Can anyone state the vertex of the graph?

The angle C = 103.85° using the sine rule and rounded to the nearest hundredth.

In trigonometry, the sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

Considering the ∆ABC, the sine rule states that;

(a/sinA) = (b/sinB) = (c/sinC)

so

25/sin120° = 20/sinB

sinB = (20 × sin120°)/25 {cross multiplication}

sinB = 0.6928

B = sin^(-1)[0.6928)] {sine inverse}

B = 43. 85°

Sum of interior angles in ∆ABC is 180° so;

C = 180° - (120° + 43.85°)

C = 180° - 76.15°

C = 103.85°

With the application of the sine rule, we can conclude that the value of the angle C is 103.85° rounded to the nearest hundredth.

Learn more about sine rule here: https://brainly.com/question/25852087

#SPJ1

The slope of the line that contains the the given points is 1/5 .

The slope of the line containing the two points (x₁ , y₁) and (x₂ , y₂) is calculated using the formula

slope = (y₂ - y₁)/(x₂ - x₁)

In the question ,

it is given that the

line contains the points x [tex]=[/tex] -4 , y [tex]=[/tex] -3

and x = 1 , y = -2 .

we need two points to find the slope of the line

Substituting the values in the formula for slope ,

we get

slope = (-2 -(-3))/(1-(-4))

= (-2+3)/(1+4)

= 1/5

Therefore , The slope of the line that contains the the given points is 1/5 .

Learn more about Slope here

https://brainly.com/question/16140473

#SPJ1

Answer: 6.2

Step-by-step explanation:

Geometric Mean = √( 2 x 19 ) = 2√38 = 6.1644

The percentage decrease in the number of students in the school was 10%.

The percentage refers to the ratio or proportion of students that reduced the number of the school population for the present year in comparison to last year's.

We can compute the percentage by finding the decrease in population and taking the result as a numerator of the total number in the last year and multiplying the result by 100.

Percentages represent fractional values and are usually depicted by the percentage sign (%).

The total number of students in the school last year = 1,200

The total number of students in the school this year = 1,080

The decrease in the number of students = 120 (1,200 - 1,080)

The percentage decrease = 10% (120/1,200 x 100)

Thus, we can conclude that the school population decreased by 10%.

Learn more about percentages at https://brainly.com/question/24877689

#SPJ1

Answer:

6

Step-by-step explanation:

Step-by-step explanation:

Angle BAC = angle BCA

as sum of angles in triangle = 180

49 + 49 + ABC = 180

180 - 49 - 49 = ABC

ABC = 82°

The quantity of sugar Isabelle would need to make 4 1/5 batches of cookies is 21 cups of sugar

From the question, we are to determine the quantity of sugar that Isabelle would need to make the given number of batches. The number of batches Isabelle wants to make is 4 1/5 batches.

From the given information, Isabelle's lemon cookie recipe calls for 5 cups of sugar. If 1 batch of the lemon cookie calls for 5 cups of sugar

Then, 4 1/5 batches of the lemon cookie will call for 5 × 4 1/5 cups of sugar 5 × 4 1/5

= 5 × 21/5= 21

Hence, Isabelle will need 21 cups of sugar

Learn more on Calculating the quantity of sugar here: https://brainly.com/question/16816423

#SPJ1

The probability is 8/9.

From the question, we have

probability = (1/3)*(1/3)*(1/3) = 1/27 chance (all of them lie)

probability = (2/3)*(2/3)*(2/3) = 8/27 chance (all of them true).

Since, they all say it's heads.

Thus, the probability of it being heads = (8/27)/ ((8/27)+(1/27)) = 8/9.

Probability:

Chance is referred to as probability. This branch of mathematics studies the probability of a random event. The value is between 0 and 1. Probability is a concept that mathematics has adopted to predict the likelihood of particular events. Probability is just the measure of how likely something is to occur. With the help of this fundamental theory of probability, which is also used to describe the probability distribution, you will be able to comprehend the possible results for a random experiment. How likely something is to occur can be determined using probability. It might be challenging to predict many things with complete certainty. We can only predict whether an event will occur or how likely it is using it, not if it will actually occur.

To learn more about probability visit: https://brainly.com/question/11234923

#SPJ9

Answer:

1/2

Step-by-step explanation:

if you take the (2,2) and make it (6,10), you add 4 to the x and 8 to the y. putting this as rise over run (x/y) it comes out to four eighths (4/8). reducing that comes out to one half (4/8).

The least sample size needed to assure with 90% confidence that the sample mean will not differ from the population mean by more than 5 minutes will be 416.16.

A normal distribution is a data set design in which the majority of values cluster around the middle of the range and the remainder taper off symmetrically toward either end. Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central location, with values decreasing as one moves out from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same. The normal distribution, like any other probability distribution, defines how the values of a variable are distributed. Because it properly captures the distribution of values for many natural occurrences, it is the most important probability distribution in statistics.

Here,

The z value at the 90 percent confidence interval is 1.645.

t ≥ z*s/√n

5≥1.645*62/√n

√n≥20.398

√n≥20.4

n≥416.16

The smallest sample size required to ensure that the sample mean does not deviate from the population mean by more than 5 minutes with 90% confidence is 416.16.

To know more about normal distribution,

https://brainly.com/question/17199694

#SPJ4

Answer:

-0.86

Step-by-step explanation:

What is the slope of the line created by this equation? Round your answer out to two decimal places. 6x + 7y = 5

_____________________________________________

Slope intercept form solves for y:

y = mx + b when m = slope and b = y-intercept

First, solve for y:

6x + 7y = 5

subtract 6x from both sides:

6x + 7y - 6x = 5 - 6x

7y = 5 - 6x

divide both sides by 7:

7y/7 = (5 - 6x)/7

y = 5/7 - 6/7x

rearrange right side:

y =  - 6/7x + 5/7

Back to the equation: y = mx + b when m = slope and b = y-intercept

your slope is -6/7

in decimal form, rounded to two digits: -0.86

Answer:

111%

Step-by-step explanation:

£3 × 60 = £180

(35 × £8) + ( 25 × £4) = £380

£380 ‐ £180 = £200

200/180 × 100% = 111% (nearest whole number)

Considering the dimensions of the rectangular prism and it's volume, it is found that:

The volume of a rectangular prism is given by the multiplication of the dimensions of the prism, which are the width symbolized by w, the height symbolized by h and the length symbolized by l, that is:

V = l x w x h.

In the context of this problem, from the image, the dimensions are given as follows:

Then the polynomial expression regarding the volume of the prism is obtained as follows:

V(x) = 2x(x - 3)(2x - 5)

V(x)= 2x(2x² - 11x + 15)

V(x) = 4x³ - 22x² + 30x.

The features of the polynomial expression V(x) = 4x³ - 22x² + 30x is obtained as follows:

A similar problem, also about the volume of a rectangular prism, is presented at brainly.com/question/22070273

#SPJ1

Using the concepts of co-ordinate geometry, we got that (1.14,3.17) is best set of co-ordinates for the equipment staging if art contractors must locate an equipment staging area to serve the three construction sites, located at (x,y) coordinates (0,3), (1,4) and (5,5).

So, for x co-ordinates how we can find the output, for this we need to find that co-ordinate in which stagging area is maximum.

So that co-ordinate is given = [x-coordinate of point A + x-co-ordinate of point y)/2.0]-1.36

=>the best x-co-ordinate is =[(0+5)/2.0]-1.36

=>the best x-co-ordinate is =1.14,

Similarly, for the y-co-ordinate

the best y-co-ordinate is given by =[[y-co-ordinate of point A+ y-co-ordinate of point B]/2.0] +0.67

=>the best y-co-ordinate is given by =[(0+5)/2/0]+0.67=2.5+0.67

=>the best y-co-ordinate is given by=(

Therefore, the best x and y co-ordinate is (1.14,3.17)

Hence, when art contractors  locate an equipment staging area to serve three construction sites, located at (x,y) coordinates (0,3), (1,4) and (5,5). traffic between the staging area and each of the sites is 30 trips a week, except for the site located at (5,5), which is only 10 trips a week. the best set of co-ordinates for the equipment staging area is (1.14,3.17).

To know more about co-ordinate-geometry, visit here:

https://brainly.com/question/28899589

#SPJ4

Answer:7

Step-by-step explanation:

yabba dabba doo

Answer: You cannot.

Step-by-step explanation:

3 can be multiplied into an odd number

4 cannot be multiplied into an odd number

6 cannot be multiplied into an odd number

8 cannot be multiplied into an odd number

Overall, you will not be able to get an odd number with the numbers provided.

Answer: 4683

Step-by-step explanation:

To have an odd number, and since the only odd number you have in your list is 3, that would be in the one's place. Then, you have to put the smallest number (except for 3) in the front. Now, you have two more places to fill in (4 _ _ 3). Like the 4, put the 6 after the 4 to have the smallest possible hundreds place. Now place the eight. Your final number should be... 4683.

Answer: y = x - 3

Step-by-step explanation:

Answer:

y = x+3

Step-by-step explanation:

First of all we have to find the equation of the line

Slope-intercept form is:

[tex]y=mx+b[/tex]

Putting the value of slope

[tex]y=x+b[/tex]

Putting the point in the equation

(-4,-1)

[tex]-2=-5+b\\b=-2+5\\b=3[/tex]

So the equation is:

[tex]y=x+3[/tex]

The graph is attached with the answer

Keywords: Equation of line, slope

Learn more about slope at:

brainly.com/question/5565320

brainly.com/question/5663052

#LearnwithBrainly

The sentence that describes a benefit of short-term disability insurance is D. It provides 40% to 60% of the policyholder’s income for up to one year.

Short-term disability insurance is meant to cover a portion of a person's wages in the event that they get injured such that they are unable to work and earn a salary in that time.

The short-term disability insurance policies these days generally cover about 40% to 60% of the income that the policyholder would have made in one year and so has less premiums.

Find out more on disability insurance at https://brainly.com/question/27571970

#SPJ1

Answer:

100% - 80%=20%

Step-by-step explanation:

that's the answer

"We are 95% confident that the mean sodium content for all beef hot dogs is between 353.2 and 449.1 mg." is the correct statement.

The true parameter must be properly and contextually stated.

We are researching confidence intervals for population means rather than for particular observations. The parameter is, to put it in plain English, the average sodium content of all beef hot dogs. The phrase "We are 95% confident" would be a better translation.

Thus the correct statement is as mentioned above.

To know more about population you may visit the link which is mentioned below:

https://brainly.com/question/27779235

#SPJ4

Answer:

Step-by-step explanation:

$9.85   / 10   ≈ $0.99

Answer:

[tex] = 3 + \sqrt{25 } - \sqrt{12} \\ = 3 + 5 - \sqrt{12 \\ } \\ = 8 - \sqrt{12} [/tex]

[tex] = 8 - 2 \sqrt{3} [/tex]

option d is correct

By using a trigonometric relation we will see that the height of the kite is 8.82 feet above the point where you hold the line.

We can view this as a right triangle, where the hypotenuse has a measure of 15 feet, we know one angle that measures 36°, and the opposite cathetus to that angle is x, the height we want to find.

We want to get the value of x, which is the opposite cathetus to the given angle, then we can use the trigonometric relation:

sin(a) = (opposite cathetus)/(hypotenuse)

Replacing what we know we will get:

sin(36°) = x/15ft

Solving this for x we get:

x = sin(36°)*15ft = 8.82ft

The height of the kite is 8.82 feet.

Learn more about right triangles:

https://brainly.com/question/2217700

#SPJ1

Step-by-step explanation:

I don't see the options and how they are written, but I can tell you the right answer in numbers :

sin(F) = 3/5 = 0.6

cos(F) = 4/5 = 0.8

sin(G) = 4/5 = 0.8

cos(G) = 3/5 = 0.6

why ?

remember the norm circle (radius 1) with ask the trigonometric functions.

the sine of an angle is the vertical height from that point in the circle arc down to x-axis.

the cosine of an angle is the length on the x-axis from the center of the circle to the point, where the sine touches the x-axis.

in any case, sine and cosine enclose the right angle (90°).

each function is now defined for the norm circle with radius = 1.

for angles in larger circles we need to divide the find lengths by the actual radius (we formality do this in the norm circle too, but a division by 1 does not change anything).

for the angles at F and G the radius is the side with the length 5.

Step-by-step explanation:

8x + 24 is a simplified expression.

It is not an equation, so it can't be solved.

There are two terms in 8x + 24, 8x and 24.

The two terms are unlike terms, so they cannot be combined together.

The answer of this question can be given by using congruence
Answer is 20°

What is an example of congruence?

Congruent relates to anything that is "exactly equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.

Given That:

∡DBC = 20°

DC = AD

DB is common on both triangle

As we have hypotenuse common in both triangle and 1 side equal then we can sa it is a congruent triangle by RHS

Learn more about congruence at

https://brainly.com/question/11949261

#SPJ9

The value of x in the angle illustrated as (5x + 2)° and (4x + 6)° is 4

It is important to note that line m and line n are parallel. In the diagram, they also intersect each other.

Therefore, it should be noted that according to angle rule, (5x + 2) and (4x + 6) are alternate angles. In this case, they're equal.

These will be illustrated as:

5x + 2 = 4x + 6

Collect like terms

5x - 4x = 6 - 2

x = 4

Therefore, x is 4°.

Learn more about angles on:

brainly.com/question/25716982

#SPJ1