Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.
a. y= ?
b. y=?

Using the concept of the word problem and utilizing the provided conditions and values, The answer is 18, 20, and 22.

A word problem in mathematics is a problem or exercise that is expressed in a natural language, rather than in mathematical notation. These types of problems often present a real-world situation that involves mathematical concepts, such as numbers, operations, or measurements. They typically require the use of mathematical reasoning and problem-solving skills to understand the problem and find a solution. Examples of word problems include: "If a train travels 60 miles per hour and you want to know how far it will travel in 4 hours", "If a rectangle is 6 meters long and 4 meters wide, what is its area?", "If a bag contains 3 red balls and 4 blue balls, what is the probability of picking a blue ball?"

In a mathematical problem, the conditions refer to the specific information or constraints provided in the problem statement that must be taken into account in order to find a solution. These conditions can include information about the quantities involved in the problem, the operations that need to be performed, or the specific requirements that the solution must meet.

Let x be the smallest of the three consecutive even integers. Then the next two integers are x+2 and x+4. We know that:

x + (x+4) * 3 = 84

Expanding and solving for x:

x + 3x + 12 = 84

4x = 72

x = 18

So the three consecutive even integers are 18, 20, and 22.

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Answer:

125

Step-by-step explanation:

15/12 you get 125. Then multiple it by 100 and you get 125.

Answer:

L = ½ × pedestal × tall

L = ½ × ( 10 × 10 ) × ( 10 × 10 )

L = ½ × 100 × 100

L = 100/2 × 100

L = 10.000/2

L = 10.000 ÷ 2

L = 5.000 Cm³

To solve a system of equations by elimination method you need to have one f the variables ( x or y) with opposite coefficient in the two equations of the system.

In this case you have the variable y with opposite coefficients; -1 and +1

You add the equations as follow:

As you get that the sum of the equations is:

You solve the x:

- Divide both sides of the equation into 3:

You use this value of x to find the value of y by substitute the x in one of the equation by 10:

Solve for y:

The volume of the tower is 224 in³, which is not listed among the given options.

To find the volume of the rectangular block, we need to multiply its length, width, and height. Therefore, the volume of the single block is:
8 x 3.5 x 2 = 56 cubic inches.
Since we are stacking four blocks to create a tower, we need to multiply the volume of a single block by 4.

Thus, the volume of the tower is:
56 x 4 = 224 cubic inches.
The volume of a rectangular block can be found using the formula,

V = length × width × height.

In this case, the length is 8 inches, the width is 3.5 inches, and the height is 2 inches.

V = 8 × 3.5 × 2 V

= 28 × 2 V

= 56 in³

Now that we know the volume of one block, we can find the volume of the tower created by stacking four blocks. Tower volume = block volume × number of blocks Tower volume = 56 in³ × 4 Tower volume = 224 in³

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Answer:

Step-by-step explanation:

We can find the height using Pythagorean's Theorem.

\(34^{2} =13^{2} +h^{2} \\h=\sqrt{1,156-169}=\sqrt{987} \approx 31\)

So, the height is 31 centimeters, approximately.

Now, we use the given expression and the base and height

\(P=b^{2} +2bh=13^{2}+2(13)(31)=169+806=975 \ cm^{2}\)

Therefore, Josh is right, he needs less than 1000 square centimeters. Specifically, he needs 975 square centimeters.

From the side/angle inequality, we see that the smallest angle of a triangle must be opposite its shortest side. In this case, that angle is opposite the shortest side \(\overline{AC},\) so our answer is \(\boxed{\angle B}.\)

As for finding its measure (which I'm aware the question probably didn't ask for), we can use the law of cosines:

\(5^2=6^2+7^2-2(6)(7)\cos B\)

\(\cos B=\frac{5}{7}\implies\angle B\approx\boxed{44.4^\circ}.\)

Answer:

Smallest Angle in the triangle is angle c.

From the picture,

∠ABC + ∠DBC = ∠ABD

Substituting with data,

x + (3x + 10) = 90

4x + 10 = 90

4x = 90 - 10

4x = 80

x = 80/4

x = 20

A sequence of instructions that solves a problem is called an algorithm.

\(5(2^x+4)=15\\2^x+4=3\\2^x=-1\\x\in\emptyset\)

Answer:

no solutions

Step-by-step explanation:

5(2^x+4)=15

Divide each side by 5

5/5(2^x+4)=15/5

(2^x+4)=3

Subtract 4 from each side

2^x = 3-4

2^x = -1

This cannot happen so there are no solutions

Answer:v=-4

Step-by-step explanation:We move all terms to the left:

-5v+6-(26)=0

We add all the numbers together, and all the variables

-5v-20=0

We move all terms containing v to the left, all other terms to the right

-5v=20

v=20/-5

The constant of variation of the given problem is calculated as; 240 miles

A constant of variation (k) is defined as a ratio that represents the relationship between the independent variable (x) and the dependent variable (y).

Now, we are told that average speed, s, in miles per hour is inversely proportional to the time, t, the trip takes in hours. Thus;

s ∝ 1/t

Thus;

s = k(1/t)

where k is the constant of proportionality

we are told that If the train takes 2 hours, and the average speed is 120 mph. Thus;

120 = k(1/2)

Multiply both sides by 2 to get;

240 miles = k

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Answer:

Perimeter = 23.692 units

Step-by-step explanation:

Perimeter = sum of all his sides

then:

Perimeter = 4.15 + 7.092 + 12.45

Perimeter =  23.692 units

Applying exponent rules, the factored expression is given as follows:

125^6 - 27^15 = 5^18 - 3^45.

The expression is factored according to the like terms of the expression, which are placed into evidence.

For this problem, the expression is:

125^6 - 27^15

First, we have to factor 125 and 27, finding it's prime factors, hence:

Thus the expression can be written as:

125^6 - 27^15 = (5³)^6 - (3³)^15

There will be no like terms on the expression, as the bases are different,  of 3 and 5, hence we just apply the exponent rules, as follows:

a^b^c = a^(b x c), which is the power of power rule.

Hence:

Hence the simplified expression is given as follows:

(5³)^6 - (3³)^15 = 5^18 - 3^45.

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Answer:

the dot is the 0 rember dat

Step-by-step explanation:

Answer:it’s c

Step-by-step explanation:

the questions is c

As, a is block diagonal, with diagonal blocks of size \(m_1 \times m_1\), \(m_2 \times m_2\), \(\dots\), \(m_k \times m_k\), respectively. So,  if a commutes with d, then it must be block diagonal.

Let's suppose that d is a diagonal matrix with repeated diagonal entries grouped contiguously, i.e.,

d = \(\begin{pmatrix} D_1 & 0 & 0 & \cdots & 0 \ 0 & D_1 & 0 & \cdots & 0 \ 0 & 0 & D_2 & \cdots & 0 \ \vdots & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & D_k \end{pmatrix}\),

where \(D_1, D_2, \dots, D_k\) are scalars and appear with frequencies \(m_1, m_2, \dots, m_k\), respectively, so that \(m_1 + m_2 + \dots + m_k = n\), the size of the matrix.

Suppose that \(a\) is a matrix that commutes with d, i.e., ad = da.

Then, for any \(i \in {1, 2, \dots, k}\), we have

\(ad_{ii} = da_{ii}\)

Here, \(d_{ii}\) denotes the \(i$th\) diagonal entry of d, i.e., \(d_{ii} = D_i\) for \(i = 1, 2, \dots, k\). Since d is diagonal, \(d_{ij} = 0\) for \(i \neq j\), and

hence

\(ad_{ij} = da_{ij} = 0\)

for all \(i \neq j\).

Therefore, a is also diagonal, with diagonal entries \(a_{ii}\), and we have

\(a = \begin{pmatrix} a_{11} & 0 & 0 & \cdots & 0 \ 0 & a_{11} & 0 & \cdots & 0 \ 0 & 0 & a_{22} & \cdots & 0 \ \vdots & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & a_{kk} \end{pmatrix}\)

Thus, a is block diagonal, with diagonal blocks of size \(m_1 \times m_1\), \(m_2 \times m_2\), \(\dots\), \(m_k \times m_k\), respectively.

Therefore, if a commutes with d, then it must be block diagonal.

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The Sample space would be

        {(w,c), (w,e), (w,m), (o, c) (o,e), (o,m), (r,c), (r,e), (r,m)}

According to the question,

Colors for room are { w, o,r}

Entertainment center would be { c, e, m}

A set that consists of all possible outcomes and the result from a random experiment( real or conceptual) is called a sample set. The experiment of tossing a coin results in either of two possible outcomes; a head (H) or a tail (T). The sample space for this experiment is S= {H, T}. If we take a sample space by tossing two coins the result would be S={HH, HT, TH, TT}.

So, the Sample space would be

        {(w,c), (w,e), (w,m), (o, c) (o,e), (o,m), (r,c), (r,e), (r,m)}

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Answer:

x can be 3 or (-4) because

area of a rectangle= length × breadth

12=x×(x+1)

12=x^2+x

x^2+x-12=0

x^2 +4x-3x-12=0

x(x+4)- 3(x+4)=0

(x+4)(x-3)=0

(x+4)=0 or (x-3)=0

Therefore, x=(-4) or 3

Since, the dimensions of a rectangle cannot be negative, x=3.

Therefore, the width of a rectangle(x)=3 cm,

the length of a rectangle(x+1)=(3+1)=4 cm

Pls mark me as the brainliest.

Answer: 471.24 (with 3.14 as pi)

Step-by-step explanation:

Volume of cylinder = pi*r^2*height

Radius = 10/2 = 5

Pi*25^2*6 = 471.24

The probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 8/25 or 0.32 (rounded to the nearest millionth).

1. Calculate the total number of students on the Student Government Board by summing up the numbers in the table:

  Total Students = 2 + 2 + 2 + 4 + 0 + 3 + 4 + 2 = 19

2. Calculate the total number of graduate students on the Student Government Board:

  Total Graduate Students = 2 + 0 = 2

3. Calculate the total number of students living in on-campus housing:

  Total On-Campus Housing = 2 + 2 + 0 + 4 + 2 = 10

4. Calculate the probability of selecting a graduate student from the Student Government Board by dividing the total number of graduate students by the total number of students:

  Probability of Graduate Student = Total Graduate Students / Total Students = 2 / 19

5. Calculate the probability of selecting a student living in on-campus housing by dividing the total number of students in on-campus housing by the total number of students:

  Probability of On-Campus Housing = Total On-Campus Housing / Total Students = 10 / 19

6. Calculate the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing by summing up the probabilities from steps 4 and 5:

  Probability = Probability of Graduate Student + Probability of On-Campus Housing = 2 / 19 + 10 / 19

7. Simplify the fraction if necessary. In this case, the fraction cannot be simplified further, so the final probability is 2 / 19 + 10 / 19 = 12 / 19.

8. Convert the fraction to a decimal by dividing the numerator by the denominator: 12 / 19 ≈ 0.631578947, which rounds to 0.632 (rounded to the nearest thousandth).

9. Finally, express the probability as a fraction in lowest terms: 12 / 19 is already in lowest terms.

Therefore, the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 12/19 or approximately 0.632 (rounded to the nearest thousandth).

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Answer:

the value of m will be 20

Answer:

1

Step-by-step explanation:

Answer:

69.314718056

Step-by-step explanation:

Answer:

ccc

Step-by-step explanation:

Answer:

-x + 2

Step-by-step explanation:

The proof is given as follows:

The transitive property argues that "if two quantities are equal to the third quantity, then we may claim that all the quantities are equal to one other".

The term transitive refers to a transfer. If there are three quantities a, b, and c, and if an is connected to b by some rule and b is related to c by the same method, then a and c are related to each other by the same rule; this property is known as the transitive property of equality.

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The cylindrical coordinates of the point (4, 3, -3) are (5, 36.87°, -3).

To convert the point (x, y, z) = (4, 3, -3) to cylindrical coordinates (r, θ, z), we need to determine the magnitude of the radial distance (r), the angle (θ), and the height (z).

Magnitude of the radial distance (r):

The radial distance (r) can be found using the formula: r = sqrt(x^2 + y^2).

Plugging in the values, we have:

r = \(\sqrt{(4^2 + 3^2)}\)

= \(\sqrt{16 + 9}\)

= \(\sqrt{25}\)

= 5

Angle (θ):

The angle (θ) can be found using the formula: θ = arctan(y / x).

Plugging in the values, we have:

θ = arctan(3 / 4)

To find the value of θ, we can use a calculator or trigonometric tables. In decimal form, we have:

θ ≈ 36.87°

Height (z):

The height (z) remains the same in cylindrical coordinates.

Putting it all together, the point (x, y, z) = (4, 3, -3) in cylindrical coordinates is represented as (r, θ, z) = (5, 36.87°, -3).

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Answer:

y=x+5

Step-by-step explanation:

This is a proportional relationship because each time she sees a movie, her score increases by the same number and it's a linear equation.