The parallelograms are similar. Find x.

x is equal to 2 or -5

y is equal to 1 or 8

Step-by-step explanation:

first put your first equation in a format of y = x + _

here it will be :

[tex]y = - \times + 3[/tex]

now go and substitute this in your second equation. just like the picture. the pictures explain further

Hello there!

We are given the simultaneous equations:

[tex] \displaystyle \large{ \begin{cases} x + y = 3 \\ {x}^{2} - 3y = 1 \end{cases}}[/tex]

There are many methods to solve the equation but the best way for this problem is Substitution Method.

First, we have to isolate one-degree variable. I will choose the first equation to isolate. We are going to isolate y-variable so we can substitute the first equation in the second.

[tex] \displaystyle \large{ \begin{cases} x + y = 3 \\ {x}^{2} - 3y = 1 \end{cases}}[/tex]

Subtract x both sides for first equation.

[tex] \displaystyle \large{ \begin{cases} x - x+ y = 3 - x \\ {x}^{2} - 3y = 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} - 3y = 1 \end{cases}}[/tex]

After isolating y-term, we can finally substitute y = 3-x in the second equation.

[tex] \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} - 3(3 - x) = 1 \end{cases}}[/tex]

Expand -3 in. Recall that negative × negative = positive and negative × positive = negative.

[tex] \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} -9 + 3x= 1 \end{cases}}[/tex]

Notice that the second equation is in quadratic pattern. We are going to convert in the standard form to solve the equation.

Subtract both sides by 1.

[tex] \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} -9 - 1 + 3x= 1 - 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} -10 + 3x= 0 \end{cases}}[/tex]

Arrange the expression in ax^2+bx+c = 0.

[tex] \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} -9 - 1 + 3x= 1 - 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} + 3x - 10= 0 \end{cases}}[/tex]

Factor the expression.

What two numbers add or subtract each others and equal to 3? (These numbers must not multiply each others and be greater than 10)

What two numbers multiply each others and equal to -10?

Check the number above and multiply two numbers.

Two numbers would be 5 and -2. Factor the expression in two brackets.

[tex] \displaystyle \large{(x + 5)(x - 2) = 0}[/tex]

Then we solve like a linear equation, isolate both x.

[tex] \displaystyle \large{x= - 5,2}[/tex]

We've got two x-values. But we are not done yet.

We are going to use these values to substitute in the simultaneous equation. You can substitute in any equations; the first or second. I will choose to substitute x = -5 or x = 2 in the first equation since it is faster.

[tex] \displaystyle \large{ \begin{cases} y= 3 - x \\ {x}^{2} - 3y = 1 \end{cases}}[/tex]

Substitute x = -5

[tex] \displaystyle \large{ \begin{cases} y= 3 - ( - 5)\\ {x}^{2} - 3y = 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y= 3 + 5\\ {x}^{2} - 3y = 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y= 3 - ( - 5)\\ {x}^{2} - 3y = 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y= 8\\ {x}^{2} - 3y = 1 \end{cases}} [/tex]

When we substitute x = -5, y = 8.

Next, substitute x = 2

[tex] \displaystyle \large{ \begin{cases} y= 3 -2\\ {x}^{2} - 3y = 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y= 1\\ {x}^{2} - 3y = 1 \end{cases}}[/tex]

When we substitute x = 2, y = 1.

Therefore,

OR

Let me know if you have any questions!

Topic: Simultaenous Equations

Step-by-step explanation:

$334,654 ×14,5% = $34,024.83

therefore that is your answer

Answer: 5

Step-by-step explanation:

2 pizzas ten slices eatch, so 20 slices. 20 slices devided by 4 is five. :)

Answer:

above the sea level means height than the sea and below sea level means lower than sea height

Answer:

5 more matches was won by yu-na kim

Answer:

Mean = 58.18

Median = 60

Modes = 55 and 60

Step-by-step explanation:

To find the mean/average, add up all the numbers and divide the sum by the # of numbers there are (ex. there are 11 numbers so divide the sum by 11).

The median is the middle number of a set.  In this case, the middle number is easy to see because the # of numbers is odd, but if it was even, just find the average of the two middle numbers.

The mode is/are the most frequent number(s) in the set.  In this set, the numbers that appear the most are 55 and 60.

I think it’s 55%

Bc 55+45=100

45/50 90% 100-90 = 10

Step-by-step explanation:

10% is correct

Lets find f(n) formula

[tex]\boxed{\sf f(n)=\dfrac{1680}{n}}[/tex]

Now

[tex]\\ \sf\longmapsto f(10)=\dfrac{1680}{10}=168[/tex]

[tex]\\ \sf\longmapsto f(12)=\dfrac{1680}{12}=140[/tex]

[tex]\\ \sf\longmapsto f(16)=\dfrac{1680}{16}=105[/tex]

[tex]\\ \sf\longmapsto f(14)=\dfrac{1680}{14}=120[/tex]

9514 1404 393

Answer:

  no

Step-by-step explanation:

2π ≈ 6.28

√44 ≈ 6.63

  2π < √44

Answer:

x = y/5 + 6/5

Answer:

1) answer 3)88 students for 4 classes

10)answer=285parts

Answer:

(1,4)

Step-by-step explanation:

Let y (upper eq) = y (lower eq)

x+3 = 3x+1

(transposing similar numbers)

3x-x = 3-1

2x = 2

then x = 1

substituting x in any of the equation, say

y = x+3

y = 1 +3

y = 4

therefore (1,4)

check again the lower equation

y = 3x + 1

y = 3(1) + 1

y = 4

therefore (1,4)

Answer 61

Step-by-step explanation:

The answer is 61 bc the pattern is +5

Answer:

26, 31, 36, 41, 46, 51, 56, 61

the eighth number is 61.

Step-by-step expanation:

Answer:

11

Step-by-step explanation:

if pq = qr, x+1 = 11+1=12

thus x = 1

Answer:

$7.20

Step-by-step explanation:

First, we would have to find out how much to subtract from $62.

We need to multiply 90% and 62 or 0.9 x 62

When we finish this equation we get 54.8, which is what we need to subtract from 62 to see what 90% off is.

62 - 54.8 = 7.2, so therefore our answer is $7.20

Answer:

[tex]slope = \frac{y2 - y1}{x2- x1} \\ = \frac{9 - 16}{9 - 1} \\ = \frac{ - 7}{8} \\ slope = \frac{ - 7}{8} \\ thank \: you[/tex]

Answer:

6 numbers

Step-by-step explanation:

25

26

52

56

62

65

Answer:

Step-by-step explanation:

187 divided by 7 is 6.5

Answer: 29

Step-by-step explanation:

174 = dividend

6 = divisor

The divisor (6) goes into the first digit of the dividend (1), 0 time(s). Therefore, put 0 on top Multiply the divisor by the result in the previous step (6 x 0 = 0) and write that answer below the dividend. Subtract the result in the previous step from the first digit of the dividend (1 - 0 = 1) and write the answer below.

Move down the 2nd digit of the dividend (7) like this:

0

6 ⟌ 1 7 4

- 0

1 7

Multiply the divisor by the result in the previous step (6 x 2 = 12) and write that answer at the bottom:

0 2

6 ⟌ 1 7 4

- 0

1 7

1 2

Subtract the result in the previous step from the number written above it. (17 - 12 = 5) and write the answer at the bottom.

0 2

6 ⟌ 1 7 4

- 0

1 7

- 1 2

5

Move down the last digit of the dividend (4) like this:

0 2

6 ⟌ 1 7 4

- 0

1 7

- 1 2

5 4

Multiply the divisor by the result in the previous step (6 x 9 = 54) and write the answer at the bottom:

0 2 9

6 ⟌ 1 7 4

- 0

1 7

- 1 2

5 4

5 4

Subtract the result in the previous step from the number written above it. (54 - 54 = 0) and write the answer at the bottom.

0 2 9

6 ⟌ 1 7 4

- 0

1 7

- 1 2

5 4

- 5 4

0

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 174 divided by 6 calculated using Long Division is:

29

0 Remainder

Its long but your welcome :)

[tex]\\ \sf\longmapsto 5x+5+4x-5=180[/tex]

[tex]\\ \sf\longmapsto 5x+4x+5-5=180[/tex]

[tex]\\ \sf\longmapsto 9x=180[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{180}{9}[/tex]

[tex]\\ \sf\longmapsto x=20[/tex]

Step-by-step explanation:

hope this helps u ✌️✌️

Make mister as brainliest

Answer:

The choose C. 24x+6y

Step-by-step explanation:

[tex]3(8x + 2y) = 24x + 6y[/tex]

I hope I helped you^_^

(a) Concerning the coefficients of the equation for the volume of the eggplant ( [tex]V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}[/tex]), the units of the coefficients with values [tex]3.53 \times 10^{-2}[/tex] and 2 are cubic feet and [tex]\frac{1}{h^{2}}[/tex], respectively.

(b) Regarding the determination of the coefficients by linear regression, the scientist must plot the square of time versus the natural logarithm of the volume and he would have obtained that the intercept is the natural logarithm of constant A and the slope is constant B.

(c) After the solicitation of the European distributor of the film, the new formula is [tex]V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}[/tex], where volume is in cubic meters and time is in seconds.

Note - The statement reports typing mistakes. We present the correct statement below:

The climatic moment in the film "The Eggplant that Ate New Jersey" comes when the brilliant young scientist announces his discovery of the equation for the volume of the eggplant: [tex]V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}[/tex], where [tex]t[/tex] is the time in hours from the moment the vampire injected the eggplant with a solution prepared from the blood of the beautiful dental hygienist.

(a) What are the units of [tex]3.53\times 10^{-2}[/tex] and [tex]2[/tex]?

(b) The scientist obtained the formula by measuring [tex]V[/tex] and [tex]t[/tex] and determining the coefficients by linear regression. What would he have plotted versus what on what kind of coordinates? What would he have obtained as the slope and intercept of his plot?

(c) The European distributor of the film insists that the formula must be given for the volume in cubic meters ([tex]m^{3}[/tex]) as a function of time, in seconds. Derive the formula.

(a) In this exercise, we must make use of principles for dimensional analysis. We know that the equation for the volume of the eggplant is represented by:

[tex]V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}[/tex] (1)

Dimensionally speaking, we have the following case:

[tex][L]^{3} = [A]\cdot e^{[B]\cdot [t]^{2}}[/tex] (2)

By direct inspection and some algebraic handling, we conclude that:

[tex][A] = [L]^{3}[/tex]

[tex][B] = [t]^{-2}[/tex]

Therefore, the units of [tex]3.53 \times 10^{-2}[/tex] and 2 are cubic feet and [tex]\frac{1}{h^{2}}[/tex], respectively.

(b) The curve fit for the exponential expression used by the scientist is of the form:

[tex]V = A\cdot e^{B\cdot t^{2}}[/tex] (3)

If we apply logarithms on both sides of the expression above, then we have the following form:

[tex]\ln V = \ln A\cdot e^{B\cdot t^{2}}[/tex]

[tex]\ln V = \ln A + B\cdot t^{2}[/tex] (4)

The scientist must plot the square of time versus the natural logarithm of the volume and he would have obtained that the intercept is the natural logarithm of constant A and the slope is constant B.

(c) An hour equals 3600 seconds and a cubic feet equals 0.028 cubic meters. Hence, we can adapt (1) to fulfill the requirements of the European film distributor by using the following conversions:

[tex]t' = 3600\cdot t[/tex] (5)

[tex]V' = 0.028\cdot V[/tex] (6)

Where:

By applying (5) and (6) in (1), we have the resulting formula:

[tex]V' = 0.028\cdot [3.53\times 10^{-2}\cdot e^{2\cdot \left(\frac{t'}{3600} \right)^{2}}][/tex]

[tex]V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}[/tex]

The new formula is [tex]V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}[/tex], where volume is in cubic meters and time is in seconds.

We kindly invite to check this question on exponential functions: https://brainly.com/question/2456547

After a small online search, I've found that the volume equation is:

[tex]V[ft^3] = 3.53 \cdot10^{-2} \cdot exp(2 \cdot t^2)[/tex]

a) We want to see what are the units of the first factor:

[tex]3.53 \cdot10^{-2}[/tex]

You can see that the volume is in cube feet, and the only part in the equation that can have units is this one, so the units of this factor should be cube feet.

b) On the vertical coordinate he would see the volume and on the horizontal coordinate he would see the time.

The graph of this function is an increasing exponential function, that grows slow at the beginning and then grows faster.

c) Remember that the term with the units is:

[tex]3.53 \cdot10^{-2}[/tex]

So we should write this as:

[tex]3.53 \cdot10^{-2} ft^3[/tex]

Now we know that:

[tex]1m^3 = 35.3 ft^3\\\\1 = \frac{1 m^3}{35.3 ft^3}[/tex]

Now we can multiply our measure by this to get:

[tex]3.53 \cdot10^{-2} ft^3 = ( \frac{1 m^3}{35.3 ft^3})*(3.53 \cdot10^{-2} ft^3) = 0.1 m^3[/tex]

Then the equation is:

[tex]V = 0.1m^3\cdot exp(2 \cdot t^2)[/tex]

If you want to learn more you can read:

https://brainly.com/question/172096

Answer:

[tex]4g^{2}h-12gh^{2}-9gh[/tex]

Copy and paste version:

4g^2h-12gh^2-9gh

Step-by-step explanation:

[tex](4g^{2}h-gh-9gh^{2})+(8gh-3gh^{2})=\\4g^{2}h-gh-9gh^{2}+8gh-3gh^{2}=\\4g^{2}h-9gh-12gh^{2}=\\4g^{2}h-12gh^{2}-9gh[/tex]

Answer:

4g^2h-12gh^2-9gh

Step-by-step explanation:

Answer:

The equation would be 5-3x=7

Step-by-step explanation:

5 less than indicates subtraction, and 3 times a number indicates both values being multiplied with each other, so it's 3x. Hope that helped.

[tex]\begin{array}{l}\begin{cases} \begin{array}{l}\sin \alpha =\frac{x}{12} \Leftrightarrow x=12\sin \alpha \end{array}\\\cos \alpha =\frac{y}{12} \Leftrightarrow y=12\cos \alpha \end{cases}\\\\\text{Thus,\ the\ area\ is}\\\\A=\frac{xy}{2} =\frac{12\sin \alpha \cdotp 12\cos \alpha }{2}\\\\\Longrightarrow A=72\sin \alpha \cos \alpha \end{array}[/tex]

D

Answer:

$8.27

Hope this is right <3