Triangle ABC is similar to triangle YBX. Find the value of n. The figure is not drawn to scale.

Answer:

The horizontal distance travelled by an arrow is  70.6  m.

Step-by-step explanation:

Given : An archery arrow is shot with a speed of 45 m/s at an angle of 10°.

To find : How for  horizontally can the arrow travel before hitting a target at the same height  from which it was released?

Solution :

The expression for the range of the projectile motion is

[tex]R=\frac{V^2\sin 2\theta}{g}[/tex]

Where, the velocity of an arrow is V = 45 m / s

The angle of release of an arrow is  [tex]\theta=10^\circ[/tex]

The acceleration due to gravity is g =9.81  m/s²

Substitute the values,

[tex]R=\frac{45^2\sin 2(10)}{9.81}[/tex]

[tex]R=\frac{2025\sin (20)}{9.81}[/tex]

[tex]R=70.6\ m[/tex]

Therefore, the horizontal distance travelled by an arrow is  70.6  m.

The arrow travels approximately 70.9 meters.

To determine how far the arrow travels horizontally, we need to break the initial velocity into horizontal and vertical components and use the projectile motion equations.

Step-by-step solution:

The arrow travels approximately 70.9 meters horizontally before hitting a target at the same height from which it was released.

Answer:

x = 32

Step-by-step explanation:

Step 1:  Subtract 12 from both sides

x/8 + 12 - 12 = 16 - 12

x/8 = 4

Step 2:  Multiply both sides by 8

x/8 * 8 = 4 * 8

x = 32

Answer:  x = 32

Answer:

Step-by-step explanation:

[tex]\frac{x}{8}+12=16\\\\\frac{x}{8}=16-12\\\\\frac{x}{8}=4\\\\x=4*8\\\\x=32[/tex]

Answer: Therefore, They both have the same amount!

Step-by-step explanation:

Carter=  20+10+4(5)+2(1)=

             30+20+2= 52 dollars

Aubrey=  2(10)+5(5)+7(1)=

                20+25+7=52 dollars

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Square B

The complete question is written in a comment above. The doctor's office where you work needs to store eight filing cabinets with patient information in one of three secure storage rooms. We know that the filing cabinets need a total of 55 square feet of space. You need to identify in which room the filing cabinets will fit. So we have three rooms:

FIRST OFFICE:

[tex]Square \ A = 8 \times 5[/tex]

In other words, for this room we have the following area:

[tex]Square \ A =40ft^2[/tex]

SECOND OFFICE:

[tex]Square \ B = 9 \times 7.5[/tex]

In other words, for this room we have the following area:

[tex]Square \ B =67.5ft^2[/tex]

THIRD OFFICE:

[tex]Square \ C = 5 \times 10[/tex]

In other words, for this room we have the following area:

[tex]Square \ C =50ft^2[/tex]

How can we know what is the room we need to choose?

Well, the room we need to choose is the one whose area is greater than the area of the filling cabinets. In other words, let's call square x the unknown room, then:

[tex]Square \ x>55ft^2[/tex]

From the, choices the only room that meets our requirements is square B because:

[tex]Square \ B>55ft^2 \\ \\ 67.5ft^2>55ft^2[/tex]

Measure the length and width of a room in feet to calculate its area. Multiply these dimensions to get the area in square feet. The filing cabinets need a room with at least 55 square feet.

To determine whether the filing cabinets will fit into a room, we must calculate the area of the room and see if it is at least 55 square feet, the space required for the filing cabinets.

To calculate the area of a room in square feet, measure the length and width of the room in feet and then multiply these numbers together.

For example, if a room is 10 feet wide and 5.5 feet long, its area would be 10 feet times 5.5 feet, which equals 55 square feet. Therefore, the filing cabinets would fit in a room of this size.

The cost of wire to purchase is Rs 264.

Step-by-step explanation:

Given,

The diameter of the circular garden is 21 m

The radius(r) = [tex]\frac{21}{2}[/tex] m

To find, the length of wire of the fence we need to find the circumference.

Formula

The circumference of the circle = 2πr meter

=2×[tex]\frac{22}{7}[/tex] ×[tex]\frac{21}{2}[/tex] m

=66 meter

So, the length of the wire = 66 m

The cost of wire Rs 4 per meter.

The total cost = Rs 4 × 66

= Rs 264

Answer:

t = 1/2

Step-by-step explanation:

6 - (3t+4) = t

Distribute the minus sign

6 - 3t -4 = t

Combine like terms

2 -3t = t

Add 3t to each side

2 -3t +3t = t+3t

2 = 4t

Divide each side by 4

2/4 =4t/4

1/2 =t

Answer:

6-(3t+4)=t

6-3t-4=t

6-4=t+3t

2=4t

t=2/4

Answer:

t=-3

Step-by-step explanation:

12t+12=-24

12t=-36

t=-3

Answer:

2.19 liters = 2190 milliliters

Step-by-step explanation:

To write the radius of the fishing line in standard form, it is 0.00025 foot. In inches, the length is 0.003 inches.

The radius of the fishing line is given as 2.5*10^-4 foot. To write this number in standard form, we first need to convert it into decimal form.

To do this, we move the decimal point four places to the left, since the exponent is negative. This gives us 0.00025.

Therefore, the number in standard form is 0.00025 foot.

To convert this into inches, we know that there are 12 inches in a foot. So, we multiply the length in feet by 12 to get the length in inches.

Therefore, the length of the fishing line in inches is 0.00025 foot * 12 inches/foot = 0.003 inches.

Answer:x<29

Step-by-step explanation:

X<29

Answer:

A.

Step-by-step explanation:

All of the other questions don't make sense because they are statistical

x = 7 and x = –7.

Solution:

Given data:

[tex]$f(x)=x^{2}+15[/tex] and [tex]f(x)=64[/tex]

To find the solutions when f(x) = 64.

Both are equations of f(x), so equate the given equations, we get

[tex]x^2+15=64[/tex]

To isolate the constant term subtract 15 from both sides.

[tex]x^2+15-15=64-15[/tex]

[tex]x^2=49[/tex]

49 can be written as 7².

[tex]x^2=7^2[/tex]

Taking square root on both sides of the equation, we get

x = ±7

The solutions to f(x) = 64 is x = 7 and x = –7.

Answer: 2^4+7 -5^3

Step-by-step explanation:

Answer:

(2 to the power of 4 )plus 7 minus( 5 to the power of 3)

Step-by-step explanation:

The Question is Incomplete, the Complete Question is with figure is below.

Answer:

Therefore,

The Measure of angle 6 is

[tex]\angle 6 =45\°[/tex]

Step-by-step explanation:

Given:

m∠1 = 135°

Lines b and c are parallel.

To Find:

m∠6 = ?

Solution:

Linear Pair:

A linear pair of angles is formed when two lines intersect.  

Two angles are said to be linear if they are adjacent angles formed by two intersecting lines.  

The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.  

Example

∠ 1 and ∠ 2 ∠ 1 and ∠ 3 ,etc

[tex]\angle 1 + \angle 3 = 180\°[/tex]

Substituting the values we get

[tex]135 + \angle 3 = 180\\\\\angle 3 = 180-135=45\°[/tex]

Now,

Lines b and c are parallel.  .Given

When Two lines are Parallel Alternate interior angles are equal

∠ 3 and ∠ 6 are Alternate Interior angles

[tex]\angle 3 = \angle 6[/tex]

But [tex]\angle 3 =45\°[/tex]

[tex]\angle 6 =45\°[/tex]     ...Transitive Property

Therefore,

The Measure of angle 6 is

[tex]\angle 6 =45\°[/tex]

Answer:

The coefficient is the number before x. So it is 6.

Answer:

Step-by-step explanation:

the answer is B) 6

Answer:

$486

Step-by-step explanation:

Step 1:  Solve

(450 * 0.9) * 1.2

405 * 1.2

486

Answer:  $486

Answer:

(x-2)(x+2)

Step-by-step explanation:

if we expand the above quadratic we can see that the -2x and + 2x will cancel eachother out therefore there is no bx in this quadratic equation

Answer:

No roots/solutions

Step-by-step explanation:

No bx means b = 0

B² - 4AC

(0)² - 4(1)(4)

-16 < 0

The length of SK = 10 units while the length of BK = 8.6602 units.

Step-by-step explanation:

Step 1:

In the given triangle, there are two right-angles triangles with 60° angles. The central line BK is the opposite side for both the triangles. For triangle RK the hypotenuse's length is 10 m. Assume BK = x units and SK = y units.

Step 2:

So first we calculate the length of BK (x).

As we have the values of the angle of the triangle and the hypotenuse, we can calculate the sine of the angle to determine the value of x.

[tex]sin R = \frac{oppositeside}{hypotenuse}, sin 60 = \frac{x}{10}.[/tex]

[tex]sin 60 = 0.86602, x = 0.86602 (10) = 8.6602 units.[/tex]

So x = BK = 8.6602 units.

Step 3:

So now we calculate the length of SK (y).

As we have the values of the angle of the triangle and the opposite side's length, we can calculate the sine of the angle to determine the value of y.

[tex]sin S = \frac{oppositeside}{hypotenuse}, sin 60 = \frac{86.602}{y}.[/tex]

[tex]sin 60 = 0.86602, y = \frac{8.6602}{0.86602} = 9.999units = 10 units[/tex]

So y = SK = 10 units.

Answer: x=16

Step-by-step explanation:subtract 26 from 90 then divide 64 by 4 and you get 16

Answer:

X=16

Step-by-step explanation:

The answer is 16. 90-26/4=16

Answer:

Reflectional Symmetry

Answer:

9.86 / 0.85 = 11.6

Step-by-step explanation:

Answer:

1,000

Step-by-step explanation:

23,000 divided by 23 is 1,000

Answer:

heine is a former member and the chief of the United nations and th t in my experience with the United states and t the u.s. government of th world and is th American standard bible in a very good country of th I think 8is the most popular among women and the men in a society where the oth was the other one that had the most of t to the world that I would not like you to be in my life and I don't know how much I

Answer: A. 80.61

Step-by-step explanation:

Answer:

29/100

Step-by-step explanation:

Answer: 29/100

Step-by-step explanation:

The 2 is in the Tenth place

The 9 is in the Hundredths place

so get 29/100

Example: .5 as a fraction

Answer: 5/10

The solutions to quadratic equation are:

[tex]x = \frac{3 + i \sqrt{3}}{2}\\\\x = \frac{3 - i \sqrt{3}}{2}[/tex]

Solution:

Given is:

[tex]x^2 - 3x + 3 = 0[/tex]

We have to find the solutions to quadratic equation

[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=-3,\:c=3:\\\\x=\frac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:3}}{2\cdot \:1}[/tex]

[tex]x=\frac{3 \pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:3}}{2\cdot \:1}\\\\x = \frac{3 \pm \sqrt{-3}}{2}\\\\x = \frac{3 \pm i \sqrt{3}}{2}[/tex]

We have two solutions :

[tex]x = \frac{3 + i \sqrt{3}}{2}\\\\x = \frac{3 - i \sqrt{3}}{2}[/tex]

The solutions to the quadratic equation x^2 - 3x + 3 = 0 can be found using the Quadratic Formula. The solutions are complex numbers: x = 3/2 ± (i*sqrt(3))/2.

The given equation is a quadratic equation of the form ax^2 + bx + c = 0. To find the solutions to this equation, we can use the Quadratic Formula: x = [-b ± sqrt(b^2 - 4ac)] / (2a).

Here a=1, b=-3, c=3.

Plugging these values into the formula,

we get x = [3 ± sqrt((-3)^2 - 4*1*3)] / (2*1).

Simplifying this equation will give us x = [3 ± sqrt((9 - 12)] / 2.

Now, note that the value under the square root is negative, indicating that the solutions will be complex.

Finally, we have the solutions:

x = [3 ± sqrt(-3)] / 2

= 3/2 ± (i*sqrt(3))/2, where 'i' is the imaginary unit.

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Answer:

warm air toward high latitudes

Step-by-step explanation:

Known to sailors around the world as the doldrums, the Inter-Tropical Convergence Zone, (ITCZ, pronounced and sometimes referred to as the “itch”), is a belt around the Earth extending approximately five degrees north and south of the equator. From google

The atmosphere balances the unequal heating of Earth’s surface by moving warm air toward high latitudes and cool air toward the equator.

An atmosphere is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body.

The atmosphere balances the unequal heating of Earth’s surface by moving warm air toward high latitudes and cool air toward the equator.

This is because the Earth's surface is heated unequally due to differences in solar radiation and other factors.

The equator receives more direct sunlight and is therefore warmer, while the poles receive less direct sunlight and are cooler.

As a result, warm air rises at the equator and cool air sinks at the poles, creating a circulation pattern in the atmosphere known as the Hadley cell.

Hence, the atmosphere balances the unequal heating of Earth’s surface by moving warm air toward high latitudes and cool air toward the equator.

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