Find the equation of a line parallel to x=−5 that contains the point (3,−2)

Answer:

4th option

Step-by-step explanation:

tanZ = \(\frac{opposite}{adjacent }\) = \(\frac{XY}{ZY}\)

Answer:

The speed of the plane in the still air is 420 miles/hour

The speed of the wind 60 miles/hour

Step-by-step explanation:

Let the speed of the plane with the wind be v

Let the speed of the plane against the wind be u

Now, speed = distance/time

With the wind,

v = (1440 miles)/(3 hours) = 480 miles/hour

v = 480 miles/hour

Against the wind,

u = (1440 miles)/(4 hours) = 360 miles/hour

u = 360 miles/hour

Now, let the speed of plane be p, and speed of wind be w,

Now, with the wind, the speed is 480 mph,

so,

speed of plane + speed of wind = 480 mph

p + w = 480  (i)

and against the wind, the speed is 360 mph,

so,

speed of plane - speed of wind = 360mph

p-w = 360 (ii)

adding equations (i) and (ii), we get,

p+w + p-w = 480 + 360

2p = 840

p = 840/2

p = 420 miles/hour

Then, the speed of the wind will be,

p + w = 480,

420 + w = 480

w = 480 - 420

w = 60 miles/hour

The speed of the plane in still air is calculated to be 420 mph, and the speed of the wind is calculated to be 60 mph by solving the two simultaneous equations obtained from the time, rate, and distance relationship.

This problem is about the rate, time, and distance relationships. The rate at which the airplane travels in still air is r (unaffected by wind), and the speed of the wind is w. When the plane flies with the wind, it is 'assisted' and therefore travels faster - at a speed of (r + w); against the wind, it travels slower - at a speed of (r - w).

From the problem, we know that:

By solving these two equations, we get the following:

Adding these two gives 2r = 840 => r = 420 mph (the speed of the plane in still air), and subtracting gives 2w = 120 => w = 60 mph (the speed of the wind).

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Answer:

For this case we know that in many times a penny shoes 20 head and 55 tails so then the total of trials are:

\( n = 20 +55=75\)

Then we are interested in the probability of getting heads and if we use the Laplace formula we have:

\( p =\frac{Possible}{total}\)

And the correct way would be:

\( p =\frac{20}{20+55}=\frac{20}{75}\)

If we simplify we got:

\( p =\frac{4}{15}\)

And the error was because she use 55 as the total number of trials and that's not the size of the sample space and for this reason she got \(\frac{20}{55}\)

Step-by-step explanation:

For this case we know that in many times a penny shoes 20 head and 55 tails so then the total of trials are:

\( n = 20 +55=75\)

Then we are interested in the probability of getting heads and if we use the Laplace formula we have:

\( p =\frac{Possible}{total}\)

And the correct way would be:

\( p =\frac{20}{20+55}=\frac{20}{75}\)

If we simplify we got:

\( p =\frac{4}{15}\)

And the error was because she use 55 as the total number of trials and that's not the size of the sample space and for this reason she got \(\frac{20}{55}\)

The inverse of the given matrix would be C. C ⁻¹ [-4.5, -3.5]

[ - 4 , - 3 ]

The formula for finding the inverse of the matrix is;

= ( 1 / determinant ) x [ d , - b ]

[ - c , a ]

The inverse is therefore:

= 1 / 2 x [ 9 , 7 ]

=  [- 4. 5 , - 3 . 5 ]

= [ - 4 , - 3 ]

So, the inverse of the matrix C is:

[ - 4. 5 , -3. 5 ]

[ - 4 , - 3 ]

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Answer:

B

Step-by-step explanation:

using the recursive rule \(a_{n}\) = 3\(a_{n-1}\) and a₁ = 10, then

a₁ = 10

a₂ = 3a₁ = 3 × 10 = 30

a₃ = 3a₂ = 3 × 30 = 90

the first 3 terms are 10 , 30 , 90

Answer:

Step-by-step explanation:

To classify the quadrilateral formed by the given points, we need to find the length of each side and the measure of each angle.

Using the distance formula, we can find the length of each side:

AB = sqrt((4 - (-3))^2 + (2 - 1)^2) = sqrt(49 + 1) = sqrt(50)

BC = sqrt((9 - 4)^2 + (-3 - 2)^2) = sqrt(25 + 25) = 5sqrt(2)

CD = sqrt((2 - 9)^2 + (-4 - (-3))^2) = sqrt(49 + 1) = sqrt(50)

DA = sqrt((-3 - 2)^2 + (1 - (-4))^2) = sqrt(25 + 25) = 5

Using the slope formula, we can find the measure of each angle:

Angle ABC: m1 = (2 - 1)/(4 - (-3)) = 1/7

m2 = (-3 - 2)/(9 - 4) = -1/5

tan(ABC) = |(m2 - m1)/(1 + m1m2)| = 3/4

ABC = arctan(3/4) ≈ 36.87°

Angle BCD: m1 = (-3 - 2)/(9 - 4) = -1/5

m2 = (-4 - (-3))/(2 - 9) = 1/7

tan(BCD) = |(m2 - m1)/(1 + m1m2)| = 3/4

BCD = arctan(3/4) ≈ 36.87°

Angle CDA: m1 = (-4 - 1)/(2 - (-3)) = -1

m2 = (1 - (-3))/(-3 - 9) = 1/2

tan(CDA) = |(m2 - m1)/(1 + m1m2)| = 7/5

CDA = arctan(7/5) ≈ 54.46°

Angle DAB: m1 = (1 - (-4))/(4 - (-3)) = 5/7

m2 = (-4 - (-3))/(-3 - 2) = 1/5

tan(DAB) = |(m2 - m1)/(1 + m1m2)| = 3/4

DAB = arctan(3/4) ≈ 36.87°

Therefore, the quadrilateral formed by the given points is a kite, because adjacent sides are congruent and one diagonal bisects the other diagonal at a right angle.

The pairs of triangles can be proven similar through SSS similarity is given by Third pair.

We know that the SSS similarity criteria will have the ratio of three corresponding sides of both triangles congruent.

1. KL / EG = HL / DG = HK / DE

3/6 = 6.5/13 ≠ 4/10

Thus, SSS similarity does not follow.

2. KL / EG = HL / DG = HK / DE

3/10 ≠ 6.5/13 ≠ 4/10

Thus, SSS similarity does not follow.

3. KL / EG = HL / DG = HK / DE

3/6 = 6.5/13 = 5/10

Thus, SSS similarity follow.

4. All three angles are congruent.

Thus, SSS similarity does not follow.

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Answer:

270°

Step-by-step explanation:

Given :-

To Find :-

Solving :-

The minimum number of trips the bus will have to make to accommodate everyone is 5.

To find the minimum number of trips the bus needs to make, we divide the total number of people by the capacity of the bus.

1. Divide the total number of people (330) by the capacity of the bus (68):

  330 / 68 = 4.85 (rounded to the nearest whole number)

2. The result is approximately 4.85, which means that 4 trips will not be enough to accommodate everyone.

3. Since we can't have a fraction of a trip, we need to round up to the nearest whole number to ensure that everyone is accommodated.

4. Therefore, the minimum number of trips the bus will have to make is 5, as it will require 5 full trips to transport all 330 people.

It's important to note that on the fifth trip, the bus will not be completely full, as only 10 people will be left to transport. However, this is the minimum number of trips needed to ensure that everyone can go sight-seeing on the bus.

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The area of the poster in inches is,

⇒ A = 4 inches²

We have to given that;

A rectangular poster is 50 centimeters long and 25 centimeters wide.

Here, 1 centimeter is approximately 0.4 inches

Hence, Lenght = 50 cm

Lenght = 50 x 0.4

            = 2 inches

Width = 25 cm

          = 25 x 0.4

           = 1 inches

Thus, The area of the poster in inches is,

⇒ A = 1 x 4

⇒ A = 4 inches²

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Answer:

A polygon is a multi sided shape

Step-by-step explanation:

I know that because poly means multiple

Answer:

A polygon is a flat, 2D shape with straight sides that is fully closed. The sides must be straight.

Polygons can have any number of sides.

good luck, i hope this helps :)

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

5x + 6 = 4

Step-by-step explanation:

Do it one step at a time.

Six more than the product of a number and 5 is 4.

x

Six more than the product of a number and 5 is 4.

5x

Six more than the product of a number and 5 is 4.

5x + 6

Six more than the product of a number and 5 is 4.

5x + 6 = 4

Answer:35

Step-by-step explanation: i used a calculator

Answer:

  $28

Step-by-step explanation:

Each round trip will be double the price of a one-way trip, so will be ...

  2 × $3.50 = $7.00

Diego and his 3 friends will require a total of 4 round-trip tickets for a cost of ...

  4 × $7.00 = $28.00

Answer:

not possible

Step-by-step explanation:

Answer:

\(493.039 \;in^3\)

Step-by-step explanation:

If each side of the cube is \(a\) then the volume of the cube is given by \(a^3\)

If Volume is \(V\) then each side \(a = \sqrt[3]{V}\)

Here we are given the volume of the smaller cube as \(85\; in^3\)

So each side of this cube = \(\sqrt[3]{85} = 4.396 \approx 4.4 \;in\)

and each side of the larger cube \(= 4.4 + 3.5 = 7.9\;in\)

Volume of larger cube \(= 7.9^3 = 493.039 \; in^3\)

The statements that must be true are:

FH ≅ GH

<DHF is a right angle

H is the midpoint of FG

A perpendicular bisector is a straight line which partitions a given line segment into two equal parts.

As such, it is at a right angle to the bisected line segment.

From the given diagram, given that line DE is the perpendicular bisector of line segment FG, then the statements that must be true are:

Hence, the statements FH ≅ GH, <DHF is a right angle, H is the midpoint of FG are true

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Answer:

C, D

Step-by-step explanation:

We can solve this graphically and analytically.

Graphically, looking at the attached image below, if we graph the two inequalities and plot the points, you can find the points which are solutions by finding the points in the overlapping area.

This obviously excludes A as it only appears in \(y \geq x+2\)

C is included as y \(\geq x+2\) includes the point on the line.

D is obviously a solution.

B is however not a solution because is lies on the line \(y = \frac{-5x}{2} - 3\), which the inequality excludes.

Analytically, if we can find one of the two inequalities where it is not a solution, it is not a solution of the system.

A: (0, 0)

\(y \geq x+2\\0 \geq 0 + 2\\0 \geq 2\\false\)

A is not a solution

B: (-2, 2)

\(y \geq x+2\\2 \geq -2 + 2\\2\geq 0\\true\)

\(y > \frac{-5x}{2} -3\\2 > \frac{-5(-2)}{2} - 3\\2 > 5 - 3\\2 > 2\\false\)

B is not a solution

C: (0, 2)

\(y \geq x+2\\2 \geq 0 + 2\\2 \geq 2\\true\\\\y>\frac{-5x}{2}-3\\2 > -3\\true\)

C is a solution

D:

\(y \geq x + 2\\6 \geq -1 + 2\\6 \geq 1\\true\\\\y > \frac{-5x}{2} - 3\\6 > \frac{-5(-1)}{2} - 3\\6 > \frac{5}{2} - \frac{6}{2}\\6 > \frac{-1}{2}\\true\)

D is a solution

Answer:

Option (1)

Step-by-step explanation:

It's given in the question, ABCDEF ~ QRSTUV,

Their corresponding sides will be proportional.

\(\frac{AB}{QR}= \frac{BC}{RS}= \frac{CD}{ST}= \frac{DE}{TU}= \frac{EF}{UV}\)

Now we choose \(\frac{DE}{TU}=\frac{CD}{ST}\)

From the figure attached,

\(\frac{6}{2.4}=\frac{5.4}{ST}\)

ST = \(\frac{5.4\times 2.4}{6}\)

ST = 2.16

Therefore, Option (1) is the correct option.

On solving the provided question, we can say that Probability(A and B) = P(A)P(B|A) and P(E or F) = P(E) + P(F) - P(E and F)

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

Probability(A and B) = P(A)P(B|A).

P(A and B) = P(B and A), this may also be written as P(A and B) = P(B)P(A|B).

Using the general multiplication rule, we have

P(E and F) = P(E)P(F|E)

.392 = P(E)(.7)

P(E) = .56

   P(E and F) = P(F)P(E|F)

.392 = P(F)(.56), so

P(F) = .7

P(E or F) = P(E) + P(F) - P(E and F)

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Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Answer:

A, B, F

Step-by-step explanation:

took the test

Answer:

Step By Step Explanation!-

57.82

÷

0.784

______

57820

÷

784

______

73.75

57.82

÷

0.784

_____

73.75

By using the division property, the value of the expression 57.82 ÷ 0.784 will be 73.75.

Algebra is the study of graphic formulas, while logic is the manipulation of those inscriptions.

Parenthesis, Exponent, Multiply, Divide, Add, and Subtraction is all part of the PEMDAS formula. To answer the problem properly and accurately, this rule is applied.

The numbers are given below.

57.82 and 0.784

Then the division between the numbers 57.82 and 0.784 will be given by putting a dividing sign between them. Then we have

⇒ 57.82 ÷ 0.784

⇒ 57.82 / 0.784

⇒ 73.75

The value of the expression 57.82 ÷ 0.784 will be 73.75.

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For each additional slice of pizza that is purchased, the total cost of lunch is increase by $2.5

First choose two points

(1, 10) and (2, 12.5)

The cost of one slice of pizza = $10

The cost of two slice of pizza = $12.5

Using these points we have to find the slope of the line

The slope of the line is the change in y coordinates with respect to the change in x coordinates of the graph

The slope of the line m = \(\frac{y_2-y_1}{x_2-x_1}\)

Where m is the slope of the line

\((x_1,y_1)\) is the coordinates of the first point

\((x_2,y_2)\) is the coordinates of the second point

Substitute the values in the equation

Slope of the line = (12.5 - 10) / (2-1)

= 2.5/1

= $2.5

Hence, for each additional slice of pizza that is purchased, the total cost of lunch is increase by $2.5

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The scale factor and the value of x for each figure is given as follows:

A) Scale factor of 1/3, x = 7 m.

B) Scale factor 0.4747, x = 4.5 in.

For Figure A, we have that the ratio between the areas is given as follows:

510/4590 = 1/9.

As the area is measured in square units, while the side lengths are measured in units, the scale factor is the square root of 1/9, hence it is given as follows:

1/3.

Then the value of x is obtained as follows:

x = 21 x 1/3

x = 7 m.

For Figure B, we have that the ratio between the areas is given as follows:

16/71 = 0.22535.

The scale factor is then the square root of 0.22535, which is given as follows:

0.4747.

Then the value of x is given as follows:

x = 9.5 x 0.4747

x = 4.5 in.

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The measure of arc angle QTP is 204 degrees.

When a tangent and a secant intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

Therefore, let's find the measure of arc angle QTP as follows:

90 = 0.5(x - 68)

90 = 0.5x - 34

0.5x = 124

x = 124 / 0.5

x = 248 degrees

Where

x = arc angle TSQ

Therefore,

arc QP = 44 degrees

Therefore,

arc QTP = 248 - 44

arc QTP = 204 degrees

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