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Travka [436]
1 year ago
11

While on a stakeout protecting Earth from the the universe, Agent K observed five men in black enter a coffee shop and get three

doughnuts and five coffees for $3.30. Next, three aliens in disguise entered the shop and got four doughnuts and three coffees for $2.75. Finally, Agent Zed from the home office entered and got a doughnut and a cup of coffee. How much was Zed's bill? (Assume there was no tax.)
Mathematics
1 answer:
taurus [48]1 year ago
3 0

Answer:

$ 0.8.

Step-by-step explanation:

1) if to assume, 'c' - price of the coffee and 'd' - price of the doughnuts, then

2) it is possible to write the equation 1 (when five MinB enter): 3d+5c=3.3;

3) it is possible to write the equation 2 (when three aliens entered): 4d+3c=2.75;

4) \ \left \{ {{3d+5c=3.3} \atop {4d+3c=2.75}} \right. \ = > \ \left \{ {{c=0.45} \atop {d=0.35}} \right.

5) if c=0.45 and d=0.35, then Ag.Z. paid 0.35+0.45=$ 0.8.

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The sum of all three numbers is 12. The sum of twice the first number, 4 times the second number, and 5 times the third number i
DaniilM [7]

Answer:

The numbers are 7, 4 and 1

Step-by-step explanation:

Let the numbers =x, y, z.

The sum of all three numbers is 12, x+y+z=12--------i

The sum of twice the first number, 4 times the second number, and 5 times the third number is 35, 2x+4y+5z=35-------ii

The difference between 8 times the first number and the second number is 52, 8x-y=52---------iii

Now, from (i),z =1-x-y--------iv

substitute (iv) in (ii),

2x+4y+5(12-x-y)=35

2x+4y+60-5x-5y=35

collect like terms

-3x-y=-25

that is, 3x-y=25--------v

solving (iii) and (v) simultaneously (add iii and v), we have

11x=77

divide both sides by 11 to obtain x=7

Put x=7 in (v)

3(7)+y=25

21+y=25

implies y=25-21=4

put x=7 and y=4 in (iv)

z=12-7-4=1

Hence, the numbers are 7, 4 and 1.

4 0
2 years ago
Write a simplified polynomial expression in standard form to represent the area of the rectangle below.
JulijaS [17]
Given:
Rectangle shape.
One side: 5x + 2
other side: x - 4

Area = length * width
Area = (5x+2)(x-4)
A = 5x(x-4) +2(x-4)
A = 5x² - 20x + 2x - 8
A = 5x² - 18x - 8
6 0
3 years ago
Read 2 more answers
What is the value of x?
uranmaximum [27]

Answer:

x=\frac{160-51}{2} =54.5°

Step-by-step explanation:

"Theorem 9-13: The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs."

Basically no matter what other circle, secant or tangent you get, you just use the formula Outer\angle=\frac{far.point - near.point}{2}

If you need the outer angle, just put the other angles in and solve

If you need the far or near point angle, re-arrange the formula to get that value.

6 0
2 years ago
Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do n
aliya0001 [1]

Answer:

f(x)=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}

Step-by-step explanation:

The Maclaurin series of a function f(x) is the Taylor series of the function of the series around zero which is given by

f(x)=f(0)+f^{\prime}(0)x+f^{\prime \prime}(0)\dfrac{x^2}{2!}+ ...+f^{(n)}(0)\dfrac{x^n}{n!}+...

We first compute the n-th derivative of f(x)=\ln(1+2x), note that

f^{\prime}(x)= 2 \cdot (1+2x)^{-1}\\f^{\prime \prime}(x)= 2^2\cdot (-1) \cdot (1+2x)^{-2}\\f^{\prime \prime}(x)= 2^3\cdot (-1)^2\cdot 2 \cdot (1+2x)^{-3}\\...\\\\f^{n}(x)= 2^n\cdot (-1)^{(n-1)}\cdot (n-1)! \cdot (1+2x)^{-n}\\

Now, if we compute the n-th derivative at 0 we get

f(0)=\ln(1+2\cdot 0)=\ln(1)=0\\\\f^{\prime}(0)=2 \cdot 1 =2\\\\f^{(2)}(0)=2^{2}\cdot(-1)\\\\f^{(3)}(0)=2^{3}\cdot (-1)^2\cdot 2\\\\...\\\\f^{(n)}(0)=2^n\cdot(-1)^{(n-1)}\cdot (n-1)!

and so the Maclaurin series for f(x)=ln(1+2x) is given by

f(x)=0+2x-2^2\dfrac{x^2}{2!}+2^3\cdot 2! \dfrac{x^3}{3!}+...+(-1)^{(n-1)}(n-1)!\cdot 2^n\dfrac{x^n}{n!}+...\\\\= 0 + 2x -2^2  \dfrac{x^2}{2!}+2^3\dfrac{x^3}{3!}+...+(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}+...\\\\=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^n\dfrac{x^n}{n}

3 0
2 years ago
Which expression is equal to the expression below?
Debora [2.8K]

Answer:

48

Step-by-step explanation:

(2*6)4

(12)4

48

Hoped it helped :)

4 0
2 years ago
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