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2 years ago

10

Diego was trying to write (5^2)^4 with a single exponent and wrote (5^2)^4=5^2+^4=5^6. What should the answer be? Explain Diego'

s error in complete sentences and thoughts.

1 answer:

o-na [289]2 years ago

4 0

Answer:

5^8

Step-by-step explanation:

Diego added the exponents. This was an error. If he was simplifying

5^2 × 5^4, then he could add the exponents and get a correct answer. But his problem had a power raised to a power. In this case, you multiply the exponents to simplify.

(5^2)^4 means

5^2×5^2×5^2×5^2

which is

5×5×5×5×5×5×5×5

which is 5^8.

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Answer:

625/17

Step-by-step explanation:

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3 years ago

Hey could someone please help me with this really hard assignment is taking me forever. Thank you marking brainliest!

rewona [7]

Answer:

Exercise 1: The length of the unknown leg is 4 inches.

Exercise 3: The following straws can be used to construct the triangle: b) $3\,in$ , c) $4.5\,in$ , d) $6.5\,in$ , e) $10\,in$ , f) $13.5\,in$

Exercise 4: Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)

Step-by-step explanation:

Exercise 1:

Let suppose that triangle represented in the figure is a right triangle, the length of the missing leg is determined by Pythagorean Theorem:

$y = \sqrt{l^{2}-x^{2}}$ (1)

Where:

$l$ - Hypotenuse, in inches.

$x$ - Known leg, in inches.

$y$ - Unknown leg, in inches.

If we know that $l = 11\,in$ and $x = 10\,in$ , then the length of the unknown leg is:

$y = \sqrt{21}$

Since 4 is the least whole number closest to $\sqrt{21}$ , then we conclude that the length of the unknown leg is 4 inches.

Exercise 3:

The range of possible lengths for the missing side of the triangle is represented by the following simultaneous inequality:

$x + y > l > x-y$ (2)

Where:

$x$ - Greater side, in inches.

$y$ - Lesser side, in inches.

$l$ - Missing side, in inches.

If we know that $x = 8\,in$ and $y = 6\,in$ , then we have the following range of missing sides:

$14\,in > l > 2\,in$

The following straws can be used to construct the triangle: b) $3\,in$ , c) $4.5\,in$ , d) $6.5\,in$ , e) $10\,in$ , f) $13.5\,in$

Exercise 4:

Let check each pair to determine possible constructions by means of the inequality used in Exercise 3:

(i) $x = 4\,in, y = 2\,in$

$6\,in>l>2\,in$

Possible choices: 5 inches.

(ii) $x = 5\,in, y = 2\,in$

$7\,in > l > 3\,in$

Possible choices: 4 inches, 6 inches.

(iii) $x = 6\,in, y = 2\,in$

$8\,in > l > 4\,in$

Possible choices: 5 inches, 6 inches.

(iv) $x = 10\,in, y = 2\,in$

$12\,in > l > 8\,in$

Possible choices: None.

(v) $x = 5\,in, y = 4\,in$

$9\,in > l > 1\,in$

Possible choices: 2 inches, 6 inches.

(vi) $x = 6\,in, y = 4\,in$

$10\,in > l > 2\,in$

Possible choices: 5 inches.

(vii) $x = 10\,in, y = 4\,in$

$14\,in > l > 6\,in$

Possible choices: None.

(viii) $x = 6\,in, y = 5\,in$

$11\,in > l > 1\,in$

Possible choices: 2 inches, 4 inches, 10 inches.

(ix) $x = 10\,in, y = 5\,in$

$15\,in > l > 5\,in$

Possible choices: 6 inches.

(x) $x = 10\,in, y = 6\,in$

$16\,in > l > 4\,in$

Possible choices: 5 inches.

Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)

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Answer:

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Step-by-step explanation:

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3 years ago

What is the height of the trapezoid?<br> O 3 units<br> o 5 units<br> o 10 units<br> 12 units

qwelly [4]

Answer:

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Step-by-step expla

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3 years ago

I NEED HELP WITH THIS PLEASE !!! AND EXPLAINED PLEASE!

Ksenya-84 [330]

Answer:

Step-by-step explanation:

Find the vertex and intercepts of y = 3x2 + x – 2 and graph; remember to label the vertex and the axis of symmetry.

This is the same quadratic as in the last example. I already found the vertex when I worked the problem above. This time, I also need to find the intercepts before I do my graph. To find the y-intercept, I set x equal to zero and solve:

y = 3(0)2 + (0) – 2

= 0 + 0 – 2 = –2

Then the y-intercept is the point (0, –2). To find the x-intercept, I set y equal to zero, and solve:

0 = 3x2 + x – 2

0 = (3x – 2)(x + 1)

3x – 2 = 0 or x + 1 = 0

x = 2/3 or x = – 1

Then the x-intercepts are at the points (–1, 0) and ( 2/3, 0).

The axis of symmetry is halfway between the two x-intercepts at (–1, 0) and at ( 2/3 , 0); using this, I can confirm the answer from the previous page:

(–1 + 2/3) / 2 = (–1/3) / 2 = –1/6

The complete answer is a listing of the vertex, the axis of symmetry, and all three intercepts, along with a nice neat graph:

The vertex is at ( –1/6 , –25/12 ), the axis of symmetry is the line x = –1/6 , and the intercepts are at (0, –2), (–1, 0), and ( 2/3, 0).

graph of y = 3x^2 + x - 2 with vertex and intercepts marked.

Find the intercepts, the axis of symmetry, and vertex of y = x2 – x – 12.

To find the y-intercept, I set x equal to 0 and solve:

y = (0)2 – (0) – 12 = 0 – 0 – 12 = –12

To find the x-intercept, I set y equal to 0 and solve:

0 = x2 – x – 12

0 = (x – 4)(x + 3)

x = 4 or x = –3

To find the vertex, I look at the coefficients: a = 1 and b = –1. Plugging into the formula, I get:

h = –(–1)/2(1) = 1/2 = 0.5

To find k, I plug h = 1/2 in for x inside y = x2 – x – 12, and simplify:

k = (1/2)2 – (1/2) – 12 = 1/4 – 1/2 – 12 = –12.25

Once I have the vertex, it's easy to write down the axis of symmetry: x = 0.5. Now I'll find some additional plot points, to fill in the graph:

T-chart

For my own convenience, I picked x-values that were centered around the x-coordinate of the vertex. Now I can plot the parabola: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved

graph of y = x^2 - x - 12

The vertex is at the point (0.5, –12.25),

the axis of symmetry is the line x = 0.5,

and the intercepts are at the points (0, –12), (–3, 0), and (4, 0).

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3 years ago