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torisob [31]
3 years ago
8

Find the solution to the system 9x−4y=−13 and 9x−2y=−20

Mathematics
1 answer:
BaLLatris [955]3 years ago
3 0

Answer:

x = -3, y = -3.5.  As an ordered pair it is (-3, -3.5).

Step-by-step explanation:

9x − 4y = −13

9x − 2y =  -20

Subtract:-

-2y = 7

y = -3.5.

Substitute for y in the first equation:

9x - 4(-3.5) = -13

9x =  -27

x = -3.

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If Diana walks forward and her angle looking to the top of the building changes to 40°, how much closer is she to the building?
elena55 [62]

The closer Diana gets to the building, the smaller the angle becomes

Diana is 17.6 feet closer to the building

<h3>How to calculate the distance from the building</h3>

To calculate the distance between her and the building, we make use of the following tangent ratio

\tan(\theta) = \frac{h}{d}

Where:

  • \theta = 40^o
  • h represents the height of the building; h = 130
  • d represents the distance from the building

So, we have:

\tan(40) = \frac{130}{d}

Make d the subject

d = \frac{130}{\tan(40)}

Evaluate tan(40)

d = \frac{130}{0.8391}

d = 154.93

Initially, Diana is at a distance of 172.53.

The difference in both distance is:

\Delta d = 172.53 - 154.93

\Delta d = 17.6

Hence, Diana is 17.6 feet closer to the building

Read more about trigonometry ratios at:

brainly.com/question/4326804

7 0
2 years ago
Marty made a $220 bank deposit using $10 bills and $5 bills. She gave the teller a total of 38 bills, how many $5 bills were in
Luda [366]

ANSWER: 32 five-dollar bills

======

EXPLANATION:

Let x be number of $5 bills

Let y be number of $10 bills

Since we have total of 38 bills, we must have the sum of x and y be 38

x + y = 38 (I)

Since the total amount deposited is $220, we must have the sum of 5x and 10y be 220 (x and y are just the "number of" their respective bills, so we multiply them by their value to get the total value):

5x + 10y = 220 (II)

System of equations:

\left\{ \begin{aligned} x + y &= 38 && \text{(I)} \\ 5x + 10y &= 220 && \text{(II)} \end{aligned} \right.

Divide both sides of equation (II) by 5 so our numbers become smaller

\left\{ \begin{aligned} x + y &= 38 && \text{(I)} \\ x + 2y &= 44 && \text{(II)} \end{aligned} \right.

Rearrange (I) to solve for y so that we can substitute into (II)

\begin{aligned} x + y &= 38 && \text{(I)} \\ y &= 38 - x \end{aligned}

Substituting this into equation (II) for the y:

\begin{aligned} x + 2y &= 44 && \text{(II)} \\ x + 2(38 - x) &= 44\\ x + 76 - 2x &= 44 \\ -x &= -32 \\ x &= 32 \end{aligned}

We have 32 five-dollar bills

======

If we want to finish off the question, use y = 38 - x to figure out number of $10 bills

y = 38 - 32 = 6

32 five-dollar bills and 6 ten-dollar bills

7 0
3 years ago
Is x + 10 a factor of the function f(x) = x3 − 75x + 250? Explain.
PtichkaEL [24]
Yes. When the function f(x) = x3 – 75x + 250 is divided by x + 10, the remainder is zero. Therefore, x + 10 is a factor of f(x) = x3 – 75x + 250. 

According to the remainder theorem when f(x) is divided by (x+a) the remainder is f(-a). 
In this case, 
f(x)=x^3-75x+250 
(x+a)=(x+10) 
Therefore, the remainder f(-a)=f(-10) 

=x^3-75x+250 
=(-10)^3-(75*-10)+250 
=-1000+750+250 
=1000-1000 
=0. 
The remainder is 0. So, (x+10) is a factor of x^3-75x+250.
8 0
3 years ago
Can someone please help me??????????
madam [21]
I hoped this help c 0.43
4 0
3 years ago
I need help with this problem
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2 x 2 x 3 x 3



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3 0
2 years ago
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