In a rhombus, an altitude from the vertex of an obtuse angle bisects the opposite side. Find the measures of the angles of the rhombus.
Answers
Drawing the altitude forms a right triangle. Let the side of the rhombus be x. The altitude bisects the opposite side, so the base of the triangle formed would be 1/2x. We have an expression for the side opposite this portion of the obtuse angle (cut by the altitude) and for the hypotenuse (the side length of the rhombus, x). opposite/hypotenuse is the ratio for sine. Our equation then looks like this:
[tex]\sin x=\frac{\frac{1}{2}x}{x} \\ \sin x=\frac{1}{2}x \div x \\ \sin x=\frac{1}{2}x \div \frac{x}{1} \\ \sin x=\frac{1x}{2} * \frac{1}{x}=\frac{1x}{2x}=\frac{1}{2}[/tex]
Now we take the inverse sine of both sides:
sin⁻¹(sin x)=sin⁻¹(1/2)
x=30
Since this portion of the triangle is 30, and the right angle is 90, the missing angle (an acute angle of the rhombus) is 180-30-90=60°. Since the acute angles and obtuse angles of a rhombus are supplementary, the obtuse angles must be 180-60=120°.
The angles of the rhombus determines the inclination of the sides of the
rhombus.
The correct response;The measures of the four angles of the rhombus are 60°, 60°, 120°, and 120°.Method used to arrive at the above response;Given;The altitude of the rhombus bisects the opposite side.
The angle of the rhombus at the vertex point of the altitude = An obtuse angle
Required:The measure of the angles of the rhombus
Solution:The length of the sides of a rhombus are equal.
The opposite angles of a rhombus are equal.
Let x represent the length of a side of the rhombus, we have;
The bisector from the vertex of the obtuse angle = An altitude
The angle the altitude forms with the side it bisects = 90°
Therefore;
The triangle formed by the altitude, half the bisected side and the side of the rhombus adjacent to the bisected side = A right triangle
The hypotenuse side to the right triangle = The side of the rhombus
Let θ represent the angle opposite the altitude, and between the sides of
the rhombus, in the right triangle by trigonometric ratios, we have;
[tex]\displaystyle cos(\theta) = \mathbf{\frac{Adjacent}{Hypotenuse}}[/tex][tex]\displaystyle cos(\theta) = \frac{0.5 \cdot x}{x} = 0.5[/tex]
θ = arccos(0.5) = 60°
Therefore, two acute (opposite) angles of the rhombus are 60°
The two obtuse angles of the rhombus are each = (360° - 2×60°) ÷ 2 = 120°
The angles of the rhombus are 60°, 60°, 120°, 120°.Learn more about trigonometric ratios here:
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Related Questions
Write the equation of the plane with normal vector n = 1, 3, 4 passing through the point (4, −1, 3) in the scalar form ax + by + cz =
d.
Answers
The equation of plane with normal vector n = (1, 3, 4) passing through the point (4, −1, 3) in the scalar form is;
⇒ x + 3y + 4z = 13
What is Equation of plane?
A equation of plane containing the point (x₁ , y₁ , z₁) and having a normal vector (a, b, c) is defined as;
⇒ a (x - x₁) + b (y - y₁) + c (z - z₁) = 0
Given that;
The normal vector n = (1, 3, 4)
And, The point = (4, −1, 3)
Now,
Since, we know that;
A equation of plane containing the point (x₁ , y₁ , z₁) and having a normal vector (a, b, c) is defined as;
⇒ a (x - x₁) + b (y - y₁) + c (z - z₁) = 0
So, We get;
A equation of plane containing the point (4, −1, 3) and having a normal vector (1, 3, 4) is defined as;
⇒ a (x - x₁) + b (y - y₁) + c (z - z₁) = 0
⇒ 1 (x - 4) + 3 (y - (-1)) + 4 (z - 3) = 0
⇒ x - 4 + 3y + 3 + 4z - 12 = 0
⇒ x + 3y + 4z = 13
Thus, The equation of plane with normal vector n = (1, 3, 4) passing through the point (4, −1, 3) in the scalar form is;
⇒ x + 3y + 4z = 13
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Can you answer these questions for me plz I need them before Monday ty
Answers
B. The answer is 14w^3 +2w^2 bc you distribute again which gives you 20w-10w^2-6w^3+12w^2 and then combine like terms (20w^3-6w^3)+(-10w^2+12w^2) and equals to 14w^3+2w^2
C. The answer is 3y^2-5y+2 bc you distribute again which is 7y^2-3y-4y^2-2y+2 and then combine like terms (7y^2-4y^2)+(-3y-2y) +2 and gives you 3y^2-5y+2
solve 1.2 = g - (-4.3)
Answers
1.2 = g + 4.3 Subtract 4.3 from both sides
1.2 - 4.3 = g Now subtract. You get a minus number.
-3.1 = g
This one really is a bit sneaky.
A car traveling at 46 mi/h slows to a speed of 23 mi/h in 5 seconds. It maintains that speed for 5 seconds and then slows to a stop after 5 more seconds. Which graph shows the car’s speed over time?
Answers
We have then:
For [0, 5]:
A car traveling at 46 mi / h slows to a speed of 23 mi / h in 5 seconds.
For [5, 10]:
It maintains that speed for 5 seconds.
For [10, 15]:
then slows to a stop after 5 more seconds.
In this case:
x axis: represents time
y axis: represents the speed.
Answer:
See attached image for the graphic v (t) vs t.
If a skateboard is 2 1/2 feet long, what is the length of 4 skateboards in yards?
Answers
Since each skateboard is 2 1/2 feet long, we can multiply that by 4 to get 10.
2 1/2 * 4 = 10
We then convert this into yards.
One yard is equal to 3 feet, so we should divide 10 by 3 to get our answer.
10/3=3 1/10
Our final answer is 3 1/10 yards.
The length of 4 skateboards is 3 2/3 yards.
What is the length of 4 skateboards in yards?The first step is to convert feet to yards.
1 feet = 1/3 yards
5/2 x 1/3 = 5/6 yards
The second step is to multiply 5/6 yards by 4
5/6 x 4 = 20 / 6 = 3 2/3 yards
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What is the area of the shaded region?
Area = ____ ft2
Answers
Consider the numbers 4/15 and 3/10 (a) Compare the numbers. (B) find a fraction between the two given numbers
Answers
As a decimal 3/10 = 0.3 [talk about close]
3/10 is bigger.
You could take an average to find something between 4/15 and 3/10
1/2(4/15 + 2/10)
1/2(8/30 + 6/30)
1/2(14/30)
1/2(7/15)
7/30 is between the two given numbers..
PLEASE HELP!!!!
Different types of parallelograms have distinguishing traits. Compare and contrast the rectangle, rhombus, and square based upon the characteristics of their angles. Which one(s) have angles whose sum is 360 degrees? Which one(s) have both pairs of opposite angles that are congruent? Which one(s) have four angles?
Answers
Either way, what you're doing here is comparing 3 shapes. The square, rectangle, and rhombus. You should definitely know what a square and rectangle look like, but in case you don't know the rhombus, it's the shape that's usually allocated with diamonds, on a 2D plane.
All of these shapes are considered parallelograms. They all have similar features and characteristics, but only to some extent.
Square=Four sides, four 90 degree angles, 2 pairs of opposite congruent angles (meaning all angles are congruent in this case), sum of 360 degrees (90*4)
Rectangle=Four sides, four 90 degree angles, 2 pairs of opposite congruent angles (meaning all angles are congruent in this case), sum of 360 degrees (90*4)
Rhombus= Four sides, Four angles in total measuring up to 360 degrees, 2 acute angles (congruent; less than 90), two obtuse angles (congruent; more than 90). Angle measurements can fluctuate within the 2 acute-2 obtuse parameters. 2 pairs of opposite congruent angles, however, these are not all congruent with each other, unlike the previous two.
All 3 sum to 360 degrees
All 3 have both pairs of opposite angles congruent
All 3 have 4 angles.
~Hope this helps!
The square, rectangle, and rhombus are all considered parallelograms. Squares have four sides, four 90 degree angles, 2 pairs of opposite congruent angles (all the angles are congruent), the angles add up to a sum of 360 degrees. Rectangles have four sides, four 90 degree angles that add up to 360 degrees, 2 pairs of opposite congruent angles (all the angles are congruent). Rhombuses have four sides, four angles in total measuring up to 360 degrees no matter the combination of angles because the oposite angles are congruent (2 acute angles and two obtuse angles).
While the rhombus is the only shape within this trio to have a pair of congruent acute and a pair of congruent obtuse angles the square and rectangle both have 4 congruent angles. All 3 shapes have a sum of 360 degrees when the angles are added together, all 3 have pairs of opposite angles being congruent, and all 3 shapes have 4 angles in total.
A rectangular prism has a width of 5 cm a height of 8cm and a depth of 5cm. What is the volume of the prism
Answers
v=l*w*h (note that depth can be substituted in this case for length)
plug in the data we know
v=5*5*8
v=200cm³
Answer=200cm³
Can you please help me out ?
Answers
Tan (x) = a / b
Where,
a: opposite side of the triangle.
b: adjacent side of the triangle.
Substituting:
Tan (x) = a / b
Tan (x) = 24/10
Tan (x) = 12/5
Answer:
Tan (x) = 12/5 (option 3)
I need help for number 13-16 and I also need an explanation please help
Answers
Find the volume in Q14, 4 2/5 * 3 1/2 * 2 1/4
Convert
[tex] \frac{12}{5} [/tex] * [tex] \frac{7}{2} [/tex] * [tex] \frac{9}{4} [/tex] = 18.9
The answers on the third one are A, C, and F
The answers on the fourth one are B, D, and E
Hopefully it helps!!
A $25,000 purchase decreases 12% in value per year. Determine the values of the purchase after 3 years and after 7 years.
Answers
After the 7 years, the depreciation amount is $1,393.22 and the value is $10,217.05
License plates are made using 2 letters followed by 3 digits. How many plates can be made if repetition of letters and digits is allowed?
Answers
number of possible combinations = 676000
Explanation:
We have:
26 possible letters (a to z)
10 possible digits(0 to 9)
2 letters followed by 3 digits
For letters, since repetition is allowed, therefore, each of the two letters can be any of the possible 26 alphabetical letters (a to z)
For digits, since repetition is allowed, therefore, each digit of the three can be any of the possible 10 digits (0 to 9)
Therefore:
number of combinations = letter * letter * digit * digit * digit
number of combinations = 26 * 26 * 10 * 10 * 10
number of possible combinations = 676000
Hope this helps :)
Use the intercepts to graph the equation 8x - 5y = 40
Answers
.. x/(40/8) +y/(-40/5) = 1
.. x/5 +y/-8 = 1
The intercepts are (5, 0) and (0, -8).
To graph the equation 8x - 5y = 40, find the x-intercept and y-intercept. The x-intercept is (5,0) and the y-intercept is (0,-8). Plot these points and draw a straight line passing through them.
Explanation:To graph the equation 8x - 5y = 40 using intercepts, we need to find the x-intercept and y-intercept. The x-intercept is the point where the line intersects the x-axis, so let y = 0 and solve for x. The y-intercept is the point where the line intersects the y-axis, so let x = 0 and solve for y.
Setting y = 0, we get 8x - 5(0) = 40, which simplifies to 8x = 40. Solving for x, we find x = 5. So the x-intercept is (5, 0).
Setting x = 0, we get 8(0) - 5y = 40, which simplifies to -5y = 40. Solving for y, we find y = -8. So the y-intercept is (0, -8).
Plotting the x-intercept (5, 0) and the y-intercept (0, -8) on a graph, we can draw a straight line passing through these two points, which is the graph of the equation 8x - 5y = 40.
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ethan took a quiz with 15 questions. if he answered 3/5 of the questions correctly, how many did he get wrong?
Answers
15-9= 6
Ethan got six questions wrong.
Is 2 yards greater less than equivalent to 5 ft
Answers
3 feet = 1 yard;
2 yards = 6 ft; therefore, 2 yards is greater than 5 ft.
I hope this helps!
Find the surface area of the composite solid and round to the nearest tenth. Explain your answer.
Answers
so, for the rectangle's sides,
front and back are two 6x3 rectangles
left and right are two 6x3 rectangles
the bottom part is a 6x6 rectangle
now, we don't include the 6x6 rectangle that's touching the triangles, because that's inside area, and is not SURFACE area, so we nevermind that one.
now, the triangles are just four triangles with a base of 6, and a height of 4, in red noted there.
so, just get the area of all those rectangles and the triangles, sum them up and that's the surface area of the composite,
[tex]\bf \stackrel{lateral~rectangles}{4(6\cdot 3)}~~+~~\stackrel{bottom~rectangle}{(6\cdot 6)}~~+~~\stackrel{triangles}{4\left( \cfrac{1}{2}(6)(4) \right)}[/tex]
HELP PLEASE! −3.64⋅|−5.3|−1.53 what is the anwser?
Answers
The expression simplifies to approximately -20.822. It involves multiplying -3.64 by the absolute value of -5.3 and then subtracting 1.53 from the result.
To calculate this expression, follow the order of operations (PEMDAS),
which stands for Parentheses, Exponents, Multiplication and Division (left-to-right), and Addition and Subtraction (left-to-right).
In expression, there are no parentheses or exponents, so we proceed with multiplication and then subtraction:
-3.64 × |-5.3| - 1.53
Calculate the absolute value of -5.3, which is 5.3.
Multiply -3.64 by 5.3.
Finally, subtract 1.53 from the result.
-3.64 × 5.3 - 1.53
Now, do the multiplication:
-19.292 - 1.53
Now, subtract:
-19.292 - 1.53 = -20.822
Therefore, the answer for the given expression -3.64 × |-5.3| - 1.53 is approximately -20.822.
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A cylinder shaped water tank has a diameter of 10 m and a height of 10 m. What volume of water does the tank hold when it's 75% full?
Answers
v = (3.14)(5)²(10)
v = (3.14)(25)(10
v= 785
785 x 0.75 = 588.75
the water tank has 588.75 m of water in it when it is 75% full.
The price of a ticket was increase from 50p to 60p. What is the increase a as a fraction in its simple form? As a percentage of the original price?
Answers
Given is the price increase of a ticket from 50p to 60p.
Using the concept of fractions, we can find the ratio of new price to old price as follows :-
[tex] \frac{new \;\; price}{old \;\; price} = \frac{60p}{50p} =\frac{6}{5} [/tex]
So the increase in price is [tex] \frac{6}{5} [/tex] times old price of the ticket.
Using the formula of percentage, we can find the percentage change in price as follows :-
[tex] Percentage = \frac{(new\;\;price \;-\; old\;\;price) }{old \;\; price}*100 \\\\
Percentage = \frac{60p-50p}{50p}*100 \\\\
Percentage = \frac{10p}{50p}*100 \\\\
Percentage = 20\;\% [/tex]
Hence, Percentage increase is 20% of the original price.
Which expression is equivalent to 3i(4 + 7i)?
Answers
I hope this helps
Which of the following are examples of exponential decay?
Answers
a yearbook page will show 20 photos displyed in rws each row must contain the same number of photos how many different ways can the photos be arranged
Answers
Answer:
6If we need all the rows to be equal, all we are doing is dividing.
20/1= 20
20/2= 10
20/4=5
20/5=4
20/10=2
20/20=1
We have 6 different ways to divide 20!
Mary’s number is eleven more than Jerry’s. The sum of their numbers is 89. What are their numbers?
Answers
x = Jerry
x + 11 = Mary
Getting Jerry's number:
x + (x + 11) = 89
2x + 11 = 89
2x = 89 - 11
2x = 78
2x/2 = 78/2
x = 39
Getting Mary's number(simplify):
x + 11
= 39 + 11
= 50
.
Therefore, Mary and Jerry's age are 50 and 39, respectively.
:)
Mary and Jerry's number will be 39 and 50.The sum of their numbers is 89.Which shows that the obtained answer is correct.
What is a linear equation?It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.
If in the linear equation one variable is present then the equation is known as the linear equation in one variable.
Let, Mary’s number be x
Mary’s number is eleven more than Jerry’s
Jerry's number is x+11
From the given condition sum of their numbers is 89.
[tex]x + (x + 11) = 89\\\\ 2x + 11 = 89\\\\ 2x = 89 - 11\\\\ 2x = 78\\\\ \frac{2x}{2} = \frac{78}{2} \\\\ x = 39[/tex]
Jerry's number will be;
[tex]x+11 \\\\ 39+11 \\\\ 50[/tex]
Hence the Mary and Jerry's number will be 39 and 50.
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Tina was involved in an accident in which she rear-ended another driver stopped at a stoplight. Tina is fully insured through her insurance company. Which of the following components of her insurance policy will cover the damages caused to Tina’s car in the accident?
a.
bodily injury
b.
property damage
c.
collision
d.
comprehensive damage
(Correct Answer Is C. Collision)
Answers
Answer:the answer is C. collision
Step-by-step explanation:
A Family spends 240.00 per week on food. If this is 16% of their income, what is the families weekly income?
*show work*
Answers
-------------------------------------------
Work Shown:
x = weekly income (in dollars)
16% of x = amount spent on food per week
16% of x = 240
(16/100)*x = 240
0.16*x = 240
0.16*x/0.16 = 240/0.16
x = 1500
The family's weekly income is $1500.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
given that,
A Family spends 240.00 per week on food. If this is 16% of their income.
let,
x = weekly income (in dollars)
16% of x = amount spent on food per week
16% of x = 240
(16/100)*x = 240
0.16*x = 240
0.16*x/0.16 = 240/0.16
x = 1500
Hence, The family's weekly income is $1500.
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what is the following product? ^3√24 x ^3√45
Answers
= ∛1080
= 6∛5
answer
C. 6(∛5)
The simplified value of the product of [tex]\sqrt[3]{24}\times\sqrt[3]{45}[/tex] is [tex]6\sqrt[3]{5}[/tex].
What are some rules of exponents?Some common rules of exponents are
xᵃ×xᵇ = xᵃ⁺ᵇ.
xᵃ/xᵇ = xᵃ⁻ᵇ.
Addition and subtraction of exponents is only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.
We know when we have the same radical we can simply multiply the values.
Given, [tex]\sqrt[3]{24}\times\sqrt[3]{45}[/tex].
= [tex]\sqrt[3]{24\times45}[/tex].
= [tex]\sqrt[3]{2\times2\times2\times3\times3\times3\times5}[/tex].
= [tex]2\times3\sqrt[3]{5}[/tex].
= [tex]6\sqrt[3]{5}[/tex].
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PPPPLLLLZZZZZ I BEG UUUU
Factor the polynomial: x^2–xy+x–xy^2+y^3–y^2
Answers
x^2–xy+x –(xy^2-y^3+y^2)
Then take out common factors in each group
=x(x-y+1) -y^2(x-y+1)
Take out the common factor (x-y+1)
=(x-y+1)(x-y^2) voilà!
a proportional relationship must graph as a line, is that false?
Answers
y = 3x² <--- parabolic graph
y = 3√x <--- parabolic as well
A high school gym class was jumping rope. They wanted to know how many jumps each student could make before they missed. The results are listed below. 2 5 6 7 9 11 12 14 14 15 17 19 21 22 23 24 27 32 35 39 39 44 47 53 60 61 82 85 88 90 93 96 101 103 114 125 What is the median number of jumps that the students made before missing? a. 32.5 c. 33.5 b. 33 d. 34
Answers
The median number of jumps that the student made before missing is calculated as: C. 33.5.
What is the Median of a Data Set?Median is the middle value or the average of the two center values of a data set.
Given the data set:
2, 5, 6, 7, 9, 11, 12, 14, 14, 15, 17, 19, 21, 22, 23, 24, 27, 32, 35, 39, 39, 44, 47, 53, 60, 61, 82, 85, 88, 90, 93, 96, 101, 103, 114, 125
The average of the two center values is: (32+35)/2 = 33.5
Therefore, the median number of jumps is: C. 33.5.
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