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Anika [276]
3 years ago
12

What is the vertex form of the equation y=x^2+12x-9

Mathematics
2 answers:
luda_lava [24]3 years ago
8 0
Find the vertex form
y = (x + 6)^2 - 45
Anika [276]3 years ago
4 0
-The vertex of the answer is 6, -45
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Triangle ABC has a right angle at C. Select all measurements which would mean it has a hypotenuse with a length of 10 units. a.
Delvig [45]

Option d: Angle A is 30 degrees, BC is 5 units

Option e: AC is 8 units, BC is 6 units

Explanation:

The triangle ABC has a right angle at C.

The length of the hypotenuse is 10 units.

The image of the triangle with this measurement is attached below:

Option a: Angle A is 20 degrees, BC is 2 units

\begin{aligned}\sin 20 &=\frac{2}{h y p} \\h y p &=\frac{2}{\sin 20} \\&=5.8476\end{aligned}

Since, hypotenuse is 10 units, Option a is not correct answer.

Option b: AC is 7 units, BC is 3 units

\begin{aligned}A B &=\sqrt{7^{2}+3^{2}} \\&=\sqrt{49+9} \\&=\sqrt{58}\end{aligned}

Since, hypotenuse is 10 units, Option b is not correct answer.

Option c: Angle B is 50 degrees, BC is 4 units

\begin{aligned}\cos 50 &=\frac{4}{h y p} \\h y p &=\frac{4}{\cos 50} \\&=6.222\end{aligned}

Since, hypotenuse is 10 units, Option c is not correct answer.

Option d: Angle A is 30 degrees, BC is 5 units

\begin{aligned}\sin 30 &=\frac{5}{h y p} \\h y p &=\frac{5}{\sin 30} \\&=10\end{aligned}

Since, hypotenuse is 10 units, Option d is the correct answer.

Option e: AC is 8 units, BC is 6 units

\begin{aligned}A B &=\sqrt{8^{2}+6^{2}} \\&=\sqrt{64+36} \\&=\sqrt{100} \\&=10\end{aligned}

Since, hypotenuse is 10 units, Option e is the correct answer.

Thus, Option d and e are the correct answers.

3 0
3 years ago
9.<br> What is the solution of the equation x^2 + 6x + 41 = 0?
ExtremeBDS [4]

Answer:

there is no solution

Step-by-step explanation:

x^2 + 6x + 41 = 0?

Δ=6^{2}-4*41=36-164=-128

Δ<0 so there is no solution

3 0
3 years ago
A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per
vladimir2022 [97]
The grocer wants to make a 10 pound mixture 
p - pounds of peanuts
c - pounds of cashews
therefore the total pounds should be equal to 10 pounds 
p + c = 10 -----> 1)
the cost for ;
peanuts - 4.00 per pound * p pounds = 4p
cashews - 6.50 per pound * c pounds = 6.5c
the price of 10 pounds mixture = 4.75 per pound * 10 pounds = 47.5
4p+6.5c = 47.5 ---> 2)

to solve for p and c lets use simultaneous equations 
p + c = 10 -----> 1)
4p+6.5c = 47.5 ---> 2)
multiply 1st equation by 4
4p + 4c = 40 ---> 3)
subtract 3rd equation from the 2nd
2.5c = 7.5
c = 3
substituting c= 3 in 1st equation
p+c = 10
p+3 = 10
p = 7
therefore 3 pounds of cashews and 7 pounds of peanuts are needed to make the mixture
6 0
3 years ago
A bucket always contains two balls. Ball colors are red and blue. Each stage in a process consists of two steps: selection and r
KonstantinChe [14]

Answer:

Probability that the fifth ball selected is red = 0.705

Step-by-step explanation:

Let

X_{n} = Number of red balls after the 4th turn

⇒X_{n}  ∈ { 0, 1, 2 }

Then,

P = \left[\begin{array}{ccc}0.8&0.2&0\\0.1&0.8&0.1\\0&0.2&0.8\end{array}\right]

⇒P^{4} = \left[\begin{array}{ccc}0.487&0.435&0.776\\0.218&0.565&0.218\\0.776&0.435&0.487\end{array}\right]

Now,

P(5th ball is red | X_{0} = 2 ) = 0. P^{4} _{20} + \frac{1}{2}P^{4} _{21} + 1. P^{4} _{22}

                                         =  \frac{1}{2} (0.4352) + 1. (0.4872) = 0.2176 + 0.4872

                                        = 0.705

∴ we get

Probability that the fifth ball selected is red = 0.705

6 0
3 years ago
If the measure of Angle C A E is 95°, what is the measure of Arc C B A?
kvasek [131]

Answer: the answer is 190

Step-by-step explanation: I multiplied 95 by two

6 0
3 years ago
Read 2 more answers
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