Answers
Note that the area of the above triangle is given as: 42.
This is solved using the SOH CAH TOA Rule and the Formula of the Right Angled Triangle
The hypotenuse is the longest side of a right triangle, a "opposite" side is the one across from a given angle, and a "adjacent" side is the one close to a given angle. Right triangle sides are described using specific terminology. A right triangle's hypotenuse is always the side opposite the right angle.
To find the area of the triangle we must obtain, the Base and the Height, that is FD and A F.
Note that we have
∠F = 90°
∠D = 30°
Since the sum of angles in a Δ = 180°,
∠A = 180 - (90 + 30)
∠A = 60°
To find the area of the triangle we must obtain, the Base and the Height, that is F D and A F.
To obtain F D, we must use the Sine rule which states:
Sine θ = O/H; that is
Sin ∠A = F D/AD
Sin 60° = F D/14
0.86602540378 = FD/14
F D = 14 * 0.86602540378
F D = 12.1243556529
F D [tex]\approx[/tex] 12. 12
Using the above Cos Rule (CAH) we can find the Adjacent Side (that is height). Thus
Cos A = A F/AD
Cos 60° = A F/14
0.5 = A F/14; multiply both sides by 14
A F = 0.5 * 14
A F = 7
Now we have Adjacent Side (Height) = 7; and the Opposite Side (Base) = 12.12
The area of the Triangle according to the Pythagorean Rule is:
1/2 B * H
= 1/2 * 12.12 * 7
= 42.42
Thus the Area of the above triangle [tex]\approx[/tex] 42
Learn more about AAS Theorem:
https://brainly.com/question/12642646
#SPJ1
Related Questions
Select the correct answer. A linear function graph of the x-axis and y-axis has a diagonal line that passes the x-axis at (minus 0.5, 0), and the y-axis at (0, 1) In the function above, the slope will be multiplied by , and the y-value of the y-intercept will be increased by 3 units. Which of the following graphs best represents the new function?
Answers
Answer: Graph Y
Step-by-step explanation:
Which expressions represent rational numbers? Check all that apply
Answers
The expressions that represent rational numbers are; √64 + 6/11, √16 + √169 and 17.43 + √49.
What are the rational expressions?A rational number is simply any integer, terminating decimal/repeating decimal or fraction.
1) √6 + √9 = √6 + 3 → Not rational
2) √64 + 6/11 = 94/11 → Rational number
3) √36 + √21 = 6 + √21 → Not rational
4) √16 + √169 = 17 → Rational number
5) 17.4343434343434343 + √49 = 24.43434343 → Rational number
6) √44 + √25 = 2√11 + 5 → Not rational
Therefore, the expressions that represent rational numbers are; √64 + 6/11, √16 + √169 and 17.43 + √49.
Learn more about rational numbers here: https://brainly.com/question/17450097
#SPJ1
ASAP PLEASEEEEE: The perimeter of a triangle is 44 inches.If one side is 5 inches longer than the smallest side and another side is 1 inch less than twice the smallest side, how many inches are there in the smallest side?
Answers
The measure of the smallest side of the triangle is 10 inches
Perimeter of a triangleA triangle is a shape that has 3 sides and angles. The perimeter of a shape is defined as the sum of the sides of the figure.
Let the length of the smallest side be x
If one side is 5 inches longer than the smallest side, then;
L1 = x + 5
If another side is 1 inch less than twice the smallest side, then;
L2 = 2x - 1
Take the sum to have:
x+x+5+2x-1 = 44
4x+4= 44
Subtract 4 from both sides
4x =44 - 4
4x = 40
Divide both sides by 4
x = 40/4
x = 10
Hence the measure of the smallest side of the triangle is 10 inches
Learn more on perimeter of triangle here: https://brainly.com/question/24487269
#SPJ1
Common significance levels are 0.01 and 0.05. why would it be unwise to use a significance level with a number like 0.0483?
Answers
Common significance levels are 0.01 and 0.05. Because the observations in the sample do not come from a random pool, it is impossible to conduct a test based on a population percentage by utilizing the normal approximation approach. This is further explained below.
What is probability?Generally, The possibility of an occurrence may be quantified using the concept of probability. There are many occurrences that cannot be foreseen with complete accuracy.
In conclusion, Both 0.01 and 0.05 are considered to be significant values. It is not feasible to perform a test based on a population percentage using the normal approximation technique because the observations in the sample do not originate from a random pool. This makes it impossible to utilize the normal approximation approach.
Read more about probability
https://brainly.com/question/11234923
#SPJ1
Hurricane Andrew swept through southern Florida causing billions of dollars of damage. Because of the severity of the storm and the type of residential construction used in the semitropical area, there was some concern that the average claim size would be greater than the historical average hurricane claims of $24,000. Several insurance companies collaborated in a data gathering experiment. They randomly selected 84 homes and sent adjusters to settle the claims. In the sample of 84 homes, the average claim was $27,5000 with a population standard deviation of $2400. Is there sufficient evidence at a 0.02 significance level to support the claim that the home damage is greater than the historical average? Assume the population of insurance claims is approximately normally distributec. Compute the value of the test statistic.
Answers
The value of the t test is 13.36, we have to conclude that there is sufficient evidence that suggests that insurance adjustment was greater than $2400.
The hypothesis formulationH0: u = 24000
H1: u > 24000
This test is a right tailed testwe have n = 84 homes
bar x = 27500
s = 2400
Next we have to find the test statistic
The formula for this is given as
[tex]t = \frac{x-u}{s/\sqrt{n} }[/tex]
When we out in the values we would have
[tex]t = \frac{27500-24000}{2400/\sqrt{84} }[/tex]
This would give us the answeer of the t test as
t test = 13. 3658
We have alpha = 0.02
the degree of freedom = 84 - 1 = 83
we have to find tα/2, df
= ±2.0865
Given that the value of the test statistic is greater than critical value we would have to then reject the null hypothesis.
Hence the conclusion that we can make is that there is sufficient evidence that suggests that insurance adjustment was greater than $2400.
Read more on statistics here
https://brainly.com/question/4219149
#SPJ1
What is the result of taking the difference between sample means, minus the null hypothesized difference, divided by the standard error of the difference between means?
Answers
The result of taking the difference between sample means, minus the null hypothesized difference, divided by the standard error of the difference between means is the t-statistic.
What is a t-statistic?When deciding whether to accept or reject the null hypothesis in a T test, the t-statistic is used. It functions similarly to a Z-score in that you choose a cutoff point, calculate your t score, and then compare the two. When you have a limited sample size or don't know the population standard deviation, you utilize the t-statistic.
On its own, the t-statistic doesn't actually reveal much. Similar to how the word "average" is meaningless on its own without any context.
Learn more about t-statistic here:
https://brainly.com/question/28000141
#SPJ4
The ratio of color paper to white is 3:8, if there is 48 white paper how many is colour
Answers
There might be 18 colored papers.
colored papers to white papers:
3:8
48 white papers
8x6 = 48
Then 3x6= 18
There might be 18 colored papers.
Ratios evaluate numbers, normally through dividing them. in case you are evaluating one facts factor (A) to another statistics factor (B), your formulation might be A/B. this indicates you are dividing data A by using information B. for example, if A is 5 and B is 10, your ratio will be 5/10.
In mathematics, a ratio indicates how many times one quantity incorporates some other. for instance, if there are 8 oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is 8 to 6. further, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the full amount of fruit is 8:14.
Ratios can be absolutely simplified just like fractions. To simplify a ratio, divide all the numbers in the ratio through the same wide variety until they can not be divided anymore.
Learn more about ratio here https://brainly.com/question/13513438
#SPJ4
Question 6 of 25
A high school teacher grades a math test. She wants to see the numerical
grade of each student. Which item should she use so she can quickly see
how many students got each score?
A. None of these
B. Frequency table
OC. Line plot
OD. Pie chart
Answers
The polygon circumscribes the circle. Which of the following is the perimeter of the polygon?
A. 39 cm
B. 56 cm
C. 61 cm
D. 78 cm
Answers
The perimeter of the polygon that circumscribes the circle is 78 cm
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The circle tangent theorem states that tangents which meet at the same point are equal in length. Hence:
The missing lengths are 8, 6, 9 and 16.
Perimeter of the polygon = 2(8) + 2(6) + 2(9) + 2(16) = 78 cm
The perimeter of the polygon that circumscribes the circle is 78 cm
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
The ratio of butter:flour:sugar in a recipe is 1:9:6. When using 8 cups of sugar in this recipe, how many total cups of ingredients will be used
Answers
Answer:
21 and a third cups bxisjsbdn
13. If 3x = xy - 5 and y = 6, what is the value of x? (A) (C) / (B) 3) - 5 (D) slas1 5 اقعا our win
Answers
Answer:
x = 5/3
Step-by-step explanation:
3x = xy - 55
3x = x*6 - 5
3x = 6x - 5
3x = 5
x = 5/3
what is x and y? i’m having trouble finding what x and y are
Answers
Answer:
y is 7, x is 14
Step-by-step explanation:
This is a 30-60-90 triangle,
The hypotenuse, the side opposite of the 90 degree angle, is twice the length of the side opposite of the 30° angle,
The side opposite of the 60° degree angle, is root 3 times the side opposite of the 30° degree angle
So y is
[tex] \frac{7 \sqrt{3} }{ \sqrt{3} } = 7 = y[/tex]
Then, that means x is
[tex]7 \times 2 = 14[/tex]
Triangle RST has sides measuring 22 inches and 13 inches and a perimeter of 50 inches. What is the area of triangle RST? Round to the nearest square inch.
Heron’s formula: Area
19 square inches
37 square inches
60 square inches
95 square inches
Answers
Using the Heron's formula, the area of the triangle is: D. 95 square inches.
What is the Heron's Formula?Area = √[s(s - a)(s - b)(s - c)] where s is half the perimeter, or (a + b + c)/2.
Given the following:
s = semi-perimeter = 1/2(50) = 25 in.
a = length of side a = 22 in.
b = length of side b = 13 in.
c = length of side c = 50 - 22 - 13 = 15 in.
Plug in the values
Area = √[25(25 - 22)(25 - 13)(25 - 15)]
Area = √[25(3)(12)(10)]
Area ≈ 95 square inches.
Learn more about the Heron's formula on:
https://brainly.com/question/10713495
#SPJ1
Answer:
d
Step-by-step explanation:
Mrs. Anderson had twice as many chickens as ducks. she sold 272 chickens and 16 ducks. She then had half as many chickens as ducks. How many chickens does she have?
Answers
The number of chickens she had was 352
Applications of equationsFrom the question, we are to determine the number of chicken she has
Let c represent chicken
and d represent ducks
From the given information,
Mrs. Anderson had twice as many chickens as ducks
c = 2d ---------- (1)
She sold 272 chickens and 16 ducks and then had half as many chickens as ducks
(c-272) = 1/2(d -16) ---------- (2)
Put equation (1) into (2)
2d - 272 = 1/2(d - 16)
2(2d - 272) = d- 16
4d - 544 = d - 16
4d - d = 544 - 16
3d = 528
d = 528/3
d = 176
Substitute the value of d into equation (1)
c = 2d
c = 2(176)
c = 352
Hence, the number of chickens she had was 352
Learn more on Equations here: https://brainly.com/question/148035
#SPJ1
After working 80 hours at his job, Tyshawn earned a total of $1080. How much does Tyshawn earn
per hour?
Answers
The amount Tyshawn earn per hour is $13.5
Ratio and proportionFractions are written as a ratio of two integers
If after working 80 hours at his job, Tyshawn earned a total of $1080, then;
80 hrs = $1080
In order to calculate the amount earned per hour
Amount per hour = 1080/80
Amount per hour = $13.5
Hence the amount Tyshawn earn per hour is $13.5
Learn more on ratio here: https://brainly.com/question/25927869
#SPJ1
20 PIONTSSS TO WHOEVER ANDWER THIS QUESTION !!! NEED HELP
Answers
The surface area of prism 1 is 36 cm²
Calculating surface areaFrom the question, we are to calculate the surface area of prism 1
From the given information, we have that the two hexagon-based prism are similar
Since the shapes are similar, we can write that
(Length of a side in prism 1)² / (Length of the similar side in prism 2)² =
Area of prism 1 / Area of prism 2
From the given information,
Length of a side in prism 1 = 3 cm
Length of the similar side in prism 2 = 8 cm
Area of prism 2 = 256 cm²
Thus,
3² / 8² = Area of prism 1 / 256
Area of prism 1 = (256 × 3²)/ 8²
Area of prism 1 = (256 × 9)/ 64
Area of prism 1 = (2304)/ 64
Area of prism 1 = 36 cm²
Hence, the surface area of prism 1 is 36 cm²
Learn more on Calculating area here: https://brainly.com/question/21406326
#SPJ1
Which piece of additional information can be used to prove triangle cea triangle cdb
Answers
Answer:
well I don't get the question
How many triangles are there?
Answers
Answer:
15 triangles.
Step-by-step explanation:
just count them eventually you will reach there.
Use the graph to find the solution.
Given the graph of w(x), w(2) = ?
(the graph is below)
THE FIRST ANSWER WILL GET BRAINLIEST OR 5 STARS! PLEASE ANSWER QUICK :)
Answers
Answer:
W(2) = 5
Step-by-step explanation:
Because when you look at the graph, the y value is 5 when the x value is 2.
Answer:
w(2) = 5
Step-by-step explanation:
by using rise over run to find the slope easily, you get a slope of 4 and an equation of w(x) = 4x - 3, -3 being the y-intercept
to calculate w(2):
w(2) = 4(2) - 3
w(2) = 8 - 3
w(2) = 5
or you could just look at when y is 2 and see that the corresponding x value is 5 but i wanted to provide a longer explanation in case :)
After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly.
The relationship between the elapsed time ttt, in seconds, and the number of bacteria, B_{\text{second}}(t)B
second
(t)B, start subscript, start text, s, e, c, o, n, d, end text, end subscript, left parenthesis, t, right parenthesis, in the petri dish is modeled by the following function:
Bsecond(t)=6000⋅(1516)t
Complete the following sentence about the rate of change in the number of bacteria in minutes.
Answers
After a special medicine is introduced into a petri dish full of bacteria, Every second, the number of harmful bacteria remaining in the body decays by a factor of 0.97
What is bacteria?Generally, a kind of unicellular bacteria that has characteristics with many disease-causing organisms, such as having a cell wall but lacking organelles and an organized nucleus.
In conclusion, When a certain medication is put into a petri dish that is full of bacteria, the amount of pathogenic bacteria that are still present in the body decreases by a factor of 0.97 every single second.
Read more about bacteria
https://brainly.com/question/8008968
#SPJ1
Which of the following values is not a perfect square?
a.81
b.125
c.49
d.100
Answers
Answer: b. 125
Step-by-step explanation:
Find the square roots of each, and if the square root is a decimal, it is not a perfect square.
Square root of 81: 9
Square root of 49: 7
Square root of 100: 10
That leaves 125.
C:49
How to find the answers?
Answers
The computation shows that the value of blue which is represented by x is 12.
How to calculate the value?From the information given, it was stated that 30 people were in the kindergarten.
Green = 10
Red = 8
Blue (x) = 30 - (10 + 8)
= 30 - 18
= 12
Since the teacher want to paint the class with the most favorite color, the appropriate color to use will be blue.
Learn more about computations on:
brainly.com/question/4658834
#SPJ1
An angle measures 8.8° more than the measure of its complementary angle. What is the measure of each angle?
Answers
Based on the definition of complementary angles, the two angles are: 49.4° and 40.6°.
What are Complementary Angles?Angles that are complementary angles have a sum of 90 degrees.
Let the angle be represented as x
Complement of the angle = (90 - x)
Therefore, we would have:
x = (90 - x) + 8.8
x = 90 - x + 8.8
x = 98.8 - x
x + x = 98.8
2x = 98.8
x = 98.8/2
x = 49.4°
The second angle would be: 90 - 49.4 = 40.6°
The angles are 49.4° and 40.6°.
Learn more about complementary angles on:
https://brainly.com/question/16281260
#SPJ1
Find the missing side length in the image below.
Answers
Answer:
6 is the ?
Step-by-step explanation:
place 3 numbers between 12 and 60 to make a sequence of 5 numbers with a common difference
Answers
Answer:
12-24-36-48-60
if I'm wrong I will try to get back to you and right my wrong
You start driving west for 20 miles, turn left, and drive south for another 14 miles. At the end of driving, what is your straight line distance from your starting point? Round to the nearest tenth of a mile
Answers
Answer:
24.4
Step-by-step explanation:
Which one of the following foods is the top source of protein chosen by Americans in the United States?
Answers
Answer:
The correct answer is beef
Step-by-step explanation:
I took the quiz and got it correct
Angle 0 intersects the unit circle at point (-0.9483, -0.3173). What is the value of tan(0)
Answers
The tangent in the unit circle is equal to 0.334.
How to calculate the value of the function tangent with the help of a unit circle
In trigonometry, unit circles are representations of a circle with radius 1 and centered at the origin of a Cartesian plane commonly use to estimate and understand angles and trigonometric functions related to them.
Angles are generated by line segments whose coordinates are of the form (x, y), where x is the position of the terminal point along the x-axis and y is the position of the terminal point along the y-axis.
In addition, the tangent of the angle generated in a unit angle is defined by the following equation:
tan θ = y / x (1)
If we know that x = - 0.9483 and y = - 0.3173, then the tangent of the angle generated in the unit circle is:
tan θ = (- 0.3173)/(- 0.9483)
tan θ = 0.334
The tangent in the unit circle is equal to 0.334.
To learn more on trigonometric functions: https://brainly.com/question/23599274
#SPJ1
all numbers less than 7 and greater than 7
Answers
Step-by-step explanation:
123456 less then 7
unlimited greater then 7
The numbers from negative infinity to 7, excluding 7."are less than 7 and "all numbers from 7 to positive infinity, excluding 7" are more than 7.
The combination of positive, negative numbers including 0 are called as integers.
The numbers less than 7 are:
This set includes all real numbers that are strictly less than 7.
It can be denoted as (-∞, 7), which means "all numbers from negative infinity to 7, excluding 7."
The numbers greater than 7 are:
This set includes all real numbers that are strictly greater than 7. It can be denoted as (7, +∞), which means "all numbers from 7 to positive infinity, excluding 7."
Thus, there are infinite numbers which are less than 7 and more than 7.
Learn more about integers here:
https://brainly.com/question/28992018
#SPJ3
help pls im so confused
10(1^2*2^-2)
Answers
Answer:
2.5(or 5/2 or 2 1/2)
Step-by-step explanation:
Remember PEMDAS
10 * (1^2 * 2^-2)
10 * (1 * 0.25)
10 * 0.25 =
2.5