1. Angelina received 10% off a $50 pair of shoes. How much did she save?

Answer:

The coordinates of the point C that minimizes AC + BC are (-20, 0) or (4, 0)

Step-by-step explanation:

The given coordinates of the points A and B are A(1, 6) and B(8, 8)

The location of the point C = The x-axis

Therefore;

The coordinates of the point C = (x, 0)

The length of the segment AC = √((1 - x)² + (6 - 0)²) = √((1 - x)² + 6²)

The length of the segment BC = √((8 - x)² + (8 - 0)²) = √((8 - x)² + 8²)

At minimum distance of AC + BC, we have;

d(√((1 - x)² + 6²) +√((8 - x)² + 8²))/dx = 0 = (1 - x) × 2 × (0.5 - 1)× (√((1 - x)² + 6²)^(0.5 - 1) + (8 - x) × 2 × (0.5 - 1)× √((8 - x)² + 8²)^(0.5 - 1)

∴ d(√((1 - x)² + 6²) +√((8 - x)² + 8²))/dx = 0 = -(1 - x)/√((1 - x)² + 6²) - (8 - x)/√((8 - x)² + 8²)

-(1 - x)/√((1 - x)² + 6²) = (8 - x)/√((8 - x)² + 8²)

(8 - x)·√((1 - x)² + 6²) = -(1 - x)·√((8 - x)² + 8²)

Squaring both sides gives;

(8 - x)²·((1 - x)² + 6²) = (1 - x)²·((8 - x)² + 8²)

Expanding, using an online tool, we get;

x⁴ - 18·x³ + 133·x² -720·x + 2368 = x⁴ - 18·x³ + 161·x² - 272·x + 128

Which gives;

(161 - 133)·x² - (272 - 720)·x + 128 - 2368 = 28·x² + 448·x - 2240 = 0

Dividing by 28 gives;

x² + 16·x - 80 = 0

(x + 20)·(x - 4) = 0

Therefore, x = -20 or x = 4

The coordinates of the point C that minimizes AC + BC are (-20, 0) or (4, 0)

The coordinates of a point is the position of the point, on the coordinate plane.

The point C that minimizes AC + BC are (-20, 0) and (4, 0)

The given parameters are:

[tex]\mathbf{A = (1,6)}[/tex]

[tex]\mathbf{B = (8,8)}[/tex]

From the question, we understand that point C is on the x-axis.

This means that:

[tex]\mathbf{C = (x,0)}[/tex]

Calculate segments AC and BC using the following distance formula

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

So, we have:

[tex]\mathbf{AC = \sqrt{(1 - x)^2 + (6 - 0)^2}}[/tex]

[tex]\mathbf{AC = \sqrt{(1 - x)^2 + 6^2}}[/tex]

[tex]\mathbf{BC = \sqrt{(8 - x)^2 + (8 -0)^2}}[/tex]

[tex]\mathbf{BC = \sqrt{(8 - x)^2 + 8 ^2}}[/tex]

Add both distance

[tex]\mathbf{AB + BC = \sqrt{(1 - x)^2 + 6^2} + \sqrt{(8 - x)^2 + 8^2}}[/tex]

Differentiate, to calculate the minimum distance

[tex]\mathbf{d' = (1 - x) \times 2 \times (0.5 - 1) \times ((1 - x)^2 + 6^2)^({0.5 - 1}) + (8 - x) \times 2 \times (0.5 - 1) \times ((8 - x)^2} + 8^2))}^{(0.5 - 1)} }[/tex]

Simplify

[tex]\mathbf{d' = -\frac{1 - x}{\sqrt{(1 - x)^2 + 6^2}}- \frac{8 - x}{\sqrt{(8 - x)^2 + 8^2}}}[/tex]

Set to 0

[tex]\mathbf{ -\frac{1 - x}{\sqrt{(1 - x)^2 + 6^2}} - \frac{8 - x}{\sqrt{(8 - x)^2 + 8^2}} = 0}[/tex]

Rewrite as:

[tex]\mathbf{ -\frac{1 - x}{\sqrt{(1 - x)^2 + 6^2}} = \frac{8 - x}{\sqrt{(8 - x)^2 + 8^2}} }[/tex]

Cross multiply

[tex]\mathbf{(8 - x) \times\sqrt{(1 - x)\² + 6\²} = -(1 - x) \times\sqrt{(8 - x)\² + 8\²}}[/tex]

Square both sides

[tex]\mathbf{(8 - x)^2 \times (1 - x)\² + 6\² = (-(1 - x))^2 \times (8 - x)\² + 8\²}[/tex]

[tex]\mathbf{(8 - x)^2 \times (1 - x)\² + 6\² = (1 - x)^2 \times (8 - x)\² + 8\²}[/tex]

Expand

[tex]\mathbf{x^4 - 18x^3 + 133x^2 -720x + 2368 = x^4 - 18x^3 + 161x^2 - 272x + 128}[/tex]

Evaluate like terms

[tex]\mathbf{133x^2 -720x + 2368 = 161x^2 - 272x + 128}[/tex]

Collect like terms

[tex]\mahbf{161x^2 - 133x^2 - 272x + 720x + 128 - 2368 = 0}[/tex]

[tex]\mathbf{28x^2 + 448x - 2240 = 0}[/tex]

Factor out 28

[tex]\mathbf{28(x^2 + 16x - 80) = 0}[/tex]

Divide through by 28

[tex]\mathbf{x^2 + 16x - 80 = 0}[/tex]

Expand

[tex]\mathbf{x^2 + 20x - 4x - 80 = 0}[/tex]

Factorize

[tex]\mathbf{x(x + 20) + 4(x + 20) = 0}[/tex]

Factor out x + 20

[tex]\mathbf{(x + 20)(x - 4) = 0}[/tex]

Solve for x

[tex]\mathbf{x =- 20\ or\ x = 4}[/tex]

Hence, the point C that minimizes AC + BC are (-20, 0) and (4, 0)

Read more about coordinate points a:

https://brainly.com/question/18154638

Answer:

Q is -7

Step-by-step explanation:

Q×2+5=x

Q-2=x

Q=-7

Answer:

−16×5 / 5×11

= -16/11

Answer:

I is 1/2 Y is 1/2 in Z is a half

Answer:

3) B is congruent toE

Step-by-step explanation:

B is congruent to E helps you prove triangle ◇ABC is similar to ◇ DEF, not congruent to it.

Answer:

4 pounds of turkey

Step-by-step explanation:

Each person eats 2/6 pound of turkey

Multiply 2/6 by 12 because you have 12 people

Answer:

Im not 100% sure but i think these are the right answers

Step-by-step explanation:

∠2 = 82°

∠3 = 98°

∠4 = 82°

Answer:

-4x-1

Step-by-step explanation:

Perpendicular means opposite i think

Answer:

The slope would be -4 since perpendicular lines are lines that meet at a right angle

Answer:

liquid

Step-by-step explanation:

Answer:

approximately 56 cents

Step-by-step explanation:

4.5/8

Answer:

I dunno

Step-by-step explanation:

Answer:

(3x-8)

Step-by-step explanation:

6x^2-13x-8=(3x-8)(2x+1)

Thus, (3x-8) is one of the factors of the formula.

Answer: My favorite thing to do with my mom is either go shopping with her or cooking yummy desserts, like cookies, brownies, Etc...

The downside is that my mom get's really annoyed with me so i don't really go shopping especially with all this Coronavirus stuff going on.... And also what's your favorite thing to do with your mom???

Thank you so much!!! :D Stay safe and have a great day/night!!! :D

Complete question :

Sathish is going on a 2100-kilometer road trip with 2 friends, whom he will pick up 150 kilometers after he begins the trip and drop off when there are 150 kilometer remaining. The car consumes 6 liters of gas for every 100 kilometers, and gas costs $1.20 per liter.

Sathish will pay for all of the gas when he is alone in the car, but he and his friends will split the cost evenly when they are together.

How much will Sathish pay for gas?

Answer:

$64.8

Step-by-step explanation:

Given that :

Total length of trip = 2100 km

Length of journey with Satish alone in the car:

(150km) beginning + (150km) ending = 300km

Length of journey with Satish and 2 friends :

2100 km - 300 km = 1800 km

Gas consumption:

6 liters per 100km

Cost of gas = $1.2 / litre

Consumption when Satish is alone :

(6 litres /100 km) * 300km = 18 litres

Cost = $1.2 * 18 = $21.6

Consumption with his 2 friends :

(6 litres /100 km) * 1800 km = 10800 / 100 = 108 litres

Cost = $1.2 * 108 = $129.6

Since amount is shared equally :

Amount paid by sattish = $129.6 / 3 = $43.2

Hence, total amount paid by Sattish is :

$21.6 + $43.2

= $64.8

Answer:

64.80 or 64.8

Step-by-step explanation:

whatever works <333

Answer:

g

Step-by-step explanation:

Answer:

x=14

Step-by-step explanation:

create an equation out of it. 4x+2x-6=90. Or 6x=84

Answer:

A. y - 6 = ¼(x - (-2))

Step-by-step explanation:

Equation of a line can be represented in the point-slope form, y - b = m(x - a),

Where, (a, b) is a point that the line passes through, and m is the slope of the line.

The equation of line WX, is given in the slope-intercept form, y = mx + b. Which is y = ¼x + 4.

Thus, the slope (m) = ¼.

Since we know the value of m = ¼, and we have a point that the line runs through, (a, b) = (-2, 6), let's write the equation in point-slope form by substituting m = ¼, a = -2, and b = 6 into y - b = m(x - a).

We have:

y - 6 = ¼(x - (-2))

The answer is A

Answer:

Answer:y - 6 = - 4(x - (-2))

Step-by-step explanation:

Answer:

1223 ÷ 23 = 53.1739130435

Answer:

the answer to that, f= -5/3

Answer:

-41

Step-by-step explanation:

The change is -2

(-2*20)-1 = -41

Answer:

no

\

Step-by-step explanation:

Answer:

distributive property

Answer:

distributive prop.

Step-by-step explanation:

Answer:

3972.72 specimens

Step-by-step explanation:

We solve using the z score formula:

z = (x-μ)/σ where

x is the raw score = 73 cm

μ is the population mean = 147 cm

σ is the population standard deviation = 30 cm

N is the number of samples = 4000

For x > 73

z = 73 - 147/30

z = -2.46667

Probability value from Z-Table:

P(x<73) = 0.0068189

P(x>73) = 1 - P(x<73) = 0.99318

The probability of having a height greater than 73cm is: 0.99318

The number of specimens that have a height greater than 73cm is calculated as: 0.99318 × 4000

= 3972.72 specimens

Answer: C.x = 5

2x - 4 = 6

⇔ 2x = 10

⇔ x = 10/2 = 5

Step-by-step explanation:

Answer:

X = 4

Step-by-step explanation:

Given : Both the triangles are congruent.

And, LM = QR ;

Therefore,

=>. 2x + 11 = 3x - 9

By interchanging.....

=> 11 + 9 = 3x + 2x

=>. 20 = 5x

=> 4 = x

Or,

=> x = 4

Answer:

horizontal translation of 9 units right and 2 units up

Step-by-step explanation:

I think this is right.

Answer:

she has walked half of the journey

can i have brainliest please