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mixer [17]
1 year ago
14

Sean earns $7.00 per hour working after school. He needs at least $230 for a stereo system. Write and solve an inequality that d

escribes how many hours he must work to reach his goal.
Mathematics
1 answer:
Fofino [41]1 year ago
8 0

earnings = $7 per hour

He needs at least $230 . This means he needs an amount greater than or equals to $230.

let

t = hour many hours he works

Therefore,

7t\ge230\begin{gathered} 7t\ge230 \\ t\ge\frac{230}{7} \\ t\ge32.8571428571 \\ t\ge33 \end{gathered}

He needs to work approximately 33 hours or more to get at least $230 for his sterio. This means t is greater than or equals to approximately 33.

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An obtuse triangle has two angles 45 n 18 ,and a third unknown angle theta what's the value of the unknown angle​
zlopas [31]

<u>Answer:</u>

An obtuse triangle has two angles 45 and 18. The value of the unknown angle is 117^{\circ}

<u>Solution:</u>

Given that two angles of an obtuse triangle is 45 and 18.  

Third angle is θ  

We are asked to find the value of third unknown angle theta

According to <em>angle sum property of triangle</em>, sum of three angles of triangle is 180^{\circ}

This means in our case sum of 45, 18 and θ should be 180^{\circ}

\begin{array}{l}{=>45+18+\theta=180} \\ {=>\theta=180-63=117^{\circ}}\end{array}

Hence value of unknown third angle of an obtuse triangle is 117^{\circ}

7 0
3 years ago
3 determine the highest real root of f (x) = x3− 6x2 + 11x − 6.1: (a) graphically. (b) using the newton-raphson method (three it
Juliette [100K]

(a) See the first attachment for a graph. This graphing calculator displays roots to 3 decimal places. (The third attachment shows a different graphing calculator and 10 significant digits.)

(b) In the table of the first attachment, the column headed by g(x) gives iterations of Newton's Method. (For Newton's method, it is convenient to let the calculator's derivative function compute the derivative f'(x) of the function f(x). We have defined g(x) = x - f(x)/f'(x).) The result of the 3rd iteration is ...

... x ≈ 3.0473167

(c) The function h(x₁, x₂) computes iterations using the secant method. The results for three iterations of that method are shown below the table in the attachment. The result of the 3rd iteration is ...

... x ≈ 3.2291234

(d) The function h(x, x+0.01) computes the modified secant method as required by the problem statement. The result of the 3rd iteration is ...

... x ≈ 3.0477377

(e) Using <em>Mathematica</em>, the roots are found to be as shown in the second attachment. The highest root is about ...

... x ≈ 3.0466805180

_____

<em>Comment on these methods</em>

Newton's method can have convergence problems if the starting point is not sufficiently close to the root. A graphing calculator that gives a 3-digit approximation (or better) can help avoid this issue. For the calculator used here, the output of "g(x)" is computed even as the input is typed, so one can simply copy the function output to the input to get a 12-significant digit approximation of the root as fast as you can type it.

The "modified" secant method is a variation of the secant method that does not require two values of the function to start with. Instead, it uses a value of x that is "close" to the one given. For our purpose here, we can use the same h(x1, x2) for both methods, with a different x2 for the modified method.

We have defined h(x1, x2) = x1 - f(x1)(f(x1)-f(x2))/(x1 -x2).

6 0
3 years ago
If the length of a rectangle is (x + 7) inches and the width is (3x+2) inches. Which expression represents the rectangle's area?
konstantin123 [22]

Answer:

The answer is no 1:

3x ^{2}  + 23x + 14

5 0
3 years ago
Find an equation for the nth term of the arithmetic sequence. 9, 11, 13, 15...
saul85 [17]

Answer:

2n+7

Step-by-step explanation:

find the difference

and see the difference from the 2 Times table to the original sequence

and write it as an equation for this sequence

3 0
3 years ago
Read 2 more answers
Which of the following is true?
EleoNora [17]
The options can be rewrited as follow:
A. 5<4
B. 5<5
C. 5<4
D. 4<-5

∴ Answer is none of the above.

Unless perhaps you have written down the question incorrectly.
8 0
3 years ago
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