I WILL GIVE 100 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT. Refer to the given figure and select the answer that correctly completes the sentence below.

The acute angle between the lines 6x - y = 2 and 5x + y = 7 is approximately 55 degrees.

To find the acute angle between two lines, we need to determine the angle between their direction vectors.

First, let's rewrite the given lines in slope-intercept form:

Line 1: 6x - y = 2 => y = 6x - 2

Line 2: 5x + y = 7 => y = -5x + 7

The direction vector of Line 1 is (6, -1), and the direction vector of Line 2 is (5, -1).

To find the angle between two vectors, we can use the dot product formula:

cos(theta) = (v · w) / (|v| |w|)

where v and w are the direction vectors of the lines, and |v| and |w| are their magnitudes.

Calculating the dot product:

v · w = (6 * 5) + (-1 * -1) = 30 + 1 = 31

Calculating the magnitudes:

|v| = sqrt(6^2 + (-1)^2) = sqrt(36 + 1) = sqrt(37)

|w| = sqrt(5^2 + (-1)^2) = sqrt(25 + 1) = sqrt(26)

Plugging the values into the formula:

cos(theta) = 31 / (sqrt(37) * sqrt(26))

Using an inverse cosine function to find theta:

theta ≈ acos(31 / (sqrt(37) * sqrt(26))) ≈ 54.8 degrees

Rounding to the nearest degree, the acute angle between the lines is approximately 55 degrees.

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The points on the curve where the tangent is horizontal: (1, 0) & (-1, 0),  and where the tangent is vertical: (0, 1) & (0, -1)

To find the points on the curve x=cos(theta) where the tangent is horizontal or vertical, we need to find the derivative of x with respect to theta.

Taking the derivative of x with respect to theta, we get:

dx/dtheta = -sin(theta)

When the tangent is horizontal, the derivative is equal to zero. So we need to solve the equation -sin(theta) = 0 for theta.

This equation is true when theta = n*pi, where n is an integer. So the points on the curve x=cos(theta) where the tangent is horizontal are:

(1, 0) for n=2k, where k is an integer

(-1, 0) for n=2k+1, where k is an integer

When the tangent is vertical, the derivative is undefined. This happens when cos(theta) = 0, which is true when theta = (2k+1)*pi/2, where k is an integer.

So the points on the curve x=cos(theta) where the tangent is vertical are:

(0, 1) for n=2k+1, where k is an integer

(0, -1) for n=2k, where k is an integer

Therefore, the points on the curve where the tangent is horizontal are (1, 0) and (-1, 0), and the points on the curve where the tangent is vertical are (0, 1) and (0, -1).

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To find:

The method of drwaing the graph of given inequality.

Solution:

Given inequality: -3m +18 < 30.

Solve the inequality:

To draw the graph, draw a dotted line on -4. Since, the solution set contains all numbers greater than -4,so, shade the portion that lies to right side of -4.

Answer:

Y=6x+7

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

for many infinite amount of answer possibilities the equation has to be the same

Answer:

4

Step-by-step explanation:

every 2 servings, 8 oz. every 1 serving, 4 oz.

Answer:

try looking up rise over run method. that's what i was taught to use for rate of change. it's easier so basically it's x over y

Step-by-step explanation:

In order to find the value of the expression, first let's calculate the operations inside the parenthesis:

Then, calculating the exponential expression and after that the product, we have:

So the final value is 112.

The unit the answer would have is dollars $.

The area of the field would have to be rewritten so as to have the same exponent value as the cost per square meter.

The operation that would be used to solve the problem is multiplication.  

It does not make sense to give the answer in scientific form because prices are not usually written in that form.

Scientific notation is used in expressing large numbers in smaller numbers. It is used to transform large numbers into smaller number.

In order to carry out any mathematical operation using scientific notation, all the numbers must have the same exponents. If the exponents are not the same, adjustments have to be made so that the exponents are equal.

The total cost of reseeding the filed = area of the field x cost per square meter

(7.14 x 10³) × ($0.04)

The exponents are not the same, thus the multiplication operation cannot be carried out without adjusting the numbers.

7140 x 0.04 = $285.60

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In linear equation, 14 teachers teach at both schools.

What in mathematics is a linear equation?

Let

A =  Albers Elementary School

B = Bothel Elementary School

According to the question:

n(A) = 44, n(B) = 74, n(A U B) = 87.

Using the union formula we get

n(A U B ) = n(A) + n(B) - n ( A ∩ B )

 51 =  45 + 20 - n ( A ∩ B )

n ( A ∩ B ) = 65 - 51

n ( A ∩ B ) = 14

So, 14 teachers teach at both schools.

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The solution for x in the equation given as 3/2 (4x – 1) – 3x = 54 –(x + 2) is 13.375

From the question, the algebraic expression is given as

3/2 (4x – 1) – 3x = 54 –(x + 2)

There is no constant to multiply or divide in the expression

3/2 (4x – 1) – 3x = 54 –(x + 2)

Open the brackets

So, we have

6x – 3/2 - 3x = 54  - x - 2

Collect the like term in the above equation

This gives

6x - 3x + x = 54 - 2 + 3/2

Evaluate the like term in the above equation

So, we have the following representation

4x = 53.5

Divide through by 4

x = 13.375

The above equation cannot be solved further

Hence, the solution is x = 13.375

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Answer:

3.36

Step-by-step explanation:

.20 x 2.80 = .56

2.80 + .56 = 3.36

Answer:

\(\sqrt{10}\)

Step-by-step explanation:

Using the distance formula, we see that the distance between (-4,4) and (-7,3) is \(\sqrt{10}\).

Given statement solution is :- The mass of x refers to the probability mass function (PMF) values for each value of x.

Plot of the probability mass function (PMF):

The PMF plot represents the probabilities of the different values of x.

css

Copy code

x  |  P(X=x)

---|--------

0  |  0.362

1  |  0.442

2  |  0.153

3  |  0.037

4  |  0.006

5  |  0.0005

The cumulative distribution function (CDF) of x is a function that gives the probability that X takes on a value less than or equal to a given x-value.

a. The possible values of x are 0, 1, 2, 3, 4, and 5. This represents the number of hearts you can get from the 5 cards dealt.

b. The mass of x refers to the probability mass function (PMF) values for each value of x. We can calculate the mass as follows:

P(x = 0) = (39/52) * (38/51) * (37/50) * (36/49) * (35/48)

P(x = 1) = 5 * (13/52) * (39/51) * (38/50) * (37/49) * (36/48)

P(x = 2) = 10 * (13/52) * (12/51) * (39/50) * (38/49) * (37/48)

P(x = 3) = 10 * (13/52) * (12/51) * (11/50) * (39/49) * (38/48)

P(x = 4) = 5 * (13/52) * (12/51) * (11/50) * (10/49) * (39/48)

P(x = 5) = (13/52) * (12/51) * (11/50) * (10/49) * (9/48)

Note: The coefficients in front of each probability correspond to the different ways of selecting x hearts from the available hearts in the deck.

c. Plot of the probability mass function (PMF):

The PMF plot represents the probabilities of the different values of x.

css

Copy code

x  |  P(X=x)

---|--------

0  |  0.362

1  |  0.442

2  |  0.153

3  |  0.037

4  |  0.006

5  |  0.0005

d. The cumulative distribution function (CDF) of x is a function that gives the probability that X takes on a value less than or equal to a given x-value.

The CDF of x can be calculated by summing up the probabilities of all the values less than or equal to x.

CDF(x = 0) = P(x = 0)

CDF(x = 1) = P(x = 0) + P(x = 1)

CDF(x = 2) = P(x = 0) + P(x = 1) + P(x = 2)

CDF(x = 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)

CDF(x = 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)

CDF(x = 5) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5)

e. Plot of the cumulative distribution function (CDF):

The CDF plot represents the cumulative probabilities for the different values of x.

scss

Copy code

x  |  CDF(X<=x)

---|-----------

0  |  0.362

1  |  0.804

2  |  0.957

3  |  0.994

4  |  1.000

5  |  1.000

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The pair of algebraic expressions which are like terms is; 20x and 0.8x.

Algebraic expressions are pronounced as like terms if the terms contain the same variable raised to the same exponent.

check all options:

20x, 0.8x

same variable and exponent

17, 3x

Not same variable

14x, 14x²

Same variable, not same exponent

0.5x, 0.5y

Not same variable

On this note, it follows that the terms 20x and 0.8x are like terms.

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D. 75 cm

Step-by-step explanation:

fill in the y with 20.5, so you get 20.5=0.3x-2. Add the 2 to the 20.5 so you get 22.5=0.3x. Divide both by 0.3 to get 75=x.

sorry if it's a bd explanation, hope this helps :)

Answer:

75 cm

Step-by-step explanation:

This is Maps Testing I did it already

Answer:

5 red, 5 yellow, and 4 blue

Step-by-step explanation:

Answer:

5 red, 5 yellow, and 4 blue :)

Step-by-step explanation:

Answer: 18

Explanation: Divide the diameter by 2.

Answer:

18 centimeters.

Step-by-step explanation:

Radius is half of the diameter of a circle. Half of 36 centimeters is 18 centimeters, so the radius of the circle is 18 centimeters.

Hope this helps...have a great day!! ^^

The cost to repair a bicycle equals 150X, where X has the following probability function: f(x)=20x(1−x)3 Thus standard deviation of the repair cost is approximately 0.267.

To calculate the standard deviation of the repair cost, we need to find the variance first. The variance of a random variable X can be calculated using the formula:

Var(X) = E(X^2) - [E(X)]^2

First, let's calculate E(X):

E(X) = ∫(x * f(x)) dx, integrated from 0 to 1

E(X) = ∫(x * 20x(1−x)^3) dx, integrated from 0 to 1

E(X) = ∫(20x^2(1−x)^3) dx, integrated from 0 to 1

E(X) = 20 * ∫(x^2(1−x)^3) dx, integrated from 0 to 1

Solving the integral, we find E(X) = 4/7.

Next, let's calculate E(X^2):

E(X^2) = ∫(x^2 * f(x)) dx, integrated from 0 to 1

E(X^2) = ∫(x^2 * 20x(1−x)^3) dx, integrated from 0 to 1

E(X^2) = ∫(20x^3(1−x)^3) dx, integrated from 0 to 1

E(X^2) = 20 * ∫(x^3(1−x)^3) dx, integrated from 0 to 1

Solving the integral, we find E(X^2) = 4/15.

Now, we can calculate the variance:

Var(X) = E(X^2) - [E(X)]^2

Var(X) = (4/15) - (4/7)^2

Var(X) = 4/15 - 16/49

Var(X) = 40/105 - 48/105

Var(X) = -8/105

The standard deviation (σ) is the square root of the variance:

σ = sqrt(-8/105)

Thus, the standard deviation of the repair cost is approximately 0.267.

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Answer: \(\frac{3}{6}\)

Step-by-step explanation:

\(Three\ divided\ by\ 6\ is\ \ \frac{3}{6} \ or\ simplified\ to\ \frac{1}{2}\)

Answer: 3/6  = 0.5

Step-by-step explanation: Divide 3 divided by 6 as a fraction and that should give you 0.5 if your teacher tells you the answer cannot be a decimal then the answer will be 12 or if he tells u to simplify then the answer wil be 1/2

Answer:

The determinant of C is zero and does not have inverse.

Step-by-step explanation:

Let \(C = \left[\begin{array}{ccc}2&4&6\\3&6&9\\4&8&12\end{array}\right]\), since it is a matrix with 3 rows and 3 columns, we can determine its determinant by the Sarrus' rule:

\(\det(C) = \left|\begin{array}{ccc}2&4&6\\3&6&9\\4&8&12\end{array}\right|\)

\(\det(C) = (2)\cdot (6)\cdot (12)+(3)\cdot (8)\cdot (6)+(4)\cdot (4)\cdot (9)-(4)\cdot (6)\cdot (6)-(3)\cdot (4)\cdot (12)-(2)\cdot (8)\cdot (9)\)

\(\det (C) = 0\)

Since the determinant of C is equal to zero, then we conclude that C does not have an inverse according to the following definition of inverse matrix. That is:

\(C^{-1} = \frac{1}{\det(C)}\cdot adj(C)\) (1)

Where \(adj(C)\) is the adjugate matrix of C, defined as the transpose of the cofactor matrix of C.

The result of this expression is undefined due to the determinant.  

Answer:

Since the amount dropped to 1/2 of the initial amount over a period of 7 years, you can assume the half-life is 7 years.

m(t) = m0 (0.5)t/7,

t = years elapsed from the time the amount was m0

In grams,

m(t) = 8 (0.5)t/7

m(8) = 8 (0.5)8/7 g ≅ ? g

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

pls give me brainliest

Answer:

A cylinder is a three-dimensional figure like a prism, but with bases that are circles. A sphere is a three-dimensional figure in which all cross-sections in every direction are circles.

Option is B

Step-by-step explanation:

Answer:

Step-by-step explanation:

slope formula: \(\frac{y2-y1}{x2-x1}\)

                       : \(\frac{-2--5}{1--11}\)

                       : \(\frac{1}{4}\) ............this is our slope, m.

using y - y1 = m ( x - x1 )

⇒     y - 2 = \(\frac{1}{4}\) ( x - 1 )

⇒      \(y =\) \(\frac{x}{4}\) + \(\frac{7}{4}\)

Answer:

\(y=\frac{1}{4}x - \frac{9}{4}\)

Step-by-step explanation:

\(m= \frac{y2-y1}{x2-x1}\)

So, plug in (-11,-5) and (1,-2),

\(m=\frac{(-2) - (-5)}{1-(-11)}\)

Subtract,

\(m=\frac{3}{12}\)

Divide 3 by 12:

\(m=\frac{3}{12} = .25\) or \(\frac{1}{4}\)

The slope is .25 or \(\frac{1}{4}\)

So, the equation so far is:

\(y=\frac{1}{4} x + b\)

Now, we have to find the y-intercept.

\(y=\frac{1}{4}x+b\)

Substitute the x for 1 and -2 in place of y.

\(-2=\frac{1}{4}(1) +b\)

Now solve.

\(-2=\frac{1}{4}(1) +b\\-2=\frac{1}{4} +b\\-\frac{1}{4} -\frac{1}{4} \\\\-2\frac{1}{4} =b\)

the y-intercept is: \(-2\frac{1}{4}\) or \(-\frac{9}{4}\)

The full equation is : \(y=\frac{1}{4}x - \frac{9}{4}\)

Hope this helps! Brainliest would be much appreciated! Have a great day! :)

i didn't know the answer sorry

Answer:

7.28

Step-by-step explanation.

4 is rounded down to 80 and if you just take away the 0 in 80 its 8.

Answer:

it already is

Step-by-step explanation:

.2 is the tenth .28 is the hundredth and .284 id the thousandth. there arent any more decimals after that thousandth so you cant round up or down

Answer:

Below in bold.

Step-by-step explanation:

2x + 20 > 4x         ( as triangle WXY is a right triangle and the longest side's length ( the hypotenuse) is 2x + 20.

2x + 20  > 4x

20 > 2x

x < 10.

Answer:

15 cents

Step-by-step explanation:

2.25 /15 = .15

Answer:

\(a_n=112\left(-\frac{1}{4}\right)^{n-1}\)

Step-by-step explanation:

Geometric Sequences

There are two basic types of sequences: arithmetic and geometric. The arithmetic sequences can be recognized because each term is found as the previous term plus a fixed number called the common difference.

In the geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.

We are given the sequence:

112, -28, 7, ...

It's easy to find out this is a geometric sequence because the signs of the terms are alternating. If it was an arithmetic sequence, the third term should be negative like the second term.

Let's find the common ratio by dividing each term by the previous term:

\(\displaystyle r=\frac{-28}{112}=-\frac{1}{4}\)

Testing with the third term:

\(\displaystyle -28*-\frac{1}{4}=7\)

Now we're sure it's a geometric sequence with r=-1/4, we use the general equation for the nth term:

\(a_n=a_1*r^{n-1}\)

\(a_n=112\left(-\frac{1}{4}\right)^{n-1}\)

Answer:

50m       ..........................................................................................