solve using elimination 3x+5y=4; -3x+y=8​

Answer:

28

Step-by-step explanation:

140 / 5 = 28

Answer:

y = -2x + 2

General Formulas and Concepts

Pre-Alg

Algebra I

Slope-Intercept Form: y = mx + b

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Step-by-step explanation:

Step 1: Define

Point (-1, 4)

y-intercept (0, 2)

Step 2: Find slope m

Step 3: Write linear equation

y = -2x + 2

Answer:

a) x = 1.5 or x = -0.3

b) x = 5 or x = -8

Explanation:

Quadratic formula:

\(\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \:\: ax^2 + bx + c = 0\)

Here given equation: 5x² - 6x  - 2 = 0

Identify variable constants: a = 5, b = -6, c = -2

Putting these values into equation:

\(\sf x = \dfrac{ -(-6) \pm \sqrt{(-6)^2 - 4(5)(-2)}}{2(5)}\)

\(\sf x = \dfrac{ 6 \pm \sqrt{36 + 40}}{10}\)

\(\sf x = \dfrac{ 6 \pm \sqrt{76}}{10}\)

\(\sf x = \dfrac{ 3\pm \sqrt{76}}{5}\)

\(\sf x = \dfrac{ 3+ \sqrt{76}}{5} \quad or \quad \dfrac{ 3- \sqrt{76}}{5}\)

In one decimal point:

\(\sf x = 1.5 \quad or \quad -0.3\)

b) Here use "middle term split" method

⇒ x² + 3x = 40

relocate

⇒ x² + 3x - 40 = 0

The factors of 40 are 8 and 5

⇒ x² + 8x - 5x - 40 = 0

factor common terms

⇒ x(x + 8) - 5(x + 8) = 0

collect into groups

⇒ (x - 5)(x + 8) = 0

set to zero

⇒ x - 5 = 0 or x + 8 = 0

relocate

⇒ x = 5 or x = -8

Step-by-step explanation:

a) The quadratic formula can help find answers to a quadratic equation when it is equal to 0. The formula is \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) for a quadratic equation of the form \(ax^2+bx+c=0\).

In this question, a is 5, b is -6, and c is -2. Let's put them in the equation and solve.

\(x=\frac{6\pm\sqrt{(-6)^2-4(5)(-2)}}{2(5)}\\x=\frac{6\pm\sqrt{36+40}}{10}\\x=\frac{6\pm\sqrt{76}}{10}\\x=\frac{6\pm2\sqrt{19}}{10}\\x=\frac{3\pm\sqrt{19}}{5}\)

This means that the value of x is both \(\frac{3+\sqrt{19}}5\) and \(\frac{3-\sqrt{19}}5\), since both values make x equal to 0. Putting both into the calculator, we get that \(x=1.5\) or \(x=-0.3\).

b) We can easily solve this equation using factoring, which turns a quadratic into two factors, and finds the solutions by setting both to 0. This will only work if the quadratic is equal to 0.

\(x^2+3x-40=0\)

Now, we have to find two numbers that add to 3 and multiply to -40. The numbers 8 and -5 work, as 8-5=3 and 8*-5 is -40.

we can now make our factors x+8 and x-5

\((x+8)(x-5)=0\)

If two numbers, say A and B, are being multiplied and equal 0, then either A is 0, or b is 0, or both. Similarly, if x+8 and x-5 are being multiplied and equal 0, either x+8 = 0, or x-5=0.

\(x+8=0\\x=-8\)    \(x-5=0\\x=5\)

This makes our solutions x=-8 and x=5.

If you are not familiar with factoring or the process I have went through above, I highly recommend learning about it.

Answer:

look at the picture .................

Reason:

The central angle is the same measure as the arc it subtends.

(C) Regression analysis is the statistical method commonly used to estimate the level and trend in a time series by modeling the relationship between the data and independent variables.

Regression analysis is the statistical method used to estimate the level and trend in a time series. Time series data represents observations taken at different points in time and is commonly used to analyze trends and patterns over time.

Regression analysis allows us to model the relationship between a dependent variable (in this case, the time series data) and one or more independent variables (such as time or other relevant factors). By using regression analysis, we can identify the underlying trend in the time series and estimate its level.

The regression model captures the relationship between the dependent variable (the time series) and the independent variable(s) by fitting a line or curve that best represents the data. This line or curve helps to identify the overall trend and level of the time series.

While moving average, simulation method, covariance analysis, and correlation analysis are useful techniques in analyzing time series data, they are not specifically designed to estimate the level and trend in a time series. Therefore, (C) regression analysis is the most appropriate method for estimating the level and trend in a time series.

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The standard error of the sampling distribution of the sample mean is a measure of the variability of sample means that would be obtained from repeated sampling of the same population. It is calculated as the standard deviation of the sampling distribution of the sample mean.

In other words, the standard error reflects how much the sample means from different samples would be expected to vary from the true population mean. As the sample size increases, the standard error decreases because the sample means become more representative of the population mean. Conversely, as the sample size decreases, the standard error increases because the sample means become less representative of the population mean.

The formula for calculating the standard error of the sample mean is:

Standard Error = Standard Deviation / Square root of Sample Size

where the standard deviation is the variability of the population and the sample size is the number of observations in the sample.

The standard error is an important concept in statistical inference because it is used to calculate confidence intervals and hypothesis tests for population means based on sample means. A larger standard error indicates that there is more uncertainty in the estimate of the population mean, and a smaller standard error indicates that the estimate is more precise. In conclusion, the standard error of the sampling distribution of the sample mean is a measure of the variability of sample means that would be obtained from repeated sampling of the same population. It is a key concept in statistical inference and is used to calculate confidence intervals and hypothesis tests for population means based on sample means.

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Beta decay is a type of radioactive decay that occurs in certain atomic nuclei. It involves the transformation of a neutron or proton within the nucleus into the other.

In the case of Lanthanum-144 (La-144), a neutron undergoes beta decay to convert into a proton, resulting in the formation of Cerium-144 (Ce-144).

The equation for the beta decay of La-144 into Ce-144 is as follows:

La-144 → Ce-144 + β¯

In this equation, the La-144 nucleus decays into the Ce-144 nucleus. To conserve charge, a beta particle (β¯) is emitted. The beta particle can be either an electron (β-) or a positron (β+), depending on the specific type of beta decay occurring in the nuclide.

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Answer:

decrease 1°C

Step-by-step explanation:

Solution:

\(-4-(-3)\\ =-4+3\\ =-1\)

decrease 1°c

Answer:

the answer is a positive 1 degrees

Step-by-step explanation:

Answer:

\(12\) cm

Step-by-step explanation:

If Kelsey knit a total of \(6\) cm of scarf over \(2\) nights, then we know that she can knit \(\frac{6}{2}=3\) cm each night. Therefore, after \(4\) nights of knitting, Kelsey would have knit a total of \(3*4=12\) cm of scarf in total. Hope this helps!

The Difference in the amounts that Tsion and Ibrahim paid for their watches is £3.85.

To find the difference in the amounts that Tsion and Ibrahim paid for their watches, we need to convert the prices to the same currency. We can use the exchange rates given to convert both prices to pounds.

1 Singapore dollar = £0.58

72 Singapore dollars = 72 x £0.58 = £41.76

1 Hong Kong dollar = £0.09

399 Hong Kong dollars = 399 x £0.095 = £37.91

Therefore, Tsion paid £41.76 for the watch and Ibrahim paid £37.91 for the same model of watch.

To find the difference in the amounts paid, we can subtract the smaller amount from the larger amount:

£41.76 - £37.91 = £3.85

Therefore, the difference in the amounts that Tsion and Ibrahim paid for their watches is £3.85.

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if ​Y=1​+X+u​, where X​, Y​, and ​u=v+X are random​ variables, v is independent of X​; ​E(v​)=0, ​Var(v​)=1​, ​E(X​)=1, and ​Var(X​)=2, then Var(Y|X​) = Var ( 1 + X + u | X)  = 0 + 4*2 + 1 = 8 + 1 = 9

if ​Y=1​+X+u​, where X​, Y​, and ​u=v+X are random​ variables, v is independent of X​; ​E(v​)=0, ​Var(v​)=1​, ​E(X​)=1, and ​Var(X​)=2, the variance of the following cases are calculated as:

Var(u|X​=1) = Var( v + X | X = 1) = Var( v + 1 )    

                = Var(v) + Var(1)                            

                 = 1 + 0 = 1

Var(Y|X​=1) = Var( 1 + X + u | X = 1 )

                = Var (1 + X + v + X|X=1)

                = Var(1 + 1 + v + 1)                      

                = Var(3) + Var(v)                      

                = 0 + 1 = 1

​Var(u|X​) = Var ( v + X | X)

            = Var ( v + X)

            = Var(v) + Var(X)

            =  1 + 2  = 3

Var(Y|X​) = Var ( 1 + X + u | X)

            = Var ( 1 + X + v + X | X)

            = Var ( 1 + 2X + v)

            = Var(1) + Var(2X) + Var(v)

              = 0 + 4*2 + 1 = 8 + 1 = 9

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Answer:

Percentage Calculator: What is the percentage increase/decrease from 8. to 9.5? = 18.75.

Answer:

Step-by-step explanation:

Given the function

Substitute x with a + 1

The value of f(0) in the function is 0.

To find f(0), in the given function we can use the given equation:

ff(x) = f(x+1)

Substituting x = 0, we get:

ff(0) = f(1)

Since we are given that f(1) = 0, we have:

ff(0) = 0

Now we can substitute x = -1 into the original equation:

ff(x) = f(x+1)

to get:

ff(-1) = f(0)

Since we know that ff(x) = 0 (from ff(0) = 0), we have:

f(0) = ff(-1) = 0

Therefore, we have found that f(0) = 0.

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The particular solution that satisfies the initial conditions is:

y(x) =\(3e^(-x)cos(2x) + 8e^(-x)sin(2x)\)

To solve the homogeneous second-order initial value problem y" + 2y' + 5y = 0, with initial conditions y(0) = 3 and y'(0) = 5, we can assume a solution of the form y(x) = e^(rx), where r is a constant to be determined.

Plugging this assumed solution into the differential equation, we get:

y" + 2y' + 5y = 0

\((e^(rx))" + 2(e^(rx))' + 5e^(rx) = 0\)

Differentiating, we have:

\(r^2e^(rx) + 2re^(rx) + 5e^(rx) = 0\)

Factoring out e^(rx), we get:

\((e^(rx))(r^2 + 2r + 5) = 0\)

For this equation to hold for all x, the factor\((r^2 + 2r + 5)\)must be zero:

\(r^2 + 2r + 5 = 0\)

Using the quadratic formula, we find:

r =\((-2 ± sqrt(2^2 - 4(1)(5))) / (2(1))\)

r = (-2 ± sqrt(-16)) / 2

r = (-2 ± 4i) / 2

r = -1 ± 2i

Therefore, the general solution of the homogeneous differential equation is:

y(x) =\(C1e^((-1+2i)x) + C2e^((-1-2i)x)\)

Using Euler's formula e^(ix) = cos(x) + i*sin(x), we can rewrite the solution as:

y(x) = \(C1e^(-x)cos(2x) + C2e^(-x)sin(2x)\)

To find the particular solution that satisfies the initial conditions, we substitute the values of y(0) = 3 and y'(0) = 5 into the general solution and solve for C1 and C2.

y(0) = \(C1e^(-0)cos(20) + C2e^(-0)sin(20) = C1\)

C1 = 3

y'(x) = \(-C1e^(-x)cos(2x) + C1e^(-x)(-sin(2x)) + C2e^(-x)cos(2x) + C2e^(-x)sin(2x)\)

y'(0) = -\(C1e^(-0)cos(20) + C1e^(-0)(-sin(20)) + C2e^(-0)cos(20) + C2e^(-0)sin(20) = -C1 + C2\)

-3 + C2 = 5

C2 = 8

Therefore, the particular solution that satisfies the initial conditions is:

y(x) =\(3e^(-x)cos(2x) + 8e^(-x)sin(2x)\)

b) To solve the homogeneous second-order initial value problem y" + 6y' + 9y = 0, with initial conditions y(0) = 2 and y'(0) = 3, we can follow a similar procedure.

Assuming a solution of the form y(x) = e^(rx), we plug it into the differential equation:

\((e^(rx))" + 6(e^(rx))' + 9e^(rx) = 0\)

Simplifying, we get:

\(r^2e^(rx) + 6re^(rx) + 9e^(rx) = 0\)

Factoring out e^(rx), we have:

\((e^(rx))(r^2 + 6r + 9) = 0\)

For this equation to hold for all x, the factor (r^2 + 6r + 9) must be zero:

(r + 3)^2 = 0

This gives us a repeated root at r = -3.

The general solution of the homogeneous differential equation is:

y(x) =\((C1 + C2x)e^(-3x)\)

To find the particular solution that satisfies the initial conditions, we substitute the values of y(0) = 2 and y'(0) = 3 into the general solution and solve for C1 and C2.

C1 = 2

\(y'(x) = (C2 - 3C2x)e^(-3x)\\y'(0) = (C2 - 3C2(0))e^(-3*0) = C2\)

C2 = 3

Therefore, the particular solution that satisfies the initial conditions is:

y(x) = \((2 + 3x)e^(-3x)\)

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The relationship between the points on the line and solutions to the linear equation is, the equation has a solution at each point along the line.

In the given question, we have to find the relationship between the points on the line and solutions to the linear equation.

The equation has a solution at each point along the line. This simply means that it is easy to tell whether an ordered pair is a solution to an equation. The ordered pair is a solution to the equation if it lies on the line drawn by the linear equation.

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The forecasts using a three-period moving average for the number of cans of soft drinks sold each week are 278.33, 254, 285.67, 300.67, 312, 293.67, 281.67, and 282.67.

Using a three-period moving average, we can calculate the forecasts for the number of cans of soft drinks sold each week based on the given data: 338, 219, 278, 265, 314, 323, 299, 259, 287, 302.

To calculate the forecasts, we take the average of the sales for the current week and the two previous weeks. The moving average is then shifted forward one period for each subsequent forecast.

The calculations are as follows:

Forecast 1: (338 + 219 + 278) / 3 = 278.33

Forecast 2: (219 + 278 + 265) / 3 = 254

Forecast 3: (278 + 265 + 314) / 3 = 285.67

Forecast 4: (265 + 314 + 323) / 3 = 300.67

Forecast 5: (314 + 323 + 299) / 3 = 312

Forecast 6: (323 + 299 + 259) / 3 = 293.67

Forecast 7: (299 + 259 + 287) / 3 = 281.67

Forecast 8: (259 + 287 + 302) / 3 = 282.67

In summary, the forecasts using a three-period moving average for the number of cans of soft drinks sold each week are 278.33, 254, 285.67, 300.67, 312, 293.67, 281.67, and 282.67.

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Answer:

54

Step-by-step explanation:

Answer:

X >= 6.7

Step-by-step explanation:

So first of all, what you need is write out the equation from the given prompt

x + 2.7 >= 9.4
Next, what you really want to do is

Subtract 2.7 both side
x >= 9.4 - 2.7
x >= 6.7

Answer:

x = -2, y = 3

Step-by-step explanation:

Given equations are,

4x + 5y = 7 ---------(1)

3x - 2y = -12 ----------(2)

Multiply equation (1) by 3

12x + 15y = 21 ------(3)

Multiply equation (2) by (-4)

-12x + 8y = 48 --------(4)

Now add equations (3) and (4),

(12x + 15y) + (-12x + 8y) = 21 + 48

(12x - 12x) + (15y + 8y) = 69

23y = 69

y = 3

From equation (2),

3x - 2(3) = -12

3x - 6 = -12

3x = 6 - 12

x = -2

Therefore, x = -2 and y = 3 will be the answer.

Answer:

What is the solution to this system of equations?

\(4x +5y = 7\)

\(3x-2y=-12\)

The solution is ✔ \((-2,3)\) .

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ S(\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\qquad V(\stackrel{x_2}{-4}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ SV=\sqrt{[-4 - 6]^2 + [3 - (-2)]^2}\implies SV=\sqrt{(-10)^2+(3+2)^2} \\\\\\ SV=\sqrt{125}\implies SV\approx 11.18\implies \underset{\textit{rounded up}}{SV\approx 11.2}\)

Answer:

11.2 units is the answer

The values for h and k used to write the function f(x) = x² + 12x + 6 in vertex form are h = -6 and k = -9. So the option D is correct.

A vertical parabola's equation in vertex form is equal to

f(x) = a(x - h)² + k

where, (h, k) is the vertex and a is a coefficient.

We have the function:

f(x) = x² + 12x + 6

Now illustrate the function in the form of vertical parabola's equation.

Subtract 6 on both side, we get

f(x) - 6 = x² + 12x

To make x² + 12x as a perfect square we add 36 on both side

f(x) - 6 + 36 = x² + 12x + 36

Now, we can write it as:

f(x) + 30 = (x + 6)²

Subtract 30 on both side, we get

f(x) = (x + 6)² - 30

Now comparing with the equation of vertical parabola

h = -6, k = -30

So the option D is correct.

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The complete question is:

Which values for h and k are used to write the function f(x)=x² + 12x + 6 in vertex form?

A. h = 6, k = 36

B. h = −6, k = −36

C. h = 6, k = 30

D h = −6, k = −30

Answer:

Total number of students = 10

Probability that all 4 in the group are boys =

\( \frac{4}{10} \\ = 0.4\)

Answer:

1st, 3rd

and 4th - "4th" from different answer :)

Step-by-step explanation:

Have a good day :)

Answer:

1,3 and 4

Step-by-step explanation:

Answer:

well,

Step-by-step explanation:

as you see.....uhhh.....hmmmm.....if you first a _________________________________

Answer:

A. y=x and y=x+2

Step-by-step explanation:

A.

y=x and y=x+2

The equations both match the slope and intercept of the graphed equations.

Can I have the pancakes instead of the donkey?