If using the method of completing the square to solve the quadratic equation
x2 + 10x + 16 = 0, which number would have to be added to "complete
the square"?

Answer:

12

Step-by-step explanation:

6y - 3z

6(4) - 3(4)

24 - 12

12

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The equation of the line in slope-intercept form is y = 2x + 2.

The equation of the line that corresponds to the given table can be written in slope-intercept form y = mx + b where m is the slope and b is the y-intercept.

For finding the slope, we can use the formula:m = (y2 - y1) / (x2 - x1)We can choose any two points from the table to calculate the slope.

Let's take the first two points from the table (1, 4) and (3, 8)m = (y2 - y1) / (x2 - x1)m = (8 - 4) / (3 - 1)m = 4 / 2m = 2Now we have the slope which is 2.

To find the y-intercept we can substitute one of the points from the table and the slope into the equation and solve for b

y = mx + b4 = 2(1) + b4 = 2 + bb = 2Now we have the y-intercept which is 2. Therefore, the equation of the line in slope-intercept form is y = 2x + 2.

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Answer:

f(x) = 1/4x +2

Step-by-step explanation:

The y-intercept formula is y = mx + b. b is the y-intercept. The line crosses the y-axis at 2, so the y-intercept is 2. m is the slope and it is rise/run (rise over run). It rises (from the y-axis) once and runs 4 times. Therefore, the slope is 1/4. The equation is f(x) = 1/4x +2.

a) The characteristic equation for matrix A, given as 0 3 -1 0 -1 3, is entered as [tex]p^3 - 3p^2 + 2p = 0[/tex].

b) The eigenvalues of the matrix A are entered as p = 0, p = 1, p = 2.

c) To find a matrix P that orthogonally diagonalizes A, further information is needed.

a) The characteristic equation is obtained by finding the determinant of (A - pI), where A is the given matrix and p is the parameter. In this case, the matrix A is 0 3 -1 0 -1 3. Subtracting p from the diagonal entries, the determinant is calculated, resulting in [tex]p^3 - 3p^2 + 2p = 0[/tex].

b) To find the eigenvalues, we set the characteristic equation equal to zero and solve for p. In this case, we have [tex]p^3 - 3p^2 + 2p = 0[/tex]. By factoring out p, we get [tex]p(p^2 - 3p + 2) = 0[/tex]. The roots of this equation are p = 0, p = 1, and p = 2. Therefore, the eigenvalues of matrix A are 0, 1, and 2.

c) To find a matrix P that orthogonally diagonalizes A, we need to determine the corresponding eigenvectors for each eigenvalue. However, the information provided does not include the eigenvectors or specify any additional requirements to find matrix P. Without the eigenvectors or further instructions, it is not possible to determine the matrix P that orthogonally diagonalizes matrix A.

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The probability of getting exactly one queen when selecting 49 cards from a shuffled deck is 28.3%.

To determine the probability of selecting a queen from a shuffled deck of cards, you should divide the number of queen cards by the total number of cards in the deck.

Since there are 4 queens in a standard deck of 52 cards, the probability of drawing a queen from a shuffled deck is 4/52, or 1/13.

To calculate the probability of getting a queen when selecting 49 cards from a shuffled deck, you need to use the binomial probability formula.

In this case, the probability of getting a queen on any one draw is p = 1/13, and the number of trials is n = 49.

The formula is:

[tex]P(x) = nCx * p^x * (1-p)^(n-x)[/tex]

where x is the number of successes, and nCx is the number of combinations of n things taken x at a time.

In this case, x = 1 because we want to find the probability of getting one queen. So,

[tex]P(1) = 49C1 * (1/13)^1 * (12/13)^48[/tex]

P(1) = 49 * (1/13) * 0.7328

P(1) = 0.283

This means that the probability of getting exactly one queen when selecting 49 cards from a shuffled deck is approximately 0.283 or 28.3%.

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Median length of time required to review an application = (45 + 100)/2= 72.50 Hence, the correct option is A, 72.50

Given times (in minutes) that several underwriters took to review applications for similar insurance coverage are 100, 110, 42, and 45 and we need to find the median length of time required to review an application.What is the median?The median is the middle value when a data set is ordered from least to greatest.To find the median of a data set, the first step is to write the data set in order from least to greatest. In the above given dataset,Let's first order these numbers from least to greatest;42, 45, 100, 110 Now we can see the median will be between 45 and 100, so we just need to find the mean of these two numbers. the correct option is A

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The probability that a randomly chosen car will need no repairs is 72%. The probability that a car will need no more than one repair is 92%. The probability that a car will need some repairs is 28%.

To find the probability of no repairs, we subtract the sum of the probabilities of needing one, two, or three or more repairs from 1. The probability of needing one repair is 17%, so the probability of no repairs is 1 - 0.17 = 0.83. However, we also need to consider the probabilities of needing two repairs (7%) and three or more repairs (4%). So, the probability of no repairs is adjusted by subtracting these probabilities as well. Thus, the final probability of no repairs is 1 - (0.17 + 0.07 + 0.04) = 0.72, or 72%.

To find the probability of no more than one repair, we need to sum the probabilities of needing no repairs and needing one repair. As mentioned earlier, the probability of no repairs is 0.72. The probability of needing one repair is 0.17. Therefore, the probability of no more than one repair is 0.72 + 0.17 = 0.89, or 89%.

Finally, to find the probability of some repairs, we subtract the probability of no repairs from 1. We already determined that the probability of no repairs is 0.72. Therefore, the probability of some repairs is 1 - 0.72 = 0.28, or 28%.

In summary, the probability that a car chosen at random will need no repairs is 72%. The probability of no more than one repair is 89%, and the probability of some repairs is 28%.

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Answer:

number of members in 2006=190

230members on 2010

Step-by-step explanation:

2008-2006=2

20*2+150= 190 ans (1)

b)

20x+150=230

20x=230-150= 80

x= 80/20=4---ans (2)

In other words, everything but -30.

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

Explanation:

Let's solve for x

[tex]-\frac{1}{5}x + 3 \le 7\\\\-\frac{1}{5}x \le 7-3\\\\-\frac{1}{5}x \le 4\\\\x \ge 4*(-5)\\\\x \ge -20\\\\[/tex]

Note how the inequality sign flips when we multiply both sides by the negative number.

Since x can be -20 or larger, this means that the values -20,-10,0,10,20 are all solutions. Only -30 is a non-solution. It might help to draw out a number line to see which values work and don't work.

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

An alternative method is to plug each value from the set {-30,-20,-10,0,10,20} into the original inequality and simplifying. If you get a true statement at the end, then the value is a solution.

I'll show an example with x = -30 and x = -20 to show a non-solution and a solution. I'll let you check the others.

So let's start with x = -30

[tex]-\frac{1}{5}x + 3 \le 7\\\\-\frac{1}{5}(-30) + 3 \le 7\\\\6 + 3 \le 7\\\\9 \le 7\\\\[/tex]

The last statement is false because 9 is not 7 or smaller than 7. So that's why x = -30 is not a solution.

Now let's try x = -20

[tex]-\frac{1}{5}x + 3 \le 7\\\\-\frac{1}{5}(-20) + 3 \le 7\\\\4 + 3 \le 7\\\\7 \le 7\\\\[/tex]

This is a true statement since any number is equal to itself.

You should find that x = -10, x = 0, x = 10, and x = 20 lead to true statements.

Answer:A

Step-by-step explanation:

the girl that said it first i stoled it

Answer:

We can't make plots here, but I can give an explanation.

A scatter plot provides a visual representation of the showcased data as opposed to a numerical display, as such allowing more ease of use when extracting data.

Step-by-step explanation:

Answer:

8 times

Step-by-step explanation:

15+11+9+12+6+11=64

11 out of 64 is purple

so ?:50

    11:64

do the ratio:

64/1.28=50

11/1.28=8.59375

So Rosa would pick it about 8 times

Answer:

c. 31(-10) = -310

Step-by-step explanation:

because...........

The correct answer is (1) 3/7. they can finish the ditch in (3/7) of the time that the worker takes working alone.

To solve this problem, let's assume that the worker takes 1 unit of time to complete the ditch working alone.

The worker's rate of work is 1 ditch per unit of time.

Each assistant works at a rate that is 2/3 as fast as the worker. Therefore, each assistant's rate of work is (2/3) ditch per unit of time.

When all three of them work together, their combined rate of work is the sum of their individual rates.

Worker's rate + 2 Assistants' rate = 1 + 2(2/3) = 1 + 4/3 = 7/3

Hence, they can finish the ditch in (3/7) of the time that the worker takes working alone.

Therefore, the correct answer is (1) 3/7.

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Answer:

See below

Step-by-step explanation:

Let the number be n or m

1: The product of a number and 8÷4

2: five times a number decreased by eight

3: The sum of the square of a number and a second number

4: three times the difference of a number and seven

5: 9.85 less than the product of 37 and a number

Answer: 82 miles per hour

Step-by-step explanation:

246/3

82 miles per hours

Answer:

82 miles per hour

Step-by-step explanation:

246/3

Answer:

Vertex : (-2,-121)

Roots : x=9,-13

Step-by-step explanation: Rewrite the vertex form and use this form to fine the vertex (h,k).

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with zero and solve for x.

I hope this helps you out.

The magnitude of the electrostatic force that acts on each sphere are: 1.6×10⁻⁹N. The electrostatic force is repulsive.

The electrostatic force is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the charges. Hence, if two charges of like signs are brought close to each other, the force between them is repulsive and if two charges of opposite signs are brought close to each other, the force between them is attractive.

Given that two very small spheres are initially neutral and separated by a distance of 0.50m. Suppose that 3.0 x 10¹³ electrons are removed from one sphere and placed on the other.A charge of - 3.0 × 10¹³ electrons is transferred from one sphere to the other. Hence, one sphere becomes negatively charged while the other one becomes positively charged. The magnitude of the charge on each sphere can be determined as follows:

We know that the elementary charge on one electron = 1.6 × 10⁻¹⁹ C. Therefore, the charge on 3.0 × 10¹³ electrons = 3.0 × 10¹³ × 1.6 × 10⁻¹⁹ C= 4.8 × 10⁻⁶ C.

The magnitude of the electrostatic force that acts on each sphere is given by Coulomb's law as:

F = k × (q1 × q2) / r²Here,k = Coulomb's constant = 9 × 10⁹ Nm²/C²q1 = charge on sphere 1 = 4.8 × 10⁻⁶ Cq2 = charge on sphere 2 = 4.8 × 10⁻⁶ Cr = separation between the spheres = 0.50 m

Substituting these values in the Coulomb's law expression, we get:

F = 9 × 10⁹ × (4.8 × 10⁻⁶)² / (0.50)²= 1.6 × 10⁻⁹ N.

Thus, the magnitude of the electrostatic force that acts on each sphere is 1.6 × 10⁻⁹ N. Since both the spheres have the same charge (one positive and the other negative), the force between them is repulsive.

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Step-by-step explanation:

(x - 2) 2 - 16 =0

2 - 16 (x - 2) =0

2x - 16x - 4 + 32 = 0

2x - 16x = 0 + 4 - 32

-14x = -28

x = -28/-14

x = 2

Double Checking Answer:

2 - 16 (2 - 2)

2 - 16 (0)

=0

OR

2 - 16 × (2 - 2)

4 - 32 - 4 + 32

= 0

;)

Answer:

[tex](-6 ,3 )[/tex]

Step-by-step explanation:

Midpoint Formula: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]

Simply plug in your 2 coordinates into the midpoint formula to find midpoint:

[tex](\frac{-2+-10}{2} ,\frac{7+-1}{2} )[/tex]

[tex](\frac{-2-10}{2} ,\frac{7-1}{2} )[/tex]

[tex](\frac{-12}{2} ,\frac{6}{2} )[/tex]

[tex](-6 ,3 )[/tex]

The range of the exponential function y is [0, 62,150]

In the given function of the exponential function, [tex]y = 62,150 (0.9999)^x[/tex], x is the number of months since the car was purchased.

The initial value of the function is 62,150. The car depreciates over time because the function decreases when the value of x increases. The base of the exponential function is 0.9999 which is less than 1.

The range of the exponential function y based on its equation and the context of the problem is [0, 62,150].The reason for this is because the initial value of the function is 62,150.

This means that the value of y can never be more than 62,150. Also, the base of the exponential function is less than 1 which means that the function decreases over time.

Therefore, the minimum value of the function is 0. Therefore, the range of the exponential function y is [0, 62,150]. Hence, the answer is [0, 62,150].

An exponential function is what?

Calculating the exponential growth or decay of a given set of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.

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Answer:

LHK =  101

Step-by-step explanation:

LGK + LHK = 180

79 + LHK = 180

LHK = 180 -79

LHK =  101

A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven.

Answer: LHK= 101

The simplified ratio f:h:w is 20:15:8.

The ratio of f:h:w, we need to combine the given ratios of f:h and f:w.

The ratio f:h is given as 4:3 means that for every 4 units of f, there are 3 units of h.

The ratio f:w is given as 5:2 means that for every 5 units of f, there are 2 units of w.

To simplify the ratio f:h:w, we need to find the common factors among the three quantities (f, h, and w).

The common factor is f.

So, the simplified ratio is obtained by dividing each quantity by the common factor f.

Dividing f by f results in 1, which simplifies the ratio.

Dividing h by f gives us h/f, and dividing w by f gives us w/f.

Therefore, the simplified ratio f:h:w is 1:h/f:w/f.

Since h/f = 3/4 and w/f = 2/5, the simplified ratio becomes:

1 : 3/4 : 2/5

To remove the fractions, we can multiply each term by a common multiple of the denominators.

The least common multiple (LCM) of 4 and 5 is 20.

Multiplying the ratio by 20, we get:

20 : (3/4) × 20 : (2/5) × 20

which simplifies to:

20 : 15 : 8

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Answer:

B./8

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Answer:

D because it’s D

x+2-3=7

x-1=7

x=8

Answer:Eight 8 8 The answer is 8

Step-by-step explanation: