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3 years ago

Select "Yes" or "No" to indicate whether the ordered pair is on the graph of the function f(x)=−25^x+1.

Mathematics

2 answers:

Verdich [7]3 years ago

5 0

Hello! Just took the test:

(1,625) No

(0,-25) Yes

(-1,-1) Yes

KengaRu [80]3 years ago

3 0

<span>(1,625) No (0,-25) No (-1,-1) No Think about what an integer exponent means for an negative base and you'll understand this problem. For instance the powers of -25 would be -25^1 = -25 -25^2 = (-25) * (-25) = 625 -25^3 = (-25)*(-25)*(-25) = -15625 and so on, giving 390625, -9765625, 244140625, etc. But that's a different subject. For the ordered pairs given, let's check them out. (1,625) -25^1 + 1 = -25 + 1 = -24. And -24 is not equal to 625, so "No". (0,-25) -25^0 + 1 = 1 +1 = 2. Note: Any real number other than 0 raised to the 0th power is 1. And 2 is not equal to -25, so "No". (-1,-1) -25^(-1) + 1 = 1/(-25^1) + 1 = 1/-25 + 1 = 24/25. And 24/25 is not equal to -1, so also "No".</span>

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Two sides of a triangle have measures 3 ft and 6 ft. Also, these sides form a vertex whose angle measures 60 degrees. Calculate

Basile [38]

Answer:

A. The length of the third side is approximately 5 feet.

B. A = $88^{o}$ , B = $60^{o}$ and C = $32^{o}$ .

Step-by-step explanation:

Let the triangle be ABC. Given two sides and an included angle, let us apply the cosine rule to determine the third length.

A. Let side a = 6 feet and c = 3 feet, thus;

$b^{2}$ = $a^{2}$ + $c^{2}$ - 2ac Cos B

= $6^{2}$ + $3^{2}$ - 2(6 x 3) Cos $60^{o}$

= 36 + 9 - 36 x 0.5

= 45 - 18

$b^{2}$ = 27

b = $\sqrt{27}$

= 5.1962

b = 5.2 feet

b ≅ 5 feet

The length of the third side is approximately 5 feet.

B. Given that B = $60^{o}$ , then let us apply the Sine rule to determined the measure of A.

$\frac{a}{SinA}$ = $\frac{b}{SinB}$

So that,

$\frac{6}{Sin A}$ = $\frac{5.2}{Sin60^{o} }$

Sin A = $\frac{0.886*6}{5.2}$

Sin A = 0.99923

A = $Sin^{-1}$ 0.99923

= 87.75

A ≅ $88^{o}$

Since the sum of angle in a triangle = $180^{o}$ .

Then,

A + B + C = $180^{o}$

$88^{o}$ + $60^{o}$ + C = $180^{o}$

$148^{o}$ + C = $180^{o}$

C = $180^{o}$ - $148^{o}$

= $32^{o}$

C = $32^{o}$

Thus,

A = $88^{o}$ , B = $60^{o}$ and C = $32^{o}$ .

5 0

3 years ago

Identify the graph of x^2-8y=0 for theta=90º and write and equation of the translated or rotated graph in general form.

vredina [299]

Answer:

The answer is parabola; (y')² - 8x' = 0 ⇒ answer (b)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy² + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

* x² - 8y = 0

∵ A = 1 , B = 0 , C =

∴ B² - 4AC = (0)² - 4(1)(0) = 0

∵ B² - 4AC = 0

∴ it will be a parabola.

∵ Ф = 90°

* The point (x , Y) will be (x' , y')

∵ x = x'cosФ - y'sinФ and y = x'sinФ + y'cosФ

∵ cos(90) = 0 and sin(90) = 1

∴ x = -y' and y = x'

* lets substitute x and y in the first equation

∴ (-y')² - 8(x') = 0

∴ (y')² - 8x' = 0

* We notice that the x' took the place of y and y' took the place of x

∴ The parabola rotated around the origin by 90°

∴ The equation of the parabola is (y')² - 8x' = 0

* The answer is parabola, with angle of rotation 90°

* The equation is (y')² - 8x' = 0

* Look to the graph

- The blue is x² - 8y = 0

- The green is (y')² - 8x' = 0

7 0

3 years ago

Read 2 more answers

Teri incorrectly solved the system of equations below. Correctly identify the error Teri made. 2x - 10 y = -30 x - 5y = 20 Step

umka21 [38]

Answer:

See explanations below

Step-by-step explanation:

Given the system of equation

2x - 10 y = -30 ... 1

x - 5y = 20 ... 2

Step: From 2;

x = 20 + 5y ...3

Step 2: Substitute equation 3 into 1

2x - 10y = -30

2(5y+20) - 10y = -30

Open the bracket

10y + 40 - 10y = -30

10y - 10y + 40 = -30

0+40 = -30

40 = -30

The steps taken by Teri are correct all through. He didn't make any error whatsoever

3 0

2 years ago

Problem and incorrect solution. Explanation of Errors Made. (Some have more than one mistake).in one box and then correct soluti

irga5000 [103]

Answer:

In the second step, the +16 should be -16

In the 3rd step, you should add 16 instead of subtracting 16

m=0

3 0

2 years ago

If 56% of people own a dog and 5 people are chosen at random, what is the probability that at least one person owns a dog?

wariber [46]

Answer:

2.8

Step-by-step explanation:

we do 56% times 5= 2.8

so 2.8 is your answer

(this answer was given by my friend who claims this is true.)

4 0

2 years ago