Solve the system of equations:
3x-8y+z=8
-x+y-z = -1
x-3y = 3
X=
Y=
Z=

The solution to the system of linear inequalities is the shaded region that satisfies both inequalities.

We have,

To find the solution to the system of linear inequalities:

2x - 3y < 12

y ≤ 2

We first graph the line 2x - 3y = 12:

To graph the line, we can find the x and y intercepts:

When x = 0, we have -3y = 12, then y = -4, so (0, -4) is a point on the line.

When y = 0, we have 2x = 12, then x = 6, so (6, 0) is a point on the line.

Plot these two points and draw the line passing through them:

Next, we shade the region that satisfies the inequality 2x - 3y < 12:

We can choose a test point not on the line, such as (0,0).

Substitute the coordinates into the inequality:

2(0) - 3(0) < 12, which is true.

Now,

We shade the region that satisfies the inequality y ≤ 2:

We shade the region below the horizontal line y = 2:

Therefore,

The solution to the system of linear inequalities is the shaded region that satisfies both inequalities.

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Answer:

m = [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, - 1 ) and (x₂, y₂ ) = (3, 8 )

m = [tex]\frac{8-(-1)}{3-(-3)}[/tex] = [tex]\frac{8+1}{3+3}[/tex] = [tex]\frac{9}{6}[/tex] = [tex]\frac{3}{2}[/tex]

Answer:

3/2

Step-by-step explanation:

To find the slope, we use the slope formula

m = ( y2-y1)/(x2-x1)

    = (8- -1)/( 3 - -3)

    = (8+1)/(3+3)

     = 9/6

    = 3/2

It should be noted that the ratio between the lengths of the two legs is B. 1: ✓3.

It should be noted that the ratio between the lengths of the two legs will be equal to the tangent.

In this case, tan (30°) = ✓3/3

Tan (60°) = ✓3

Therefore, the ratio between the lengths of the two legs of a 30-60-90 triangle will be 1 : ✓3.

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Answer: 40 cups per min = 2.5 gallons per hour

Step-by-step explanation:

There are two ways to solve this problem: use the formula for the area of a trapezoid, or break the trapezoid up into 3 shapes.

Formula for the Area of a Trapezoid: A = 1/2(b1 + b2) x h

A = 1/2(17 + 9) x 8

A = 1/2(26) x 8

A = 13 x 8

A = 104 m^2

Trapezoid = 2 right triangles + 1 rectangle

Area of a triangle = 1/2 x base x height

A(triangle) = 1/2 x 4 x 8

A(triangle) = 16

A(both triangles in the trapezoid) = 32 m^2

A(rectangle) = 8 x 9

A(rectangle) = 72 m^2

Total area = 72 + 32 = 104 m^2

Answer: A = 104 m^2

Hope this helps!

Answer:

trapezium

Step-by-step explanation:

it is a quadrilateral in which only one pair of opposite sides is parallel

Answer:

Trapezium

Step-by-step explanation:

That shape is a Trapezium as it is a quadrilateral having one pair of parallel sides.

Answer:

Step-by-step explanation:

A:  V = πr²h

B:  V = 1/3π(2r)²(2h) = 1/3π(4r²)(2h) = 1/3π8r²h = 8/3πr²h

C:  V = π(2r)²(2h) = π(4r²)(2h) = π8r²h = 8πr²h

D:  V = 1/3πr²(2h) = 2/3πr²h

The required dimensions are

22. x = 9.45

23. perimeter = 198.2

24. angle NSR = 110

25. x = 10

22. The value of x is solved using Pythagoras theorem

x² = (7.4 + 4.6)² - 7.4²

x² = 144 - 54.76

x = √89.24 = 9.45

23. perimeter of tringle GHI

solving for x

7x + 4 = 12x - 20

x = 4.8

perimeter = 52 + (52 - 15 + 7x + 4) + 15 + 12x - 20

perimeter = 52 + (52 - 15 + 7(4.8) + 4) + 15 + 12(4.8) - 20

perimeter = 198.2

24. angle NSR = 1/2 (170 + 50 )

angle NSR = 1/2 (220) = 110

25.

angle V = 1/2 * 290 = 145

4x - 5 + 145 = 180

4x - 5 + 145 = 180

4x + 140 = 180

4x = 40

x = 10

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y=1/2x-3

"The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point."

Also, 1/2 (m= slope)

Also, rise⬆️/run↔️ is a good way to remember how to graph them. If the "Rise"(1) is positive it will go up. if it is negative it will go down. if the "Run" (2) is positive, youll go right, if it is negative youll go left.

17.55% is the probability for any day, the number of special orders sent out will be exactly 5

The given situation describes a Poisson distribution with a mean of 5 special orders per day. The probability of getting exactly 5 special orders in a day can be calculated using the Poisson probability formula, which is:

P(X = k) = (e^(-λ) * λ^k) / k!

where X is the random variable representing the number of special orders, λ is the mean number of special orders per day, and k is the number of special orders we want to find the probability for.

Plugging in the given values, we get:

P(X = 5) = (e^(-5) * 5^5) / 5!

Simplifying this expression, we get:

P(X = 5) = 0.1755

Therefore, the probability of getting exactly 5 special orders in a day is 0.1755 or 17.55%, rounded to four decimal places.

Intuitively, this means that out of many days, we can expect around 17.55% of them to have exactly 5 special orders sent out. The Poisson distribution is commonly used to model the number of events occurring in a fixed period of time, given a known average rate of occurrence. In this case, the Poisson distribution can be used to estimate the likelihood of a particular number of special orders being sent out in a day.

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The length of the remaining rope is 166/63 meters, or approximately 2.635 meters when rounded to three Decimal places.

To find the length of the remaining rope, we need to subtract the sum of the lengths of the two pieces that were cut from the original length of the rope.

Original length of the rope = 8 m

Length of the first piece cut = 15/7 m

Length of the second piece cut = 29/9 m

Therefore, the length of the remaining rope can be found as:

Remaining length = Original length - Length of first piece - Length of second piece

Remaining length = 8 - 15/7 - 29/9

To perform the subtraction, we need to find a common denominator for 7 and 9, which is 63.

Remaining length = 504/63 - 135/63 - 203/63

Remaining length = (504 - 135 - 203)/63

Remaining length = 166/63

To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 1.

Remaining length = 166/63 meters

Therefore, the length of the remaining rope is 166/63 meters, or approximately 2.635 meters when rounded to three decimal places.

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Answer: 2500

Step-by-step explanation: If you calculate out 5x6 that equals 30 and 5x5-5 equals 20, when you do 30+20 that equals 50 and 50 to the 2nd power is 50x50 and that would equal 2500

Answer:

To rotate a point 90 degrees clockwise about another point, you can follow these steps:

1. Subtract the coordinates of the center of rotation from the coordinates of the point you want to rotate to translate the center of rotation to the origin.

A translated point A would be: (5 - 0, 4 - 1) = (5, 3)

2. Perform the rotation by swapping the x and y coordinates and negating the new x-coordinate.

The rotated point A' would be: (3, -5)

3. Add the coordinates of the original center of rotation to the rotated coordinates to translate the origin back to the center of rotation.

The final coordinates of point A' would be: (3 + 0, -5 + 1) = (3, -4)

The transformations that when applied to a triangle on a coordinate grid that would preserve congruence are

(x, y) -> (x + 7, y - 8)

A reflection of the triangle across the x-axis

Rigid transformations refer to transformations in geometry that preserve shape and size

In other words when an object is transformed using a rigid transformation the object does not change its size or shape hence preserving congruence.

The types of rigid transformations translations rotations and reflections.

The first transformation: (x, y) -> (x + 7, y - 8)

is a translation of 7 units to the right and translation of 8 units down

While a reflection of the triangle across the x-axis also preserves congruence

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The solution to a system of two linear equations is x = 3; y = 9. the following response is form the solution

1. From the origin, move 3 units right and 9 units up

2. The point of intersection of the two lines

3.Yes, if both lines are the same exact line

4. Can you have exactly two solutions to a Linear system of equations?

5. No, because lines are straight

6. Yes, if the lines are parallel

Parallel lines refers to lines that has equal slopes, such lines do no intersect each other at any point.

Hence we say that no solution is obtained in when linear equations turns out to be parallel lines.

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Correct equation best represents the relationship between x , the age of the machine in years, and y , the value of the machine in dollars over this 10-year period is,

⇒ y = 500x + 8000

We have to given that;

The graph models the value of a machine over a 10 -year period.

Now, Let two points on graph are, (0, 8000) and (8, 4000)

Since, The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Hence,  on substituting the values in above result, we get;

y - 8000 = (4000 - 0) / (8 - 0) (x - 0)

y - 8000 = 500x

y = 500x + 8000

Thus, The correct equation is,

y = 500x + 8000

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The next time trains to Aybrin and Bleechtree leave the station together is 280 minutes (or 4 hours and 40 minutes) after 7 am.

To find the next time trains to Aybrin and Bleechtree leave the station together, we need to determine the least common multiple (LCM) of 35 and 40, which represents the time interval at which both train schedules align.

The prime factorization of

35 = 5 x 7,

and 40 = 2 x 2 x 2 x 5

Now, the highest power of each prime factor that appears in either factorization.

So the LCM of 35 and 40 = 2 x 2 x 2 x  5 x  7 = 280.

Therefore, the next time trains to Aybrin and Bleechtree leave the station together is 280 minutes (or 4 hours and 40 minutes) after 7 am.

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The volume of this of rectangular container is equal to 19,425 cubic centimeter.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

Volume of rectangular container = 25 × 37 ×  21

Volume of rectangular container = 19,425 cubic centimeter.

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Complete Question:

A rectangular container is 25cm by 37cm by 21cm. What is the volume of this rectangular container?

Answer:

-2

Step-by-step explanation:

The expression with the greatest quotient can be found by computing each expression and comparing the results.

-20 ÷ -5 = 4

8 ÷ -4 = -2

-6 ÷ -3 = 2

12 ÷ -3 = -4

Therefore, the expression with the greatest quotient is -2, since it has the largest absolute value.

The required, -x is also 13 units from 0, but to the right of 0 instead of to the left.

The statement about -x is that it is 13 units to the right of 0. This is because the original number, which is 13 units to the left of 0, is represented by a point on the number line to the left of 0. If we negate this number to get -x, then we are reflecting it across the origin (0) to the right side of the number line. This means that the distance of -x from 0 is the same as the distance of the original number from 0, which is 13 units.

Therefore, -x is also 13 units from 0, but to the right of 0 instead of to the left.

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The length of  segment BD of the right triangle is 7 units.

The length of  segment BC of the right triangle is  7√2.

The length of each segment of the triangle is calculated applying trig ratio as follows;

The length of segment BD is calculated as follows;

tan 45 = opposite side / adjacent side

The adjacent side of the right triangle is given as 7 units, the opposite side which is the height (BD) is calculated as follows;

tan 45 = BD/7

BD = 7 x tan 45

BD = 7 x 1

BD = 7

The segment BC is calculated as follows;

cos 45 = CD / BC

cos 45 = 7 / BC

BC = 7/ cos 45

BC = 7√2

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The value of x is 3 and angle Q is 39°

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

A circle theorem states that : angles in thesame segment are equal.

With this theorem is means that angle 13x is equal to angle x +36 .

Therefore;

13x = x +36

collecting like terms

13x -x = 36

12x = 36

divide both sides by 12

x = 36/12

x = 3

therefore the value of angle Q = 13 × 3

= 39°

Therefore the value of angle Q is 39°

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Answer:

We can use the law of cosines to solve for c:

c^2 = 20^2 + 15^2 - 2(20)(15)cos(125°)

c^2 = 400 + 225 + 600cos(125°)

c^2 = 625 + 600cos(125°)

c = sqrt(625 + 600cos(125°))

c ≈ 32.7

Therefore, the length of c is approximately 32.7 units.

The weight before the party could be any positive number

The weight of the bag of ice after the party was 7/8 pounds. So we can set up an equation:

x - weight used at the party = 7/8

We know that the weight used at the party is the weight before the party minus the weight after the party.

So we can substitute 3x for the weight before the party:

3x - (7/8) = weight used at the party

We don't know the exact weight used at the party, but we do know that it was less than or equal to the weight before the party.

So we can set up another inequality:

weight used at the party ≤ 3x

Putting it all together:

3x - (7/8) ≤ 3x

Simplifying:

-(7/8) ≤ 0

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The baker would need 47. 25 cups of floor

We need to know that proportion is a form of mathematical comparison with two equations made equal to each other.

From the information given, we have that;

baker used 33 3/4 cups of flour to make 15 batches of cookies

This is represented as;

Convert to improper fractions

135/4 cups = 15 batches of cookies

Then, x cups = 21 batches of cookies

cross multiply the values

15x = 708. 75

Divide both sides by the coefficient of x, we have ;

x = 708. 75/15

x = 47. 25 cups of floor

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Answer:

Tickets Sold: 146

Step-by-step explanation:

Let's assume that the number of adult tickets sold is "x".

According to the problem, the number of student tickets sold is three times the number of adult tickets sold. Therefore, the number of student tickets sold is 3x.

The total number of tickets sold is 584, so we can set up an equation:

x + 3x = 584

Simplifying the equation, we get:

4x = 584

Dividing both sides by 4, we get:

x = 146

Therefore, the number of adult tickets sold is 146.

Answer: 146

Step-by-step explanation:

let x = # of adult tickets sold

let y = # of student tickets sold

x + y = 584

this is because the sum of adult tickets and student tickets is 584.

3x = y

this equation is written because there is 3 times more students there than adults

using substitution, we can find the equation :

x + (3x) = 584

4x = 584

x = 146

since x is equal to the number of adult tickets sold, your answer is 146.

Answer:

Step-by-step explanation: 78 +3x+x=180 deg.

                                                 4x=180-78

                                                 4x=102/:4

                                                    x=25.5 deg

Step-by-step explanation:

180 = 78° + 3x°

78° + 3x° = 180°

3x°= 180° - 78°

3x = 102°

x = 102°/3

The experimental probability of rolling a total of 9 on two number cubes is 2/50, or 0.04.

To calculate the experimental probability,we divide the number of successful outcomes by the total   number of trials.

In this case, there were 2 successful outcomes (the sum of the number cubes was 9) and 50 total trials.

Therefore, the experimental probability is

2/50 = 0.04.

It is important to note that this is just an experimental probability, and the actual probability of rolling a total of 9 may be different.

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sure the answer is c and a or b but the correct one is c