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Ymorist [56]
3 years ago
14

Ralph is an electrictian.he charges an initial fee of $32 plus $33 per hour. If Ralph earned $189 on a Job,how long did The Job

take ?
Mathematics
1 answer:
aleksley [76]3 years ago
6 0

Answer:

5 hours

Step-by-step explanation:

189-32=157

157/33 is about 4.76

4.76 rounded is 5 so the job took 5 hours

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Solve for x in the equation x2 - 12x+ 36 = 90
12345 [234]

Answer:

6 + 3\sqrt{10\\} or 6 - 3\sqrt{10\\}

Step-by-step explanation:

x^2 - 12x + 36 = 90

x^2 - 12x - 54 = 0

x = \frac{-b +/- \sqrt{b^{2} + 4ac }}{2a}

a = 1, b= -12, c= -54

6 + 3\sqrt{10\\} or 6 - 3\sqrt{10\\}

6 0
3 years ago
Ben and Josh went to the roof of their 40-foot tall high school to throw their math books offthe edge.The initial velocity of Be
Taya2010 [7]

Answer

Josh's textbook reached the ground first

Josh's textbook reached the ground first by a difference of t=0.6482

Step-by-step explanation:

Before we proceed let us re write correctly the height equation which in correct form reads:

h(t)=-16t^2 +v_{o}t+s       Eqn(1).

Where:

h(t) : is the height range as a function of time

v_{o}   : is the initial velocity

s     : is the initial heightin feet and is given as 40 feet, thus Eqn(1). becomes:

h(t)=-16t^2 + v_{o}t + 40        Eqn(2).

Now let us use the given information and set up our equations for Ben and Josh.

<u>Ben:</u>

We know that v_{o}=60ft/s

Thus Eqn. (2) becomes:

h(t)=-16t^2+60t+40        Eqn.(3)

<u>Josh:</u>

We know that v_{o}=48ft/s

Thus Eqn. (2) becomes:

h(t)=-16t^2+48t+40       Eqn. (4).

<em><u>Now since we want to find whose textbook reaches the ground first and by how many seconds we need to solve each equation (i.e. Eqns. (3) and (4)) at </u></em>h(t)=0<em><u>. Now since both are quadratic equations we will solve one showing the full method which can be repeated for the other one. </u></em>

Thus we have for Ben, Eqn. (3) gives:

h(t)=0-16t^2+60t+40=0

Using the quadratic expression to find the roots of the quadratic we have:

t_{1,2}=\frac{-b+/-\sqrt{b^2-4ac} }{2a} \\t_{1,2}=\frac{-60+/-\sqrt{60^2-4(-16)(40)} }{2(-16)} \\t_{1,2}=\frac{-60+/-\sqrt{6160} }{-32} \\t_{1,2}=\frac{15+/-\sqrt{385} }{8}\\\\t_{1}=4.3276 sec\\t_{2}=-0.5776 sec

Since time can only be positive we reject the t_{2} solution and we keep that Ben's book took t=4.3276 seconds to reach the ground.

Similarly solving for Josh we obtain

t_{1}=3.6794sec\\t_{2}=-0.6794sec

Thus again we reject the negative and keep the positive solution, so Josh's book took t=3.6794 seconds to reach the ground.

Then we can find the difference between Ben and Josh times as

t_{Ben}-t_{Josh}= 4.3276 - 3.6794 = 0.6482

So to answer the original question:

<em>Whose textbook reaches the ground first and by how many seconds?</em>

  • Josh's textbook reached the ground first
  • Josh's textbook reached the ground first by a difference of t=0.6482

3 0
3 years ago
Find the slope of the line that passes through the following points. (-8,-1) (-4,-2)
lana [24]

Answer:

-1/4

Step-by-step explanation:

We can find the slope of a line given two points by using

m = (y2-y1)/(x2-x1)

    = (-2- -1)/( -4 - -8)

    = (-2+1)/(-4+8)

     = -1/4

8 0
3 years ago
Read 2 more answers
6-2(x+6)=3x+4 <br><br><br> ...............................
juin [17]

Answer:

x=−2

Step-by-step explanation:

1 Expand.

6-2x-12=3x+4

6−2x−12=3x+4

2 Simplify  6-2x-126−2x−12  to  -2x-6−2x−6.

-2x-6=3x+4

−2x−6=3x+4

3 Add 2x2x to both sides.

-6=3x+4+2x

−6=3x+4+2x

4 Simplify  3x+4+2x3x+4+2x  to  5x+45x+4.

-6=5x+4

−6=5x+4

5 Subtract 44 from both sides.

-6-4=5x

−6−4=5x

6 Simplify  -6-4−6−4  to  -10−10.

-10=5x

−10=5x

7 Divide both sides by 55.

-\frac{10}{5}=x

−

5

10

​

=x

8 Simplify  \frac{10}{5}

5

10

​

  to  22.

-2=x

−2=x

9 Switch sides.

x=-2

x=−2

4 0
3 years ago
What is the value of n in this equation?<br>n+ 134 = 379<br>423<br>245<br>334​
alexira [117]

Answer:

the answer to this question is 245

Step-by-step explanation:

n+134=379

-134 -134

n=245

5 0
3 years ago
Read 2 more answers
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