(20pts, 5pts each) The median of AMND from vertex N of the
isosceles trapezoid MNFD is 5cm. The diagonal ND is
perpendicular to the leg MN. The shorter base NF = 6cm and the
32cm².
A
MNFD
=
Find: MD, the altitude of the trapezoid h, the length of the
legs of the trapezoid and the ratio between the areas of AMND and
ANFD.
Answers
Answer:
MD = 10 cmh = 4 cmMN = FD = 2√5 cm ≈ 4.47 cmarea ratio = 5 : 3Step-by-step explanation:
Given isosceles trapezoid MNFD with short base NF = 6 cm, diagonal ND perpendicular to leg MN, and triangle MND median NX = 5 cm, you want ...
length MDaltitude h of the trapezoidlengths of MN and FDratio of areas of ∆MND and ∆NFDMDMD is the hypotenuse of right triangle MND. The median from the right angle of a right triangle is half the length of the hypotenuse, so ...
MD = 2·NX = 2·(5 cm)
MD = 10 cm
AltitudeIn the attached diagram, we see that right triangle XYN has side XY = 3 (half of NF), and hypotenuse NX = 5 (given). These are two sides of a 3-4-5 right triangle, so the remaining side, altitude h, is 4.
h = 4 cm
Side lengthsThe attache diagram shows congruent side lengths MN and FD are the hypotenuse of a right triangle with sides YM = 2 and YN = 4. The Pythagorean theorem tells us the length of side MN is ...
MN² = MY² +NY²
MN² = 2² +4² = 4 +16 = 20
MN = √20
MN = FD = 2√5 ≈ 4.47
Area ratioTriangle MND has a base length MD = 10 and a height h = 4. Triangle NFD has a base length NF = 6 and a height h = 4. The ratio of the areas of these two triangles is ...
[tex]\dfrac{A_{MND}}{A_{NFD}}=\dfrac{\frac{1}{2}\cdot10\cdot4}{\frac{1}{2}\cdot6\cdot4}=\dfrac{10}{6}=\boxed{\dfrac{5}{3}}[/tex]
The ratio between the areas is 5 : 3.
__
Additional comment
We are also given the area of the trapezoid as 32 cm². That can be used to find the longer base and/or the altitude, or to check the answers we have for those values. It is redundant information.
The midpoint X of MD is the center of the circumscribing circle of the trapezoid and right triangles MND and MFD. The midpoint of the hypotenuse of a right triangle is always the circumcenter, so knowing the length NX tells us the radius of that circle, hence MX and XD.
Related Questions
Simply the expression below.
10-8.3
Answers
there are 19 members in a committee. in how many different ways can a president vice president secretary and treasure be chosen
Answers
Given:
Total members in the committee = 19
Let's find the number of ways a president, vice president, secretary and treasurer can be chosen.
Here, we are to use permutation formula:
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]Where:
n = 19
r = 4
Thus, we have:
[tex]\begin{gathered} ^{19}P_4=\frac{19!}{(19-4)!} \\ \\ ^{19}P_4=\frac{19!}{(15)!} \\ \\ =\frac{19*18*17*16*15!}{15!} \\ \\ =19*18*17*16 \\ \\ =93024 \end{gathered}[/tex]Solving further:
Therefore, the number of ways they can be chosen is 93024 ways.
ANSWER:
93024 ways
common errors for Rational Numbers.
Answers
Answer:
Sometimes people think negative numbers are irrational.
They aren't. They are actually rational because they can be divided and multiplied to make 0.
The fractions are often mistaken as irrational as well.
The only irrational numbers are π, terminating decimals, and non-perfect squares.
Step-by-step explanation:
Btw, Brainliest? Thanks!
QUESTION 2
First Street and Second Street run parallel to each other and both are one-way streets. First Street runs West, Second Street runs East. The city is planning to build a new road, also one way, that runs NE and cuts through both First Street and Second Street at an angle. Traffic turning off of Second Street will have to make a 53° turn onto the new road (see angle f). What angle would traffic turning off of First Street have to make turning onto the new road(See angle a)? Provide your answer and the step-by-step process you used to find it!
Answers
Answer:
127°
Step-by-step explanation:
Angles f and d are supplementary because they are consecutive interior angles. This means that d is 123°.
a and d are vertical angles, which are congruent, meaning angle a is 127°.
Leah can run 720 yards in 4.5 minutes. How many yards can she run in 2 minutes at the same rate?
A. 350
B. 320
C. 160
D. 110
Answers
If she ran 160 yards per one minute then we can find out how much she ran in 2 minutes simply by doing multiplication.
160 x 2 = 320.
She ran 320 yards in 2 minutes.
Apologies if anything is incorrect.
(Practice problem)
Avery ran 200 yards in 8 minutes. How many yards could she run in 10 minutes?
(Solve)
(250 yards.)
Once again I apologize if anything is incorrect.
Vincent earned 24$ for 3 hours worked. Later he earned 72$ for 9 hours of work. How much money does he earn per hour
Answers
let v be a vector space over a field of characteristic not equal to two. (a) let u and v be distinct vectors in v. prove that {u, v} is linearly independent if and only if {u v, u − v} is linearly independent. (b) let u, v, and w be distinct vectors in v. prove that {u, v, w} is linearly independent if and only if {u v, u w, v w} is linearly independent.
Answers
Thus {u, v} is linearly independent if and only if {u v, u − v} is linearly independent
It is given that {u,v} be a linearly independent set of a set S.
This means that there exist constant a,b such that if:
au+bv=0
then a=b=0
Now we are asked to prove that:
{u+v,u-v} is a linearly independent set.
Let us consider there exists constant c,d such that:
c(u+v)+d(u-v)=0
To show: c=d=0
The expression could also be written as:
cu+cv+du-dv=0
( Since, using the distributive property)
Now on combining the like terms that is the terms with same vectors.
cu+du+cv-dv=0
i.e.
(c+d)u+(c-d)v=0
Since, we are given that u and v are linearly independent vectors this means that:
c+d=0------------(1)
and c-d=0 i.e c=d-----------(2)
and from equation (1) using equation (2) we have:
2c=0
i.e. c=0
and similarly by equation (2) we have:
d=0
Hence, we are proved with the result.
We get that the vectors {u+v,u-v} is linearly independent.
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If the 20th term is -40 and your 28th term is -73, what will be the first term
Answers
Answer:
The first term will be 38.375
Step-by-step explanation:
aₙ = a₁ + (n - 1) * d
a₂₀ = -40
a₂₈ = -73
-40 = a₁ + 19d
-73 = a₁ + 27d
When we have two similar equations with two unknowns, we can subtract them to get an answer.
-40 = a₁ + 19d --> -40 = a₁ + 19d
-(-73 = a₁ + 27d) --> 73 = -a₁ - 27d
-------------------------------------------------
33 = -8d
Solve for d by dividing by -8
d = -4.125
Now plug d into one of the original equations to solve for a₁
-40 = a₁ + 19(-4.125)
-40 = a₁ - 78.375
a₁ = 38.375
a researcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of this sample. under what conditions can that sample mean be treated as a value from a population having a normal distribution? question content area bottom part 1 select all that apply. a. the researcher collects more than 30 samples. b. if the population of grade-point averages has a normal distribution. c. if the population of statistics students has a normal distribution.
Answers
An sample mean can be thought to be the worth from populace having a typical dissemination when both or both of these circumstances is met:
1) The populace from which the example is being taken is Regularly circulated. So for this situation, if the number of inhabitants in grade-point midpoints is regularly circulated, the example mean would be treated as a worth from a populace having a typical dissemination
2) The example size is more prominent than 30. On the off chance that we don't know about the populace, yet the example size is more prominent than 30, the example mean can be considered as a worth from a populace having a typical conveyance.
what’s the least common denominator of 5/7 and 4/5
Answers
Answer: It's 35
Step-by-step explanation:5 and 7 both go into 35
a box contains 7 green marbles, 4 blue marbles, and 8 red marbles. three marbles are selected at random from the box, one at a time, without replacement. find the probability that the first two marbles selected are not red, and the last marble is red.
Answers
i hope that this helps
goodluck :)
If you solve an equation by graphing each side as a separate line, which of the following corresponds to the solution of the equation? a. there is only a solution if the lines are identical c. the y–coordinate of the intersection point b. both the x–coordinate and the y–coordinate of the intersection point d. the x–coordinate of the intersection point Please select the best answer from the choices provided A B C D
Answers
Answer:
d. the x–coordinate of the intersection point
Step-by-step explanation:
The solution of the system with two lines is the x-coordinate of their intersection point.
a. there is only a solution if the lines are identical
No, it gives infinitely many solutions.b. both the x–coordinate and the y–coordinate of the intersection point,
No, only the x-coordinate is consideredc. the y–coordinate of the intersection point
No, only the x-coordinate is consideredd. the x–coordinate of the intersection point
Yes, correctUse the negative fractions -4/5 and -5/6
PART A
Find the decimal equivalents for each fraction.
PART B
Which is a repeating decimal? Which digit is
repeating?
Answers
Answer:
see below
Step-by-step explanation:
-4/5 using long division gives -0.8
-5/6 using long division gives -0.8333333 => repeats forever
the 3 is repeating
If x=a/b, a does not equal b, and b does not equal 0, find the value of (a+b)/(a-b) in terms of x
Answers
Answer:
[tex]\frac{x+1}{x-1}[/tex]
Step-by-step explanation:
given
x = [tex]\frac{a}{b}[/tex] ( multiply both sides by b )
bx = a
substitute a = bx into the expression
[tex]\frac{a+b}{a-b}[/tex]
= [tex]\frac{bx+b}{bx-b}[/tex] ← factor out b from each term on the numerator and denominator
= [tex]\frac{b(x+1)}{b(x-1)}[/tex] ← cancel b on numerator / denominator
= [tex]\frac{x+1}{x-1}[/tex]
Valeria is a physical therapist who specializes in pediatric leg injuries. Her patients differ in age and type of injury. Knee pain Ankle pain
0-12 years old 1 4
13-19 years old 4 3
What is the probability that a randomly selected patient is 0-12 years old given that the patient suffers from ankle pain?
Answers
The probability that a randomly selected patient is 0-12 years old given that the patient suffers from ankle pain is 4/7.
What is the probability?
Probability is used to determine the likelihood that a random event would happen. The odds that the random event happens has a probability value that lies between 0 and 1. The more likely it is that the event would occur, the closer to one, the probability value would be.
The probability that a randomly selected patient is 0-12 years old given that the patient suffers from ankle pain = number of 0 - 12 that suffer from ankle pain / total number of people that suffer from ankle pain
= 4 / (4 + 3) = 4 / 7
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in her garden pam plants the seed 2 1/4 in below the ground. After one month the tomato plant has grown a total of 10 1/2 in. How many inches is the plant above the ground.?
Answers
The plant is 8 inches above the ground
How to calculate the height of the plant above the ground ?The height of the seed below the ground is 2 1/4
9/4
After one month, the tomatoes has grown 10 1/2
10 1/2
= 21/2
The height of the plant above the ground is
21/2 - 9/4
= 8
Hence the height of the plant above the ground is 8 inches
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Solve for A
R= X (A+ B)
Answers
Answer:
Step-by-step explanation:
R=X(A+B)
distribute the x to get:
R=AX+BX
subtract BX from both sides
R-BX=AX
divide both sides by X
A=(R-BX)/X
please answer area only
Answers
Answer:10
Step-by-step explanation:
found area
consider the population p of deer in salt lake county as a function of time t, where t is the number of years after 1990. what values are in the range of this function?
Answers
The range of the function is for the population of the deer in the salt lake if found as [P, ∞).
What is defined as the range of the function?A function's range is the set of outputs it produces when applied to its entire set of outputs. The range is the collection of objects that actually come from the machine when individuals feed it all the inputs with in function machine metaphor.The number of deer is proportional to t, the number of years since 1990.
As a result, time t becomes the independent variable as well as the number of deer becomes the dependent variable; the number of deer DEPENDS upon the year.
A function's range is the set of values that the dependent variable can take.
The values in the range in this example represent the number of deer throughout salt lake in specific years.
Let 'P' be the population of the deer in salt lake.
Range: [P, ∞)
Then, the range of the function is for the population of the deer in the salt lake if found as [P, ∞).
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Find a quadratic function to model the values in the table.
Answers
The quadratic function to model the values in the table will be,
y = 3x² + 3x - 3
Option 1 is true.
What is Quadratic equation?
An algebraic equation of the second degree in x is called Quadratic equation.
Given that;
The values of x and y are,
x = -1, 0, 3
y = -3, -3, 33
Let a quadratic function is,
y = ax² + bx + c ... (i)
Then, It satisfy all the values given in table.
So, Substitute point (x, y) = (-1, -3) in equation (i) we get;
- 3 = a - b + c ... (ii)
And, Substitute point (x, y) = (0, -3) in equation (i) we get;
-3 = c .. (iii)
And, Substitute point (x, y) = (3, 33) in equation (i) we get;
33 = 9a + 3b + c ... (iv)
Now, Substitute c = -3 from (iii) in equations (ii) and (iv) we get;
From (ii);
- 3 = a - b - 3
a - b = 0 ... (v)
From (iv);
33 = 9a + 3b - 3
Divide by 3;
11 = 3a + b - 1
3a + b = 12 .... (vi)
Solve equations (v) nd (vi) we get;
a = 3 and b = 3
Thus, Substitute the values a = 3, b = 3 and c = -3 in quadratic equation we get;
y = ax² + bx + c
y = 3x² + 3x - 3
So, The quadratic function to model the values in the table will be,
y = 3x² + 3x - 3
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How many vehicles does the dealership sell for each 1000 spent on advertising
Answers
Alice went to the movie with 2 of her friends and spent $10.50. 30% of the total wad spent on movie snacks. Which proportion could be used to calculate the total amount that Alice spent on movie snacks?A. 30/100 = x/10.5B. 30/100 = 10.5/ xC. 10.5/100 = 30/xD. x/100 = 10.5/30
Answers
Alice spend a total of $10.50, and the 30% of total was spent on snacks.
So, if we call x the money spent on snacks we have that the ratio between x and total spent money is 30%:
[tex]\frac{x}{10.5}=\frac{30}{100}[/tex]Help please:):)
Create a table of data for two different linear functions. The table should use that same values of x for both functions. Based on your table, will the graph of these two functions intersect? Explain your answer
Answers
A table of data for two different linear functions using the same values of x for both functions is shown below:
x | y=2x+7 y=-x+4 -3 | 2(-3)+7=-6+7=1| -(-3)+4=3+4=7 -2 | 2(-2)+7=-4+7=3|-(-2)+4=2+4=6 -1 | 2(-1)+7=-2+7=5|-(-1)+4=1+4=5 0 | 2(0)+7=0+7=7 |-(0)+4=0+4=4 1 | 2(1)+7=2+7+9 |-(1)+4=-1+4=3 2 | 2(2)+7=4+7=11|-(2)+4=-2+4=2 3 | 2(3)+7=6+7=13|-(3)+4=-3+4=1 From the table, it can be seen that when x = -1, the function y = 2x + 7 has a value of 5 and the function y = -x + 4 has a value of 5. Therefore, the graph of the two functions will intersect at (1, 5)
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What is the equation of a line that passes through (8,-5) and is parallel to the graphed line? In a linear graph line diagram, A line passes through (minus 4, minus 6) and (8, 3) which intersects the x-axis at 4 units and the y-axis at minus 3 units.
Answers
The formula for the line that intersects at (8,-5) and is parallel to line x+y = 8 is given by the algebraic expression y = -x +3.
What is Algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. Variables and constants can both be used in an algebraic expression.A coefficient is any quantity that is added before a variable and then multiplied by it.The Algebraic expression in this case is:
x + y = 8
which traverses points (8,-5)
Let's start by utilizing the point-intercept equation of line, which is provided by: to determine the slope of line m, that is parallel towards the line x + y = 8.
y = mx + c →(1)
x + y = 8
y = -x + 8
Comparing the aforementioned Algebraic expression to equation (1), we obtain
m = -1
The slope of the line parallel to the line x + y = 8 will now be the same, and it will be m = -1.
Let's use the point-slope equations of line to determine the linear equation now:
(y-y₁) = m(x-x₁)
Changing every value in the equation above to obtain the Algebraic expression for a line
(y-(-5)) = -1(x-8) (x-8)
(y+5) = -x+8
y + 5 = -x +8
y = -x +3
The formula for the line that intersects at (8,-5) and is parallel to line x+y = 8 is given by the algebraic expression y = -x +3.
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Step-by-step explanation:
Show whether or not each pair of triangles are similar, if possible. Justify your answer, and write a similarity statement when the triangles are similar.
Answers
If the matching sides and angles of two triangles are proportional, then the triangles are said to be similar.
Triangles that share the same form but differ in size are said to be similar.
Examples of related objects are all equilateral triangles and squares with any side length. In other words, two similar triangles have similar sides that are proportionately equal and similar angles that are congruent. Three triangle-specific theorems can be used to easily identify between related triangles. SSS, SAS, ASA, AAS, and HL are the five ways to determine whether two triangles are congruent.SSS (side, side, side) (side, side, side) SSS, which stands for "side, side, side," denotes that there are two triangles with equal sides. . AAS (angle, angle, side), ASA (angle, side, angle), SAS (side, angle, side), and HL (angle, angle, side) (hypotenuse, leg)Hence from the above properties we can find if any two triangles are similar.
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Question 2 of 10
Find f(3) if f(x)=x^3+2x²-x-1
Answers
IN THE PLACE OF X PLUG IN 3 AND SIMPLIFY
[tex]f(3) = ({3})^{3} + 2( {3})^{2} - (3) - 1 \\ f(3) = 27 + 2(9) - 3 - 1 \\ f(3) = 27 + 18 - 4 \\ f(3) = 45 - 4 \\ f(3) = 41[/tex]
ATTACHED IS THE SOLUTION.
24) Find the greatest common factor of 10 and 125.
A) 1
B) 2
C) 5
D) 10
Answers
Domenica is creating a banner to hang outside her business. Her design is shown below. It is composed of a square and two equal right triangles, one on either side of he square.
Answers
Take into account that the figure at the center is a square. Its area is given by:
A1 = (8 ft)² = 64 ft²
To the area of the other two triangles, first determine the length of the below side of the triangle, as follow:
20 ft - 8 ft = 12 ft
12 ft is the length of the two sides. Due to both triangles are equal, the length of their sides is:
12 ft/2 = 6 ft
Then, the area of the triangles is:
A2 = (6 ft)(8 ft)/2 = 48 ft/2 = 24 ft
Hence, the total area of the figure is:
AT = A1 + A2 + A2
AT = 64 ft² + 24 ft² + 24 ft² = 112 ft²
The toal area of the figure is 112 ft²
Use the long division method to find the result when 3x³ +19x² + 23x + 15 is
divided by 25.
Answers
The result by using long division method for the given polynomial equation is: 25[(1/3x³) +(1/19x²) + (1/23x) + (1/15)]
What is long division method?
In mathematics, the long division method can be performed on the polynomial equations. Basically, in this big equation can be solved by making smaller group of equations to make the calculation simple. It divide the dividend with divisor.
According to the question, the given polynomial equation is 3x³ +19x² + 23x + 15. Using long division method, divide it by 25
Therefore, the expression can be written as:
Required expression: [tex]\frac{3x^{3} +19x^{2} + 23x + 15 }{25}[/tex]
Dividing it by 25, we get:
(25/3x³) +(25/19x²) + (25/23x) + (25/15)
⇒ 25[(1/3x³) +(1/19x²) + (1/23x) + (1/15)]
Hence, the result by using long division method for the given polynomial equation is: 25[(1/3x³) +(1/19x²) + (1/23x) + (1/15)]
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109% as a mixed or whole number
Answers
Answer:
1 9/100Step-by-step explanation:
In order to convert 109/100 to mixed number, you follow these steps :
Divide the numerator by the denominator
109 ÷ 100 = 1 with a remainder of 9
Write down the whole number 1 and then write down the remainder as new numerator (9) above the denominator (100), As below :
1
9
100
Answer:
109/100 or 1.09