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Burka [1]
3 years ago
14

Solve for x in the equation x^2-4x-9=29

Mathematics
1 answer:
Kipish [7]3 years ago
5 0
X = 2 + √42,2- √42
decimal form: 8.480741, -4.480741
sorry if my answer isn't right
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Cannon balls for an antique cannon are stacked next to it in four layers to form a square pyramid. How many cannon balls are in
labwork [276]
The amount of balls in a given layer can be found by squaring the layer it is in

4 layers
top layer (1st) is 1
2nd is 4
3rd layer is 9
4th is 16

add them up
1+4+9+16=30

30 in that pyramid
7 0
3 years ago
The heat developed in an electric wire varies jointly as the wires resistance, the time the current flows, & the square of t
never [62]

Answer:

4 ohms

Step-by-step explanation:

The question is "In two minutes a current of 5 amps develops 1,200 heat units in a wire of 8 ohms resistance. What resistance does a similar wire have, which develops 6,000 heat units with a current of 10 amps in 5 minutes?"

Current, I₁ = 5 A

Heat, Q₁ = 1200 units

Resistance, R₁ = 8 ohms

Time, t₁ = 2 min = 120 s

New heat, Q₂ = 6000 units

Current, I₂ = 10 A

New time, t₂ = 5 min = 300 s

We need to find the new resistance.

Heat developed is given by :

Q=I^2Rt

\dfrac{Q_1}{I_1^2R_1t_1}=\dfrac{Q_2}{I_2^2R_2t_2}\\\\R_2=\dfrac{Q_2\times I_1^2R_1t_1}{Q_1I_2^2t_2}\\\\R_2=\dfrac{6000\times 5^2\times 8\times 120}{1200\times 10^2\times 300}\\\\=4\ \Omega

So, the new resistance is 4 ohms.

5 0
2 years ago
Determine the volume of the parallelepiped with one vertex at the origin and the three vertices adjacent to it at (2, â1, â1), (
valentinak56 [21]

Answer:

23

Step-by-step explanation:

Here is the complete question

Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 0, -3), (1, 2, 4), and (5, 1, 0).

Solution

We find the volume of the parallelepiped by making a 3 × 3 column matrix whose columns are the corresponding coordinates of the vertices of the parallelepiped.

So, (1, 0, -3), (1, 2, 4)  and (5, 1, 0)

A = \left[\begin{array}{ccc}1&1&5\\0&2&1\\-3&4&0\end{array}\right]

The determinant of A is the volume of the parallelepiped. So,

detA = 1(2 × 0 - 4 × 1) - 1(0 × 0 - (-3) × 1) + 5(0 × 4 - (-3) × 2)

= 1(0 - 4) - 1(0 + 3) + 5(0 + 6)

= 1(-4) - 1(3) + 5(6)

= -4 - 3 + 30

= 23

So the volume of the parallelepiped is 23

4 0
2 years ago
Tickets to a concert cost $2 for children, $3 for teenagers and $5 for adults. When 570 people attended the concert, the total t
-Dominant- [34]

Let

x--------> the number of children

y------> the number of teenagers

z------> the number of adults

we know that

2x+3y+5z=1,950 ------> equation A

x+y+z=570 -----> equation B

y=\frac{3}{4}x

x=\frac{4}{3}y -------> equation C

Substitute equation C in equation A and equation B

2[\frac{4}{3}y]+3y+5z=1,950

\frac{17}{3}y+5z=1,950 --------> equation D

[\frac{4}{3}y]+y+z=570

\frac{7}{3}y+z=570 --------> equation E

Multiply equation E by -5

-\frac{35}{3}y-5z=-2,850 --------> equation F

Adds equation D and equation F

\frac{17}{3}y+5z=1,950\\\\-\frac{35}{3}y-5z=-2,850\\\\---------\\\\-\frac{18}{3}y=-900\\\\y=3*900/18\\\\y=150\ teenagers

therefore

<u>the answer is the option</u>

150\ teenagers


4 0
2 years ago
Read 2 more answers
1 USD is 1.37 CAD 86 CAR is how many USD
laiz [17]

Answer:

67.64

Step-by-step explanation:

6 0
2 years ago
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