To verify that a given parallelogram is a rectangle, you can calculate the lengths of all sides, and show that both pairs of opposite sides are congruent and calculate the slopes of every side, and show that adjacent sides are perpendicular.
Answer: 1st one and last one
Step-by-step explanation:
(13+29-2)÷2
show your work
Answer:
[tex](13 + 29 - 2) \div 2 \\ (42 -2 ) \div 2 \\ 40 \div 2 \\ = 20[/tex]
Answer:
(13+29-2)÷240÷220hope it helps.
stay safe healthy and happy..evaluate f(3) if (x) = -4x+5
Answer:
-7
Step-by-step explanation:
complete the table of values for y=x^2-2x+2
find the next four terms of the sequence 5, 4, 9, 13, 22
Hello,
It is the Fibonacci 's suit.
[tex]u_1=5\\u_2=4\\u_3=u_1+u_2=5+4=9\\u_4=u_2+u_3=4+9=13\\u_5=u_3+u_4=9+13=22\\u_6=13+22=35\\u_7=22+35=57\\u_8=35+57=92\\u_9=57+92=149\\\\\\\boxed{u_{n+2}=u_{n}+u_{n+1}}\\[/tex]
(a) A pentagon ABCDE has sides AE and CD parallel and the line EC
is parallel to side AB. Sides ED and BC, when extended, meet at a
point F. ZABC is equal to ZCDE. Show that ZAEC = ZCFD.
(b) If, furthermore, triangles EDC and DFC are both isosceles, with
ED = DC and DF = FC, find the angles of the pentagon.
(a) ∠AEC = ∠CFD, by transitive property of equality
(b) ∠CDE = 108°, ∠DCB = 108°, ∠ABC = 108°,∠EAB = 144°, ∠AED = 72°
The reason the above values are correct is as follows:
(a) The given parameters are;
Figure ABCDE is a pentagon
The sides AE is parallel to side CD
Line EC is parallel to side BC
The point of intersection of the extension off side ED and BC = Point F
∠ABC = ∠CDE
Required:
To show that ∠AEC = ∠CFD
Method:
Draw the pentagon ABCDE and include the added construction
Analyze the drawing
Solution:
∠ECF and ∠ABC are corresponding angles between parallel lines EC ║BC
∴ ∠ECF ≅ ∠ABC by corresponding angles formed by parallel lines are congruent
∠ECF = ∠ABC by definition of congruency
∠ABC = ∠CDE = ∠ECF by transitive property
∠ECD ≅ ∠AEC by alternate angles formed between parallel lines having a common transversal
∠ECD = ∠AEC by definition of congruency
∠ECF = ∠FCD + ∠ECD by angle addition postulate
∠CDE = ∠FCD + ∠CFD by exterior angle theorem
From ∠CDE = ∠ECF above, we have;
∠ECF = ∠FCD + ∠ECD = ∠FCD + ∠CFD
∴ ∠ECD = ∠CFD by addition property
∠ECD = ∠AEC, therefore;
∠AEC = ∠CFD, by transitive property
(b) Given that ΔEDC and ΔDFC are both isosceles triangles, with sides;
ED = DC, and DF = FC;
Let r represent ∠CFD, we have;
∠FCD = ∠CDF by base angles of isosceles triangle ΔDFC
∠ECD = ∠CED by base angles of isosceles triangle ΔEDC
∠AEG = ∠CDE by corresponding angles formed by parallel lines having a common transversal
∠AEC = ∠ECD by alternate angles
∴ ∠AEG + ∠AEC + ∠CED = 180° Sum of angles on a straight line
∠CDE = ∠CFD + ∠FCD
∠CDE + ∠CDF = 180° (linear pair angles)
∴ ∠AEG + ∠CDF = 180° by transitive property
∠AEC + ∠CED = ∠CDF by transitive property
∠AEC = ∠ECD = ∠CED = ∠CFD = r
∴ ∠CFD + ∠CFD = ∠CDF
2·r = ∠CDF
∠CDE = ∠FCD + ∠CFD
∠FCD = ∠CDF = 2·r
∴ ∠CDE = 2·r + r = 3·r
∠CDE = 3·r
The angles of the pentagon are;
∠CDE + ∠DCB + ∠ABC + ∠EAB + ∠AED = 540° sum of angles in a pentagon
∠DCB = 180° - ∠FCD
∠DCB = 180° - 2·r
∠ABC = ∠CDE = 3·r
∠EAB = ∠CEH corresponding angles
∠CEH = 180 - ∠AEC
∴ ∠EAB = 180° - ∠AEC
∴ ∠EAB = 180° - r
∠AED = ∠AEC + ∠CED = r + r = 2·r
∠AED = 2·r
Therefore, we have;
3·r + 180° - 2·r + 3·r + 180° - r + 2·r = 540°
5·r + 360° = 540°
r = (540° - 360°)/5 = 36°
r = 36°
∠CDE = 3 × 36° = 108°
∠DCB = 180° - 2×36° = 108°
∠ABC = 3 × 36° = 108°
∠EAB = 180° - 36° = 144°
∠AED = 2 × 36° = 72°
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I have a lot of algebra problems. Someone help me even with this one please!
X -Y =44 will represent the number of glasses of ice tea .
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the systems of equations to their solutions.
[tex]x = 2 \\ y = 7[/tex]
is the answer to:
[tex]y = 11 - 2x \\ 4x - 3y = - 13[/tex]
_________________________________________
[tex]x = 5 \\ y = 2[/tex]
is the answer to:
[tex]2x + y = 12 \\ x = 9 - 2y[/tex]
_________________________________________
[tex]x = 3 \\ y = 5[/tex]
is the answer to:
[tex]2x + y = 11 \\ x - 2y = - 7[/tex]
_________________________________________
[tex]x = 7 \\ y = 3[/tex]
is the answer to:
[tex]x + 3y = 16 \\ 2x - y = 11[/tex]
An x-method chart shows the product a c at the top of x and b at the bottom of x. Below the chart is the expression a x squared + b x + c. What are the factors of x2 – 144? And
Answer:
[tex](x -12)(x + 12)[/tex]
Step-by-step explanation:
Given
See attachment for chart
Required
The factors of [tex]x^2 - 144[/tex]
First, express [tex]x^2 - 144[/tex] as [tex]ax^2 + bx + c[/tex]
So, we have:
[tex]x^2 - 144 = x^2 + 0x - 144[/tex]
Compare the above expression to: [tex]ax^2 + bx + c[/tex]
We have:
[tex]ax^2 + bx + c = x^2 + 0x - 144[/tex]
So:
[tex]a =1[/tex]
[tex]b =0[/tex]
[tex]c = -144[/tex]
and
[tex]a * c = d * e[/tex]
Calculate ac
[tex]a* c = 1 * -144[/tex]
[tex]a* c = -144[/tex]
Rewrite as:
[tex]a* c = -12 * 12[/tex]
Recall that:
[tex]a * c = d * e[/tex]
Hence:
[tex]d = -12; e = 12[/tex]
So, on the x chart, we have:
ac
d e
b
This gives:
-144
-12 12
0
The factors are
[tex](x + d)(x + e)[/tex]
[tex](x -12)(x + 12)[/tex]
Answer:
✔ (x – 12)
and
✔ (x + 12)
Step-by-step explanation:
What is the value of k?
Answer:
Step-by-step explanation:
recall that the inside angles of a triangle add up to 180°
and also that the angle 115° is the other part of a 180° total
180=115+y
180-115 =65
then the inside angle at Y is 65°
add the three inside (interior of the triangle) angles up
180= 65 + (4k+5) + (6k+10)
180 = 65 + 10k + 15
180 = 80 + 10k
100 = 10k
10 = k
see how I did that?
Monique wants to have an equal number of cups and napkins. What
is the least number of packages of cups and the least number of
packages of napkins Monique should buy to have an equal number
of cups and napkins?
Ethan buys 4 pack of muffins. he uses a coupon an saves 2$ off total.
Which expression represents his total cost?
Answer:
4x-2
Step-by-step explanation:
X=muffins
What is the least possible value of (x +1)(x+2)(x+3)(x +4)+2019 where x is a real
number?
MANY POINTS
Answer:
f(x)=(x+1)(x+2)(x+3)(x+4)+2019
f(x)=(x2+5x+4)(x2+5x+6)+2019
Suppose that y=x2+5x
Hence we have f(y)f(y)=(y+4)(y+6)+2019=y2+10y+24+2019=y2+10y+25+2018=(y+5)2+2018≥2018[∵(y+5)2≥0,∀y∈R]
and therefore…. min (f(x))=2018
ANSWER = 2018
Step-by-step explanation:
hope that helps >3
Answer:
2018
Step-by-step explanation:
By grouping the first, last and two middle terms, we get ([tex]x^{2}[/tex]+5x+4)([tex]x^{2}[/tex]+5x+6) + 2019. This can then be simplified to ([tex]x^{2}[/tex]+5x+2)^2 - 1 + 2019 Noting that squares are nonnegative, and verifying that [tex]x^{2}[/tex] + 5x + 5 = 0 for some real x, the answer is 2018.
if a real estate company gives 3% commission on to it's agents. if an agent sold a piece of land for 12,50,000, how much cccommision did the agent get ?
Answer:
$37500
Step-by-step explanation:
Given data
Selling price=$1250000
Commission= 3%
Let us find 3% of 1250000
=3/100*1250000
=0.03*1250000
=$37500
Hence the commission will be $37500
Can someone help me with this math homework please!
Can someone help me with this math homework please!
Answer:
1 = Input G
2 = Input F
3 = Input H
Step-by-step explanation:
The sum of a father's and his son's age is 60. Eight years ago, the father's age was 3 times that of his son. How old is each of them?
Answer:
Father=41
Son=19
Step-by-step explanation:
Father=f
Son=s
f+s=60
Eight years ago would mean that 16 is subtracted from 60 since there is both of them
3s+s=4s
4s=44
s=11
11+8=19
33+8=41
After 3 points have been added to every score in a sample, the mean is found to be M 5 83 and the standard deviation is s 5 8. What were the values for the mean and standard deviation for the original sample
Answer:
Hence the value for the mean is 80 and the standard deviation for the original sample is 8.
Step-by-step explanation:
Mean = 83-3 = 80.
Here the standard deviation didn't change = 8.
Can someone help me with this math homework please!
Answer:
Step-by-step explanation:
Please help with (ii). thank you!!!
Answer:
Exact surface area = 500+20pi square cm
=============================================================
Explanation:
A = area of the bottom face = 10*12 = 120B = area of the left face = 7*12 = 84C = area of the right face = 7*12 = 84D = area of the front face = 7*10-0.5*pi*2^2 = 70 - 2piE = area of the back face = 7*10-0.5*pi*2^2 = 70 - 2piF = area of the top face = 2*3*12+0.5*2*pi*2*12 = 72+24piAll areas mentioned are in square cm, which can be abbreviated to cm^2.
Faces A,B,C are straight forward as they are simply rectangles. The remaining 3 other faces are a bit tricky.
Faces D and E involve subtracting off the area of a semicircle of radius 2 from a 7 by 10 rectangle area. The formula pi*r^2 is the area of a full circle, while 0.5*pi*r^2 is the area of a semicircle. From there, I then plugged in r = 2.
The top face is really a combination of 3 different pieces (two flat, one curved in the middle). Each flat part is of area 3*12 = 36, so that doubles to 2*3*12 when accounting for both flat parts. The curved portion will involve the lateral surface area of a cylinder formula which is
LSA = 2*pi*r*h
but since we're only dealing with half the lateral area, we multiply that by 0.5 to get 0.5*2*pi*r*h. From there, I plugged in r = 2 and h = 12.
-----------------------
In summary we have these six areas for the faces
bottom = 120left = 84right = 84front = 70 - 2piback = 70 - 2pitop = 72 + 24piAdd up those sub areas to get the full surface area of this particular 3D solid.
120+84+84+(70-2pi)+(70-2pi)+(72+24pi)
(120+84+84+70+70+72)+(-2pi-2pi+24pi)
500+20pi
This is the exact surface area in terms of pi. If you want the approximate version of this, then you could replace pi with 3.14 and compute to get 562.8 cm^2
Use more decimal digits in pi to get a more accurate value. If you use your calculators version of pi, then you should get somewhere around 562.831853 cm^2
In this case, I think it's better to stick with the exact surface area (unless your teacher instructs otherwise).
The total profit P of manufacturing x hundred DVD's is given by the equation below.
P = 600 + 1,500x − 100x2
Find x if the total profit is $5,600.
Answer:
x = -7.5
Step-by-step explanation:
P = 600 + 1,500x − 100x^2
P = − 100x^2 + 1,500x + 600
x = -b/2a
1500/ (2 x -100)
x = -7.5
Which number produces an irrational number when multiplied by 3/4
any irrational number would do, like pi or root(2)
What does the point (1994, 400) on the graph represent?
Answer: There are 400 tadpoles in the year 1994.
This is because any point is of the form (x,y) where in this case
x = year number
y = tadpole population number
So (x,y) = (1994, 400) means x = 1994 and y = 400 pair up together.
In short, the year x = 1994 corresponds to the population of y = 400 tadpoles.
From the years 1990 to 1992, the population is increasing since the curve goes upward when moving from left to right. Then from 1992 to 1993, the population decreases hitting its lowest point in that specific region. From 1993 to 1997, the population increases before it decreases again from 1997 to 1999.
I NEED HELP SOMEONE HELP ME OUTTT!!
If a/2 =b/3, What is the value of 6a-4b ?
a. 0
b. 1
c. 2
d. 3
Answer:
A
Step-by-step explanation:
6 (2) - 4 (3)
12 - 12
0
hope this helps you
Which action taken by a central bank would reflect expansionary monetary policy?
A. Lowering the discount rate to provide more loans to banks
B. Raising the interest that it pays to banks on the balance of their reserves
C. Raising reserve requirements for all banks
D. Selling treasury securities to banks to reduce the money supply
Answer:
b
Step-by-step explanation:
well when raising the intrest on other banks it will cause a effect the money supply. the expansionaty monetary policy revolves around intrest rates. B is the only answer that best explains what im trying to say
The action of lowering the reserve requirements for all banks and sales of treasury securities to banks to help reduce money supply reflect the expansionary monetary policy.
What is expansionary monetary policy?An expansionary monetary policy is an economy policy used to stimulate a declining economy and gross domestic policy.
The 3 expansionary monetary policy includes
lowering of interest rates
lowering of banks reserve requirements
buying of government securities.
Therefore, the action of lowering the reserve requirements for all banks and sales of treasury securities to banks to reduce the money supply reflect the expansionary monetary policy.
Hence, the Option C and D is correct
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When the angle of elevation of the sun is
42°, fnd the length of the shadow, to the
nearest foot, cast by a tree 60 feet tall.
Answer:
The shadow length is 67
Step-by-step explanation:
solution shown in the picture
The amount of time needed to complete a job, t, varies inversely with the number of workers, w. If
9 workers can complete a job in 56 minutes, how many minutes would it take 14 workers?
Do not include the units in your answer.
Answer:
38
Step-by-step explanation:
If 9 workers can complete a job in 56 minutes, then it takes 36 minutes for 14 workers.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that amount of time needed to complete a job, t, varies inversely with the number of workers, w.
t=k/w
k is a constant
9 workers can complete a job in 56 minutes
t=56 and w=9
56=k/9
Apply cross multiplication
k=9×56
k=504
We need to find how many minutes would it take for 14 workers.
t=504/14
t=36
Hence, it takes 36 minutes for 14 workers.
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help me solve pleassee
Answer:
122.5 cm²
Step-by-step explanation:
the area of shaded region =
(14×10) - (7 × 2.5)
= 140 - 17.5
= 122.5 cm²
Answer:
points for points .....
1. If f(x) = 6x + 13x + 2x - 5 and f(-1) = 0, find the
factors of f(x)
Answer:
-26
Step-by-step explanation:
Insert the f(-1) into the equation.It'll be f(-1) = 6(-1) + 13(-1) + 2(-1) - 5After you times all of it. You'll get 7-13-2-5Solve it and you'll get -26 If and are the zeroes of the polynomial 2x^2+3x+5 then the value of 1/alpha + 1/beta
Pls answer fast..I’ll mark the brainlest
Answer:
-4/15
Step-by-step explanation:
Mathematically, we know that;
alpha= -b/a and beta = c/a
a refers to the coefficient of the x^2 which is 2
b is the coefficient of x which is 3
c is the last number which is 5
alpha = -b/a = -3/2
beta = c/a = 5/2
1/alpha = -2/3
1/beta = 2/5
so we have the sum as;
-2/3 + 2/5
= -5(2) + 3(2)/15 = (-10 + 6)/15 = -4/15
