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Fudgin [204]
2 years ago
7

A staff gauge measures the height of the water level in a river compared to the average water level. At one gauge the river is 1

ft below its average water level of 10 ft. It begins to rise by a constant rate of 1.5 ft per hour.
Will the river reach a level of 7 ft above normal after 5 hours? Explain.
Mathematics
1 answer:
Juli2301 [7.4K]2 years ago
5 0

The river will not reach a level of 7 ft. after 5 hours.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Let y represent the height of the water level after x hours.

Since the  river is 1 ft below its average water level and  begins to rise by a constant rate of 1.5 ft per hour. Hence:

b = -1, m = 1.5. The equation becomes:

y = 1.5x - 1

To reach a level of 7 ft. That is y = 7:

7 = 1.5x - 1

1.5x = 8

x = 5.3 hours

The river will not reach a level of 7 ft. after 5 hours.

Find out more at: brainly.com/question/13911928

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Answer:

21 girls.

Step-by-step explanation:

50% of 42 students are girls.

So 42/2 = 21.

Therefore 21 of the students are girls.

<em>Hope I helped</em>

3 0
1 year ago
Parallelogram ABCD has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain.
Hoochie [10]

Answer:

The correct option is parallelogram ABCD is a rhombus, because the diagonal bisects two angles

Step-by-step explanation:

In triangle ABD:

∠B = ∠D

Thus AB=AC by the property of opposite sides of equal angles are equal

In triangle CBD

∠B = ∠D

Thus CB=CD  by the property of opposite sides of equal angles are equal

Thus all four sides of quadrilateral ABCD are equal  

And diagonal BD bisects the angles  

So, it is a rhombus

Therefore the correct option is  parallelogram ABCD is a rhombus, because the diagonal bisects two angles....

5 0
3 years ago
432 students went on a field trip. Eight buses were filled with students. The
olga_2 [115]
Each bus was filled with 54 students
3 0
2 years ago
Rewrite the system of linear equations as a matrix equation AX = B.
iren2701 [21]

Answer:

\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]*\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]=\left[\begin{array}{ccc}5\\6\\7\end{array}\right]

Step-by-step explanation:

Let's find the answer.

Because we have 3 equations and 3 variables (x1, x2, x3) a 3x3 matrix (A) can be constructed by using their respectively coefficients.

Equations:

Eq. 1 : x1 + 2x2 + 5x3 = 5

Eq. 2 : x1 + x2 + x3 = 6

E1. 3 : 4x1 + 6x2 + 5x3 = 7

Coefficients for x1 ; x2 ; x3

From eq. 1 : 1 ; 2 ; 5

From eq. 2 : 1 ; 1 ; 1

From eq. 3 : 4 ; 6 ; 5

So matrix A is:

\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]

And the vector of vriables (X) is:

\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]

Now we can find the resulting vector (B) using the 'resulting values' from each equation:

\left[\begin{array}{ccc}5\\6\\7\end{array}\right]

In conclusion, AX=B is:

\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]*\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]=\left[\begin{array}{ccc}5\\6\\7\end{array}\right]

7 0
3 years ago
How is the sum expressed in sigma notation? <br> 1/64+1/16+1/4 + 1 + 4
shusha [124]

9514 1404 393

Answer:

  sum = ∑[n=1,5] 4^(n-4)

Step-by-step explanation:

First of all, you need to be able to describe the n-th term.

Here, we  have ...

  term #: 1, 2, 3, 4, 5

  value: 4^-3, 4^-2, 4^-1, 4^0, 4^1

That is, the exponent of 4 is 4 less than the term number. So, the n-th term is 4^(n-4). The sum of the 5 terms shown is then ...

  \displaystyle sum=\sum_{n=1}^5{4^{n-4}}

5 0
2 years ago
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