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3 years ago

The x coordinate of the solution to the system of equations y=x+4 and 3y=-2x+2

Mathematics

2 answers:

djyliett [7]3 years ago

6 0

Answer:

The x coordinate of the solution is -2

Step-by-step explanation:

* To find the x-coordinate of the solution to the system of the

equations y = x + 4 and 3y = -2x + 2 solve the equations by the

substitution method

- In the substitution method we substitute one of the two variables

by the other to make an equation of one variable

∵ y = x + 4 ⇒ (1)

∵ 3y = -2x + 2 ⇒ (2)

- Substitute the value of y in equation (2) by the value of y in equation (1)

∵ The value y = 4 + x in the equation (1)

- Put this value of y in the equation (2)

∴ 3(x + 4) = -2x + 2 ⇒ open the bracket

∴ 3x + 12 = -2x + 2 ⇒ subtract 12 from both sides

∴ 3x = -2x - 10 ⇒ add 2x to both sides

∴ 5x = -10 ⇒ divide both sides by 5

∴ x = -2

* The x coordinate of the solution is -2

Vera_Pavlovna [14]3 years ago

3 0

<h2>Hello!</h2>

The answer is:

The x-coordinate of the solution to the system of equations is:

$x=-2$

We can solve the problem writing both equations as a system of equations.

So, we are given the equations:

$\left \{ {{y=x+4} \atop {3y=-2x+2}} \right.$

Then, solving by reduction we have:

Multiplying the first equation by 2 in order to reduce the variable "x", we have:

$\left \{ {{2y=2x+2*4} \atop {3y=-2x+2}} \right.$

$5y=2x-2x+8+2\\\\5y=8+2\\\\y=\frac{10}{5}=2$

Now, substituting "y" into the first equation, to isolate "x" we have:

$y=x+4\\\\2=x+4\\\\x=2-4=-2$

Hence we have that the x-coordinate of the solution to the system of equations is

$x=-2$

Have a nice day!

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kiruha [24]

Answer:

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Part B) $\$55,250$

Step-by-step explanation:

Part A) Express the value of the bulldozer, V, as a function of how many years old it is, t.

Let

V ----> the value of the bulldozer (dependent variable or output value)

t ----> the number of years (independent variable or input value)

we know that

The linear function in slope intercept form is equal to

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we have the ordered pairs

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The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{15,000-101,250}{15-0}$

$m=-\$5,750\ per\ year$ ----> is negative because is a decreasing function

The value of b is the initial value

$b=\$101,250$

substitute

$V(t)=-5,750t+101,250$

Part B) The value of the bulldozer after 8 years is

For t=8 years

substitute the value of t in the linear equation

$V(t)=-5,750(8)+101,250=\$55,250$

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2 years ago

Two numbers have a sum of 1,212 and a difference of 518. What are the two numbers?

guapka [62]

Answer:

The two numbers are

518

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Step-by-step explanation:

As per requirements the two equations will be

X+Y=1212

X-Y=518

When we subtract these equations we get

X=1212-518

X=694

Now put the X value and find the Y value in any equation

X+Y= 1212

Y=1212-X

Where X = 694

Y=1212-694

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3 years ago

Dina planted a six-foot tree in her backyard which she expects to grow at the rate of 4 feet per year. Find the equation of the

Scrat [10]

Answer:

y = 6 + 4x

After 4 years, the tree would be 22 ft tall.

Step-by-step explanation:

Hi there!

Let x = the number of years that pass

Let y = the height of the tree (ft)

We're given that the 6-foot tree grows at a rate of 4 ft per year. This means that the height of the tree will be equal to 6 ft, the original height, plus another 4 ft every year that passes.

Height of tree = 6 feet + 4 feet × number of years that pass

y = 6 + 4x

To solve for how tall the tree would be 4 years after Dina plants it, replace x with 4, since 4 years have passed:

y = 6 + 4(4)

y = 6 + 16

y = 22

Therefore, the tree would be 22 ft tall.

I hope this helps!

8 0

2 years ago

Sarah claims that the thickness of the spearmint gum she produces is 7.5 one-hundredths of an inch. A quality control specialist

satela [25.4K]

Answer:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

$p_v =2*P(t_{(9)}>1.539)=0.158$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

Step-by-step explanation:

Data given and notation

Data: 7.65, 7.60, 7.65, 7.7, 7.55, 7.55, 7.4, 7.4, 7.5, 7.5

We can begin calculating the sample mean given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And the sample deviation given by:

$s=\sart{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And we got:

$\bar X=7.55$ represent the sample mean

$s=0.103$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =7.5$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 7.5 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 7.5$

Alternative hypothesis: $\mu \neq 7.5$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=10-1=9$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(9)}>1.539)=0.158$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

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