The equations of four lines are given. Identify which lines are perpendicular.

Line 1: y=2
Line 2: y=15x−3
Line 3: x=−4
Line 4: y+1=−5(x+2)

Answer:

See explanation

Step-by-step explanation:

Maximum weight = 20 kg

Bag 1 = 3.5kg

Bag 2 = 15 kg

Bag 3 = 2kg

Bag 4 = 1.5kg

Total weight of bags = 22 kg

Excess weight of his luggage = Total weight of bags - Maximum weight

= 22 kg - 20 kg

= 2 kg

Express the excess weight as a percentage of his maximum weight allowed = excess weight / maximum weight × 100

= 2/20 × 100

= 0.1 × 100

= 10%

Express the excess weight as a percentage of his maximum weight allowed = 10%

Given:

The graph of a scatter plot.

To find:

The function that best fits the given points.

Solution:

From the given graph it is clear that the linear function is the best fit for the given points because the points lie on a straight line or near to it.

So, options B and C are incorrect because they represent exponential and quadratic function respectively.

Let as assume the two points on the graph are (0.80,-12.82) and (2,-12.79).

Using this two points, the equation of line is:

[tex]y-(-12.82)=\dfrac{-12.79-(-12.82)}{2-0.80}(x-0.80)[/tex]

[tex]y+12.82=\dfrac{-12.79+12.82}{2-0.80}(x-0.80)[/tex]

[tex]y+12.82=0.025(x-0.80)[/tex]

[tex]y+12.82=0.025x-0.02[/tex]

[tex]y=0.025x-0.02-12.82[/tex]

[tex]y=0.025x-12.84[/tex]

[tex]y=-12.84+0.025x[/tex]

It is the approximate function to the function that is in option A.

Therefore, the correct option is A.

Answer:

Step-by-step explanation:

1kg=1000

Answer:

WO [tex]\sqrt{13}\ \ \ \frac{3}{2}[/tex]

OR [tex]\sqrt{13}\ \ \ - \frac{3}{2}[/tex]

RM [tex]\sqrt{13}\ \ \ \frac{3}{2}[/tex]

MW [tex]\sqrt{13}\ \ \ - \frac{3}{2}[/tex]

Step-by-step explanation:

One has to find the slope, and the distance between the successive points on the plane. Use the slope and distance formula to achieve this.

Slope formula:

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

Distance formula:

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

Remember, the general format for the coordinates of a point on a Cartesian coordinate plane is the following:

[tex](x,y)[/tex]

1. WO

Coordinates of point (W): (3, -5)

Coordinates of point (O): (6, -3)

Find the slope:

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

[tex]\frac{(-5)-(-3)}{(3)-(6)}=\frac{-5+3}{3-6}=\frac{-2}{-3}=\frac{2}{3}[/tex]

Find the distance:

[tex]\sqrt{((-5)-(-3))^2+((3)-(6))^2}[/tex]

[tex]\sqrt{(-2)^2+(-3)^2}\\=\sqrt{4+9}\\=\sqrt{13}\\[/tex]

2. OR

Coordinates of point (O): (6, -3)

Coordinates of point (R): (4, 0)

Find the slope:

[tex]\frac{y_2-y_1}{x_2-x_1}\\=\frac{(0)-(-3)}{(4)-(6)}=\frac{3}{-2}=-\frac{3}{2}[/tex]

Find the distance:

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

[tex]\sqrt{((0)-(-3))^2+((4)-(6))^2}=\sqrt{(3)^2+(2)^2}=\sqrt{9+4}=\sqrt{13}[/tex]

3. RM

Coordinates of point (R): (4, 0)

Coordinates of point (M): (1, -2)

Find the slope:

[tex]\frac{y_2-y_1}{x_2-x_1}\\=\frac{(0)-(-2)}{(4)-(1)}=\frac{2}{3}[/tex]

Find the distance:

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

[tex]\sqrt{((-2)-(0))^2+((1)-(4))^2}=\sqrt{(-2)^2+(-3)^2}=\sqrt{4+9}=\sqrt{13}[/tex]

4. MW

Coordinates of point (M): (1, -2)

Coordinates of point (W): (3, -5)

Find the slope:

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

[tex]=\frac{(-5)-(-2)}{(3)-(1)}=\frac{-3}{2}=-\frac{3}{2}[/tex]

Find the distance:

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

[tex]=\sqrt{((3)-(1))^2+((-5)-(-2))^2}=\sqrt{(2)^2+(3)^2}=\sqrt{4+9}=\sqrt{13}[/tex]

Basically count/add up the total amount of degrees that are include in the angle <FHD.

-- (central angles)

So, 35 + 65 = 100 degrees

Answer:

$532

Step-by-step explanation:

We do 51,072 / 96 which is 532.

Each employee received $532.

Answer:

B option is your answer

Step-by-step explanation:

please mark as brainliest

Answer:

B. 4th root of 7

Step-by-step explanation:

denominator is the root. numerator is the exponent

Answer:

0 to 10

What is the constant of luck as shown in the graph

Answer:

x ≥ 54

Step-by-step explanation:

x+x-4 ≥ 104

2x ≥ 104 + 4

2x ≥ 108

x ≥ 54

Answer:

B

Step-by-step explanation:

Volume = Volume of cylinder + Volume of semi sphere

= pi*r^2*h+(2/3)*pi*r^3

=pi*(4*12+16/3)=pi*53.3

Answer:

there was a decrease of 2.25%

Step-by-step explanation:

Let me illustrate with an example

Assume the population is 100

percentage increase = 100 + 15 = 115% = 1.15%

Population after 15% increase = 100 x 1.15 = 115

Percentage decrease = 100 - 15 = 85% = 0.85

Population after 15% decreases 115 x 0.85 = 97.75

rate of increase = (97.75 / 100) - 1 = -2.25%

Answer:

Step-by-step explanation:

Volume of a cuboid = length × breadth × height

lenth = 7

Breadth = 10

Height = 9

7 x 10 x 9

= 630 yd^2

Answered by G a u t h m a t h

please mark it as brainliest and thank it, if it helped you!

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Explanation:

We'll use the distance formula here. Rather than compute the distance d based on two points given, we'll go in reverse to use the given distance d to find what the coordinate must be to satisfy the conditions.

We're given that d = 5

The first point is [tex](x_1,y_1) = (5,2)[/tex] and the second point has coordinates of [tex](x_2,y_2) = (x,5)[/tex] where x is some real number.

We'll plug all this into the distance formula and solve for x.

[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\5 = \sqrt{(5-x)^2+(2-5)^2}\\\\5 = \sqrt{(5-x)^2+(-3)^2}\\\\5 = \sqrt{(5-x)^2+9}\\\\\sqrt{(5-x)^2+9} = 5\\\\(5-x)^2+9 = 5^2\\\\(5-x)^2+9 = 25\\\\(5-x)^2 = 25-9\\\\(5-x)^2 = 16\\\\5-x = \pm\sqrt{16}\\\\5-x = 4 \ \text{ or } \ 5-x = -4\\\\-x = 4-5 \ \text{ or } \ -x = -4-5\\\\-x = -1 \ \text{ or } \ -x = -9\\\\x = 1 \ \text{ or } \ x = 9\\\\[/tex]

This means that if we had these three points

Then segments AB and AC are each 5 units long.

Answer:

The answers are all bolded below. If you can, please read the explanation so you can pass a test if asked.

Step-by-step explanation:

First, the quadratic equation we are starting with is -x^2 + 10x + 9.5

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For the first part, it's asking for how high it is when it starts, commonly, we use 0 as the start point so if we plug 0 into the quadratic equation, we have 9.5. The height is 9.5 feet at start.

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For the second part I'm assuming it's asking for either a minimum or a maximum and because the equation has a -x^2, that means the parabola has a maximum. You can tell by -x^2 being negative, if it was x^2 (positive) it would have a minimum.  

The maximum is found using the vertex formula(because the vertex is the max or min), -b/2a, where a is -1, b is 10, and c is 9.5 found in the equation because the quadratic is in standard form ax^2 + bx + c. This gives a vertex of 5.

We plug 5 back in the equation to get (5, 34.5).

5 is the x-coordinate so it is 5 feet horizontally and 34.5 feet high

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For the last part it's asking for a root, or when the parabola touches the x axis/the ground.

-x^2 + 10x + 9.5

You would use the quadratic formula but I'm too lazy so I just put it into a calculator.

That gives roots of around x=−0.87367 and x=10.8737.

You can't have a negative root so you're left with x= 10.8737, rounding to the tenth decimal place, 10.9.

I think that's correct, could be wrong, if it is wrong just follow the steps and it should be fine.

Answer is 1st and 3rd shape

Whose area is 4 units

Answered by Gauthmath must click thanks and mark brainliest

Answer:

First option

Remove 2 tiles

Answer:

C

Step-by-step explanation:

Consider trapezoid ABCD with

A is the midpoint of ED

C is the midpoint of BF

=> AC is the median of trapezoid EBFD

=>(EB+DF) / 2 = AC

=>(13+x) / 2 = 19

=> 13+x = 38

=> x= 25

The value of x is 5.

According to the Triangle Proportionality Theorem, if a line is parallel to one side of a triangle and intersects the other two sides, it divides those two sides proportionally. In mathematical terms, we can express this as:

(a/b) = c

Where the values of a = 13, b = 19

Now, we can substitute the given values into the proportionality equation:

(13/19) = c

Next, we can cross-multiply the equation:

c = 0.68

Then the value of x is calculated by adding 4.32 on it then we get the value of x as

=>  x = 0.68 + 4.32

=> x = 5

Hence the correct option is (b).

To know more about triangle here

https://brainly.com/question/8587906

#SPJ2

Answer:

B

Step-by-step explanation:

this is just common sense. if you would have tried you could have easily answered this yourself.

the sequence starts with 6. that is a1.

so, the formula simply has to add "something" to 6.

therefore, A and D are out.

and then we see immediately that the sequence is built by subtracting 4 (or adding -4) for every step.

so, we need to add multiples of -4.

therefore, only B is correct (C adds multiples of +4).

Answer:

10 hours

Step-by-step explanation:

45 pages per 1 hour and 30 minutes,  or 60 min +30 min =90 min

90 minutes / 45 pages has to be equal to an equivalent fraction where we have 300 pages

90 minutes /45 pages = ? minutes / 300 pages , multiply both sides by 300

? minutes = 90*300/45 = 600 minutes

to read 300-page book will take 600 minutes = 10 hours

Answer: M³+ M³ = M⁹

Step-by-step explanation:

Answer:

m^6

Step-by-step explanation:

Simple rule of addition of indices, a^x + a^y = a^x+y, m^3+3 = m^6

Answer:

Step-by-step explanation:

For Part A, use the pythagorean theorem to find the height, which ca be found by finding one length of the leg. Using the imaginary bisector, you can determine one of the legs is 5 cm, and the hypotenuse is 13 cm

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse. Plug in the values to solve for one leg, you get 25+b^2=169

Solve algebraically, b^2= 144, so b=12, which is the height.

Part B

Determine the surface area of each cardboard piece, and add together.

20 × 13 × 2 = 520

1/2 × 10 × 12 × 2 = 120

20 × 10 = 200

So approximately 840 cm of cardboard was used

Answer:

A

Step-by-step explanation:

Given the 2 equations

2x + y = - 5 → (1)

- x + 3y = 6 → (2)

Multiplying (2) by 2 and adding to (1) will eliminate the x- term

- 2x + 6y = 12 → (3)

Add (1) and (3) term by term to eliminate x

0 + 7y = 7

7y = 7 ( divide both sides by 7 )

y = 1

Substitute y = 1 into either of the 2 equations and solve for x

Substituting into (1)

2x + 1 = - 5 ( subtract 1 from both sides )

2x = - 6 ( divide both sides by 2 )

x = - 3

solution is (- 3, 1 ) → A

it is 3.75 lbs my shlime                                                                                                            

Answer:

the answer is 3.75 pounds

it says one pound is 16 ounces

so divide the ounces with pound

60/16

then we get 3.75 pounds

Answer:    b. 33

Step-by-step explanation:

The range is when you subtract the lowest value in the number set by the highest number in the number set. For this particular example, it would be 34-1= 33.

Hope this helps you!

Hi there!

Looking at the graph, the first intersection point is clear. The red parabola and  blue line clearing intersect at the point (0, -1).

Find the second intersection point by setting the equations of both graphs equal to each other.

Line: y = 3x - 1

Parabola: y = 4x² - 1

Find another intersection point by setting these two equations equal to each other:

4x² - 1 = 3x - 1

Bring all terms onto one side:

4x² - 3x = 0

Factor out x:

x(4x - 3) = 0

Set 4x - 3 to 0 and solve:

4x - 3 = 0

4x = 3

x = 3/4

Plug in this value of x into an equation to solve for the y-coordinate. Use the linear equation for ease:

y = 3(3/4) - 1

y = 9/4 - 1

y = 5/4

(3/4, 5/4)

Answer:

A

Step-by-step explanation:

Observe the coordinates of C, it's (5,2). Now observe C' which is (2, - 5). Hence the rule is (x, y) -> (y, - x)

Step-by-step explanation:

10 % of 2700 = 270

so he had 2970 rupee

20% of 2970 = 594

so customer have to pay 2970 + 594 = 3564

Answer:

Step-by-step explanation:

if you connect the 2 pointy parts of this shape at the top, what you have is a square. That means that the cut out part is a half circle. To find the area of the shaded portion, subtract the area of the half circle from the area of the square. Let's start with the square, cuz that's the super easy one.

A = s*s so

A = 64 in squared.

Now for the half circle. Let's just do this: let's find the area of the whole circle and then cut it in half, how about?

If the length of one of the sides is 8, then half that length is 4, right? Since the circle is touching the sides of the square, the diameter of the circle is the same as the measure of the side of the square. That means that the radius is 4. The area for the circle is

[tex]A=\pi r^2[/tex] and filling in:

[tex]A=(3.14)(4^2)[/tex] so

A = 50.24 in squared. Divide that in half and the area of half the circle is 25.12 in squared.

Subtract 25.12 from 64 to get 38.88 in squared