The angle between a diagonal and the longer base of the isosceles trapezoid MNFD is 45°. NK is an altitude to the longer base. If MD = 9 and NF = 5, find:
- NK
- MK
- MF
- [tex]A_{AMNFD}[/tex]
Answers
Answer:
[tex]NK \approx 7.001[/tex], [tex]MK = 2[/tex], [tex]MF \approx 7.001[/tex], [tex]A_{AMNFD} = 49.007[/tex]
Step-by-step explanation:
According to the statement, we find the following inputs:
[tex]\angle MDK = \angle DMF = 45^{\circ}[/tex] (Due to the condition of isosceles trapezoid)
[tex]MD = 9[/tex]
[tex]NF = 5[/tex]
Given than longer base and shorter base are parallel to each other, we conclude that:
[tex]\angle KND = 180^{\circ} -\angle NKD - \angle KDN[/tex]
[tex]\angle KND = 180^{\circ}-90^{\circ}-45^{\circ}[/tex]
[tex]\angle KND = 45^{\circ}[/tex]
[tex]\angle FND = 90^{\circ}-\angle KND[/tex]
[tex]\angle FND = 45^{\circ}[/tex] (By definition of complementary angles)
[tex]\angle FND = \angle NFM = 45^{\circ}[/tex] (Due to the condition of isosceles trapezoid)
[tex]\angle MDK = \angle DMF = \angle FND = \angle NFM = 45^{\circ}[/tex]
[tex]\angle NOF = \angle MOD = \angle MOF = \angle FOD = 90^{\circ}[/tex] (By definitions of complementary and vertical angles and the theorem that states that sum of internal angles within a triangle equals 180º)
[tex]MO = DO = \frac{\sqrt{2}}{2}\cdot MD[/tex] (By theorem for 45-45-90 Right Triangle)
[tex]NO = OF = \frac{\sqrt{2}}{2}\cdot NF[/tex] (By theorem for 45-45-90 Right Triangle)
If we know that [tex]MD = 9[/tex] and [tex]NF = 5[/tex], then we find that:
[tex]DO = MO \approx 6.364[/tex]
[tex]NO = OF \approx 3.536[/tex]
The value of MK is obtained from the following relationship:
[tex]MK = \frac{MD-NF}{2}[/tex]
[tex]MK = \frac{9-5}{2}[/tex]
[tex]MK = 2[/tex]
And the value of KD is calculated from this expression:
[tex]KD = MD-MK[/tex]
[tex]KD = 9-2[/tex]
[tex]KD = 7[/tex]
Now by the Pythagorean Theorem we find that:
[tex]NK = \sqrt{(NO+DO)^{2}-KD^{2}}[/tex]
[tex]NK = \sqrt{9.9^{2}-7^{2}}[/tex]
[tex]NK \approx 7.001[/tex]
And considering the symmetry characteristics of an isosceles trapezoid, we determine MF:
[tex]MF = NO + DO \approx 7.001[/tex]
Lastly, the area of the isosceles trapezoid is determined by the following formula:
[tex]A_{AMNFD} = NF\cdot NK + MK\cdot NK[/tex]
[tex]A_{AMNFD} = NK\cdot (NF+MK)[/tex]
If we know that [tex]NK \approx 7.001[/tex], [tex]NF = 5[/tex] and [tex]MK = 2[/tex], then the area of the figure is:
[tex]A_{AMNFD} = (7.001)\cdot (5+2)[/tex]
[tex]A_{AMNFD} = 49.007[/tex]
Related Questions
PLEASEEEEEE ANSWEERRRRRRRRR
Sally and Joan were able to dust the house in 3 hours together. It takes
Joan 10 hours to finish the same job alone. Without help, how long
would it take Sally to finish the same job ?
Answers
Answer:14hrs
Step-by-step explanation:joan=10hrs
joan+sally=3hrs
representing joan and sally's time taken in fractions 1/10+-------=1/3
1/3-1/10=7/30
7/30 by 60min(in an hour)
=14hrs
Solve by substitution
-X-4y=8
x+4y=-1
Answers
Answer:
Your answer is: No solution
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Step-by-step explanation:
Hope this helped : )
Logan bought a baseball bat on a trip. The baseball bat is 29 inches long.
Logan thinks he can bring the baseball bat home in his suitcase. Is he correct? Use your understanding of the Pythagorean Theorem to explain your answer.
The length of the suit case is 24 inches while the height is 18 inches
Give me the answer in i will give you brainliest
Answers
Step-by-step explanation:
Given that,
The length of a baseball is 29 inches
Logan thinks he can bring the baseball bat home in his suitcase.
The length of the suit case is 24 inches while the height is 18 inches. We can find the diagonal (x) of the suitcase using Pythagorean Theorem as follows :
[tex]x^2=24^2+18^2\\\\x=\sqrt{900} \\\\x=30\ \text{inches}[/tex]
The diagonal of the suitcase is 30 inches. It means that he can put the baseball bat in the suitacse easily.
What are the solutions to the quadratic equation 4(x + 2)2 = 36
Answers
Answer:
x=5/2
Step-by-step explanation:
What is x in 7-onethirdx =11
Answers
Answer:
[tex]\frac{-1}{3} x = 11-7\\\\\frac{-1}{3} x = 4\\\\-1x = 4*3\\-1x = 12\\\\x = -12[/tex]
Evelyn can run 3 miles in 40 minutes. Which equation can be solved to
find m, the number of miles Evelyn can run in 60 minutes?
3
1
=
40
m
m
B
3
40
=
1
3
m
60
40
60
D
3
40
Answers
Answer:
4.5 miles
Step-by-step explanation:
you do 40/3 and get .75, then do .75 times 60 and you get 4.5 miles. her mile a minute ratio is 13 mins and about 23 seconds
Find the value of the following expression
(2^8 5^-5 19^0) x [5^-2 over 2^3]^4 x 2^28 (5 points)
Write your answer in simplified form. Show all of your steps. (5 points)
Answers
Looks like the expression is
(2⁸ • 5⁻⁵ • 19⁰) • (5⁻² / 2³)⁴ • 2²⁸
First, any positive number raised to 0 is 1:
(2⁸ • 5⁻⁵ • 1) • (5⁻² / 2³)⁴ • 2²⁸
(2⁸ • 5⁻⁵) • (5⁻² / 2³)⁴ • 2²⁸
Exponents in a denominator can be rewritten as negative exponents in the numerator:
(2⁸ • 5⁻⁵) • (5⁻² • 2⁻³)⁴ • 2²⁸
Distribute the 4th power across the product 5⁻² • 2⁻³ :
(5⁻² • 2⁻³)⁴ = 5⁻⁸ • 2⁻¹²
so we have
(2⁸ • 5⁻⁵) • (5⁻⁸ • 2⁻¹²) • 2²⁸
Multiplication is associative, so we can ignore the parentheses. Combine factors with equal bases and simplify the exponents:
2⁸ • 5⁻⁵ • 5⁻⁸ • 2⁻¹² • 2²⁸
2⁸⁻¹²⁺²⁸ • 5⁻⁵⁻⁸
2²⁴ • 5⁻¹³
Rewrite the negative exponent as a positive one:
2²⁴ / 5¹³
4/5 divided by 1/3 / fraction
Answers
The solution (quotient) when [tex]\frac{4}{5}[/tex] is divided by [tex]\frac{1}{3}[/tex] is [tex]2\frac{2}{5}[/tex]
To determine the solution of 4/5 divided by 1/3,
First, let us write the fractions properly before carrying the division operation
That is,
[tex]\frac{4}{5}[/tex] divided by [tex]\frac{1}{3}[/tex]
Now, we will carry out the division operation
[tex]\frac{4}{5} \div \frac{1}{3} = \frac{4}{5} \times \frac{3}{1}[/tex]
Then,
[tex]\frac{4}{5} \times \frac{3}{1} = \frac{12}{5}[/tex]
[tex]= 2\frac{2}{5}[/tex]
Hence, the solution (quotient) when [tex]\frac{4}{5}[/tex] is divided by [tex]\frac{1}{3}[/tex] is [tex]2\frac{2}{5}[/tex]
Learn more here: https://brainly.com/question/13124034
Please Help
How is an object's acceleration affected by its mass and the forces acting on it?
Answers
Answer:
Step-by-step explanation:
The acceleration of an object increases with increased forced and decreases with increased mass which is in the same direction as the force.
4) -4x - 10.2
I need the answer to this question asap please.
Answers
Answer: -2.55
Explanation: First add 10.2, and then the equation becomes -4x = 10.2.
Then, you just divide by -4 from both sides of the equation, and you get x = -2.55. :]
Answer:
21 - 4x
Step-by-step explanation:
Multiply 10 and 2 to get 20.
41 - 4x - 20
Subtract 20 from 41 to get 21.
21 - 4x
what is the sum of all positive integer cubes that are less than 100
Answers
Step-by-step explanation:
2^3=8
3^3=27
4^3=64
so if you add all the positive integer cubes it will be 8+27+64=99
hence 99 is less than 100
Hence solved.
Which function has a domain of all real numbers?
A. y=-x½+5 B. y=(2x)⅓-7 C. y=(x+2)¼ D. y=-2(3x)⅙?
Answers
Answer:
B.
Step-by-step explanation:
B. Because the others have exponents whose denominators are even so the results of , for example x^1/2, if x is negative is not defined.
For example:
For A, when x is -4, (-4)^1/2 is not real.
For B, when x = -4, (2*-4)^ 1/3 = -8^(1/3) = = -2.
Answer:
Step-by-step explanation:
For all Plato users
Joel opened a checking account. His bank charges him a service fee of $4.95
each month. Assume y = total cost of having the account and x = number of months.
Answers
it needs to be 20 characters so here’s this ndnsoxid
6/5 58.9% 1.77 0.169 =
Order from least to greastest
Answers
The answer fam is.........
0.169
58.9%
1.77
6/5
At a local department store, jeans typically cost $20. However, due to a special, the jeans are reduced to $14. What percent of the original price have the jeans been reduced to?
Answers
Answer:
25%
Step-by-step explanation:
What is the Coefficients in 9k + 7 - k + 4
Answers
Answer:
9 and -1
Step-by-step explanation:
a coefficient is a number attatched to a variable. 9 is next to k, as well as the negative sign, which represent -1.
help please cant find the answers on google lolz
Answers
Answer:
24/7 or 6.75 or 6 3/4
Step-by-step explanation:
Answer:
1) 22.4
2) 91
3) 6
explanation:
i converted the fraction to decimals or whole numbers and multiplied
PLEASEEEEE help I don’t know what to put!!!!
Answers
Also can I please have Brainliest??
Only if I'm right of course...
Divide. Round your answer to the nearest tenth.
39,527 = 7
HELPPP MEEEE
Answers
Answer:
3,266.53
Rounded to the nearest 0.01 or
the Hundredths Place.
Step-by-step explanation:
Can anyone help me graph this plssss !
y−3=1/2(x+3)
I need this answer fasttt
Answers
Answer:
Slope=
2.000
1.000
=0.500
x−intercept=
−1
9
=−9.00000
y−intercept=
2
9
=4.50000
Step-by-step explanation:
Slope = 1.000/2.000 = 0.500
x-intercept = 9/-1 = -9.00000
y-intercept = 9/2 = 4.50000
4 ( y+2 ) = 2( y+4 )
Answers
Answer:
y=0
Step-by-step explanation:
8=8
Kristen is trying to finish 1/2 of her test every 2/3 hour. How many hours will it take Kristen to complete her whole test?
Answers
Answer:
4/3
Step-by-step explanation:
Please help i don’t understand
Answers
Is that everything for the problem??
||-//
what is the equation for f(x)= |x| shifted to the right 3 units and Shifted down 4 units.
Answers
Answer:
The equation for f(x)=|x| if it is what is the equation for f(x)= |x| shifted to the right 3 units and Shifted down 4 units is f(x)=|x-3|-4
Step-by-step explanation:
We need to write equation for f(x)=|x| if it is what is the equation for f(x)= |x| shifted to the right 3 units and Shifted down 4 units.
When the graph is shifted towards right h units the equation becomes f(x)=(x-h) using it for our scenario:
If x is shifted right 3 units it will become f(x)=|x-3|
When the graph is shifted down h units the equation becomes f(x)=x-h using it for our scenario:
and Shifted down 4 units the equation will become: f(x)=|x-3|-4
So, the equation for f(x)=|x| if it is what is the equation for f(x)= |x| shifted to the right 3 units and Shifted down 4 units is f(x)=|x-3|-4
The height of a widescreen television varies directly with its width. A television that is 60 cm wide and 33.75 cm high. Write and solve a direct variation equation to find the height of a television screen that is 90 cm wide.
Answers
90 in + 60 in= 130 square inches? I guess you can do that
Have a good day
Two different grocery stores are having a special on cereal:
HEB is selling 3 boxes of cereal for $4.29
Walmart is selling 2 boxes of cereal for $2.94.
Which grocery store has the cheaper price per box?
Answers
Answer: HEB
Step-by-step explanation:
A notebook, a pencil case, and a calculator weigh 600 grams total. The notebook weighs 240 grams and the calculator weighs 265 grams. How much does the pencil case weigh?
Answers
Answer: 95 grams
Step-by-step explanation:
Add the notebook weight and the calculator weight. 240 + 265 = 505 now subtract 505 from 600. That equals 95
Gabrielle is 7 years younger than Mikhail. The sum of their ages is 41. What is Mikhail's age?
Answers
What is the order fractions least to greatest 3/5 1/4 1/2 2/5
Answers
Answer:
1/4, 2/5, 1/2, 3/5
Step-by-step explanation:
1/4=0.25
3/5=0.6
2/5=0.4
1/2=0.5
Answer:
[least] 1/4, 2/5 , 1/2, 3/5 [greatest]
Step-by-step explanation:
Well lets find out LCD (least common denominator) for 4,5 and 2
LCD-20
12/20 =used to be 3/5
5/20=used to be 1/4
10/20=used to be 1/2
8/20=used to be 2/5
Now that you know all of them and have common denominator lets order!!
[least] 1/4, 2/5 , 1/2, 3/5 [greatest]
Hope this helps :3
What is the slope and y-intercept of the function:
y=9x
Answers
Answer:
slope= 9
y-intercept= 0
Step-by-step explanation:
Because 9 is in the m spot and bis 0