How many triangles exist with the given angle measures? 30°, 65°, 85° A. Exactly one unique triangle exists with the given angle measures. B. More than one unique triangle exists with the given angle measures. C. No triangle exists with the given angle measures.

Answer:

[tex]sec\ y = \frac{6}{b}[/tex]

Step-by-step explanation:

Given

[tex]sin\ y = \frac{a}{6}[/tex]

[tex]tan\ y = \frac{a}{b}[/tex]

Required

sec y

From trigonometry;

[tex]sec\ \theta = tan\ \theta\ /\ sin\ \theta[/tex]

Substitute y for θ

[tex]sec\ y= tan\ y\ /\ sin\ y[/tex]

Substitute values for tan y and sin y

sec y = a/b ÷ a/6

[tex]sec\ y= \frac{a}{b} /\ \frac{a}{6}[/tex]

[tex]sec\ y= \frac{a}{b} *\ \frac{6}{a}[/tex]

[tex]sec\ y= \frac{6 * a}{a *b}[/tex]

[tex]sec\ y= \frac{6 a}{ab}[/tex]

Divide numerator and denominator by a

[tex]sec\ y= \frac{6}{b}[/tex]

Hence, the value of sec y is

[tex]sec\ y= \frac{6}{b}[/tex]

Answer:

-3p^8/4q^3

Step-by-step explanation:

<3

Answer:

7x+7 is obviously divisible by 7.

put in any value high enough and you can find the two three digit numbers.

Step-by-step explanation:

Two three-digit numbers divisible by 7 are 98 and 105.

Two three-digit numbers divisible by 7 are 98 and 105.To create an expression that is divisible by 7, we can use the property that the difference between two numbers is divisible by 7 if the numbers themselves are divisible by 7.

Let's represent a three-digit number divisible by 7 as "7k" where k is an integer. To find two three-digit numbers divisible by 7, we can use the following expression:

7k - 7

For example, if we substitute k = 15, we get:

7(15) - 7 = 105 - 7 = 98

So, the first three-digit number divisible by 7 is 98.

Similarly, for the second three-digit number, let's substitute k = 16:

7(16) - 7 = 112 - 7 = 105

Therefore, the two three-digit numbers divisible by 7 are 98 and 105.

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Answer:

Option C, Scatter Plot. Hope this helps!

Step-by-step explanation:

Answer:

The answer is C on edge 2020.

Step-by-step explanation:

Answer:

Option (A).

Step-by-step explanation:

The function f(x) = x² + 4 is defined over the interval (-2, 2)

Total number of equal parts between this interval = 5

If the interval is divided into n equal parts, height of the right endpoint of each rectangle = [tex]\frac{5}{n}[/tex]

Height of the endpoint of the k rectangles = [tex]k.\frac{5}{n}[/tex]

Therefore, height of the endpoint of the kth rectangle = Height of first rectangle + height of k rectangles

= -2 + [tex]k.\frac{5}{n}[/tex]

Option (A). will be the answer.

The height of the right endpoint of the kth rectangle h = -2 + k (5/n)

The height is a vertical distance between two points. In the case of the triangle, the height will be the distance between the base and the top vertex of the triangle.

The function f(x) = x² + 4 is defined over the interval) (-2, 2 )

Total number of equal parts between this interval = 5

If the interval is divided into n equal parts, the height of the right endpoint of each rectangle = (5/n)

Height of the endpoint of the k rectangles = k (5/n)

The height of the endpoint of the kth rectangle:-

= Height of first rectangle + height of k rectangles

= -2   +  k (  5/n )

Therefore the height of the right endpoint of the kth rectangle h = -2 + k (5/n)

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Hey there! :)

Answer:

d ≈ 3.49 units

Step-by-step explanation:

Use the distance formula for polar coordinates to determine the distance:

[tex]d = \sqrt{r_{1} ^{2}+r_{2} ^{2}-2r_{1}r_{2}cos(0_{1}- 0_{2} ) }[/tex] (The '0' is supposed to be theta)

Plug in the values given in the question. Convert radians to degrees to simplify the process.

217π/180 = 217°

-23π/36 = -115°.

Therefore:

[tex]d = \sqrt{7 ^{2}+5 ^{2}-2(7)(5)cos(217-(-115) ) }[/tex]

Begin simplifying:

[tex]d = \sqrt{74-70cos(332) }[/tex]

[tex]d = \sqrt{74-61.81 }[/tex]

Solve:

[tex]d = \sqrt{12.19 }[/tex]

d ≈ 3.49 units

Answer:

Step-by-step explanation:

As you show, the weight differences are different for the same week differences, so the table is not linear. A graph (attached) can also show you the table is not linear.

__

The highest rate of weight loss shown in the table is 7 lbs in 3 weeks, or 4 2/3 pounds in 2 weeks. The lowest rate of weight loss shown in the table is 5 lbs in 3 weeks, or 3 1/3 pounds in 2 weeks. Based on the rates shown in the table, we might expect the starting weight to be between 3 1/3 and 4 2/3 pounds more than the first table value:

  Week 0 weight: between 184 1/3 and 185 2/3 lbs, estimated.

_____

A "line of best fit" for the data has a y-intercept of about 185 pounds, which is the midpoint between our two estimates above.

Answer:

[tex]\dfrac{1}{7}[/tex]

Step-by-step explanation:

There are 7 days in a week.

For the first person, we select one day out of the 7 days. The first person has 7 options out of the 7 days.

Let Event A be the event that the first person was born on a day of the week.

Therefore:

[tex]P(A)=\dfrac{7}{7}=1[/tex]

The second person has to be born on the same day as the first person. Therefore, the second person has 1 out of 7 days to choose from.

Let Event B be the event that the second person was born.

Therefore, the probability that the second person was born on the same day as the first person:

[tex]P(B|A)=\dfrac{1}{7}[/tex]

By the definition of Conditional Probability

[tex]P(B|A)=\dfrac{P(B \cap A)}{P(A)} \\$Therefore:\\P(B \cap A)=P(B|A)P(A)[/tex]

The probability that both were born on the same day is:

[tex]P(B \cap A)=P(B|A)P(A) = \dfrac{1}{7} X 1 \\\\= \dfrac{1}{7}[/tex]

Answer:

Hello!

~~~~~~~~~~~~~~~``

Simplifying

2x + 3y = 45

Solving

2x + 3y = 45

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3y' to each side of the equation.

2x + 3y + -3y = 45 + -3y

Combine like terms: 3y + -3y = 0

2x + 0 = 45 + -3y

2x = 45 + -3y

Divide each side by '2'.

x = 22.5 + -1.5y

Simplifying

x = 22.5 + -1.5y

Hope this helped you! Brainliest would be nice.

Answer:

30 is not included

Step-by-step explanation:

The way this stem works is that it separates the numbers for better sorting.

Example:

Set that records 11, 12, 24, 28, 32, 32

The stem and leafs would look like

1    1 2

2   4 8

3   2 2

The sampled bold number indicates that 2 and 8 make up 28.

If you look at the plot, there was no 3 and 0 that would make 30. So that does not exist.

Answer:

105.6 miles

Step-by-step explanation:

In the diagram

The angle at B = 59.7°-29°=30.7°

The angle at A =180°-(78.9°+59.7°)=41.4°

Using the sum of angles in a triangle, Angle C = 107.9°

Applying the Law of Sines

[tex]\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\\b=\dfrac{c}{\sin C} \times \sin B\\\\=\dfrac{456.2}{\sin 107.9^\circ} \times \sin 30.7^\circ\\\\AC=b=244.76$ miles[/tex]

Similarly

[tex]\dfrac{a}{\sin A}=\dfrac{c}{\sin C}\\a=\dfrac{c}{\sin C} \times \sin A\\\\=\dfrac{456.2}{\sin 107.9^\circ} \times \sin 41.4^\circ\\\\BC=a=317.04$ miles[/tex]

Therefore:

AC+BC=244.76+317.04 =561.8 miles

Difference

561.8 - 456.2 =105.6 miles

Therefore, Adam would receive 105.6 miles more frequent flyer miles.

Problem 1

Explanation: Circle or highlight the angles 10 and 15. They are alternate interior angles with line d being the transversal cut. It might help to try to erase line c to picture the transversal line d better. With d as the transversal, and angles 10 and 15 congruent, this must mean lines a and b are parallel by the alternate interior angle theorem converse.

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

Problem 2

Explanation: The angles at the top are 32 degrees, 90 degrees, and x degrees which is the missing unmarked angle at the top (all three angles are below line m). The three angles must add to 180 to form a straight angle

32+90+x = 180

x+122 = 180

x = 180-122

x = 58

The missing angle is 58 degrees. This is very close to 57 degrees at the bottom. Though we do not have an exact match. This means lines m and n are not parallel. The alternate interior angles must be congruent for m and n to be parallel, as stated earlier in problem 1.

Answer: 8y⁸

Step-by-step explanation:

To find the square root of the expression, you want to find the square root of each term.

The square root of 64 is 8. You can write y¹⁶ as (y⁸)². We can pull out this 2 from the square root because it cancels out with the square root. Therefore, the answer is 8y⁸.

Answer:

5x + 10 = 25

Subtract 10 on each side to make x alone

5x = 15

divide by 5 on each side

x=3 so x=3

3x + 12 = 48

48-12=36

3x=36

divide by 3

x=12

4x + 8 = 16

4x = 8

x=2

2x + 15=25

2x=10

x=5

5x + 20 = 50

5x=30

x=6

hope this helps

1. 3

2.12

3.2

4.5

5.6

Step-by-step explanation:

Answer:

Step by step explanation

First:

Solution,

1. 5x + 10 = 25

Move constant to the R.H.S and change its sign:

5x = 25 - 10

Calculate the difference

5x = 15

Divide both sides by 5

5x/5 = 15/5

calculate

X = 3

2. 3x + 12 = 48

or, 3x = 48 - 12

or, 3x = 36

or, 3x/x = 36/3

x = 12

3. 4x + 8 = 16

or, 4x = 16 - 8

or, 4x = 8

or, 4x/x = 8/4

x = 2

4. 2x + 15 = 25

or, 2x = 25 - 15

or, 2x = 10

or, 2x/x= 10/2

x = 5

5. 5x + 20 = 50

or, 5x = 50-20

or, 5x = 30

or, 5x/x = 30/5

x = 6

Hope this helps...

Good luck on your assignment...

Answer:

z = 10

Step-by-step explanation:

The value of the z-statistic is given by:

[tex]z = \frac{X - \mu}{s}[/tex]

In which:

X is the measured value.

[tex]\mu[/tex] is the expected value.

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex] is the standard deviation of the sample. [tex]\sigma[/tex] is the standard deviation of the population.

In this question:

The mean length was 2.9 inches, and the population standard deviation is 0.1 inch.

This means that [tex]\mu = 2.9, \sigma = 0.1[/tex]

Random sample of 100 screws.

This means that n = 100.

To see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be?

3 inches, so [tex]X = 3[/tex]

[tex]s = \frac{0.1}{\sqrt{100}} = 0.01[/tex]

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{3 - 2.9}{0.01}[/tex]

[tex]z = 10[/tex]

Answer:

-10

Step-by-step explanation:

If we first note the denominator of fraction numerator sigma over denominator square root of n end fraction equals fraction numerator 0.1 over denominator square root of 100 end fraction equals fraction numerator begin display style 0.1 end style over denominator 10 end fraction equals 0.01

Then, getting the z-score we can note it is z equals fraction numerator x with bar on top minus mu over denominator begin display style 0.01 end style end fraction equals fraction numerator 2.9 minus 3 over denominator 0.01 end fraction equals negative 10

This tells us that 2.9 is 10 standard deviations below the value of 3, which is extremely far away.

Hey there! :)

Answer:

10 miles.

Step-by-step explanation:

To solve for the diagonal side, we can simply visualize the sides of the rectangle as sides of a right triangle with the diagonal being the hypotenuse.

We can use the Pythagorean Theorem (a² + b² = c²), where:

a = length of short leg

b = length of long leg

c = length of the diagonal

Solve:

c² = a² + b²

c² = 6² + 8²

c² = 36 + 64

c² = 100

c = 10 miles. This is the length of the pedestrian route.

Answer:

Solution,

Hypotenuse (h) = R

Perpendicular (p) = 8 miles

Base (b) = 6 miles

Now,

Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

Plugging the values:

[tex] {r}^{2} = {(8)}^{2} + {(6)}^{2} [/tex]

Calculate:

[tex] {r}^{2} = 64 + 36[/tex]

[tex] {r}^{2} = 100[/tex]

[tex]r = \sqrt{100} [/tex]

[tex]r = 10 \: miles[/tex]

Length of route = 10 miles

Hope this helps...

Good luck on your assignment...

Answer:

z = (X-Mean)/SD

X = Mean + (z*SD)

The z value which separates the bottom 75% (100%-25%) from the top 25% is + 0.6745

Therefore, Q3 = X = 107 + (0.6745*16) = 117.8

Step-by-step explanation:

Answer:

  Always true

Step-by-step explanation:

If you can't express the number as a ratio of integers, multiplying or dividing it by integers will not make it so you can.

If π is irrational, 2π is also irrational.

It is always true that the product of a rational and an irrational number is irrational.

Answer:

all ways true

Step-by-step explanation:

Answer:

[tex]\frac{16}{9}[/tex].

Step-by-step explanation:

[tex](2^8*3^{-5}*6^0)^{-2}*(\frac{3^{-2}}{2^3})^4*2^{28}\\ (2^8*\frac{1}{3^5}*1)^{-2}*\frac{\frac{1}{3^8} }{\frac{2^{12}}{1} }*2^{28} \\ (\frac{2^8}{3^5})^{-2} * \frac{1}{2^8*3^{12}} *2^{28}\\ \frac{1}{\frac{2^8*2}{3^{5*2}} } * \frac{1}{2^8*3^{12}} *2^{28}\\ \frac{\frac{1}{1} }{\frac{2^{16}}{3^{10}} } * \frac{1}{2^8*3^{12}} *2^{28}\\ \frac{3^{10}}{2^{16}} * \frac{1}{2^8*3^{12}} *2^{28}\\ \frac{2^{28}}{2^{24}*3^2} = \frac{2^4}{3^2}=\frac{16}{9}[/tex]

Answer:

Tublu has more than enough paint to cover the tank surface in one layer coating

Step-by-step explanation:

Height of the cylinder = 1.4 m

diameter of the cylinder = 1.1 m

total volume of paint available = 2 litres

It takes 250 ml to cover 1 m^2 of the tank body

Since only the body is to be painted, we find the perimeter of the circle formed by the body of the tank.

perimeter of the circle formed by the body of the  tank = [tex]\pi d[/tex]

==> 3.142 x 1.1 = 3.456 m

This perimeter, if spread out, will form a rectangle with a height of 1.4 m from the base.

The area of the rectangle that will be formed =  (perimeter of the cylinder body) x ( height of the cylinder)

==> 3.456 x 1.4 = 4.838 m^2

This is the area that needs to be painted.

Converting the paint volume,

250 ml = 0.25 litres

To paint the above calculated are, we will need 4.838 x 0.25 = 1.21 litres of paint, (of course, excluding the base)

The volume of paint available = 2 litres

volume of paint needed = 1.21 litres

Tublu has more than enough paint to cover the tank surface in one layer coating

Answer:

Step-by-step explanation:

According to the central limit theorem, if independent random samples of size n are repeatedly taken from any population and n is large, the distribution of the sample means will approach a normal distribution. The size of n should be greater than or equal to 30. Given n = 100 for both scenarios, we would apply the formula,

z = (x - µ)/(σ/√n)

a) x is a random variable representing the salaries of accounting graduates. We want to determine P( x > 52000)

From the information given

µ = 50402

σ = 6000

z = (52000 - 50402)/(6000/√100) = 2.66

Looking at the normal distribution table, the probability corresponding to the z score is 0.9961

b) x is a random variable representing the salaries of finance graduates. We want to determine P(x > 52000)

From the information given

µ = 49703

σ = 10000

z = (52000 - 49703)/(10000/√100) = 2.3

Looking at the normal distribution table, the probability corresponding to the z score is 0.9893

c) The probabilities of either jobs paying that amount is high and very close.

Answer:

The answer is "As the number of files increases, the storage space used decreases."

Step-by-step explanation:

When the music files are put into storage they take up space, this causes the storage space to decrease.

Answer:

As the number of files increases, the storage space used increases.

Question:

A cinema can hold 270 people at one performance 5/9 of the seats were occupied of the occupied seats 40% we occupied by concessionary ticket holders.

What is the number of seats occupied by concessionary ticket holders?.

Answer:

60 seats

Step-by-step explanation:

Given

Number of seats = 270

Occupied Seats = 5/9

Concessionary ticket holders = 40% of occupied Seats

Required

The number of seats occupied by concessionary ticket holders

First the number of occupied seat has to be calculated.

[tex]Occupied\ Seats = \frac{5}{9} * 270[/tex]

[tex]Occupied\ Seats = \frac{1350}{9}[/tex]

[tex]Occupied\ Seats = 150[/tex]

Next is to determine the number of seats occupied by concessionary ticket holders.

[tex]Number = 40\%\ of\ occupied\ seats[/tex]

[tex]Number = 40\%\ of\ 150[/tex]

Convert percentage to decimal

[tex]Number = 0.4 * 150[/tex]

[tex]Number = 60[/tex]

Hence, 60 seats were occupied by concessionary ticket holders.

Answer:

  A.)  The graph of g(x) is the graph of f(x) expanded vertically by a factor of 2, and translated 6 unit(s) up.

Step-by-step explanation:

For vertical expansion by a scale factor of k, the graph of f(x) is transformed to ...

  g(x) = k·f(x)

For translation up by k units, f(x) is transformed to ...

  g(x) = f(x) +k

___

Comparing the following ...

  f(x) = log(x)

  g(x) = 2·log(x) +6

We see that a multiplication factor and an addition factor have been applied. That means ...

  g(x) is f(x) expanded vertically by a factor of 2, and translated up 6 units.

Answer:

A.)  The graph of g(x) is the graph of f(x) expanded vertically by a factor of 2, and translated 6 unit(s) up.

Step-by-step explanation:

For vertical expansion by a scale factor of k, the graph of f(x) is transformed to ...

 g(x) = k·f(x)

For translation up by k units, f(x) is transformed to ...

 g(x) = f(x) +k

___

Comparing the following ...

 f(x) = log(x)

 g(x) = 2·log(x) +6

We see that a multiplication factor and an addition factor have been applied. That means ...

 g(x) is f(x) expanded vertically by a factor of 2, and translated up 6 units.

Step-by-step explanation:

I just used this and I got it correct

Answer:

Step-by-step explanation:

Hello,

We just need to apply the formula using the discriminant

[tex]-6x^2-2x+1=0\\\\\Delta = b^2-4ac = (-2)^2-*4(-6)*1=4+24=28[/tex]

so we have two distinct real solutions

[tex]x_1=\dfrac{2+\sqrt{28}}{2*(-6)}=\dfrac{2+2\sqrt{7}}{2*(-6)}=-\dfrac{\sqrt{7}+1}{6} \\\\ and \\\\x_2=\dfrac{\sqrt{7}-1}{6}[/tex]

Hope this helps

Answer:

245 might be the answer

Step-by-step explanation:

(7*7*10)/2

Answer:

( x, y ) = ( -20, 20 )

Step-by-step explanation:

Given data

Y = y(x)

3x + 2y = 20 ---------- equation 1

2x + 3y = 20 ---------- equation 2

find (x, y )

solving equation 1 and equation 2

3x + 2y = 20 * 2 = 6x + 2y = 40 --------- EQUATION 3

2x + 3y = 20 * 3 =  6x + 3y = 60 --------- EQUATION 4

cancelling out ( x )

Add both equation 3 and equation 4

5y = 100.  hence  y = 100/5 = 20

back to equation equation 2

2x + 3(20) = 20

2x = - 40

x = -20

attached is the graph  to check the answer

Answer:

the answer is C.

Step-by-step explanation:

64 ÷ 8 = 8

Answer:

c- 8cm squared

Step-by-step explanation:

plato

Answer:

7x-1

Step-by-step explanation:

The solution is : If f(x) = 5x – 2 and g(x) = 2x + 1, then the value of  (f+g)(x) is : 7x-1.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

given that,

If f(x) = 5x – 2 and g(x) = 2x + 1,

now, we have to find (f+g)(x).

so, we have,

f(x) = 5x – 2

and g(x) = 2x + 1

now,

(f+g)(x)

=f(x)+g(x)

=5x-2+(2x+1)

=5x-2+2x+1

=7x-1

Hence, The solution is : If f(x) = 5x – 2 and g(x) = 2x + 1, then the value of  (f+g)(x) is : 7x-1.

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Answer:

4 = 4

Step-by-step explanation:

=> 2x = 4

Putting x = 2

=> 2(2) = 4

=> 4 = 4

Answer:

Solution,

X= 2

Now,

2x=4

plugging the value of X,

2*2= 4

4 = 4 ( hence it is true)