the measures of the three angles of a triangle is 180
in a triangle, the measures of the three angles are x, x + 18, and x - 6. what is the measure of each angle

Here’s some information about what Pi (π) is:

Intro

Pi (π) is a number whose decimal digits go on forever and they don’t repeat itself. It’s in the category called irrational numbers, because you can’t rationalize pi.

History

Before pi was created, famous philosophers used tape measure to measure the ratio between the circumference and diameter of a circle. And when they did, they found out that the ratio between the circumference and diameter was roughly about 3.1. But as mankind evolved to have better tape measures and more technology they can use, they found out that the ratio between the circumference and diameter had a number that kept on going forever. It would go like 3.1415926.... and it would go on and on. So, the number pi was introduced by scientists and mathematicians found out that pi turned out to be an irrational number.

Daily Usage

Pi was turned into the symbol π so people don’t have to write the full digits of pi. But now we use pi now in our daily mathematical lives. Pi is almost in every form of mathematics, especially in geometry and trigonometry. Pi is full of new things and it really expanded our understanding of mathematics.

Pi (π) truly has an interesting and fascinating history

Hope this helps! :)

Answer:

25x2-36

1-16x2

Step-by-step explanation:

Slope = change in y / change in x

Use the two pints shown on the graph.

Slope = ( 0- -2) / ( -6 -2)

Slope = 2/-8

Slope = -1/4

answer: slope = -1/4

Slope

The limit of the function As x → - ∞, f(x) → 2.

The limit of a function is the value the function tends to as the independent variable tends to a given value.

Given the graph of the function above, to find the limit of the function As x → -∞, f(x) →? We proceed as follows

Looking at the graph, we see that f(x) has a horizontal asymptote at y = 2. Now, we see that As x → -∞, f(x) approaches 2.

So, As x → - ∞, f(x) → 2.

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Finding the complex numbers and subtracting them, it is found that z2 - z1 = (0, -4).

They are in the format:

z = a + bi.

In which:

In a graph, the real part is the horizontal axis, while the imaginary part is the vertical axis. Hence, the numbers are given by:

To find the result of the subtraction, we subtract each part, hence:

z2 - z1 = (2,1) - (2,5) = (2 - 2, 1 - 5) = (0, -4).

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Answer:

Hope you can understand my handwriting though

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

Work Shown:

a:b = 1:3

a/b = 1/3

a*3 = b*1 ... cross multiply

3a = b

b = 3a

Since b is a one digit number, this means that the largest it can get is 9

\(b \le 9\\\\3a \le 9\\\\a \le \frac{9}{3}\\\\a \le 3\)

The largest possible value of 'a' is 3

Answer:

final price $42,624

price decrease $5376

Step-by-step explanation:

multiply 11.2 percent by 48000 and then get the answer from that and subtract from total

Decrease:-

\(\\ \rm\Rrightarrow 0.112(48000)\)

\(\\ \rm\Rrightarrow 5376\$\)

New price:-

\(\\ \rm\Rrightarrow 48000-5376\)

\(\\ \rm\Rrightarrow 42624\$\)

Answer: 75 coins total, 51 nickels and 24 dimes.

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

The range is found by taking the largest number and subtracting the smallest number

The largest number is 38

The smallest number is 3

38-3 = 35

Complete Question

Newly purchased automobile tires of a certain type are supposed to be filled to a pressure of 30 psi. Let μ denote the true average pressure. Find the P-value associated with each of the following given z statistic values for testing H0: μ = 30 versus Ha: μ 30 when σ is known. (Give the answers to four decimal places.)

calculate for each

(a) z = 2.30

(b) z = -1.7

Answer:

a

\(p-value = 0.021448\)

b

\(p-value = 0.08913\)

Step-by-step explanation:

From the question we are told that

   The population mean is \(\mu = 30 \ psi\)

   The null hypothesis \(H_o : \mu = 30\)

    The alternative hypothesis is  \(H_a : \mu \ne 30\)

Considering question a  

 Here  the test statistics is (a) z = 2.30  

 From the z table  the probability of  (Z >  2.30)  is  

      \(P(Z > 2.30 ) = 0.010724\)

Generally the p-value is mathematically represented as

      \(p-value = 2 * P(Z > 2.30 )\)

=>   \(p-value = 2 * 0.010724\)

=>   \(p-value = 0.021448\)

Considering question b

 Here  the test statistics is (a) z = -1.7

 From the z table  the probability of  (Z <  -1.7)  is  

      \(P(Z < -1.7 ) = 0.044565\)

Generally the p-value is mathematically represented as

      \(p-value = 2 * P(Z < -1.70 )\)

=>   \(p-value = 2 * 0.044565\)

=>   \(p-value = 0.08913\)

Answer:

Mathematics is very important in a small business is because when you make money transactions with other people you need to know how to count money correctly and your calculations can’t be wrong. When we sign up for jobs like police, or firefighter, we need to use math. Math helps us solve real-world problems.

Step-by-step explanation:

Answer: 30%.

Step-by-step explanation:

The percentage decrease for the shoes will be calculated as:

= (Decrease in shoes / Original cost price) × 100

= (50 - 35) / 50 × 100

= 15/50 × 100

= 30%

The percentage decrease for the shoes is 30%

Answer:

\(x = \frac{ - 13}{16} \)

Step-by-step explanation:

\(f(x) = {x}^{3} + 3 \\ g(x) = {x}^{2} + 2\)

At the point of intersection, f(x)=g(x)

\( {x}^{3} + 3 = {x}^{2} + 2 \\ collect \: like \: terms \\ {x}^{3} - {x}^{2} + 3 - 2 = 0 \\ {x}^{3} - {x}^{2} + 1 = 0\)

\( {x}^{3} - {x}^{2} + 1 = 0\)

The above graph is that of the equation

\( {x}^{3} - {x}^{2} + 1 = 0\)

The solution is = -0.755 which is approximately -0.8

From the option provided;

For option A, x = -13/16 = -0.8125

For option B, x = -5/4 = -1.25

For option C, x = -15/16 = -0.9375

For option D, x = -7/8 = -0.875

From the option provided, The closest to the solution is Option A

Because - 0.8125 is approximately -0.8

Answer:

Step-by-step explanation:

We are given that in 2016, the aquarium had x fish, and in 2019, there were x3 fish. We also know that in 2019, there were 512 fish. So we can set up the equation:

x3 = 512

To solve for x, we need to take the cube root of both sides of the equation:

x = ∛512

Using a calculator or simplifying by prime factorization, we can find that:

512 = 2^9

So,

∛512 = ∛2^9 = 2^3 = 8

Therefore, there were 8 fish in the aquarium in 2016.

Answer:

Let's use algebra to solve the problem. We can start by using the information given to set up an equation relating the number of fish in 2016 (x) to the number of fish in 2019 (x3):

x3 = 512

To solve for x, we can isolate x by dividing both sides of the equation by 3:

x = 512/3

x = 170.67 (rounded to two decimal places)

Therefore, there were approximately 170.67 fish in the aquarium in 2016. However, since we cannot have a fraction of a fish, we can round up to the nearest whole number to get the final answer:

x ≈ 171

So there were 171 fish in the aquarium in 2016.

Step-by-step explanation:

Answer:

Step-by-step explanation:

ΔSRQ and ΔVTU are similar Triangle.

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

Given two triangles, ΔRQS and ΔVUT such that,

RS = 16, QR= 64 and VT = 8, UT = 32

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

From the above condition since,

∠R = ∠T

and

\(\frac{QR}{SR} = \frac{UT}{VT} = \frac{4}{1}\)

Thus,

ΔSRQ and ΔVTU are similar from the congruency  property of SAS.

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Answer:  

-27/7 or -3 6/7

Step-by-step explanation:

Just plug in 19 for x

The length of line segment AB is of approximately 8.25 units.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The endpoints of the segment are given as follows:

A(2,2) and B(-6,4).

The length of the segment is given by the distance between these two points, as follows:

\(d = \sqrt{(-6 - 2)^2 + (4 - 2)^2}\)

d = 8.25 units.

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In the given diagram, the perimeter of the shaded part is  100 cm

From the question, we are to determine the perimeter of the shaded part in the given diagram.

Perimeter of a shape is the distance around the shape

First, we will determine the length of the arcs surrounding the shaded area,

Length of arc = θ/360° × 2πr

Where θ is the angle subtended by the arc

and r is the radius

θ = 180° (Angle subtended by a semicircle)

Diameter of the semicircle = 26 cm

Thus,

Radius = 26 cm / 2

Radius = 13 cm

Then,

Length of arc = 180°/360° × 2π × 13 cm

Length of arc = 1/2 × 2π × 13 cm

Length of arc = 13π cm

Thus,

Perimeter of the shaded part = 37 cm + 13 cm + 37 cm + 13 cm

Perimeter of the shaded part = 100 cm

Hence,

The perimeter is 100 cm

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Answer:

2.5 gallons of black paint

17.5 gallons of white paint

Step-by-step explanation:

2.5 gallons of black paint and 17.5 gallons of white paint needs to mix 20 gallons of gray paint.

An equation is an expression that shows the relationship between two or more numbers and variables. The solution to an equation is finding values of the variable included in the considered equation for which the equation considered evaluates to be true.

We have been given that the painter mixes gray paint by using 1 gallon of black paint for every 7 gallons of white paint.

Also, the painter needs to mix 20 gallons of gray paint

Let x be the gallon of black paint and y be the gallons of white paint.

Therefore, the equation will be;

x + 7y = 20

x = 20 - 7y

2.5 = 20 - 7(17.5)

Hence, 2.5 gallons of black paint and 17.5 gallons of white paint needs to mix 20 gallons of gray paint.

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Answer:

1/10 per sec

Step-by-step explanation:

When he's walked x feet in the eastward direction, the angle Θ that the search light makes has tangent

tanΘ = x/18

Taking the derivative with respect to time

sec²Θ dΘ/dt = 1/18 dx/dt.

He's walking at a rate of 18 ft/sec, so dx/dt = 18.

After 3seconds,

Speed = distance/time

18ft/sec =distance/3secs

x = 18 ft/sec (3 sec)

= 54ft. At this moment

tanΘ = 54/18

= 3

sec²Θ = 1 + tan²Θ

1 + 3² = 1+9

= 10

So at this moment

10 dΘ/dt = (1/18ft) 18 ft/sec = 1

10dΘ/dt = 1

dΘ/dt = 1/10 per sec

At 1/10 per second is the rate when the light turns 3 seconds after he started walking east.

It is given that a man starts at point A and walks 18 feet north. He then turns and walks due east at 18 feet per second.

It is required to find at what rate is the light turning 3 seconds after he started walking east.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

The \(\rm tan\theta\) is the ratio of the perpendicular to the base.

When he started walking eastward direction, the searchlight makes an angle \(\theta\)

Let the distance is x

And the  \(\rm tan\theta = \frac{x}{18}\)

After performing the derivate with respect to time, we get:

\(\rm sec^2\theta\frac{d\theta}{dt} = \frac{1}{18} \frac{dx}{dt}\) ...(1)    ( the differentiation of \(\rm tan\theta \ is \ sec^2\theta\\\))

He walking at the rate of 18 ft per second ie.

\(\rm \frac{dx}{dt} = 18\)  

After 3 seconds  \(\rm Speed=\frac{Distance}{Time}\)

By using speed- time formula we can calculate the distance:

Distance x = 18×3 ⇒ 54 ft.

\(\rm tan\theta = \frac{54}{18}\)  ⇒3

We know that:

\(\rm sec^2\theta = 1+tan^2\theta\)

\(\rm sec^2\theta = 1+3^2\\\\\rm sec^2\theta = 10\\\)

Put this value in the (1) equation, we get:

\(\rm 10\frac{d\theta}{dt} = \frac{1}{18} \times18\)    ∵ \(\rm (\frac{dx}{dt} =18)\)

\(\rm 10\frac{d\theta}{dt} = 1\\\\\rm \frac{d\theta}{dt} = \frac{1}{10} \\\\\)per second.

Thus, at 1/10 per second what rate is the light turning 3 seconds after he started walking east.

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According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

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ex=1+x2+x3/2!+x4/3!  is the Taylor series centered.

The function itself evaluated at a = 0 as well as the first three derivatives are therefore required to determine the first four terms using this formula (because the 0t h derivative equals the function itself).

The fourth derivative can be used to determine the next term as the fourth derivative is required to obtain four non-zero terms using this function and the 0th term is zero. This is likely why the first four derivatives were chosen.

f(0)=0(e0)=0

ex=1+x+x2/2!+x3/3!

ex=x(1+x+x2/2!+x3/3!)

ex=1+x2+x3/2!+x4/3!

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The value οf the expressiοn is \(-cot^2x\).

Trigοnοmetry deals in a right angled triangle by giving the ratiο οf variοus sides οf the right angled triangle.

An equatiοn is a fοrmula in mathematics that expresses the equality οf twο expressiοns by cοnnecting them with the equals sign (=). The wοrd equatiοn and its cοgnates in οther languages may have subtly different meanings; fοr example, in French, an équatiοn is defined as cοntaining οne οr mοre variables, whereas in English, an equatiοn is any well-fοrmed fοrmula cοnsisting οf twο expressiοns linked by an equals sign.

\(\frac{sin^2(\frac{\pi }{2}-x) }{cos^2-1} \\= \frac{cos^2x}{cos^2-1} \\=\frac{cos^2x}{cos^2x-sin^2x-cos^2x} \\=\frac{cos^2x}{-sin^2x} =-cot^2x\)

Hence, the value of the expression is \(-cot^2x\).

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Answer:

The answer is C

Step-by-step explanation:

i got it right on edge

Side AB = 13.7 miles, ∠A = 33.3° , ∠B = 56.7°

The correct answer is an option (c) Side AB = 13.7 miles, angle A = 33.3 degrees, angle B = 56.7 degrees.

"It is a triangle whose one of the angle measures 90° "

"It is a longest side of the right triangle."

"For triangle PQR,

\(\frac{sinP}{p} =\frac{sinQ}{q} =\frac{sinR}{r}\)

where side QR is p, side PQ is r, and side PR is q"

"In right triangle, \(a^{2}+ b^{2}=c^{2}\) where c is the hypotenuse, a, b are other two sides of right triangle. "

For given question,

We have been given a triangle ABC.

Angle C = 90°

This means, triangle ABC is a right triangle.

Hypotenuse side AB is c,

And side CB is a, side CA is b.

Also given that, Side BC = 7.50 miles, Side AC = 11.43 miles

⇒ a = 7.5 miles and b = 11.43 miles

First we find the hypotenuse AB using Pythagoras theorem.

Using Pythagoras theorem,

⇒ AB² = BC² + AC²

⇒ AB² = (7.50)² + (11.43)²

⇒ AB² = 56.25 + 130.65

⇒ AB² = 186.9

⇒ AB = 13.67 miles

⇒ c = 13.67 miles

Using sine rule for triangle ABC,

\(\Rightarrow \frac{sin~A}{a} =\frac{sin~B}{b}= \frac{sin~C}{c}\\\\\Rightarrow \frac{sin~A}{7.50} =\frac{sin~B}{11.43} =\frac{sin~C}{13.67}\)

Consider,

\(\Rightarrow \frac{sin~A}{7.50} =\frac{sin~C}{13.67}\\\\\Rightarrow \frac{sin~A}{7.50} =\frac{sin~90}{13.67}\\\\\Rightarrow \frac{sin~A}{7.50} =\frac{1}{13.67}\)

⇒ 13.67 × sin A = 7.50

⇒ sin A = 0.5486

⇒ ∠A = 33.3°

We know that the sum of all angles of triangle is 180°

⇒ ∠A + ∠B + ∠C = 180°

⇒ 33.3° + ∠B + 90° = 180°

⇒ ∠B + 123.3° = 180°

⇒ ∠B = 56.7°

Therefore, Side AB = 13.7 miles, ∠A = 33.3° , ∠B = 56.7°

The correct answer is an option (c) Side AB = 13.7 miles, angle A = 33.3 degrees, angle B = 56.7 degrees.

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Answer:

\(\frac{0.93}{0.57}\)

Step-by-step explanation:

Simplify both of the fractions so \(\frac{14}{15}\) to get 0.93 and \(\frac{4}{7}\) to get 0.57.

Then you put them back into fraction form.

(a) The mean of the data item from the group data is 161.

(b) The deviation from the mean for each data is -6,-5,1,3 and 7. respectively.

(c) The sum of the deviation is 0

Grouped data are data formed by aggregating individual observations of a variable into groups, so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data.

(a) To find the mean of the data, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

(b) To calculate the deviation from the mean (M') for each of the data item we use the formula below.

M' = x-M

For data 115,

For data 156,

For data 162,

For data 164,

For data 168,

(c) The sum of the deviation is

Hence, the mean, the diaviation from the mean is -6,-5,1,3 and 7  and the sum of the deviation of the data is 161 and 0 respectively,

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Answer:

1 torr = 760 atm

1 torr = 1 mmHg

Answer: 5/3a + 4/2b

Step-by-step explanation:

\(\dfrac{4}{3} a-\dfrac{1}{2} b+\dfrac{1}{3} a+\dfrac{5}{2} b\)

Rearrange:

\(\dfrac{4}{3} a+\dfrac{1}{3} a-\dfrac{1}{2} b+\dfrac{5}{2} b\)

Combine Like Terms:

\(\dfrac{4}{3} a+\dfrac{1}{3} a=\dfrac{5}{3} a\\-\dfrac{1}{2}b+\dfrac{5}{2} b=\dfrac{4}{2} b\)

\(\fbox{$\dfrac{5}{3}$a + $\dfrac{4}{2}$b}\)