Find the value of x in the given diagram.​

The equation of the line through (3,-5) and perpendicular to -3x + 2y = 12 in slope-intercept form is y =  -2/3x + 1

The equation of a line is expressed as;

y = mx + b

m is the slope

b is the y-intercept

Given the equation -3x + 2y = 12

2y = 3x + 12

y = 3/2x + 6

From the equation, the slope that is perpendicular to the slope is -2/3

Determine the equation

y-(-5) = -2/3(x-3)

y+5 = -2/3x + 6

y =  -2/3x + 6 - 5

y =  -2/3x + 1

Hence the equation of the line through (3,-5) and perpendicular to -3x + 2y = 12 in slope-intercept form is y =  -2/3x + 1

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Answer:

20

Step-by-step explanation:

Answer: C(-6.125,-4.125)

Step-by-step explanation:

[tex]\displaystyle\\A(-8,-6)\ \ \ \ B(-3,-1)\\Let\ \frac{3}{5}=\lambda \\Hence,\\\boxed {x_C=\frac{x_1+x_2\lambda}{1+\lambda} }\ \ \ \ \ \ \boxed {y_C=\frac{y_1+y_2\lambda}{1+\lambda} }\\\\x_1=-8\ \ \ \ x_2=-3\\\lambda=\frac{3}{5} \\\\\lambda=\frac{0.6*5}{5}\\\\\lambda=0.6\\\\x_C=\frac{-8+(-3)*0.6}{1+0.6} \\\\x_C=\frac{-8-1.8}{1.6} \\\\x_C=\frac{-9.8}{1.6} \\\\x_C=-\frac{9.8*10}{1.6*10} \\\\x_C=-\frac{98}{16} \\\\x_C=-6.125\\\\\\[/tex]

[tex]\displaystyle\\y_1=-6\ \ \ \ y_2=-1\ \ \ \ \lambda=0.6\\\\y_C=\frac{-6+(-1)*0.6}{1+0.6} \\\\y_C=\frac{-6-0.6}{1.6}\\\\y_C=\frac{-6.6}{1.6} \\\\y_C=-\frac{6.6*10}{1.6*10} \\\\y_C=-\frac{66}{16} \\\\y_C=-4.125[/tex]

[tex]Thus,\ C(-6.125,-4.125)[/tex]

Answer:

C

Step-by-step explanation:

hduodoydiyd9ydiydoyeykdoyx95eeykyei6djj

Step-by-step explanation:

a) 5

The area of the shaded region is 294.4 square meters

The given parameters are represented on the figure

By this;

The area of the shaded region is the sum of the area of the major sector and the area of the triangle

The area of the major sector is

A1= ∅/360 * πr²

The area of the triangle is

A2 = 0.5r²sin(x)

So, the total area is

Total = ∅/360 * πr² + 0.5r²sin(x)

This gives

Total = (360 - 130)/360 * 3.14 * 11.1^2 + 0.5 * 11.1^2 * sin(130 deg)

Evaluate

Total = 294.4

Hence, the area of the shaded region is 294.4 square meters

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Answer:thr lerrkmaf

Step-by-step explanation:

and we are so cool DEA

Answer:

c between 30 and 40 mins

Step-by-step explanation:

if you look at the graph that's the only line going down.

Answer:

82 cents per ounce

Step-by-step explanation:

There are 8 oz in a cup so two cups = 16 ounces

$6 .56 / 8 oz =  $ .82 / oz

In linear equation the solution set of the equations x = 1/2, y = -3.

What in mathematics is a linear equation?

Multiply both sides of the equation by a

coefficient -  2(4x - 3y ) = 11 × 2

                     3 ( 10x + 2y ) = ( - 1 ) × 3

apply multiplicative distribution law

8x - 6y = 11 × 2

3( 10x + 2y ) = (-1) × 3

calculate the first terms

8x - 6y = 22

3( 10x + 2y ) = ( -1) × 3

remove the parentheses

8x - 6y = 22

30x + 6y = -3

add up the two equation

8x - 6y + ( 30x + 6y ) = 22 + ( -3)

remove parentheses  - 8x - 6y + 30x + 6y = 22 -3

cancel the unknown variables - 8x + 30x = 22 -3

combine like terms - 38x = 22 - 3

calculate the sum or difference - 38x = 19

reduce the greatest common factor on both

sides of equation - 2x = 1

divide both sides of the equation by the coefficient of variable - x = 1/2

substitute one unknown quantity into the elimination 8 * 1/2 - 6y = 22

reduce the expression to the lowest term 4-6y = 22

reduce the greatest common factor on both sides of the equation

2 - 3y = 11

Rearrange unknown terms to the left side of the equation - 2 - 3y = 11

calculate the sum or difference  -3y = 9

reduce the greatest common factor on both sides of the equation   -y = 3

divide both sides of the equation by the coefficient of variable   y = -3

the solution set of the equations

x = 1/2

y = -3

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Answer:

28

Step-by-step explanation:

By the angle addition postulate,

[tex]54=\frac{1}{2}x+22+\frac{1}{4}x+11 \\ \\ 54=\frac{3}{4}x+33 \\ \\ 21=\frac{3}{4}x \\ \\ x=28[/tex]

Using a system of equations, it is found that there are 204 boys at the school.

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are given as follows, considering the situation described:

The average of the number of boys, girls, male teachers, and female teachers is 117, hence:

(x + y + z + w)/4 = 117

x + y + z + w = 468.

The average of the number of boys, girls, and male teachers is 151, hence:

(x + y + z)/3 = 151

x + y + z = 453.

Then:

x + y + z + w = 468.

453 + w = 468

w = 15.

There are 6 fewer male teachers than there are female teachers, hence:

z = w - 6 = 15 - 6 = 9.

So:

x + y + z = 453.

x + y = 444.

The number of female teachers is 1/16 the number of girls, hence:

There are 204 boys at the school.

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Answer:

2,739 and 2,489

Step-by-step explanation:

There are many solutions to both problems:

(Rules)
If the number is 5 or higher round (up)
If the number is 4 or lower round (down)

2,739⇒3,000
  ↑↑↑
  Higher than 500 so round up to get 3,000

2,489⇒2,500
    ↑↑
    Higher than 50 so round up to get 2500

2,739 and 2500 are both possible solutions.

Answer: 150, 4/2, 0.5/2

Step-by-step explanation:

The value of the expression (12 - 3/5√25)^2 + (2 - 4)^2 is 85

The expression is given as

(12 - 3/5√25)^2 + (2 - 4)^2

Evaluate the square root of 25

So, we have

(12 - 3/5√25)^2 + (2 - 4)^2 = (12 - 3/5 * 5)^2 + (2 - 4)^2

Evaluate the product

So, we have

(12 - 3/5√25)^2 + (2 - 4)^2 = (12 - 3)^2 + (2 - 4)^2

Evaluate the difference

So, we have

(12 - 3/5√25)^2 + (2 - 4)^2 = 9^2 + (2 - 4)^2

Evaluate the exponent and the sum

So, we have

(12 - 3/5√25)^2 + (2 - 4)^2 = 85

Hence, the value of the expression (12 - 3/5√25)^2 + (2 - 4)^2 is 85

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Answer Im thinking 7 but i don't know for sure

Step-by-step explanation:

The Perimeter of the quadrilateral = 16.93 units

The perimeter of the quadrilateral with the given vertices is the sum of the distance between every vertices.

Calculate the distance between the vertices using the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Name the vertices as shown below:

A(1,4)

B(-1,-2)

C(2,0)

D(4,0)

Distance between A and B:

AB = √[(−1−1)² + (−2−4)²]

AB = √(4 +36)

AB = 6.32 units

Distance between B and C:

BC = √[(−1−2)² + (−2−0)²]

BC = 3.61 units

Distance between C and D:

CD = √[(4−2)² + (0−0)²]

CD = 2 units

Distance between A and D:

AD = √[(4−1)² + (0−4)²]

AD = 5 units.

Perimeter of the quadrilateral = AB + BC + CD + AD = 6.32 + 3.61 + 2 + 5

Perimeter of the quadrilateral = 16.93 units

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Answer:

-3/2

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (3 - (-6))/(-2 - 4)

slope = (3 + 6)/(-6) = 9/(-6)

slope = -3/2

Answer:

Step-by-step explanation: 3/-2

What is 10.0833333 as a fraction?

To write 10.0833333 as a fraction you have to write 10.0833333 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

10.0833333 = 10.0833333/1 = 100.833333/10 = 1008.33333/100 = 10083.3333/1000 = 100833.333/10000 = 1008333.33/100000 = 10083333.3/1000000 = 100833333/10000000

And finally we have:

10.0833333 as a fraction equals 100833333/10000000

Answer: -118

Step-by-step explanation:

49^((1)/(2))- 25^((3)/(2))=

49^(1/2) -25^(3/2)=

7-25^((2+1)/2)=

7-25^((2/2)+(1/2))=

7-25^(1+1/2)=

7-25^(1) *25^(1/2)=

7-(25*5)=

7-125=-118

Answer:

15 (x + 2\/5)^2 + 28\/5

Step-by-step explanation:

The number of medals won by team A is 15 medals while the number of medals won by Team B is 9 medals.

Team A won 3 more medals than two times the medals won by Team B.

If the number of medals won by team B is x, than;

Number of medals won by team A = 3 + 2x

Number of medals won by team B = x

Also, we are told that Team A won 9 more medals than Team B.

Thus;

(3 + 2x) = x + 9

2x - x = 9 - 3

x = 6

3 + 2x = 3 + 2(6) = 15 medals

Thus, we conclude that the number of medals won by team A is 15 medals while the number of medals won by Team B is 9 medals.

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Answer:

29282829939999999 and yea

The number of customers waiting in line at the bank over a 24-hour period is a discrete variable type.

A variable whose value is determined by counting is referred to as a discrete variable. examples: the number of pupils in attendance. how many red marbles are in the container. when triple coins are turned, the count of heads. The number of pupils, kids, the shoe size, and so forth are some typical examples of discrete data. A statistical variable is referred to as a discrete variable if it presupposes a finite collection of data and a countable number of values. Contrarily, a continuous variable is a quantitative variable that accepts an endless quantity of data and an uncountable number of values.

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Answer:

Step-by-step explanation:

2x+18=6y

2x=6y−18

(2x)/2=(6y−18)/2

x=3y−9

Answer:

Step-by-step explanation:

2x  +  18+− 18=6y  +  −18

2x  =  6y − 18

2x / 2= 6y −18 / 2

x  =  3y −9

The value of z = 2.25

Given that z is a standard normal random variable.

Now the area under a standard normal curve between two z -values gives the probability of z lying between these two z-values.

Given that the area to the right of z = 0.0122

That is probability that the standard normal random variable lies after z = 0.0122

Total probability = 1

Therefore half the area under the standard normal curve = 0.5

Therefore, 0.5 - 0.0122 = 0.4878

We will find the corresponding z-value for this probability value from the normal tables. This is because normal tables gives area between two standard normal variables.

The table value corresponding to 0.4878 = 2.25

Therefore, z -value = 2.25

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