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The line segment joining points (2,6) and (6,2) forms a diagonal of a square. Which of the following could be the coordinates of another vertex of that square?

The Slope of the line q equals 3.

Given the slope of line r is -

slope = perpendicular / base

Finding the equation of line using coordinates (2,3) and (-1,4)

putting the values in the equation,

y2 - y1 / x2 - x1

⇒ 4-3 / -1 -2

⇒ 1/-3

⇒ -1/3

Slope of the line r is -1/3

As line q is perpendicular to line r,

Using the property, 2 lines perpendicular to each other have slope = negative reciprocal of slope 1

the slope of line q becomes 3

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Answer: ales revenue = 1,386,000 dollars Increase sales in percent = 10 percent Increase sales in dollars = 1,386,000 dollars * 0,1 = 138,600 dollars New sales goal in dollars = 1,386,000 dollars + 138,600 dollars = 1,524,600 dollars

New sales goal is 1,524,600 dollars.

Step-by-step explanation:

Answer:

(y+5)(y-3)

Step-by-step explanation:

..........

Answer:

y^2-3y+5y-15

y(y-3)+5(y-3)

(y-3) (y+5)

Using proportions, it is found that the scale of the rectangle is of 1:14.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication and division to find the unit rates.

One example of application of proportions is for scale problems, as the scale is given by the following equation:

Scale = Drawn distance : Actual distance.

For this problem, we have that:

Hence the scale is of:

6.1 : 85.4.

We can simplify dividing 85.4 by 6.1, hence:

85.4/6.1 = 14.

Hence the simplified scale is:

1:14.

This problem is incomplete and could not be found on any search engine, hence we are going to suppose that it asks for the scale of the drawing of the rectangle.

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[tex]x^{2} + 2x - 15 = 0[/tex] -> [tex](x+1)^{2} - 16 = 0[/tex]

-> [tex](x+1)^{2} = 16[/tex]
-> x+ 1 = 4 or -4
-> x = 3 or -5

Answer:

[tex]x=3, \quad x=-5[/tex]

Step-by-step explanation:

Given quadratic equation:

[tex]x^2+2x-15=0[/tex]

Step 1

Move the constant to the right side of the equation:

[tex]\implies x^2+2x-15+15=0+15[/tex]

[tex]\implies x^2+2x=15[/tex]

Step 2

Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:

[tex]\implies x^2+2x+\left(\dfrac{2}{2}\right)^2=15+\left(\dfrac{2}{2}\right)^2[/tex]

[tex]\implies x^2+2x+1=15+1[/tex]

[tex]\implies x^2+2x+1=16[/tex]

Step 3

Factor the perfect square trinomial on the left side:

[tex]\implies (x+1)^2=16[/tex]

Step 4

Square root both sides:

[tex]\implies \sqrt{(x+1)^2}=\sqrt{16}[/tex]

[tex]\implies x+1=\pm4[/tex]

Step 5

Subtract 1 from both sides:

[tex]\implies x+1-1=-1\pm4[/tex]

[tex]\implies x=-1\pm4[/tex]

Solutions

[tex]\implies x=-1+4=3[/tex]

[tex]\implies x=-1-4=-5[/tex]

Therefore, the solutions of the given quadratic equation are:

[tex]x=3, \quad x=-5[/tex]

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The maximum height of the skateboarder is 40.25 feet after 0.875 seconds

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Let h(t) represent the height of the skateboarder after t seconds.

h(t) = -16t² + 28t + 8

The maximum height is at h'(t) = 0

h'(t) = -32t + 28

-32t + 28 = 0

32t = 28

t = 0.875s

h(0.875) = -16(0.875)² + 28(0.875) + 8 = 40.25 feet

Maximum height is 40.25 feet

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Question 1

[tex]2l+2w=48 \\ \\ 2l+20=48 \\ \\ 2l=28 \\ \\ l=14\text{ cm}[/tex]

Question 2

[tex]2l+7.2=48 \\ \\ 2l=40.8 \\ \\ l=20.4 \text{ cm}[/tex]

Question 3

[tex]2l+2w=48 \\ \\ l+w=24 \\ \\ w=24-l[/tex]

Answer:

x = 70

Step-by-step explanation:

(2x - 5) and 45 are same- side interior angles and sum to 180° , that is

2x - 5 + 45 = 180

2x + 40 = 180 ( subtract 40 from both sides )

2x = 140 ( divide both sides by 2 )

x = 70

The midpoint of the given coordinates of points (0,-10) and (-6,-8) is  ( -3,-9 )

A midpoint is simply a point that divides a line segment into two equal halves.

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point 1( 0,-10 )

Point 2( -6,-8 )

Midpoint = ?

To determine the midpoint, plug the given points into the midpoint formula above and simplify.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

M = ( ( 0 + (-6) )/2, ( (-10) + (-8) )/2 )

M = ( ( 0 - 6) )/2, ( -10 - 8 )/2 )

M = ( ( -6 )/2, (-18 )/2 )

Midpoint M = ( -3,-9 )

Therefore, the midpoint of the coordinates is ( -3,-9 ).

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Thee surface area of the water tower is 1664 square feet

It is important to note that the formula for determining the surface area of a cylinder is expressed as;

Surface area = 2πr² + 2πrh

Where;

Also, note that the formula for diameter is expressed as;

Diameter = 2r

Substitute the value of diameter

30 = 2r

r = 15 feet

Now, substitute the values into the formula

Surface area = 2(3.14)(15)² + 2(3.14)(40)

expand the bracket

Surface area = 1413 + 251. 2

Add the values

Surface area = 1664. 2

Surface area = 1664 square feet

Hence, the value is 1664 square feet

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Answer:

i dunno

Step-by-step explanation:

hard man

Answer:

f=4

Step-by-step explanation:

I think it's right but not 100% sure

Step-by-step explanation:

3 ................

.

........................

Answer:

3

Step-by-step explanation:

–4 + (–16) + 23

–4 – 16 + 23

–20 + 23

= 3

a collection of 65 coins contains one with two heads. the remainder of the coins are fair. if a coin, selected randomly from the collection, turns up heads 6 times in 6 tosses, 1/65 is the probability it’s a two-headed coin

Definition of probability

(1) : the chance that a given event will occur. (2) : the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

We know that one coin in a collection of 65 has two heads. If a coin, chosen at random from the lot and then tossed, turns up heads 6 times in a row. We calculate the probability that it is the two-headed coin.

We calculate  the number of possible combinations:

C₁⁶⁵= 65!/1!(65-1)!

     = 65

Number of favorable combinations is 1.

Therefore, the probability is

P=1/65.

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The definition based on the given biconditional is B. A polygon is a hexagon with six sides.

A conditional statement combined with its opposite is known as a biconditional statement. As a result, one conditional is only true if and when the other is also true. It frequently employs the phrase "if and only if" or the abbreviation "if." It serves as a reminder that the conditional must be true in both directions by using the double arrow.

The biconditional statement is that the polygon is a hexagon if and only if it has six sides.

Therefore, the correct option that illustrates this is B.

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Answers:

a)  2710 kg/m³

b)  5149 kg

====================================================

Work shown for part a)

density = mass/volume

density = (6775 kg)/(2.5 m³)

density = (6775/2.5) kg/m³

density = 2710 kg/m³

-----------------------------------

Work shown for part b)

density = mass/volume

mass = density * volume

mass = (2710 kg/m³) * (1.9 m³)

mass = (2710*1.9) kg

mass = 5149 kg

Answer:

D. The last 26/8, 3-32, -Pi, -4 2/3

Step-by-step explanation:

26/8= 3.25

3-32=3.17

-Pi= -3.14

-4 2/3= -4.67

The most appropriate choice of percentage will be given by-

£47 after 24% decrease becomes £35.72

What is Percentage?

Percentage is a ratio expressed as a percentage of 100.

Here,

Original Price = £47

Percentage decrease = 24 %

Decrease in Price = £([tex]\frac{24}{100} \times 47\\[/tex])

                              = £11.28

New Price = £(47 - 11.28)

                 = £35.72

So, £47 after 24% decrease becomes £35.72

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Answer:

25 mph

Hope this helps! :)

There are 450 triangles, we can pick that do not form an equilateral triangles when 15 dots are evenly spaced on the circumference of a circle.

Let's calculate the total no. of possible triangles, it depends on the combination. To make a triangle, we have to choose 3 dots out of 15.

Here, we will use the combination rule to find out the possible triangles,Thus, the total number of possible triangles = 15C3                                                                      = (15.14.13) / (1.2.3) = 455

Note that an equilateral triangle would be formed by connecting 3 equally spaced dots.

For an equilateral triangle, out of 15 dots, there would be 15 - 3 = 12 dots that will not be connected.

And 12/3 = 4 dots would be between any two connecting dots.

Taking 1st connecting dot, the second connecting dot would be

1 + 4 + 1 = 6th

Similarly, the third connecting dot would be 6 + 4 + 1 = 11th

So, the following connecting dots will form equilateral triangles: (1, 6, 11); (2, 7, 12); (3, 8, 13); (4, 9, 14); (5, 10, 15);

After applying the combination rule we found the total number of the possible triangle and there are 5 equilateral triangles:

So, there are 455 - 5 = 450 triangles that are not equilateral triangles.

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Answer:

£32

Explanation:

so 1/5 = 0.2

to make 0.2 a percent just multiply by 100 so 0.2 • 100 = 20%

so the discount would be 20%, meaning the game holds 80% of its value since

100-20 = 80

so to make 80% a decimal, divide by 100 so 80/100 = 0.8

so then you just multiply: 40 • 0.8 = 32

so the game is £32

hope this helps :)

The price of the computer game on sale is  £32.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, The normal price of a computer game is £40.

The price is reduced by 1/5 in a sale.

∴ The price of the computer game on discount can be obtained if we subtract the fraction of the discount times the normal price from the normal price which is,

= {(40 - (1/5)×40}.

= {40 - 8}.

= £32.

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Answer:

350%

Step-by-step explanation:

1) To convert a decimal to a percentage multiply the given decimal by 100. So,

3.5 x 100 = 350

2) 350% is the final answer

The 3 : 7 ratio of the leg lengths and the 42 cm length of the hypotenuse side using Pythagorean theorem, gives the lengths of the sides (the legs of the right triangle) as follows;

[tex]147 \cdot \sqrt{ \frac{2}{29} } [/tex] and [tex] 63 \cdot \sqrt{ \frac{2}{29} }[/tex]

Pythagorean theorem states the square that has the hypotenuse of a right triangle as its side length is equal in area to the sum of the areas of the two squares formed by legs of the right triangle.

Given;

The possible given parameters are;

The ratio of the length of the sides (the legs) of the triangle is 3 : 7

The length of the hypotenuse side = 42 cm

Required: The lengths of the other two sides of the triangle

Solution;

The lengths of the two sides are found as follows;

Let a and b represent the lengths of the legs of the right triangle, according to Pythagorean theorem, we have;

a² + b² = 42²

The ratio of the leg lengths gives;

a/b = 3/7

Therefore;

a = (3/7)•b

Which gives;

((3/7)•b)² + b² = 42²

b²•((3/7)² + 1) = 42²

b = 42²/(((3/7)² + 1)) = 42²×(58/49)

[tex]b = 147 \cdot \sqrt{ \frac{2}{29} } [/tex]

Which gives;

[tex]a =\frac{3}{7} \times 147 \cdot \sqrt{ \frac{2}{29} }= 63 \cdot \sqrt{ \frac{2}{29} }[/tex]

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Answer:

21

Step-by-step explanation:

If it loses 3 gallons every mile, then multiply it by 7.

3*7 = 21

Another way to solve this is by using linear equations

y=3x

replace x with 7 and y would be equal to 21

When x is made the subject of m= n+ x/p,

          x = mp - n

How is  x  made the subject of m = n +x/p ?

[tex]m = \frac{n+x}{p} \\\\mp = n+x\\\\mp -n = x\\\\x = mp-n[/tex]

How is x being made the subject?

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Description of a Function : Consider two nonempty sets, X and Y. A relation that links exactly one element from X to Y is known as a function from X into Y.

f(x) = 5x-2 ?

Solution:

f(x) = 5x-2

5x-2 = 0

 5x = 2

    x = 0.4

f(0.4) = 5(0.4)-2

          = 0

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Answer:

Yes, the friend is correct.

Step-by-step explanation:

Twice a number of x is the same as saying multiply x by 2, which equals 2x. At most means 2x can only reach -24 at the very max, so solving for x will give you an answer that should only either be less than or equal to -24. This equation is an inequality because an inequality compares two values; in this case, the inequality is comparing 2x is at most -24, which is the same as saying 2x is less than or equal to -24.

Answer:

21

Step-by-step explanation:

You are 14 right now if you were 7 yo 7 years ago. Add 7 more years to 14 and you get 21