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3 years ago

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12. What is the equation of the following parabola?

1 answer:

Vladimir79 [104]3 years ago

6 0

Answer:

c

Step-by-step explanation:

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On a map, 2.5 inches represents 52 miles. What is the actual distance represented by 5 inches on the map?

nikklg [1K]

Answer:

104 miles

Step-by-step explanation:

52/2.5 = 20.8

20.8 miles = 1 inch

20.8 x 5

104 miles = 5 inches

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3 years ago

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Factor completely 64x2 − 49. (1 point)

Roman55 [17]

Answer:

(8x-7)(8x+7)

Step-by-step explanation:

This is a difference of squares polynomial of the form $a^2-b^2=(a+b)(a-b)$ . Since 64 and 9 are both perfect squares then take the square root of each so a=8 and b=7.

Factors:(8x-7)(8x+7)

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3 years ago

Mitchell went on a shopping trip to Kensington. He purchased a pair of headphones originally priced at $50 but discounted 60%. I

MrRa [10]

Answer:

$24.50

Step-by-step explanation:

60% of $50= $30

$50-$30= $20

15% of $20= $4.50

$20+$4.50= $24.50

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3 years ago

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Find the angle between the given vectors. Round your answer, in degrees, to two decimal places. u=⟨2,−6⟩u=⟨2,−6⟩, v=⟨4,−7⟩

NISA [10]

Answer:

$\theta = 108.29$

Step-by-step explanation:

Given

$u =$

$v =$

Required:

Calculate the angle between u and v

The angle $\theta$ is calculated as thus:

$cos\theta = \frac{u.v}{|u|.|v|}$

For a vector

$A =$

$A = a * b$

$cos\theta = \frac{u.v}{|u|.|v|}$ becomes

$cos\theta = \frac{.}{|u|.|v|}$

$cos\theta = \frac{2*6+4*-7}{|u|.|v|}$

$cos\theta = \frac{12-28}{|u|.|v|}$

$cos\theta = \frac{-16}{|u|.|v|}$

For a vector

$A =$

$|A| = \sqrt{a^2 + b^2}$

So;

$|u| = \sqrt{2^2 + 6^2}$

$|u| = \sqrt{4 + 36}$

$|u| = \sqrt{40}$

$|v| = \sqrt{4^2+(-7)^2}$

$|v| = \sqrt{16+49}$

$|v| = \sqrt{65}$

So:

$cos\theta = \frac{-16}{|u|.|v|}$

$cos\theta = \frac{-16}{\sqrt{40}*\sqrt{65}}$

$cos\theta = \frac{-16}{\sqrt{2600}}$

$cos\theta = \frac{-16}{\sqrt{100*26}}$

$cos\theta = \frac{-16}{10\sqrt{26}}$

$cos\theta = \frac{-8}{5\sqrt{26}}$

Take arccos of both sides

$\theta = cos^{-1}(\frac{-8}{5\sqrt{26}})$

$\theta = cos^{-1}(\frac{-8}{5 * 5.0990})$

$\theta = cos^{-1}(\frac{-8}{25.495})$

$\theta = cos^{-1}(-0.31378701706)$

$\theta = 108.288386087$

<em></em> $\theta = 108.29$ <em> (approximated)</em>

4 0

2 years ago

If neither a nor b are equal to zero, which answer most accurately describes the product of (a + bi)(a - bi)?

Scrat [10]

Answer: the correct option is

(D) The imaginary part is zero.

Step-by-step explanation: Given that neither a nor b are equal to zero.

We are to select the correct statement that accurately describes the following product :

$P=(a+bi)(a-bi)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following formula :

$(x+y)(x-y)=x^2-y^2.$

From product (i), we get

$P\\\\=(a+bi)(a-bi)\\\\=a^2-(bi)^2\\\\=a^2-b^2i^2\\\\=a^2-b^2\times (-1)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }i^2=-1]\\\\=a^2+b^2.$

So, there is no imaginary part in the given product.

Thus, the correct option is

(D) The imaginary part is zero.

3 0

3 years ago