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malfutka [58]
3 years ago
11

Bob’s monthly phone bill is made up of a $10 fee plus $0.05 per minute. Bob’s phone bill for July was $22. Write an equation to

model the situation using m to represent the number of minutes. Solve the equation to determine the number of phone minutes Bob used in July.
Mathematics
2 answers:
Blizzard [7]3 years ago
5 0

Answer:

equation: 10 + 0.05x=22

Step-by-step explanation:

the next step after writing the equation would be to subtract 10 from both sides to get 0.05x=12. after this you would then have to divide 12 by 0.05 to get 240 minutes. you could check it by putting 240 in for x to get 10+0.05(240)=22. you would then multiply 0.05 by 240 to get 12 and then add 10 onto it to get 22 which was already given.

PIT_PIT [208]3 years ago
3 0

9514 1404 393

Answer:

  equation: 10 +0.05m = 22

  solution: Bob used 240 minutes in July

Step-by-step explanation:

Bob's bill is the total of the fixed fee and the charges based on minutes. The latter is 0.05m, where m is the number of minutes. Hence, Bob's July bill is ...

 10 + 0.05m = 22 . . . . . total of charges for July is $22

__

The equation is solved by subtracting the constant and dividing by the coefficient of m.

  0.05m = 12 . . . . . subtract 10

  m = 12/0.05 = 240

Bob used 240 minutes in July.

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Pepsi [2]

Step-by-step explanation:

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\text{Other solution}\\\\(x^2-y^2)^2\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\= [(x-y)(x+y)]^2\\\\\text{use}\ (ab)^n=a^nb^n\\\\=(x-y)^2(x+y)^2

7 0
3 years ago
Find the area of the triangle with the given vertices. Use the fact that the area of the triangle having u and v as adjacent sid
Gnom [1K]

Answer:

The area of the triangle is A=\sqrt{\frac{4027}{2}}

Step-by-step explanation:

Using the fact that the area of the triangle having u and v as adjacent sides is given by

A=\frac{1}{2}||{\bf u} \times {\bf v} ||

We know that we want to take a cross product to compute the area of the triangle, but we need to be careful because it doesn't make sense if we take the cross product of points.

The first step is to build some vectors that describe this triangle.

According with the graph we can build the vectors:

{\bf AB} and {\bf AC}

The vector {\bf AB} is the difference of point B minus point A

{\bf AB}=(5-3,5-5,0-9)=(2,0,-9)

and the vector {\bf AC} is the difference of point C minus point A

{\bf AC}=(-4-3,0-5,2-9)=(-7,-5,-7)

Next we need to find the cross product of this vectors.

{\bf AB} \times {\bf AC}=\begin{pmatrix}2&0&-9\end{pmatrix}\times \begin{pmatrix}-7&-5&-7\end{pmatrix}

This is the definition of cross product of two vectors in space:

Let {\bf u} = u_1{\bf i}+u_2{\bf j}+u_3{\bf k} and {\bf v} = v_1{\bf i}+v_2{\bf j}+v_3{\bf k} be vectors in space. The cross product of {\bf u} and {\bf v} is the vector

{\bf u} \times {\bf v}=(u_2v_3-u_3v_2){\bf i}-(u_1v_3-u_3v_1){\bf j}+(u_1v_2-u_2v_1){\bf k}

Applying this definition we get

{\bf AB} \times {\bf AC}=\begin{pmatrix}2&0&-9\end{pmatrix}\times \begin{pmatrix}-7&-5&-7\end{pmatrix}

\begin{pmatrix}0\cdot \left(-7\right)-\left(-9\left(-5\right)\right)&-9\left(-7\right)-2\left(-7\right)&2\left(-5\right)-0\cdot \left(-7\right)\end{pmatrix}\\\\\begin{pmatrix}-45&77&-10\end{pmatrix}

||{\bf AB} \times {\bf AC}||=\sqrt{(-45)^2+(77)^2+(-10)^2} \\\\||{\bf AB} \times {\bf AC}||=\sqrt{2025+5929+100}\\\\||{\bf AB} \times {\bf AC}||=\sqrt{8054}

The area of the triangle is

A=\frac{1}{2}||{\bf AB} \times {\bf AC} ||=\frac{1}{2}\sqrt{8054}=\sqrt{\frac{4027}{2}}

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4 years ago
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marishachu [46]

Given the two triangles, and the sine ratio formula is equal to:

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H is the hypotenuse of the triangle

 

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So the answer is

Sin (P) = 16/20 = 4/5

<span>So angle P has the sine ratio of 4/5</span>

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3 years ago
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