Which shows the equation below written in the form ax² + bx + c = 0?
x+ 9 = 2(x-1)²

Answer:

3.5 × 10 to the 8th power

Step-by-step explanation:

The value of x is 5

Question is based on the Pythagorean theorem :

Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple

Consider the triangle given above:

Where “a” is the perpendicular,

“b” is the base,

“c” is the hypotenuse.

According to the definition, the Pythagoras Theorem formula is given as:

X is the side opposite to the right angle, hence it is a hypotenuse.

Now, by the theorem we know;

Hypotenuse2 = Base2 + Perpendicular2

x2 =[tex]4^{2} +3^{2}[/tex]

x2 = 16+9

x = [tex]\sqrt{25}[/tex]

Therefore, the value of x is 5

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The height of the tree in Jasmines drawing is; 6.25 inches tall

The scale factor used by Louis is; 3in : 10 ft

The scale factor used by Jasmine is; 5in : 20ft

We are told that the tree in front of the school in Luis's drawing is 7.5 inches tall. Thus;

True height of tree in Louis drawing is; (7.5 * 10)/3 = 25 ft

Thus, height of tree in Jasmines drawing = (25 * 5)/20 = 6.25 inches tall

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Answer:

37.5

Step-by-step explanation:

5x5 = 25. That's your square. For the triangle, 5x5 = 25. 25/2 = 12.5 25+12.5 = 37.5.

Answer:

The number is 11

Step-by-step explanation:

First turn this into a mathematical equation

8+3x=41

subtract 8 from both sides

3x=33

divide both sides by 3

x=11

The probability that Alphonso gets ticket 14 and Cordell gets ticket 23 is = 1/2450

Alphonso can pick a ticket from 50 tickets in 50 ways;

When Alphonso pick a ticket, then Cordell can pick a ticket in 49 ways;

Total number of ways = 50 × 49 = 2450;

Alphonso can get ticket 14 and Cordell can get ticket 23 in only one way;

So, the probability that Alphonso gets ticket 14 and Cordell gets ticket 23 is = 1/2450;

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The image of D (1, 2) is D' ( 2, 7).

The image of E (-3 -5) is E' ( -10, 0).

The image of F (4, -1) is F' ( 11, 4).

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given points are;

D (1, 2), E(-3, -5) and F(4, -1)

Now, The rule is to find the image of points is;

(x, y) → (3x - 1, y + 5)

Hence,

The image of D (1, 2) = (3 * 1 - 1, 2 + 5)

                               = (3-1, 7)

                               = (2, 7)

The image of E (-3 -5) = (3*-3 - 1, -5 + 5)

                                 = (-9-1, 0)

                                 = (-10, 0)

The image of F (4, -1) = (3*4 - 1, -1 + 5)

                                = (12-1, 4)

                                = ( 11, 4 )

Therefore, The image of D (1, 2) is D' ( 2, 7).

The image of E (-3 -5) is E' ( -10, 0).

The image of F (4, -1) is F' ( 11, 4).

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By inductive reasoning we can say that the conclusion is based on observing the four numbers in the sequence.

We are given the arithmetic series as;

5, 10, 15, 20, .......

From the formula of the nth term of an arithmetic series, we know that;

a_n = a + (n - 1)d

where;

a is first term

n is position of term

d is common difference

Thus, for this series, it is clear that the common difference is 5. Thus the fifth term is;

a_5 = 5 + (5 - 1)5

a_5 = 5 + 20

a_5 = 25

Thus, by inductive reasoning we can say that the conclusion is based on observing the four numbers in the sequence.

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The two similar triangles in this problem are given by:

C. QRS and TUV

Similar triangles share these two features:

Hence, the similar triangles are QRS and TUV, as the side lengths proportions are given as follows:

3/6 = 2.4/4.8 = 1.8/3.6.

Hence option C is correct.

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Answer:  

> y²⁴- 256 = 0

> (y⁴)

x-256 = 0

or

x= 256

Step-by-step explanation: i have no idea if i am right but pls lmk if i am wrong have a good day/night (: <3

Using the Fundamental Counting Theorem, it is found that 2,322,432 codes can be generated.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Considering that the ode will have one digit followed by four letters, the parameters are given as follows:

[tex]n_1 = 7, n_2 = n_3 = n_4 = n_5 = 24[/tex]

Hence the number of codes that can be generated is:

N = 7 x 24 x 24 x 24 x 24 = 2,322,432.

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Step-by-step explanation:

I assume the grid units are single units (1, 2, 3, ...).

to be a function every value of x must have exactly one value of y.

but that is violated at x = 2. at that point y can be either +3 or -3 (indicated by the 2 points at x=2).

so, no, it is not a function.

the domain is the interval or set of all valid x (input) values.

since we have no continuous curve but single points, it is a set :

x € {-4, -3, -2, 1, 2, 3, 6}

the range is the interval or set of all valid y (function result) values. again, it is a set for the same reasons :

y € {-3, -2, 0, 1, 3, 4}

The conclusion is that 68% of all tires will have a life between 28000 km and 32000 km.

The empirical rule in statistics states that for a normal distribution,

We are given;

Mean (μ) = 30000 km

Standard deviation (σ) = 2000 km

Using the empirical rule of 68% which lies within one standard deviation from the mean, we have;

μ ± σ = 30000 ± 2000 = (28000, 32000)

Thus, we conclude that 68% of all tires will have a life between 28000 km and 32000 km.

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Answer:

Range is 21

I believe

Step-by-step explanation:

[tex]31\% = \frac{31}{100} = 0.31 > 0.275 \\ 32.6\% = \frac{32.6}{100} = 0.326 > 0.310 \\ 0.325 = \frac{32.5}{100} = 32.5\% > 27.5\% \\ 0.310 = \frac{31}{100} = 31\% < 32.5\%[/tex]

Answer:

Letter B is the answer

Step-by-step explanation:

A. 31% < 0.275

31% < 27.5%

B. 32.6% > 0.310

32.6% > 31%

C. 0.325 < 27.5%

32.5% < 27.5%

D. 0.310 > 32.5%

31% > 32.5%

Answer:

10

Step-by-step explanation:

10*10*10=1000

10^3=1000

Answer:

Step-by-step explanation:

Answer: 144

Step-by-step explanation:

Answer: ok here is ur answer The cost for 1 chair is $2.75 and the cost for 1 table is $8.75

Use the elimination method of linear equations to find your answer.

Our equations for this problem are:

3c+5t=52 and 9c+7t=86

1. Multiply the entire first equation by -3.

-3(3c+5t=52)

2. Simplify the equation from above:

-9c-15t=-156

3. Stack the two equations on top of each other and add/subtract:

-9c-15t=-156

9c+7t=86

4. You should be left with -8t=-70. Simplify this to find the value of t:

t=8.75

5. Plug the value of t into any of the original equations and solve for c.

3c+5(8.75)=52

6. Simplify the equation above:

3c+43.75=52

7. Subtract 43.75 from both sides of the equation:

3c=8.25

8. Divide both sides by 3 to get your c value:

c=2.75

Step-by-step explanation: i really hope this helps pls lmk if i am wrong (:

The third side of the triangle have to greater than the difference of the two provided sides.

A triangle is polygon with 3 edges and 3 vertices.

So possible answers could be:

Answer:

A= 204 in²

Step-by-step explanation:

The base is 12 in, and the height is 17 in.

A=b h=12·17=204 in²

it it right  

The area of the circle based on the information illustrated is C. 28.26ft².

It should be noted that the area of a circle is given as:

= πr²

In this case, the radius is 3ft.

Therefore, the area will be:

= πr²

= 3.14 × 3²

= 3.14 × 9

= 28.26 ft²

In conclusion, the area of the circle is 28.26ft².

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The difference between the highest and the lowest points of the country is 5771 feet.

The operation of subtraction is used to calculate the difference between two numbers. If you have an object group and remove a couple of them, the object group gets smaller.

The process of subtracting one number from another is called subtraction. The way to calculate the difference between two numbers is by using the basic arithmetic operation of subtraction, which is represented by the symbol (-).

Let the sea level be x.

The highest point of the country is 5,762 feet above the sea. So, we can write it as

x+5,762

Since the lowest point is 9 feet below sea level, we can write this expression:

x-9

The difference is the result of subtraction. Therefore, we can find the expression that represents the difference between the elevations by subtracting  x+5,762 and  x-9:

(x+5,762)-(x-9)

= x+5762-x+9

= 5762+9

=5771 feet

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The sign of the other integer is positive. Value of other integer is greater than 5.

When we add two numbers of the same sign, final number has the same sign of the initial numbers

For example, we add 3 and 8,

3+8= 11

Both the numbers 3 and 8 are positive so our result is also positive.

On the other hand when we add -3 and -8, then the result will be

-3 +(-8)= -11

Both the numbers are negative, so our result also negative.

When two numbers of different sign are being added then the sign of the larger number decide the sign of the final number

For example, we add -3 and 8.

-3+8= 5

8 is larger than 3, and has positive sign, so the result will also be positive.

Suppose other number is x.

-5+x>0 (As the sum is positive)

Add 5 on both the sides

-5+x+5>0+5

x>5

As we can see the number is greater than 5 and has a positive value.

Final answer: The sign of the other integer is positive. Value of other integer is greater than 5.

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Answer:

Length = 22, Width = 16

Step-by-step explanation:

Let L be the length of the garden and W the width

The area, A = L x W = 352 ft²

It is given that L = W + 6

Substituting for L in the area equation we get

L x W

==>  (W + 6) x W = 352

Expanding the brackets

==> W.W + 6.W = 352

==> W² + 6W = 352

Subtract 352 from both sides:

W² + 6W - 352 = 0

This is a quadratic equation which can be solved using the quadratic formula.

- 352 = - 16 x 22 and -16 + 22 = 6

So we can factor the quadratic equation as
(W - 16) (W + 22) = 0

==> W = 16 or W = -22

Since we can disregard negative values in this context,

W = 16 and L = W + 6 = 16 + 6 = 22

Dimensions are Length = 22, Width = 16

Answer:

180-(35+95)=50

Step-by-step explanation:

Any triangle in the world sum of its angle equal 180

If [tex]f,g[/tex] are inverses of one another, then

[tex]f\circ g(x) = g\circ f(x) = x[/tex]

Given [tex]f(x)=x^2-1[/tex] and [tex]g(x)=\sqrt{x-8}[/tex], then

[tex]f\circ g (x) = f(g(x)) = f(\sqrt{x-8}) = \left(\sqrt{x-8}\right)^2 - 1 = \boxed{x - 9} \neq x[/tex]

so right away we know [tex]f[/tex] and [tex]g[/tex] are not inverses.

In the other direction, we come to the same conclusion.

[tex]g\circ f(x) = g(f(x)) = g(x^2 - 1) = \sqrt{(x^2-1)-9} = \boxed{\sqrt{x^2 - 9}} \neq x[/tex]