a child find 29 nickels and dimes. how many dimes are there if the total value of the coins are $2.10?

To find the height of the mat off the ground, we can use trigonometry.

To find the height of the mat off the ground, we can use trigonometry. Since the angles of the right triangle formed by the mat are 60° and 30°, we can determine the height using the sine function. The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.

In this case, the side opposite the 30° angle is the height of the mat, and the hypotenuse is the length of the mat, which is 5 feet. So, we have sin(30°) = height/5. Solving for the height, we get height = 5 * sin(30°) = 5 * 0.5 = 2.5 feet.

Therefore, the mat is 2.5 feet off the ground.

The correct answer is option B. The height of the gymnastics mat off the ground is [tex]\frac{5\sqrt{3}}{3}}[/tex] feet.

Given that the gymnastics mat extends 5 feet across the floor, this length corresponds to the side opposite the 60° angle in the right triangle.

Let's denote the length of the side opposite the 30° angle as [tex]$x$[/tex].

According to the properties of a 30-60-90 triangle, the side opposite the 60° angle is [tex]\sqrt{3}[/tex] times the side opposite the 30° angle, so we have:

[tex]\[ 5 = x\sqrt{3} \][/tex]

To find [tex]$x$[/tex], we divide both sides of the equation by [tex]$\sqrt{3}$[/tex]:

[tex]\[ x = \frac{5}{\sqrt{3}} \][/tex]

To rationalize the denominator, we multiply the numerator and the denominator by [tex]$\sqrt{3}$[/tex]:

[tex]\[ x = \frac{5\sqrt{3}}{3} \][/tex]

The complete question is:

From the side view, a gymnastics mat forms a right triangle with other angles measuring 60° and 30°. The gymnastics mat extends 5 feet across the floor. How high is the mat off the ground?

A. [tex]\frac{5}{2}[/tex] ft.

B. [tex]\frac{5\sqrt{3}}{3}[/tex] ft.

C. [tex]5\sqrt{3}}[/tex] ft.

D. 10 ft.

Answer:

After the 4 second arrow is released, it will hit the ground.

Step-by-step explanation:

Consider the provided formula.

[tex]h(t)=64t-16t^2[/tex]

We need to find how long after the arrow is released does it hit the ground.

If the arrow hit the ground that means the value of h(t)=0.

Substitute the value of h(t)=0 and solve the equation as shown.

[tex]64t-16t^2=0[/tex]

[tex]16t(4-t)=0[/tex]

Now use zero product rule: If ab=0 then either a=0 or b=0

[tex]16t=0\ or\ 4-t=0[/tex]

[tex]t=0\ or\ -t=-4[/tex]

[tex]t=0\ or\ t=4[/tex]

Hence, after the 4 second arrow is released, it will hit the ground.

Area=1/2 bh
6=1/2bh
12=bh
height is x, base 3x

12=3x^2
x^2=4

x=2
height = 2 feet

 base = 3*2 = 6 feet

The selling price of the house decreased by 16%.

To find the percentage decrease in the selling price of the house, we need to calculate the difference between the initial selling price and the final selling price, and then divide that by the initial selling price. Finally, we multiply the result by 100 to get the percentage decrease.

Therefore, the selling price of the house decreased by 16%.

The selling price of the house decreased by 16%.

To find the percentage decrease in the selling price of the house, we can use the following formula:

Percentage decrease = ((Initial price - Final price) / Initial price) x 100

In this case, the initial price is $250,000 and the final price is $210,000. Plugging these values into the formula, we get:

((250,000 - 210,000) / 250,000) x 100 = (40,000 / 250,000) x 100 = 0.16 x 100 = 16%

Therefore, the selling price of the house decreased by 16%.

The total wage for full-time workers is 84000$.

Simplifying a value simply means finding it in its most basic form. To simplify the problem, we use a number of approaches, including PEMDAS and BODMAS. Aside from the value, the variables must also be made simpler.

Given, A factory employs 3 full-time workers and 6 part-time workers; the amount earned by each is $36,000 for the production supervisor; $27,000 for the machine operator; $21,000 for the general assistant; a total of $50,000 for part-time staff.

The Total wage for the full-time staff =  36000 + 27000 + 21000

The total wage for the full-time staff = 84000

Therefore 84000$ was the wage bill for the 3 full-time staff.

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Answer: $6554.52

Step-by-step explanation:

Total number of shares bought by Carmen =153

A constant yearly dividend paid by each share=$7.14

Thus, 153 shares pays yearly dividend =[tex]153\times7.14=\$1092.42[/tex]

After 6 years, total dividend received by Carmen=[tex]6\times1092.42=\$6,554.52[/tex]

Hence, The total dividend received by Carmen in 6 years = $6554.52

110% =1.10

 multiply the old price by that

2.85 *1.10 = 3.135

 round to 3.14

 new price is $3.14

Answer:

Which expression will equal a rational product even though it is multiplying an irrational number times another irrational number?

A

Hello,

The correct answer is A) m < 9

Hope this helps!!!! Happy Holidays!!!! (:

The height of the building from the top of the ladder is 12.6 ft

The situation forms a right angle triangle.

A right angle triangle is a triangle that has one of its sides as 90 degrees.

Therefore,

The length of the ladder is the hypotenuse side.

The bottom of the ladder distance from the base of the building is the adjacent side of the triangle. Therefore,

The height of the building from the top of the ladder is the opposite sides. Therefore, using Pythagoras theorem.

c² = a² + b²

14² - 6² = b²

b² = 196 - 36

b² = 160

b = √160

b = 12.6491106407

b = 12.6 ft

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