A triangle has the vertices of P(2,5),Q(-4,7) and R(-2,-1) classify the triangle is scalene, Isoceles or an equilateral triangle

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]

[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]

Answer:

- Reflected over the x-axis  

- Compressed by a factor of 0.4.

- Translated 2 units left

Step-by-step explanation:

Given

[tex]y = \sqrt[3]{x}[/tex]

[tex]y' = -(0.4)\sqrt[3]{x-2}[/tex]

Required

The transformation from y to y'

First, y is reflected over the x-axis.

The transformation rule is:

[tex](x,y) \to (x,-y)[/tex]

So, we have:

[tex]y = \sqrt[3]{x}[/tex] becomes

[tex]y' = -\sqrt[3]{x}[/tex]

Next, it was compressed by a scale factor of 0.4

The rule is:

[tex]y' = k * y[/tex]

Where k is the scale factor (i.e. k = 0.4)

So, we have:

[tex]y' = 0.4 * -\sqrt[3]{x}[/tex]

[tex]y' = -(0.4)\sqrt[3]{x}[/tex]

Lastly, the function is translated 2 units left;

The rule is:

[tex](x,y) \to (x-2,y)[/tex]

So, we have:

[tex]y' = -(0.4)\sqrt[3]{x - 2}[/tex]

Answers:

-reflected over the x-axis

-translated 2 units right

-compressed by a factor of 0.4

any irrational number would do, like pi or root(2)

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.

Answer:

38

Step-by-step explanation:

If 9 workers can complete a job in 56 minutes, then it takes 36 minutes for 14 workers.

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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Answer:

Step-by-step explanation:

1) Least common denominator of 4 and 2 is 4

To eliminate the fraction, each term should be multiplied by 4

ANS:option c

2) Mercury level of water 'y' years = Initial measure +rate of increase 'y' years

0.05 +0.1y = 0.12+0.06y

Ans : Option c

3) 4b +6 = 2 - b + 4

Add 'b' to both sides

4b + b + 6 = 2 + 4

5b + 6 = 6

Subtract 6 from both sides

5b = 6 - 6

5b = 0

 b = 0

Ans : Option b

4) Maximum decimal places in this equation is 2. So, to eliminate decimal places, The equation should be multiplied by 100

Ans: option d

5) y +6 = -3y + 26

Add 3y to both the sides

y + 6 + 3y =  26

y + 3y + 6 = 26

4y + 6 = 26

Subtract 6 from both sides

4y = 26-6

4y = 20

Divide bothe sides by 4

y = 20/4

y = 5

Ans: option c

6) '2x' is  subtracted from both side of the equation.

Ans: option a - subtraction property of equality

Answer:

Step-by-step explanation:

Answer:

it doesn't show anything

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?  

Answer:

-26

Step-by-step explanation:

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

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 .....

Answer:

Exact surface area = 500+20pi square cm

=============================================================

Explanation:

All 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

Add 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).

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.

X -Y =44 will represent the number of glasses of ice tea .

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.

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

Answer:

-7

Step-by-step explanation:

Answer:

1 = Input G

2 = Input F

3 = Input H

Step-by-step explanation:

(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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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.

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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Answer:

4x-2

Step-by-step explanation:

X=muffins

Answer:

16

Step-by-step explanation:

Number of attires Clara has initially = x

lends half her collection of formal attires to her sister

Attires remaining after lending = Number of attires Clara has initially - attires she lent her sister

= x - 1/2x

= 1/2x

Clara then buys four more attires

= 1/2x + 4

If she has 12 attires now

12 = 1/2x + 4

12 - 4 = 1/2x

8 = 1/2x

x = 8 ÷ 1/2

= 8 × 2/1

= 16

x = 16

Number of attires Clara has initially = x = 16

Answer:

The shadow length is 67

Step-by-step explanation:

solution shown in the picture