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2 years ago

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Devon exercised the same amount of time each day for 5 days last week. e His exercise included walking and swimming. e Each day

he exercised, he walked for 10 minutes . He exercised for a total of 225 minutes last week. What is the number of minutes Devon swam each of the 5.days last week?

1 answer:

prohojiy [21]2 years ago

8 0

I think that Devon swam at least 35 minutes each day for 5 days because if he exercised 225 minutes and each day he walked for 10 minutes then if you divide 225 by 5 you get 45 so every day he exercised 45 minutes and since he walked for 10 minutes you subtract 10 from 45 which gives you 35 so he swam for 35 minutes.

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The value of which of these expressions is closest to e?

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Answer:

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2 years ago

Let ff be the function given by f(x)=e2x−1 x f(x)=e2x−1 x. Which of the following equations expresses the property that f(x)f(x)

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2 years ago

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Which of the following shows the extraneous solution to the logarithmic equation? log Subscript 4 Baseline (x) + log Subscript 4

vekshin1

<u>Given:</u>

The given equation is $\log _{4}(x)+\log _{4}(x-3)=\log _{4}(-7 x+21)$

We need to determine the extraneous solution of the equation.

<u>Solving the equation:</u>

To determine the extraneous solution, we shall first solve the given equation.

Applying the log rule $\log _{c}(a)+\log _{c}(b)=\log _{c}(a b)$ , we get;

$\log _{4}(x(x-3))=\log _{4}(-7 x+21)$

Again applying the log rule, if $\log _{b}(f(x))=\log _{b}(g(x))$ then $f(x)=g(x)$

Thus, we have;

$x(x-3)=-7 x+21$

Simplifying the equation, we get;

$x^2-3x=-7 x+21$

$x^2+4x=21$

$x^2+4x-21=0$

Factoring the equation, we get;

$(x-3)(x+7)=0$

Thus, the solutions are $x=3, x=-7$

<u>Extraneous solutions:</u>

The extraneous solutions are the solutions that does not work in the original equation.

Now, to determine the extraneous solution, let us substitute x = 3 and x = -7 in the original equation.

Thus, we get;

$\log _{4}(3)+\log _{4}(3-3)=\log _{4}(-7 \cdot 3+21)$

$\log _{4}(3)+\log _{4}(0)=\log _{4}(0)$

Since, we know that $\log _{a}(0)$ is undefined.

Thus, we get;

Undefined = Undefined

This is false.

Thus, the solution x = 3 does not work in the original equation.

Hence, x = 3 is an extraneous solution.

Similarly, substituting x = -7, in the original equation. Thus, we get;

$\log _{4}(-7)+\log _{4}(-7-3)=\log _{4}(-7(-7)+21)$

$\log _{4}(-7)+\log _{4}(-10)=\log _{4}(49+21)$

$\log _{4}(-7)+\log _{4}(-10)=\log _{4}(70)$

Simplifying, we get;

Undefined = $\log _{4}(70)$

Undefined = 3.06

This is false.

Thus, the solution x = -7 does not work in the original solution.

Hence, x = -7 is an extraneous solution.

Therefore, the extraneous solutions are x = 3 and x = -7

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1 year ago

Read 2 more answers

During a field trip, 60 students are put into equal-sized groups. Describe two ways to interpret 60÷5 60 ÷ 5 in this context. Fi

Afina-wow [57]

The second question:

Consider the division expression $7\frac{1}{2} / 2$ . Select all multiplication equations that correspond to this division expression.

$2 * ? = 7\frac{1}{2}$ $7\frac{1}{2} * ?= 2$ $? * 2 = 7\frac{1}{2}$

$2* 7\frac{1}{2} = ?$ $? * 7\frac{1}{2} = 2$

Answer:

1. See Explanation

2. $2 * ? = 7\frac{1}{2}$ and $? * 2 = 7\frac{1}{2}$

Step-by-step explanation:

Solving (a):

Given

$Students = 60$

$Group = Equal\ Sized$

Required

Interpret $\frac{60}{5}$ in 2 ways

<u>Interpretation 1:</u> Number of groups if there are 5 students in each

<u>Interpretation 2:</u> Number of students in each group if there are 5 groups

<u>Solving the quotient</u>

$Quotient = \frac{60}{5}$

$Quotient = 12$

<u>For Interpretation 1:</u>

The quotient means: 12 groups

<u>For Interpretation 2:</u>

The quotient means: 12 students

Solving (b):

Given

$7\frac{1}{2} / 2$

Required

Select all equivalent multiplication equations

Let ? be the quotient of t $7\frac{1}{2} / 2$

So, we have:

$7\frac{1}{2}/2 = ?$

Multiply through by 2

$2 * 7\frac{1}{2}/2 = ? * 2$

$7\frac{1}{2} = ? * 2$

Rewrite as:

$? * 2 = 7\frac{1}{2}$ --- This is 1 equivalent expression

Apply commutative law of addition:

$2 * ? = 7\frac{1}{2}$ --- This is another equivalent expression

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1 year ago