Angles in a Triangle

Certainly!

The text is asking how to solve the equation x² - 14x + 9 = 0 using the factoring method. Factoring is a method of finding the roots of a quadratic equation by expressing it as a product of two linear factors. The roots of a quadratic equation are the values of x that make the equation equal to zero. In this case, we are trying to find the values of x that satisfy the equation x² - 14x + 9 = 0.

Therefore, the expression 6r² + 31r + 18 factors completely into (3r + 2)(2r + 9).

In mathematics, factoring is the process of finding the factors or divisors of a given number or algebraic expression. When we factor a number or expression, we find the numbers or expressions that can be multiplied together to obtain the original number or expression. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, since these numbers can be multiplied together in different combinations to obtain 12. Factoring is an important skill in algebra, as it helps us to simplify algebraic expressions and solve equations.

Here,

To factor the quadratic expression completely, we need to find two binomials whose product is equal to the given expression. We can start by looking for two numbers whose product is 6 x 18 = 108 and whose sum is 31. After some trial and error, we find that the numbers are 6 and 18.

We can now write the expression as:

=6r² + 31r + 18

18*6=108

27*4=108

27+4=31

= 6r² + 27r + 4r + 18

= 3r(2r + 9) + 2(2r + 9)

= (3r + 2)(2r + 9)

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Answer:

log b.c^z

Step-by-step explanation:

from the theorem a log b=log b^a

z log c= log c^z

from the theorem log a + log b= log ab

log b+ log c^z= logb. c^z will be the final answer

The base angles a and b have their measures to be 45 degrees each

If the diagonal of a square produces an isosceles right triangle, then the two legs of the right triangle are congruent, meaning the two base angles are congruent as well.

Since the triangle is a right triangle, one of the base angles must be 45 degrees (which is half of the right angle).

Therefore, both base angles are 45 degrees.

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Step-by-step explanation:

Use a compounding formula like this:

    P (t) = 280 000 (1 + .0725) ^t    

                                      t is years    .0725 is  7.25%  in decimal form

P (12) = 280 000 ( 1.0725)^12 = 648,523 population

The first shape does NOT have a Hamilton circuit

The second shape has a Hamilton circuit

The third shape does NOT have a Hamilton circuit

In mathematical graph theory, a Hamiltonian circuit- named after its originator William Rowan Hamilton, an acclaimed Irish mathematician of the 19th century– is a path within a graph that covers every vertex only once and begins and ends at the same vertex.

To put it differently, it's an enclosed movement that goes through each point in the graph exactly once. When the graph consists of a Hamiltonian circuit, this indicates to be a Hamiltonian graph. One can see many practical uses of Hamiltonian circuits such as computer science where they play a crucial role in algorithm analysis and design.

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Answer:  B, C, B

Step-by-step explanation:

see images for explanation

Answer:

[tex]\textsf{11)} \quad \text{b.}\;\;2\frac{3}{4}[/tex]

[tex]\textsf{12)} \quad \text{c.}\;\;7\frac{1}{2}[/tex]

[tex]\textsf{13)} \quad \text{b.}\;\;\dfrac{2}{3}x+4=10[/tex]

Step-by-step explanation:

To find the answer to the given equation when y = 4, substitute y = 4 into the equation:

[tex]\begin{aligned} y=4 \implies \dfrac{3}{4}+\dfrac{2(4)}{4}&= \dfrac{3}{4}+\dfrac{8}{4}\\\\&= \dfrac{3}{4}+2\\\\&= 2\frac{3}{4}\end{aligned}[/tex]

Therefore, the answer is 2³/₄.

[tex]\hrulefill[/tex]

To find the answer to the given equation when y = 8, substitute y = 8 into the equation:

[tex]\begin{aligned}y=8 \implies \dfrac{12}{8}+\dfrac{3(8)}{4}&= \dfrac{12}{8}+\dfrac{24}{4}\\\\&= \dfrac{12}{8}+6\\\\&= \dfrac{8+4}{8}+6\\\\&= \dfrac{8}{8}+\dfrac{4}{8}+6\\\\&= 1+\dfrac{1}{2}+6\\\\&=7\frac{1}{2}\end{aligned}[/tex]

Therefore, the answer is 7¹/₂.

[tex]\hrulefill[/tex]

To determine which equation is true if x = 9, substitute x = 9 into each equation.

[tex]\begin{aligned} \text{a)} \quad \dfrac{2}{3}(9)-6&=12\\\\\dfrac{18}{3}-6&=12\\\\6-6&=12\\\\0&=12\end{aligned}[/tex]

[tex]\begin{aligned} \text{b)} \quad \dfrac{2}{3}(9)+4&=10\\\\\dfrac{18}{3}+4&=10\\\\6+4&=10\\\\10&=10\end{aligned}[/tex]

[tex]\begin{aligned} \text{c)} \quad 3(9)-12&=21\\27-12&=21\\15&=21\end{aligned}[/tex]

[tex]\begin{aligned} \text{d)} \quad 3(9)+12&=19\\27+12&=19\\39&=19\end{aligned}[/tex]

Therefore, the only equation that holds true is option b.

The value of x in the equation is B) None of these.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation is 36x+31=535

Now substitute x=1 then,

=> 36(1)+31=535

=> 36+31=535

=> 67 ≠ 535

Now substitute x = 12 then

=> 36(12)+31=535

=> 432+31 = 535

=> 463 ≠ 535

Now substitute x= 17 then

=> 36(17)+31=535

=> 612+31 = 535

=> 643 ≠ 535.

Hence the correct option is B) None of these.

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Answer:

Your answer is 90% of 60 = 54.

The probability that between 35 and 37 of the murders, inclusive, were cleared is 0.12.

(a) The probability that exactly 40 of the murders were cleared can be found using the binomial probability formula.  

In this case, n = 50, k = 40, and p = 0.65. Thus, the probability that exactly 40 of the 50 murders were cleared is P(40 successes) = (50C40)(0.65)⁴⁰(0.35)¹⁰ = 0.064.

(b) The probability that between 35 and 37 of the murders, inclusive, were cleared can be found by adding the probabilities of each individual outcome.

For example, the probability of exactly 35 successes is (50C35)(0.65)³⁵(0.35)¹⁵ = 0.069.

Similarly, the probability of exactly 36 successes is (50C36)(0.65)³⁶(0.35)¹⁴ = 0.051.

Adding these two probabilities together gives the probability of between 35 and 37 successes, inclusive, as 0.069 + 0.051 = 0.120.

(c) It would not be unusual if fewer than 20 of the murders were cleared. This is because the probability of this outcome can be calculated using the same formula as before. In this case, if k = 19, then P(19 successes) = (50C19)(0.65)¹⁹(0.35)³¹ = 0.057, which is a relatively high probability.

Therefore, the probability that between 35 and 37 of the murders, inclusive, were cleared is 0.12.

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a. It should be noted that about 10.56% of pregnancies last more than 267 days.

b. It should be noted that about 26.76% of pregnancies last between 255 and 261 days.

c. The probability that a randomly selected pregnancy lasts no more than 245 days is about 6.68%.

d. Only about 1.22% of pregnancies are extremely preterm, a somewhat uncommon event.

In this case, to see, to see if very preterm babies are uncommon, we must compare the likelihood of a pregnancy lasting less than 239 days to some criterion. We can employ the z-score:

z = (239 - 257) / 8 = -2.25

To the left of 239, there is:

P(X < 239) = P(Z < -2.25) = 0.0122

This suggests that only about 1.22% of pregnancies are extremely preterm, a somewhat uncommon event. As a result, very premature newborns are considered rare.

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a. It should be noted that about 10.56% of pregnancies last more than 267 days.

b. It should be noted that about 26.76% of pregnancies last between 255 and 261 days.

c. The probability that a randomly selected pregnancy lasts no more than 245 days is about 6.68%.

d. Only about 1.22% of pregnancies are extremely preterm, a somewhat uncommon event.

In this case, to see, to see if very preterm babies are uncommon, we must compare the likelihood of a pregnancy lasting less than 239 days to some criterion. We can employ the z-score:

z = (239 - 257) / 8 = -2.25

To the left of 239, there is:

P(X < 239) = P(Z < -2.25) = 0.0122

This suggests that only about 1.22% of pregnancies are extremely preterm, a somewhat uncommon event. As a result, very premature newborns are considered rare.

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Answer:

44 butterfly stamps

Step-by-step explanation:

1/8=2/16

2/16+3/16=5/16

16/16-5/16=11/16

64÷16=4

4×11=44

44/64

Answer:

dont know either

Step-by-step explanation:

dont know either

The museum in relation to her hotel is at distance and direction as 3 blocks to the west and 4 blocks to the north.

Given that,

Ruby is visiting San francisco.

The figure representing the situation is given below.

Here it is easier to find the relation of the museum with the hotel.

When Ruby walk a certain distance to the west, she will reach straightly north to the museum.

Distance to the west = 7 - 4 = 3 blocks

Then she can walk 3 + 1 = 4 blocks to reach the museum.

Hence the museum is at a distance of 3 blocks to the west and 4 blocks to the north.

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Answer:

h ≥ -14

Step-by-step explanation:

-1h ≤ 14

h ≥ -14

So, the answer is h ≥ -14

The length of side b is given as follows:

b = 2.86 m.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

The sum of the measures of the internal angles of a triangle is of 180º, hence the missing angle is obtained as follows:

B + 30 + 80 = 180

B = 70º.

Then the relation, by the law of sines, is given as follows:

sin(70º)/b = sin(80º)/3

Meaning that the length of side b is given as follows:

b = 3 x sine of 70 degrees/sine of 80 degrees

b = 2.86 m.

The triangle is given by the image presented at the end of the answer.

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Answer:

44 feet in 10 seconds = 44 x 6 (since there are 60 seconds in a minute) = 264 feet per minute

264 feet per minute x 60 minutes (since there are 60 minutes in one hour) = 15,840 feet per hour

15,840 feet per hour / 5,280 feet (since there are 5,280 feet in 1 mile) = 3 miles per hour

Answer:

(a) 4.356% (b) 1.089%

Step-by-step explanation:

The rolling of a single die is an example of a discrete uniform distribution, where each of the six possible outcomes has an equal probability of 1/6.

(a) After 1010 rolls of the die, observing a "one" 44 times, the proportion of rolls resulting in a "one" is:

Proportion = Number of "ones" / Total number of rolls

= 44 / 1010

= 0.04356

Therefore, approximately 4.356% of the rolls resulted in a "one".

(b) After 2020 rolls of the die, observing a "one" 22 times, the proportion of rolls resulting in a "one" is:

Proportion = Number of "ones" / Total number of rolls

= 22 / 2020

= 0.01089

Therefore, approximately 1.089% of the rolls resulted in a "one".

Answer:

A) 40%

B) 10%

Step-by-step explanation:

A) p = 4/10 = 40%

B) p = 2/20 = 10%

Answer:

C. d = 163t

Step-by-step explanation:

This equation represents a direct proportionality between the number of dollars earned (d) and the amount of time worked (t), with a constant of proportionality of 163 dollars per hour.

Hope this helps!

Yes, the shape can be cut into 3 congruent parts but not 4. This is a whole number division problem. See the attached shape for how to divide the figure into 3 congruent parts.

In mathematics, when two numbers are divided without remainders, it is known as integer division or whole number division.

This specific kind of calculation comes in handy when you desire to find out just the quotient or how many times one number divides into another, disregarding any leftover fraction.

For instance, if we utilize integer division to calculate what happens when ten is divided by two; we're left with five as our answer since two divides equally into ten precisely five times without remaining any leftovers.

Conversely speaking though and in regards to regular arithmetic calculations; dividing ten by three amounts up to three with a remainder value attached since three cannot do so equally.

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The most descriptive name for the illustration below is C. rhombus.

Because it has four sides, a rhombus is a geometric shape that is a quadrilateral. Because its opposite sides are parallel and their angles are equal, it is a unique kind of parallelogram.

The most descriptive name for the illustration above is C. rhombus.

A rhombus is a type of quadrilateral with four sides of equal length and opposite angles that are equal to each other. It can also be defined as a parallelogram with equal diagonals. The illustration appears to have all sides of equal length and opposite angles that are equal, thus making it a rhombus.

While the other options, such as quadrilateral, polygon, and trapezoid, also apply to the illustration, they are less specific than the term rhombus.

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The formula for how far the rocket travels in t seconds is d(t) = 8,000t.

In Mathematics and Science, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using the following unit of measurement;

In Mathematics and Science, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Making distance the subject of formula, we have:

Distance, d(t) = speed × time

Distance, d(t) = 8,000 × t

Distance, d(t) = 8,000t

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When be graph the functions given, we find that option A is correct.

What is meant by to graph a function?

To graph a function, you have to select x-values and plug them into the equation. Once you plug those values into the equation, you will get a y-value. Your x-values and your y-values make up your coordinates for a single point. Keep plugging in x-values to get coordinates to plot more points on the graph, and then you will see your graphed function once the dots are connected.

Using the graph,

For x < = -2, y = 5.

For -2 < x < 1, the function is a polynomial.

We have two options, either y = x² - 5 or y = x² + 5

The polynomial must have the point (0,-5) on it.

For y = x² - 5 , when x = 0, y = -5.

Hence, it is the correct option.

For x >= 1,

Using graph, we see that when y = 0, x lies between 3 and 4.

For equation, y = 2⁽ˣ⁻²) - 2 , when y = 0, x = 3, so it is not correct.

For equation, y = 2⁽ˣ⁻²) - 3 , when y = 0, x = 3.584, hence it is correct.

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Answer:

  500

Step-by-step explanation:

You want to know the total number of plantings if 190 trees comprise 38% of them.

The given relationship can be written as the equation ...

  190 = 0.38 × total

  total = 190/0.38 = 500 . . . . . . . divide by the coefficient of 'total'

There are 500 plantings in the garden.

According to the concept of compound interest, the effective annual yield on your investment of $1800 at a 6.3% interest rate compounded daily is 6.49%.

To find the effective annual yield, we need to use the formula for compound interest:

A = P(1 + r/n)ⁿˣ

Where A is the amount of money at the end of the investment period, P is the principal amount invested, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the number of years.

In this case, we know that the principal amount P is $1800, the annual interest rate r is 6.3%, and the interest is compounded daily, which means that n is 365 (the number of days in a year). We need to find the effective annual yield, which is the total amount of interest earned in one year.

To calculate the effective annual yield, we can use the following formula:

Effective Annual Yield = (1 + r/n)ⁿ - 1

Plugging in the values, we get:

Effective Annual Yield = (1 + 0.063/365)³⁶⁵ - 1

Effective Annual Yield = 0.0649 or 6.49%

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Since line segment SP is a diameter, the measure of arc PTS is 180 degrees. 180 - 42 = 138 degrees, which is the measure of arc PT. 97 + 42 + 138 = 277 degrees for the measure of arc PTR

The probability that an American will disapprove or have no opinion on the issue is 13%.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event. Probability is used to describe random phenomena, such as the roll of a dice, the flip of a coin, the occurrence of an earthquake, or the outcome of a hand of poker. It is also used to describe the likelihood of certain events happening based on past data or current conditions.

This can be calculated by subtracting the reported approval rate of 87% from 100%. This means that 13% of Americans disapprove or have no opinion on the issue of human embryonic stem cell research.

It is important to note that this survey's data only pertains to the opinions of Americans and not to any other group of people. Therefore, the probability that any individual randomly selected from the global population will disapprove or have no opinion on the issue may be different.

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The ratio of the sand is 3:7 and it can be write as 6:14 or 7:21 ... They means the same thing.

Now we know that we have 56 bags of sand, the left side of the number should be 56. Like this:

? : 56

Since we know that 3:7 can be write as 6:14 or 7:21 ... we can even write it as 24:56, it's still 3:7.