Express the length of the kite string in terms of trigonometric ratios. A) 70cos40° B) 70sin40° C) 40 sin70° D) 70 sin40°

Answer:

Translate 6 units to the right.

Step-by-step explanation:

The y = x^2 function is a quadratic function with vertex at (0,0). It can be transformed to have a vertex of (6,0) like the function y = (x-6)^2 by shifting it 6 units to the right. It is now the graph of y = (x-6)^2.

The equation y = (x - 6)² represents a transformation of the graph y = x², specifically a horizontal shift 6 units to the right on the 2-dimensional (x-y) plane.

To transform the graph of y = x² to the graph of the equation y = (x – 6)², you must understand that these both take the form of a quadratic equation, producing a parabola when graphed. The difference between these two equations is indicated by the term '– 6' in the x of the second equation which corresponds to a horizontal shift in the graph.

In the equation y = (x – 6)², this specifically means that the graph of y = x² is shifted 6 units to the right. This shift doesn't change the shape of the graph, it only moves the location in the 2-dimensional (x-y) plane. So, when you plot data pairs for both y = x² and y = (x – 6)², the second graph would be identical to the first, just moved 6 units to the right.

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Answer:

Step-by-step explanation:

If the ratio is soda to juice, set up the proportion like this:

[tex]\frac{s}{j}[/tex]

and everything related to soda goes on top and everything related to fruit juice goes on the bottom.  You just want the ratio, so it is best stated as follows:

[tex]\frac{soda}{juice}[/tex]

just to be clear on what s and j mean!

You could use this proportion to solve problems with one unknown.

Answer:

It's C.

Step-by-step explanation:

The red curve  pass through the point (0, 1) and also y = 2 when x = 1 ,  so this is y = 2^x. The inverse is the reflection of  f(x) in x = y so the blue curve is y = log2 x.

The two equation shown in the graph are y = e^x and y = lnx.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable).

The red line shown in the graph represents y = e^x

The graph of y = e^x will never have a negative value of y, as the value of x increases the value of y will keep on increasing till ∞ . The value of y at x = 0 is 1, so the graph will cross the y-axis at (0,1).

The blue line shown in the graph represents y = lnx

The value of y will be negative when the value of x lies between 0 and 1 after that the value of y will keep on increasing and the point (1,0) satisfies the equation so it will cross the X - axis at (1,0)

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Answer: its not possible

Step-by-step explanation: there are 17 nickels, 11 dimes and 19 pennies, NO dollars

Answer: your mum gay

Step-by-step explanation:

Answer:

The third choice is correct

Step-by-step explanation:

The given expression is

[tex]2^n-1[/tex]

when n=7, we substitute into the formula to obtain;

[tex]2^7-1[/tex]

Note that;

[tex]2^7=2\times 2\times 2\times 2\times 2\times 2\times 2=128[/tex]

[tex]2^7-1=128-1=127[/tex]

The third choice is correct

Answer:

  B.  14.34

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between the side opposite the angle of interest and the hypotenuse:

  Sin = Opposite/Hypotenuse

For the given triangle, this means ...

  sin(35°) = b/25

  b = 25·sin(35°)

  b ≈ 14.34

Answer:

A(2,15)

Step-by-step explanation:

Plug it in on the desmos calculator!!! Put the equation first and then add the points and see which one touches the line.

The ordered pair which is on the graph of the given function is (2, 15).

Given: Function

y = 8x - 1

Now, among the given ordered pair (x, y), the pair that satisfies the given function is the point on the graph.

Option (A): (2, 15)

⇒ y = 8x - 1

⇒ 15 = 8(2) - 1

⇒ 15 = 16 - 1

⇒ 15 = 15

Hence, this ordered pair is on the graph of the given function.

This option is correct.

Option (B): (8, -1)

⇒ y = 8x - 1

⇒ -1 = 8(8) - 1

⇒ -1 = 64 - 1

⇒ -1 ≠ 63

Hence, this ordered pair is not on the graph of the given function.

This option is incorrect.

Option (C): (8, 1)

⇒ y = 8x - 1

⇒ 1 = 8(8) - 1

⇒ 1 = 64 - 1

⇒ 1 ≠ 63

Hence, this ordered pair is not on the graph of the given function.

This option is incorrect.

Option (D): (15, 2)

⇒ y = 8x - 1

⇒ 2 = 8(15) - 1

⇒ 2 = 120 - 1

⇒ 2 ≠ 119

Hence, this ordered pair is not on the graph of the given function.

This option is incorrect.

Therefore, (2, 15) is the only ordered pair on the graph of the given function.

Hence, Option (A) is correct.

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Answer:

7 miles west of the city hall

Step-by-step explanation:

The city hall on a coordinate plane is at the origin (0, 0).  That means that if the library is 3 miles straight east, its coordinates are (3, 0).  If the mall is 10 miles straight west of the library, we find its coordinates by subtracting 10 from 3, which puts us at the coordinate (-7, 0).  That means that the mall is 7 miles west of the city hall.

Answer:

[tex]\boxed{\text{seven miles west}}[/tex]

Step-by-step explanation:

Think of this as a number line in which city hall is at 0.

East of city hall is the positive direction and west is negative.

Start at city hall and go three miles east to the library. You are at +3.

Then go 10 mi west to the mall. You end up at -7.

+3 – 10 = -7

[tex]\text{The mall is \boxed{\textbf{seven miles west}} of city hall.}[/tex]

Answer:

23 students expected to have scores greater than 60.

Step-by-step explanation:

60 is 2 standard deviations above the mean.  This translates into a z-score of +2.  According to a table of z-scores, the area under the standard normal curve to the left of z = 2 is 0.9772; that to the right of z = 2 is 1.0000 - 0.9772, or 0.0228.  This 0.0228 represents the probability that a given score is greater than 60.

This fraction (0.0228) of 1000 students comes out to 23 (rounded up from 22.75).

Final answer:

To find the expected number of students who had scores greater than 60 on a standardized test, we can calculate the probability using the properties of the normal distribution. The expected number is approximately 23 students.

Explanation:

To find the expected number of students who had scores greater than 60, we can use the properties of the normal distribution. We know that the mean score is 50 and the standard deviation is 5. We want to find the probability of getting a score greater than 60. First, we need to calculate the z-score for a score of 60 using the formula:

z = (x - μ) / σ

where x is the score, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:

z = (60 - 50) / 5 = 2

Next, we use a z-table or calculator to find the area to the right of z = 2. This represents the probability of getting a score greater than 60. A z-table or calculator will give us a value of approximately 0.0228.

Finally, we multiply this probability by the total number of students (1000) to find the expected number of students who had scores greater than 60:

Expected number = probability * total number of students = 0.0228 * 1000 = 22.8

Therefore, we can expect approximately 23 students to have scores greater than 60.

Answer:

Trapezoid area = ((sum of the bases) ÷ 2) • height

Trapezoid area = (.2 + .6 / 2) * .2

Trapezoid area = (.8 / 2) * .2

Trapezoid area = .4 * .2 = .08

Step-by-step explanation:

Answer:

[tex]\large\boxed{x=4}[/tex]

Step-by-step explanation:

[tex]3\log_4x=\log_432+\log_42\qquad\text{use}\ \log_ab^c=c\log_ab\ \text{and}\ \log_ab+\log_ac=\log_a(bc)\\\\\log_4x^3=\log_4(32\cdot2)\\\\\log_4x^3=\log_464\iff x^3=64\to x=\sqrt[3]{64}\\\\x=4[/tex]

Answer: 4

Step-by-step explanation: Its on EDG

The circumference of the circle is 18.84 cm and the area is 28.26 cm².

To find the circumference of a circle, we use the formula C = πd, where d is the diameter. In this case, the diameter is 6 cm, so the circumference is:

C = 3.14 × 6 = 18.84 cm

To find the area of a circle, we use the formula A = πr², where r is the radius. Since the radius is half the diameter, the radius in this case is 6/2 = 3 cm. So the area is:

A = 3.14 × 3² = 28.26 cm²

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Answer:

I have no idea what you're asking for but I got y= -3/4x+3 as the equation for the line.

ANSWER

[tex]y = \frac{3}{4}x + 15[/tex]

EXPLANATION

The given line passes through the point

(-8,9) and has a slope be of

[tex]m = \frac{3}{4} [/tex]

We obtain the equation of this line using

[tex]y-y_1=m(x-x_1)[/tex]

We plug in the values into the formula to get,

[tex]y - 9 = \frac{3}{4} (x - - 8)[/tex]

[tex]y = \frac{3}{4} (x + 8) + 9[/tex]

Expand the parenthesis to get:

[tex]y = \frac{3}{4}x + 6 + 9[/tex]

[tex]y = \frac{3}{4}x + 15[/tex]

Answer:

Y=-3x+4

Step-by-step explanation:

The Slope is -3 and the Y intercept is +4

Answer:

-3

Step-by-step explanation:

We can find the slope of a line by finding 2 points

(0,4) and (2,-2) are two points on the line

m = (y2-y1)/(x2-x1)

   = (-2-4)/(2-0)

   = -6/2

   =-3

Answer:

C $2392

Step-by-step explanation:

Answer:

56.1 cm²

Step-by-step explanation:

In any circle the area (A) of a sector is

A = area of circle × fraction of circle

   = πr² × [tex]\frac{81}{360}[/tex]

   = π × 8.91² × [tex]\frac{81}{360}[/tex]

   = [tex]\frac{8.91^2(81)\pi }{360}[/tex] ≈ 56.1 cm²

interior is the angle

Answer:

1 = 139 degrees

Step-by-step explanation:

You can use the corresponding angles theorem

[tex] {2}x^{2} + 8 {y}^{2} = 16 \\ \\ 1. \: {2x}^{2} = - 8 {y}^{2} + 16 \\ 2. \: {x}^{2} = - 4y^{2} + 8 \\ 3. \: x = \sqrt{ - 4y^{2} + 8} \\ x = - \sqrt{ - 4y^{2} + 8 } \\ \\ answer \\ x = \sqrt{ - 4y^{2} + 8 } \\ x = - \sqrt{ - 4y^{2} + 8} [/tex]

Answer:

Step-by-step explanation:

2x² + 8y² = 16

divide both sides of equation by the constant

2x²/16 + 8y²/16 = 16/16

x²/8 + y²/2 = 1

x² has a larger denominator than y², so the ellipse is horizontal.

General equation for a horizontal ellipse:

  (x-h)²/a² + (y-k)²/b² = 1

with

  a² ≥ b²

  center (h,k)

  vertices (h±a, k)

  co-vertices (h, k±b)

  foci (h±c, k), c² = a²-b²

Plug in your equation, x²/8 + y²/2 = 1.

(x-0)²/(2√2)² + (y-0)²/(√2)² = 1

h = k = 0

a = 2√2

b = √2

c² = a²-b² = 6

c = √6

center (0,0)

vertices (0±2√2,0) = (-2√2, 0) and (2√2, 0)

co-vertices (0, 0±√2) = (0, -√2) and (0, √2)

foci (0±√6, 0) = (-√6, 0) and (√6, 0)

Answer:

First part

The answer is (5 square root 2, 45°), (-5 square root 2, 225°) ⇒ answer (d)

Second part

The equation in standard form for the hyperbola is y²/81 - x²/19 = 1 ⇒ answer(b)

Step-by-step explanation:

First part:

* Lets study the Polar form and the Cartesian form

- The important difference between Cartesian coordinates and

  polar coordinates:

# In Cartesian coordinates there is exactly one set of coordinates

  for any given point.

# In polar coordinates there is an infinite number of coordinates

   for a given point. For instance, the following four points are all

   coordinates for the same point.

# In the polar the coordinates the origin is called the pole, and

  the x axis is called the polar axis.

# The angle measurement θ can be expressed in radians

   or degrees.

- To convert from Cartesian Coordinates (x , y) to

  Polar Coordinates (r , θ)

# r = ± √(x² + y²)

# θ = tan^-1 (y / x)

* Lets solve the problem

- The point in the Cartesian coordinates is (5 , 5)

∵ x = 5 and y = 5

∴ r = ± √(5² + 5²) = ± √50 = ± 5√2

∴ tanФ = (5/5) = 1

∵ tanФ is positive

∴ Angle Ф could be in the first or third quadrant

∵ Ф = tan^-1 (1) = 45°

∴ Ф in the first quadrant is 45°

∴ Ф in the third quadrant is 180 + 45 = 225°

* The answer is (5√2 , 45°) , (-5√2 , 225°)

Second part:

* Lets study the standard form of the hyperbola equation

- The standard form of the equation of a hyperbola with  

  center (0 , 0) and transverse axis parallel to the y-axis is

  y²/a² - x²/b² = 1, where

• the length of the transverse axis is 2a

• the coordinates of the vertices are (0 , ±a)

• the length of the conjugate axis is 2b

• the coordinates of the co-vertices are (±b , 0)

•      the coordinates of the foci are (0 , ± c),  

• the distance between the foci is 2c, where c² = a² + b²

* Lets solve our problem

∵ The vertices are (0 , 9) and (0 , -9)

∴ a = ± 9 ⇒ a² = 81

∵ The foci at (0 , 10) , (0 , -10)

∴ c = ± 10

∵ c² = a² + b²

∴ (10)² = (9)² + b² ⇒ 100 = 81 + b² ⇒ subtract 81 from both sides

∴ b² = 19

∵ The equation is  y²/a² - x²/b² = 1

∴  y²/81 - x²/19 = 1

* The equation in standard form for the hyperbola is y²/81 - x²/19 = 1

Answer:

i think its 20

Step-by-step explanation:

Answer:

x = 12.8 cm

Step-by-step explanation:

Using the sine ratio in the right triangle to solve for x

sin70° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{12}{x}[/tex]

Multiply both sides by x

x × sin70° = 12 ( divide both sides by sin70° )

x = [tex]\frac{12}{sin70}[/tex] ≈ 12.8

ANSWER

D. 6

EXPLANATION

We want to find the y-coordinate of the point of intersection of

-3x+2y=6

and

4x-y=2

Solve for y in equation (2) to get:

y=4x-2

Put y=4x-2 into the first equation:

-3x+2(4x-2)=6

-3x+8x-4=6

-3x+8x-4=6

[tex]5x=10[/tex]

Divide both sides by 5 to get

x=2

This implies that:

y=4(2)-2

y=8-2=6

Answer:

360 km

Step-by-step explanation:

The length on the ground will be ...

(24·10^-2 m)·(1.5·10^6) = 36·10^4 m = 360·10^3 m = 360 km

Answer:

The length of river is 360km

Explanation:

Length on the map of Severn river = 24cm

Scale on the map = x:y axis

                               =1:1500000

Where y is the length  

Hence 1 cm= 15 km

Therefore

Length of the river

=24[tex]\times[/tex]15

=360 km

Hence the length of river is 360 km

2 bill of 20 and 3 of 1

Answer:

Debit card

Step-by-step explanation:

Answer:

  see attached

Step-by-step explanation:

nCk models k objects taken from a group of n.

  nCk = n!/(k!·(n-k)!)

Fill in n=8 and k=3 to get ...

  8C3 = 8!/(3!·5!)

the answer of this question is 8 bro..........................................................

Answer it depends

Step-by-step explanation: how much are there a pice or how much are all 9 . 72-9= 63

But the cost of 1 bracelet is $7

Answer:

c. 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean

Step-by-step explanation:

In a normal distribution, the shape is bell-shaped; this means it is symmetric.

The area under a normal distribution will always be equal to 1.

The mean, median and mode in a normal distribution are equal.

However, the data assumes values within 1 standard deviation above or below the mean 68% of the time, not 99.72% of the time.  This is the characteristic that doesn't fit.

The statement which is not a characteristic of the normal distribution is:

c. 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean.

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Answer:

d. 4,-5,-2

Step-by-step explanation:

The values of {a}, {b} and {c} in the quadratic equation are a = 4, b = 5, c = 2 respectively.

A quadratic equation is a equation that is of the form -

y = f{x} = ax² + bx + c.

Given is the quadratic equation as follows -

5x + 4x² + 2 = 0

The given quadratic equation is -

5x + 4x² + 2 = 0

4x² + 5x + 2 = 0

A quadratic equation is of the form -

ax² + bx + c

So, on comparing, we get -

a = 4, b = 5, c = 2

Therefore, the values of {a}, {b} and {c} in the quadratic equation are a = 4, b = 5, c = 2 respectively.

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1/42

First, find the probability of Willie winning the grand prize. He has 1 ticket out of the 7 total tickets, so the probability is 1/7.

Now, find the probability of Emily winning the second prize. After the grand prize winner has been announced, there are only 6 tickets left. Emily has 1, so the probability is 1/6.

Finally, multiply the two probabilities together to find the probability that they will both happen together. To multiply fractions, multiply the numerators together and multiply the denominators together. This leaves us with (1 * 1) / (7 * 6), which is easy to simplify to 1/42, which is the final probability.

Answer:

1/42

Step-by-step explanation: