PLEASE HELP ME !!!
x² + 12x -
2
8 can be written in the form
(x + a)² + b, where a and b are numbers.
Work out the values of a and b.

In the given graph the correct statements are:

q ⊥ n

m ║ n

p ⊥ m

Parallel lines are two straight lines that never intersect and are located in the same plane. They are equidistant lines that are always at the same distance from one another. Parallel lines are denoted by the apostrophe ||. AB || CD, for instance, denotes that line AB and line CD are parallel. Perpendicular lines, on the other hand, are when two lines cross at an angle of 90 degrees. The symbol stands for perpendicular lines. Line PQ is perpendicular to line RS, for instance, if PQ RS. Examine the following illustration and the characteristics of parallel and perpendicular lines to recognize and distinguish between them.

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The total change in the cats weight for all 3 months is -0.5 pounds.

Since we have 3 months which is from April to June, Now let add up the change in weight in pounds so as to find the total change

Let x represent the total change

x = -0.7 + 0.5 + (- 0.3 )

x = -0.5 pounds

Therefore the -0.5 pound is the change in weight.

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The speed of the car is 40mph

A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

Distance covered by car = 160 miles

distance covered by plane = 840 miles

let the time taken to cover 160 miles by car be x

speed of car = 160/x

speed of plane which is 170mph faster than speed of car = 170 + 160/x

time taken to cover 840 miles by plane,

time = distance/speed = [tex]\frac{840}{170 + \frac{160}{x} }[/tex]

By simplifying,

time taken by plane = [tex]\frac{840x}{170x + 160}[/tex]

since it takes same time for both to get to their destination,

Then,

x =  [tex]\frac{840x}{170x + 160}[/tex]

By cross multiplying

x( 170x + 160) = 840x

divide both sides by x, it reduces to

170x + 160 = 840

170x = 840 - 160

170x = 680

x = 680/170

x = 4

Speed of car = 160/x

speed of car = 160/4

speed = 40mph

In conclusion, the care moves at the speed of 40mph

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Answer:

Step-by-step explanation:

1. List out the numbers and divide

-1/6/2/9=

2. In division for fractions, the number or numbers on the right of the division side flip and change to multiply!

-1/6/2/9= -1/6*9/2= -9/12

3. Simplify!

-9/12= -3/4

Answer:

-3/4

Step-by-step explanation:

so you leave -1/6 but then you change the sign to multiply and the other fraction change it so if you had 2/9 it will be 9/2

so we get -1/6×9/2.

if you don't know how to multiply fractions i can explain just ask.

I hope this helps. Have a great rest of your day!

The area of the circle with the circumference 18 units is 25.80 square units

The given parameters are

Circumference = 18 units

As a general rule, circumference are represented by the variable C

So, we have the following representation equation

C = 18

The circumference of the circle can be calculated as

C = 2πr

Next, we substitute the value of the variable C in the above equation

i.e. C = 18

So, we have the following equation

2π * r = 18

Divide both sides by 2π

r = 9/π

The area of the circle can then be calculated using the following area formula

A = πr²

Next, we substitute the value of the variable r in the above equation

i.e. r = 9/π

A = π * (9/π)²

Evaluate the exponents

This gives

A = π * 81/π²

Evaluate the products

So, we have

A = 81/π

As a general notation, π = 3.14

So, we have the following equation

A = 81/3.14

Evaluate the quotient

A = 25.80

Hence, the area is 25.80 square units

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If we start with the parent quadratic function, then the transformation is:

g(x) =  (x - 17)^2 + 4

The definitions of translations are:

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

If N is positive, the shift is to the left.If N is negative, the shift is to the right.

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

If N is positive, the shift is upwards.If N is negative, the shift is downwards.

Then if the parent function is:

f(x) = x^2

The translation of 17 units to the right and 4 units up is:

g(x) = f(x - 17) + 4 = (x - 17)^2 + 4

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The amount that Katy would have saved in her savings account in 2 years is $16, 000

Given that the interest on the savings account is not compounded, the amount that Katy would have saved in 2 years can be found by the formula:
= Principal x Interest Rate x Time

Principal = $100, 000

Interest rate = 8%

Time = 2 years

The amount that Katy would have saved is:

= Principal x Interest Rate x Time

= 100, 000 x 8% x 2

= $16, 000

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For the given triangle ABC,

The perimeter of ABC is 32.443 unit
The area of ABC is 30 unit^2

What is a vertex?
A triangle is created geometrically by the intersection of three line segments. Each side of a triangle has two ends, and the three sides' endpoints may intersect at three distinct places in a plane to form the triangle. The three locations where they cross each other are referred to as a triangle's vertices.

Solution explained:

The distances are found using the distance formula:

D=[tex]\sqrt{((y2-y1)^2+(x2-x1)^2)}[/tex]

Given A(2,8),B(16,2),C(6,2)

Now, calculate the distance

AB=[tex]\sqrt{((16-2)^2+(2-8)^2)}[/tex]=[tex]\sqrt{(14^2+6^2)}[/tex]=[tex]\sqrt{232}[/tex]

BC=[tex]\sqrt{((6-16)^2+(2-2)^2)}[/tex]=[tex]\sqrt{(10^2+0)}[/tex]=10

CA=[tex]\sqrt{((2-6)^2+(8-2)^2)}[/tex]=[tex]\sqrt{(4^2+6^2)}[/tex]=[tex]\sqrt{(16+36)}[/tex]=[tex]\sqrt{52}[/tex]

Perimeter=AB+BC+CA
               =32.443 unit

For the area (we note that BC is horizontal (parallel to the x-axis)), so

Area = (1/2)base * height

        =(1/2)10*(ya-yb)

        =(1/2)10*(8-2)

        =(1/2)10*6

        =30 unit^2

Hence, the perimeter is 32.443 units and the area is 30 unit^2

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The midpoint of the segment with the given endpoints.-5 and 4 is -0.5.

What are coordinates?

A pair of numbers is used to express a point's position on a coordinate plane using the horizontal and vertical distinctions from the two reference axes.

What is a midpoint?

A midpoint is a point that lies on a line connecting two other locations and is in the middle of the line.

Here,

A midpoint can also be written as an average or mean of two points.

Mean of -5 and 4 = (- 5 + 4)/2 = -0.5

Hence "The midpoint of the segment with the given endpoints.-5 and 4 is -0.5".

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A graph of the given inequality (x + y ≥ 500) is shown in the image attached below.

In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of data on both the horizontal and vertical axes of a cartesian coordinate, which are the x-coordinate and y-coordinate.

Next, we would translate the word sentence into an inequality as follows:

x + y greater than or equal to 500 ⇒ x + y ≥ 500

Subtracting x from both sides of the inequality, we have the following equation:

x + y - x ≥ 500 - x

y ≥ 500 - x

Rearranging the equation in slope-intercept form, we have:

y ≥ -x + 500

In conclusion, we can reasonably and logically deduce that both the x-intercept and y-intercept of this linear inequality (equation) is equal to 500.

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The number of pavers required is 961.

The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.

Given data

A driveway is being surfaced with concrete pavers in the shape of regular hexagons. If the driveway is a 24-by-26-foot rectangle with pavers 6 inches wide across the flats.

We have to determine how many pavers are needed

We know that area of a regular hexagon

A = (3√3)/2 a^2

= (3√3)/2 〖(6)〗^2

= (3 x 1.732)/2  x 36

= 93.528 sq.inches

Now area of rectangle

= l x w

= 24 x 26 x (12)2        (1feet = 12 inches)

= 89856 sq.inches

Now pavers required

= 89856/93.528

= 960.73

= 961

Therefore the number of pavers required is 961.

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Answer: x < 3

Explanation: Once you reach step 3, you divide -2 on both sides. -2x cancels out, and -6 divided by -2 is 3

Answer:

t = 12

Step by step explanation:

(t + 6)(t - 8) = 72

t² - 8t + 6t - 48 = 0

t² - 2t - 120 = 0

(t + 10)(t - 12) = 0

t + 10 = 0 OR t - 12 = 0

t = -10 OR t = 12

(reject)

The average power exerted on the flag of mass 2 kg by the student is 58.8 Watt.

Power can defined as the rate at which work is done.

To calculate the average power exerted on the flag, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the average power exerted is 58.8 Watt.

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The term that defines a circle is "all coplanar points equidistant from a given point". Then the correct option is D.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The definition of the circle is written as "A circle is a shape comprising of all places in a plane that are at a given separation from a given point, the middle."

The circle is a two-dimensional shape.

The term that defines a circle is "all coplanar points equidistant from a given point". Then the correct option is D.

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Answer: D) all coplanar points equidistant from a given point

Step-by-step explanation:

Answer:

A:

Answer:65Step-by-step explanation:C^2= A^2 + B^2C^2 = (60)^2 + (25)^2 C^2 = 4225Take the square root of CC = 65

Answer:

A hiker walks 10 km East, then 5 km in a direction 60 degrees North of West, then 8.7 km in a direction 30 degrees South of West. Find her resultant displacement.

Since you walk 10km North then turn and walk 5km East, your displacement from where you started is approximately 11.18 km.

From the information given, we have that you walked 10 km north (which represents the vertical side of the triangle) and 5 km east Using the Pythagorean theorem, the displacement (d) can be determined  as;

[tex]d^2 = (10 km)^2 + (5 km)^2[/tex]

Find the square values, we get

d² = 100 km² + 25 km²

add the squares, we get

d² = 125 km²

Find the square root of both sides of the equation, we have;

d = 125km²

d =  11.18 km

Therefore, your displacement from where you started is approximately 11.18 km.

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Answer: 3 busses

Step-by-step explanation:

The rate of libraries per 100000 is 88.05   .

In the question ,

it is given that ,

the number of public libraries in New York City = 207 libraries

the population of the New York City = 8.805 million

we have to find the rate of libraries per 100000  .

for this we first have to express the population in numbers .

the population 8.805 million expressed in numbers is 8805000 ,

the rate of libraries per 100000 is

= 8805000/100000

On further simplification ,

we get ,

= 88.05

Therefore , The rate of libraries per 100000 is 88.05   .

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Applying angle relationships, the measures of the numbered angles are:

m∠1 = 90°

m∠2 = 68°

m∠3 = 112°

m∠4 = 112°

m∠5 = 68°

m∠6 = 56°

m∠7 = 124°

m∠8 = 124°

To calculate angle measurements that are formed by a transversal and parallel lines, we can apply the knowledge of the angle relationships that exist between the angle pairs in concerned. Some angle relationships are:

m∠1 = right angle [corresponding angles is the angle relationship]

m∠1 = 90°

m∠2 = 180 - m∠1 - 22 [triangle sum theorem]

Substitute

m∠2 = 180 - 90 - 22

m∠2 = 68°

m∠3 = 180 - m∠2

Substitute

m∠3 = 180 - 68

m∠3 = 112°

m∠4 = m∠3

m∠4 = 112°

m∠5 = 180 - m∠4

m∠5 = 180 - 112

m∠5 = 68°

m∠6 = 1/2(180 - m∠5)

m∠6 = 1/2(180 - 68)

m∠6 = 56°

m∠7 = 180 - 56

m∠7 = 124°

m∠8 = m∠7 [alternate interior angles is the angle relationship]

m∠8 = 124°

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Answer:

Step-by-step explanation:

The Horizontal asymptote of y = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.

Hope this helps!

Have a great day!!

Yes, Wilson is right since "negative numbers" don't exist when you find the absolute value.

Therefore, Wilson is correct as there is no negative term in absolute value.

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The require angle of x is 52.4°

Given is a quadrilateral

The given diagonal divides the quadrilateral in two parts

the first part is a right angled triangle

Thus to find the side BD

we will use the Pythagoras theorem ;

So according to this theorem

AB² + AD² = BD² [ because BD is the hypotenuse ]

Given AB = 8 cm and AD = 6 cm

8² + 6² = BD²

this implies 64 + 36 = BD²

100 = BD which implies BD = 10 cm

To find x

we know that in triangle BCD

BD = 10 cm and CD = 13 cm

tan theta = [tex]\frac{13}{10}[/tex]

this means theta = [tex]tan^{-1}[/tex] [tex]\frac{13}{10}[/tex]

theta = 52.4°

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Answer:

39.07

use pythagros to find bd then use the sine rule substitute in the values

bd=10

beacuse a²+b²=c²

substitute in 8²+6²=c²

Step-by-step explanation:

that is the same as calculating the perimeter of the rectangle (the way 1 time around the rectangle).

the perimeter of a rectangle is

2×length + 2×width

in our case that is

2×11 + 2×4 = 22 + 8 = 30 ft

the stripping costs $5 per foot, and we have 30 ft.

so, the total costs are

5 × 30 = $150

Answer:

9

Step-by-step explanation:

I hope this helps!