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The zeros of this expression are irrational, so it cannot be factored using integers.

When factoring a quadratic expression, we are trying to express it as the product of two binomial factors.

In some cases, such as when the quadratic has irrational zeros, it may not be possible to factor it using integers.

In the case of the quadratic expression x² - 12x + 13, the discriminant (b^2 - 4ac) is equal to (-12)² - 4(1)(13)

= 144 - 52

= 92.

Since the discriminant is positive and not a perfect square, the zeros of the quadratic are irrational.

This means that the expression cannot be factored into two binomial factors with integer coefficients.

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Answer: z=3

Step-by-step explanation:

In the equation [tex]y = -2(0.5)^x[/tex], the initial amount (a) is -2, and the growth/decay factor (b) is 0.5.

In the given equation, [tex]y = -2(0.5)^x[/tex], we can identify the initial amount and the growth/decay factor.

The equation is in the form of exponential decay, as the base (0.5) is between 0 and 1, resulting in the function decreasing as x increases.

The initial amount, denoted as "a," is the coefficient in front of the exponential term. In this case, the initial amount is -2. This means that when x = 0, y = -2.

The growth/decay factor, denoted as "b," is the base of the exponential term. In this equation, the base is 0.5. The value of the base determines how quickly the function decreases or decays.

To summarize:

Initial amount (a) = -2

Growth/decay factor (b) = 0.5

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The solution to the system of equations is  x = 5.4 and y = -1.4

From the question, we have the following parameters that can be used in our computation:

-x=y-4 y=4x+9

So, we have

-x = y - 4

y = 4x + 9

Rewrite the equation as

x = -y + 4

y = 4x + 9

So, we have

y = 4(-y + 4) + 9

Open the bracket and evaluate

5y = 9 - 16

So, we have

y = -1.4

Recall that

x = -y + 4

So, we have

x = 1.4 + 4

Evaluate

x = 5.4

Hence, the solution is  x = 5.4 and y = -1.4

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Answer:

Step-by-step explanation:

Area of parallelograph = bh

b=20  h =42

A=(20)(42) = 840 mm²

The reflections are described below.

We know that,

There are two types of reflection:

Reflection with respect to X-axis:

The x-coordinates of a point stay constant when it is mirrored across the X-axis. However, the Y-coordinates are changed into their inverse signs.

As a result, the X-axis reflection of the point (x, y) is (x, -y).

Reflection with respect to Y- axis:

The Y-coordinates of a point stay constant when it is mirrored across the Y-axis. However, the X-coordinates are changed into their inverse signs.

As a result, the Y-axis reflection of the point (x, y) is (-x, y).

Now the reflection is as following:

The point (x, y) when reflected across the x-axis becomes (x', y') = (x, -y)

The point (x, y) when reflected across the y-axis becomes (x', y') = (-x, y)

The point (x, y) when reflected across the line y = x becomes (x', y') = (y, x)

The point (x, y) when reflected across the line y = -x becomes (x', y') = (-y, x)

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Answer: 49.4 thats the answer i devided it

Using a trigonometric relation, we can see that the value of x is 10.39

Here we have a right triangle. We can see that we know the measures of the hypotenuse, and the angle opposite to the side x.

Then to get the value of x, we can use the trigonometric relation:

sin(a) = (opposite cathetus)/hypotenuse.

Replacing the values that we know, we will get.

sin(60°) = x/12

solve that for x:

12*sin(60°) = x

10.39 = x

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The relationship between angles 8 and 7 is that they are supplementary. option B is correct.

Given that a quadrilateral, with three parallel lines, we need to find the relation between angles 8 and 7,

We know that the adjacent angles between the parallel lines are supplementary,

We know that,

Supplementary angles are a pair of angles that add up to 180 degrees. In other words, if you have two angles that are supplementary, the sum of their measures will always be 180 degrees.

So,

The relation between the angles is that they are Supplementary angles.

Hence the option B is correct.

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Answer:

Step-by-step explanation:

Option (D) D. Points Q and R is used to removed to make this relation a function.

To determine which two points could be removed to make the relation a function, we need to check if there are any repeated x-values (inputs) in the given set of points. In a function, each input should have a unique output.

Let's analyze the given options:

A. Points R and S: (R, 3), (S, 5)

B. Points Q and T: (Q, 2), (T, 5)

C. Points P and Q: (P, 1), (Q, 2)

D. Points Q and R: (Q, 2), (R, 3)

In this case, if we remove points Q and R, we eliminate the repeated x-value of 2, which ensures that each input has a unique output. Therefore, the answer is:

D. Points Q and R.

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Answer:

0.168 ft aprox

Step-by-step explanation:

To solve this problem, we can use similar triangles and proportions. Let's denote the distance ahead of the car where the light beam hits the ground as "x" (in feet).

According to the given information, the light beam drops 2 inches for every 26 feet horizontally. We can set up the following proportion:

2 inches / 26 feet = x inches / x + 26 feet

To solve for x, we can cross-multiply and solve the resulting equation. Let's convert inches to feet to maintain consistent units:

2 inches = 2/12 feet = 1/6 feet

1/6 feet / 26 feet = x feet / x + 26 feet

1/6 * (x + 26) = 26 * x

x/6 + 26/6 = 26x

x + 26 = 156x

156x - x = 26

155x = 26

x = 26 / 155 ≈ 0.168 ft

Therefore, the headlights will hit the ground approximately 0.168 feet (or 2.016 inches) ahead of the car.

Answer:

-3.8 > -4.5

Step-by-step explanation:

Convert the fraction to decimal and then compare.

[tex]\sf -4\dfrac{1}{2}=\dfrac{-9}{2}[/tex]

          = -4.5

Now compare (-3.8) & (-4.5)

-3.8 > -4.5

Answer:

solution:  (0,3)

Step-by-step explanation:

You can find the solution when the two lines intersect.

Answer:

[a] 12 units

Step-by-step explanation:

The answer is (D) 44 units

1. The formula for the area of a rhombus is A= [tex]\frac{d_{1} d_{2}}{2}[/tex]

2. Fill in the information we know:

3. Now work backward:

4. Solve it:

Hence 44 units (D) is your answer

Answer:

a set of numbers in order of least to greatest

Step-by-step explanation:

ln 54.60 = 4         e^x both sides

e ^ (ln 54.60) = e^4

         54.60 = e^4                 Done.

The quadratic equation in standard form that corresponds to the graph shown above is f(x) = x² + 2x - 8

In Mathematics and Geometry, the standard form of a quadratic function can be modeled and represented by using the following mathematical expression;

y = ax² + bx + c

Where:

In this scenario and exercise, we would write a quadratic function that represent f(x) in standard form and with a leading coefficient of 1 by using the roots (-4, 0) and (2, 0) as follows;

f(x) = (x + 4)(x - 2)

f(x) = x² - 2x + 4x - 8

f(x) = x² + 2x - 8

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The solution of the given equations is: (3,-1).

Here, we have,

from the given graph we get,

1st line passes through ( 0,2 ) and (2,0)

so, equation: y = -x+2 .....1

2nd line passes through ( 0,-4 ) and (4,0)

so, equation: y = x-4 .....2

now, from 1 and 2 we get,

-x + 2 = x -4

or, 2x = 6

or, x = 3

so, we have, y = -1

so, the point of intersection is (3, -1)

Hence, The solution of the given equations is: (3,-1).

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Answer:

Step-by-step explanation:

Given the following quadratic sequences, you want the value of x and the expression for the n-th term.

One way to determine x is to look at the differences between terms. The "second difference" is constant for a quadratic sequence, and the third difference is zero.

The quadratic equation for the n-th term can be found by solving for its coefficients. The three known values of the sequence can give rise to three linear equations in the three unknown coefficients. These can be solved by your favorite method. We use this approach in the following.

First differences are the differences between each term and the one before:

  {6, x-5, 35-x}

Second differences are the differences of these:

  {x -11, 40 -2x}

Third differences are zero:

  51 -3x = 0   ⇒   x = 17

The value of x is 17.

The expression for the n-th term of the sequence can be written as ...

  an = a·n² +b·n +c

We are given values of a1, a2, and a4. This lets us write 3 equations for a, b, and c. The solution of those is shown on the first line of the first attachment. (The second line shows the evaluation of this quadratic equation for n=3. It gives 17, which we already knew.)

  an = 3n² -3n -1

The last line of the first attachment shows us the expression for the third differences. The value of that is zero, so ...

  -3x +60 = 0   ⇒   x = 20

The value of x is 20.

As in the above problem, the matrix of equations for the quadratic coefficients can be reduced to give the coefficient values. That tells us the n-th term of this sequence is ...

  an = 3n² -4n +5

The last line in the second attachment tells us this expression for the n-th term properly computes the 3rd term (x), as above.

__

Additional comments

You can also use quadratic regression to find the coefficients of the formula for the quadratic sequence. This is shown in the 3rd attachment.

If you're trying to avoid using a calculator, you can write the equations out and solve them in an ad hoc way. In case you cannot tell, the equations for the coefficients of an = a·n² +b·n +c for the first problem are ...

You can also use the first values of the sequence (p), first difference (q), second difference (r) to write the quadratic:

  an = p +(n -1)(q +(n -2)/2(r))

For (p, q, r) = (-1, 6, 6), this is an = -1 +(n -1)(3n) . . . . . . for the first sequence.

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The number of combinations of the 5 white balls and 1 red ball are possible is 1.

We are given that;

White balls=5

Red ball=1

Now,

To find the number of combinations of 5 white balls and 1 red ball, we can use the combinations formula12:

[tex]nCr = n! / (r! (n-r)!)[/tex]

where n is the total number of objects, r is the number of objects to be selected, and ! is the factorial operator.

we can plug in these values into the formula:

[tex]6C6 = 6! / (6! (6-6)!) 6C6 = 6! / (6! 0!) 6C6 = 1 / (1 1) 6C6 = 1[/tex]

So, there is only one combination of 5 white balls and 1 red ball. This makes sense because the order of selection does not matter in a combination. No matter how we arrange the balls, we will always have the same group of 5 white balls and 1 red ball.

Therefore, by combinations and permutations the answer will be 1.

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The value of the given expression is,

[tex]4^{- 5/2[/tex] =  1/32

[tex](1/16) ^ {- 3/2[/tex] = 64

We have to given that,

Expressions to solve are,

⇒ [tex]4^{- 5/2[/tex]

And, [tex](1/16) ^ {- 3/2[/tex]

We  know that,

Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself

Now, We can simplify the given expression,

By using law of exponents

We get,

⇒ [tex]4^{- 5/2}[/tex]

⇒ [tex]2^{2(- 5/2)}[/tex]

⇒ 2⁻⁵

⇒ 1/2⁵

⇒ 1/32

Thus,

The value of   [tex]4^{- 5/2[/tex] =  1/32

The given expression is,

⇒[tex](1/16) ^ {- 3/2[/tex]

By using law of exponents

We get,

⇒ [tex]16 ^{3/2}[/tex]

⇒ [tex](4^2)^{3/2}[/tex]

⇒ 4³

⇒ 64

The value of  [tex](1/16) ^ {- 3/2[/tex] = 64

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The missing side of the right triangle is √57

To find the missing side of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

Let's assume the missing side is represented by the variable x.

According to the Pythagorean theorem:

(2√6[tex])^2 + x^2 = 9^2[/tex]

Simplifying, we have:

[tex]4 \times 6 + x^2 = 81\\24 + x^2 = 81\\x^2 = 81 - 24\\x^2 = 57[/tex]

Taking the square root of both sides, we get:

x = √57

Thus, the missing side of the right triangle is √57

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The degrees of freedom for a sample size of 27 is 26, the alpha or significance level for a 98% confidence level is 0.02, and the t-critical value can be found using the t-table corresponding to a 98% confidence level and 26 degrees of freedom.

To find the degrees of freedom, alpha (significance level), and the t-critical value using the t-table, we need to consider the given information:

n = 27: This represents the sample size, which is 27 in this case.

CL = 98%: CL stands for the confidence level.

It indicates the level of confidence we want to have in our interval estimate.

In this case, the confidence level is 98%.

Degrees of Freedom (df): For a t-distribution, the degrees of freedom depend on the sample size.

Since we have a sample size of 27, the degrees of freedom would be n - 1.

Therefore, the degrees of freedom would be 27 - 1 = 26.

Alpha (α): Alpha, or the significance level, represents the probability of making a Type I error, which is rejecting a true null hypothesis.

The alpha level is determined by subtracting the confidence level from 1. In this case, the alpha level would be 1 - 0.98 = 0.02.

T-Critical Value: To find the t-critical value corresponding to a specific confidence level and degrees of freedom, we can consult the t-table. Since we have a confidence level of 98% and degrees of freedom of 26, we need to find the value that corresponds to the area of 0.01 (half of 1 - 0.98) in the t-distribution table.

The t-critical value would be the value from the table that matches these criteria.

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The slope of the line that is perpendicular to the line y = 3x - 8 is -1/3.

The given line has an equation in slope-intercept form, which is y = 3x - 8. In this form, the coefficient of x represents the slope of the line.

Therefore, the slope of the given line is 3.

To find the slope of a line perpendicular to the given line, we need to take the negative reciprocal of the slope.

The negative reciprocal of 3 is -1/3.

Therefore, the slope of the line that is perpendicular to the line y = 3x - 8 is -1/3.

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The amount of fabric required is 400.551 ft².

We have,

CB= 8 feet

CF= 13 feet

AM = 8 feet

Using Pythagoras

AC² = AM² + CM²

AC = √64+16 = √80 = 4√5 feet

Now, the formula for Triangular prism is

= (Sum of three sides of triangle face)l + base area

= (4√5 + 4√5 + 8)13 + 8 x 8

= 104√5 + 104 + 64

= 104√5 + 168

= 232.551 + 168

= 400.551 ft²

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Answer:

A. 16.7%

B. 89.5%

Step-by-step explanation:

A) Inside the Square

length:4

The square has an area of 16 square units. The rectangle has an area of 96 square units. The probability of a point chosen randomly inside the rectangle being in the square is:

(area of square)/(area of rectangle)

= 16/96

= 0.16666666666666666

This is equal to 16.7%.

B) Outside the right angles Triangle

base:4 height 5

The triangle has an area of 10 square units. The rectangle has an area of 96 square units. The probability of a point chosen randomly inside the rectangle being outside the triangle is:

(area of rectangle - area of triangle)/(area of rectangle)

= (96 - 10)/96

= 0.8958333333

This is equal to 89.5%.