determine the discriminat and use it to determine the number of x-intercepts for the graph of f(x) = 2x^2 - 8x + 9

Given:

m∠C = 70°

m∠CDE = 130°

Question 1:

To find ∠CDB, let's use the exterior angle theorem.

The exterior angle theorem states that the sum of 2 opposite interior angles is equal to the exterior angle.

Thus,

m∠C + m∠B = 130

70 + m∠B = 130

Subtract 70 from both sides:

70 - 70 + m∠B = 130 -70

m∠B = 60°

Now, use the triangle angle sum theorem to find ∠CDB.

The triangle angle sum theorem states that the sum of interior angles in a triangle is 180°

∠CDB = 180 - 70 - 60 = 50°

∠CDB = 50°

Question 2:

∠CBA = ∠C + ∠CDB

∠CBA = 70 + 50 = 120°

∠CBA = 120°

ANSWER:

∠CDB = 50°

∠CBA = 120°

Given:

The triangle having two similar angles.

This is the isosceles traingle.

Draw the altitude to the given traingle,

D divides the side BC into two equal side having length,

Now, use the tan ratio for right triangle ABD,

Using the pythagorean theorem,

The length of the sloping side of the roof is 23.3 feet.

We have the next two points:

- (1/2,5)

- (5/2,9)

And we must use the point-slope formula to write an equation of a line in slope-intercept

First, we need to calculate the slope of the line using the point-slope formula

Where (x1, y1) and (x2, y2) are the two points

Now, replacing the points

Now, we must replace the slope and one of the two points in the point-slope formula:

Replacing m = 2 and (1/2, 5)

Finally, we must simplify to obtain the slope-intercept form

ANSWER:

y = 2x + 4

Answer:  Table A has a proportional relationship

See the diagram below

==================================================

Explanation:

Table A has a proportional relationship because all the points are on the same straight line. That line in this case is y = 2x

Whatever x is, multiply it by 2 and you'll get the y value

Example: If x = 4, then y = 2*x = 2*4 = 8 which gives the point (4,8)

Another phrase for "proportional relationship" is "direct variation".

Answer:

68

Step-by-step explanation:

Explanation.

The question wants us to determine the circumference of the circle.

Circumference of a circle simply means the perimeter of a circle, and the formula to be used is

By Angle-Angle theorem similarity ΔABC is similar to ΔA'B'C'.

Given two triangles are ABC and A'B'C'.

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

1) Triangle ABC is reduced to triangle A'B'C'

∠ABC=∠A'B'C'=90°

∠BAC=∠B'A'C'

So, by AA similarity

ΔABC≈ΔA'B'C'

2) Triangle ABC is enlarged to triangle A'B'C'

∠ABC=∠A'B'C'

∠BAC=∠B'A'C'

So, by AA similarity

ΔABC≈ΔA'B'C'

Therefore, by Angle-Angle theorem similarity ΔABC is similar to ΔA'B'C'.

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The number of pounds and ounces that we have in 134 ounces is; 8 pounds 6 ounces

We know that in units conversion, there are different units and their conversion rates. For example;

1 meters = 100 cm

1000 meters = 1 kilometer

1000 grams = 1 kilograms

100 cents = 1 dollar

Now, we want to convert ounces to pounds.

The conversion rate for ounces to pounds is;

1 ounce = 0.0625 pounds

We are given 134 ounces of cold cuts for a party. Converting that to pounds gives us;

134 * 0.0625/1 = 8.375 pounds

Now, we want it in pounds and ounces and so we convert the decimal part to ounces

1 pound = 16 ounces

0.375 pounds = 0.375 * 16/1 = 6 ounces

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The number of lineups possible is the combination of selecting 5 songs from 8 songs.

8C5 = 56.

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The most appropriate unit for Nathan to use instead of centimeters per minute is centimeters per year.

An earthquake simply means a rapid motion of the solid layer of the Earth.

In this case, Nathan told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10^-6 centimeters per minute.

Since the year is being discussed, the unit should be based on the year.

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Answer:

(0, -2)

Step-by-step explanation:

Add the x value and divide by 2

[tex]\frac{13-13}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0

Add the y value and divide by 2

[tex]\frac{-14 + 10}{2}[/tex] = [tex]\frac{-4}{2}[/tex] = -2

Measure of CAB is 84.4, by using supplementary angle theory.

In geometry, two angles are referred to as supplementary angles if their sum is 180 degrees. For instance, if A + B = 180°, then A and B are considered supplementary angles. Complementary angles always result in a straight angle when combined (180 degrees).

Angles that add up to a precise 90 degree angle are said to be complementary. For instance, 30 degrees and 60 degrees are complementary angles.

We have given, CAB= 4x+14 and DAB = 6x-18

Both are supplementary angle

Therefore, CAB + DAB = 180

4x+14+6x-18=180

10x-4=180

10x=176

x=17.6

hence, CAB = 4(17.6)+14 = 84.4

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Hence, the minimum number of sets of knives kaj should buy is 48  sets.

Given this, a restaurant must have at least 736 knives.

At the moment, it possesses 155 knives.

Every set includes 12 knives.

Let the number of knife sets be.

Reason: Minimum number of sets indicates ≥

This means ≤ the maximum amount of sets

Step: 2

In light of the inquiries,

[tex]155+s*12\geq 736[/tex]

[tex]12s\geq 736-155[/tex]

[tex]12s\geq 581[/tex]

[tex]s\geq \frac{581}{12}[/tex]

[tex]s\geq 48.42[/tex]

Step 3: Count the number of knife sets [tex]s\geq 48.42[/tex]

that is greater than or equal to 48

Therefore, the required minimum is 48 sets of knives.

What are sets?

In mathematics, a set is a well-defined collection of objects. Sets are named and represented using capital letters. In the set theory, the elements that a set comprises can be any kind of thing: people, letters of the alphabet, numbers, shapes, variables, etc.

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The graph that represents the system of inequalities is the graph attached below.

The graph that would represent the system of inequalities must be two lines that intersect each other and have the exact slope and y-intercept of each of the lines on the graph.

Determine the slope and y-intercept of each of the inequalities, and also determine their boundary lines based on which inequality sign they have.

The line that represents the inequality, y ≥ ½x + 1, will be a solid line that has a slope of ½, and a y-intercept of 1.

The second line that represents the inequality, y ≥ -x - 2, will be a dashed line that has a slope of 1, and a y-intercept of -2.

Therefore, the graph that represents the features stated above for both lines is shown in the diagram below.

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For this type of probability question, there are different ways to solve the same question but let's analyze the situation and calculate as simple as possible.

For our question, there are two parts, the first one first is the probability to pick someone who is a woman. Once there are 60 people of which 30 are women, it means this probability is 30/60. Let's keep this probability.

Now let's move on to the second part. The situation where we pick someone who is without a date. once there are 60 people and all 30 women have a date and 16 men also have a date it means 30 + 16 - 60 = 14 people does not have a date. So the probability to pick someone without a date is 14/60.

Now once we have analyzed the two parts of the question, and we have two probabilities all we need is to sum our probabilities, as follows:

But why do we sum and do not multiply? Because we use the proposition OR at "Find the probability of picking someone at random and getting a person who is a woman OR without a date" If the proposition was AND we would have multiplied both probabilities.

Answer: 57

Given:

We are asked to find the 15th term, meaning n = 15

Therefore, the 15th term is 57.

The distance remaining is given by the equation d = 270 - 60t

Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance / time

Let d represent the distance from Las Vegas to Los Angeles and t represent the remaining time after departure.

A car travels from Las Vegas to Los Angeles at about 60 mi/h. The distance from Las Vegas to Los Angeles is 270 miles.

Hence distance remaining is:

d = 270 - 60t

The distance remaining is d = 270 - 60t

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In order to solve this system of equations, we can add both equations, this way we can find the value of y and then the value of x:

So the solution to this system is (3, 1).

No. of girls = 14

No. of Boys =16

Therefore the ratio, from girls to boys is,

Which can also be written as,

Therefore, the wrong ratio is option D.

That is,

So, the answer is option D.

We know that

• There are two true/false questions.

• There are two multiple-choice questions with three choices each.

In the true/false questions, there are 4 ways to answer since each question has only two choices.

In the multiple-choice questions, there are 6 ways to answer since there are 3 choices per question.

Given the equation:

y = 828000 - 2700x

Where y is the value of the building and x is the number of months of use.

Let's find when the value of the building will be $666,000.

To find when the value will be $666,000, substitute 666000 for y in the equation and solve for x.

y = 828000 - 2700x

666000 = 828000 - 2700x

Subtract 828000 from both sides:

666000 - 828000 = 828000 - 828000 - 2700x

-162000 = -2700x

Divide both sided by -2700:

The value of the building will be $666,000 after 60 months.

Now, let's convert from months to years.

Where:

12 months = 1 year

Therefore, the value of the building will be $666,000 after 5 years.

ANSWER:

5 years.

Given data:

The box is given.

The given expression can be written as,

Thus, the option (c) is correct.

Solution: X-value of vertex=-3

Y-value of vertex=-4

Zeros of the parabola: X=-5 and x=-1

Analysis

We can find the x-coordinate of the vertex, calculating -b/2a. First, we identify the a and b values of y=ax^2+bx+c of your quadratic equation.

b=6

a=1

Now, let's find the zeros of the parabola. We factorize the quadratic equation:

Answer:

2S-a1n/n

Step-by-step explanation:

S = n(a1 + an)/2

2S = n(a1 + an)

2S = na1 + nan

nan = 2S - na1

an = (2S - n a1)/n

{3,8} give the values of set that implies the set has two elements 3 and 8. [3,8] give the range of values that can be used in any functions with values from 3, 4, 5, 6, 7, 8 both 3 and 8 included.

Sets are collections of well-defined objects or elements in mathematics. A set is denoted by a capital letter symbol, and the number of elements in a finite set is denoted by the cardinal number of a set enclosed in a curly bracket{...}.

A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output. Every function has a domain and a codomain, as well as a range.

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Using the congruency of the triangle we can prove all the conditions.

The dimensions of the sides and angles of two or more triangles determine whether they are congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. Two triangles are said to be congruent if pairings of corresponding sides and corresponding angles are equal. They are the exact same size and form.

D is the midpoint of AC

so AB = BC

and also AD = CD

so the triangle ADB is congruent to triangle CDB

Therefore,

angle ADB = angle CDB

angle ABD = angle CBD

angle BAD = angle BCD

Using congruency of the triangle.

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The number of rankings that are possible when the company has 40 salespeople is 78960960.

Based on the information given, permutations will be used. The formula is illustrated thus:

Permutations = n! / (n – r)!

N is the number of things you are choosing from,

r is the number of items.

“!” is a factorial of a number

The company has 40 salespeople and the board member at the company asks for a list of the top 5. This will be;

= 50! / (40 - 5)!

= 40! / 35!

= 40 × 39 × 38 × 37 × 36

= 78960960

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Answer:

a.

Fee of whole band = Fee of writer + guitarist + singer

Fraction of fee of whole band = 4/12 + 1/12 + 1/12

= 4+1+1/12

=6/12

=1/2

b.

Fee of writer= 4/12 of £3000

=3000 × 4/12

= £1000

Fee of singer= 1/12 of £3000

= 3000 × 1/12

= £250

Fee of guitarist= Fee of singer

= £250