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Roman55 [17]
3 years ago
14

Write an equation and then use it to solve: Sasha gives half of her books to the local library and keeps the other half. Her bes

t friend gives her 3 more books. She now has 57 books. How many books did she have to begin with?
Mathematics
1 answer:
boyakko [2]3 years ago
8 0

Answer:

120 books

Step-by-step explanation:

57 + 3 = 60

60 x 2 = 120

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Given that the following two geometric series(meetkundige reekse) are covergent 1+x+x²+x³+... And 1-x+x²-x³+... Determine the va
Oksanka [162]

The sets are (1,-1) or (-1,1)

Lets see

Take until 4terms

#1

\\ \rm\longmapsto S_4=1+1+1^2+1^3=1+1+1+1=4(1,-1)

\\ \rm\longmapsto S_4=1+(-1)+(-1)^2+(-1)^3=1-1+1-1=0(-1,1)

#2

\\ \rm\longmapsto S_4=1-(-1)+(-1)^2-(-1)^3=1+1+1+1=4(1,-1)

\\ \rm\longmapsto S_4=1-1+(1)^2-1^3=1-1+1-1=0(-1,1)

Hence verified

Another set can be (0,0)

Proof:-

\\ \ast\rm\longmapsto S_3=1+0+0^2=1

\\ \ast\rm\longmapsto S_3=1-0+0^2=1

Hence verified.

3 0
2 years ago
Complete the table of values for the function f(x) = (1/3)x for a, b, and c. x : -2, -1, 0, 1, 2. f(x) : a, b, c, 1/3, 1/9
balu736 [363]

Given:

The function is

f(x)=\left(\dfrac{1}{3}\right)^x

To find:

The missing values for a, b, and c in the given table.

Solution:

We have,

f(x)=\left(\dfrac{1}{3}\right)^x

At x=-2,

f(-2)=\left(\dfrac{1}{3}\right)^{-2}

a=\left(3\right)^{2}         \left[\because \left(\dfrac{a}{b}\right)^{-n}=\left(\dfrac{b}{a}\right)^{n}\right]

a=9

At x=-1,

f(-1)=\left(\dfrac{1}{3}\right)^{-1}

b=\left(3\right)^{1}         \left[\because \left(\dfrac{a}{b}\right)^{-n}=\left(\dfrac{b}{a}\right)^{n}\right]

b=3

At x=0,

f(0)=\left(\dfrac{1}{3}\right)^{0}

c=1         \left[\because a^0=1, a\neq 0\right]

Therefore, the missing values of a,b and c are 9, 3, and 1 respectively.

8 0
2 years ago
Read 2 more answers
Two stabilizing wires extend from the top of a pole to the ground, forming right triangles on
FrozenT [24]

Answer: the height of the pole is 16.1 m.

Step-by-step explanation:

The scenario is illustrated in the attached photo.

x represents the height of the pole.

y represents the distance from the foot of one stabilizing wire to the foot of the pole.

30 - y represents the distance from the foot of the other stabilizing wire to the foot of the pole.

In solving the triangles, we would apply the tangent trigonometric ratio which is expressed as

Tan θ, = opposite side/adjacent side.

Considering triangle ACD,

Tan 60 = x/y

x = ytan60 = y × 1.732

x = 1.732y- - - - - - - - -1

Considering triangle BCD,

Tan 38 = x/(30 - y)

x = (30 - y)tan38 = 0.781(30 - y)

x = 23.43 - 0.781y- - - - - - - - -2

Substituting equation 1 into equation 2, it becomes

1.732y = 23.43 - 0.781y

1.732y + 0.781y = 23.43

2.513y = 23.43

y = 23.43/2.513

y = 9.3

x = 1.732y = 1.732 × 9.3

x = 16.1 m

6 0
3 years ago
What number complete the fallowing equation? 8×(40+7)=(8×_)+(8×7) A=40 B=47 C=320 D =376
11Alexandr11 [23.1K]

8x40=320 (+) 8x7=56 (=) 376.

A=40

hope this helped


3 0
3 years ago
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My teacher wrote the answer on the right but he wants me to show how he did it
Airida [17]

865 is the answer of this question...

4 0
2 years ago
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