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Andrew [12]
3 years ago
7

Is y = 3/2x +5/4 and -2x+8y=-25 a solution

Mathematics
1 answer:
nekit [7.7K]3 years ago
7 0

Answer: x=-35/10

              y=-4

Step-by-step explanation:

y = 3/2x +5/4

-2x+8y=-25

--------------------

replace y in second equation with: y = 3/2x +5/4

-2x+8(3/2x+5/4)= -25

-2x+12x+10= -25

10x=-35

x=-35/10

x=-3.5

7+8y= -25

8y=-32

y=-4

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John looked at his bank account and noticed that he had $2,029.90 in his account. All that he could remember is that he created
Over [174]

We will have that for the previous year, he had in the account:

m_{y6}=2029.90-\frac{2029.90\cdot6}{100}\Rightarrow m_{y6}=1908.106

For the year previous to that one, he had:

m_{y5}=1908.106-\frac{1908.106\cdot6}{100}\Rightarrow m_{y5}=1793.61964

For the previous year to that, he had:

m_{y4}=1793.61964-\frac{1793.61964\cdot6}{100}\Rightarrow m_{y4}=1686.002462

For the year previous to that one, he had:

m_{y3}=1686.002462-\frac{1686.002462\cdot6}{100}\Rightarrow m_{y3}=1584.842314

For the second year that the money was in the account, there was:

m_{y2}=1584.842314-\frac{1584.842314\cdot6}{100}\Rightarrow m_{y2}=1489.751775

And the orinial ammount of money that was in the account was:

m_{y1}=1489.751775-\frac{1489.751775\cdot6}{100}\Rightarrow m_{y1}=1400.366669

From this, we know that Jhon had originally $1400.37 in the bank account.

6 0
9 months ago
when camping alone , mr adam uses all of the water in 12 days, then when mrs adams and mr adams camp together they use all of th
professor190 [17]

Using the together rate, it is found that if Mrs Adams camps alone, she will use all the water in 24 hours.

<h3>What is the together rate?</h3>

The together rate is the sum of each separate rate.

In this problem, the rates are:

  • Together: 1/8.
  • Mr Adam: 1/12.
  • Mrs Adams: 1/x.

Hence:

\frac{1}{12} + \frac{1}{x} = \frac{1}{8}

\frac{x + 12}{12x} = \frac{1}{8}

12x = 8x + 96

4x = 96

x = \frac{96}{4}

x = 24

If Mrs Adams camps alone, she will use all the water in 24 hours.

More can be learned about the together rate at brainly.com/question/25159431

6 0
2 years ago
Complete the square and write in standard form. Show all work.What would be the conic section:CircleEllipseHyperbolaParabola
mote1985 [20]

ANSWER

This is an ellipse. The equation is:

\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1

EXPLANATION

We have to complete the square for each variable. To do so, we have to take the first two terms and compare them with the perfect binomial squared formula,

(a+b)^2=a^2+2ab+b^2

For x we have to take 16x² and -32x. Since the coefficient of x is not 1, first, we have to factor out the coefficient 16,

16x^2-32x=16(x^2-2x)

Now, the first term of the expanded binomial would be x and the second term -2x. Thus, the binomial is,

(x-1)^2=x^2-2x+1

To maintain the equation, we have to subtract 1,

16(x^2-2x+1-1)=16((x-1)^2-1)=16(x-1)^2-16

Now, we replace (16x² - 32x) from the given equation by this equivalent expression,

16(x-1)^2-16+9y^2+72y+16=0

The next step is to do the same for y. We have the terms 9y² + 72y. Again, since the coefficient of y² is not 1, we factor out the coefficient 9,

9y^2+72y=9(y^2+8y)

Following the same reasoning as before, we have that the perfect binomial squared is,

(y+4)^2=y^2+8y+16

Remember to subtract the independent term to maintain the equation,

9(y^2+8y)=9(y^2+8y+16-16)=9((y+4)^2-16)=9(y+4)^2-144

And now, as we did for x, replace the two terms (9y² + 72y) with this equivalent expression in the equation,

16(x-1)^2-16+9(y+4)^2-144+16=0

Add like terms,

\begin{gathered} 16(x-1)^2+9(y+4)^2+(-16-144+16)=0 \\ 16(x-1)^2+9(y+4)^2-144=0 \end{gathered}

Add 144 to both sides,

\begin{gathered} 16(x-1)^2+9(y+4)^2-144+144=0+144 \\ 16(x-1)^2+9(y+4)^2=144 \end{gathered}

As we can see, this is the equation of an ellipse. Its standard form is,

\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1

So the next step is to divide both sides by 144 and also write the coefficients as fractions in the denominator,

\begin{gathered} \frac{16(x-1)^2}{144}+\frac{9(y+4)^2}{144}=\frac{144}{144} \\  \\ \frac{(x-1)^2}{\frac{144}{16}}+\frac{(y+4)^2}{\frac{144}{9}}=1 \end{gathered}

Finally, we have to write the denominators as perfect squares, so we identify the values of a and b. 144 is 12², 16 is 4² and 9 is 3²,

\frac{(x-1)^2}{(\frac{12}{4})^2}+\frac{(y+4)^2}{(\frac{12}{3})^2}=1

Note that we can simplify a and b,

\frac{12}{4}=3\text{ and }\frac{12}{3}=4

Hence, the equation of the ellipse is,

\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1

3 0
1 year ago
What's the solution of the equation 4[x+2(3x-7)]=22x-65
padilas [110]

Answer:

x = -3/2

Step-by-step explanation:

Let's solve your equation step-by-step.

4(x+2(3x−7))=22x−65

Step 1: Simplify both sides of the equation.

4(x+2(3x−7))=22x−65

(4)(x)+(4)(2(3x−7))=22x+−65(Distribute)

4x+24x+−56=22x+−65

(4x+24x)+(−56)=22x−65(Combine Like Terms)

28x+−56=22x−65

28x−56=22x−65

Step 2: Subtract 22x from both sides.

28x−56−22x=22x−65−22x

6x−56=−65

Step 3: Add 56 to both sides.

6x−56+56=−65+56

6x=−9

Step 4: Divide both sides by 6.

6x = -9

6       6

x =  -3/2

8 0
2 years ago
What is point A on the coordinate plane
Zinaida [17]

Answer:

4,1

Step-by-step explanation:

8 0
3 years ago
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