Answer: option c
Step-by-step explanation:
You need to use this formula:
[tex]A=\frac{h}{2}(B+b)[/tex]
Where "h" is the height of the trapezoid, "B" is the larger base and "b" is the smaller base.
You know that:
[tex]B=16.8yd\\b=6.9yd\\h=2yd[/tex]
Then you need to substitute these values into the formula [tex]A=\frac{h}{2}(B+b)[/tex].
Therefore, the area of this trapezoid is:
[tex]A=\frac{2yd}{2}(16.8yd+6.9yd)[/tex]
[tex]A=23.7yd^2[/tex]
Answer:
23.7 yd2
Step-by-step explanation:
Please answer thank you
Answer:
Yes, (0,4) is a solution
Step-by-step explanation:
We have to plug in 0 in x and 4 in y IN BOTH THE INEQUALITIES.
IF BOTH ARE TRUE, then the system of inequalities is TRUE.
Let's check:
y ≤ -3x+4
4 ≤ -3(0)+4
4 ≤ 4
Is 4 less than OR equal to 4? Yes. THis is satisfied.
Now, checking 2nd one:
y > x^2 + 3x - 2
4 > (0)^2 + 3(0) - 2
4 > -2
Is 4 greater than -2? Yes, it is. So this is satisfied as well.
Hence, (0,4) is a solution to the system of inequalities shown.
Answer:
Yes, it is the solution
Step-by-step explanation:
You are given the system of two inequalities
[tex]\left\{\begin{array}{l}y\le -3x+4\\ \\y>x^2+3x-2\end{array}\right.[/tex]
To check whether point (0,4) is the solution to this system, substitute x=0 and y=4 into each inequality:
1.
[tex]4\le -3\cdot 0+4\\ \\4\le 4 \ [\text{true}][/tex]
2.
[tex]4>0^2+3\cdot 0-2\\ \\4>0+0-2\\ \\4>-2\ [\text{true}][/tex]
Since the coordinates of the point (0,4) satisfy both inequalities, the point (0,4) is the solution to the system
220 students were asked if they liked chocolate or vanilla ice cream. 140 said they liked chocolate and 120 said they like vanilla. How many student like both?
We have 220 students total.
140 like Chocolate.
120 like Vanilla.
140+120=260.
260 is 40 more than 220.
Therefore there are 40 students who said they like both.
I hope this helps! :)
Final answer:
By applying the principle of inclusion-exclusion, we found that 40 students like both chocolate and vanilla ice cream.
Explanation:
To determine how many students like both chocolate and vanilla ice cream, we need to use the principle of inclusion-exclusion. This principle is a fundamental counting technique in mathematics that considers the overlap of two sets.
According to the principle, if we have two overlapping sets, we can find the number of elements that are in both sets by adding the number of elements in each set (in this case, the number of students who like chocolate and the number of students who like vanilla) and then subtracting the number of elements that have been counted twice (the students who like both).
The formula we will use is: Number of students liking both = (Number of students liking chocolate) + (Number of students liking vanilla) - (Total number of students surveyed).
Applying the formula:
Number of students liking chocolate = 140
Number of students liking vanilla = 120
Total number of students surveyed = 220
Number of students liking both = 140 + 120 - 220 = 40.
Therefore, 40 students like both chocolate and vanilla ice cream.
Which of the following is recommended when paying a credit card bill?A. Pay the minimum amount every month.B. Pay exactly half the minimum amount every month.C. Pay less than the minimum amount every month.D. Pay more than the minimum amount every month.
Answer: d
Step-by-step explanation:
However much more you pay over the minimum will be applied to the principle, which means it will take less time to pay the credit card bill off
When paying a credit card bill, it is recommended to pay more than the minimum amount every month to reduce the principal balance faster and avoid accruing high interest. This practice leads to less overall cost and faster debt elimination.
The recommended practice when paying a credit card bill is D. Pay more than the minimum amount every month. This is crucial because paying only the minimum amount mostly covers the interest and only a small part of the principal balance. Interest accrues on the remaining balance, leading to higher overall costs.
By paying more than the minimum, you reduce the principal balance faster, thereby reducing the amount of interest that can accumulate. For instance, if two friends both have $2,000 in credit card debt but one pays just the minimum while the other adds an additional $10 each month, the latter will pay off their debt quicker and accrue less interest overall.
Managing credit effectively involves more than just timely payments; it's also about managing your credit utilization and striving to pay off the full balance as quickly as possible. This avoids the high-interest rates that can double the initial amount over time if only minimum payments are made.
$3.36 for 1.4 pounds of grapes what is the unit rate per pound of grapes??????? I really need to know.... Yeet
Answer: 2.4 per pound you have to divide $3.36 and 1.4 pounds and you get your answer. Please mark me the brainliest answer? Hope this helped have a good day :)
OMG IS THAT A CURSED IMAGE?!?!?! :D
Based on the information given the unit rate per pound is 2.4.
Using this formula
Unit rate per pound=Costs/Pounds
Where:
Cost=$3.36
Pounds=1.4 pounds of grapes
Let plug in the formula
Unit rate per pound=$3.36/1.4
Unit rate per pound=2.4
Inconclusion the unit rate per pound is 2.4.
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Paul has 183 stamps his friends gave 15 stamps for his birthday how many stamps does Paul have after he received stamps from his friend?
Answer:
198.
Step-by-step explanation:
183+15=198
Hello!
If Paul already has 183 stamps, just add 15 more because that is how much his friend gave him and you will get 198 stamps
The diagram below shows the dimensions of Tessa’s garden.
C) Tessa decided that she liked the shape of her garden but wanted to have 2 times the area. She drew a design for a garden with every dimension multiplied by 2. Explain the error in Tessa’s design.
Answer:
Tessa's mistake was to have multiplied each dimension by two instead of multiplying by a square root of two.
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z -----> the scale factor
x ----> the area of the enlarged garden
y ----> the area of the original garden
[tex]z^{2}=\frac{x}{y}[/tex]
we have that
If Tessa multiplies each dimension by 2, then the scale factor equals 2.
[tex]z=2[/tex]
substitute
[tex]2^{2}=\frac{x}{y}[/tex]
[tex]4=\frac{x}{y}[/tex]
[tex]x=4y[/tex]
The area of the enlarged garden will be equal 4 times the area of the original garden
so
If Tessa wanted to have twice as much surface, she must multiply each dimension by a square root of 2.
therefore
Tessa's mistake was to have multiplied each dimension by two instead of multiplying by a square root of two.
An equilateral triangle has sides of length 20. To the nearest tenth, what is the height of the equilateral triangle.
A). 10.0
B).11.5
C).17.3
D).23.1
Answer:
C. 17.3
Step-by-step explanation:
Using Pythagoras theorem
Divide the triangle into half
c^2=a^2+b^2
20^2=a^2+10^2
400=a^2+100
400-100=a^2
300=a^2
17.32=a^2
The height of the equilateral triangle to the nearest tenth is 17.3
Given that:
An equilateral triangle has sides of length 20.
Equilateral triangles are the type of triangles which has all the sides equal to each other.
That is, three sides will have equal length.
So all the side of the triangle is 20.
The height of the triangle is the perpendicular line drawn from any of these vertices.
Since this is an equilateral triangle, the height divides the base into equal lengths.
So each half will be 20/2 = 10.
Here, a right angle is formed.
Using Pythagoras theorem,
h = √(20² - 10²)
= √(400 - 100)
= √300
= 17.3
Hence the correct option is C.
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what is a rational number whose square root is a whole number?
Answer:
4
Step-by-step explanation:
For example, 4.
4 is rational since it can be written as a fraction of integers. 4 = 4/1
The square root of 4 is 2, and 2 is a whole number.
the number of cells in a sample doubles every minute. A doctor with a sample of 25 cells and predicted that, after 5 minutes, he would have 32 cells. Is his prediction reasonable? Explained
Answer: No, his prediction is unreasonable. After 5 minutes, the number of cells would be 400, not 32. See the explanation below for details.
-------
Remember:
[tex]a_{n}[/tex] = [tex]n[/tex]th term[tex]n[/tex] = number of terms[tex]a_{1}[/tex] = first term[tex]r[/tex] = common ratio-------
Identify the given information.
[tex]a_{1}[/tex] = 25
[tex]r[/tex] = 2
Use the explicit formula for geometric sequences.
[tex]a_{n} = a_{1} r^{n - 1}[/tex]
Substitute the given values.
[tex]a_{n} = (25)(2)^{n - 1}[/tex]
Substitute in 5 for [tex]n[/tex] to find out how many cells there would be after 5 minutes.
[tex]a_{5} = (25)(2)^{5 - 1} \\\\a_{5} = (25)(2)^{4} \\\\a_{5} = (25)(16)\\\\a_{5} = 400[/tex]
Final answer:
The doctor's prediction of 32 cells after 5 minutes is not reasonable, because based on exponential growth of doubling every minute, 25 initial cells should grow to 800 cells in that time period.
Explanation:
The given question involves the calculation of cell numbers in a growing population, which relates to the field of exponential growth. Using the information provided that the number of cells doubles every minute, we can apply the formula for exponential growth, which is [tex]2^{n}[/tex], where 'n' is the number of generations or minutes in this case.
Starting with 25 cells, after 5 minutes, the expected number of cells would be calculated by multiplying 25 by 25 (since the cells double every minute). This calculation gives us 25 * 32, which equals to 800 cells after 5 minutes. Therefore, the doctor's prediction that there would only be 32 cells after 5 minutes is not reasonable, as the correct calculation suggests the number should be much higher.
3. Pamela also makes and sells custom dog collars. If she sells small conta
nd sells custom dog collars. If she sells small collars for $4.75 and
large ones for $7.75, what was her revenue last month if she sold 20 small and 14 large
collars?
____________________________________________________
Answer:
$203.5
____________________________________________________
Step-by-step explanation:
In order to find the answer to your question, we would need to find how much money she made when selling the collars.
Lets gather the important information:
$4.75 for small collar
$7.75 for large collar
With the information above, we can solve the problem.
What we would do is multiply the amount of collars that was sold to the right price.
Therefore, we would multiply 4.75 by 20, since small collars cost 4.75 and she sold 20 of them. We would also multiply 7.75 by 14, since large collars cost 7.75 and she sold 14 of them.
Lets calculate:
[tex]4.75*20=95\\\\7.75*14= 108.50[/tex]
Now, we would add the final prices together in order to find how much revenue she made off of the collars.
[tex]95+108.50=203.5[/tex]
When you're done soplving, you should get 203.5.
This means that her revenue last month was $203.5.
$203.5 should be your FINAL answer.
____________________________________________________
Answer:
205.50
Step-by-step explanation:
Evaluate the function!!! 10 points. Help needed!
ANSWER
[tex]f( - 3) = - \frac{9 }{7} [/tex]
EXPLANATION
The given function is
[tex]f(x) = \frac{2 {x}^{2} }{3x - 5} [/tex]
We want to find f(-3)
We substitute x=-3 into the function to get;
[tex]f( - 3) = \frac{2 {( - 3)}^{2} }{3( - 3) - 5} [/tex]
Simplify;
[tex]f( - 3) = \frac{2 \times 9 }{ - 9- 5} [/tex]
[tex]f( - 3) = - \frac{18 }{ 14} [/tex]
[tex]f( - 3) = - \frac{9 }{7} [/tex]
A right triangle has a leg of 12 cm and a hypotenuse of 19 cm.
What is the length of the other leg?
Round to the nearest tenth.
7.0 cm
14.7 cm
22.5 cm
217.0 cm
Answer:
B. 14.7
Step-by-step explanation:
You would need to use the Pythagorean Theorem to find the length of the other leg. But you basically have to use it backwards. The theorem is a^2+b^2=c^2.
Substitute the values: a^2+12^2=19^2
Calculate the exponents: a^2+144=361
Subtract 144 from both sides: a^2=217
Find the square root of 217: 14.70309
Round to the nearest tenth: 14.7
almost done please help
Answer:
[tex]a_{n} =1.7n+(n-1)0.5[/tex]
Step-by-step explanation:
I hope this helps.
Answer:
an = .5n +1.2
Step-by-step explanation:
The formula for an arithmetic sequence is given by
an =a1 + d(n-1) where a1 is the first term and d is the common difference
an = 1.7 + .5 (n-1)
Distribute
an = 1.7 + .5n - .5
Combine like terms
an = .5n +1.2
Verify that parallelogram ABCD with vertices...
PLEASE HELP ME ASAP! I’m in a dead line!!! Please help!
Answer:
Its diagonals are perpendicular, then it is a rhombus
Step-by-step explanation:
* Lets revise the properties of the parallelogram and the rhombus
- In the parallelogram each two opposite sides are parallel
- In the parallelogram each two opposite sides are equal in length
- In the parallelogram the diagonals bisect each other
- In the rhombus each two opposite sides are parallel
- In the rhombus all the sides are equal in length
- In The rhombus the diagonals are perpendicular to each other
- Parallelogram is a rhombus if two adjacent sides are equal in length
- Parallelogram is a rhombus if its two diagonals are perpendicular
* Now lets solve the problem
∵ The vertices of the parallelogram are
A(-3 , 2) , B(-2 , 6) , C (2 , 7) , D (1 , 3)
- The slope of the line which passes through points (x1 , y1) and (x2 , y2)
is m = (y2 - y1)/(x2 - x1)
* lets find the slopes of the sides and the diagonals
∵ The slope of AB = (6 - 2)/(-2 - -3) = 4/1 = 4
∵ The slope of BC = (7 - 6)/(2 - -2) = 1/4 = 1/4
∵ The slope of CD = (3 - 7)/(1 - 2) = -4/-1 = 4
∵ The slope of DA = (2 - 3)/(-3 - 1) = -1/-4 = 1/4
- The product of the slopes of the perpendicular line is -1
∵ AB and BC are two adjacent sides and the product of their slopes
= 4 × 1/4 = 1 ≠ -1
∴ AB and BC are not perpendicular
∴ The parallelogram can not be a rectangle
- Lets check the slopes of the diagonals
∵ The diagonals of the parallelogram are AC and BD
∵ The slope of AC = (7 - 2)/(2 - -3) = 5/5 = 1
∵ The slope of BD = (3 - 6)/(1 - -2) = -3/3 = -1
∵ The product of the slopes of AC and BD = 1 × -1 = -1
∴ AC and BD are perpendicular
∴ ABCD is a rhombus
What is the simplified expression for the expression below? 4(3x – 2) + 6x(2 – 1) 24x – 3 18x – 8 18x – 7 24x – 14
Answer:
18x-8
Step-by-step explanation:
Given expression:
=4(3x-2)+6x(2-1)
The expression has to be simplified using the basic rules of mathematics,
In order to simplify the given expression,
We can see that the expression written in second bracket (2-1) which can be solved so,
=4(3x-2)+6x(1)
Multiplying 4 inside the bracket (3x-2)
=12x-(4)(2)+6x
=12x-8+6x
=18x-8 ..
Answer:
The answer is 18x - 8
Step-by-step explanation:
What is the relationship between ∠3 and ∠4?
Answer:
Angle 3 and angle 4 are linear pair
Step-by-step explanation:
* Lets revise the types of angles
- If two line intersected at a point, there are two types of
pairs of angles
- Two vertically opposite angles equal in measure
- Linear pair of angles their sum is 180°
* Now lets solve the problem
- There are two lines intersect each other at a point
- They formed between them 4 angles
- Angle 2 and angle 4 are vertical opposite angles, equal in measure
- Angle 1 and angle 3 are vertical opposite angles, equal in measure
∴ m∠2 = m∠4
∴ m∠1 = m∠3
- Angle 1 and angle 2 formed a line
∴ They are linear pair of angles
- Angle 3 and angle 4 formed a line
∴ They are linear pair, of angles
∵ m∠1 + m∠2 = 180°
∴ m∠3 + m∠4 = 180°
* Angle 3 and angle 4 are linear pair
What is the y-intercept of the function f(x)=-2/9x+1/3?
To find the y intercept replace the x in the equation with zero and solve
-2/9(0) + 1/3
0 + 1/3
The y-intercept is:
(0, 1/3)
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
y intercept is 1/3
Step-by-step explanation:
[tex]f(x)=-\frac{2}{9} x+ \frac{1}{3}[/tex]
To find y intercept we plug in 0 for x
Y intercept point is a point where the graph f(x) crosses y axis.
At y intercept, the value of x is 0
to find y intercept we plug in 0 for x
[tex]f(0)=-\frac{2}{9} (0)+ \frac{1}{3}[/tex]
[tex]f(0)=\frac{1}{3}[/tex]
Would appreciate the help.
Answer:
a° = 80° , b° = 40° , c° = 40° , d° = 100°
Step-by-step explanation:
* Lets study the information in the question to solve it
- There is a circle and two chords of it are parallel
∵ The two chords are parallel
- The measure of b° is the same with the angle of measure 40°
because they are alternate angles
∴ b° = 40°
- The vertex of the angle of measure 40° is on the circle
∴ This angle is inscribed angle subtended by the arc of measure a°
- There is a relation between the inscribed angle and its subtended arc,
the measure of the arc is twice the measure of the angle
∵ The measure of the angle is 40°
∴ a = 40° × 2 = 80°
∴ a° = 80°
- In the circle any two inscribed angles subtended by the same arc
are equal in measure
∵ The angle of measure 40° and the angle of measure c° are
inscribed angles subtended by the same arc of measure a°
∴ c° = 40°
- The sum of the measures of the interior angles in any triangles is 180°
∴ b° + c° + d° = 180° ⇒ interior angles of a Δ
∵ b° = 40° , c° = 40°
∴ 40° + 40° + d° = 180° ⇒ add
∴ 80° + d° = 180° ⇒ subtract 80 from both sides
∴ d° = 100°
20 points for the RIGHT answer! help a sis out asap
Answer:
1. B nearly 70%
2. C nearly 9%
Step-by-step explanation:
1. There are 26 people which agree with the question and 61 people which disagree with the question. In total, 26+61=87 people.
So,
[tex]\dfrac{61}{87}\cdot 100\%\approx 70\%[/tex]
disagree with question 1.
2. There are 87 people in total and only 8 females agree with question, so
[tex]\dfrac{8}{87}\cdot 100\%\approx 9\%[/tex]
of females agree with the question 1.
Answer:
Q1: about 70%
Q2: about 9%
Step-by-step explanation:
Question 1:
The grand total number of people is the right and bottom most cell, which is the addition of the column or the row. So grand total = 60 + 27 = 87 (or 61 + 26 = 87)
The number of people (BOTH MALE AND FEMALE) that disagreed with question 1 is 61.
As a percentage, that would be (61/87) * 100 = 70.11%, which is about 70%
Question 2:
Here, the total number of people is still the same, 87. We want the number of females that agreed. So we move in line with agree and in line with female is the table. We see that it is 8, so 8 females agreed with question 1.
As a percentage, (8/81) * 100 = about 9%
dentify all of the following solutions of square root of x plus 10 end root minus 4 equals x
Answers
x = −6
x = −1
x = −6 and x = −1
None of the above
Answer:
x = -1.
Step-by-step explanation:
√(x + 10) - 4 = x
√(x + 10) = x + 4
Squaring both sides:
x + 10 = x^2 + 8x + 16
x^2 + 8x - x + 6 = 0
x^2 + 7x + 6 = 0
(x + 6)(x + 1) = 0
x = -6, -1.
Check for any extraneous roots:
√(x + 10) - 4 = x
Try x = -6:
√(-6 + 10) - 4 = 2 - 4 = -2.
but we found x = -6 , so -6 is not a root.
Try x = -1:
√(-1 + 10) - 4 = 3 - 4 = -1. So x = -1 is a root.
x=-1
Step-by-step explanation:
sqrt(x+10) -4= x
sqrt(x+10) = x+4
square each side
x+10=(x+4)^2
x+10= x^2+8x+16
subtract x+10 from each side
x^2+7x+6=0
(x+6)(x+1)=0
x=-6 x=-1
Then we plug both back into the equation.
sqrt(-1+10) -4= -1
sqrt(9) -4= -1
3-4 = -1
-1=-1. this works out.
sqrt(-6+10) -4 = -6
sqrt(4) -4= -6
2-4= -6
-2= -6. this does not work so the only solution is x=-1
A county in Alabama has a population of 90,000 people. It has an area of 800 mi2. How many people are there per square mile?
Answer:
112.5 people per square mile
Step-by-step explanation:
Find the "unit rate:"
90,000 people
----------------------- = 112.5 people per square mile
800 miles²
In the auditorium there are 7 Red chairs and 43 blue chairs what's the ratio of number of red chairs to the total number of chairs
Answer:
7 to 50
Step-by-step explanation:
In a circle, a 90° sector has area 36π ft2. What is the radius of the circle?
Answer: The radius is 12 feet
Step-by-step explanation:
You know that the formula used to calculate the area the a sector of a circle is:
[tex]A=\frac{C\pi }{360}*r^2[/tex]
Where C is the central angle in degrees and r is the radius of the circle
Solve for "r" from this formula:
[tex]360*A=C\pi*r^2\\\\\frac{360*A}{C\pi}=r^2\\\\r=\sqrt{\frac{360*A}{C\pi}}[/tex]
You know the that the angle is 90 degrees and you know that the area of the sector is 36π ft², then substituting values you get that the radius of this circle is:
[tex]r=\sqrt{\frac{360(36\pi ft^2)}{90\°\pi}}=12ft[/tex]
What are the factors of the polynomial a^2 + a - 2? Select all that apply.
A) a - 1
B) a + 2
C) a + 1
D) a - 2
Answer:
A) a - 1 and B) a + 2Step-by-step explanation:
[tex]a^2+a-2=a^2+2a-a-2=a(a+2)-1(a+2)=(a+2)(a-1)[/tex]
1. A person preparing medicine wants to convert 15% alcohol solution into 32% alcohol
solution. Find how much pure alcohol should he mix with 400 mL of 15% alcohol
solution to obtain it.
Pls give me an answer to this. I will give 10 points.
Answer: 100mL
Step-by-step explanation:
A 15% alcohol solution contains 15mL alcohol in 100mL solution
In 400ml there will be 400mL·15/100 = 6,000mL/100 = 60mL alcohol
Let the volume of pure alcohol to be added V.
In the new solution there will be (60 + V)mL alcohol
And the total volume will be (400 + V)mL
Concentration required 32% = 0.32
Concentration = (60 + V)mL/(400 + V)mL = 0.32
60mL + VmL = 0.32(400 + V)mL
60mL + VmL = 128mL + V·*0.32mL
VmL - V·0.32mL = 128mL - 60mL = 68mL
V(1 - 0.32)mL = 68mL
V·0.68mL = 68mL
VmL = 68mL/0.68 = 100mL ► alcohol volume to be added
Answer : 100mL
Verification
New solution
There will be 400mL + 100mL = 500mL total volume
There will be 60mL alcohol + 100mL alcohol = 160mL alcohol
The concentration will be 160mL/500mL = 0.32 = 32%
[tex]\textit{\textbf{Spymore}}[/tex]
Which logarithmic graph can be used to approximate the value of y in the equation 3^y = 4?
Answer:
c
Step-by-step explanation:
which is the slope of the line y= -3x+2?
Answer:
The slope is -3
Step-by-step explanation:
This is because the slope of a line in an equation is m. In the equation given m=-3, so that makes the slope -3.
Answer:
I'm pretty sure the slope is -3.
what is x^2+11x=0? im confused on what my “c value” is.
Answer:
c=0
Step-by-step explanation:
x² + 11x + 0 = y
x² + 11x + 0 = 0
U already know that y=0 by looking at the equations above,
But your worksheet never state "c", so we will take that c is 0 (look at the equations above.)
So c is just 0.
In a quadratic equation of the form ax^2 + bx + c=0, 'c' is the constant term. In your equation x^2 + 11x = 0, therefore the 'c' value is 0.
Explanation:The equation you provided, x^2 + 11x = 0, is a quadratic equation of the form ax^2 + bx + c = 0. In this equation, 'a' is the coefficient of x^2, 'b' is the coefficient of x, and 'c' is the constant. Comparing your equation with this form, the values of 'a', 'b', and 'c' in your equation are 1, 11, and 0 respectively. Therefore, in your equation, the 'c' value is 0.
To find roots or solutions for the equation, we use the quadratic formula: -b ± √(b^2 - 4ac) / 2a. Substituting 'a', 'b' and 'c' values from your equation will help to find the value of 'x'.
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I don’t understand numbers 19,20,21 and 22. The question is find the value of each trigonometric ratio to the nearest ten-thousandth.
Answer:
19) sin 48° ≅ 0.7431
20) sin 38° ≅ 0.6157
21) cos 61° ≅ 0.4848
22) cos 51° ≅ 0.6293
Step-by-step explanation:
* Lets explain the meaning of trigonometry ratio
- In any right angle triangle:
# The side opposite to the right angle is called the hypotenuse
# The other two sides are called the legs of the right angle
* If the name of the triangle is ABC, where B is the right angle
∴ The hypotenuse is AC
∴ AB and BC are the legs of the right angle
- ∠A and ∠C are two acute angles
- For angle A
# sin(A) = opposite/hypotenuse
∴ sin(A) is the ratio between the opposite side of ∠A and the hypotenuse
# cos(A) = adjacent/hypotenuse
∴ cos(A) is the ratio between the adjacent side of ∠A and the hypotenuse
# tan(A) = opposite/adjacent
∴ tan(A) is the ratio between the opposite side of ∠A and the
adjacent side of A
# The approximation to the nearest ten-thousandth, means look to
the fifth number before the decimal point if its 5 or greater than 5
ignore it and add the fourth number (ten-thousandth) by 1 if it is
smaller than 5 ignore it and keep the fourth number as it
* Now lets solve the problems
19) sin 48° is the ratio between the side opposite to the angle of
measure 48° and the hypotenuse of the triangle
∴ sin 48° = 0.74314 ≅ 0.7431 ⇒ to the nearest ten-thousandth
20) sin 38° is the ratio between the side opposite to the angle of
measure 38° and the hypotenuse of the triangle
∴ sin 38° = 0.61566 ≅ 0.6157 ⇒ to the nearest ten-thousandth
21) cos 61° is the ratio between the side adjacent to the angle of
measure 61° and the hypotenuse of the triangle
∴ cos 61° = 0.48480 ≅ 0.4848 ⇒ to the nearest ten-thousandth
22) cos 51° is the ratio between the side adjacent to the angle of
measure 51° and the hypotenuse of the triangle
∴ cos 51° = 0.62932 ≅ 0.6293 ⇒ to the nearest ten-thousandth
Can you answer 9, 10, 11?
Answer:
9. 1620°
10. 360°
11. 180°
Step-by-step explanation:
The answers of problems 10 and 11 give you the way to find the answer to problem 9.
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10. The sum of exterior angles of any convex polygon is 360°.
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11. An internal angle and an external angle are a linear pair, so always sum to 180°.
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9. At every vertex, the sum of interior and exterior angles is 180°, so the total of those angles at all vertices is n·180°. Of that total, 360° is the sum of exterior angles, so the total of interior angles of an n-gon is ...
n·180° -360° = (n -2)·180°
For an 11-gon, the sum of interior angles is ...
(11 -2)·180° = 1620°