The equations of four lines are given. Identify which lines are parallel.
Line 1: y= 2 - 6
Line 2: 3 - 2y = -1
Line 3: y = 4x + 6
Line 4: y+3= 1 (2-6)

Answer:

Hello!

`~~~~~~~~~~~~`

(2a-b)^2 -4(2a-b) -13 =

\(v = 4a^{2} - 4ab + b^{2} - 8a +4b - 13\)

~~~~~~~~~~~~`

Step-by-step explanation: All you have to do is Factor the polynomial.

Hope this helped you. Brainliest would be nice!

______________❤︎______________

Answer:

The answer is: y - (-4)= 5(x-3)

Point slope form is:

y-y1=m(x-x1)

m is your slope. They tell us the slope is 5. They also give you an ordered pair. Substitute this ordered pair into the point slope equation for the x1 and y1 values.

brainlest plz

Step-by-step explanation:

Answer:

k/3 + 6 < 7 = k< 3

2 + p/2 ≥ 7 = p  ≥  10

5 − 4n < 8 − 5n = n < 3

−3n −4 > 4n + 10 = n < -2

9w − 4w + 6 ≥1 + 5w = I couldn't get a solution for this one sorry

Step-by-step explanation:

Hope this helps

A gas station is open 365 day a year, 24 hours a day. If the gas station served 40,000 cups of coffee last year, then it served an average of 5 cups of coffee per hour.

The problem can be solved using the average value approach.

Average value = total amount or sum of data / number of data

In the given problem,

total amount = total coffee served last year

total amount = 40,000

number of data = number of hours in a year

number of data = 365 day/year x 24 hours/day = 8760 hours

Hence,

Average value = total amount or sum of data / number of data

                         = 40000 / 8760

                         = 4,6 ≈ 5 (round to the nearest whole cup)

Hence, the average coffee served is 5 cups per hour.

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Jared bought 7 cans of paint. Let the number of red paint cans that Jared bought be x. The number of black paint cans he bought would be 7 - x. A can of red paint costs $3.75 and a can of black paint costs $2.75.

He spent $22 in all. Therefore we can write:3.75x + 2.75(7 - x) = 22 Multiplying out the second term and collecting like terms gives:0.5x + 19.25 = 22Subtracting 19.25 from both sides:0.5x = 2.75Dividing by 0.5:x = 5.5Since Jared can't buy half a can of paint, we should round the answer to the nearest integer. Hence, he bought 5 cans of red paint and 2 cans of black paint. The total cost of the 5 cans of red paint would be 5 x $3.75 = $18.75.The total cost of the 2 cans of black paint would be 2 x $2.75 = $5.50.The total cost of all 7 cans of paint would be $18.75 + $5.50 = $24.25.We spent more than Jared's budget. The value of $24.25 exceeds Jared's budget of $22. Hence, there is a problem with this problem statement.

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Answer:

137

Step-by-step explanation:

All you have to do is divide 1,375 In 10 and then multiply the answer my 10 to make sure it’s the right one

Based on the context of the problem, the range of the exponential function y = \(45,529(0.78)^x\) is y > 0.

The exponential function for depreciation given in the problem is:

y = 45,529(0.78)^x

This function gives us the value of Sharlene's truck in dollars after x months of ownership, assuming that the depreciation follows a constant rate and is modeled by an exponential function.

To find the range of the function, we need to consider the minimum value that y can take. Since depreciation leads to a decrease in value over time, y should always be greater than zero. In other words, the range of the function is:

y > 0

In practical terms, this means that Sharlene's truck will always have some positive value, even if its market value has decreased due to depreciation. In other words, a truck is never worth zero or less than zero (unless it has additional debts associated with it), and Sharlene's truck will always have some resale or scrap value even if it has depreciated significantly.

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By addition, $1,850 is the right response. Mrs. Jones' company spent $1,850 on business expenditures in March, including $480 on raw materials, $1,200 on labour, and $170 on other expenses.

The other three fundamental operations are subtraction, multiplication, and division. Addition is one of the four basic operations. The sum or total of these combined values is obtained by adding two integers. The process of merging two or more numbers is known as addition in mathematics. Numbers are added together to form addends, and the outcome of this operation, or the final response, is referred to as the sum. This is one of the crucial mathematical operations we employ on a regular basis. You would add numbers in a variety of circumstances. Combining two or more numbers is the foundation of addition. You can learn the fundamentals of addition if you can count.

Mrs. Jones's business spent $480 on raw materials

Mrs. Jones' company spent $1,850 on business expenditures in March,

$1,200 on labour

$170 on other expenses.

by addition

Total = 1200+480+170 = $1850

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Answer:

48 ounces

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Answer:

The answer would be 60 degrees

Step-by-step explanation:

I got the answer from the question after getting it wrong

Answer:

X= 0.5

Step-by-step explanation:

There is only one optimal solution for this linear programming problem, and it can be found by solving the problem using appropriate linear programming techniques.

Based on the given linear programming problem, the best option that fits the empty space above is "only one optimal solution."

To determine the number of optimal solutions, we need to consider the objective function and the constraints of the problem. The objective function, Z = 3x1 + 9x2, represents the quantity we want to minimize.

The constraints of the problem are as follows:

2x1 + 4x2 ≤ 16

5x1 + 15x2 ≤ 30

6x1 + 14x2 ≤ 42

x1 ≤ 55

x1, x2 ≥ 0

The feasible region is the area in the xy-plane that satisfies all the constraints. In this case, the feasible region is a bounded region since all constraints involve inequalities.

Since the objective function is a linear function and the feasible region is a bounded region, linear programming theory guarantees that there exists at least one optimal solution.

In this case, the optimal solution is the point within the feasible region that minimizes the objective function Z.

Therefore, there is only one optimal solution for this linear programming problem, and it can be found by solving the problem using appropriate linear programming techniques, such as the simplex method or graphical method.

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The limit lim (x² + 5) / (x - 2) as x approaches 2 is undefined.

To find the limit of the given expression lim (x² + 5) / (x - 2) as x approaches 2, we can directly substitute the value of 2 into the expression.

However, this would result in an undefined form of 0/0. We need to simplify the expression further.

Let's simplify the expression step by step:

lim (x² + 5) / (x - 2) as x approaches 2

Step 1: Substitute the value of x into the expression:

(2² + 5) / (2 - 2)

Step 2: Simplify the numerator:

(4 + 5) / (2 - 2)

Step 3: Simplify the denominator:

(9) / (0)

At this point, we have an undefined form of 9/0. This indicates that the limit does not exist. The expression approaches infinity (∞) as x approaches 2 from both sides.

As x gets closer to 2, the limit lim (x2 + 5) / (x - 2) is indeterminate.

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Answer:

-20 Absalute value=20

14 Absalute value=14

20+14=34

Step-by-step explanation:

Answer: -2

Step-by-step explanation:I'am in a rush right now sorry

The equation in point-slope form for the  perpendicular line is y-5= x+1.

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

The slope of the line y= -x-6 is   -1.

Perpendicular lines slopes satisfy the condtion:

\(m_{1} m_{2} = -1\)

then the slope of the perpendicular line is 1.

The equation in point-slope form of the line that passes through the point (-1, 5) is

y-y1=m(x-x1)

y-5=1(x-(-1))

y-5= x+1

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Answer:

5 cm

Step-by-step explanation:

The volume (V) of milk in the container is calculated as

V = 8 × 15 × 12 = 480 cm³

After change of position with depth d then

8 × 15 × d = 480

120d = 480 ( divide both sides by 120 )

d = 4 cm

Answer: The answer is (264)×(261)(525), because (264)×(261) are the possibilities for choosing 4 red cards and 1 black card from a deck of 52 cards, while (525) are the possibilities for choosing 5 cards from a deck of 52 cards.

So, your first solution is almost correct. On why your second solution is wrong, you'll have to explain your thought process.

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

6/15=favorable amount/total amount

6/15=2/5

2/5*20

Answer: 40%

6/15 can be simplified to 2/5. multiply by 20 on both sides to get 40/100 (40%)

The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

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6/2=3 men per hour

3•3 = 9 men for 3 hours

Answer:

0

Step-by-step explanation:

The area of each of the given triangle is:

4. 21 units²; 5. 12 units²; 6. 12 units²

7. 35 ft²; 8. 8 in.²; 9. 24 cm²

To find the area of a triangle, find one-half the product of the height and the base length of the triangle.

Therefore, area = 1/2(base * height).

4. A = 1/2 * 6 * 7 = 21 units²

5. A = 1/2 * 4 * 6 = 12 units²

6. A = 1/2 * 6 * 4 = 12 units²

7. A = 1/2 * 7 * 10 = 35 ft²

8. A = 1/2 * 8 * 8 = 8 in.²

9. A = 1/2 * 6 * 8 = 24 cm²

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Answer:

48

Step-by-step explanation:

by parallel laws

132 + x = 180

x = 48

so x must be 48

Answer: 2(n - 12)

n is “the number”

Step-by-step explanation:

Hope that helps :D

Answer:

2(n - 12)

Step-by-step explanation:

Step 1: The proposed probe for flaw detection in type 316L austenitic stainless steel plates is an eddy current probe with a suitable height, diameter, and frequency.

Step 2: Eddy current testing is an effective non-destructive testing method for detecting flaws in conductive materials. In this case, the eddy current probe should have a suitable height, diameter, and frequency to ensure accurate flaw detection.

The height of the probe should be adjusted to maintain a constant lift-off of 0.2 mm, which is the distance between the probe and the surface of the material being tested. This ensures consistent measurement conditions and reduces the influence of lift-off variations on the test results.

The diameter of the probe should be selected based on the size of the flaws and the desired spatial resolution. It should be small enough to accurately detect the flaws but large enough to cover the entire flaw area during scanning.

The frequency of the eddy current probe determines the depth of penetration into the material. Higher frequencies provide shallower penetration but higher resolution, while lower frequencies provide deeper penetration but lower resolution. The frequency should be chosen based on the expected depth of the flaws and the desired level of sensitivity.

Overall, the eddy current probe with suitable height, diameter, and frequency can effectively detect the artificial flaws in type 316L austenitic stainless steel plates fabricated using a powderbed-based laser metal additive manufacturing machine.

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Answer:

----------------------

hope it helps...

have a great day!!

Answer:

x=5

Step-by-step explanation:

Answer:

a) 21, 24, 29

b) 5 terms in the sequence are less than 50

Step-by-step explanation:

\(t_n = n^2+20\\t_1 = 1^2+20 = 1+20= 21\\t_2 = 2^2+20 = 4+20= 24\\t_3 = 3^2+20 = 9+20= 29\\\\\\t_5 = 5^2+20 = 25+20= 45\\\\\\t_6 = 6^2+20 = 36+20= 56\\\)

Since, 5th term is less than 50 and 6th term exceeds 50, therefore 5 terms in the sequence are less than 50.

Answer:

Correct options are B) and C)

Step-by-step explanation:

The given equation is 2x+y=10.

Clearly, x=3 and y=4 satisfy this equation.

Therefore , x=3 and y=4 is one of the solution of given equation.

Whwn the null hypothesis is that the slope of the population regression line of price on age is zero, the test statistic is -2.43.

The test statistic is calculated as follows:

t = (b - 0) / SE(b)

In this case, the slope of the regression line is estimated to be -11.50, the standard error of the slope is 4.77, and the hypothesized value of the slope is 0.

t = (-11.50 - 0) / 4.77

= -2.43

The test statistic is -2.43, The p-value for this test statistic can be calculated using a t-table. The degrees of freedom for this test are 5 - 2 = 3. The p-value for a t-statistic of -2.43 with 3 degrees of freedom is 0.048.

Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.

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