find the perimeter of the quadrilateral. if x = 2 the perimeter is ___ inched.

The value of y is 3

Solving linear equation mean calculating the unknown variable from the equation.

Let the linear equation : y = mx + c

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

m → gradient of the line

( 0 , c ) → y - intercept

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

[tex]\large {\boxed {m = \frac{y_2 - y_1}{x_2 - x_1}} }[/tex]

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

[tex]\large {\boxed {y - y_1 = m ( x - x_1 )} }[/tex]

Let us tackle the problem.

Firstly , we will calculate the gradient of the line that passes through the point S( -5 , 0 ) and T( 5 , 2 ) .

[tex]m_{ST} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m_{ST} = \frac{2 - 0}{5 - (-5)}[/tex]

[tex]m_{ST} = \frac{2}{10}[/tex]

[tex]\large {\boxed {m_{ST} = \frac{1}{5} } }[/tex]

Next , we will calculate the gradient of the line that passes through the point V( 0 , -2 ) and W( -1 , y ) .

[tex]m_{VW} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m_{VW} = \frac{y - (-2)}{-1 - 0}[/tex]

[tex]\large {\boxed {m_{VW} = \frac{y + 2}{-1} } }[/tex]

The conditions of the line perpendicular to each other will satisfy the following formula.

[tex]m_{ST} \times m_{VW} = -1[/tex]

[tex]\frac{1}{5} \times \frac{y + 2}{-1} = -1[/tex]

[tex]\frac{y + 2}{-5} = -1[/tex]

[tex]y + 2 = -5 \times -1[/tex]

[tex]y + 2 = 5[/tex]

[tex]y = 5 - 2[/tex]

[tex]\large {\boxed {y = 3} }[/tex]

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point

The opposite sides of a parallelogram can be proved congruent by joining the diagonal of the parallelogram and proving the two triangles congruent by ASA .In any parallelogram opposite sides are parallel.We prove the triangles to be congruent by taking the property of parallel lines that  Alternate interior angles are congruent.

When the triangles are proved congruent the opposite sides of parallelogram can be proved equal by using the property Corresponding parts of congruent triangles are congruent.,

The options which hold true to prove opposite sides of a parallelogram are congruent are options C and D.

C. Alternate interior angles are congruent.

D. Corresponding parts of congruent triangles are congruent.,

D) T(x,y) = (x, y - 2); The transformation slides the original image a given distance in a given direction. Is the CORRECT answer

The law that will be used to simplify the expression is the law of exponents.

Exponents are the powers of the base numbers.

The law of exponents will be used to simplify the expression (x⁴)⁹

According to the law of exponents,

(aⁿ )ˣ = [tex]\rm a^{xn}[/tex]

So,

(x⁴)⁹ = x³⁶

Therefore, the law that will be used to simplify the expression is the law of exponents.

To know more about Exponents

https://brainly.com/question/15993626

#SPJ2

Answer:

Perimeter  = 42 inches

Explanation:

The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all the four sides. In case of any diagram or figure, we add all the outer sides of the figure to get perimeter.

Here, outer sides are :

4, 4, 4, 4, 4, 4, 4, 6, 8

Now add all the sides together.

Permeter = 4 + 4 + 4 + 4 + 4 + 4 + 4 + 6 + 8 = 42 inches.

Final answer is 42 inches

Answer:

42 inches

Step-by-step explanation:

Answer:

The function of the graph is y = f(x) = x².

Step-by-step explanation:

From the graph we have

At x = 0, y = 0

Therefore f(x) = ax + c where c = 0

At x = 1  y = 1

At x = 4 y = 2

At x = 9 y = 3

At x = 16 y = 4

Therefore the graph is of the form, y= f(x) = x²

That is the graph can be plotted  with a slope given by dy/dx = 2x an an intercept of c = 0.

Values of the graph are as follows

      x                       y

      1                        1

      2                     √2

      3                     √3

      4                       2

      5                      √5

      6                      √6

      7                      √7

      8                      2√2

      9                       3.

Answer:

Option A. [tex]4[/tex]

Step-by-step explanation:

we know that

The sum of a geometric series is equal to

[tex]Sum=a(\frac{1-r^{n}}{1-r})[/tex]

where

a is the first term

r is the common ratio

n is the number of terms

In this problem we have

[tex]a=2,r=0.5,n=16[/tex]

substitute the values

[tex]Sum=2(\frac{1-0.5^{16}}{1-0.5})=4[/tex]

Answer:

The solution set is [tex]x=-9[/tex]

Step-by-step explanation:

we have

[tex](x+9)(x+9)=0[/tex]

we know that

[tex](x+9)(x+9)=x^{2}+18x+81[/tex]

so

[tex]x^{2}+18x+81=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2}+18x+81=0[/tex]

so

[tex]a=1\\b=18\\c=81[/tex]

substitute in the formula

[tex]x=\frac{-18(+/-)\sqrt{18^{2}-4(1)(81)}} {2(1)}[/tex]

[tex]x=\frac{-18(+/-)\sqrt{0}} {2}[/tex]

The radicand is equal to zero, therefore, the solution has only one real solution

[tex]x=\frac{-18} {2}=-9[/tex]

The answer will be 27/35

Probability is the number of outcomes out of total outcomes present or  the extent to which something is likely to happen. In the given problem there are two dices which means there are total 36 outcomes because each dice has 6 sides. So the probability of the given case will be

Probability of getting two doubles on both dice = 1/36

Probability of getting just one double = 5/36

Similarly

Probability of getting no doubles on both dice is = 5/6.  

So in order to find the probability we add the products of the probabilities and solve:

12/36 + 5*(3-x)/36 - 5*x/6 = 0

x = 27/35

Which simply means the player should lose 27/35 points for not rolling a double.

The volume of one paper cone if the diameter is 4 inches and the height, is 7 inches is equal to 29in³.

We have given that,

Mrs. McDonnell is making 25 paper cones to fill with popcorn for her daughter's birthday party.

The volume of one cone would be 29 in³.

The formula for the volume of a cone is V=(1/3)πr²h.  

Substituting our information we have:

V=(1/3)(3.14)(4/2)²(7)

We divide the diameter by 2 because the radius is half of the diameter.  This gives us:

V=1/3(3.14)(28)

V= 29.306

V≈ 29in³

Therefore the volume of one paper cone if the diameter is 4 inches and the height, is 7 inches is equal to 29in³.

To learn more about the volume visit:

https://brainly.com/question/1972490

#SPJ2

Answer:

The correct option is C. The image of N for a 144° counterclockwise rotation about the center is P.

Step-by-step explanation:

The number of vertices of a regular pentagon is 5.

The central angle between two consecutive vertices is

[tex]\frac{360}{5}=72[/tex]

It means the central angle between two consecutive vertices is 72 degrees.

We have to find the image of N for a 144° counterclockwise rotation about the center.

If pentagon rotates 72 degree counterclockwise rotation about the center, then the image of N is E.

If pentagon rotates (72+72) degree counterclockwise rotation about the center, then the image of N is P.

The image of N for a 144° counterclockwise rotation about the center is P.

Therefore the correct option is C.

The lengths of segments in the circle are determined by the tangent-secant theorem. Given RT = 9 inches and ST = 4 inches, we can use this theorem to find that TU will be approximately 8.06 inches.

In this complex geometry problem involving circles and tangents, there are several relationships at play. You're looking at a circle that has a secant, RT, and a tangent, TU, creating several segments within the figure.

(a) According to the tangent-secant theorem, the squared length of the tangent segment is equal to the difference in the squared lengths of the entire secant and its external part. This can be expressed mathematically as TU² = RT² - ST².

(b) We can use this theorem with the given lengths for RT and ST to find the length of TU. Plugging in, we get TU² = 9² - 4² = 65. The length of TU is the square root of this, which is approximately 8.06 inches.

https://brainly.com/question/33808128

#SPJ2

The number of sundaes they can serve with 7 cups of sprinkles is 56.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Matt's Ice Cream Shoppe has 7 cups of sprinkles to use on sundaes for the rest of the day.

Number of sundaes = Total quantity of sprinkles/Number of cups of sprinkles in each serving

= 7÷ 1/8

= 7×8

= 56

Therefore, the number of sundaes they can serve with 7 cups of sprinkles is 56.

To learn more about the unitary method visit:

brainly.com/question/22056199.

#SPJ3

Answer:

[All reals]............