Write in exponential form
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The distance between two points on the coordinate geometry is [tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex].

From the attachment, we have:

[tex]A = (20,35)[/tex] --- Arthur

[tex]J = (45,20)[/tex] -- Jamie

[tex]C = (65,40)[/tex] --- Cameron

The distance between Arthur and Cameron is:

[tex]AC = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

So, we have:

[tex]AC = \sqrt{(20- 65)^2 + (35 - 40)^2}[/tex]

[tex]AC = \sqrt{2050}[/tex]

[tex]AC = 45.3m[/tex]

Hence, the distance between Arthur and Cameron is 45.3 m

To determine the closest to Cameron, we simply calculate the distance between Cameron and Jamie

[tex]CJ = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

So, we have:

[tex]CJ = \sqrt{(45 - 65)^2 + (20 -40)^2}[/tex]

[tex]CJ = \sqrt{800}[/tex]

[tex]CJ = 28.3m[/tex]

By comparison, 28.3 m is less than 45.3 m.

Hence, Jamie is closer to Cameron than Arthur

Also, we have:

[tex]S=(35,60)[/tex]

To determine the closest to the soccer ball, we simply calculate the distance between each person and the ball using:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

So, we have:

[tex]AS = \sqrt{(20 - 35)^2 + (35 - 60)^2} = \sqrt{850} =29.2[/tex] --- Arthur

[tex]JS = \sqrt{(45 - 35)^2 + (20 - 60)^2} = \sqrt{1700} =41.2[/tex]  --- Jamie

[tex]CS = \sqrt{(65 - 35)^2 + (40 - 60)^2} = \sqrt{1300} =36.1[/tex] --- Cameron

By comparing the calculated values, 29,2 is the smallest.

Hence, Arthur is the closest to the soccer ball

Read more about distance at:

https://brainly.com/question/17207276

Answer:

4+7(11)

Step-by-step explanation:

the square root of 121 is 11 so it would be 4+7(11)

Answer:

4 + 7 × 11

Step-by-step explanation:

[tex]4 + 7 \sqrt{ {5}^{3} - 4} [/tex]

[tex] = 4 + 7 \sqrt{125 - 4} [/tex]

[tex] = 4 + 7 \sqrt{121} [/tex]

simplify the square root of 121

[tex] \boxed{\green{\boxed{\bold{= 4 + 7 \times 11}}}}[/tex]

[tex] = 4 + 77[/tex]

[tex] = 81[/tex]

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★ . ꜝꜞ ᳝ ࣪ hope that helped!  ʬʬ

Answer:

[tex] \sqrt{45 {x}^{2} } + \sqrt{5 {x}^{2} } + 4x \sqrt{5} \\ = 3 \sqrt{5} x + \sqrt{5} x + 4x \sqrt{5} \\ = 8x \sqrt{5} \\ thank \: you[/tex]

Answer:0.95833333333333.

Step-by-step explanation:

Which decimal is equal to the following fraction?

Answer: 0.95833333333333

Answer:

2.5

Step-by-step explanation:

Answer:

[tex]thank \: you[/tex]

Answer:

The 1st term is -67

Step-by-step explanation:

I. When Sn = [tex]\frac{n}{2}[/tex]([tex]a_{1} + a_{n}[/tex])

   If  Sn = 124, n = 8 and [tex]a_{n}[/tex] = 98

                124 = 8/2(a + 98)

                124 = 4(a + 98)

                124 = 4a + 392

                124 - 392 = 4a

                -268/4 = a

                -67 = [tex]a_{1}[/tex]

Hope that help :D

Answer: FH = 16

Concept:

Bisect means to cut or divide something into two equal parts.

In mathematics, usually bisect means cutting a segment or an angle.

If you are still confused, you may refer to the attachment below for a graphical explanation or tell me.

Solve:

Given information

FG is 16 less than 3 times the length of GH

Let x be the length of GH

Given expression

FG = GH

Set equation

3x - 16 = x

Add 16 on both sides

3x - 16 + 16 = x + 16

3x = x + 16

Subtract x on both sides

3x - x = x + 16 - x

2x = 16

Divide 2 on both sides

2x / 2 = 16 / 2

x=8

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Concept:

In order to find the length of FH, we need to know the idea of the segment addition postulate.

The Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.

Solve:

Given information

FG = GH = x

x = 8

Given expression deducted from the segment addition postulate

FH = FG + GH

Substitute values into the expression

FH = x + x

FH = 8 + 8

[tex]\boxed {FH=16}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

2000 J

Step-by-step explanation:

We know that

KE = ½ mv²

KE = ½ × 10 × (20)²

KE = 5 × 400

KE = 2000 J

Now we have to,

find the required kinetic energy.

The formula we use,

→ KE = 1/2 mv²

The given information is,

→ Mass (m) = 10 kg

→ Velocity (v) = 20 m/s

Let's find the kinetic energy,

→ 1/2 mv²

→ 1/2 × 10 × (20)²

→ 5 x 400

→ [2000 J]

Thus, kinetic energy is 2000 J.

Answer:

n= -2

Step-by-step explanation:

3(4n+5)=-7n-23

expand brackets

12n + 15 =-7n-23

collect like terms

12n + 7n= -23-15

19n= -38

dividing throughout by 19

19n/19=-38/19

n= -2

Answer:

n = -2

Step-by-step explanation:

3(4n+5)= -7n -23

Distribute the 3,

12n + 15 = -7n -23

subtract 15 from both sides,

12n = -7n -38

add 7n to both sides,

12n + 7n = -38

simplify,

19n = -38

divide both sides by 19,

n = -2

Answer:

Distribute 2 to (x + 6) and 3 to (x – 4).

Step-by-step explanation:

While solving for:

2(x+6) = 3(x-4) + 5

Firstly, we need to open the parenthesis. For this, we've to distribute 2 to (x+6) and 3 to (x-4).

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

same as we did for the other question,

5y=-x-20

then divide the 5

y= (-1/5)x-4

Answer:

Step-by-step explanation:

Given,

Area of a triangle = 40

Therefore,

Side of the square

[tex] = \sqrt{40} [/tex]

= 6.3245553203

= 6.3 (estimated) (Ans)

Answer:

∠1 = 56

Step-by-step explanation:

To find ∠1 we need to

∠1 + ∠2 = ∠ABD

∠1 + 17 = 75

∠1 = 75 -17

∠1 = 56

Answer:

I need more information

Step-by-step explanation:

Jfjdkdjdjdndkdknskdd

Answer:

6, 24, 30, 48, 66

1, 4, 5, 8, 11

Step-by-step explanation:

Just by the first column we know that the scale ratio is 6. To find the second one we will multiply (6 * 4 = 24). To find the third one we will divide (30 / 6 = 5). To find the fourth one we will mulyiply (8 * 6 = 48). To find the fifth one we will divide (66 / 6 = 11).

Best of Luck!

Answer:

48.2

Step-by-step explanation:

We have a right angle so we can do our three trig ratios,

Sine Cosine Tangent

Remeber SOHCAHTOA.

We are given some angle theta, and we are given a side adjacent to the angle and the hypotenuse. We are going to use the cosine rule.

[tex] \cos(theta) = \frac{36}{54} [/tex]

[tex] \cos(theta) = \frac{2}{3} [/tex]

Take the inverse of both sides

[tex] \cos {}^{ - 1} ( \frac{2}{3} ) = x[/tex]

Theta is equal to

[tex]48.2[/tex]

Answer:

CHEESE

Step-by-step explanation:

SKDMALSD

4 no. one i guess 10

not sure

Answer:

13 inches

Step-by-step explanation:

in an equilateral triangle all sides had we the same length.

so, the perimeter is simply 3×one triangle side.

and the perimeter of the square is 4×one square side.

x = triangle side length

y = square side length

3x = 4y + 15

x = y + 7

we use the second equation as substitution in the first equation.

3(y + 7) = 4y + 15

3y +21 = 4y + 15

6 = y

x = y + 7 = 6 + 7 = 13 inches

Answer:

832.42

Step-by-step explanation:

.12 per KWH x KWH = 99.89

KWH = 99.89/.12

KWH = 832.42 hours

Answer:

[tex]\frac{5+\sqrt{17}}{4}[/tex],      [tex]\frac{5-\sqrt{17}}{4}[/tex]

Step-by-step explanation:

One is asked to find the root of the following equation:

[tex]2x^2+1=5x[/tex]

Manipulate the equation such that it conforms to the standard form of a quadratic equation. The standard quadratic equation in the general format is as follows:

[tex]ax^2+bx+c=0[/tex]

Change the given equation using inverse operations,

[tex]2x^2+1=5x[/tex]

[tex]2x^2-5x+1=0[/tex]

The quadratic formula is a method that can be used to find the roots of a quadratic equation. Graphically speaking, the roots of a quadratic equation are where the graph of the quadratic equation intersects the x-axis. The quadratic formula uses the coefficients of the terms in the quadratic equation to find the values at which the graph of the equation intersects the x-axis. The quadratic formula, in the general format, is as follows:

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

Please note that the terms used in the general equation of the quadratic formula correspond to the coefficients of the terms in the general format of the quadratic equation. Substitute the coefficients of the terms in the given problem into the quadratic formula,

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

[tex]\frac{-(-5)(+-)\sqrt{(-5)^2-4(2)(1)}}{2(2)}[/tex]

Simplify,

[tex]\frac{-(-5)(+-)\sqrt{(-5)^2-4(2)(1)}}{2(2)}[/tex]

[tex]\frac{5(+-)\sqrt{25-8}}{4}[/tex]

[tex]\frac{5(+-)\sqrt{17}}{4}[/tex]

Rewrite,

[tex]\frac{5(+-)\sqrt{17}}{4}[/tex]

[tex]\frac{5+\sqrt{17}}{4}[/tex],      [tex]\frac{5-\sqrt{17}}{4}[/tex]

Answer:

FOIL stands for multiply the first, outside, inside, and last terms together. When you FOIL a binomial times itself, the product is called a perfect square. For example, (a + b)2 gives you the perfect-square trinomial a2 + 2ab + b2.

Step-by-step explanation:

Step-by-step explanation:

f(x) = |x-7| + 3

when x is equal to 4, then

f(4) = |4-7| + 3

=-3+3

=0

Answer:

[tex]\boxed {\boxed {\sf f(4)= 6}}[/tex]

Step-by-step explanation:

We are asked to find f(4) for a function. We are finding the output or y-value when the input or x-value is 4.

[tex]f(x)= |x-7| +3[/tex]

Substitute 4 for x in the function.

[tex]f(4) = |4-7| +3[/tex]

Solve inside the absolute value signs.

[tex]f(4)= |-3|+3[/tex]

The absolute value of a number is its distance from 0 on a number line.  It is always the positive version of a number, so the absolute value of -3 is 3.

[tex]f(4)= 3+3[/tex]

Add.

[tex]f(4)= 6[/tex]

For the function f(x)= |x-7| +3, f(4) is equal to 6.

Answer:

$624,000

Step-by-step explanation:

100-4 = 96

96/100 = 0.96

650,000 x 0.96 = 624,000

= $624,000

Answer:

11+x

Step-by-step explanation:

Let the number be x

11 more than the more will be

11+x

here is answer, hope u understand:)

Answer:

a = 1

Step-by-step explanation:

Adding 3 as x into the equation will give you 2(3) + y = 7.  3 x 2 = 6, so now the equation is 6 + y = 7.  

Now subtract 6 from both sides of the equation to get y by itself, so you'll have y = 1.

CHECK:

2(3) + 1 = 7

6 + 1 = 7

7 = 7 ⇆

Step-by-step explanation:

2x+y=7

2×3+y=7

6+y=7

y=7-6

y=1