vertical anges are always equal to each other

The torque at the end is equal to 45 Nm.

Torque can be defined as a measure of the amount of force which causes a physical object to rotate about an axis. This ultimately implies that, torque is a force which tends to cause the rotation of a physical object about an axis.

Mathematically, torque can be calculated by using this formula:

τ = Fd

Where:

In this scenario, we can reasonably infer and logically deduce that the torque at the end would be equal to 45 Newton meter (Nm) because the force was not applied over a perpendicular distance.

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Given the equation system:

To solve this system using the elimination method, the first step is to multiply the first equation by 4 so that the leading coefficient is the same, i.e., both equations start with "4x"

Then subtract the second equation from the first one

From the resulting expression, you can calculate the value of y

Next, you have to substitute the value of y in either the first or second equation to find the value of x:

The solution of the system is (-2,-6)

Since the function describing the height is a quadratic function with negative leading coefficient this means that this is a parabola that opens down. This also means that the maximum height will be given as the y component of the vertex of the parabola, then if we want to find the maximum height, we need to write the function in vertex form so let's do that:

Hence the function can be written as:

and its vertex is at (1.9,19.9) which means that the maximum height of the ball is 19.9 m

The statement holds true for all true values of is cos²θ = 1 − sin²θ

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reduce the square root of

There is no square root for the negative number

so, this is represent a complex number

So,

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

factor:

5x - 8

Step 02:

difference of squares:

(5x - 8)(5x + 8) = 25x² - 64

The answer is:

25x² - 64

Answer:

20 Students

Explanation:

Let the total number of students in the class = x

Number of students that have pets = 15

Percentage of students that have pets = 75%

Therefore:

We then solve for x.

We have 20 students in total in the class.

The figure for the height of flagpole, wire and ground is,

Determine height of the pole by using the pythagoras theorem in triangle.

Thus, height of the flagpole is 32.08 feet.

Step-by-step explanation:

what is the problem ?

first you need to put "1" in place of the x and calculate, and then you need to put "2" in place of the x and calculate.

just simple calculation !

(a)

R(1) = 1000×1² / (1² + 4) = 1000 / 5 = 200

$200 million

(b)

R(2) = 1000×2² / (2² + 4) = 4000 / 8 = 500

$500 million

there ! that's all that was needed.

1.

First, divide the figure into 3 different figures.

Find the area of each figure, and then add them:

A1 is a rectangle:

Area of a rectangle: Lenght x width

A1 = 8 x 5.3 = 42.4 in2

A2 is also a rectangle:

Lenght = 4

width = 8 - 5.3 = 2.7

A2 = 4 x 2.7 = 10.8 in2

A3 is a triangle:

Area of a triangle = (base x height) / 2

base = 2.7

Height = 8-4 = 4

A3= ( 2.7 x 4 ) / 2 = 5.4 in2

Total area = A1 + A2 + A3 = 42.4 + 10.8 + 5.4 = 58.6 in2

Answer = 58.6 in2

Lets call x to the number of ducks

and y the number of pigs.

Then:

Because there are 2 legs per duck and 4 legs per pig.

If the total of animals is 37, then:

Then:

And replacing on the first equation we get:

There are 12 pigs and therefore 25 ducks.

Given:-

let

5x-4y=1 be the equation 1

-5x-10y=-15 be the equation 2

step 1-

add equation 1 and 2

we get=

-14y=-14

y=1

this is required value of y

we are going to put this value of y in equation 1

we get

5x-4(1)=1

5x-4=1

5x=1+4

5x=5

x=1

this is required value of x

hence value of x and y are(1,1)

Given the expression

Given:

Find-: Factor using the formula of the sum or difference of cube.

Sol:

Factoring sum and differences of cubs is:

Apply for the given information.

Given:

Graph is given.

6a.

6b.

6c.

Answer:

h≥48​

Explanation:

If all riders must be at least 48 inches tall, it can mean the following.

0. The height of the riders can be ,exactly 48 inches, tall (h=48)

1. The height of the riders can be, greater than 48 inches,, (h>48).

Combining the two, we have:

h≥48​

The percent change is given by:

The old value is $390

Answer

D. Observations of constellations show that stars have moved over time.

Explanation:

A scientific claim is basically an observation in science.

Constellation changes there position over time because of earth's rotation around sun. So, observation of constellations shows that stars have moved over time is a scietific claim. If stars would not move then constellation will not form.

Using scientific notation, we have that:

a) As an ordinary number, the number is written as 0.51.

b) The value of the product is of 1445.

An ordinary number written in scientific notation is given as follows:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1.

For item a, to add one to the exponent, making it zero, we need to divide the base by 10, hence the ordinary number is given as follows:

5.1 x 10^(-1) = 5.1/10 = 0.51.

For item b, to multiply two numbers, we multiply the bases and add the exponents, hence:

(1.7 x 10^4) x (8.5 x 10^-2) = 1.7 x 8.5 x 10^(4 - 2) = 14.45 x 10².

To subtract two from the exponent, making it zero, we need to multiply the base by 2, hence the base number is given as follows:

14.45 x 100 = 1445.

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Explanation

Step 1

we have a perpendicular line, its slope is

two lines are perpendicular if

replace

so, our slope is 3/2

Step 2

using slope=3/2 and P(-5,2) find the equation of the line

We have the following:

We subtract the equations:

for y:

therefore, the answer is:

(0,6) and (5,16), the option D.

The maximum number of calling minutes you can use for $50 is 210 minutes.

To solve this, we have the function cost C(x) that depends on the amount of acalling munutes (x)

We want this cost to be $50 or lower. This means:

Then we can create an inequality:

And now we can solve for x:

Thus, with $50 we can talk up to 210 minutes.

To be sure of the result, let's plug x = 210 in the function and it should give us a cost of C(210) = 50:

This confirms the result.

Answer:

seven and one-tenth.

Explanation:

To name decimal number, we first name the values before the decimal point, in this case, seven

Then, we add an and that corresponds to the decimal point

Finally, we say the number after the decimal point and the place of this number, in this case, one-tenth.

Therefore, the name of the decimal number 7.1 is:

seven and one-tenth.

The algebraic expressions can be written as

The given expression is,

The vertex of a quadratic function can be found by using the following expression:

Where "a" is the number multiplying x² and b is the number multiplying x. For this function a = -2 and b = 5. Applying these on the problem we have:

To find the y coordinate of the vertex we need to use the value for x that we found above. We have:

The ordered pair for this function's vertex is (1.25, 14.125)

Answer: We have to find the radio stations in 2015, which is 13.8% more than the radio stations in 2005 which were 744:

The given information is

We are given a tangent and a chord of a circle. The angle ABC form by the intersection of the tangent and the chord is half the arc they both intersect, therefore, we must find the major arc of the circle, we can do that with the fact that the total arc of the circle is 360, therefore:

Therefore, the angle is:

Angle ABC is 155 degrees.