In the figure, p || q.



Identify each pair of equal angles as vertical angles, corresponding angles, alternate interior angles, or alternate exterior angles.

m<3 = m<7:

m<1 = m<4:

m<5 = m<8:

m<1 = m<5:

m<1 = m<8:

m<2 = m<6:

m<2 = m<3:

m<4 = m<8:

m<6 = m<7:

m<3 = m<6:

m<2 = m<7:

m<4 = m<5:

The given equation is :

[tex] 2x^{2} =27+3x [/tex]

Now let us write it in standard form:

[tex] 2x^{2} -3x-27=0 [/tex]

Comparing it with general standard form:

[tex] ax^{2} +bx+c=0 [/tex]

So we have a=2, b=-3 and c=-27

First option is correct answer .

Answer:

x≤-6 or 0<x≤6.Option D.

Step-by-step explanation:

Given:

[tex]\frac{x}{4} \leq \frac{9}{x}.[/tex]

Subtract [tex]\frac{9}{x}[/tex]  from both sides,

[tex]\frac{x}{4}-\frac{9}{x} \leq[/tex] 0

Simplifying by taking common denominator:

[tex]\frac{x^2-36}{4x}\leq[/tex]0

Factoring numerator:

[tex]\frac{(x+6)(x-6)}{4x}\leq[/tex]0

Computing the signs and selecting that one satisfies ≤ 0:

x≤ -6,0<x≤6.

Option D is the right answer.

To find the value of x in the triangle, set up an equation using the triangle angle sum theorem and solve for x. The value of x is 21 degrees.

The problem involves finding the value of x in a triangle with given angle measures. According to the triangle angle sum theorem, the sum of the angles in any triangle is always 180 degrees. In this case, we are given two expressions for the angles in terms of x: x - 4 degrees and 3x degrees, plus a given angle of 100 degrees.

To solve for x, set up an equation using the given angles:

x - 4 + 3x + 100 = 180

Combine like terms to solve for x:

4x - 4 + 100 = 180

4x + 96 = 180

4x = 180 - 96

4x = 84

x = 84 / 4

x = 21

Answer: Dilation.

Step-by-step explanation:

From the given picture , it can be seen that the size of trapezoid P'Q'R'S' is decreased from trapezoid PQRS .

Reflection , rotation and translation are rigid motions that produces congruent images and do not change the size of the shapes.

But dilation is not a rigid motion because it changes the size of the shape by using a scale factor.

Hence, the transformation maps trapezoid PQRS onto trapezoid P'Q'R'S' is "Dilation".

The net change of temperatures between the planets is required.

Neptune to Mars is [tex]154^{\circ}\text{C}[/tex]

Earth to Neptune is [tex]228^{\circ}\text{C}[/tex]

Venus to Earth is [tex]446^{\circ}\text{C}[/tex]

The net change value is the distance of the net change from zero.

So, the absolute value of the change will be the net change.

Difference in temperature of Neptune and Mars

[tex]|-214-(-60)|=154^{\circ}\text{C}[/tex]

Difference in temperature of Neptune and Earth

[tex]|-214-14|=228^{\circ}\text{C}[/tex]

Difference in temperature of Venus and Earth

[tex]|460-14|=446^{\circ}\text{C}[/tex]

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Answer:

154 for neptune to mars is correct. The 228 and 446 is wrong.

Step-by-step explanation:.

Answer:

Step-by-step explanation:

Given: c is parallel to d and ∠4=∠5.

To prove: ∠7=∠8

Proof:

Statement                                                Reason

1. c║d, ∠4=∠5                                           Given

2.∠4=∠7                                    If lines ||, alternate interior angles are equal.

3.∠5=∠8                                             Vertical angles are equal

Since, ∠4=∠5, therefore ∠7=∠8

4.∠7=∠8                                               Substitution

Final answer:

To find the number of red bricks used, the ratio 5:2 is represented as 5x:2x. Solving the equation 7x = 175 gives x = 25. Multiplying this by 5, there were 125 red bricks used.

Explanation:

The question asks us to find the number of red bricks used to build a wall when the ratio of red bricks to gray bricks is 5:2 and there were 175 bricks used in total. To solve this, we set up the ratio 5x:2x where 'x' represents the multiplier for the number of bricks, and the sum of red and gray bricks which is 5x + 2x equals the total number of bricks, 175.

First, we combine like terms: 5x + 2x = 7x. Next, we solve for 'x' by dividing both sides of the equation by 7.

7x = 175

x = 175 / 7

x = 25

We then multiply this value by 5 to find the number of red bricks: 5 * 25 = 125.

Therefore, 125 red bricks were used to build the wall.

The answer is m∠A= 135°

the set of all points in a plane for which the sum of the distances to two fixed points equals a certain constant

To solve a linear equation in two variables, at least two equations are required. There are 60 lemonade and 40 orange juice cups.

A linear equation in two variable can be written as ax + by = 0 where a and b are not equal to zero. It is used to represent a straight line.

Given that, rate of lemonade per cup = $2.

And,  rate of orange juice per cup = $3.

Total number of cups sold = 100.

Total earning = $240.

Suppose the number of lemonade cup be x,

And, the number of orange juice cup be y.

Then, as per the question two equations can be formed given as,

x + y = 100 -------------------------(1)

2x + 3y = 240  -------------------------(2)

To find x and y, multiply equation (1) by 2 and substract it from equation (2),

2x + 3y - 2(x + y) = 240 - 2×100

=> y = 40

Substitute y =40 in equation (1) to get x as,

x + 40 = 100

=> x = 60.

Hence the number of lemonade cups are 60 and orange juice cups are 40.

To know more about Linear equation in two variable refer to,

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Final answer:

The ratio of x to y, given the equation 3x = 8y, is 8:3. This is found by dividing both sides of the equation by 3y and simplifying.

Explanation:

To find the ratio of x to y, given the equation 3x = 8y, you can divide both sides of the equation by 3 to solve for x in terms of y, or vice versa.

Dividing both sides by 3y yields:

x/y = (8y)/(3y)

Assuming y is not zero, the y terms cancel out on the right side of the equation, giving us:

x/y = 8/3

Method 2: Using fraction notation:

Rewrite the equation with x isolated:

x = (8/3) × y

This also shows that the ratio of x to y is 8:3.

Both methods lead to the same answer: x : y = 8 : 3.

Thus, the ratio of x to y is 8:3.

The reasonable domain for the given cost function, considering the context of lamp production, is all positive integers (C) because lamps can only be produced in whole, positive quantities.

The lamp manufacturer's daily production costs are given by the function C = 0.25n2 - 10n + 800, where C represents the total cost in dollars and n is the number of lamps produced. Considering the context of the problem, where production numbers must be whole and non-negative, the reasonable domain for this function is all positive integers, which represents the count of lamps that can be produced. This is because the manufacturer cannot produce a fraction of a lamp, nor can they produce a negative number of lamps. Hence, the correct choice for the domain is (C) all positive integers.

Answer:

Khan Academy said 45 hope it helps! :)

Reflection symmetry is a symmetry with respect to the reflection and is also know as mirror symmetry, line symmetry or mirror-image symmetry.

When a figure undergoes a reflection and does not change , then the figure is said to has the reflectional symmetry.

An object with reflectional symmetry can be created by reflecting it about an axis called the Line of Symmetry.

Hope this helps ..!!

Thank you :)

Answer

Maximum area A_max = 11250 ft^2

Step-by-Step Explanation

Declaring Variables:-

The length of the rectangle = y

The width of the rectangle = x

Solution:-

- The perimeter of a rectangle can be expressed using the above two variables as follows:

                             Perimeter (P) = 2*Length + 2*Width

                                                     = 2* ( x + y )

- Since the barn is used as one of the sides (let's say y) we can subtract y

we don't need fencing for this side. The length of the fence required L is:

                            Length (L) = P - y

                                                = 2*x + y

- We are given 300 feet of fencing. So we equate the length equal to 300 and develop a linear relationship between width and length of the barn.

                              300 = 2x + y

                              y = 300 - 2x

- The area (A) of the rectangle is given by the following expression:

                              A = Length*width

                              A = x*y

- Substitute the relationship developed between x and y in the Area (A) expression above. Then we have:

                              A = x*(300 - 2x)

                              A = 300x - 2x^2

- We will take first derivative of the expression of area (A) developed with respect to x and find the critical point of the area function by setting the first derivative A'(x) = 0.

                             A(x) = 300x - 2x^2

                             A'(x) = 300 - 4x

                             0 = 300-4x

                             x = 300 / 4 = 75 ft

- The critical point of the given function lies for the width (x) of 75 ft. We will plug in the critical value x = 75 ft back into the original function of Area and find the maximum area.

                             A(x) = 300x - 2x^2

                             A(75) = 300 (75) - 2(75)^2

                             A_max = A(75) = 11250 ft^2

- The maximum area that can be enclosed by the fencing is 11250 ft²

Answer:11250

Step-by-step explanation:

Variable: h = hours worked

linear equation: 30.50 = 2.50 +8h

Answer: 35.5 [tex]unit^2[/tex]

Step-by-step explanation:

For finding the area of this polygon we can divide it into triangles and rectangle,

By the below diagram,

The area of this polygon = Area of rectangle having dimension 4× 3 + Area of triangle having base 4 unit and height 3 unit +Area of triangle having base 7 unit and height 3 unit + Area of triangle having base 7 unit and height 2 unit,

=[tex]12 + \frac{1}{2}\times 4\times 3 + \frac{1}{2}\times 7\times 3 + \frac{1}{2}\times 7\times 2[/tex]

= [tex]12 + 6 + 10.5 + 7[/tex]

= [tex]35.5\text{ square unit}[/tex]

Answer:

Option D -8.3 cm, 5.8 cm

Step-by-step explanation:

Given : An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. A second side of the triangle is 6.9 cm long.

To find : The longest and shortest possible lengths of the third side of the triangle?

Solution :

First we create the image of the question,

Refer the attached figure below.

Let a triangle ABC , where angle A has a bisector AD such that D is on the side BC.

The theorem is stated for angle bisector is

"Each angle bisector of a triangle divides the opposite side into segments proportional in length to the adjacent sides".

So, according to question,

Let BD=6 cm, DC=5 cm, AB=6.9 cm

and we have to find AC.

Applying the theorem,

[tex]\frac{BD}{DC}=\frac{AB}{AC}[/tex]

[tex]\frac{6}{5}=\frac{6.9}{AC}[/tex]

[tex]AC=\frac{6.9\times 5}{6}[/tex]

[tex]AC=\frac{34.5}{6}[/tex]

[tex]AC=5.75[/tex]

[tex]AC=5.8 cm[/tex]

If we let AC=6.9 cm, find AB

Then,

[tex]\frac{BD}{DC}=\frac{AB}{AC}[/tex]

[tex]\frac{6}{5}=\frac{AB}{6.9}[/tex]

[tex]AB=\frac{6.9\times 6}{5}[/tex]

[tex]AB=\frac{41.4}{6}[/tex]

[tex]AB=8.28[/tex]

[tex]AB=8.3 cm[/tex]

Therefore, The shortest possible length is 5.8 cm and longest possible is 8.3 cm.

Hence, Option D is correct.

Answer:

The wedding planner must have purchased 28 small lanterns and 12 large lanterns.

Step-by-step explanation:

Let the number of small and large lanterns purchased be S and L respectively.

S + L = 40  ........ Equation 1

L = 40 - S

25S + 40L = 1180  ....... Equation 2

25S + 40(40 - S) = 1180

25S + 1600 - 40S = 1180

-15S = 1180 - 1600

-15S = -420

S = 28

L = 40 - S

L = 40 - 28

L = 12

The wedding planner must have purchased 28 small lanterns and 12 large lanterns.

Reduced odds for rolling a 2, 4, or 5: 1:1

Reduced odds against rolling a 2, 4, or 5: 1:1

To determine the reduced odds for and against rolling a 2, 4, or 5 on a fair six-sided die, we need to calculate the probabilities of these events.

Step 1: Calculate the probability of rolling a 2, 4, or 5.

There are three favorable outcomes (rolling a 2, 4, or 5) out of a total of six possible outcomes.

[tex]\[ P(\text{rolling a 2, 4, or 5}) = \frac{3}{6} = \frac{1}{2} \][/tex]

Step 2: Calculate the probability of not rolling a 2, 4, or 5.

There are three unfavorable outcomes (rolling a 1, 3, or 6) out of a total of six possible outcomes.

[tex]\[ P(\text{not rolling a 2, 4, or 5}) = \frac{3}{6} = \frac{1}{2} \][/tex]

Step 3: Calculate the odds for rolling a 2, 4, or 5.

Odds for an event are given by the ratio of the number of favorable outcomes to the number of unfavorable outcomes.

[tex]\[ \text{Odds for rolling a 2, 4, or 5} = \frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}} = \frac{3}{3} = 1:1 \][/tex]

Step 4: Calculate the odds against rolling a 2, 4, or 5.

Odds against an event are given by the ratio of the number of unfavorable outcomes to the number of favorable outcomes.

[tex]\[ \text{Odds against rolling a 2, 4, or 5} = \frac{\text{Number of unfavorable outcomes}}{\text{Number of favorable outcomes}} = \frac{3}{3} = 1:1 \][/tex]

Therefore, The reduced odds for and the reduced odds against the event of rolling a fair die and getting a 2, 4, or 5

Reduced odds for rolling a 2, 4, or 5: 1:1

Reduced odds against rolling a 2, 4, or 5: 1:1