Susan graphed a system of equations for the lines y = 3x + 1 and y = 3x - 10. Which statement is true about Susan's lines?
The lines intersect once at a right angle because they are perpendicular.
The lines intersect at all points because they are the same line.
The lines intersect three times because each has a slope of three.
The lines do not intersect because they are parallel and have different y-intercepts.

Angles are formed when two or more lines intersect. Angles are majorly measured in degrees.

The required proof is as shown below:

Whenever a transversal passes through two parallel lines, angles are formed which have some similar properties.

             STATEMENTS                                           REASONS

1. AB ║DC                                                          Given.

2. < FDC ≅ < FBA                                              Alternate angle theorem.

3. <AFB  ≅ < DFC                                              Vertical opposite angle rule.

4. DF ≅ BF                                                         Given

5. ΔDFC  ≅ Δ BFA                                            Angle-Angle-Side property

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The time it took the rider to reach the ground level is 171.651seconds

Quadratic functions are functions that has a leading degree of 2.

Given the equation that represents  roller coaster’s height as shown

h = –0.025t^2 + 4t + 50

The coaster will reach the ground when h = 0

Substitute

0 = –0.025t^2 + 4t + 50

Factorize

On factorizing, the time it took the rider to reach the ground level is 171.651seconds

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Answer:

171.65 seconds

Step-by-step explanation:

did the test and got it right

Considering the given tree diagram, there is a 0.5 = 50% probability of an investor choosing either stocks or bonds from portfolio C.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

At each node, the sum of the probabilities is of 1, hence:

0.2 + 0.3 + Z = 1.

Z = 0.5.

There is a 0.5 = 50% probability of an investor choosing either stocks or bonds from portfolio C.

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Answer:

[tex]x^2+(y-3)^2=36\\[/tex] and [tex]x^2+(y+8)^2=36[/tex]

Step-by-step explanation:

So the general formula for a circle is usually represented as: [tex](x-h)^2+(y-k)^2=r^2[/tex] where (h, k) is the center of the circle and r is the radius of the circle.

Since the diameter is 12, the radius is going to be 6, because the radius is half the diameter. We now square that value (since it's squared in the equation), you get 36, which is going to be on the right side.

The last thing to know is since it's on the y-axis, that means h=0, since if h didn't equal 1, it would either be to the right or left of the y-axis. So the equation should look something like this: [tex]x^2+(y-k)^2=36[/tex] where k can be any real number.

So this gives you the two equations:
[tex]x^2+(y-3)^2=36\\[/tex] and [tex]x^2+(y+8)^2=36[/tex]

The ordered pair that is a solution to the equation 2x − 3y = 1 is; (2, 1)

We are given the equation;

2x - 3y = 1

Now, the ordered pair that is a solution simply means the least whole numbers for x and y that will make the equation valid.

Now, since the coefficient before x is bigger than the coefficient before y which is negative, then it means x must be larger than y. Thus, let us try x = 2 and y = 1 to get;

2(2) - 3(1) = 1

This makes the equation valid.

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Answer:

B

Step-by-step explanation:

15% off means 85 % of original price

400 * .85        now increase this price by 25%

400* .85   *  1.25    = $425

The distance from the base of the tree to the tallest would be 14.21 cm

X1 = 8 feet

y1 = 16 feet

x2 = 11 feet

y2 = 9 feet

To proceed with the solution we have to

We have to solve for the shorter tree

[tex]\sqrt{(y2 -y1)^2 + (x2-x1)^2} \\\\= \sqrt{9-0^2 + 11-0^2}[/tex]

= 9² + 11²

= √81 +121

= 14.21

√8² + 16²

= √64 +256

= 17.89

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The x values to make a suitable ordered pair must be a multiple of 5

The function is given as:

y = -2/5x + 2

The slope of the above equation is:

m = -2/5

The above is a fraction with a denominator of 5.

So, the x values to make a suitable ordered pair must also be a multiple of 5

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Answer:

factoring

Step-by-step explanation:

The correct decision for the statements are

This is further explained below.

Generally, alcohol is a colorless liquid that is volatile and combustible. It is created during the natural fermentation of carbohydrates and is the component that gives wine, beer, spirits, and other beverages their intoxicating properties. Additionally, alcohol is utilized as an industrial solvent and as fuel.

In conclusion, The appropriate response for each of the statements is

Alcohol is a significant factor in the large percentage of students who struggle academically and drop out of college, which is true. It's true that drinking more alcohol brings a drop in GPA. Students who consume more alcohol miss the same number of courses as students who consume less alcohol. This statement is false. Students who drink more spend less time studying, which is true. Students with a grade point average of 2.0 (C) drink on average two times as much alcohol as students with a grade point average of 4.0 (A) (A).

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Answer:

y=6.72x^0.996x

Step-by-step explanation:

Answer:

a.) C(x) = 10x + 8,000

Step-by-step explanation:

The fixed cost does not change regardless of the variable. Therefore, it should be attached to no variable. However, the variable cost does depend on the number of alarms and thus should be attached to the variable.

This makes the algebraic expression:

C(x) = 10x + 8,000

Your graph should look very similar to this. Keep in mind that our axis are slightly different. You can plot specific points on your graph by plugging random "x" values into your algebraic expression and finding the subsequent "y" values.

Answer:

a) Perfect square.

b) 9

Step-by-step explanation:

The given numbers are perfect squares.

64 = 8*8

49 = 7*7

36 = 6*6

25 = 5*5

16 = 4*4

So, the next number will be 3 *3 = 9

Answer: D. 12

Step-by-step explanation: The mode is the most popular number in a set of numbers. In this set, there are 3 sevens, 3 twelves, 2 nines, and 2 fifteens. If the mode is twelve, you need one more 12 because there are the same amounts of twelves and sevens. So that means the answer is 12!

Answer:

  44.7 mg

Step-by-step explanation:

The equation for exponential decay can be written in the form ...

  y = a·b^(t/p)

where 'a' is the initial value, 'b' is the decay factor, 'p' is the period over which the decay factor is applicable, and t is time in the same units as p.

Using the above equation, we have ...

  a = initial value = 110 mg

  b = decay factor = 55/110 = 1/2 over time period p=20 hours

Then the equation is ...

  y = 110·(1/2)^(t/20) . . . . amount remaining after t hours

We want the amount remaining after 26 hours. That will be ...

  y = 110·(1/2)^(26/20) ≈ 44.67

About 44.7 milligrams will remain after 26 hours.

The equation of the circle with a center (-5, -6) and a radius of 5 is (x + 5)² + (y + 6)² = 25.

The standard equation for writing the equation of a circle is: (x - h)² + (y - k)² = r².

Given the following:

Center (-5, -6) = (h, k)

Radius = 5 = r

Plug in the values into the formula

(x + 5)² + (y + 6)² = 5²

(x + 5)² + (y + 6)² = 25

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Answer:

They can type 825 words in 25 minutes.

Step-by-step explanation:

First, we need to find how many words they can type per minute. To do that, we need to divide 495 by 15.

[tex]495 \div 15 = 33[/tex]

Now, we know how many words per minute, and the question is how many words they can type in 25 minutes. So to find our answer, we need to multiply 33 by 25, since 33 is how many words in one minute.

[tex]33 \times 25=825[/tex]

So now we know our answer: 825 words in 25 minutes.

It is expected the height of the melted wax in this shape is 9.57 inches, this height would make the volume remain constant.

The volume of a sphere can be calculated using the formula V = 4/3 πr³. Let's use this formula to calculate the volume of the spherical ball of wax:

Considering the volume should be the same  (2144.66 cubic inches) and the volume of this shape can be calculated by multiplying the sides, this would be the equation:

This means the height would be 9.57 inches.

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The simplification of the expression (2x - 3)(5x⁴ - 7x³ + 6x² - 9) is 10x^5 - 29x⁴ + 33x³ - 18x² - 18x + 27

(2x - 3)(5x⁴ - 7x³ + 6x² - 9)

= 10x^5 - 14x⁴ + 12x³ - 18x - 15x⁴ + 21x³ - 18x² + 27

= 10x^5 - 14x⁴ - 15x⁴ + 12x³ + 21x³ - 18x² - 18x + 27

= 10x^5 - 29x⁴ + 33x³ - 18x² - 18x + 27

The simplified expression is 10x^5 - 29x⁴ + 33x³ - 18x² - 18x + 27

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The new price after the price increase of Nu 40 will be Nu 840.

The price of a pant after n Nu 40 price increases will be:

= 800 + 40

= 840

The expected weekly sales as a function of the number of price increases will be:

= n - 1) × 800

= (30 - 1) × 800

= 29 × 800

= 23200

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Step-by-step explanation:

in a number like 125,734,016

the right most position has the weight 10⁰ = 1

so, 6×1 = 6.

the second right most position has the weight 10¹ = 10.

so, 1×10 = 10

the third right most position has the weight 10² = 100.

so, 0×100 = 0

the 4th right most position has the weight 10³ = 1000.

so, 4×1000 = 4,000

the 5th right most position has the weight 10⁴ = 10000.

so, 3×10000 = 30,000

the 6th right most position has the weight 10⁵ = 100000.

so, 7×100000 = 700,000

the 7th right most position has the weight 10⁶ = 1000000.

so, 5×1000000 = 5,000,000

the 8th right most position has the weight 10⁷ = 10000000

so, 2×10000000 = 20,000,000

and so on.

as we can see, the 2 (the 8th most position from the right or the second position from the left) has the value of 20,000,000.

From rectangular component, the distance of the port north of the reef is 25.9808 km.

It is given that a fishing trawler sails 30 km from port on a bearing of 120° until it reaches a submerged reef.

Thus the direction of the fishing trawler is given to be 120° with respect to the movement of the trawler.

Resolving the direction by the horizontal and vertical components, we get

The horizontal component of distance is |30*cos(120°)| = 15 km

The vertical component of distance is |30*sin(120°)| = 25.9808 km

Thus as we have to find the north direction or the vertical component, the distance is 25.9808 km.

Therefore, from rectangular component, the distance of the port north of the reef is 25.9808 km.

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Answer:

Step-by-step explanation:

2=27

3=27

5=27

1=126

4=126

Answer:

12.11069457

Step-by-step explanation:

You start by using sin(48) = 9/x
You then multiply both sides by x to give you

xsin(48) = 9

you then divide both sides by sin(48) to get x by itself

x = 9/sin(48)

this gets you

x=12.11069457

The factorized form of the given function, f(x) = 2x⁴ - x³ - 18x² + 9x, is, f(x) = x(2x - 1)(x + 3)(x - 3), and the complete statement is, From left to right, function f has zeros at x = -3, x = 0, x = 1/2, and x = 3.

In the question, we are asked to find the factors of the function f, and complete the given statement.

The function f, given to us is:

f(x) = 2x⁴ - x³ - 18x² + 9x.

To factor the function, we first group the terms as follows:

f(x) = (2x⁴ - 18x²) - (x³ - 9x).

Now, we take common terms out of the group as follows:

f(x) = 2x²(x² - 9) - x(x² - 9).

Now, we again take common terms, as follows:

f(x) = (2x² - x)(x² - 9),

or, f(x) = x(2x - 1)(x + 3)(x - 3).

This is the factored form of the given function, f.

The statement given to us is:

From left to right, function f has zeros at x = _, x = _, x = _, and x = _.

To find the zeroes of the function, we equate the factorized form to 0.

x(2x - 1)(x + 3)(x - 3) = 0.

By zero-product rule, the zeroes are at:

x = 0,

2x - 1 = 0, or, x = 1/2,

x + 3 = 0, or, x = -3,

x - 3 = , or, x = 3.

Arranging these in ascending order, the zeroes are at: -3, 0, 1/2, and 3.

Thus, the factorized form of the given function, f(x) = 2x⁴ - x³ - 18x² + 9x, is, f(x) = x(2x - 1)(x + 3)(x - 3), and the complete statement is, From left to right, function f has zeros at x = -3, x = 0, x = 1/2, and x = 3.

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For the complete question, refer to the attachment.

Answer: Edmentum/plato

Step-by-step explanation:

Answer:

No, they can't

Step-by-step explanation:

According to the Triangle Inequality Theorem, the largest side cannot be greater than the sum of the other two sides.

2+4= 6<7

As you can see from this Equation NOT any two side are greater than the third making this NOT possibly be a tringle.

2+7=9>4

4+7=11>2

Answer:

Option D

Step-by-step explanation:

The triangle ABJ is equitorial

So area

Then mBJ is a arc which is 1/6th of circle

Area.

So area of unshaded region

Answer:

[tex]\textsf{d.} \quad r^2\left(\dfrac{\pi}{6}- \dfrac{\sqrt{3}}{4}\right)[/tex]

Step-by-step explanation:

To find the area of the unshaded region, subtract the area of ΔJGB from the area of sector JGB.

The measure of an arc is equal to its corresponding central angle measure.  Therefore, the central angle of sector JGB is 60°.

As the two sides of ΔJGB adjacent the central angle are the radii of the circle (and therefore equal in length), ∠GJB = ∠GBJ.  

Interior angles of a triangle sum to 180°.  Therefore, all interior angles of ΔJGB are 60° which makes it an equilateral triangle.

Area of an equilateral triangle:

[tex]\sf A=\dfrac{\sqrt{3}}{4}a^2 \quad \textsf{(where a is the side length)}[/tex]

As the side length of the given equilateral triangle is the radius (r):

[tex]\implies \sf Area\:of\:triangle=\dfrac{\sqrt{3}}{4}r^2[/tex]

To find the area of the sector, first convert degrees to radians by multiplying the degrees by π/180 :

[tex]\implies 60^{\circ}=60 \times \dfrac{ \pi}{180}=\dfrac{\pi}{3}\:\:\sf radians[/tex]

Area of a sector of a circle

[tex]\textsf{A}=\dfrac12 r^2 \theta \quad \textsf{(where r is the radius and the angle }\theta \textsf{ is in radians)}[/tex]

Substituting the angle in radians, the area of the sector is:

[tex]\implies \sf A=\dfrac{1}{2}r^2\left(\dfrac{\pi}{3}\right)[/tex]

[tex]\implies \sf A=\dfrac{\pi}6}r^2[/tex]

Area of the unshaded region:

[tex]\begin{aligned}\textsf{Area of unshaded region} & =\textsf{Area of sector} - \textsf{Area of triangle}\\\\& = \dfrac{\pi}{6}r^2 - \dfrac{\sqrt{3}}{4}r^2\\\\& = r^2\left(\dfrac{\pi}{6}- \dfrac{\sqrt{3}}{4}\right)\end{aligned}[/tex]

Therefore, the solution is option D.

The measurement of the angle is 15° (if initial angle is 0°).

Turning Through One-degree Angles

An angle is said to have an angle measure of n degrees if it rotates across n one-degree angles. Since turning through one degree means making an angle of one degree, every time you take a turn of one degree, you rotate through one degree more. Thus, turning through n one-degree angles give rise to an angle of n degrees.

Measurement of the Angle

It is given that the angle has turned through 15 one-degree angles. Thus, the angle will turn through 15°.

Let us assume the initial angle to be x°.

Then, the new angle after 15 one-degree turns would be (x+15)°

If initial angle, x = 0°, the measurement of the angle formed is 15°.

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