Why is it most logical to let x represent Dianna’s current age?

Answer:

C 9 inches

Step-by-step explanation:

Answer:

The answer is 1

Step-by-step explanation:

Answer:

125 feet

Step-by-step explanation:

Given :

On a softball field, home plate is 43 feet from the pitcher’s mound.

A ball is hit at an angle of 27° east of the pitcher’s mound.

The ball travels 162 feet before it is caught by an outfielder.

To Find : Rounded to the nearest foot, the outfielder must throw the ball feet to return it to the pitcher.

Solution:

Law of cosines: [tex]a^2 = b^2 + c^2 -2bc cos A[/tex]

∠A = 27°

b = 43

c = 162

Substitute the given values

[tex]a^2 = 43^2 + 162^2 -2(43)(162) cos 27^{\circ}[/tex]

[tex]a^2 = 15679.497105[/tex]

[tex]a = \sqrt{15679.497105}[/tex]

[tex]a =125.21[/tex]

The outfielder must throw the ball 125 feet to return it to the pitcher.

Using the formula V = πr²h, the volume of the cylinder is calculated as 188.4954 cubic inches, which can be rounded to 188 cubic inches, corresponding to answer choice D.

To calculate the volume of the cylindrical container holding sugar, we can use the formula for the volume of a cylinder, which is V = πr²h. Here, π is a constant (approximately 3.14159), r is the radius of the cylinder, and h is the height of the cylinder.

The diameter of the container is given as 4 inches, so the radius (r) is half of the diameter, which is 2 inches. The height (h) is given as 15 inches. Plugging these values into the volume formula, we get:

V = π(2 inches)²(15 inches)
= π(4 square inches)(15 inches)
= 60π cubic inches

Using 3.14159 as the value for π, the volume calculates to:

V = 60 * 3.14159 cubic inches = 188.4954 cubic inches

So, the closest estimate to the volume of the sugar container would be 188 cubic inches, which corresponds to answer choice D.

What is the exact value of the trigonometric expression in simplest form? 2 cos(3π/4)−4 sin(7π/6)

[tex] 2 cos(\frac{3\pi}{4})-4sin(\frac{7\pi}{6}) [/tex]

Let us find the value of cos([tex] \frac{3\pi}{4} [/tex]) and [tex] sin(\frac{7\pi}{6} ) [/tex]

[tex] cos(\frac{3\pi}{4} )=cos(\pi -\frac{\pi}{4} ) [/tex]

The angle [tex] \pi -\frac{\pi}{4} [/tex] lies in second quadrant.

So, [tex] cos(\frac{3\pi}{4} )=-cos(\frac{\pi}{4} ) =-\frac{1}{\sqrt{2}} [/tex]

[tex] So, cos(\frac{3\pi}{4} )=-\frac{1}{\sqrt{2}} [/tex]

Now, Let us find the value of [tex] sin(\frac{7\pi}{6} ) [/tex]

[tex] sin(\frac{7\pi}{6} ) =sin(\pi +\frac{\pi}{6} )=-sin(\frac{\pi}{6} ) =\frac{-1}{2} [/tex]

[tex] sin(\frac{7\pi}{6} ) =\frac{-1}{2} [/tex]

[tex] 2 cos(\frac{3\pi}{4})-4sin(\frac{7\pi}{6}) [/tex]=2*[tex] \frac{-1}{\sqrt{2}} [/tex]-4*[tex] \frac{-1}{2} [/tex]

=[tex] \frac{-2}{\sqrt{2}} +\frac{4}{2} [/tex]

=[tex] \frac{-2\sqrt{2}}{2} +\frac{4}{2} [/tex]

=[tex] \frac{-1\sqrt{2}}{1} +\frac{2}{1} [/tex]

=[tex] -\sqrt{2} +2 [/tex]

=[tex] 2-\sqrt{2} [/tex]

[tex] 2 cos(\frac{3\pi}{4})-4sin(\frac{7\pi}{6})=2-\sqrt{2} [/tex]

Answer:

Step-by-step explanation:

Answer:

The measure of angle A is 30 degree, measure of angle B is 90 degree and measure of angle C is 60 degree.

Step-by-step explanation:

The measures of given sides are 6, 12, [tex]6\sqrt{3}[/tex].

According to the Law of Cosine:

[tex]\cos A=\frac{b^2+c^2-a^2}{2bc}[/tex]

Using Law of Cosine, we get

[tex]\cos A=\frac{(12)^2+(6\sqrt{3})^2-(6)^2}{2(12)(6\sqrt{3})}[/tex]

[tex]\cos A=\frac{216}{144\sqrt{3}}[/tex]

[tex]\cos A=\frac{3}{2\sqrt{3}}[/tex]

[tex]\cos A=\frac{\sqrt{3}{2}[/tex]

[tex]A=30^{\circ}[/tex]

Similarly,

[tex]\cos B=\frac{a^2+c^2-b^2}{2ac}[/tex]

[tex]\cos B=\frac{(6)^2+(6\sqrt{3})^2-(12)^2}{2(6)(6\sqrt{3})}[/tex]

[tex]\cos B=\frac{0}{36\sqrt{3}}[/tex]

[tex]\cos B=0[/tex]

[tex]B=90^{\circ}[/tex]

Therefore, measure of angle A is 30 degree and measure of angle B is 90 degree.

According to angle sum property, the sum of interior angles of a triangle is 180 degree.

[tex]A+B+C=180^{\circ}[/tex]

[tex]30^{\circ}+90^{\circ}+C=180^{\circ}[/tex]

[tex]C=60^{\circ}[/tex]

Therefore the measure of angle C is 60 degree.

The triangle with sides 6, 12, and 6√3 has angles of 30 degrees, 60 degrees, and 90 degrees.

Given a triangle with sides 6, 12, and 6√3, we can find the angles using the Law of Cosines.

First, we use the formula for the Law of Cosines,
c² = a² + b² - 2ab * cos(C).

Let a = 6, b = 6√3, and c = 12.
We substitute these values into the formula to find angle C,

cos(C) = (6² + (6√3)² - 12²) / (2 * 6 * 6√3)

Compute the values inside the formula:

6² = 36

(6√3)² = 108

12² = 144

cos(C) = (36 + 108 - 144) / 72

cos(C) = 0

Therefore, angle C = 90 degrees.

To find the other angles, we use the Law of Sines,
(sin A / a) = (sin B / b) = (sin C / c).

We already know C = 90°, so (sin C / 12) = 1/12.

For angle A,

sin(A) / 6 = 1/12

sin(A) = 6/12 = 1/2

A = 30 degrees

For angle B:

B = 180° - 90° - 30° = 60 degrees

Therefore, the angles of the triangle are 30 degrees, 60 degrees, and 90 degrees.

Answer:The answer is below Hope this help and tthanjs for answer please like and vote excellent thanks and have a good day.

Step-by-step explanation

  3      0

  4  

   5      455

    6     6

    7     89  

Answer:

15. It was right for me, not sure for anyone else

Step-by-step explanation:

Answer:

Just took the test Its C

Answer:

360°/d = kn.

Step-by-step explanation:

To know if a regular polygon can tessellate, we divide 360 by the interior angle of the polygon and the result needs to be an integer, but not in all cases you get the number of sides of the polygon, you get a multiple of the number of sides. So, none of the options are correct, the correct would be

360/d = kn, where k is an integer.

option: c.   graph of line going through (1, 4) and (3, 10)

It is given that:

Margo has a coin collection.

She was given 1 coin as a gift, and she adds 3 coins per year.

i.e. she started with a initial of one coin and add 3 coins each year.

That is this situation can be represented with the help of a function:

C(t) which represents the number of coins she has in 't' years.

Now,

C(0)=1

Also,

C(t)=3t+1-------------(A)

Hence, we will check each of the given functions whether at the value of t they passes through that point or not.

a)

it is given that:

Graph passes through (1,2) and (3,4)

i.e. when t=1   C(t)=2

and when t=3 C(t)=4

but on putting the value of t in equation (A) it does not hold true.

same could be done for option (b) and option (d).

But in option (c)

It hold true.

         Since,

          when t=1

            C(t)=3×1+1=4

         when t=3

            C(t)=3×3+1=10

Hence, the correct answer is:

c.)   graph of line going through 1, 4 and 3, 10

Using exponential function concepts, it is found that it represents growth of 4%.

An exponential function is modeled by:

[tex]y(t) = y(0)(1 + r)^t[/tex]

In which:

In this problem, the equation is:

[tex]y = 8700(1.04)^t[/tex]

Hence:

[tex]1 + r = 1.04[/tex]

[tex]r = 0.04[/tex]

Since r = 0.04 is positive, it represents a growth of 4%.

To learn more about exponential function concepts, you can take a look at https://brainly.com/question/24757163

Final answer:

The function y = 8700(1.04)^4 represents an exponential growth with a rate of increase of 4% per time period over four periods.

Explanation:

The given function is y = 8700(1.04)^4. This represents an exponential growth because the base of the exponent, 1.04, is greater than 1. To determine the percentage rate of increase, we observe that the base, 1.04, when written as a percentage, is 104%. This means that the amount increases by 4% over each time periodperiod. Since the exponent is 4, this growth occurs over four time periods. However, the overall increase is not simply 4% multiplied by 4, as exponential growth compounds wicompoundsth each time period.

relative minimum is -2 when x is -3

Answer:

480cm². Verified by correct test results.