What is the tangent ratio for ∠A?

Answer:

x = 8.3

Step-by-step explanation:

Given a tangent and 2 secants drawn to the circle from an external point then

The square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant.

Using the secant with measure 4 + x, then

4(4 +x) = 7²

16 + 4x = 49 ( subtract 16 from both sides )

4x = 33 ( divide both sides by 4 )

x = 33 ÷ 4 = 8.25 ≈ 8.3 ( nearest tenth )

Answer:

Step-by-step explanation:

The product of two even numbers will have at least two factors of 2, so will be even: even numbers are closed under multiplication.

The product of two odd numbers will be an even number plus 1, so will be odd: odd numbers are closed under multiplication.

The product of two cubes will be the cube of the product of their cube roots: cubes are closed under multiplication.

__

The product of two negative numbers will be positive, so the set of negative numbers is not closed under multiplication.

Answer:

Part 4) [tex]sin(\theta)=\frac{12}{13}[/tex]

Part 10) The angle of elevation is [tex]40.36\°[/tex]

Part 11) The angle of depression is [tex]78.61\°[/tex]

Part 12) [tex]arcsin(0.5)=30\°[/tex]  or [tex]arcsin(0.5)=150\°[/tex]

Part 13) [tex]-45\°[/tex]  or [tex]225\°[/tex]

Step-by-step explanation:

Part 4) we have that

[tex]cos(\theta)=-\frac{5}{13}[/tex]

The angle theta lies in Quadrant II

so

The sine of angle theta is positive

Remember that

[tex]sin^{2}(\theta)+ cos^{2}(\theta)=1[/tex]

substitute the given value

[tex]sin^{2}(\theta)+(-\frac{5}{13})^{2}=1[/tex]

[tex]sin^{2}(\theta)+(\frac{25}{169})=1[/tex]

[tex]sin^{2}(\theta)=1-(\frac{25}{169})[/tex]  

[tex]sin^{2}(\theta)=(\frac{144}{169})[/tex]

[tex]sin(\theta)=\frac{12}{13}[/tex]

Part 10)

Let

[tex]\theta[/tex] ----> angle of elevation

we know that

[tex]tan(\theta)=\frac{85}{100}[/tex] ----> opposite side angle theta divided by adjacent side angle theta

[tex]\theta=arctan(\frac{85}{100})=40.36\°[/tex]

Part 11)

Let

[tex]\theta[/tex] ----> angle of depression

we know that

[tex]sin(\theta)=\frac{5,389-2,405}{3,044}[/tex] ----> opposite side angle theta divided by hypotenuse

[tex]sin(\theta)=\frac{2,984}{3,044}[/tex]

[tex]\theta=arcsin(\frac{2,984}{3,044})=78.61\°[/tex]

Part 12) What is the exact value of arcsin(0.5)?

Remember that

[tex]sin(30\°)=0.5[/tex]

therefore

[tex]arcsin(0.5)[/tex] -----> has two solutions

[tex]arcsin(0.5)=30\°[/tex] ----> I Quadrant

or

[tex]arcsin(0.5)=180\°-30\°=150\°[/tex] ----> II Quadrant

Part 13) What is the exact value of [tex]arcsin(-\frac{\sqrt{2}}{2})[/tex]

The sine is negative

so

The angle lies in Quadrant III or Quadrant IV

Remember that

[tex]sin(45\°)=\frac{\sqrt{2}}{2}[/tex]

therefore

[tex]arcsin(-\frac{\sqrt{2}}{2})[/tex] ----> has two solutions

[tex]arcsin(-\frac{\sqrt{2}}{2})=-45\°[/tex] ----> IV Quadrant

or

[tex]arcsin(-\frac{\sqrt{2}}{2})=180\°+45\°=225\°[/tex] ----> III Quadrant

Answer:

D. 46

Step-by-step explanation:

Put 12 where n is, then do the arithmetic.

t12 = 4·12 -2 = 48-2 = 46

Answer:

  down

Step-by-step explanation:

Subtracting 1 from the y-coordinate moves a point down 1 unit. You know this because you know that the y-coordinate tells you the number of units the point is above the x-axis.

Every point on the graph of f(x) has coordinates (x, f(x)). If you subtract 1 from the y-coordinate, you have (x, f(x) -1) = (x, g(x)). The graph of this is a graph of f(x) that is 1 unit down from its original position.

In the equation g(x)=f(x)-1, g(x) translates the original function, f(x), one unit downward. This is an instance of vertical translation in mathematics.

In the equation g(x)=f(x)-1, the function g(x) is a translation of the function f(x). This process is specifically called a vertical translation. The -1 in the function g(x) = f(x) - 1 implies that the translation is downward. Therefore, g(x) translates the function f(x) 1 unit downward.

To further illustrate, let's consider the function f(x) = x^2 and its translation g(x) = x^2 - 1. If we graph both of these functions, you can observe that the graph of g(x) is exactly the same as the graph of f(x), but it is shifted one unit downward. This is the meaning of vertical translation in mathematics.

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Answer:

[tex]\boxed{5x^{11}, x < 0}[/tex]

Step-by-step explanation:

[tex]5\sqrt{x^{22}}[/tex]

Remember that we evaluate the term under the radical first.

Even though x < 0, x²² > 0

So,

[tex] 5\sqrt{x^{22}} = 5x^{11}[/tex]

The simplified expression is

[tex]\boxed{5x^{11}, x < 0}[/tex]

Answer:

  y = –4x + 5

Step-by-step explanation:

We can put the offered choices into standard form and compare.

y = –4x + 5 ⇒ 4x +y = 5 . . . . . intersecting line; one solution

y = 4x – 5 ⇒ 4x -y = 5 . . . . . .  same line, infinite solutions

2y = 8x – 10 ⇒ 4x -y = 5 . . . .  same line, infinite solutions

–2y = –8x – 10 ⇒ 4x -y = -5 . . . . parallel line, no solutions

Answer:

IS A: y = –4x + 5

Hope this helps!

Answer:

B. 60

Step-by-step explanation:

The opposite sides of a parallelogram are parallel and congruent.

This implies that:

|UV|=|XW|

From the diagram; |UV|=15

and [tex]|XW|=\frac{1}{4}y[/tex]

We equate the two side lengths to get:

[tex]15=\frac{1}{4}y[/tex]

We multiply both sides by 4 to obtain:

[tex]4\times 15=4\times \frac{1}{4}y[/tex]

This implies that:

y=60

Answer:

B!

Step-by-step explanation:

Answer:

In the figures attached, the complete question is shown.

What is the difference between a minor arc and a major arc?

the measure of a minor arc is less than 180°

the measure of a major arc is greater than 180°

How many letters do we use to name a MINOR arc? 2

How many letters do we use to name a MAJOR arc? 3

How many degrees are in a semi-circle? 180°

How many letters to name a SEMI CIRCLE? 3

1. Name of arc: AB Type of arc: minor

2. Name of arc: ADB Type of arc: major

3. Name of arc: PSQ  Type of arc: semi-circle

4. AE: minor

5. AEB: semi-circle

6. FDE: semi-circle

7. DFB: major

8. FA: minor

9. BE: minor

10. BDA: semi-circle

11. FBD: major

12. PQ and ST

13. QPT and  PUS

14. PUT and QPU

15. There are 360° degrees in a circle.

16. There are 180° degrees in a semi-circle.

17. The measure of the arc is equal to the measure of the central angle.

18. mPQ: 50°, mPXQ: 310°

19. mPQ: 90° , mPRQ: 270°

20. mPQ: 150° , mPXQ: 210°

21. mQS: 45°, mQRS: 315°

22. mGH: 30°, mGFH: 330°

23. mAB: 75°, mADB: 285°

Answer:

Option C. 44 degree

Step-by-step explanation:

Let

A-----> the angle of the elevation of the sun

we know that

The tangent of angle A is equal to divide the opposite side angle A by the adjacent side angle A

In this problem

The opposite side is 30 meters

The adjacent side is 31 meters

[tex]tan(A)=\frac{30}{31}[/tex]

[tex]A=arctan(\frac{30}{31})=44\°[/tex]

Answer:

Final answer is approx 6.644 years.

Step-by-step explanation:

Given that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The growth in the sale of motorcycles is 16% every year and that of cars is 25% every year.

So we can use growth formula:

[tex]A=P\left(1+r\right)^t[/tex]

Then we get equation for motorcycles and cars as:

[tex]A=5.75\left(1+0.16\right)^t[/tex]

[tex]A=3.5\left(1+0.25\right)^t[/tex]

Now we need to find about when the sale of cars will be more than the sale of motorcycles. So we get:

[tex]3.5\left(1+0.25\right)^t>5.75\left(1+0.16\right)^t[/tex]

[tex]3.5\left(1.25\right)^t>5.75\left(1.16\right)^t[/tex]

[tex]3.5\left(1.25\right)^t>5.75\left(1.16\right)^t[/tex]

[tex]\frac{\left(1.25\right)^t}{\left(1.16\right)^t}>\frac{5.75}{3.5}[/tex]

[tex]\left(\frac{1.25}{1.16}\right)^t>1.64285714286[/tex]

[tex]t\cdot\ln\left(\frac{1.25}{1.16}\right)>\ln\left(1.64285714286\right)[/tex]

[tex]t>\frac{\ln\left(1.64285714286\right)}{\ln\left(\frac{1.25}{1.16}\right)}[/tex]

[tex]t>6.6436473051[/tex]

Hence final answer is approx 6.644 years.

Final answer:

To determine when car sales will surpass motorcycle sales given their growth rates, we use exponential growth formulas for both, set them equal to find the crossover point, and solve for the time required.

Explanation:

To find when the sale of cars will be more than the sale of motorcycles given their respective annual growth rates, we'll use the concept of exponential growth.

The initial sale of motorcycles is 5.75 million with an annual growth rate of 16%, and the initial sale of cars is 3.5 million with an annual growth rate of 25%. We will set up an equation where the sales of cars equals the sales of motorcycles and solve for the number of years it takes for this to occur.

The formula for exponential growth is:

Final Amount = Initial Amount × (1 + Growth Rate) ^ Years

For motorcycles, the formula becomes:

M = 5.75 × (1 + 0.16)^t

For cars, the formula becomes:

C = 3.5 × (1 + 0.25)^t

We want to find when C > M, so we set the formulas equal to each other and solve for t:

5.75 × (1 + 0.16)^t = 3.5 × (1 + 0.25)^t

After finding a common base and applying logarithms, we can solve for t, the number of years until the sale of cars surpasses that of motorcycles.

Answer:

  x = √5

Step-by-step explanation:

The Pythagorean theorem tells you the square of the diagonal is the sum of the squares of the two sides:

  (√7)² = (√2)² + x²

  7 = 2 + x² . . . . . . simplify

  5 = x² . . . . . . . . . subtract 2

  √5 = x . . . . . . . . . take the square root

Answer:

5 meters

Step-by-step explanation:

If the perimeter of the rectangle on the right is 24 m, and the length is 8, the width has to be 4, since 8+4+8+4=24. Since the scale factor is 24÷30=0.8 or 4/5, and the width of the rectangle on the right is 4, 4÷0.8=5, which is the width of the rectangle on the left.

Hope this helps! (P.S. I got it right on Edgenutiy, spelled wrong on purpose).

The width of the original rectangle is 5m.

The perimeter of a shape can be described as the path or boundary that surrounds it .

Perimeter of Rectangle = 2 (L + B)

L = length of rectangle

B = breadth of rectangle

Perimeter of the reduced rectangle = 24m

Let the length of original rectangle be L1

Let the breadth of original rectangle be B1

Let L1 = 8m, B1 = 4m

P = 2( L1 + B1) = 2(8 + 4) = 24m

Scale factor = P(Original Rectangle) / P(reduced rectangle)

Scale factor = 30 / 24 = 1.25

So, width of original rectangle = Scale factor * reduced width

Width of original rectangle = 1.25 * 4 = 5m

Hence, the width of the original rectangle is 5m.

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Answer:

There are 13 boys in Mr. Marshals class

Step-by-step explanation:

Hello there! Mr. Marshal has 9 boys.

To find the number of boys Mr. Marshal has, start by finding the ratio. If there are 6 boys and 14 girls, the boys to girls ratio is 6:14. Simplified, the ratio is 3:7. So, if there are 21 girls, you want to find how many boys there are. To find this, find what you need to multiply 7 by to get 21 by and multiply 3 by that number.

21/7 = 3.

So, now we multiply 3 by 3 to get the number of boys.

3 x 3 = 9.

This means there are 9 boys, with a ratio of 9:21. If we simplify this, we get 3:7, making this answer correct.

I hope this helps and have a great day!

Answer:

Here's what I get.

Step-by-step explanation:

Question 10

The general equation for a sine function is

y = a sin[b(x - h)] + k

Here's what the parameters control:

a = amplitude

k = vertical shift

b = the period (period = 2π/b; If period = 2π/3, b = 3)

h = horizontal shift

Reflect across y-axis (x ⟶ -x)

Your sine function will be:

[tex]\begin{array}{rllll}y = & a \text{ sin}[ & b(x- & h)] + & k)\\& \downarrow & \downarrow & \downarrow & \downarrow\\& 4 & 3 & \frac{\pi}{4} & 3\\\end{array}[/tex]

Here are the effects of each parameter.

(a) Amp = 4

Increases the amplitude by a factor of 4 (Fig. 1)

(b) Up 3

k = 3. The graph shifts up three units (Fig. 2).

(c) Period = 2π/3

Set k = 3. The period changes from 2π to 2π/3 (Fig. 3).

Notice that you now hav3 three waves between 0 and 2π, where originally you had one.

(d) Right π/4.

Set h = 4. The graph shifts right by π/4.

notice how the trough at ½π shifts to ¾π.

(e) Reflect about y-axis

Set x equal to -x. Notice how the trough at (¾π, -1) is transformed to the trough at (-¾π, -1) (Fig. 5).

Question 12

y = a cos[b(x - h)] + k

a = 2

Per = 10π/3 ⟶ b = 3/5

h = 0

k = 0

Reflect over x-axis: y ⟶ -y

(a) a = 2

The amplitude is doubled.

(b) Per = 10π/3 ⟶ b = 3/5

The period (peak-to-peak distance) lengthens to 10π/3.

(c) Reflect about x-axis (y ⟶ -y)

All peaks are transformed into troughs and vice-versa.

Answer:

The relationship is linear; y – 5 = 5/4*(x – 1)

Step-by-step explanation:

We have been given the following data set;

x: 1, 5, 9, 13

y: 5, 10, 15, 20

The values of x increase by 4 while those of y increase by 5. This would imply that the average rate of change between any pair of points is a constant and thus the relationship exhibited by the data is linear.

The average rate of change is equivalent to the slope;

(change in y) / (change in x)

Using the first two pair of points we have;

(10-5) / ( 5-1) = 5/4

The point-slope form of equation of the line is thus;

y - 5 = 5/4 (x - 1)

Answer:

3x^2+2x-1

Step-by-step explanation:

Start by plugging in the 2 equations into their assigned places then simplify.

Answer:14

Step-by-step explanation:( 3X2+1)-(1-X)

=3X2+1 -1+X

=3X2+X

ANY WHERE WE SEE X WE PLACE 2

=3(2)(2)+2

3*4+2

=12+2

14

Use trigonometry to find the ramp distance.

sin(4.76°) = 2/r

Let r = ramp distance in feet

r = 2/sin(4.76°)

r = 24.1015718106

Round off to the nearest foot.

Doing so we get r = 24 feet.

The ramp is 24.0 feet long.

Answer: Choice C

Answer:

y = 4

That's a straight line.

The slope is 0.

There is no x-intercept.

The y-intercept is 4.

I'm only a few Brainliests away from ranking up, so one would be much appreciated. Thank you, and good luck!

Answer:

the slope is 0

the x intercept is 0

the y intercept is 4

Answer:

Part 1) The ratio of the perimeters of the larger figure to the smaller figure is equal to [tex]\frac{16}{13}[/tex]

Part 2) The ratio of the areas of the larger figure to the smaller figure is [tex]\frac{256}{169}[/tex]

Step-by-step explanation:

Part 1) What is the ratio of the perimeters of the larger figure to the smaller figure?

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor

Let

z-----> the scale factor

In this problem

The scale factor is equal to

[tex]z=\frac{32}{26}[/tex]

Simplify

[tex]z=\frac{16}{13}[/tex]

Remember

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

so

The ratio of the perimeters of the larger figure to the smaller figure is equal to [tex]\frac{16}{13}[/tex]

Part 2) What is the ratio of the areas of the larger figure to the smaller figure?

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

we have

[tex]z=\frac{16}{13}[/tex]

so

[tex]z^{2}=(\frac{16}{13})^{2}=\frac{256}{169}[/tex]

therefore

The ratio of the areas of the larger figure to the smaller figure is [tex]\frac{256}{169}[/tex]

[tex]C=2\pi r =2\pi10=20\pi\approx\boxed{62.8}[/tex]

The answer is D.

The circumference of a circle with a radius of 10 inches is approximately 62.8 inches, calculated using the formula C = 2πr, resulting in the answer choice D. 62.8.

To calculate the circumference of a circle when the radius is given, we use the formula C = 2πr. Given that the radius (r) of the circle is 10 inches, we can calculate the diameter (d) as 2×10 inches, which equals 20 inches. Now, we multiply the diameter by π (approximately 3.1416) to find the circumference:

C = πd = 3.1416 × 20 inches = 62.832 inches.

Based on standard rounding rules, this is approximately 62.8 inches. Thus, the correct answer is D. 62.8 square inches.

Answer: The volume is about 226 feet squared

Step-by-step explanation:

Jackie's total spending on 2 packages of paper and 4 notebooks is represented by the equation 2(5.80) + 4d = 32, where d stands for the cost per notebook.

The student is looking to create an equation to represent the cost of Jackie's purchases of paper packages and notebooks. The given information is that Jackie bought 2 packages of papers for $5.80 each and 4 notebooks for d dollars each, and in total, she spent $32. To formulate the equation, we can use the following expression:

We know the cost of the paper packages is 2 multiplied by $5.80, and the cost of the notebooks is 4 multiplied by d dollars.

So the equation using D that represents the situation is:

Where d represents the cost of each notebook, and solving for d would give us the price per notebook.

Answer:

x = 74°

Step-by-step explanation:

The angle whose vertex lies on the circle, that is angle x is one- half the measure of it's intercepted arc, that is

x = 0.5 × 148° = 74°

Answer:

Step-by-step explanation:

first fit:

115 -> 300

500-> 600

358 -> 750

200 -> 350

375 -> not able to allocate  

Best fit:

115 -> 125

500 -> 600

358 -> 750

200 -> 200

375 -> not able to allocate

worst fit:

115 -> 750

500 -> 600

358 -> not able to allocate

200 -> 350

375 -> not able to allocate

Answer:

-11, 11

Step-by-step explanation:

You have to find when the function crosses the x-axis. You could find this using algebra by solving for x in the equation but I prefer to simply graph it using something like desmos and see when it crosses the x-axis. Doing that I can see the answers would be -11 and 11

Answer:

x = -11,11

Step-by-step explanation:

G(x)=4x^2-484

To find the zero's, set the function equal to zero

0 = 4x^2 - 484

Add 484 to each side

484 = 4x^2 -484+484

484 = 4x^2

Divide each side by 4

484/4 = 4x^2/4

121 = x^2

Take the square root of each side

sqrt(121) = sqrt(x^2)

±11 =x

x = -11,11

Answer:

b.  .897x - 3.790 (that's in slope-intercept form; same thing as putting the y-intercept first)

Step-by-step explanation:

On your calculator, hit the "stat" button.  Hit #4 to "ClrList", then hit 2nd and the number 1 to clear the list in L1.  Then do the same to clear the list in L2.  Hit #4, then hit 2nd and the number 2 to clear the list in L2.

Hit "stat" then 1 (edit) and you'll be at your table to enter the values.  Use the left arrow key if needed to make sure you're entering your first values under column L1, which is our x values.  Enter one at a time, hitting "enter" after each, even the last one.  Then arrow over to the right and enter the y values one at a time under L2.  Hit enter after each, even the last one.  When you're done, hit "stat" again and arrow over to "calc".  If you have a TI 83, choose "4:LinReg" and hit "enter".  If you have a TI 84+, you will have to arrow down to choose "calculate".  When the word "calculate" is highlighted, hit enter and you'll have your equation!

  Equation of the regression line for the data given will be represented by the equation given in option B.  

    By using the utility for the regression line of the given data, equation of the regression line will be,

y = 0.89745x - 3.79005

y = 0.897x - 3.79

Or y = -3.79 + 0.897x

   Therefore, equation of the regression line given in option B will be the answer.

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Answer:

  1,417.64 km³

Step-by-step explanation:

The formula for the volume of a cylinder in terms of its diameter is ...

  V = (π/4)d²·h

Fill in the given numbers and do the arithmetic.

  V = π/4×(19 km)²×(5 km) ≈ 1,417.64 km³

The volume of a cylinder is found using the formula V = πR²h. To find the radius, we divide the diameter by 2, giving us 9.5 km. The volume is therefore approximately 1413.716 km³.

To find the volume of a cylinder, we use the formula: V = πR²h. In this case, we are given the diameter and height of the cylinder. The diameter is double the radius, so to find the radius, we divide the diameter (19km) by 2, which gives us 9.5km. Substitute the radius and height into the formula, we get: V = π * (9.5 km)² * 5 km.

Now, we can calculate it. π is approximately 3.14159, (9.5 km)² equals 90.25 km², and multiply it all together with the height (5 km), we get approximately 1413.716 km³.

This is the volume of the cylinder.

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Answer:

157 cm²

Step-by-step explanation:

volume = (1/3) * π * r² * h

volume = (1/3) * π * 5² * 6

volume = (1/3) * π * 25 * 6

volume = (1/3) * π * 150

volume = (1/3) * 471

volume = 157 cm²

Answer:

157 cubic centimeters

Step-by-step explanation:

What we have here is called INTERSECTING CHORDS IN A CIRCLE.

The equation is:

10 times x = 7 times 7

10x = 49

x = 49/10

x = 4.9

answer 4.9cm

10times x=7times7(multiple it)

10x=49

x=49/10

x=4.9