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2 years ago

6

On the first swing, a pendulum swings through an arc of length 65 cm. On the successive swing, the length of the arc is 85% of t

he length of the previous swing.
Write a rule to model this situation.

1 answer:

Crazy boy [7]2 years ago

3 0

you mutliply 65 to 85%/0.85 and you get 55.25cm as your answer

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Jake made a total of 7 copies at a copy shop, with some being black-and-white copies and some being color copies. Black-and-whit

Arada [10]

Jake spent a total of 70 cents.
b = black-and-white = 8 cents
c = color = 15 cents

70 = 8b + 15c

he made a total of 7 copies
b + c = 7

system of equation:
70 = 8b + 15c
b + c = 7

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

b + c = 7
b + c (-c) = 7 (-c)
b = 7 - c

plug in 7 - c for b

70 = 8(7 - c) + 15c
Distribute the 8 to both 7 and - c (distributive property)

70 = 56 - 8c + 15c
Simplify like terms

70 = 56 - 8c + 15c
70 = 56 + 7c

Isolate the c, do the opposite of PEMDAS: Subtract 56 from both sides

70 (-56) = 56 (-56) + 7c
14 = 7c

divide 7 from both sides to isolate the c

14 = 7c
14/7 = 7c/7
c = 14/7
c = 2

c = 2
---------------

Now that you know what c equals (c = 2), plug in 2 for c in one of the equations.
b + c = 7
c = 2
<em>b + (2) = 7
</em><em />Find b by isolating it. subtract 2 from both sides
b + 2 = 7
b + 2 (-2) = 7 (-2)
b = 7 - 2
b = 5

Jake made 5 black-and-white copies, and 2 color copies

hope this helps

8 0

2 years ago

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Peter wants to cut a rectangle of size 6x7 into squares with integer sides. What is the smallest number of squares he can get

Semmy [17]

He can cut 5 squares, by making 1 4 × 4, 2 3 × 3 and 2 2 × 2 squares.

5 0

2 years ago

Which table can be created using the equation below? –2 + 4x = y A 2-column table with 3 rows. Column 1 is labeled x with entrie

Pachacha [2.7K]

The correct answer is C. A 2-column table with 3 rows. Column 1 is labeled x with entries negative 5, 0, 3. Column 2 is labeled y with entries negative 18, negative 2, 10.

Explanation:

The purpose of an equation is to show the equivalence between two mathematical expressions. This implies in the equation "–2 + 4x = y" the value of y should always be the same that -2 + 4x. Additionally, if a table is created with different values of x and y the equivalence should always be true. This occurs only in the third option.

x y

5 -18

0 -2

3 10

First row:

-2 + 4 (5) = y (5 is the value of x which is first multyply by 4)

-2 + 20 = -18 (value of y in the table)

Second row:

-2 + 4 (0) y

-2 + 0 = -2

Third row:

-2 + 4 (3) = y

-2 + 12 = 10

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2 years ago

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Two planes, A and B, start from the same place and move in different directions, making an angle of 50º between them. The speed

cluponka [151]

Answer: The distance between them is 230.65 miles.

Step-by-step explanation:

Since we have given that

Speed of plane A (b) = 200 miles per hour

Speed of plane B (c) = 300 miles per hour

Angle between them = 50°

So,

We will use the "Cosine formula", we get

$a^2=b^2+c^2-2bc\cos A\\\\a^2=200^2+300^2-2\times 200\times 300\cos 50\textdegree\\\\a^2=40000+90000-120000\cos 50\textdegree\\\\a^2=130000-120000\times 0.64\\\\a^2=130000-76800\\\\a^2=53200\\\\a=\sqrt{53200}\\\\a=230.65\ miles\ per\ hour$

So, distance between the two planes after one hour will be

$Distance=\frac{Speed}{time}=\frac{230.65}{1}=230.65\ miles$

So, the distance between them is 230.65 miles.

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2 years ago

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Lyn invested $7,000 into a investment paying 3% interest, compounded semi-annually, twice a year. After five years, how much wou

gayaneshka [121]

Answer:

Option B.) $8,123.79

Step-by-step explanation:

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=5\ years\\ P=\$7,000\\ r=0.03\\n=2$

substitute in the formula above

$A=\$7,000(1+\frac{0.03}{2})^{2*5}$

$A=\$7,000(1.015)^{10}=\$8,123.79$

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2 years ago