The equation x2 - 10x + 17 = - y2 - 2y describes a circle in the coordinate plane. Find the radius of the circle and the coordinates of its center.

Answer:

45.98

Step-by-step explanation:

there ya go I did this before so I know the correct answer

The fill up for the 3rd  step is y - 250 =  340x.

Note that:

y-250 = 250 + 340 x - 250

y = 250 + 340x.

Make x the subject of the formula:

y - 250 =  340x.

then y-250/340 = x

Then  [tex]x = \frac{y-250}{340}[/tex]

The justification for the second step is subtraction property of equality because it undergoes subtraction and the collection of like terms and then subtracting them from one another as shown below:

y-250 = 250 + 340 x - 250

y= 250 + 340x - 250 + 250

Note that (-250 + 250) = 0

y = 250 + 340x.

Lastly, The fill up of the 6th step is substitution of the amount of money  saved and  then simplifying it.

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let x = horses

5x = cows

x + 5x = 132

6x = 132

Divide both sides by 6

X = 22

he has 22 horses and 110 cows

There are 22 horses and 110 cows.

"It is a mathematical statement which consists of equal symbol between two mathematical expressions."

For given question,

Let 'c' represents the number of cows and 'h' represents the number of horses.

A rancher raises 5 times as many cows as horses.

So, we get an equation,

⇒ c = 5 × h                        .................(i)

There are 132 animals.

So, we get an equation,

⇒ c + h = 132                    ..................(ii)

Substitute the value of c = 5h in equation (ii)

⇒ c + h = 132

⇒ 5h + h = 132

⇒ 6h = 132

⇒ h = 22

This means, there are 22 horses.

Substitute the vale of h in equation (i),

⇒ c = 5 × h  

⇒ c = 5 × 22

⇒ c = 110

This means, there are 110 cows.

Therefore, there are 22 horses and 110 cows.

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Answer:

Area of the triangle = 210 cm^2 .

Step-by-step explanation:

Perimeter of triangle = 4x + 1 + 3x - 1 + 3x = 70

10x = 70 - 1 + 1 = 70

x = 7.

Area A = 1/2 * base * height

= 1/2 * 3x * (3x - 1)

= 1/2 * 3(7) * (3(7)  -1)

= 1/2 * 21 * 20

= 210.

The true statement about h(x) is (c) the function is decreasing on the interval (0, ∞)

The function is given as:

h(x) = -5√x

Next, we plot the graph of the function h(x)

From the attached graph, we can see  that:

As x increases from 0, the function value decreases

Hence, the true statement about h(x) is (c) the function is decreasing on the interval (0, ∞)

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Answer:

X=-2 or x=-7

Step-by-step explanation:

(x+2)(x+7)=0

X=-2 or x=-7

Answer:

5 minutes.

44 x 5 = 220,

since 44 x 4 = 176 < 209

48.

Because 46+48 equals 94.

You can easily find out equations to this by subtracting the 46 from 94 to see what p is equal to.

HAVE A NICE DAY!

The exact area of the isosceles trapezoid inscribed in a circle is determined as 196 sq units.

The height of the trapezoid is calculated as follows;

From the image, the sum of h1 and h2 is the height of the trapezoid.

Each of the height will be calculated using Pythagoras theorem as follows;

h1² = r² - (b1/2)²

h1² = 10² - 6²

h1² = 64

h1 = √64

h1 = 8

h2² = r² - (b1/2)²

h2² = 10² - 8²

h2² = 36

h2 = √36

h2 = 6

Total height = 8 + 6 = 14

A = ¹/₂(b₁ + b₂)H

A = ¹/₂(12 + 16) x 14

A = 196 sq units.

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The probability of drawing a black ball on the second draw will be 3/5.

From the information given, the total number of balls will be:

= 2 + 3 = 5 balls.

When the first ball is black and the second is red. This will be:

= 2/5 × 3/4

= 3/10

When the first is red and the second is black, this will be:

= 3/5 × 2/4

= 3/10

Therefore, the probability of drawing a black ball on the second draw will be:

= 3/10 + 3/10

= 3/5.

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A second-degree polynomial takes the form

[tex]f(x) = ax^2 + bx + c[/tex]

for some constants a, b, and c. Such a function is continuous and differentiable everywhere in its domain.

Differentiating f(x) with respect to x gives

[tex]\dfrac{df}{dx} = 2ax + b[/tex]

We're told that

• f(x) is increasing on [0, 8]

• f(x) is decreasing on ]-10, 0]

and since df/dx is continuous, this tells us that df/dx = 0 when x = 0. It follows that b = 0, and we can write

[tex]f(x) = ax^2 + c[/tex]

We're also given that the curve passes through the point (-8, 4), which gives rise to the constraint

[tex]f(-8) = 64a - 8b + c = 4 \implies 64a + c = 4[/tex]

Since f(x) is decreasing on ]-10, 0], we have df/dx < 0 when x = -8, so

[tex]2ax+b < 0 \implies -16a < 0 \implies a > 0[/tex]

This means f(x) is minimized when x = 0, with min{f(x)} = c, so the co-domain of f(x) is the set {f(x) ∈ ℝ : f(x) ≥ c}.

Without another condition, that's all we can say about the co-domain. There are infinitely many choices for the constants a and c that satisfy the given conditions. For example,

a = 1, c = -60   ⇒   f(x) = x² - 60   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -60}

a = 2, c = -124   ⇒   f(x) = 2x² - 124   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -124}

etc.

[tex](-4x+12)^{1/2}=x\\\sqrt{-4x+12}=x\\\\D:-4x+12\geq0\wedge x\geq0\\D:4x\leq12\wedge x\geq0\\D:x\leq3\wedge x\geq0\\D:x\in\langle0,3\rangle\\\\\sqrt{-4x+12}=x\\-4x+12=x^2\\x^2+4x-12=0\\x^2-2x+6x-12=0\\x(x-2)+6(x-2)=0\\(x+6)(x-2)=0\\x=-6 \vee x=2\\\\-6\not \in D\\\\\boxed{x=2}[/tex]

The attached graph represents the graph of the equation y1 = 17,105 + 1.31x

The equation is given as:

y1 = 17,105 + 1.31x

To plot and graph the equation, we set some values for x and calculate the corresponding y values.

Let x = 0, 1, 2 and 3.

So, we have:

y1 = 17,105 + 1.31 * 0 = 17105

y1 = 17,105 + 1.31 * 1 = 17106.31

y1 = 17,105 + 1.31 * 2 = 17107.62

y1 = 17,105 + 1.31 * 3 = 17108.93

The graph can then be plotted using the above points

See attachment

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The meaning of (e−l)(4) in this situation is that there are 92 people in the amusement park 4 hours after the gates open.

e(x) =  0.03x³ + 2

l (x) =  0.5x + 1

Therefore, ( e - l) =   [ .03x^3 + 2 ]  -  [ .5x + 1 ] will be:

=  0.03x³  - 0.5x + 1

Therefore, (e - l ) (4)  =  0.03(4)³  - 0.5(4) +  1  = 92  

Therefore, it means that  4 hours after the park opens, the rate that the number of people is changing is 92 people per hour

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Answer:

a=2

Step-by-step explanation:

-13 + 5a = 3a -9 Distribute 3 through the parentheses

-13 + 5a - 3a = -9 Move the variable to the left hand side and change the sign

2a= -9 + 13 collect like terms

2a=4 Divide both sides by 2

a=2

Answer: All of them are correct I think

Step-by-step explanation:

[tex]A = B \log_x C\\\\\text{Given that,}~~ A = 11, ~B = 4~ C = 190\\\\~~~~~~~~11 = 4 \log_x (190)\\\\\implies \log_x (190) = \dfrac{11}4\\\\\implies x^{\tfrac{11}4} = 190\\\\\implies x = 190^{\tfrac 4{11}}\\\\ \implies x \approx 6.7397[/tex]

Answer:

2

Step-by-step explanation:

The match up  are:

The square root, in mathematics is known to be the factor of a number that, is said to be multiplied only by itself and thus it gives the original number.

For example:

[tex]\sqrt{4}[/tex] will give you 2.

Therefore, The match up  are:

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The number of dots tells us how many times we need to add the actual number underneath the dots. So you need to use both.

Let's suppose we have the next set:

{2, 2, 2, 4, 5, 5, 6}

If you graphed it in a dot plot, then you will have:

A total of 7 dots.

To find the mean, we just compute:

[tex]M = \frac{2 + 2 + 2 + 4 + 5 + 5 + 6}{7} = 3.7[/tex]

So the number of dots tells us how many times we need to add the actual number underneath the dots. In conclusion, to find the mean you need to use both, the number of dots and the number underneath.

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Answer:

Zoe's number is 6

Step-by-step explanation:

Let the number be 'n'

a) Multiply 'n' by 3 ⇒ n*3 = 3n

  Add 4 to '3n' ⇒ 3n + 4

Add 5 to 'n' ⇒  n +5

Multiply (n+ 5) by 2 ⇒ (n +5)*2 = 2n + 5*2 = 2n + 10

    3n + 4 = 2n + 10

b) 3n + 4 = 2n + 10

Subtract 4 form both sides

       3n = 2n + 10 - 4

       3n = 2n + 6

Subtract 2n from both sides

    3n - 2n = 6

          [tex]\sf \boxed{\bf n = 6}[/tex]

Answer:

21 is probably the best answer

Answer:

It's all real numbers except whatever makes the expression undefined

Step-by-step explanation:

(−∞,∞)

Answer:

All real numbers

Step-by-step explanation: (−∞,∞)

Answer:

C. 2

Step-by-step explanation:

Gradient = [tex]\frac{change in y}{change in x}[/tex]

Gradient = [tex]\frac{6}{3}[/tex]

Gradient = 2

Answer:

square

Step-by-step explanation:

Option A is also correct somehow

but we are not sure about first 2 if they have equal sides or angles

only square have each angle 90 and all sides equal

So Option C is correct

Answer:

C. square

Step-by-step explanation:

Congruent means "the same" (having the same shape and size).

Any four-sided, 2-dimensional shape with straight sides is called a quadrilateral.

There are 6 special types of quadrilaterals:

Rectangle

Square

Rhombus

Parallelogram

Trapezoid

Isosceles Trapezoid

Kite

Conclusion

A four-sided shape that has four congruent angles and sides is a SQUARE.

Answer:

Answer: Original price = $150   Amount Paid = $90

Step-by-step explanation:

First we make a proportion 60/x = 40/100. When we cross multiply and divided to get x by itself we get $150 dollars. This is the original price of the dress. Now we take $150-$60 and we get $90. This is what Victoria paid for the dress after the 40% discount.

Hope this helps! :)

Answer:

y=3x+1

Step-by-step explanation:

From the table when X=0,y=1 thus b=1.

When

The computation of the index shows that the value of 9 × 10² will be 900.

From the information given, we are told to calculate the value of 9 × 10². This will be calculated thus:

= 9 × 10²

Note that 10² simply means that you've to multiply 10 twice. This will be:

= 10 × 10 = 100

Therefore, 9 × 10² will be:

= 9 × 100

= 900

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The answer should be A. :)

The correct rational function of the graph is,

⇒ f (x) = 1 /(x + 5)²

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The graph is shown in fgigure.

Now, By graph of function,

The graph is not defined at x = - 5.

Hence, From equation (i);

⇒ f (x) = 1 /(x + 5)²

Clearly, Function is noy defined at x = - 5.

Hence, The correct rational function of the graph is,

⇒ f (x) = 1 /(x + 5)²

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