\sin (3.90)) \\& =1466.85 \mathrm{ft} .\end{aligned}$$[/tex]

Therefore, 3.90 represent the angle of the top to Jada.

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