Three of the vertices of square ABCD are located at A(0,3), B(4,0), and C(7,4).
Determine the area of square ABCD.​

Translating the phrase into an algebraic expression for the difference between four times a number and 10 is 4x - 10.

An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Let the number be given as x.

Therefore, 4 times will number will be 4x.

Then, difference between four times a number and 10 will be:

= 4x - 10

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

Answer:

x is 4.30 and 0.697

Step-by-step explanation:

Quadratic formular:

\(x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} \\ \)

a » 1

b » -5

c » 3

\(x = \frac{ - ( - 5)± \sqrt{ {( - 5)}^{2} - (4 \times 1 \times 3)} }{(2 \times 1)} \\ \\ x = \frac{5± \sqrt{13} }{2} \)

Therefore, values of x :

\(x = \frac{5 + \sqrt{13} }{2} \: \: and \: \: \frac{5 - \sqrt{13} }{2} \\ \\ x = 4.30 \: \: and \: \: 0.697\)

Answer:

C. 23

Step-by-step explanation:

Add then divide by 7

A. The null hypothesis H₀ and the alternative hypothesis H₁ are:

H₀: μ = 35 minutes       H₁: μ > 35 minutes

B. If the consultant decides not to reject the null hypothesis, she might be making a Type II error.

C. A Type II error would be failing to reject the hypothesis that μ is = to 35 minutes when, in fact, μ is 43 minutes.

A Type II error occurs when the null hypothesis is false, but the test does not reject it.

In this case, the consultant would be concluding that the mean shopping time is 35 minutes, when in fact it is greater than 35 minutes.

Find more exercises on Type II error;

https://brainly.com/question/29689920

#SPJ1

This axiom says that there is no upper bound to the number of elements that a set can have, thus, sets with infinite elements do exist.

First, we need to give the definition of an axiom. This is a proposition that is assumed to be true, and don't need a demonstration.

Axioms are the logical base of mathematics, so these are usually used to define concepts or basic rules.

In set theory,  the axiom of infinity just claims (and because it is an axiom, it must be true) that there are sets that have a infinite number of elements.

A trivial case is the set of real numbers, which we know has infinite elements because there are infinite real numbers.

So there is not a maximum for the number of elements that a set can have.

Learn more about set theory:

https://brainly.com/question/13458417

#SPJ1

Answer:

A (0,3) (-3,-3)

Step-by-step explanation:

A graph will match the equation if both the coordinates points replaced in the equation generate a identity.

When x = -3

\(y + 3 = 2(x + 3)\)

\(y + 3 = 2(-3 + 3)\)

\(y + 3 = 0\)

\(y = -3\)

So (-3,-3) is part of the graph.

When x = 0

\(y + 3 = 2(x + 3)\)

\(y + 3 = 2(0 + 3)\)

\(y + 3 = 6\)

\(y = 3\)

So (0,3) is part of the solution.

(-3,-3) and (0,3), so option A.

sub y = x - 1 into equation 1

2x + x - 1 = 5

3x = 6

x = 2

sub x = 2 into equation 2

y = 2 - 1

y = 1

Based on the total cards that Amanda has and the number of cards that each player gets, the number of people who can play are 2 people and 3 cards will be remaining.

Amanda has a total of 11 cards that will have to be shared to the players to play the game.

Out of this 11, players need to get 4 cards. The number of complete players who can play are therefore:

= 11 / 4 cards per player

= 2.75 players

= 2 players

The number of cards remaining:
= 11 - (4 x 2 players)

= 11 - 8

= 3 cards

Find out more cards remaining at https://brainly.com/question/12512066

#SPJ1

Answer:

triangle XYZ is similar to triangle RPQ

scale factor = 2/5

Step-by-step explanation:

Angles X and R are given as congruent.

Angles Z and Q are right angles, so they are congruent.

Then, angles Y and P must be congruent.

The similarity statement is

triangle XYZ is similar to triangle RPQ

To find the scale factor, divide the length of a side of the image by the length of the corresponding side in the original.

10/25 = 2/5

The scale factor is 2/5.

The set of transformations that could be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°

"It is a geometric transformation where all the points of an object are reflected on the line of reflection."

For the given question,

The Rectangle ABCD is formed by ordered pairs A at (-4, 2), B at (-4, 1), C at (-1, 1), D at (-1, 2)

The Rectangle A″B″C″D″ is formed by ordered pairs A" at (-4, -2), B" at   (-4, -1), C" at (-1, -1) and D" at (-1, -2)

We can observe that the coordinates of ABCD are of the form (-x, y)  where x, and y, are positive numbers

The form of the ordered pair of the vertices of the A″B″C″D″ will be (-x, -y)

The coordinates of the point (-x, y) after a reflection over the y-axis would be of the form (x, y)

And after rotation of 180°, the coordinates would be (-x -y).

Hence, the set of transformations that could be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°.

Learn more about geometric transformations here:

brainly.com/question/15577335

#SPJ1

The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

To learn more about line plot

https://brainly.com/question/16321364

#SPJ8

Answer:

33 baseball caps

Step-by-step explanation: Just do 55 times .6. I think that's right I hope it helps.

Answer:

20 hours.

Step-by-step explanation:

4 c.

Duane makes 5 bowls in 3 hours.

That is his rate is 5/3 bowls per hour.

So he makes (5/3) * 12 bowls in 5 * 12/3

= 5*4

= 20 hours.

Answer:

3). (3,-3)

Step-by-step explanation:

reflection in the x-axis : (-2,-4) → (-2,+4)

five units to right : (-2+5,+4) = (3,4)

seven units to downward : (3,4-7) = (3,-3)

Answer:

3)   (3, -3)

Step-by-step explanation:

If a point is reflected in the x-axis, the x-coordinate remains the same and the sign of the y-coordinate is changed.

Therefore, (-2, -4) reflected in the x-axis ⇒ (-2, 4)

If the point is translated 5 units right and 7 units down, add 5 units to the x-coordinate and subtract 7 units from the y-coordinate:

Therefore, (-2, 4) ⇒ (-2 + 5, 4 - 7) = (3, -3)

Answer:

\(6\sqrt{3\)

Step-by-step explanation:

Answer:

22 - 3 × 6 + 52 = 56

Step-by-step explanation:

Multiply

3×6 = 18

22-18+52

Add and subtract

22-18 = 4

4+52 = 46

Answer:

56

Step-by-step explanation:

To solve we must use the order of operations which is PEMDAS.

P-Parenthesis

E-Exponents

M-Multiplication

D-Division

A-Addition

and S-Subtraction

First we multiply -3 and 6 which gives us -18. So our equation is now 22-18+52.

Next we do addition. -18+52 is 34, plus 22 gives us 56.

Hope this helps :)

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

Ab=3.14xRadious to the power of 2

then to the area of the rectange you do B x H = YOUR ANSWER

Answer:

Choice A.

Explanation:

The sketch of the triangle is given below

The angle opposite the longest side is the widest.

The longest side is DF; therefore, the angle opposite to it (angle E) is the widest.

The second-longest side is DE; therefore, the angle opposite to it (angle F) is the second widest.

Lastly, the third-longest side is EF; therefore, the angle opposite to it (angle D) is the third widest (or the smallest angle).

Hence, the angle measures when ordered from greatest to smallest are

∠E, ∠F, ∠D

which is given by choice A.

Answer:

Step-by-step explanation:

The measure for each angle is shown below.

A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

Given:

As, ∆ABC and ∆DBE is an equilateral triangle.

In Equilateral Triangle all the angles are Equal.

So,  4x+ 3= 9x- 7

5x = 50

x= 10

and, <1 = <9 = 4x+ 3= 43

and, <4 = <5 = <6 = 180/ 3= 60

ans, <3 = <8 = 180-60= 120

Also, <2 = < 7 = 180- <1- <3= 17

Learn more about Equilateral Triangle here:

https://brainly.com/question/3461022

#SPJ2

The experimental probability farthest from the theoretical probability is P(greater than 8). The theoretical probability of rolling a 9 is 1/12 because there is one 9 out of twelve total possible outcomes.

Experimental probability refers to the probability of an event based on data acquired from repeated trials or experiments.

Theoretical probability is the probability of an event occurring based on logical reasoning or prior knowledge. In Todd’s case, he rolled a 12-sided die marked with the numbers 1 to 12.

The probabilities are as follows:P(odd number) = 18/48P(greater than 8) = 16/48P(9) = 12/48To answer the questions:1. Which experimental probability matches the theoretical probability exactly?The theoretical probability of rolling an odd number is 6/12 or 1/2 because there are six odd numbers out of the twelve total possible outcomes.

The experimental probability Todd obtained was 18/48. Simplifying 18/48 to lowest terms gives 3/8, which is equal to 1/2, the theoretical probability.

Therefore, the experimental probability that matches the theoretical probability exactly is P(odd number).2. Which experimental probability is farthest from the theoretical probability? The theoretical probability of rolling a number greater than 8 is 3/12 or 1/4 because there are three numbers greater than 8 out of twelve total possible outcomes.

The experimental probability Todd obtained was 16/48. Simplifying 16/48 to lowest terms gives 1/3, which is not equal to 1/4, the theoretical probability.

The experimental probability Todd obtained was 12/48. Simplifying 12/48 to lowest terms gives 1/4, which is not equal to 1/12, the theoretical probability.

However, the difference between the experimental probability and the theoretical probability for P(9) is smaller than that of P(greater than 8). Therefore, P(greater than 8) is the experimental probability that is farthest from the theoretical probability.

For more such questions on possible outcomes

https://brainly.com/question/30241901

#SPJ8

Answer: the answer is 39 units and it is correct

Step-by-step explanation:

The distance from the center of the Earth to the point where the net gravitational force is zero is one-ninth the distance from the Earth to the Moon.

Let's assume that the distance from the center of the Earth to this point is denoted as x.

Given:

Mass of the Moon (M\(_{moon}\)) = 1/81 × M\(_{earth}\)

Distance from Earth to Moon (d\(_{moon}\)) = distance on center

According to the principle of gravitational equilibrium, the gravitational force from the Earth and the gravitational force from the Moon acting on an object at that point must balance out. Mathematically, we can express this as:

F\(_{earth}\) = F\(_{moon}\)

The gravitational force between two objects can be calculated using Newton's law of universal gravitation:

F \(_{gravity}\)= G × (m₁ × m₂) / r²

Where:

G is the gravitational constant (approximately 6.67430 x 10⁻¹¹m²/kg/s²)

m₁ and m₂ are the masses of the two objects

r is the distance between the centers of the two objects

Considering the gravitational forces involved:

F\(_{gravity}\)\(_{earth}\) = G ₓ (M\(_{EARTH}\)  ₓ m\(_{OBJECT}\)) / (d\(_{earth}\))²

F\(_{gravity}\) \(_{moon}\) = G ₓ (M \(_{moon}\) ₓ m\(_{object}\)) / (d \(_{moon}\))²

Since we are looking for the point where the net gravitational force is zero, we set these two forces equal to each other:

G × (M\(_{earth}\) × m\(_{object}\)) / (d\(_{earth}\))²   =     G × (M \(_{moon}\) × m\(_{object}\)) / (d \(_{moon}\))²

Canceling out the common factors of G and m\(_object}\), and substituting the given values:

(M\(_{earth}\) × 1) / (d\(_{earth}\))² = (M \(_{moon}\) × 1) / (d \(_{moon}\))²

Rearranging the equation:

(d\(_{earth}\))²/ (M\(_{earth}\)) = (d \(_{moon}\))² / (M \(_{moon}\))

Taking the square root of both sides:

d\(_{earth}\) / √(M \(_{moon}\))) = d_moon / √(M \(_{moon}\))

Substituting the given values:

d\(_{earth}\) /√(M\(_{earth}\)) = d\(_{moon}\) / √(1/81 × M\(_{earth}\))

Simplifying further:

d\(_{earth}\)  / √(M\(_{earth}\)) =d\(_{moon}\)  / (1/9 × √(M\(_{earth}\)))

Multiplying both sides by √(M\(_{earth}\)):

d\(_{earth}\) = (1/9) × d\(_{moon}\)

To know more about gravitational force

https://brainly.com/question/27943482

#SPJ4

The angles between 0° and 180° that satisfy the equation sin() = 2/9 are 30°, 75°, 105°, 150°.

An angle is a figure formed by two rays, or line segments, sharing a common endpoint. It is a measure of the amount of turn between them, and is usually measured in degrees or radians. Angles are used to represent relationships between lines and surfaces, calculate distances, and to construct and measure shapes.

Since the sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse, these angles all have a side opposite them with a length equal to 2/9 of the length of the hypotenuse.

To know more about angle click-

https://brainly.com/question/28451077

#SPJ1

Since we are only looking for angles between 0° and 180°, the only angle that satisfies the equation is θ ≈ 13.7°

What is the sine function?

The sine function is a periodic function that is very important in trigonometry. The simplest way to understand the sine function is to use the unit circle. For a given angle measure θ, draw a unit circle on the coordinate plane and draw the angle centered at the origin, with one side as the positive x-axis.

We can use the inverse sine function to find the angles satisfying the equation:

sin(θ) = 2/9

Taking the inverse sine of both sides, we get:

θ = sin^{-1}(2/9)

Using a calculator, we find that:

θ ≈ 13.7° or θ ≈ 166.3°

Since we are only looking for angles between 0° and 180°, the only angle that satisfies the equation is:

θ ≈ 13.7°

Therefore, the answer is θ ≈ 13.7°

To learn more about the sine function visit:

https://brainly.com/question/12595712

#SPJ1

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Answer:

b. 5 meters

Step-by-step explanation:

1 meter = 1000 millimeters

5 meter = 5000 millimeters

Which is longer 5 meters or 400 millimeters?

5000 > 400

So, the answer is b. 5 meters.

Joey's actual speed is 143.59 mph, and his actual direction is slightly west of northwest.

Given that Joey's aircraft speed: 188 mph

Wind speed: 60 mph

Wind direction: 150 degrees (measured clockwise from due north)

We can consider the wind as a vector, which has both magnitude (speed) and direction.

The wind vector can be represented as follows:

Wind vector = 60 mph at 150 degrees

We convert the wind direction from degrees to a compass bearing.

Since 150 degrees is measured clockwise from due north, the compass bearing is 360 degrees - 150 degrees = 210 degrees.

Joey's aircraft speed vector = 188 mph at 0 degrees (due northwest)

Wind vector = 60 mph at 210 degrees

To find the resulting velocity vector, we add these two vectors together. This can be done using vector addition.

Converting the wind vector into its x and y components:

Wind vector (x component) = 60 mph × cos(210 degrees)

= -48.98 mph (negative because it opposes the aircraft's motion)

Wind vector (y component) = 60 mph×sin(210 degrees)

= -31.18 mph (negative because it opposes the aircraft's motion)

Now, we can add the x and y components of the two vectors to find the resulting velocity vector:

Resulting velocity (x component) = 188 mph + (-48.98 mph) = 139.02 mph

Resulting velocity (y component) = 0 mph + (-31.18 mph) = -31.18 mph

Magnitude (speed) = √((139.02 mph)² + (-31.18 mph)²)

= 143.59 mph

Direction = arctan((-31.18 mph) / 139.02 mph)

= -12.80 degrees

The magnitude of the resulting velocity vector represents Joey's actual speed, which is approximately 143.59 mph.

The direction is given as -12.80 degrees, which indicates the deviation from the original northwest direction.

To learn more on Speed click:

https://brainly.com/question/28224010

#SPJ1

You need to put a little more information for me to be able to answer this