What are the four types of slopes? Write an equation for each of the four types of slopes.(in slope intercept form) 9th grade geometry HELP

Answer:3

Step-by-step explanation:3

Two supplementary angles equal 180 degrees.

Let the first angle = x

The second angle is 30 degrees more so this would be x + 30

Now add the two angles together to equal 180:

X + x+ 30 = 100

Combine like terms:

2x + 30 = 180

Subtract 30 from both sides:

2x = 150

Divide both sides by 2:

X = 75

One angle = x = 75

The other angle is x + 30 = 75 + 30 = 105

The smaller angle is 75 degrees.

With the help of the figure we can say that triangles are congruent by SAS Rule

What is Congruence of Triangle?

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides are equal and all three of their corresponding angles are equal in size. These triangles can be moved, rotated, flipped, and turned to look exactly the same.

Solution:

By SAS rule, two triangles are said to be congruent if any two sides and the angle included between the sides of one triangle are comparable to the corresponding two sides and the angle included between the sides of the second triangle.

In given figure, sides AB= PQ, BC=QR and angle between AB and BC equal to angle between PQ and QR i.e. ∠B = ∠Q. Hence, Δ ABC ≅ Δ PQR.

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Answer: Solution is in the photo

Answer:Three lines creating six angles

3 angles on top, 3 angles below

Since the top left angle is a right angle

It means the line that divides the top angles from the angles below is bisected by a perpendicular line.

This means the sum of the angles of the top left = 90°

Therefore, x + 61° = 90°

x = 90° – 61°

x = 29°

The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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The length of the arc of a circle of diameter 6 meters subtended by a central angle of 5π/6 radians is approximately 7.85 meters.

To find the length of the arc of a circle of diameter 6 meters subtended by a central angle of 5π/6 radians, we will use the formula:S= rθ,whereS is the arc length,r is the radius of the circle andθ is the angle subtended by the arc.We know that the diameter of the circle is 6 meters.

Therefore, the radius of the circle, r = diameter/2 = 6/2 = 3 meters.The central angle subtended by the arc = 5π/6 radians.

Substituting the values in the formula:S = rθS = 3 × (5π/6)S = 15π/6S = 2.5π or 7.85 meters (approx)Therefore, the length of the arc of a circle of diameter 6 meters subtended by a central angle of 5π/6 radians is approximately 7.85 meters. Hence, the main answer is: 7.85 meters.

To find the length of the arc of a circle of diameter 6 meters subtended by a central angle of 5π/6 radians, we used the formula:S = rθwhere S is the arc length, r is the radius of the circle and θ is the angle subtended by the arc.

The diameter of the circle is 6 meters, therefore, the radius of the circle is half the diameter which is r = diameter/2 = 6/2 = 3 meters.

The central angle subtended by the arc = 5π/6 radians which is given in the question. The formula for calculating the length of an arc is S = rθ which is already mentioned above.

Substituting the values in the formula, we get:S = 3 × (5π/6)S = 15π/6S = 2.5π or 7.85 meters (approx)Therefore, the length of the arc of a circle of diameter 6 meters subtended by a central angle of 5π/6 radians is approximately 7.85 meters which is the answer we obtained after solving the problem.

Hence, we have calculated the length of the arc of a circle of diameter 6 meters subtended by a central angle of 5π/6 radians.

The length of the arc of a circle of diameter 6 meters subtended by a central angle of 5π/6 radians is approximately 7.85 meters. The formula we used to calculate the length of the arc is S = rθ. The radius of the circle is half the diameter, r = diameter/2.

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The points of inflection are x = 0, x = -∞, and x = ∞. These three points lie on the vertical line x = 0.

To find the points of inflection, we need to take the second derivative of the function y = (1 + x)/(1 + x²):

y' = (1 - x²)/[(1 + x²)²]
y'' = (-6x)/[(1 + x²)³]

To find the points of inflection, we need to set y'' = 0 and solve for x:

0 = (-6x)/[(1 + x²)³]
0 = -6x

This gives us three possible values for x: x = 0 (where the second derivative changes sign), and x = ±∞ (where the second derivative approaches 0).

To determine which of these points are points of inflection, we need to look at the sign of the second derivative on either side of each point. If the sign changes, then it is a point of inflection. If the sign stays the same, then it is not a point of inflection.

At x = 0, the second derivative changes sign from negative to positive, so this is a point of inflection.

At x = ±∞, the second derivative is always 0, so these are not points of inflection.

Therefore, the points of inflection are x = 0, x = -∞, and x = ∞. These three points lie on the vertical line x = 0.

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The quantity of more flour that she needs to add would be = 3/4

A fraction is defined as the representation of the part of a whole data in a form of numerator and denominator.

The quantity of flour Ryan needs for baking = 3¼

The quantity of flour she has already added = 2½

The remaining amount that she needs to add;

= 3¼-2½

= 3/4

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Answer:

Hey!

Your answer is 56 miles!

Step-by-step explanation:

To find speed, we do 294 divided by 5hrs and 15mins (5.25)

So next= 294 / 5.25

Which gives us 56 mph!

HOPE THIS HELPS!!

The car travel 56 miles per hour.

The speed can be defined as the rate at which an object covers some distance.

Here, we know that,

Speed = Distance / Time

Now, Distance = 294 miles

         Time = 5 hours and 15 minutes

                  = 5.25 hours.

Now, Speed = 294 / 5.25

                     = 56 miles per hour.

Thus, the car travel 56 miles per hour.

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Answer:

I think B

Step-by-step explanation:

I think

Answer:

The equation has no solution.

Step-by-step explanation:

\(2(3x - 8) = 8x - 2x - 8 \\ \\ 2 \times 3x - 2 \times 8 = 6x - 8 \\ \\ 6x - 16 = 6x - 8 \\ \\ 6x - 6x = 16 - 8 \\ \\ 0 = 8 \: (which \: is \: absurd) \\ \\ the \: equation \: has \: no \: solution \\ \)

Step-by-step explanation:

54, 54, 72

\(180 - 2 \times 54 = \\ = 180 - 108 = \\ = 72\)

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

Answer:

F=40

Step-by-step explanation:

you have to get rid of the five. What's the oposite of division? Mutiplaction, so you mutiply 5 times 8. The five cancels, and you are left with 40.

Hey there! :)

Answer:

v = -16.

Step-by-step explanation:

Given:

-2 = 2 + v/4

Subtract 2 from both sides:

-2 -2 = 2 - 2 + v/4

-4 = v/4

Multiply both sides by 4:

-4 · 4 = v/4 · 4

-16 = v

Answer:

3x - 1

Step-by-step explanation:

Graphed it. You can also plug in the points with each equation, but that'd take longer.

Answer:

The equation of the parabola will be:

Step-by-step explanation:

The vertex  (h, k)  is halfway between the directrix and focus.

Find the  x  coordinate of the vertex using the formula

x = (x-coordinate of focus + directrix)/2

 = (3-3)/2

 = 0/2

 =0

The  y -coordinate will be the same as the y-coordinate of the focus.

so the vertex will be: (0, 0)

Finding the distance from the focus to the vertex

The distance from the focus to the vertex and from the vertex to the directrix is |p|.

Subtract the  x  coordinate of the vertex from the x -coordinate of the focus to find  p .

\(p=3-0\)

\(p=3\)

Substitute in the known values for the variables into the equation

\(\left(y-k\right)^2=4p\left(x-h\right)\)

\(\left(y-0\right)^2=4\left(3\right)\left(x-0\right)\)

\(\:y^2=12x\)

Therefore, the equation of the parabola will be:

Answer:

Step-by-step explanation:

Let L be the Length and W be the Width of a rectangle.

We are told that:    L = 4W   [the length of a rectangle is four times its width]

Perimeter = 2L + 2W

We learn that P ≤ 130 cm

2L + 2W ≤ 130 cm

Substitute L = 4W:  

2L + 2W ≤ 130 cm

2(4W) + 2W ≤ 130 cm

10W ≤ 130 cm

W ≤ 13 cm

Options:

2w + 2 • (4w) < 130     Not correct since the < sign does not allow for the "at most 130 cm.")

2w + 2 • (4w) > 130      Must be ≤, not >

2w + 2 • (4w) ≤ 130   This option works since the ≤ sign is correct.

Answer:

The answer is B

Step-by-step explanation:

Answer:

you can use law of sines

Plug in the values (lol sorry i dont have time)

x / sin(angle)  =  y / sin(angle)

Where x and y are separate sides.

Hope this Helps! :3

Answer:

Option : D

Step-by-step explanation:

Hope it helps you!

Answer:

d. 78 in

Step-by-step explanation:

Perimeter of the figure = Perimeter of parallelogram - 14 + Perimeter of semicircle

\( = 2(21 + 14) - 14+ \frac{1}{2} \times \pi \: d \\ \\ = 2 \times 35 - 14 + \frac{1}{2} \times 3.14 \times 14 \\ \\ = 70 - 14 + 3.14 \times 7 \\ \\ = 56 + 21.98 \\ \\ = 77.98 \: \\ \\ \approx \: 78 \: in\)

The two tanks will contain the same amount of water after 13 minutes and the amount will be 75 gallons .

In the question ,

it is given that

rate at which the water is filling in the green tank = 4 gallons per minute

rate at which the water is filling in the red tank = 5 gallons per minute

amount of water present in the green tank = 23 gallons

amount of water present in the red tank = 10 gallons .

the green tank has (23 - 10) = 13 gallons more water  than red tank .

in 1 minute red tank will fill (5-4) = 1 gallon water more than green tank .

So , the red tank will take 13/1 = 13 minutes to contain same amount of water as of green tank

and amount of water will be

= 23 + 4t

= 23 + 4*13

= 23 + 52

= 75 gallons .

Therefore ,The two tanks will contain the same amount of water after 13 minutes and the amount will be 75 gallons .

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The number of ways to form such strings is 48.

To find the number of ways to form the specified strings, we can break down the problem into cases:

Case 1: x and y are consecutive with x before y

In this case, we can consider x and y as a single entity, denoted as XY. The remaining three letters can be chosen from the set {u,v,w,z}, giving us 4 options. The XY entity can be arranged in 2 ways (XY or YX). Therefore, the total number of strings in this case is 4 * 2 = 8.

Case 2: x and y are consecutive with y before x

Similar to Case 1, we consider yx as a single entity. The remaining three letters can be chosen from {u,v,w,z}, resulting in 4 options. The yx entity can be arranged in 2 ways (yx or xy). Hence, the total number of strings, in this case, is also 4 * 2 = 8.

Case 3: All other cases

In this case, x and y are not consecutive. We need to select one position for x, one position for y, and two positions for the remaining letters. The positions can be chosen in 6 * 5 * 4 * 3 = 360 ways. However, we need to divide by 2! to account for the arrangement of x and y. Thus, the total number of strings, in this case, is 360 / 2 = 180.

Adding up the results from the three cases, we get a total of 8 + 8 + 180 = 196.

Therefore, the number of ways to form strings of length 5 from the set {u,v,w,x,y,z} that satisfy the given conditions is 196.

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The constant ratio of successive y-values. is 1.5

From the question, we have the following parameters that can be used in our computation:

The table of values of an exponential function

From the table, we have

x    y

0   11.25

1     16.875

Divide the y values

so, we have the following representation

Ratio = 16.875/11.25

Evaluate

Ratio = 1.5

Hence, the constant ratio of successive y-values. is 1.5

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Answer:

Step-by-step explanation:

To find the constant ratio of successive y-values of an exponential function, you need to divide one term by the previous term. That ratio should match for all y values1.

In this case, we can find the constant ratio by dividing each y-value by the previous one. For example, 7.5/5 = 1.5 and 11.25/7.5 = 1.5 and so on. Therefore, the constant ratio of successive y-values is 1.5

Answer:

i don't understand

Step-by-step explanation:

if Ibacteria are measured to be in a dirt sample that weighs 1 gram, Then he sample of bacteria that would be in a sample weighing 18 grams t is mathematically given as

x=1.044×10^9

Question Parameter(s):

5.8×10^7 bacteria are measured to be in a dirt sample that weighs 1 gram.

Generally, the equation for the statement  is mathematically given as

5.8×10^7=1g

x=18grams

Therefore

x=\frac{5.8×10^7*18}{1}

x=1.044×10^9

In conclusion,  the sample of bacteria is

x=1.044×10^9

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Answer:

-9/20

put 45 over 100, then divide them both by 5.

Answer: m<2 = 18°

Step-by-step explanation:
m<1 + m<2 = 90°

7x - 19 + x + 5 = 90°
     First add common variables; 7x + x = 8x || -19 + 5 = -14
8x - 14 = 90°
     Second add 14 on both sides;

8x - 14 = 90°

     +14   +14

8x = 104°
      Third divide 8 to 104
\(\frac{8x}{8} = \frac{104}{8}\)

x = 13

m<1 7(13) - 19 + m<2 (13) + 5 = 90°
13 * 7 = 91
91 - 19 = 72
72 + 13 = 85
85 + 5 = 90°

m<2 = 13 + 5 = 18°

Hope this helps! :]
--Blu