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2 years ago

Ten boys share 7 cereal bars equally.What fraction of a cereal bar does each boy get?

1 answer:

5 0

7/10 I'd say. Each would get less than one whole bar. There is no way to further simplify 7/10 so that'd be your final answer.

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Write the expression using a single exponent.

Ipatiy [6.2K]

Answer: D. 7^11

Reason:

The rule we use is $a^b*a^c = a^{b+c}$

When multiplying exponentials of the same base, we add the exponents.

The exponents 5 and 6 add to 5+6 = 11

So,

$7^5 \times 7^6 = 7^{5+6} = 7^{11}$

The base stays the same the entire time.

6 0

1 year ago

Read 2 more answers

Questions are in the picture

gtnhenbr [62]

The closest point is (3.5, 1.9) and the distance is 1.96 units

<h3>How to determine the point and the distance?</h3>

The coordinate is given as:

(4, 0)

The equation of the function is

y = √x

The distance between two points is calculated using

d = √(x2 - x1)^2 + (y2 - y1)^2

So, we have the following points

(x1, y1) = (4, 0) and (x2, y2) = (x, 0)

This gives

d = √(x - 4)^2 + (√x - 0)^2

Evaluate the difference

d = √(x - 4)^2 + (√x)^2

Evaluate the exponent

d = √x^2 - 8x + 16 + x

Evaluate the like terms

d = √x^2 - 7x + 16

Next, we differentiate using a graphing calculator

d' = (2x - 7)/[2√(x^2 - 7x + 16)]

Set to 0

(2x - 7)/[2√(x^2 - 7x + 16)] = 0

Cross multiply

2x - 7 = 0

Add 7 to both sides

2x = 7

Divide by 2

x = 3.5

So, we have:

Substitute x = 3.5 in y = √x

y = √3.5

Evaluate

y = 1.9

So, the point is (3.5, 1.9)

The distance is then calculated as:

d = √(x2 - x1)^2 + (y2 - y1)^2

This gives

d = √(3.5 - 4)^2 + (1.9 - 0)^2

Evaluate

d = 1.96

Hence, the closest point is (3.5, 1.9) and the distance is 1.96 units

Read more about distance at:

brainly.com/question/23848540

#SPJ1

3 0

1 year ago

Please answer with process

laila [671]

$\mathsf{Given : a - b = 5}$

$\mathsf{Squaring\;on\;both\;sides,\;we\;get :}$

$\mathsf{\implies (a - b)^2 = 5^2}$

$\mathsf{\implies a^2 + b^2 - 2(a.b) = 25}$

$\mathsf{Given : a^2 + b^2 = 29}$

$\mathsf{\implies 29 - 2(a.b) = 25}$

$\mathsf{\implies 2(a.b) = 29 - 25}$

$\mathsf{\implies 2(a.b) = 4}$

$\mathsf{\implies (a.b) = 2}$

6 0

2 years ago

The graph of an inverse trigonometric function passes through the point (1, pi/2). Which of the following could be the equation

rodikova [14]

Answer: C) $y=sin^-1 x$

Step-by-step explanation:

Since, the graph of an inverse trigonometric function will pass through the point $(1,\frac{\pi}{2})$ ,

If this point satisfies the function,

For the function $y=cos^{-1} x$

If x = 1

$y=cos^{-1}1=0$

Thus, $(1,\frac{\pi}{2})$ is not satisfying function $y=cos^{-1} x$ ,

⇒ The graph of $y=cos^{-1} x$ is not passing through the point $(1,\frac{\pi}{2})$

For the function $y=cot^{-1}x$

If x = 1

$y=cot^{-1}1=\frac{\pi}{4}$

Thus, $(1,\frac{\pi}{2})$ is not satisfying function $y=cot^{-1}x$ ,

⇒ The graph of $y=cot^{-1}x$ is not passing through the point $(1,\frac{\pi}{2})$

For the function $y=sin^{-1} x$

If x = 1

$y=sin^{-1}1=\frac{\pi}{2}$

Thus, $(1,\frac{\pi}{2})$ is satisfying function $y=sin^{-1} x$ ,

⇒ The graph of $y=sin^{-1} x$ is passing through the point $(1,\frac{\pi}{2})$ .

For the function $y=tan^{-1}x$

If x = 1

$y=tan^{-1}1=\frac{\pi}{4}$

Thus, $(1,\frac{\pi}{2})$ is not satisfying function $y=cos^{-1} x$ ,

⇒ The graph of $y=tan^{-1} x$ is not passing through the point $(1,\frac{\pi}{2})$ .

Hence, Option C is correct.

3 0

2 years ago

Alana and Petra go to a used book sale, where every book is the same price. Alana buys 4 books and Petra buys 2 books. They run

galben [10]

Answer:

each book is 2 dollars

Step-by-step explanation:

x=price per book

angus=16x-15

16x-15-5=4x+2x

=16x-20=6x

=-20=-10x

2=x

tadaa!!

your very welcome

3 0

2 years ago