If (3+√5)(4-√5)=a+b√5, where a and b are integers, then what is the value of a + b?

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Explanation:

We'll use the distance formula here. Rather than compute the distance d based on two points given, we'll go in reverse to use the given distance d to find what the coordinate must be to satisfy the conditions.

We're given that d = 5

The first point is [tex](x_1,y_1) = (5,2)[/tex] and the second point has coordinates of [tex](x_2,y_2) = (x,5)[/tex] where x is some real number.

We'll plug all this into the distance formula and solve for x.

[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\5 = \sqrt{(5-x)^2+(2-5)^2}\\\\5 = \sqrt{(5-x)^2+(-3)^2}\\\\5 = \sqrt{(5-x)^2+9}\\\\\sqrt{(5-x)^2+9} = 5\\\\(5-x)^2+9 = 5^2\\\\(5-x)^2+9 = 25\\\\(5-x)^2 = 25-9\\\\(5-x)^2 = 16\\\\5-x = \pm\sqrt{16}\\\\5-x = 4 \ \text{ or } \ 5-x = -4\\\\-x = 4-5 \ \text{ or } \ -x = -4-5\\\\-x = -1 \ \text{ or } \ -x = -9\\\\x = 1 \ \text{ or } \ x = 9\\\\[/tex]

This means that if we had these three points

Then segments AB and AC are each 5 units long.

Answer:

c = 12

Step-by-step explanation:

i'm Attaching the work

Answer:

113.1 cm²

Step-by-step explanation:

V = [tex]\frac{1}{3}[/tex] [tex]\pi[/tex] r² h

h = 12 cm , r = 3 cm , [tex]\pi[/tex] = [tex]\frac{22}{7}[/tex]

V ≈ 113.1 cm²

Answer:

<5 and <6 are supplementary angles

<1 and <6 are vertical angles

Answer:

136

Step-by-step explanation:

Surface area=2*(lb+bh+lh)

=2*(12+42+14)=2*68=136

I'm guessing the power series given is

[tex]\displaystyle \sum_{n=1}^\infty (-1)^{n+1}\frac{(x-8)^n}{8^n}[/tex]

which you can condense somewhat into

[tex]\displaystyle -\sum_{n=1}^\infty \left(\frac{8-x}8\right)^n[/tex]

You should recognize this as a geometric series, which converges for

[tex]\left|\dfrac{8-x}8\right|<1 \implies |8-x|<8 \implies \boxed{0 < x < 16}[/tex]

The answer to part A is correct. You basically have to find the area of that L shape, and subtract off the area of the shaded trapezoid.

To get part B, you need to find the perimeter. This is because the trim runs along the bottom edge of the wall. Refer to the diagram below. Adding up the exterior sides gets us:

12+12+4+8+8+4 = 48

So she needs 48 meters of trim.

I'm not sure what your teacher means by "what assumptions do you make". If your teacher is referring to something like making room for a door, then we'll have to subtract some value from that 48. The problem with this though is that we don't have any clue how wide the door is. So you'll have to ask your teacher for clarification.

Luckily, this value 48 is an overestimate of the amount of trim Jennifer needs to buy. In my opinion, it's better to overestimate than underestimate, which saves from having to make another trip to the hardware store.

The question is incomplete, the complete question is;

A factory produces 1,250,000 toys each year. The number of toys is expected to increase by about 150% per year. Which model can be used to find the number of toys being produced, n (in millions), in t years?

A. n= 2.5(1.5)/t, t cannot = 0

B. n= 1.5t^2 + 1.25

C. n= 1.5t + 1.25

D. n= 1.25(2.5^t)

Answer:

D. n= 1.25(2.5^t)

Step-by-step explanation:

This is an exponential growth problem. In mathematics, for an exponential growth problem;

P = Po(1 + r)^t

Where;

P= amount at time t

Po =initial amount

r= rate

t= time

In the context of the question we have;

n= 1.25(1 + 150/100)^t

n= 1.25(2.5)^t

Answer:

W

Step-by-step explanation:

I done it before

Answer:

Answer

5.0/5

2

poojamaurya21

Virtuoso

133 answers

14.9K people helped

Answer:

): "x2" was replaced by "x^2". 4 more similar replacement(s).

Step by step solution :

Step 1 :

Step 2 :

Pulling out like terms :

2.1 Pull out like factors :

x6 - x5 + x4 - x3 + x2 - x =

x • (x5 - x4 + x3 - x2 + x - 1)

2.2 Factor x5 - x4 + x3 - x2 + x - 1

Try to factor this 6-term polynomial into (2-term) • (3-term)

Begin by splitting the 6-term into two 3-term polynomials:

-x2 + x - 1 and x5 - x4 + x3

Next simplify each 3-term polynomial by pulling out like terms:

-1 • (x2 - x + 1) and x3 • (x2 - x + 1)

Note that the two simplified polynomials have x2 - x + 1 in common

Now adding the two simplified polynomials we get

(x3 - 1) • (x2 - x + 1)

Answer:

it's the 3rd option

Step-by-step explanation:

f(x) 0 over the intervals (–∞ –3)

Hope it's right

Answer:

1. 3 yards= 9 feet

2. 78 cups=5 gallons

3. 72 inches = 2 yards

4. 80 ounces = 5 pounds

5. 84 inches = 7 feet

6. 24 feet = 8 yards

7. 40 pints = 5 gallons

8. 16 cups = 5 quarts

9. 144 inches = 4 yard

10. 48 ounces = 3 pounds

Answer:

See below.

Step-by-step explanation:

Call the sum of the first n terms S.

S = a + ar + ar^2 + ar^3 + ... + ar^(n -1)

Multiply both sides by r.

Sr = ar + ar^2 + ar^3 + ar^4 + ... + ar^n

No subtract S - Sr.

      S =  a + ar + ar^2 + ar^3 + ar^4 + ... + ar^(n -1)

(-)    Sr =       ar + ar^2 + ar^3 + ar^4 + ... + ar^(n - 1) + ar^n

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

  S - Sr = a - ar^n

S(1 - r) = a(1 - r^n)

S = a(1 - r^n)/(1 - r)

S = a(r^n - 1)/(r - 1)

a + ar + ar^2 + ar^3 + ... + ar^(n -1) = a(r^n - 1)/(r - 1)

Answer:

300 raisins

Step-by-step explanation:

sum the parts of the ratio, 3 + 27 = 30 parts

Divide the total by 30 for the value of one part of the ratio.

3000 ÷ 30 = 100 ← value of 1 part of the ratio , then

3 parts = 3 × 100 = 300 ← number of raisins in a box

Answer:

verdical lines have an undefined slope so it might be 4

Answer:

[tex] \frac{21}{4} + \frac{35}{8} \\ = \frac{77}{8} \\ = 9 \frac{5}{8} [/tex]

Answer:

13/9

Step-by-step explanation:

Given

5/9 + 8/9

Both fractions have the same denominator.

Therefore, pick one of the denominator and add the numerators

5/9 + 8/9

= (5+8) / 9

= 13/9

5/9 + 8/9 = 13/9

Given height and surface-area-to-volume ratio: r = 2 * h / (h * SA:V - 2) , Given volume and lateral area: r = 2 * V / A_l , Given base area: r = √(A_b / (2 * π)) , Given lateral area and total area: r = √((A - A_l) / (2 * π)) .

Answer:

Area = 14.8

Step-by-step explanation:

Area = 5/2 + a^2*sqrt(5 + 2 sqrt(5) )

This formula given the side length, calculates the area.

a = 2

Area = 2.5 + 2^2 * sqrt(5 + 2*sqrt(5) )

Area = 2.5 + 4 * sqrt(5 + 2*2.236)

Area = 2.5 + 4* sqrt(5+ 4.4721)

Area = 2.5 + 4*sqrt(9.4721)

Area = 2.5 + 4*3.0776

Area = 2.5 + 12.3107

Area = 14.8107

Answer:

A ≈ 30.8 m2

Step-by-step explanation:

Mark Brainliest if correct:

x = -2, 9

Step-by-step explanation:

x2: x + 2 = 0

x = -2

x1: x - 9 = 0

x = 9

x = -2, 9

Answer:

Step-by-step explanation:

r = d/2

r = 2.4 m/2 = 1.2

h = 1.8

pi = 3.14

Volume = pi * r^2 * h

Volume = 3.14 * 1.2^2 * 1.8

Volume = 8.139

Volume = 8 to the nearest m^3

Answer:

27 litros de leche de búfalo equivalen a 45.9 litros de leche de vaca.

Step-by-step explanation:

Sabiendo que un litro de leche de búfala equivale a 1.7 litros de leche de vaca, podemos calcular el equivalente de capacidad de la vaca para 27 litros de leche de búfala mediante Regla de Tres Simple:

[tex]x = 27\,L\times \frac{1.7\,L}{1\,L}[/tex]

[tex]x = 45.9\,L[/tex]

27 litros de leche de búfalo equivalen a 45.9 litros de leche de vaca.

Answer:

The answer is -51146

Step-by-step explanation:

Just substract simple

2x+5

x+1

2+3.......

x+1

Answer:

ask your teachehope help

and search on somewhere I search it there is so many answer

Answer:

x=80°

Step-by-step explanation:

Triangles always add up to 180°.

As you have 2 angles, you would have to add them together and then take it away from 180° to get your answer.

50+50=100°

180-100=80°

Hope this helps :)

Answer:

x = 80°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the given angles from 180 for x

x = 180° - (50 + 50)° = 180° - 100° = 80°

Answer:

(8 × 2) × 6 = 8 × (2 × 6) represents associative property of whole number.

[tex]\\ \sf\longmapsto 2(5m-4)-3(m-5)^2[/tex]

[tex]\\ \sf\longmapsto 10m-8-3(m^2-10m+5^2)[/tex]

[tex]\\ \sf\longmapsto 10m-8-3(m^2-10m+25)[/tex]

[tex]\\ \sf\longmapsto 10m-8-3m^2+30m-75[/tex]

[tex]\\ \sf\longmapsto -3m^2+30m+10m-75-8[/tex]

[tex]\\ \sf\longmapsto -3m^2+40m-83[/tex]

Answer:

given values are:

1200 = 20×30 + 1/2 × 30²a

1200= 600 + 1/2 × 900a

600 = 450a

a = 600 / 450

a = 1.33 m/s²

v² = 20² +2 × 1.33 × 1200

v²= 400 + 3192

v = √3592

v = 59.9 ≈ 60 m/s