Yvonne is solving the quadratic equation 6x2 + 24x + 7 = 0 by completing the square. Her first four steps are shown in the table.

A table listing the first few steps in deriving the quadratic formula
In which step did Yvonne first make an error?

The equation of the circle will be (x – 3/4)² + (y – 1/2)² = 9/25. Then the correct option is A.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x – h)² + (y – k)² = r²

We have

(h, k) = (3/4, 1/2)

r = 3 / 5

Then the equation of circle will be

(x – 3/4)² + (y – 1/2)² = (3/5)²

(x – 3/4)² + (y – 1/2)² = 9/25

Then the correct option is A.

The missing options are given below.

A. (x – 3/4)² + (y – 1/2)² = 9 / 25

B. x² + y² = 9/25

C. (x – 3/4)² + (y – 1/2)² = 25 / 9

D. (x – 1/2)² + (y – 3/4)² = 9/25

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The rational number among all the answer choices is; Pi + √16.

A rational number by definition, is one that can be represented as the quotient a/b of two integers in which case b ≠ 0.

On this note, it follows that since the constant pi is; 22/7, the number pi + √16 can be represented as a rational number as follows;

22/7 + 4 = 50/7.

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Answer:

The answer is b.

Step-by-step explanation:

goodluck

Step-by-step explanation:

A number that is negative is less than 0, so

[tex]3x + 6 < 0[/tex]

[tex]3x < - 6[/tex]

[tex]x < - 2[/tex]

So this function is negative, when x is less than -2

Hi !

[tex]3x+6\leq 0\\3x\leq -6\\x\leq \frac{-6}{3} =-2[/tex]

g(x)≤0 for x∈ ]-∞;-2]

Have a nice day

Answer:

ans : general term = (2n +8)/(4^n) * (-1)^n

Answer:

Domain : [-5,5]

Range : [-3,4}

Step-by-step explanation:

By definition:

Domain is the set of all inputs for which the given function is defined

Range is the set of all outputs

Answer:

Types of numbers

Natural Numbers - Common counting numbers.

Prime Number - A natural number greater than 1 which has only 1 and itself as factors.

Composite Number - A natural number greater than 1 which has more factors than 1 and itself.

Whole Numbers - The set of Natural Numbers with the number 0 adjoined.

Integers - Whole Numbers with their opposites (negative numbers) adjoined.

Rational Numbers - All numbers which can be written as fractions.

Irrational Numbers - All numbers which cannot be written as fractions.

Real Numbers - The set of Rational Numbers with the set of Irrational Numbers adjoined.

Complex Number - A number which can be written in the form a + bi where a and b are real numbers and i is the square root of -1.

Step-by-step explanation:

Answer: 3x+4-5x

Step-by-step explanation:

3x+4=5x

3x+4-5x=0

Answer:

2q+6

Step-by-step explanation:

So basically, you would do this.

-2q-6+6q+12-2q

Next

-4q+6q = 2q

12-6=6

2q+6

Answer:

2q + 6

Step-by-step explanation:

To simplify, we will use the distributive property.

-(2q + 6) simplifies to -2q - 6 (In this case we are distributing the - sign or -1)

3(2q + 4) simplifies to 6q + 12

So if we recombine: -2q - 6 + 6q + 12 - 2q

Let's combine like terms (q's with q's, numbers with numbers)

-2q + -2q + 6q = 2q

-6 + 12 = 6

So if we recombine: 2q + 6

Step-by-step explanation:

for 1st triangle on the left

sin(x) = 24/38

x = inverse sin(24/38)

x = 39.1667 deg

for triangle 2

cos(x) = 20/52

x = inverse cos (20/52)

x = 67.38 deg

Step-by-step explanation:

the expected value is calculated by multiplying each of the possible outcomes by their probability, and then summing up all these results.

tossing a coin 2 times gives us 4 possible different outcomes (all with the same probability of 0.25) :

head - tail

head - head

tail - head

tail - tail

to have exactly one head is 2 out of these 4 possible outcomes, and the probability is 0.5.

everything else is also 2 out of these 4 possible outcomes, and the probability for that is therefore 0.5 too.

the expected value (from your point of view) is

9×0.5 - 15×0.5 = -$3.00

The value of the exponential function when x = 2 is 64

The standard form of exponential equation is expressed as y = ab^x

Given the exponential function expressed as:

f(x) = 2^x

For the value f(6)

f(6) = 2^x

f(6) = 2^6

f(6) = 64

Hence the value of the exponential function when x = 2 is 64

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The  two possible decisions that the graduate student  is that:

If the test is not inside the critical region, the graduate student cannot reject the null hypothesis.

Suppose that the test statistic is 3.29 and the boundary to the critical region is 2.576. The test statistic is outside the critical region. So:

The test statistic is not in the critical region.

2. Therefore, the graduate student cannot reject the null hyopthesis,

3. and she cannot conclude that the level of contrast between eye color and skin tone affects how feminine a face is considered.

Note that a failure to reject the null hypothesis in any kind of significance test does not imply that the null hypothesis holds true. It only imply that the person was not able to give enough evidence for the alternative hypothesis.

See options for the last question

Options for the last section...

1. The test statistic is ____not in/in_____ the critical region.

2. Therefore, the graduate student _____can/cannot_____ reject the null hyopthesis,

3. and she ______can/cannot_______ conclude that the level of contrast between eye color and skin tone affects how feminine a face is considered

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The time 0.825 is 49.5 minutes based on the conclusion that the sum of the different amounts of time was 7.825 hours.

Proportion in time refers to the relationship between two or more ratios or quantities expressed in time measurements.

One hour = 60 minutes

One minute = 60 seconds

0.825 of an hour = 49.5 minutes (0.825 x 60 minutes)

0.5 minutes = 30 seconds (0.5 x 60)

Thus, we can conclude that the total time involved is 7 hours, 49 minutes, and 30 seconds.

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The solutions of the equation x² – 5x – 24 = 0 will be 8 and -3. Then the correct option is D.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The quadratic equation is given below.

x² – 5x – 24 = 0

Then the factor of the equation will be

       x² – 5x – 24 = 0

x² – 8x + 3x – 24 = 0

x(x – 8) + 3(x – 8) = 0

       (x – 8)(x + 3) = 0

                          x = 8, -3

Then the correct option is D.

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Compute the gradient of [tex]f[/tex].

[tex]\nabla f(x,y) = \left\langle 3x^2 - 6y, -6x + 3y^2\right\rangle[/tex]

Set this equal to the zero vector and solve for the critical points.

[tex]3x^2-6y = 0 \implies x^2 = 2y[/tex]

[tex]-6x+3y^2=0 \implies y^2 = 2x \implies y = \pm\sqrt{2x}[/tex]

[tex]\implies x^2 = \pm2\sqrt{2x}[/tex]

[tex]\implies x^4 = 8x[/tex]

[tex]\implies x^4 - 8x = 0[/tex]

[tex]\implies x (x-2) (x^2 + 2x + 4) = 0[/tex]

[tex]\implies x = 0 \text{ or } x-2 = 0 \text{ or } x^2 + 2x + 4 = 0[/tex]

[tex]\implies x = 0 \text{ or } x = 2 \text{ or } (x+1)^2 + 3 = 0[/tex]

The last case has no real solution, so we can ignore it.

Now,

[tex]x=0 \implies 0^2 = 2y \implies y=0[/tex]

[tex]x=2 \implies 2^2 = 2y \implies y=2[/tex]

so we have two critical points (0, 0) and (2, 2).

Compute the Hessian matrix (i.e. Jacobian of the gradient).

[tex]H(x,y) = \begin{bmatrix} 6x & -6 \\ -6 & 6y \end{bmatrix}[/tex]

Check the sign of the determinant of the Hessian at each of the critical points.

[tex]\det H(0,0) = \begin{vmatrix} 0 & -6 \\ -6 & 0 \end{vmatrix} = -36 < 0[/tex]

which indicates a saddle point at (0, 0);

[tex]\det H(2,2) = \begin{vmatrix} 12 & -6 \\ -6 & 12 \end{vmatrix} = 108 > 0[/tex]

We also have [tex]f_{xx}(2,2) = 12 > 0[/tex], which together indicate a local minimum at (2, 2).

The probability that the family has two dogs or two cats will be 0.5.

From the information, the head represents cats and rte tails represent dogs.

The experimental probability that the family has two dogs or two cats will be:

= (1/2 × 1/2) + (1/2 × 1/2)

= 1/4 + 1/4

= 1/2

= 0.5

Also, the theoretical probability that they have three dogs or three cats is 0.5.

The simulation to generate data for three pets will be to add a new coin and category for the new pet.

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Answer:

Step-by-step explanation:

One number is 2 more than another. The difference between their squares is 24. What are the numbers?

(x + 2)² - x² = 24

x² + 4x + 4 - x² = 24

4x + 4 = 24

4x = 20

x = 20 : 4

x = 5

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

5 + 2 = 7

check

(5 + 2)² - 5² = 24

49 - 25 = 24

24 = 24

the answer is good

Answer:

A

Step-by-step explanation:

The equation of the line that passes through the points (-9,-7) and (-12,-2) is

y = -5/3x-22

and

equation of the line that passes through the points (1, 9) and (6, 6) is

y = -3/5x+48/5

clearly it is not the same line,

[tex]\frac{-5}{3}.\frac{-3}{5} \neq -1[/tex] (lines are not perpendicular)

[tex]\frac{-5}{3}\neq \frac{-3}{5}[/tex] (not parallel)

The frequency table for grouped data using four classes is shown in the picture.

Statistics is a mathematical tool defined as the study of collecting data, analysis, understanding, representation, and organization. Statistics is described as the procedure of collecting data, classifying it, displaying that in a way that makes it easy to understand, and analyzing it even further.

We have:

A small startup company wishes to know how many hours, per week.

The number of hours for each employee are shown below:

1,2,18,4,13,18,12,3,17,10,3,12,15,2 15,8,5,17,18,18

Make the group of 1-5, 6-10, 11-15, and 16-20

And count the numbers lies between the interval.

Thus, the frequency table for grouped data using four classes is shown in the picture.

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Answer:  [tex]\frac{28}{96}[/tex]

Step-by-step explanation:

       We will figure out what needs to happen to the denominator to get to 96, then we will do the same to the numerator.

               [tex]\displaystyle \frac{7}{24}=\frac{?*x}{24*x=96} =\frac{7*4}{24*4}=\frac{28}{96}\\\\ \\\text \\\;\;\;\;\;\; \frac{28}{96}[/tex]

Answer:

28/96

Step-by-step explanation:

Equalize the equivalent fractions according to the desired denominator and solve for the numerator "x"

[tex]\frac{7}{24} =\frac{x}{96}[/tex]

[tex]x=\frac{(96)(7)}{24} =\frac{672}{24} =28[/tex]

The equivalent fraction is

[tex]\frac{28}{96}[/tex]

Hope this helps

Answer:

z = 3[tex]\sqrt{13}[/tex]

Step-by-step explanation:

According to Euclidian theorem we can find the measure of z using the following equation:

z^2 = 9*(9+4)

z^2 = 9*13 multiply

z^2 = 117 find the root of both sides

z = 3[tex]\sqrt{13}[/tex]

Answer: Option (3)

Step-by-step explanation:

The slope of the given line is

[tex]\frac{-2-4}{-6-2}=\frac{-6}{-8}=\frac{3}{4}[/tex]

Thus, the answer must be Option (3)

Answer:

• mean = 61

• mode = 50

• median = 57.5

Step-by-step explanation:

• The mean is calculated by adding all the values together, and dividing the result by the number of values.

∴ mean =  [tex]\frac{60 + 50 + 50 + 70 + 40 + 80 + 65 + 55 + 50 + 90}{10}[/tex]

⇒ mean = [tex]\frac{610}{10}[/tex]

⇒ mean = 61

• The mode of a set of values is the value that is the most common (has highest frequency) among them.

50 is the most common value.

∴ mode = 50

• The median is the middle-value of a set of ordered values.

∴ We have to first rearrange the set:

⇒  40, 50, 50, 50, 55, 60, 65, 70, 80, 90

Now we need to find the middlemost value:

Since we have 10 values, which is an even number, we have to use the formula:

median = [tex]\frac{(n/2)^{th} \space\ term \space\ + \space\ [(n/2) + 1]^{th} \space\ term }{2}[/tex]

where n is the number of values.

∴ median =  [tex]\frac{(10/2)^{th} \space\ term \space\ + \space\ [(10/2) + 1]^{th} \space\ term }{2}[/tex]

⇒ median =  [tex]\frac{5^{th} \space\ term \space\ + \space\ 6^{th} \space\ term }{2}[/tex]

The 5th and 6th terms in our ordered series are 55 and 60 respectively.

∴ median = [tex]\frac{55 + 60}{2}[/tex]

⇒ median = 57.5

The value of P is 50 degree , Option D is the correct answer.

According to the exterior angle property the measure of exterior angle is equal to the sum of opposite interior angles.

In the given figure it can be seen that one of the exterior angle is 90 degree ,

which is making a supplementary angle with the interior angle corresponding to it , angle B in the figure

Therefore the interior angle B is 90 degree ,

The value of angle C = p degree

To determine the value of angle C

The exterior angle next to angle A = 140 degree

By the exterior angle property

140 = 90 +p

p = 50 degree

The value of P is 50 degree , Option D is the correct answer.

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Step-by-step explanation:

believe it or not, the area of any triangle is

baseline × height / 2

we have here 2 triangles, both with the same baseline (8 cm), but with 2 different heights : 6.5 cm and 4.6 cm.

so, their areas are

8 × 6.5 / 2 = 4 × 6.5 = 26 cm²

8 × 4.6 / 2 = 4 × 4.6 = 18.4 cm²

so, in total, the shaded region is

26 + 18.4 = 44.4 cm²

Answer:

x = 59°, y = 31°

Explanation:

Angles (x) and (x - 28) sum ups to 90° on a straight line.

→ x + (x - 28) = 90

→ 2x - 28 = 90

→ 2x = 90 + 28

→ 2x = 118

→ x = 59°

Then find value of y

Angle y, x, 90° lies on a straight line which sum ups to 180°

→ x + y + 90° = 180°

→ 59 + y + 90° = 180°

→ y = 180° - 149°

→ y = 31°

The prove that the angle ABCD is said to be a parallelogram that shows both pairs of opposite sides as parallel figure is given below.

The four points in the shape above are : A, B, C, D.

Where

A = (-2,-4)

B = (1,2)

C = (2,10)

D = (-1,4)

We place or sit vector AB with vector DC and vector AD  with vector BC

and so we find and place their coordinates.

vector AB (1-(-2), 2-(-4))

vector DC (2-(-1),10-4)

vector AD (-1-(-2), 4-(-4))

vector BC (2-1,10-2)

So we obtained:

vector AB (3,6)

vector DC (3,6)

vector AD (1,8)

vector BC  (1,8)

Next step is to calculate for the lengths :

AB=   [tex]\sqrt{3^{2} + 6^{2} }[/tex]  DC= [tex]\sqrt{3^{2} + 6^{2} }[/tex]

Thus, AB = DC

AD = [tex]\sqrt{1^{2} + 8^{2} }[/tex]     BC =[tex]\sqrt{1^{2} + 8^{2} }[/tex]

Hence one can say that  AD is equal to  BC.

Therefore, angle ABCD IS known to be a parallelogram .

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The box plot that represents the data is the first box plot.

A box plot is graph that is used to study the distribution and level of a set of scores. The box plot consists of two whiskers and a box. The end of the first whisker represents the minimum number and the end of the second whisker represents the maximum number. The difference between the values of the whiskers gives the range of the dataset.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. The difference between the upper quartile and the lower quartile is the interquartile range.

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Answer:

The box plot that represents the data is the first box plot.

Step-by-step explanation: