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Anastasy [175]
1 year ago
8

Maggie brought oranges and sandwiches to a picnic. The number of oranges was three more than twice the number of sandwiches. Mag

gie brought 9 oranges to the picnic. How many sandwiches did she bring?
Mathematics
1 answer:
tatuchka [14]1 year ago
8 0

Maggie brought 3 sandwiches to the picnic .

In the question ,

it is given that

Maggie bought oranges and sandwiches to a picnic .

given the number of oranges = 9

also given that , number of oranges was three more than twice the number of sandwiches

let the number of sandwiches Maggie brought to a picnic be x .

So , the number of oranges is = 2x + 3

So , 2x + 3 = 9

Subtracting 3 from both the sides ,

we get ,

2x = 9 - 3

2x = 6

On dividing both sides by 2,

we get ,

x = 6/2

x = 3

Therefore , the number of sandwiches = 3  .

Learn more about Equations here

brainly.com/question/924389

#SPJ1

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3 years ago
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riadik2000 [5.3K]

Let

S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n

where we assume |r| < 1. Multiplying on both sides by r gives

r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}

and subtracting this from S_n gives

(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}

As n → ∞, the exponential term will converge to 0, and the partial sums S_n will converge to

\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}

Now, we're given

a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a

a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}

We must have |r| < 1 since both sums converge, so

\dfrac{15}a = \dfrac1{1-r}

\dfrac{150}{a^2} = \dfrac1{1-r^2}

Solving for r by substitution, we have

\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)

\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}

Recalling the difference of squares identity, we have

\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}

We've already confirmed r ≠ 1, so we can simplify this to

\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15

It follows that

\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12

and so the sum we want is

ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

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2 years ago
7. Jimmy wants to make a model of a ball that has half of the volume of the original ball. What scale factor should he use?
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Answer:

Part a) (2m+7n)(2m-7n)

Part b) x^2-16xy+64y^2

Part c) 216a^3b^6

Part d)  (a^2-b^2)

Step-by-step explanation:

Part a) The difference of the squares of 2m and 7n.

we know that

The difference of the squares formula is equal to

(a^2-b^2)=(a+b)(a-b)

substitute

(2m)^2-(7n)^2=(2m+7n)(2m-7n)

Part b) The square of the difference of x and 8y

The formula of the square of the difference between two numbers is equal to

(a-b)^2=a^2-2ab+b^2

substitute

(x-8y)^2=x^2-2(x)(8y)+(8y)^2=x^2-16xy+64y^2

Part c) The tripled product of 6a and b^2

we have

(6ab^{2})(6ab^{2})(6ab^{2})=(6ab^{2})^3=(6^3)(a^3)(b^{2})^3=216a^3b^6

Part d) The product of the sum of a and b and their difference

The expression is equal to

(a+b)(a-b)

The expression represent the difference of the squares between a and b

so

(a+b)(a-b)=(a^2-b^2)

7 0
3 years ago
Sendo a= {1, 2, 3, 5, 7, 8} b= {2, 3, 7} indique qual é o completar de b em a ?
Yuki888 [10]

Answer:

For english people:

Since a = {1, 2, 3, 5, 7, 8} b = {2, 3, 7} indicate what is the completion of b in a?

Step-by-step explanation:

7 0
4 years ago
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