What number should be added to both sides of the equation to complete the square? x^2 â 10x = 7?

The solutions to the equation c² = 5c are c = 0 and c = 5.

We have,

To solve the equation c² = 5c by factoring,

we can rearrange it as:

c² - 5c = 0

Then we can factor out the common factor of c, giving:

c(c - 5) = 0

Now we can apply the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero.

So we have:

c = 0 or c - 5 = 0

Solving for c in each case, we get:

c = 0 or c = 5

Therefore,

The solutions to the equation c² = 5c are c = 0 and c = 5.

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The correct answer to fill in the blank is:

“Cognitive flexibility”

Cognitive flexibility refers to a person’s ability to adapt the mental processing strategies to face new and unexpected situations or problems. In this case, some of the students who initially did not solve the problem transformed their way of solving the puzzle after the discussion thus getting it right the next time.

Answer:

its answer d

Step-by-step explanation:

It's better to describe the center of distribution in Bakery A using the mean because the data is symmetric, while for Bakery B, the median is preferred due to asymmetric data.

To determine whether it's better to describe the centers of distribution in terms of the mean or the median for each bakery, we need to consider the shape of the data distribution.

For Bakery A:

- The data appears to be relatively symmetric, with values ranging from 34 to 61.

- There are no extreme outliers that significantly skew the data.

For Bakery B:

- The data is not symmetric; there is a wide range of values from 10 to 57.

- There is a notable outlier (10) that is much lower than the rest of the data.

Given these observations:

- For Bakery A, since the data is symmetric and there are no significant outliers, the mean (average) would be an appropriate measure of the center.

- For Bakery B, because the distribution is not symmetric and there is a significant outlier, the median (middle value) would be a more robust measure of the center.

So, the correct answer is:

C) Mean for Bakery B because the data is symmetric; median for Bakery A because the data is not symmetric.

Complete Question:

The number of bagels sold daily for two bakeries is shown in the table:

Bakery A 45 52 51 48 61 34 55 46

Bakery B 48 42 25 45 57 10 43 46

Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.

A) Mean for both bakeries because the data is symmetric

B) Median because the distribution is not symmetric for both bakeries

C) Mean for Bakery B because the data is symmetric; median for Bakery A because the data is not symmetric

D) Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric

The correct answer is B): Median because the distribution is not symmetric for both bakeries.

Let's first calculate the mean and median for each bakery:

Bakery A:

Data: 45, 52, 51, 48, 61, 34, 55, 46

Mean (average):

[tex]\[ \text{Mean} = \frac{45 + 52 + 51 + 48 + 61 + 34 + 55 + 46}{8} = \frac{392}{8} = 49 \][/tex]

Median (middle value):

Arrange the data in ascending order: 34, 45, 46, 48, 51, 52, 55, 61

[tex]\[ \text{Median} = \frac{48 + 51}{2} = 49.5 \][/tex]

For Bakery A, the mean is 49 and the median is 49.5. The median (49.5) is slightly higher than the mean (49), indicating a slight right skew in the data.

Bakery B:

Data: 48, 42, 25, 45, 57, 10, 43, 46

Mean (average):

[tex]\[ \text{Mean} = \frac{48 + 42 + 25 + 45 + 57 + 10 + 43 + 46}{8} = \frac{316}{8} = 39.5 \][/tex]

Median (middle value):

Arrange the data in ascending order: 10, 25, 42, 43, 45, 46, 48, 57

[tex]\[ \text{Median} = \frac{43 + 45}{2} = 44 \][/tex]

For Bakery B, the mean is 39.5 and the median is 44. The mean (39.5) is lower than the median (44), indicating a left skew in the data.

Bakery A: The median (49.5) is slightly higher than the mean (49), suggesting a slight right skew. Given this slight skewness, the  median might be a better measure of central tendency for Bakery A.

Bakery B: The mean (39.5) is noticeably lower than the median (44), indicating a left skew. Therefore, the median would likely be a better measure of central tendency for Bakery B.

Based on this analysis, the correct answer is B): Median because the distribution is not symmetric for both bakeries.

Complete Question:

The number of bagels sold daily for two bakeries is shown in the table:

Bakery A 45 52 51 48 61 34 55 46

Bakery B 48 42 25 45 57 10 43 46

Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.

A) Mean for both bakeries because the data is symmetric

B) Median because the distribution is not symmetric for both bakeries

C) Mean for Bakery B because the data is symmetric; median for Bakery A because the data is not symmetric

D) Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric

Part A. To solve for the distance travelled during the interval, all we have to do is to plug in values of t = 3 and t = 3.5 in the equation and the difference would be the answer:

when t = 3: s = 16 (3)^2 = 144 m

when t = 3.5: s = 16 (3.5)^2 = 196 m

Therefore the distance travelled within the interval is:

196 m – 144 m = 52 m

Part B. The velocity is calculated by taking the 1st derivative of the equation. v = ds / dt

s = 16 t^2

ds / dt = 32 t = v

when t = 3: v = 32 (3) = 96 m / s

when t = 3.5: v = 32 (3.5) = 112 m / s

Therefore the average velocity is:

(96 + 112) /2 = 104 m / s

Part C. We can still use the formula v = 32 t and plug in the value of t = 3

v = 32 t = 32 (3)

v = 96 m / s

To calculate the distance and velocities for the ball in question, we use the formula s(t)=16t^2, calculate differences, and use limits as the intervals approach an instant.

The formula s(t)=16t2 gives the distance s(t) in feet that a ball has traveled after t seconds when dropped from a state of rest. To find the distance during the time interval [3,3.5], we calculate s(3.5) and s(3), and then find the difference: s(3.5) = 16 × (3.5)2 and s(3) = 16 × (3)2.

The average velocity over the interval [3,3.5] is the change in distance divided by the change in time, which is computed as ∆ s/ ∆ t.

For the instantaneous velocity at t=3, we compute the average velocities over smaller and smaller intervals approaching the instant t=3. As these intervals become smaller, the average velocity approaches the instantaneous velocity.

Answer:

C is the answer.

Step-by-step explanation:

52.5 + 75 = x

x + 75 = 52.5

75 – 52.5 = x

x – 52.5 = 75

Final answer:

When solving math problems with rules of exponents, it is important to understand key concepts such as multiplication of exponentials, taking square roots of exponentials, and dividing exponentials.

Explanation:

When solving math problems with rules of exponents, there are several key concepts to keep in mind:

It is important to understand these rules and practice applying them to various problems in order to master solving math problems with rules of exponents.

In the given diagram, the points that are shown to be collinear are H and E.

Collinearity in geometry refers to the condition where three or more points lie on the same straight line. In this case, points H and E are collinear as they lie on the same straight line, which is represented by a vertical double-headed arrow passing through them.

The diagram consists of two parallelograms, labeled 'I M' and 'E P', with three points inside each. In the parallelogram 'I M', the points are labeled as I, H, and J from top to bottom. Similarly, in the parallelogram 'E P', the points are labeled as F, E, and G from top to bottom. Among these points, only H and E share the same straight line, making them collinear. The other points do not share this line and hence are not collinear with H and E. This concept is fundamental in understanding geometric relationships and properties.

Rational functions are functions that can be written as the ratio of two polynomial functions, while inverse variations are a type of rational function where the product of two varying quantities is a constant.

A rational function is any function that can be written as the ratio of two polynomial functions. Both the numerator and the denominator are polynomials. For example, f(x) = (2x^2 + 3)/(x - 5) is a rational function where 2x^2 + 3 and x - 5 are polynomial functions.

On the other hand, an inverse variation, or inverse proportion, is a specific type of rational function where the product of two varying quantities is a constant. It is in the form of y = k/x, where k is a nonzero constant. For example, if y varies inversely as x, then the product of x and y is constant, which means xy = k.

To summarize, all inverse variations are rational functions since they can be expressed as a ratio of two polynomials. However, not all rational functions are inverse variations since not all can be written in the form y = k/x.

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6^2 + 3^2 = x^2

36 + 9 = x^2

45=X^2

X= sqrt(45) = 3squareroot5

 answer is A

Answer:  Option 'd' is correct.

Step-by-step explanation:

Since we have given that

[tex]f(x) = x^2[/tex]

We need to shift the function f(x) 3 units to the right to obtain the graph of g(x).

As we  know that shifting right is the horizontal shift.

And f(x-h) = g(x) , here f shift right h units.

so, After shifting 3 units right, we get that

[tex]g(x)=(x-3)^2[/tex]

Hence, Option 'd' is correct.

Answer:

Option C is correct.

The missing steps in this proof is; [tex]\angle 1 \cong \angle 4[/tex] and [tex]\angle 3 \cong \angle 5[/tex].

Explanation:         

Given ΔABC.

Prove that:  The sum of the interior angle measures of ΔABC is [tex]180^{\circ}[/tex]

Let A ,B and C forms a triangle    [Given]

Parallel lines are those two lines that are always the same distance apart and never touch.

then, by the definition of parallel lines and labeling angles

DE be the line passing through B, parallel to AC, with angles as labelled in the figure as shown below in the attachment.

Alternative Interior Angle theorem states that the angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles also this theorem says that when the lines are parallel, then the alternate interior angles are equal.

Then,

[tex]\angle 1 \cong \angle 4[/tex] and                              

[tex]\angle 3 \cong \angle 5[/tex]        [By Alternative Interior angle theorem]            

Angles are always congruent if their measures in degrees are equal.

therefore,

[tex]m\angle 1 =m\angle 4[/tex] and

[tex]m\angle 3=m\angle 5[/tex]      [By Congruent Angle have equal measure]                                                                   ......[1]

Straight Angles states that angles on one side of a straight line always add to 180 degrees.

From the given figure;

By the addition angle and definition of straight angle we get;

[tex]m\angle 4 +m\angle 2 +m\angle 5 =180^{\circ}[/tex]      ......[2]

Substituting equation [1] in [2] we get;

[tex]m\angle 1 +m\angle 2 +m\angle 3 =180^{\circ}[/tex]  

Therefore, the sum of the interior angles measures of triangle ABC is [tex]180^{\circ}[/tex]

Simplified form of the expression 4m+5−3m:

m + 5

Expression : Degree of m is 1 , so the expression is linear.

Given , that expression: 4m+5−3m

Now to simplify the expression,

⇒ 4m + 5 − 3m

Combine like terms,

⇒ (4m - 3m) + 5

⇒ m + 5

Thus the simplified form is m + 5 .

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Answer:

The first six terms of the sequence are: -1, -2, -4, -8, -16 and -32

Step-by-step explanation:

The sequence is:

[tex]a_1=-1\\a_n=2*a_{n-1}[/tex]

So, for finding the first six terms of the sequence, we need to replace n by the numbers 1 to 6 and we get:

[tex]a_1=-1\\a_2=2*a_{2-1} =2*a_1\\a_3=2*a_{3-1} =2*a_2\\a_4=2*a_{4-1} =2*a_3\\a_5=2*a_{5-1} =2*a_4\\a_6=2*a_{6-1} =2*a_5\\[/tex]

That means that the term n is 2 times the last term. Then, replacing the values of [tex]a_1, a_2, a_3, a_4[/tex] and [tex]a_5[/tex], we get:

[tex]a_1=-1\\a_2=2*(-1)=-2\\a_3=2*(-2)=-4\\a_4=2*(-4)=-8\\a_5=2*(-8)=-16\\a_6=2*(-16)=-32\\[/tex]

So, The first six terms of the sequence are: -1, -2, -4, -8, -16 and -32