The lines intersect at
1 point.
different. The
parallel.
Do You Understand?
1. Essential Question How are slopes and
y-intercepts related to the number of solutions
of a system of linear equations?

Answer:

None. [tex]24+25+26[/tex] is the only valid answer

Step-by-step explanation:

We can create an expression for the sum of 3 consecutive numbers.

[tex]S=x+(x+1)+(x+2)[/tex]

Which we can simplify to

[tex]S=x+x+1+x+2[/tex]

[tex]S=3x+3[/tex]

In this example we are given a sum of 75.

[tex]75=3x+3[/tex]

Lets solve for [tex]x[/tex].

Subtract 3 from both sides.

[tex]72=3x[/tex]

Divide both sides by 3.

[tex]24=x[/tex]

To find out what the 3 numbers are we can plug in 24 for x

[tex]x+(x+1)+(x+2)[/tex]

[tex]24+(24+1)+(24+2)[/tex]

[tex]24+25+26[/tex]

Answer:

  4 other ways (5 ways, total).

Step-by-step explanation:

You want to know how many other ways 75 can be written as the sum of consecutive whole numbers other than 24+25+26.

If 75 is written as the sum of an odd number of integers, the middle integer of the set will be 75 divided by the number of integers. The divisors of 75 are {1, 3, 5, 15, 25, 75}. If the numbers in the sum are non-negative, the number of integers involved cannot be more than √(2·75) ≈ 12. Then allowed odd numbers of integers in the sum are 3 and 5.

If 75 is written as the sum of an even number of integers, the quotient when 75 is divided by the number of integers must be 1/2 more than a whole number. Such integer divisors are 2, 6, and 10.

  37 + 38 = 75 . . . . 2 integers

  24 + 25 + 26 = 75 . . . . 3 integers (the given sum)

  13 + 14 + 15 + 16 + 17 = 75 . . . . 5 integers

  10 + 11 + 12 + 13 + 14 + 15 = 75 . . . . 6 integers

  3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 75 . . . . 10 integers

There are 4 other ways to use consecutive non-negative integers to make a sum of 75.

The solution is, the value of JL = 15.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Two similar triangles, ∆ABC and ∆JKL are shown.

so, from the diagram we get,

BC/KL = AB/JK = AC/JL

so, 1/3 = AC/JL

or, JL  = 3 * 5

or, JL = 15

Hence, The solution is, the value of JL = 15.

To learn more on triangle click:

brainly.com/question/29126067

#SPJ1

Answer:

Step-by-step explanation:

Dont cheat on your homework

Answer:

AAS

Step-by-step explanation:

There are two pairs of congruent angles, and the pair of congruent sides is not included in between the angles.

Answer:

Solution to system of inequalities is y≥ 3x-2

Graph attached

Step-by-step explanation:

We have the following two inequalities:
y>-3x-5

y≥ 3x-2

To get the solution and graph

1. Graph each inequality separately

2. Choose a test point to determine which side of the line needs to be shaded

3. The solution will be the area where the shadings from each inequality overlap one another

The graph is attached. The heavily shaded region is the set of all points which satisfy all inequalities

We see that any point that satisfies y≥ 3x-2  also satisfies y>-3x-5

In other words, the solution set for y≥ 3x-2 is a subset of the solution set for   y>-3x-5

The six trigonometric functions of the angle θ for the given point (-4, -1) are sin θ = -1/5, cos θ = -4/5, tan θ = 1/4, cot θ = -4, sec θ = -5/4, and csc θ = -5.

The six trigonometric functions of an angle θ are sine (sin θ), cosine (cos θ), tangent (tan θ), cotangent (cot θ), secant (sec θ), and cosecant (csc θ). These functions can be used to calculate the coordinates of a point on the terminal side of θ when the angle and one coordinate are known.

For example, if you know the angle θ and one coordinate (in this case, -4) of a point on the terminal side of θ, you can use the six trigonometric functions to calculate the remaining coordinate. In this case, the point is (-4, -1). The sine of θ is equal to the y-coordinate (-1) divided by the hypotenuse (distance from the origin). Therefore, sin θ = -1/5. The cosine of θ is equal to the x-coordinate (-4) divided by the hypotenuse. Therefore, cos θ = -4/5. The tangent of θ is equal to the y-coordinate (-1) divided by the x-coordinate (-4). Therefore, tanθ = -1/-4 = 1/4. The cotangent of θ is equal to the x-coordinate (-4) divided by the y-coordinate (-1). Therefore, cot θ = -4/-1 = -4. The secant of θ is equal to the hypotenuse (distance from the origin) divided by the x-coordinate (-4). Therefore, sec θ = 5/-4 = -5/4. The cosecant of θ is equal to the hypotenuse divided by the y-coordinate (-1). Therefore, csc θ = 5/-1 = -5.So, the six trigonometric functions of the angle θ for the given point (-4, -1) are sin θ = -1/5, cos θ = -4/5, tan θ = 1/4, cot θ = -4, sec θ = -5/4, and csc θ = -5.

Learn more about trigonometric here:

https://brainly.com/question/9083711

#SPJ4

The equation 2 and 3 would not present linear functions.

What is linear function?

A linear function is one in which the maximum power of the variables is one.

A linear function is a function that has the form f(x) = mx + b, where m and b are constants. In other words, a linear function is a straight line when plotted on a graph.

Out of the given relationships, the following do not represent a linear function:

2) The ant population for a colony that begins with 5 ants and doubles in number every two weeks.

This relationship is not linear because the rate of change (the number of ants per unit time) is not constant. The number of ants increases exponentially, which results in a curve rather than a straight line when plotted on a graph.

3) A history student's grade on a test that begins at 100 but decreases by 4 points for each question answered incorrectly.

This relationship is not linear because the rate of change (the decrease in points per incorrect question) is not constant. The decrease in points results in a curve rather than a straight line when plotted on a graph.

The other two relationships do represent linear functions.

Therefore, The equation 2 and 3 would not present linear functions.

To know more about  linear functions visit,

https://brainly.com/question/4025726

#SPJ1

The right triangle ABC with right angle at vertex B has the length of the segment is; 4√2 unit.

The Pythagorean theorem state that in any right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the two shorter sides. In this case, side AC is the hypotenuse and side AB and BC are the two shorter sides.

We can find the lengths of all three sides using the Pythagorean theorem and the information given. Side AB is equal to the square root of the sum of the squares of sides AC and BC. Since we are given that angle ABC is a right angle, we can find that side BC is equal to the length of side AB.

The side lengths are 8/2 = 4

Now, Another side length that is x

So , the equation formed is;

xcos45 = 4

x/√2 = 4

x = 4√2

Hence the length of the segment is; 4√2 unit.

Learn more about Pythagorean theorem here:

brainly.com/question/14930619

#SPJ1

There are 35 ways to choose two toppings for a pizza, one topping from a group of 5 kinds of meats and the other topping from a group of 7 kinds of vegetables.

The multiplication rule of counting in Permutation and Combinations states that if there are n ways to perform one task and m ways to perform a second task, then there are n x m ways to perform both tasks in sequence.

The number of ways to choose a meat topping from 5 kinds of meats = 5.

The number of ways to choose a vegetable topping from 7 kinds of vegetables = 7.

Using the multiplication rule, the number of ways to choose one meat topping and one vegetable topping is = 5 x 7 = 35 ways.

Learn more about multiplication rule of counting from the below link:

https://brainly.com/question/15096318

#SPJ4

Bob tardó 55 minutos en limpiar el garaje, por lo que debemos convertir ese tiempo a segundos para saber cuánto tiempo tardó exactamente.

Sabemos que 1 minuto tiene 60 segundos, por lo que podemos utilizar esta información para convertir los 55 minutos a segundos. La fórmula para realizar esta conversión es:

Segundos = Minutos * 60

Aplicando esta fórmula a los 55 minutos que Bob tardó en limpiar el garaje, obtenemos:

Segundos = 55 * 60

Segundos = 3300

Por lo tanto, Bob tardó 3300 segundos, o aproximadamente 55 minutos, en limpiar el garaje.

Es importante destacar que la conversión de tiempo de minutos a segundos es una operación común en matemáticas y cálculo, y es útil para resolver problemas en los que es necesario trabajar con diferentes unidades de tiempo. Además, entender la relación entre diferentes unidades de tiempo es esencial para realizar cálculos precisos y resolver problemas de manera efectiva.

To know more about Bob tardó click here:

brainly.com/question/28789438

#SPJ4

Based on the Venn diagram, the number of people in each set are follows:

The number of people in each set in the Venn diagram is calculated as follows:

The universal set has a total of 50 people

Let the intersection of A and B be x

A∩B = x

The number of people in A alone = 24 - x

The number of people in B alone = 30 - x

x + (24 - x) + (30 - x) + 7 = 50

61 - x = 50

x = 61 - 50

x = 11

A∩B = 11

Hence;

The number of people in A alone = 24 - 11

The number of people in A alone = 13

The number of people in B alone = 30 - 11

The number of people in B alone = 19

Learn more about Venn diagrams at: https://brainly.com/question/2099071

#SPJ1

So the simplified expression of the expression given in the question is: 1.17 - 3.99a

To simplify the expression, we can combine the like terms, which are terms with the same variable and exponent. Starting with the first two terms: 1.17 - 0.07a. The next two terms are the opposite of each other, so we can add them: 1.17 - 0.07a + (-3.92a) = 1.17 - 0.07a - 3.92a. Finally, we can simplify the expression by combining the like terms, which are terms with the same variable: 1.17 - 0.07a - 3.92a = 1.17 - (0.07 + 3.92)a = 1.17 - 3.99a. So the simplified expression is: 1.17 - 3.99a

To learn more about variable and exponent click here

brainly.com/question/24177809

#SPJ4

Complete Question

Combine like terms to simplify the expression:

1. 17 − 0. 07 + ( − 3. 92 )  1. 17−0. 07a+(−3. 92a)

The situation that matches the information in the graph is a boy rides a bicycle on flat ground and goes quickly down a large hill (option A).

The graph shows how the movement of a body changes over time. In general, it can be observed the movement is first linear as in moving on a flat surface, then the body goes down, then it goes up, and finally, the movement is linear again.

Based on this, it can be concluded that the option that describes the graph is a boy rides a bicycle on a flat group, then he goes down a large hill and finally he drives on flat ground again (option A).

Learn more about graphs in https://brainly.com/question/17267403

#SPJ1

The pole is 34.93 feet tall. The solution has been obtained by using trigonometry.

What is trigonometry?

Trigonometry is the branch of mathematics that focuses on the study of the sides, angles, and connections of the right-angle triangle.

We are given that Leon is standing 67 feet from a telephone pole. Leon's angle of sight up to the bird is 24° and his eyes are 5.1 feet above the ground.

From this, a figure is obtained which is attached below.

Using trigonometry,

We know that tan theta = opposite side/ adjacent side

So,

⇒tan θ = x/67

Here, θ = 24°

So,

⇒tan 24° = x/67

⇒x = 67 tan 24°

⇒x = 67 * 0.4452

⇒x ≈ 29.83

The height of the pole = 29.83 + 5.1 = 34.93 feet

Hence, the pole is 34.93 feet tall.

Learn more about trigonometry from the given link

https://brainly.com/question/13729598

#SPJ1

Answer:

22

Step-by-step explanation:

x+35=56

56-35=22

x=22

Rudy has 3003 different ways to choose 6 toppings from a menu of 14 toppings if each topping can only be chosen once.

The number of ways to choose 6 toppings from a menu of 14 toppings where each topping can only be chosen once is 14!/(14-6)! = 14!/(8!) = 3003. This is because for the first topping, Rudy has 14 options, for the second topping he has 13 options, for the third topping he has 12 options, and so on. To calculate the total number of combinations, we use the formula n!/(n-r)! where n is the number of items and r is the number of items to choose. This formula gives us the number of ways to choose r items from a set of n items without regard to order, which is the number of combinations.

The formula for combinations is given by n!/(n-r)! where n is the number of items and r is the number of items to choose. Here, n = 14 (the number of toppings on the menu) and r = 6 (the number of toppings Rudy wants to choose). So, the number of combinations is 14!/(14-6)! = 14!/(8!).

The factorial (!) is the product of all positive integers up to that number. For example, 4! = 4 x 3 x 2 x 1 = 24.

So, 14! = 14 x 13 x 12 x ... x 2 x 1 = 87178291199, and 8! = 8 x 7 x 6 x ... x 2 x 1 = 40320.

Now, to calculate the number of combinations, we divide 14! by 8!: 14!/(8!) = 87178291199/40320 = 3003.

Therefore, Rudy has 3003 different ways to choose 6 toppings from a menu of 14 toppings if each topping can only be chosen once.

To learn more about toppings please click on below link.

https://brainly.com/question/29858706

#SPJ4

Answer:

X = 48

Step-by-step explanation:

x/4 - 6 = x/12 + 2​

= 3x-72=x+24

= 3x=x+96

= 2x=96

= x=48

Answer:

x=48

Step-by-step explanation:

You can solve by x by simplifying both sides of the equation, then isolating the variable

Answer:

Step-by-step explanation:

The variability of the data is very small (close to 0) because all the scores are approximately the same.

The variability of these data can be calculated using the variance formula, which is the average squared difference from the mean. In this case, the mean is 3.8 (the sum of 4, 4, 4, 4, and 3 divided by 5). Therefore, the variance is 0.08 (the sum of the squared differences [4-3.8, 4-3.8, 4-3.8, 4-3.8, 3-3.8] divided by 5). This indicates that the variability of the data is very small (close to 0) because all the scores are approximately the same.

Learn more about variability here:

https://brainly.com/question/16906863

#SPJ4

The translation of a function and coordinates are given below..

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

The following functions:

y = x²

y = 2x

The transformation is:

Translate two units to the left.

So,

y = (x - 2)²

y = 2(x - 2)

Translation 5 units up.

y = x² + 5

y = 2x + 5

The following coordinates:

Translate 2 units to the right.

(1, 4) = (1 + 2, 4) = (3, 4)

(5, 8) = (5 + 2, 8) = (7, 8)

Translation 5 units down.

(1, 4) = (1, 4 - 5) = (1, -1)

(5, 8) = (5, 8 - 5) = (5, 3)

Thus,

The translation of a function and coordinates are given above.

Learn more about translation here:

https://brainly.com/question/124

#SPJ1

The sample is approximately 50,000 years old, as the amount of Carbon-14 in it is lower than that of a contemporary sample.

1) Calculate the ratio of Carbon-14 in the sample compared to a contemporary sample.

Ratio = (60/100) = 0.6

2) Calculate the number of half-lives since the sample was alive.

Number of half-lives = ln(0.6) / ln(0.5) = 0.69897

3) Calculate the age of the sample.

Age of sample = (0.69897 x 5730) = 4020 years

60% of the Carbon-14 identified in a sample taken from a waste site close to the Strait of Magellan was present in the sample from the trash deposit. We must first determine the sample's carbon-14 ratio in relation to a more recent sample in order to determine the sample's age. This ratio is equivalent to the sample's 60% carbon-14 content, or 0.6, when divided by 100. The number of half-lives since the sample has been alive may then be determined by taking the natural log of the ratio and dividing it by the natural log of 0.5, which is 0.69897. By dividing the quantity of half-lives by the 5730-year half-life of carbon-14, we may finally determine the sample's age.

Learn more about sample here

https://brainly.com/question/11045407

#SPJ4

The statement "If f(n) = O(g(n)) and g(n) = Ω(h(n)), then f(n) = Θ(h(n))" is actually true.

This can be proven using the formal definitions of the O-notation, Ω-notation, and Θ-notation:

f(n) = O(g(n)) means that there exist positive constants c and n0 such that |f(n)| ≤ c|g(n)| for all n ≥ n0.

g(n) = Ω(h(n)) means that there exist positive constants c' and n0' such that |g(n)| ≥ c'|h(n)| for all n ≥ n0'.

f(n) = Θ(h(n)) means that there exist positive constants c1, c2, and n1 such that c1|h(n)| ≤ |f(n)| ≤ c2|h(n)| for all n ≥ n1.

If we assume that f(n) = O(g(n)) and g(n) = Ω(h(n)), we can use the definitions above to show that f(n) = Θ(h(n)).

Since g(n) = Ω(h(n)), we have |g(n)| ≥ c'|h(n)| for some positive constants c' and n0', and since f(n) = O(g(n)), we have |f(n)| ≤ c|g(n)| for some positive constants c and n0.

Combining these two inequalities, we get:

|f(n)| ≤ c|g(n)| ≤ c(c'/c)|h(n)|

Therefore, f(n) = Θ(h(n)) with constants c1 = 1 and c2 = c(c'/c), and n1 = max(n0, n0').

To learn more about statement here:

https://brainly.com/question/17029275

#SPJ4

The proportion EF/DF = BC/AC is true. Hence, option A is the accurate answer to this question.

We are given that the two triangles ΔABC and ΔDEF are similar.

According to the definition of a similar triangle, we know that the ratio of the corresponding sides is proportional and the corresponding angles are always congruent.

Since ΔABC and ΔDEF are similar, this implies that -

∠A corresponds to ∠D,

∠B corresponds to ∠E, and

∠C corresponds to ∠F.

Thus we can say -

EF/DF = BC/AC

AB/DF = DE/AC

AB/EF = DE/BC

Only option A satisfies the condition. Hence, the proportion EF/DF = BC/AC is true.

Read more about the similarity of triangles:

brainly.com/question/8045819

#SPJ4

The complete question is -

The triangle abc and triangle def are similar. Which proportion must be true?

Answer:

Part A: If (26)x = 1, the value of x is approximately 0.03846.

Part B: If (50)x = 1, the possible value of x is approximately 0.02.

Step-by-step explanation:

Part A: To find the value of x in the equation (26)x = 1, we need to find the value that, when raised to the power of 26, will equal 1. This value can be found by taking the reciprocal (or multiplicative inverse) of 26 and taking the natural logarithm of both sides.

Using the formula x = 1/26, we get:

x = 1/26 = 0.03846

So, the value of x in the equation (26)x = 1 is approximately 0.03846.

Part B: To find the possible values of x in the equation (50)x = 1, we need to find the values that, when raised to the power of 50, will equal 1. This value can be found by taking the reciprocal (or multiplicative inverse) of 50 and taking the natural logarithm of both sides.

Using the formula x = 1/50, we get:

x = 1/50 = 0.02

So, the possible value of x in the equation (50)x = 1 is approximately 0.02.

If we are only interested in the total number of games the Yankees win, the possible events for the two games are: 0 wins: LL , 1 win: LW, WL and 2 wins: WW

What is event in probability ?

In probability, an event is a subset of the sample space of a random experiment. In other words, an event is a collection of possible outcomes of the experiment.

For example, consider flipping a fair coin. The sample space of this experiment is {heads, tails}. An event could be defined as "getting heads", which is a subset of the sample space that includes only one outcome.

There are four possible outcomes for the double-header, which can be represented using W for a win and L for a loss:

WW (Yankees win both games)

WL (Yankees win the first game, but lose the second game)

LW (Yankees lose the first game, but win the second game)

LL (Yankees lose both games)

Therefore , If we are only interested in the total number of games the Yankees win, the possible events for the two games are: 0 wins: LL , 1 win: LW, WL and 2 wins: WW

To learn more about Event from given link.

https://brainly.com/question/17089724

#SPJ1

Answer:

3

Step-by-step explanation:

1 loop around the block is 1/4 of a mile. multiply both sides by three. 3 loops is 3/4 of a mile.

Answer:

she mostly likely found 1 result .

The best measure of center for this data is the median, and its value is 49.

What is the median in statistics?

In statistics, the median is a measure of central tendency that represents the value separating the higher half of a dataset from the lower half.

To find the median of a dataset, the values must first be arranged in order of magnitude. If the dataset has an odd number of values, the median is the middle value. If the dataset has an even number of values, the median is the average of the two middle values.

To determine the best measure of center for this data, we need to consider the shape of the distribution. Looking at the histogram, we can see that the data is skewed to the right, with a long tail of higher values.

In this case, the median is the best measure of center, because it is not affected by the extreme values in the dataset. The median is the middle value of the dataset when it is arranged in order, and in this case, the middle value is between 49 and 50. Since there are an even number of data points, we take the average of the two middle values, which gives a median of 49.

We are given that;

The list of donation is as follows

11, 18, 35, 39, 45, 45, 46, 47, 49, 49, 50, 50, 50, 50, 56, 57, 58, 59

Now,

Mean is the middle term of the data

Here,

Middle term of data = 49

Therefore, the mean of the given list will be 49.

Therefore, the best measure of center for this data is the median, and its value is 49.

To learn more about the median in statistics, visit:

https://brainly.com/question/7730356

#SPJ1

Answer: The median of 49 is the most accurate to use, since the data is skewed.

Step-by-step explanation:

Answer:

30.

Step-by-step explanation:

We can write an equation for the number of gallons of water in the bathtub using the rate of change (drainage) and the elapsed time. Let y be the number of gallons of water in the tub after t minutes. Then, the equation can be written as:

y = 42 - (drainage rate) * t

Since we know that after 2 minutes, the tub holds 30 gallons of water, we can use this information to solve for the drainage rate:

30 = 42 - (drainage rate) * 2

12 = (drainage rate) * 2

drainage rate = 6 gallons per minute

Substituting this value into the original equation, we get:

y = 42 - 6t

So, the equation that represents the number of gallons of water in the tub after 2 minutes is:

y = 42 - 6 * 2 = 42 - 12 = 30.

Answer:

The equation representing the number of gallons of water in the tub after t minutes can be represented by a linear function y = mx + b, where y is the number of gallons of water, x is the number of minutes, m is the rate of change (or the slope) and b is the y-intercept.

Since the bathtub is draining at a constant rate, the slope (m) can be found by finding the difference between the initial number of gallons of water (42) and the number of gallons after 2 minutes (30), and dividing by the difference in time (2 minutes):

m = (42 - 30) / 2 = 6 gallons per minute

The y-intercept (b) can be found using the initial conditions of the problem, when t = 0:

b = 42 - (6 * 0) = 42

Therefore, the equation representing the number of gallons of water in the tub after t minutes can be written as:

y = 6t + 42

So, after 2 minutes, y = 6 * 2 + 42 = 54 gallons of water.