Determine which sides of the given quadrilateral are parallel. Q (0, 4), R (4, 0), S (0, −4), T (−4, 0)

Answer:

\(\tan D=\frac{7}{4},\\\\\sin D=\frac{7}{8.1}, \\\\\cos D=\frac{4}{8.1}, \\\\GI=5.0\)

Step-by-step explanation:

In any right triangle, the following is true:

The sine of any angle is equal to its opposite side divided by the hypotenuse of the triangle. (o/h)

The cosines of any angle is equal to its adjacent side divided by the hypotenuse. (a/h)

The tangent of any angle is equal to its opposite side divided by its adjacent side. (o/a)

Thus,

\(\text{3. }\\\tan D=\frac{7}{4},\\\\\sin D=\frac{7}{8.1}, \\\\\cos D=\frac{4}{8.1},\)

\(\text{4. }\tan 68^{\circ}=\frac{GI}{2},\\GI=2\tan68^{\circ}=4.95017370683\approx \boxed{5.0}\)

Steps to construct a regular hexagon inscribed in a circle are given by:

Step 1

Draw a circle with center A and a point on the circle B.

Step 2

Measure AB with a compass to get the distance of the radius.

Step 3

Place compass on point B and draw another circle with the same radius.

Step 4

Mark the new intersection points C and D. Move compass to point C with the same setting and draw another circle with the same radius.

Step 5

Continue drawing the circles this way until you have 6 points of intersection.

Step 6

Connect all intersection points to form the hexagon.

Case 1: a = 0; b = 0 --> Real Number

Case 2: a = 0; b ≠ 0 --> Non-Real Complex Number

Case 3: a ≠ 0; b = 0 --> Real Number

Case 4: a ≠ 0; b ≠ 0 --> Non-Real Complex Number

For each case, we can determine whether the expression a + bi represents a real number or a non-real complex number based on the values of a and b.

Case 1: a = 0; b = 0

In this case, both a and b are zero. The expression a + bi simplifies to 0 + 0i, which is equal to 0. Therefore, the expression represents a real number.

Case 2: a = 0; b ≠ 0

Here, a is zero, but b is nonzero. The expression a + bi becomes 0 + bi, where b is a nonzero real number multiplied by the imaginary unit i. Since the expression contains a nonzero imaginary part, it represents a non-real complex number.

Case 3: a ≠ 0; b = 0

In this case, a is nonzero, but b is zero. The expression a + bi simplifies to a + 0i, which is equal to a. As there is no imaginary part in the expression, it represents a real number.

Case 4: a ≠ 0; b ≠ 0

Here, both a and b are nonzero. The expression a + bi contains both a real part (a) and an imaginary part (bi). Thus, it represents a non-real complex number.

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(c) The argument is valid, and we can conclude that Penelope missed class because she got a detention.

(e) The argument is valid, and we can conclude that Penelope did not miss class because she got an A and did not get a detention.

(c) To prove this argument's validity, we need to define the predicates and express the hypotheses and conclusion using them:

Let "M(x)" be the predicate "x missed class", and "D(x)" be the predicate "x got a detention".

Hypotheses: M(Penelope), D(Penelope)

Conclusion: M(Penelope)

Using modus ponens, which states that if P implies Q and P is true, then Q must be true, we can conclude that M(Penelope) is true:

From M(Penelope) and "Every student who missed class got a detention", we have D(Penelope)

From D(Penelope), we have M(Penelope)

So, the argument is valid, and we can conclude that Penelope missed class because she got a detention.

(e) To prove this argument's validity, we need to define the predicates and express the hypotheses and conclusion using them:

Let "M(x)" be the predicate "x missed class", "D(x)" be the predicate "x got a detention", and "A(x)" be the predicate "x got an A".

Hypotheses: A(Penelope), ~D(Penelope)

Conclusion: ~M(Penelope)

Using modus tollens, which states that if P implies Q and Q is false, then P must be false,

we can conclude that M(Penelope) is false:

From A(Penelope) and "Every student who missed class or got a detention did not get an A",

we have ~M(Penelope) & ~D(Penelope)

From ~D(Penelope), we have ~M(Penelope)

So, the argument is valid, and we can conclude that Penelope did not miss class because she got an A and did not get a detention.

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Answer:

B.) 36cm2

Step-by-step explanation: I just did it and got it right

Answer:

333234

Step-by-step explanation:

333234$ for the next 4 years and the ecvation is 69$+-2$

Answer:

4/15

Step-by-step explanation:

2/5 drive

1/3 bus

and rest walk

fraction of those who walk is 1-(2/5+1/3)

2/5+1/3=(6+5)/15=11/15

15/15-11/15=4/15

The square form of r^2 + 4r + 4. is (r + 2) (r + 2)= 0 and the value of co-interior angle x is 140 degrees.

Co-interior angles, also known as consecutive interior angles, are those between two lines that are split by a third line (transversal), and are located on the same side of the transversal.

Given that, r^2 + 4r + 4.

Expand the terms as follows:

r^2 + 4r + 4.

r^2 + 2r + 2r + 4 = 0

r(r + 2) + 2(r + 2) = 0

(r + 2) (r + 2)= 0

The sum of co-interior angles is 180 degrees:

x + 40 = 180

x = 140 degrees.

Hence, the square form of r^2 + 4r + 4. is (r + 2) (r + 2)= 0 and the value of co-interior angle x is 140 degrees.

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Answer:

1/343

Step-by-step explanation:

hope it helps you not like that other person

The decimal 0.00291545189 in fraction form is 91545189/100000000000.

The given decimal, 0.00291545189, has 11 decimal places.

To convert it to a fraction, the decimal as the numerator and the denominator as 1 followed by 11 zeros:

= 0.00291545189

= 291545189/100000000000

Simplifying the fraction, if possible, by dividing both the numerator and denominator by their greatest common divisor, we get:

= 291545189/100000000000

Therefore, 0.00291545189 in fraction form is 91545189/100000000000.

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Answer:

\(37=5x-2y,\,1=5x-2y\)

Step-by-step explanation:

If \((x_1,y_1),\,(x_2,y_2),\,(x_3,y_3)\) are coordinates of a triangle then area of a triangle is equal to \(\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

Let point P be \((x,y)\)

Put \((x_1,y_1)=(5,3),\,(x_2,y_2)=(3,-2),\,(x_3,y_3)=(x,y)\)

Area of a triangle = \(\frac{1}{2}|5(-2-y)+3(y-3)+x(3+2)|\)

\(=\frac{1}{2}|-10-5y+3y-9+5x|\\\\=\frac{1}{2}|-19+5x-2y|\)

Also,

Area of a triangle = 9 square units

\(9=\frac{1}{2}|-19+5x-2y|\\\\18=|-19+5x-2y|\)

±18 = -19 + 5x - 2y

\(18=-19+5x-2y,\,-18=-19+5x-2y\\\\37=5x-2y,\,1=5x-2y\)

Answer:

Their are 166 students

are brought food

Answer:

3xz5+2x+4y−2z

Step-by-step explanation:

2x−5y+3z5x+9y−2z

=2x+−5y+3xz5+9y+−2z

Combine Like Terms:

=2x+−5y+3xz5+9y+−2z

=(3xz5)+(2x)+(−5y+9y)+(−2z)

=3xz5+2x+4y+−2z

The rank of the matrix is 3, since there are three linearly independent rows.

The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It is denoted by the symbol "rank(A)" for a matrix A.

To find the rank of the matrix:

[-2, -1, -3, -1] [ 1, 2, -3, -1] [ 1, 0, 1, 1] [ 0, 1, 1, -1]

We can perform row operations to reduce the matrix to row echelon form, which will help us determine the rank.

\(R_2 = R_2 + 2R_1 R_3 = R_3 + 2R_1 R_4 = R_4 + R_2\)

This gives us the following matrix:

[-2, -1, -3, -1] [ 0, 0, -9, -3] [ 0, -1, -1, 1] [ 0, 0, -4, -4]

We can see that the third row is not a linear combination of the first two rows, and the fourth row is not a linear combination of the first three rows. Therefore, the rank of the matrix is 3, since there are three linearly independent rows.

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Answer:

\(\Huge \boxed{\text{13.66$\%$}}\)

Step-by-step explanation:

To find the rate, we need to use the following formula:

\(\LARGE \boxed{ \boxed{\text{Rate = $\frac{\text{Portion}}{\text{Base}}$$\times$100}}}\)

Where "Portion" is the part of the whole and "Base" is the whole.

Now, let's plug in the given values:

\(\large \text{Rate = $\frac{\text{50}}{\text{366}}$$\times$100 = 13.66 (Rounded to the nearest tenth of a percent)}\)

Therefore, the rate is 13.66% (rounded to the nearest tenth of a percent).

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

Therefore the result of adding the system of equations  2x + y = 4  ,

6=3x-y is 5x =10

Equations are statements in mathematics containing the equals (=) sign flanked on either side by two algebraic expressions. The relationship between the expressions printed on the left and right sides is shown to be equal in this way. In all mathematical equations, LHS = RHS  is used. You can solve equations to find the value of an unknown variable that stands in for an unknown quantity. If a sentence lacks a "equal to" sign, it is not considered an equation. It will be considered to be a phrase.

Here,

Given:

we have to solve the system of equations given. .Each equation is added together to remove the variable Y.

2x + y = 4  

+

3x - y = 6

________

=> 5x =10

Therefore the result of adding the system of equations  2x + y = 4  ,

6=3x-y is 5x =10

The value of x :

x =10 / 5 = 2

⇒ x=2

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Answer:

$17,559

Step-by-step explanation:

The present value of $2,500 per year for 10 years, discounted back to the present at 7 percent, is approximately $17,559.

\(\qquad \qquad\huge \underline{\boxed{\sf Answer}}\)

The required additional information required to prove the Triangles congruent are :

\(\qquad \sf  \dashrightarrow \: 1. \: X V= FD\)

The Triangles will be congruent by HL congruency.

\(\qquad \sf  \dashrightarrow \: 2. \: MH = MI\)

The Triangles are congruent by LL congruency.

\(\qquad \sf  \dashrightarrow \: 3. \: \angle EDC = \angle VUC\)

The Triangles are congruent by HA congruency.

\(\qquad \sf  \dashrightarrow \: 4. \: \angle J = \angle C\)

The Triangles are congruent by LA congruency.

Answer:

A.  A'(32, 16) B'(48, 16) C'(64, 48)

Step-by-step explanation:

Dilation is a transformation in geometry that changes the size of a figure while preserving its shape. It involves multiplying the coordinates of each point by a scale factor relative to a fixed center of dilation to create a new figure that is either larger or smaller than the original. The center of dilation serves as the fixed point around which the figure is expanded or contracted.

To dilate a figure where the center of dilation is the origin (0, 0), simply multiply each coordinate point by the scale factor.

In this case, as we have not been given a center of dilation, so we can assume it is the origin. The given scale factor is 4.

Given coordinates of the vertices of triangle ABC:

To find the new coordinates after dilation with the origin as the center of dilation, multiply each coordinate point by the scale factor of 4.

A' = (8 · 4, 4 · 4) = (32, 16)

B' = (12 · 4, 4 · 4) = (48, 16)

C' = (16 · 4, 12 · 4) = (64, 48)

Therefore, the new coordinates of the dilated triangle are:

Answer:

n ≤ 1 or n ≥ 7

Step-by-step explanation:

solve each part separately

86n + 13 ≤ 99 ( subtract 13 from both sides )

86n ≤ 86 ( divide both sides by 86 )

n ≤ 1

n + 90 ≥ 97 ( subtract 90 from both sides )

n ≥ 7

solution is n ≤ 1 or n ≥ 7

The graphical summary of salaries is an example of b. descriptive statistics.

Descriptive statistics is the branch of statistics that is used to summarize, organize, and describe data. It is used to present data in a clear and meaningful way, so that patterns, relationships, and trends can be easily understood. A graphical summary of all employees' salaries, such as a histogram or a bar chart, is an example of descriptive statistics.

This graphical summary represents the entire population of employees and not a subset of it, so it's not a sample. The factory owner is not making any inferences about the population based on the data, so it's not an example of statistical inference. And this is not an experiment because no manipulation of the data was made.

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Answer:

x = 5

Step-by-step explanation:

-2 -1(coeffcient of -x) = -3

-3x +3 =-12

subtract 3 (the constant) from both sides

cancelling it on the left and leaving -3x = -15

divide each side by -3 leaving x and 5

x = 5

Answer:

11/2 times 1/3 is 11/6

Step-by-step explanation:

11/2 times 1/3,

We have to multiply the numerators and denominators,

\((11/2)(1/3) = (11*1)/(2*3) = 11/6\\11/6\)

hence we get 11/6

Answer:

4 blue marbles

Skills needed: Number Theory, Fractions

Step-by-step explanation:

1) The problem tells us that the jar contains marbles that are either red, green, or blue (No Other Color).

It also mentions that \(\frac{2}{5} (\frac{4}{10})\) of the marbles are red

and that \(\frac{1}{10}\) of the marbles are blue

- The given statement is that 20 marbles are green, and we need to find out the number of blue marbles.

2) We need to first find out the total number of marbles, and then multiply that by \(\frac{1}{10}\) to get the # of blue marbles.

---> Given \(\frac{4}{10}\) are red and \(\frac{1}{10}\) are blue, \(1-\frac{1}{10}-\frac{4}{10}\) of the marbles are green (since fractions add up to 1 whole)

\(1 - \frac{1}{10} - \frac{4}{10} = \frac{9}{10} - \frac{4}{10}=\frac{5}{10}\)

\(\frac{5}{10} \text{ is also } \frac{1}{2}\)

Half the marbles are green.

3) Let's make the total marbles the variable: \(m\)

\(\frac{1}{2} * m=20\) ---> Since half of (of signifies multiplication) the total marbles are green.

Multiply both sides by 2 to isolate: \(m = 20*2\), \(m=40\)

Total number of marbles is 40.

4) After that, we multiply this by \(\frac{1}{10}\) since one-tenth of the total is blue.

---> \(\frac{1}{10}*m = \frac{1}{10}*40=4\)

4 blue marbles is the answer.

The remainder is 5 + c, which means that the expression P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) divided by (x + 1) results in a quotient of\(5x^3 + 2x^2 - 4x + 4\) and a remainder of 5 + c.

To divide the polynomial P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) by the binomial (x + 1), we can use polynomial long division.

Let's set up the long division:

    \(5x^3 + 2x^2 - 4x + 4\)

_______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

We start by dividing the highest degree term of the dividend (5x^4) by the divisor (x + 1), which gives us 5x^3. We then multiply this quotient by the divisor (x + 1) and subtract it from the dividend:

              \(5x^3(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- (\(5x^3 + 5x^2)\)

This leaves us with a new polynomial:\(2x^3 - 7x^2 - 3x + c\). We repeat the process by dividing the highest degree term of this polynomial (2x^3) by the divisor (x + 1), resulting in 2x^2. We then multiply this quotient by the divisor and subtract it from the polynomial:

              \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

-\((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

We continue this process until we reach the constant term, resulting in the remainder of the division.

At this point, we have:

               \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- \((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

-\((2x^2 + 2x)\)

_______________________

- 5x + c

- (-5x - 5)

_______________________

5 + c

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Answer:

7 + 1 + 1 + 1 = 10

Step-by-step explanation:

This question is not very clear as to what is required, or any possible limitations. One possible solution is listed below, hope it does help.

Using the numbers 1, 6, and 7, you can get the number 10 through the following equation:

7 + 1 + 1 + 1 = 10

By adding 7 with three instances of 1, you obtain 10.

Answer:

the answer is n=- 18

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

you have to multiply 2/3 by -12 since they are on opposite sides of each other then the n is isolated and you get the answer.

Answer:

40

Step-by-step explanation:

plugging in a and b will get us:

\(2^{2} + 6^{2} = c^{2}\)

4 + 36 = \(c^{2}\)

40 = \(c^{2}\)

c= \(\sqrt{40\\\)

Answer:

The geometric mean of 6 and 30 is 13.416407864999

Answer:

x = 135

Step-by-step explanation:

All the angles of a pentagon added up make 540 degrees.

540 - 60 = 480

480 - 150 = 330

330 - 120 = 210

210 - 75 = 135

x = 135