If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the first equation is substituted into the second equation. 6x − y = 1 4x − 3y = −11 (6 points) Group of answer choices 4(−6x + 1) − 3y = −11 4(6x + 1) − 3y = −11 4x − 3(6x − 1) = −11 4x − 3(−6x − 1) = −11

Answer:

\(\dfrac{1}{2}x-10=-13\)

Step-by-step explanation:

Let x be the unknown number.

Given:

Therefore, the equation is:

\(\boxed{\dfrac{1}{2}x-10=-13}\)

Solving for x

To solve, add 10 to both sides:

\(\implies \dfrac{1}{2}x-10+10=-13+10\)

\(\implies \dfrac{1}{2}x=-3\)

Multiply both sides by 2:

\(\implies 2 \cdot \dfrac{1}{2}x=2 \cdot -3\)

\(\implies x=-6\)

Equation :-

→ (1/2)x - 10 = -13

Solution :-

→ x = -6

Step-by-step explanation:

The equation will be,

→ (1/2)x - 10 = -13

Now the required value of x will be,

→ (1/2)x - 10 = -13

→ (1/2)x = -13 + 10

→ x = -3 × 2

→ [ x = -6 ]

Hence, the value of x is -6.

Answer:

3 = 3/4

but 3/4= 0.75

3 = 0.75

x = 25

cross multiply

0.75x = 75

divide both sides by 0.75

x = 100

therefore 25miles represent 100inch on a map

The number of customers waiting in line at the bank over a 24-hour period is a discrete variable type.

A variable whose value is determined by counting is referred to as a discrete variable. examples: the number of pupils in attendance. how many red marbles are in the container. when triple coins are turned, the count of heads. The number of pupils, kids, the shoe size, and so forth are some typical examples of discrete data. A statistical variable is referred to as a discrete variable if it presupposes a finite collection of data and a countable number of values. Contrarily, a continuous variable is a quantitative variable that accepts an endless quantity of data and an uncountable number of values.

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The probability that a randomly purchased item from the manufacturer will last longer than 12 years is approximately 0.952.

To find the probability, we can use the standard normal distribution. First, we need to standardize the value of 12 years using the formula z = (x - μ) / σ, where x is the value we want to standardize, μ is the mean, and σ is the standard deviation. In this case, x = 12, μ = 14.6, and σ = 2.5.

Substituting these values into the formula, we get z = (12 - 14.6) / 2.5 = -1.04.

Next, we use a standard normal distribution table or a calculator to find the area under the curve to the right of z = -1.04. The area to the left of z = -1.04 is 0.149, so the area to the right is 1 - 0.149 = 0.851.

Therefore, the probability that an item will last longer than 12 years is approximately 0.851 or 85.1% when rounded to three decimal places.

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The number of significant digits the product should have = 2

The given numbers are:

\(4.5160 \times 10^{-3}\\ 2.09 \times 10^7\\ 5.8 \times 10^3\)

We first multiply them.

\(4.5160 \times 10^{-3}\times 2.09 \times 10^7\times 5.8 \times 10^3 = 54.743\times10^7\)

In measurement problems, we usually write it as \(5.474\times10^7\)

Significant digits are the numbers which decide the precision and accuracy in measurement problems.

The fewest number of significant digits in each factor of multiplication is considered as the significant digits of the product.

So number of significant digits in \(4.5160\times10^{-3}\) = 5

Number significant digits in \(2.09\times10^7\) = 3

Number of significant digits in \(5.8\times10^3\) = 2

So the product should be rounded into 2 significant digits.

So the product,  \(5.474\times10^7\)= \(5.5\times10^7\) with 2 significant figures.

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For the table of values gives, the equation of line is obtained as y = 1/3x.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The coordinate points for cups of flour, x and loaves of bread y is given in the table.

The slope-intercept form of an equation is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

(3 - 2)/(9 - 6)

1/3

So, the slope point is obtained as m = 1/3.

The equation becomes - y =1/3 x + b

To find the value of b substitute the values of x and y in the equation -

2 = 1/3(6) + b

2 = 2 + b

b = 2 - 2

b = 0

So, the value for b is 0.

Now, the equation becomes -

y = 1/3x + 0

y = 1/3x

The graph is plotted for the equation.

Therefore, the equation is y = 1/3x.

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The final answer depends on the specific range of values for n, denoted by a and b.

To evaluate the expression Σ12(n - 4), we need to find the sum of the terms for a given range of values of n.

The expression Σ12(n - 4) represents the sum of the terms obtained by substituting different values of n into the expression 12(n - 4). The sum is taken over a specific range of values for n.

Let's assume that the range of n is from n = a to n = b. To evaluate the expression, we need to find the sum of the terms for all values of n within this range.

Expanding the expression 12(n - 4), we get 12n - 48. Now, we can rewrite the expression as Σ(12n - 48).

To find the sum, we can use the formula for the sum of an arithmetic series:

Σ(12n - 48) = [(b - a + 1) / 2] * [first term + last term]

The first term is 12a - 48, and the last term is 12b - 48.

Using this formula, we can evaluate the sum of the expression Σ12(n - 4) for the given range of values a and b.

In conclusion, the final answer depends on the specific values of a and b.

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Complete Question:

What is the value of the sum Σ12(n - 4)?

Main answer:Long multiplication is a method of multiplying two difficult-to-multiply numbers.

supporting answer:

what is multiple long?

Finding the product is not always this simple. In such cases, the long method of multiplication is used.

body of the answer:

let us understand long multiplication by taking an example

     6.Add the two partial products

final answer: by following above steps we can perform long multiplication

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Long multiplication is a method of multiplying two difficult-to-multiply numbers.

What is multiple long?

Finding the product is not always this simple. In such cases, the long method of multiplication is used.

Let us understand long multiplication by taking an example

1. Write the two numbers one beneath the other in the order of their digits. On top, write the larger number, and on the left, a multiplication sign.

2. Multiply the top number's one digit by the bottom number's one digit.

3. Put a 0 below the one's digit,

4. Multiply the top number's ones digit by the bottom number's tens digit.

5. Multiply the top number's tens digit by the bottom number's tens digit.

6. Add the two partial products

By following the above steps we can perform long multiplication

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Answer:

An estimated 8 boxes or

7(31/36) boxes

Step-by-step explanation:

283/36=7(31/36)

or round up and get 8 boxes

To make a table of values for a linear relationship;

Choose a group of x values before creating the table. Add each x value from the left side column to the equation. Evaluate the equation (middle column) to arrive at the y value

Given,

Linear relationship;

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.

Here,

We have to make a table of values for a linear relationship;

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100 mph going there, 50 coming back

Alan can put the 11 books on the shelf, with The Iliad in the first spot and The Odyssey in the last spot, in 9! (362,880) ways

To determine the number of ways Alan can put the 11 books on his bookshelf with The Iliad in the first spot and The Odyssey in the last spot, we can follow these steps:

1. There are 11 spots on the bookshelf, but since The Iliad is in the first spot and The Odyssey is in the last spot, we are left with 9 spots for the remaining 9 books.
2. To arrange the 9 books, we can use the concept of permutations, which refers to the number of ways the books can be ordered.
3. The number of permutations for 9 books is calculated as 9! (9 factorial), which means 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.

Therefore, Alan can put the 11 books on the shelf, with The Iliad in the first spot and The Odyssey in the last spot, in 9! (362,880) ways.

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Answer:

90=square

72=nonagon

60=hexagon

45=pentagon

40=octagon

I am not entirely sure tho

Answer:

x=33

Step-by-step explanation:

The angles would need to add to 180 to be supplementary

4x+ x+15 = 180

Combine like terms

5x+15 = 180

Subtract 15 from each side

5x+15-15 =180-15

5x = 165

Divide by 5

5x/5 =165/5

x=33

Note that the box and whisker plot is attached accordingly and the measure are given as follows:

A box plot is a figure that depicts the distribution of data by showing where the majority of values reside and those values that deviate significantly from the norm, known as outliers. Box plots are sometimes known as box and whisker plots or box and whisker diagrams.

The bottom of the box indicates the first quartile, while the upper side represents the third quartile. As a result, the inter-quartile deviation is represented by the vertical width of the middlebox.

The median is the horizontal line inside the box. The vertical lines projecting from the box extend to the data set's minimum and highest values, as long as these values are not outliers. Two shorter horizontal lines represent the ends of the whiskers.

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We assume that G is a connected planar graph with no vertex of degree <= 5. We will use e <= 3v - 6 to prove that G is not a planar graph. By handshaking lemma, we know that 2e = sum of degrees of all vertices. Let d be the maximum degree of G.

Qa. Contrapositive of an implication is a new implication formed by negating both the hypothesis and the conclusion.

The contrapositive of the implication "If G is a connected planar graph, then G has at least one vertex of degree <= 5" is "If G has no vertex of degree <= 5, then G is not a connected planar graph."

Qb. Proof: We assume that G is a connected planar graph with no vertex of degree <= 5.

We will use e <= 3v - 6 to prove that G is not a planar graph. By handshaking lemma, we know that 2e = sum of degrees of all vertices.

Let d be the maximum degree of G. Since G has no vertex of degree <= 5, then d >= 6.

Thus, the sum of degrees of all vertices in G is greater than or equal to 6v/2, which is equal to 3v.

Hence, 2e >= 3v.

Substituting this inequality in e <= 3v - 6, we get 2e >= 3e - 6, which implies that e >= 6.

Since e >= 6, it follows that G is not planar.

Qc. Proof: We use proof by induction on the number of vertices of G. For a graph with one vertex, the statement is trivially true.

For a graph with n > 1 vertices, assume that every planar graph with at most n - 1 vertices can be colored with 6 (or less) colors.

Let G be a planar graph with n vertices.

By part (a), there exists a vertex v of G with degree <= 5.

We remove v and all its edges from G to get a new graph G' with n - 1 vertices.

By the induction hypothesis, we can color G' with 6 (or less) colors.

We add back v and its edges to G.

Since v has degree <= 5, at most 5 colors are used on its adjacent vertices.

We use a new color for v.

Thus, G can be colored with 6 (or less) colors.

Therefore, by induction, the statement is true for all planar graphs.

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Answer: 102 miles.

Step-by-step explanation:

You divide 17 by 5 and then multiply by 30.

Answer

Option A is the answer.

Explanation

To know which one is not equivalen to the others, we will need to solve and simplify each of them

Option A

x - 7 = x - 7

Option B

7 + (-x) = 7 - x

Option C

-x + 7 = 7 - x

Option D

7 - x = 7 - x

Hope this Helps!!!

Answer:

7.89474% decrease

Step-by-step explanation:

Solution:

Calculate percentage change

from V1 = 38 to V2 = 35

(V2−V1)|V1|×100

=(35−38)|38|×100

=−338×100

=−0.0789474×100

=−7.89474%change

=7.89474%decrease

Answer:

72 meters

Step-by-step explanation:

12 times 9 is 72

Answer:

243 m²

Step-by-step explanation:

Given the scale is 4 : 6 = 2 : 3 , then

scale of areas = 2² : 3² = 4 : 9

area of scale drawing = 12 × 9 = 108 cm²

let x be the actual area then using proportion

\(\frac{4}{108}\) = \(\frac{9}{x}\) ( cross- multiply )

4x = 972 ( divide both sides by 4 )

x = 243

Actual area = 243 m²

Work Shown:

7.12 = 7 + 0.12

7.12 = 7 + (12/100)

7.12 = 7 + (3/25)

7.12 = 7 & 3/25

The notation 7 & 3/25 means we have the whole part 7 and fractional part 3/25.

Answer: 35.07

Step-by-step explanation:

35.00 + 0.7 = 35.07 (for one tire)

140.28 (for the 4 tires in total)

Answer:

Step-by-step explanation:

7(x-2) -3(x+3) = 5(x-3) +x , distribute in parenthesis

7x -14 -3x -9 = 5x -15 +x , isolate like terms

7x -3x -5x -x = 14 +9 -15, combine like terms

-2x = 8, divide both sides by -2

x= -4

Answer:

the out put would be 49

Step-by-step explanation:

Step 1: The sample mean is (24+6+21+8+16+10+18)/7 = 15.7 (rounded to one decimal place)

Step 2: The sample standard deviation is calculated using the formula:

s = sqrt[(Σ(x - mean of x)^2) / (n - 1)]

where Σ is the sum of the squared deviations from the mean, mean of x is the sample mean, and n is the sample size.

Using the given data, we get:

s = sqrt[((24-15.7)^2 + (6-15.7)^2 + (21-15.7)^2 + (8-15.7)^2 + (16-15.7)^2 + (10-15.7)^2 + (18-15.7)^2) / (7-1)]

s = 6.679 (rounded to one decimal place)

Step 3: To find the critical value, we use a t-distribution with n-1 degrees of freedom and a confidence level of 80%. From a t-distribution table or using a calculator, we find the critical value to be 1.397 (rounded to three decimal places).

Step 4: Using the formula for the confidence interval:

CI = mean of x ± t*(s / sqrt(n))

where mean of x is the sample mean, t is the critical value, s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

CI = 15.7 ± 1.397*(6.679 / sqrt(7))

CI = (9.47, 21.93)

So the 80% confidence interval for the average net change in a student's score after completing the course is (9.47, 21.93).

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Answer:

-13 celsius

Step-by-step explanation:

5.4 * 5 = 27 degrees drop

14-27= -13

Answer:

running speed is horse power

so up with horse

it will tell its power

go and denge it

so you will get your answer by this process

Answer:

n = 8.58461538

Step-by-step explanation:

31n =111.6   /31

n = 8.58461538

Answer:

72 degrees.

2 parallel lines cut by a transversal result in alternate interior angles.