Josh is hiking Glacier National Park. He has now hiked a total of 1 7 km 17 km17, space, k, m and is 2 km 2 km2, space, k, m short of being 1 2 2 1 ​ start fraction, 1, divided by, 2, end fraction of the way done with his hike. Write an equation to determine the total length in kilometers ( h ) (h)left parenthesis, h, right parenthesis of Josh's hike.

Final answer:

To solve the equation 8x + 6 = 5x + 9, subtract 5x from both sides to get 3x + 6 = 9, then subtract 6 from both sides to get 3x = 3. Finally, divide by 3 to find x = 1.

Explanation:

The equation given is 8x + 6 = 5x + 9. To solve for x, you first want to get all terms containing x on one side and the constants on the other. This is achieved through the use of addition or subtraction. From LibreTexts™, we know that addition or subtraction of the same number on both sides of an equation maintains equality. So, subtract 5x from both sides:

8x + 6 - 5x = 5x + 9 - 5x

3x + 6 = 9

Next, you subtract 6 from both sides to isolate the x term:

3x + 6 - 6 = 9 - 6

3x = 3

Now, you divide both sides by 3, a step also indicated by LibreTexts™ as multiplication or division by the same number maintains the equation's balance:

3x / 3 = 3 / 3

x = 1

The solution to the equation is x = 1.

We have that for the Question "identify the two rational numbers. " it can be said that

Option B,C,D is rational

From the question we are told

identify the two rational numbers.

A)√2

B) 1.01

C) 1.010010001...

D) -2/5

Generally

Rational number are real number that exist is a form where the denominators are not zero

Therefore

A)√2 this is an irratioanl number as its \pm 1

B) 1.01  Rational

C) 1.010010001... rational

D) -2/5 rational

Hence

Option B,C,D is rational

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Hello There!

Median: The middle number when all the numbers are listed in oder from least to greatest.

To find the median, place the numbers in order from least to greatest.

In this case, the numbers would be 4, 5, 8, 9, 10

The middle number would be 8 so the median for this set of numbers is 8.

The next number in the series is 65. To identify the pattern in the given series and find the next number, let's look at the differences between consecutive terms.

5 - 2 = 3

11 - 5 = 6

20 - 11 = 9

32 - 20 = 12

47 - 32 = 15

As we observe, the differences between consecutive terms are increasing by 3 each time. So, to find the next difference, we add 3 to the last difference:

15 + 3 = 18

Now, to find the next number in the series, we add this difference to the last number in the series:

47 + 18 = 65

Therefore, the next number in the series is 65.

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a + b = 43 (the sum of two numbers is 43)
(a +11) = b (he larger number is 11 more than the smaller number)

so:
a + b = 43
a + (a + 11) = 43
a + a + 11 = 43
2a = 43 - 11
2a = 32
a = 16

now:
a + b = 43
16 + b = 43
b = 43 - 16
b = 27

that is:
a = 16
b = 27

 --------------------------

 checking:

b - a = 11 
27 - 16 = 11 (TRUE)

Answer:

step three is the incorrect one making step three the answer

Step-by-step explanation:

In the following steps student made the error in the third step.

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

The error occurred in Step 3.

Step 3 should be:

-2(m) = -2(6 + n)

-2m = -12 - 2n

The mistake was that the student distributed the negative sign only to the 6 and not to the n.

The correct next step is to simplify equation 2:

2m = 8 + 8n

So the student made an error in Step 3.

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Final answer:

The expression cosx (tanx+cotx) simplifies to sinx+cosx by using trigonometric identities and recognizing that tanx and cotx can be expressed in terms of sinx and cosx, allowing terms to cancel out.

Explanation:

To simplify the expression cosx (tanx+cotx), we need to use trigonometric identities. Recall that tanx = sinx/cosx, and cotx = cosx/sinx. Therefore, when we multiply cosx by tanx, the cosx in the numerator and denominator will cancel out, leaving us with sinx. Similarly, when we multiply cosx by cotx, sinx in the numerator and denominator will cancel out, leaving us with cosx.

So the simplification process will look like this:

cosx * tanx = sinx

cosx * cotx = cosx

Thus, cosx (tanx+cotx) = sinx+cosx.

This is the simplified form of the expression given. It's important to remember that trigonometric identities are a powerful tool in simplifying expressions involving trigonometric functions.

The simplification of ( n + 8) + ( n -12 ) is 2(n -2)

algebraic expression are expression with unknown.

This unknown is represented by letters and in linear algebraic equations , the highest power of the unknown is 1.

Simplifying (n + 8) + (n-12)

n + 8 + n -12

collecting like terms

n + n + 8 -12

2n -4

we can further Factorize

2( n -2)

Therefore, the simplification of ( n + 8) + ( n -12 ) is 2(n -2)

[tex] |\Omega|=8\cdot8=64\\
|A|=4\cdot6=24\\\\
P(A)=\dfrac{24}{64}=\dfrac{3}{8}=37.5\% [/tex]

Answer:

the answer is 37.5% Hope this helps!

To find (f o g)(2), substitute the value of g(2) into f. To find (f+g)(2), find f(2) and g(2) separately, then add them together.

To find (f o g)(2), we need to first find g(2), and then substitute that value into f. To find g(2), we substitute 2 into the expression for g(x). g(2) = 4(2) + 9 = 8 + 9 = 17. Now, we substitute 17 into the expression for f(x), which is 1/x. (f o g)(2) = f(g(2)) = f(17) = 1/17.

To find (f+g)(2), we first need to find f(2) and g(2) separately. f(2) = 1/2, and g(2) = 17. Now, we add them together. (f+g)(2) = f(2) + g(2) = 1/2 + 17 = 1/2 + 34/2 = 35/2 = 17.5.

Answer:

x(x+1)²

Step-by-step explanation:

x is a common factor to all terms so the first step is to factor it out:

... x(x² +2x +1)

The quadratic factor is recognizable as the square (x+1)², so the factoring is ...

... x(x +1)²

Answer:

Step-by-step explanation:x(x+1)2

Answer:c=11n+75

Step-by-step explanation:

Final answer:

To solve the expression 2 + 3 × 16 − 2 × 21 − 3, we use the order of operations rule, starting with multiplication to get 48 and 42, followed by addition and subtraction to arrive at the final answer of 5.

Explanation:

The student's question requires us to solve a mathematical expression using the correct order of operations. In the expression 2 + 3 × 16 − 2 × 21 − 3, we need to follow the BIDMAS/BODMAS/PEMDAS rule (Brackets, Indices/Orders, Division and Multiplication, Addition and Subtraction). This rule ensures that we perform multiplication and division before addition and subtraction.

First, we calculate the multiplication parts: 3 × 16 and 2 × 21.
3 × 16 = 48
2 × 21 = 42

Substituting these into the original expression gives us:
2 + 48 − 42 − 3

Next, we perform the addition and subtraction in order from left to right:
2 + 48 = 50
50 − 42 = 8
8 − 3 = 5

So, the expression simplifies to the number 5.