Simplify:

-4a + 2(a + 9)

A. -2a + 9
B. -2a + 18
C. 2a + 9
D. 2a + 18

Answer:

1) 2 × (-15) = -30

It could be 1+12 2+11 3+10 4+9 5+8 6+7 any of those

Answer:

A

Step-by-step explanation:

6 (2) - 4 (3)

12 - 12

0

hope this helps you

Answer:

1/36

Step-by-step explanation:

Since Tess rolled 2 different dices, there are 36 different possibilities. Rolling two 4's is 1 of them.

Therefore, the probability of Tess rolling 2 fair dice is 1/36

Hope this helped have a great rest of your day!

Answer:

1 out of 36 chance because add what a dice equals to then divide

(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:

$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

Answer:

A

Step-by-step explanation:

A vertical line has an undefined slope

Line A is a vertical line

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:

The shadow length is 67

Step-by-step explanation:

solution shown in the picture

Answer:

1 = Input G

2 = Input F

3 = Input H

Step-by-step explanation:

Answer:

[tex](13 + 29 - 2) \div 2 \\ (42 -2 ) \div 2 \\ 40 \div 2 \\ = 20[/tex]

Answer:

hope it helps.

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

Answer:

4x-2

Step-by-step explanation:

X=muffins

Answer:

la respuesta sería 62, escribo esto por que me está obligando la aplicación :v

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:

-26

Step-by-step explanation:

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:

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

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:

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:

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

Answer:

Step-by-step explanation:

Here's the game plan. In order to find a point on the x-axis that makes AC = BC, we need to find the midpoint of AB and the slope of AB. From there, we can find the equation of the line that is perpendicular to AB so we can then fit a 0 in for y and solve for x. This final coordinate will be the answer you're looking for. First and foremost, the midpoint of AB:

and

Now for the slope of AB:

and

 So if the slope of AB is 1/3, then the slope of a line perpendicular to that line is -3. What we are finding now is the equation of the line perpendicular to AB and going through (0, 3):

and filling in:

y - 3 = -3(x - 0) and

y - 3 = -3x + 0 and

y - 3 = -3x so

y = -3x + 3. Filling in a 0 for y will give us the coordinate we want for the x-intercept (the point where this line goes through the x-axis):

0 = -3x + 3 and

-3 = -3x so

x = 1

The coordinate on the x-axis such that AC = BC is (1, 0)

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

Explanation:

The 90 degree counterclockwise rotation rule we use is

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

the x and y coordinates swap places, and we change the sign of the first coordinate after the swap.

After using that rotation rule, we would go from (8,4) to (-4, 8) which is the final answer.

----------------

Extra info (optional section):

Define the following three points

A = (0,0)

B = (8,4)

C = (-4,8)

Use the slope formula to find that AB and AC have slopes of 1/2 and -2 in that order.

Those slopes multiply to -1, since (1/2)*(-2) = -1. This is a property of any two perpendicular lines as long as neither line is vertical and neither is horizontal. So this is sufficient to prove that the lines are perpendicular. This further means that a 90 degree rotation has taken place.

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 .....

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]

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.

Answer:

Step-by-step explanation: