Use π = 3
Calculate the area of a circle with
diameter
of 5cm

Answer:

y = -1.5x

How to build equation?

Given points: (0, 0), (2, -3)

Find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope \ (m) = \dfrac{-3-0}{2-0} = -1.5[/tex]

Then find equation:

[tex]y-y_1 = m(x - x_1)[/tex]

[tex]y - 0 = -1.5(x -0)[/tex]

[tex]y = -1.5x[/tex]

Answer:

y = (-3/2)x

Step-by-step explanation:

I am going to answer this question in slope-intercept form, which is y = mx + b (m is the slope, b is the y-intercept). The question already gives us the y-intercept, or the point at which the graph crosses the y-axis. It is (0, 0). Now, all we have to do is find the slope, which we can do using the following formula:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

In this formula, (x1, y1) and (x2, y2) are two points that are given to us [the first point is (0,0) and the second point is (2,-3). We can solve for the slope by plugging in:

[tex]m=\frac{-3-0}{2-0}=\frac{-3}{2}[/tex]

Now that we have m and b, we can plug into slope-intercept form to get our equation: y = (-3/2)x + 0 or y = (-3/2)x

One can determine the number of roots by seeing the degree of the given polynomial.

The number of roots can be determined by just seeing the highest power of the given equation.

1) for the equation  x-4=0

here, the highest power of the equation is one. So, it will have one root.

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtract multiplication, on,  and non-negative integer exponentiation of variables.

Let's check it by simplifying x-4=0  which implies x=4

Hence, the equation has only one root namely x = 4.

2) Consider a quadratic equation,

10t^2-t-3=0

here, the highest power of the equation is two. So, it will have two roots.

Let's check it by simplifying using the middle term splitting method,

10t^2+5t-6t-3=0

5t(2t+1)-3(2t+1)=0

(5t-3)(2t+1)=0

t=-3/5 or t=-1/2

Thus, the equation has two roots.

Hence, one can determine the number of roots by seeing the degree of the given polynomial.

To learn more about the polynomial visit:

https://brainly.com/question/2833285

#SPJ1

The equation of the line passing through the point (3, 0) and parallel to the y axis is x = 3.

An equation is an expression that shows the relationship between two or more variables and numbers.

The graph passes through the point (3, 0) and parallel to the y axis, the equation of this line is x = 3.

The equation of the line passing through the point (3, 0) and parallel to the y axis is x = 3.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The equation representing the cost in The Free Press is 12 + 5d.

The equation representing the cost in The Free Press will be:

= 12 + (5 × d)

= 12 + 5d

The equation representing the cost in The Banner will be:

= 8 × d

= 8d

The table of value for Free Press will be:

1st day = 12

2nd day = 17

3rd day = 22

4th day = 27

5th day = 32

The table of value for the Banner will be:

1st day = 8

2nd day = 16

3rd day = 24

4th day = 32

5th day = 40

The newspaper that will be used to run the advertisement for the first day is Free Press since it's cheaper.

The newspaper that will be used to run the advertisement for twelve days will be:

Free press = 12 + 5d

= 12 + 5(12)

= 12 + 60 = 72

The banner = 8d = 8 × 12 = 96

Therefore, for 12 days, Free Press is cheaper.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

The solution to the system of equations is x = -1 and y = 4

The system of equations is given as:

5x + 2y = 3

2x + 3y = 10

Multiply the first equation by 2 and the second by 5.

10x + 4y = 6

10x + 15y= 50

Subtract the above equations

10x - 10x + 4y - 15y = 6 - 50

This gives

-11y = -44

Divide by -11

y = 4

Substitute y = 4 in 5x + 2y = 3

5x + 2 * 4 = 3

This gives

5x + 8 = 3

Subtract 8 from both sides

5x = -5

Divide by 5

x = -1

Hence, the solution to the system of equations is x = -1 and y = 4

Read more about system of equations at:

https://brainly.com/question/12895249

#SPJ1

A team of 3 boys and 3 girls be selected from 5 boys and 4 girls in 40 ways

The selections are given as:

3 boys from 5 boys

3 girls from 4 girls

Each selection is calculated using:

[tex]^nC_r = \frac{n!}{(n- r)!r!}[/tex]

So, we have:

[tex]Ways = ^5C_3 * ^4C_3[/tex]

Apply the combination formula

[tex]Ways = \frac{5!}{2!3!} * \frac{4!}{1!3!}[/tex]

Expand

[tex]Ways = \frac{5 * 4 * 3!}{2 * 3!} * \frac{4 * 3!}{1 * 3!}[/tex]

Simplify

Ways = 5 * 2 * 4

Evaluate

Ways =40

Hence, the number of ways is 40

Read more about combination at:

https://brainly.com/question/11732255

#SPJ1

Answer: a

Step-by-step explanation:

[tex]\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)}=\frac{\sqrt{x^{2}-1}}{\sqrt{x-1}}}=\sqrt{\frac{x^{2}-1}{x-1}}=\sqrt{\frac{(x-1)(x+1)}{x-1}}=\boxed{\sqrt{x+1}}[/tex]

If the function is translated 4 units down, the resulting function will be

y = x - 4 while the vertical stretch by 3units will be y = 3(x-4)

Transformation of function is a way of changing the position of a line or curve on an xy place.

Given the equation of a line as shown;

y = x (This will serve as the parent function)

If the function is translated 4 units down, the resulting function will be

y = x - 4. If the resulting function is stretched by a factor of 3, the final function will be y = 3(x - 4)

Learn more on translation here: https://brainly.com/question/12861087

#SPJ1

Answer:

[tex]4\sqrt2[/tex]

Step-by-step explanation:

[tex]2\sqrt{2} +\sqrt{8}=2\sqrt{2}+2\sqrt{2}=4\sqrt{2}[/tex]

Step-by-step explanation:

i sent the solution in the photo pls check it

Limit of x approaches two from the left of f of x: 3. Limit of x approaches two from the right of f of x: - 1 (negative 1)

If limits exist, we can take limits of the function, where x tends to -∞ or ∞, and that limiting value will be the value the function will approach.

In order to find the limit as x approaches two from the left of f of x:

Lim x→2- f(x) = ?

According to the graph, when x approaches two from the left (x<2), the function approaches 3:

Lim x→2- f(x) = 3

IN order to find the limit as x approaches two from the right of f of x:

Lim x→2+ f(x) = ?

According to the graph, when x approaches two from the right (x>3), the function approaches -1:

Lim x→2+ f(x) = - 1

Learn more about one-sided limits here:

https://brainly.com/question/23625942

#SPJ1

The length of a in the triangle to the nearest tenth is 8.1 units.

The side a of the triangle can be found using cosine formula.

Therefore,

a²= b² + c² - 2bc cos A

a² = 10² + 12² - 2 × 10 × 12 cos 42°

a² = 100 + 144 - 240cos 42

a² = 244 - 178.354758115

a = √65.6453

a = 8.10217871933

a = 8.1

learn more on triangle here: https://brainly.com/question/7831188

#SPJ1

Answer:

true

Step-by-step explanation:

Since their wise or intelligent guess

The value of m and n that shows that point p(m,5-n) when reflected on line y=0 is m = 3, n = 3.

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

The rule for the reflection over the line y = 0 (x axis) is (x, y) ⇒ (x, -y)

If the point p(m,5-n) is reflected on line y=0, this would give (m, -(5 - n)) = p'(2m-3,2n-8). Hence:

2m - 3 = m

m = 3

Also:

-(5 - n) = 2n - 8

-5 + n = 2n - 8

n = 3

The value of m and n that shows that point p(m,5-n) when reflected on line y=0 is m = 3, n = 3.

Find out more on transformation at: https://brainly.com/question/4289712

#SPJ1

Now, ORQ is a straight angle and RS its bisector.

It means:

So, ∠ORS and ∠QRS are supplementary.

We also have ray RP, that divides the angles ORQ and QRS.

It gives us one more pair of supplementary angles:

Since ∠QRS is right angle, its parts are forming a pair of complementary angles:

In 2.44 seconds lindsey be 30 feet in the air.

A quadratic equation is a second-order polynomial equation in a single variable x, ax²+bx+c=0. with a ≠ 0 .

Given:

y= -16x²+33x+45

If the height is 30 feet.

30= -16x²+33x+45

-16x²+33x+45-30=0

-16x²+33x+15=0

16x²-33x-15=0

Solving the quadratic equation

x=-b±√b²-4ac/ 2a

x= 33 ± √2049/32

x= (33+ √2049)/32    and x=33-√2049/32

x=2.44 and -0.3833

Learn more quadratic equation here:

https://brainly.com/question/2263981

#SPJ1

Answer:

Options (1), (5), and (6)

Step-by-step explanation:

See attached image

Three pairs of measurements which are possible side lengths for the triangle are,

1.  AB = 4, BC = 4√3

5 AB = 7, AC = 14.

6. AB = 11, BC = 11√3

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Now, We get;

The sides of this triangles has lengths in the ratio x : √3x : 2x

where 2x is the hypotenuse.

Now, When C = 30,  the side AB is the small leg (=x).

When B = 90, the hypotenuse is AC ( =2x).

When A =  60, the larger leg is BC (=√3x).

1.  AB = 4, BC = 4√3 :- Are possible legs.

5 AB = 7, AC = 14. :-  AB = small leg, AC = hypotenuse.

6. AB = 11, BC = 11√3:-   AB = small, BC = larger leg.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ5

The maximum height of the projectile fired from the ground with an upward speed of 245 m/s is 3001.25 m

An equation is an expression that shows the relationship between two or more variables and numbers.

The maximum height (H) of a projectile is given as:

H = u²/2g

Where u is the initial speed = 145 m/s, g is the acceleration due to gravity = 10 m/s²

H = 245²/ 2(10) = 3001.25 m

The maximum height of the projectile fired from the ground with an upward speed of 245 m/s is 3001.25 m

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

(x + 4)(x - 2) = x · x

(option L)

Step-by-step explanation:

we know that area = length × width

So, can write out the lengths and widths that we know:

(note: I will use the square as the reference point, because we can simply say "x" for both of its side lengths--you'll see why this is easier later)

Rug A:

length = x

width = x

Rug B:

length: x + 4

(4 feet greater than rug A length)

width: x - 2

(2 feet less than rug A width)

we can now set these areas to be equal to each other:

(rug A) = (rug B)

(length · width of A) = (length · width of B)

(x · x) = [ (x + 4)(x - 2) ]

So, the equation:

(x + 4)(x - 2) = x · x

can be used to find x (the length in feet) of rug A

hope this helps!! have a lovely day :)

Answer: What you picked

Step-by-step explanation:

I can't see the dropdown menus, but those answers make sense.

Answer:

The bottom part of the chest is best modeled by rectangular prism because each face is a rectangle The top part of the chest is best modeled by part of a cylinder because some faces are curved

Step-by-step explanation:

It is given that Joe paid 14.00 for a board game this is 70% of the original price what is the original price.

Let the original price of board game be

X.

x * 70/100 = 14

x * 7/10 = 14

Multiply both sides by 10.

7x = 140

Divide both sides by 7.

x = 20

The percentage depreciation is 27 % .

What is percentage ?

Given ,

         from 4500 to 3285 is depreciation value of a motor bike.

So,

         =      [tex]\frac{( 4500 - 3285 )} {4500} * 100[/tex]

         =       [tex]\frac{1215}{4500} * 100\\[/tex]

           = [tex]\frac{121500}{4500}[/tex]

          = 27 %

Therefore, The percentage depreciation is 27 % .

Learn more about percentage depreciation brainly.com/question/13894858

#SPJ4

The fraction of 5 seconds in 1 minute or part of 5 seconds in 1 minute is 1/12.

The fraction of 5 seconds in 1 minute or part of 5 seconds in 1 minute is calculated as follows;

1 minute = 60 secs

Fraction = 5 / 60

Fraction = 1/12

Thus, the fraction of 5 seconds in 1 minute or part of 5 seconds in 1 minute is 1/12.

The complete question is below:

What is part of 1 minute is 5 seconds?

Learn more about fraction here:  https://brainly.com/question/78672

#SPJ1

Answer:

c because have great day

Using the together rate, it is found that it will take 18 hours for Erick to build the garden box himself.

The together rate is given by the sum of each separate rate.

In this problem, the rates are given as follows:

Hence:

[tex]\frac{1}{x} + \frac{2}{x} = \frac{1}{6}[/tex]

[tex]\frac{3}{x} = \frac{1}{6}[/tex]

x = 18.

Hence, it will take 18 hours for Erick to build the garden box himself.

More can be learned about the together rate at https://brainly.com/question/25159431

#SPJ1

Answer:

[tex]sin\theta=\dfrac{1}{2}[/tex]

=============

Use identity [tex]sin^2\theta+cos^2\theta=1[/tex] :

Step-by-step explanation:

the circumference of a circle is

2×pi×r

with r being the radius, which is always half of the diameter.

r = 1.8 / 2 = 0.9 cm

circumference :

2×pi×0.9 = 1.8×pi = 1.8 × 3.142 = 5.6556 cm ≈ 5.7 cm

Answer:

5.7cm

Step-by-step explanation:

circumference = π · d

(2πr)

{note: "d" is diameter; "r" is radius; "π" is pi}

we know our diameter (d) to be 1.8

let's plug this into our cicumference formula! :

π · d = circumference

(3.142) · (1.8)

3.142 · 1.8 = 5.6556

let's round our answer to 1 decimal place,

remember, if the next digit is ≥5 we round up; < 5 we keep the same

so, our answer is 5.7 cm

hope this helps!! have a lovely day :)

Using a piece-wise function, the representation of the graph is given as follows:

Walking uphill for 3 hours and downhill for 1 hour.

A piece-wise function is a function that has multiple definitions, depending on the input.

In this problem, we have that:

Hence the meaning of the graph is:

Walking uphill for 3 hours and downhill for 1 hour.

More can be learned about piece-wise functions at https://brainly.com/question/27262465

#SPJ1

the answer is

X=5

y=3

hope you like it

The probability that a person wins the game is 32.1%

Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.

Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:

= 24 + 4 = 28

The frequency table will be such that 28 or more has a relative frequency of 9. Therefore, the probability that a person wins the game will be:

= 9/28 = 32.1%

When you win 25% of the time, this illustrates that the number of products picked will be:

= 25% × 28

= 7 products.

The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:

= 1/6⁴

= 1/1296

Learn more about probability on:

https://brainly.com/question/24756209

#SPJ1