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3 years ago

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When two people play tennis it is called singles. When 4 people play it is called doubles.In doubles it is 2 players playing aga

inst 2 players.Below or Above is a diagram of a tennis court.The net divides the court in half. The two alleys on the sides are used only in doubles.What is the total length of a tennis court ___feet

2 answers:

sertanlavr [38]3 years ago

6 0

78 feet is the length of the tennis courts

ioda3 years ago

4 0

78 ft is the length of the tennis court

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Jacob solves the system of equations by forming a matrix equation.

Lyrx [107]

Simultaneous equations can be solved using inverse matrix operation.

The complete steps of Jacob's solution are:

$\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]^{-1} \cdot \left[\begin{array}{cc}4&1\\-2&3\end{array}\right]\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14}\left[\begin{array}{cc}3&-1\\2&4\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}4&1\\-2&3\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14} \left[\begin{array}{c}28&-84\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}2&-6\end{array}\right]$

We have:

$4x + y = 2$

$-2x + 4y = -22$

Calculate the determinant of $\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]$

$|A| = 4 \times 3 -1 \times -2$

$|A| = 12 +2$

$|A| = 14$

So, the inverse matrix becomes

$A = \frac{1}{14}\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]$

Replace the first column with $\left[\begin{array}{c}2&-22\end{array}\right]$ to calculate the value of x

$x = \frac{1}{14}\left[\begin{array}{cc}2&1\\-22&3\end{array}\right]$

So, we have:

$x = \frac{1}{14}(2 \times 3 - 1 \times -22)$

$x = \frac{1}{14}(6 +22)$

$x = \frac{1}{14}(28)$

$x = 2$

Replace the second column with $\left[\begin{array}{c}2&-22\end{array}\right]$ to calculate the value of y

$y = \frac{1}{14}\left[\begin{array}{cc}4&2\\-2&-22\end{array}\right]$

So, we have:

$y = \frac{1}{14}(4 \times -22 - 2 \times -2)$

$y = \frac{1}{14}(-88 +4)$

$y = \frac{1}{14}(-84)$

$y = -6$

Hence, the complete process is:

$\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]^{-1} \cdot \left[\begin{array}{cc}4&1\\-2&3\end{array}\right]\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14}\left[\begin{array}{cc}3&-1\\2&4\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}4&1\\-2&3\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14} \left[\begin{array}{c}28&-84\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}2&-6\end{array}\right]$

Read more about matrices at:

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6 0

3 years ago

I don’t understand this question someone please help

kirill [66]

Answer:

£152.40

Step-by-step explanation:

If he made 80 cakes at a ratio of 3:2:5, then he made:

24 chocolate cakes

16 lemon cake

40 fruit cakes

He sold all of the chocolate: 24x2=48

He sold 3/4 of the lemon: 3/4 of 16=12 12x1.70=20.40

He sold 7/8 of the fruit cakes: 7/8 of 40=35 35x2.4=84

48+20.40+84=152.40

7 0

3 years ago

The math club is electing new officers. There are 5 candidates for president, 6 candidates for vice-president, 2 candidates for

Andre45 [30]

Answer:

180 different combinations

Step-by-step explanation:

To find the number of different combinations possible, We first find the number of possibilities for each place, and then multiply all possibilities.

Number of possibilities for president: 5

Number of possibilities for vice-president: 6

Number of possibilities for secretary: 2

Number of possibilities for treasurer: 3

Number of different combinations: 5*6*2*3 = 180

(We can form 180 different groups of 1 president, 1 vice-president, 1 secretary and 1 treasurer)

8 0

4 years ago

Read 2 more answers

Suppose the voltage in an electrical circuit varies with time according to the formula V(t) = 40 sin(t) for t in the interval [0

grigory [225]

The numerical value of the mean voltage is 25.47 V

To find the numerical value of the mean voltage, V of V(t) = 40 sin(t), we integrate V(t) with respect to t over the interval [0.π]

So,

$V = \frac{1}{\pi } \int\limits^\pi _0 {V(t)} \, dt \\V = \frac{1}{\pi } \int\limits^\pi _0 {40sint} \, dt \\V = \frac{1}{\pi } [-40cost]_{0}{\pi } \\V = \frac{1}{\pi } -[40cos\pi - 40cos0]\\\\V = \frac{1}{\pi } (-[40 X (-1) - 40 X 1})\\V = -\frac{1}{\pi } [-40 - 40]\\V = \frac{80}{\pi } \\V = 25.465 V$

V ≅ 25.47 V

So, the numerical value of the mean voltage is 25.47 V

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7 0

3 years ago

A grapefruit has a peel that is 1cm thick and a total diameter of 12cm. What percentage of volume of the grapefruit is the peel?

ira [324]

Answer:

0.3056 or 30.56%

Step-by-step explanation:

The volume of the grapefruit with the peel is:

$V_p=\frac{4 \pi (d/2)^2}{3}\\V_p=\frac{4 \pi (12/2)^2}{3}\\V_p=48 \pi$

When removing the peel, the grapefruit diameter becomes 10 cm (take out 1 cm of peel from each side). The volume of the grapefruit without the peel is:

$V_n=\frac{4 \pi (d/2)^2}{3}\\V_n=\frac{4 \pi (10/2)^2}{3}\\V_n=33.333 \pi$

The percentage of the volume correspondent to the peel is given by the difference between both volumes, divided by the total volume:

$\%P = \frac{48\pi - 33.333\pi}{48\pi}\\ \%P =0.3056 = 30.56\%$

30.56% of volume of the grapefruit is the peel.

4 0

4 years ago