What is the length of every median in an equilateral triangle whose side length is 5?

The equation for the plane through P₀ (-1, -7, 2) perpendicular to the following line. x = -1+t , y= -7-5t , z= -2t is x - 5y - 2z = 30

The plane is passing through point P₀(-1, -7, 2)

And the parametric equation of the line is:

x = -1+t , y= -7-5t , z= -2t

L: (-1, -7, -2) + t(1, -5, -2)

The required plane passes through P₀ and perpendicular to line L.

The direction vector of L is V = <1, -5, -2>.

The equation of a plane with normal vector <1, -5, -2> passing through a given point P(x₁, y₁, z₁) is

1(x - x₁) - 5(y - y₁) - 2(z - z₁) = 0

The equation of plane P passing through point P₀ (-1, -7, 2) is:

1(x - (-1)) - 5(y - (-7)) - 2(z - 2) = 0

(x + 1) - 5(y + 7) - 2(z - 2) = 0

x - 5y-2z + 1 - 35 + 4 = 0

x - 5y - 2z = 30 is the required equation of the plane

Learn more about the equation of the plane here:

brainly.com/question/27190150

#SPJ4

The complete question is:

Find the equation for the plane through P₀ (-1, -7, 2) perpendicular to the following line. x = -1+t , y= -7-5t , z= -2t

Dupes's age is 14 year and Olu's age is 11 year now.

What is linear algebraic equations?

Unknown quantities can often be determined using linear algebra. Among linear algebra's practical uses are the following: to calculate time, distance, or speed. used by linear maps to translate a three-dimensional image into a two-dimensional plane.

Mathematical structures that can be closed under addition and scalar multiplication are the focus of this area of study, which also encompasses the theory of linear equation systems, matrices, determinants, vector spaces, and linear transformations.

Assume that Dupe is x years old and Olu is y. We may create two linear algebraic equations using the given data:

x + y = 25

(x - 8) = 2(y - 8)

This system of linear equations can be transformed into the following by using a little algebraic trickery:

x + y = 25

x - 2y = -8

To obtain x = 14 and y = 11, construct an augmented matrix and use either Gaussian elimination or Gauss-Jordan elimination.

Learn more about linear algebraic equations click here:

https://brainly.com/question/12788590

#SPJ1

Answer: There are a few different ways to approach this problem, but one common method is to use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, we want to find the probability of at least one psychologist being chosen, which is the same as 1 minus the probability of no psychologists being chosen.

To find the probability of no psychologists being chosen, we first need to calculate the total number of ways to choose 3 people from a group of 54, which is:

54 choose 3 = 54! / (3! * 51!) = 19,958

Then we need to find the number of ways to choose 3 psychiatrists from a group of 24, which is:

24 choose 3 = 24! / (3! * 21!) = 1,344

Now, we can use these values to calculate the probability of no psychologists being chosen:

P(no psychologists) = (24 choose 3) / (54 choose 3) = 1,344 / 19,958 = 0.067 or 6.7%

Finally, we can use the complement rule to find the probability of at least one psychologist being chosen:

P(at least one psychologist) = 1 - P(no psychologists) = 1 - 0.067 = 0.93 or 93%

So the probability that at least one psychologist is chosen from the conference is 93%

Step-by-step explanation:

Answer:

18 cups but each gallon = 16 cups. so 1.125 gallons

Step-by-step explanation:

ratio = 1/3 salt :1 water = 1 salt : 3 water

so 6 salt :18 water

The graph of the function is added as an attachment and the function values are y = 4 for all x values

From the question, we have the following parameters that can be used in our computation:

y=1-3sin(3/2)Theta

Express properly

So, we have the following representation

y = 1 - 3sin(3/2π)

Next, we create a plot of the graph (see attachment)

From the graph, we can see that the function is a horizontal line at y = 4

This means that for all x values, the y value is constant at 4

Read more about function at

https://brainly.com/question/28532394

#SPJ1

By using linear equations, The winning team scored 3 less 3s than the losing team.

What are linear equations?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

For winning team

let x=no. of 2s and y=no. of 3s

Therefore, these linear equations will be formed

x+y=50

2x+3y=114

After solving these we get x=36 and y=14

For losing team

let a=no. of 2s and b=no. of 3s

Therefore, these linear equations will be formed

a+b= 48

2a+3b=113

After solving these we get a=31 and b=17

Difference between 3s scored=17-14

Difference between 3s scored=3

To know more about linear equations visit the link

brainly.com/question/29739212?referrer=searchResults

#SPJ1

Answer:

30/20 = 6/4 = 2/3 (I hope this makes sense)

Step-by-step explanation:

U are dividing by LCM

The row percentage of A is 0% , B is 83.3% and of C is 15.4%.

Percentage describes the relative value of a number. Its shows the 100th part of the number with respect to a number whose value is provided in the problem.

Here various data is given about A, B and C in the format of two tables and this shows the relationship between the two.

Now, the row  percentage of A is

[tex]\frac{0}{5} * 100=0%[/tex]%

Then, the row percentage of B is

[tex]\frac{10}{12}*100 = 83.3%[/tex]%

Now, we have to find the row percentage of C

[tex]\frac{2}{13}*100 = 15.4%[/tex].%

Hence, The row percentage of A is 0, the row percentage of B is 83.3% and the row percentage of C is 15.5%.

To Learn more about the percentage visit: https://brainly.com/question/29306119

#SPJ4

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 7900\\ r=rate\to 2.3\%\to \frac{2.3}{100}\dotfill &0.023\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 7900\left(1+\frac{0.023}{1}\right)^{1\cdot 5} \implies A=7900(1.023)^5\implies A \approx 8851.26[/tex]

Taylan sold 3 wooden frames and 5 plastic frames. the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation

Given: Taylan sold 7 total frames, with the number of plastic frames being less than twice the number of wooden frames

Let x = number of wooden frames

Since the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation to represent this:

x + (x * 2) < 7

2x < 7

x < 7/2

x = 3

Therefore, Taylan sold 3 wooden frames and 5 plastic frames.

Taylan sold 3 wooden frames and 5 plastic frames. the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation

Learn more about inequality here

https://brainly.com/question/28823603

#SPJ4

The value of x and y is -10 and 5 respectively in the given equations.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The first linear equation is - x + 3y = 5

The second linear equation is - -3x - 2y = 20

On evaluating individually the equation obtained is -

-3x - 2y + x + 3y = 20 + 5

-2x + y = 25

Multiply equation (1) with 3 -

3(x + 3y) = 5 × 3

3x + 9y = 15.....(3)

Adding equation (3) and (2) -

-3x - 2y + (3x + 9y) = 20 + 15

-3x - 2y + 3x + 9y = 35

-2y + 9y = 35

7y = 35

y = 35/7

y = 5

Substituting the value of y in equation (1) -

x + 3y = 5

x + 3(5) = 5

x + 15 = 5

x = 5 - 15

x = -10

Therefore, the value of x and y is -10 and 5 respectively.

To learn more about linear equation from the given link

brainly.com/question/2226590

#SPJ1

Hey Mate,

Answer is (4,3),

Thank you .

The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50 .

The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50.

1. Calculate the price of a Deluxe room for check-in on Sunday until Thursday:

$223 / 1.70 = $131.18

2. Calculate the price of a Deluxe room for check-in on Friday and Saturday:

$131.18 x 1.25 = $163.98

3. Calculate the price of a Suite room for check-in on Friday and Saturday:

$163.98 x 1.70 = $278.50

The price per night for a Suite room for check-in on Friday and Saturday would be $278.50.

Learn more about amount here

https://brainly.com/question/8082054

#SPJ4

The zeros of this polynomial are (1, 0), (2, 0), and (0, 4).

The zeros of the polynomial can be determined by setting the equation equal to zero and solving for the roots.

For example, if the polynomial is given as [tex]ax^{2}[/tex] + bx + c, then the zeros can be determined by solving the equation [tex]ax^{2}[/tex] + bx + c=0.

Step 1: To determine the zeros of the polynomial, set the polynomial equal to 0 and solve for x.

f(x) = [tex]x^{3}[/tex] - [tex]3x^{2}[/tex] + 4 = 0

Step 2: Factor the polynomial to solve for x.

[tex]x^{3}[/tex] - [tex]3x^{2}[/tex] + 4 = 0

x([tex]x^{2}[/tex] - 3x + 4) = 0

Step 3: Factor the quadratic equation.

x(x - 1)(x - 2) = 0

Step 4: Set each factor equal to 0 and solve for x.

x = 0, x = 1, x = 2

Step 5: Plug each x-value into the original equation to determine the corresponding y-value for each zero.

When x = 0, y = 4

When x = 1, y = 0

When x = 2, y = 0

Step 6: The coordinate points of the zeros are (1, 0), (2, 0), and (0, 4).

To learn more about polynomial, visit

brainly.com/question/11536910

#SPJ1

The y-intercept of function f is 1.

f(x) = -3x -2 , -∞ < x < -2 = -x + 1, -2 ≤ x < 3  = 2x + 5, 3 ≤ x < ∞

For y-intercept, x =0, f(x) = -x + 1                   [∵ -2 < 0 < 3]

f(0) = -0 + 1 = 1

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet.

This relationship is commonly symbolized as y = f(x)—which is said “f of x”—and y and x are related such that for every x, there is a unique value of y. That is, f(x) can not have more than one value for the same x. To use the language of set theory, a function relates an element x to an element f(x) in another set.

To learn more about function refer to:

brainly.com/question/11624077

#SPJ1

if x=4, the value of  the expression x^2+2x is 24

An algebraic expression can be described as a mathematical expression comprising of variables, terms, coefficients, factors and constants.

Algebraic expressions are also known to comprise of some mathematical or arithmetic operations, such as;

From the information given, we have the expression as;

x² + 2x

For the value of x = 4, substitute the value of x as 4 in the expression, we get;

(4)² + 2(4)

find the square, we have

16 + 2(4)

expand the bracket

16 + 8

add the values

24

Thus, the value is 24

Learn more about algebraic expressions on:

https://brainly.com/question/4344214

#SPJ1

The polynomial function that has the zeros 3 and 4 - 5i is P(x) = (x - 3)((x - 4)^2 + 25)

From the question, we have the following parameters that can be used in our computation:

zeros 3 and 4 - 5i

The polynomial is represented as

P(x) = (x - zeros)

So, we have

P(x) = (x - 3)(x - (4 - 5i))(x - (4 + 5i))

Expand

So, we have

P(x) = (x - 3)((x - 4)^2 + 25)

Hence, the polynomial is P(x) = (x - 3)((x - 4)^2 + 25)

Read more about polynomial at

https://brainly.com/question/7693326

#SPJ1

Triangle ABC is similar to triangle FGH.

And the value of the x is  22.5 centimeters.

Those triangles that looks the same but different in sizes.

And in the similar triangle,

the corresponding sides in proportion to each other and corresponding angles are equal to each other.

Given:

Triangle ABC is similar to triangle FGH.

That means, the corresponding sides of the triangles are in proportion to each other.

That means,

13.5/9 = 18/12 = x/15

Now,

18/12 = x/15

x = 270/12

x =22.5 centimeters

Therefore, the value of the x is 22.5 centimeters.

To learn more about the similar triangle;

https://brainly.com/question/14926756

#SPJ1

Answer:

13.99 + 5.75 + 3.29 + 7.35 = 30.38

30.38 - .65 - 3.00 = 26.73

Step-by-step explanation:

Hope this helps! =D

Answer:

$26.73

Step-by-step explanation:

razor = $13.99 - $3.00(rebate) = $10.99

refill pack of razor blades = $5.75

shaving cream = $3.29 - $0.65(coupon) = $2.64

lotion = $7.35

The inequality in standard form that describes this situation is  10x + 57y < 999.

This refers to the relationship between two values that are not of the same value.

Solving the inequality, we have:

Let x be the number of b=racelets that can be made and y be the number of necklaces that can be made. The inequality in standard form that describes the situation is:

x = the number of bracelets

y = the number of necklaces

Number of beads / bracelets =10

Number of necklaces = 57

10x + 57y < 999.

Learn more about inequality on

https://brainly.com/question/30310292

#SPJ1

Considering the figure the side length x is solved to be 6.6

Information given from the question is interpreted as

√11 = adjacent

x = hypotenuse

The side x  is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The side x is calculated using cos, CAH

cos 60 = Adjacent / hypotenuse

cos 60 = √11  / x

x =  √11  / cos 60

x = 6.633

x = 6.6 to the nearest tenth

Learn more about SOH CAH TOA here:

https://brainly.com/question/29402966

#SPJ1

The decrease in Kaitlin's investment account is 7%, which is calculated by multiplying the initial $5200 by 0.07.

This gives a decrease of $364. The amount in her account at the end of the year is the initial $5200 minus the decrease of $364, which equals $4836.

This can be expressed algebraically as:

Let x = amount in Kaitlin's account at the end of the year

Initial Amount (x) = 5200

Decrease (%) = 0.07

Decrease in Dollars = x * 0.07

Decrease in Dollars = 5200 * 0.07

Decrease in Dollars = 364

Amount in Account at the End of the Year = 5200 - 364

Amount in Account at the End of the Year = 4836

Learn more about amount here:

https://brainly.com/question/8082054

#SPJ4

The answer is that the earthquake in Alaska was 1.5 times or 1000 times more intense than the one in Japan.

To learn more about ratio of amplitude refer:

brainly.com/question/3613222

#SPJ1

The expression to determine the distance between the lowest and the highest point is -

{x} = 14505 + |- 282|

Given is a diagram that shows several planes, lines, and points.

The correct statement with respect to line {h} is -

Line h has points on planes R, P, and T.

Therefore, line {h} has points on planes {R}, {P} and {T} is the correct alternative.

To solve more questions on planes, visit the link below -

brainly.com/question/1041084

#SPJ1

Answer: c. (5,2)

Step-by-step explanation:  We have two equations here and need to calculate the value of x and y.

The two equations are:

2x+5y = 20

3x - 4y = 7

Using the Substitution method,

2x=20-5y

x=(20-5y)/2

Now substitute the value of x in equation (2)

3 × [tex]\frac{20-5y}{2} - 4y = 7[/tex]

60-15y-8y = 14

60-23y=14

-23y = -46

y=2

Now put the value of y in any equation.

x = (20-10)/2

x=5          

Read more about it:

https://brainly.com/question/11661554

Answer:

B) Horizontal Asymptote

A horizontal asymptote is a horizontal line that the graph of a function approaches as the input values get larger or smaller. The end behavior of a rational function is determined by the degree of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the function will approach a horizontal asymptote as the x-values get larger or smaller. If the degree of the numerator is greater than the degree of the denominator, the function will not have a horizontal asymptote.

The number of centimetres in the 1 yard will be 9.144 cm.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Given that:-

Metric System Units

1 inch = 2.54 centimetres

1 foot = 0.3048 meters

1 mile = 1.61 kilometres

1 yard = 3 feet

1 yard = 36 inches

First, we will calculate 1 yard to feet.

1 yard = 3 feet

1 feet = 0.3048 meters

1 feet = 3.048 centimeters

1 yard = 3 x 3.048 centimeters

1 yard = 9.144 centimeters

Hence, the length of 1 yard in cm is 9.144 cm.

To know more about unit conversion follow

https://brainly.com/question/28308386

#SPJ1

The end behavior of the radical function represented by this graph is option C. As x decreases in value, f ⁡ ( x ) increases in value. As x increases in value, f ⁡ ( x ) decreases in value.

A radical function is a type of mathematical function that includes a radical symbol, such as a square root sign (√) or cube root sign (3√), in its equation.

The graph of a radical function is a curve that may open upward or downward, depending on the specific function. For example, the graph of the square root function, y = √x, starts at the point (0,0) and extends upward and to the right, creating a "V" shape. As the input (x) increases, the output (y) also increases, but at a decreasing rate.

Therefore, the correct answer is as given above

learn more about functions: https://brainly.com/question/10439235

#SPJ1

Answer:

The answer is 685 km hopefully I understood your question and helped you ☻

Step-by-step explanation:

710 km - 25 = 685