Solve the system of equations using Substitution


8x + 4y = 12
y = -2x + 3

Answer:

The converse is true

Step-by-step explanation:

The converse of a statement is obtained by interchanging the conclusion for the hypothesis

The given statement is presented as follows;

If a pair of angles is linear, then the angles are supplementary

Therefore, the converse statement is;

If a pair of angles are supplementary, then the angles are a linear pair

A linear pair of angles angles are the adjacent angles formed by the intersection of two lines

Supplementary angles are two angles that sum up to 180° such that the angles sum is that of the angles forming a straight line

Therefore, the converse statement, 'If a pair of angles are supplementary, then the angles are a linear pair', is true

Answer:

0.322

Step-by-step explanation:

0.350 - 0.028

The answer would be 0.322

Hope this helps

Answer:

The 3rd one is correct

(7.5 + 3) x 6 - 4)

Answer:

NOT A FUNCTION

Step-by-step explanation:

hope this helps

\(6x + y = 10 \\ y = 10 - 6x \\ y = 10 - 6x,x∈ℝ\)

Answer:

y = 10 - 6x

Step-by-step explanation:

6x + y = 10

=> y = 10 - 6x

The eigenvalues of matrix A are λ1 = 2 and λ2 = 4, and bases for the corresponding eigenspaces are {[1, 1]} and {[1, -1]}, respectively.

To find the eigenvalues of matrix A, we first need to solve for the characteristic equation:

det(A - λI) = 0

where I is the identity matrix.

So, we have:

det( [3-λ 1; -1 3-λ] ) = 0

Expanding this determinant, we get:

(3-λ)(3-λ) - (-1)(1) = 0

Simplifying and factoring, we get:

(λ - 2)(λ - 4) = 0

So, the eigenvalues of matrix A are λ1 = 2 and λ2 = 4.

Next, we need to find the eigenvectors corresponding to each eigenvalue.

For λ1 = 2, we solve the system of linear equations:

(A - 2I)x = 0

where I is the 2x2 identity matrix.

So, we have:

[1 1; -1 1]x = 0

Simplifying, we get:

x1 + x2 = 0

-x1 + x2 = 0

Solving this system, we get:

x1 = x2

So, any vector of the form [a, a] is an eigenvector corresponding to λ1 = 2. A basis for the eigenspace corresponding to λ1 is {[1, 1]}.

For λ2 = 4, we solve the system of linear equations:

(A - 4I)x = 0

where I is the 2x2 identity matrix.

So, we have:

[-1 1; -1 -1]x = 0

Simplifying, we get:

-x1 + x2 = 0

-x1 - x2 = 0

Solving this system, we get:

x1 = -x2

So, any vector of the form [a, -a] is an eigenvector corresponding to λ2 = 4. A basis for the eigenspace corresponding to λ2 is {[1, -1]}.

Therefore, the eigenvalues of matrix A are λ1 = 2 and λ2 = 4, and bases for the corresponding eigenspaces are {[1, 1]} and {[1, -1]}, respectively.

Learn more about eigenvalues here

https://brainly.com/question/15586347

#SPJ11

Answer:

The statements about arcs and angles that are true in the figure are;

1) ∠EFD ≅ ∠EGD

2) \(\overline{ED}\cong \overline{FD}\)

3) mFD = 120°

Step-by-step explanation:

1) ∠ECD + ∠CEG + ∠CDG + ∠GDE = 360° (Sum of interior angle of a quadrilateral)

∠CEG = ∠CDG = 90° (Given)

∠GDE = 60° (Given)

∴ ∠ECD = 360° - (∠CEG + ∠CDG + ∠GDE)

∠ECD = 360° - (90° + 90° + 60°) = 120°

∠ECD = 2 × ∠EFD (Angle subtended is twice the angle subtended at the circumference)

120° = 2 × ∠EFD

∠EFD = 120°/2 = 60°

∠EFD ≅ ∠EGD

∠ECD = 120°

∠EGD = 60°

∴∠EGD ≠ ∠ECD

2) Given that arc mEF ≅ arc mFD

Therefore, ΔECF and ΔDCF are isosceles triangles having two sides (radii EC and CF in ΔECF and radii EF and CD in ΔDCF

∠ECF = mEF = mFD = ∠DCF (Given)

∴ ΔECF ≅ ΔDCF (Side Angle Side, SAS, rule of congruency)

\(\\ \overline{EF}\cong \overline{FD}\) (Corresponding Parts of Congruent Triangles are Congruent, CPCTC)

∠FED ≅ ∠FDE (base angles of isosceles triangle)

∠FED + ∠FDE + ∠EFD = 180° (sum of interior angles of a triangle)

∠FED + ∠FDE = 180° - ∠EFD = 180° - 60° = 120°

∠FED + ∠FDE = 120° = ∠FED + ∠FED (substitution)

2 × ∠FED  = 120°

∠FED = 120°/2 = 60° = ∠FDE

∴ ∠FED = ∠FDE = ∠EFD =  60°

ΔEFD  is an equilateral triangle as all interior angles are equal

\(\\ \overline{EF}\cong \overline{FD}\cong \overline{ED}\) (definition of equilateral triangle)

\(\overline{ED}\cong \overline{FD}\)

3) Having that ∠EFD = 60° and ∠CFE = ∠CFD (CPCTC)

Where, ∠EFD = ∠CFE + ∠CFD (Angle addition)

60° = ∠CFE + ∠CFD = ∠CFE + ∠CFE (substitution)

60° = 2 × ∠CFE

∠CFE =60°/2 = 30° = ∠CFD

\(\overline{CF}\cong \overline{CD}\) (radii of the same circle)

ΔFCD is an isosceles triangle (definition)

∠CFD ≅ ∠CDF (base angles of isosceles ΔFCD)

∠CFD + ∠CDF + ∠DCF = 180°

∠DCF = 180° - (∠CFD + ∠CDF) = 180° - (30° + 30°) = 120°

mFD = ∠DCF (definition)

mFD = 120°.

Answer:

1,3,5

Step-by-step explanation:

right on edge 2022

The distance that you run around the track in gym class is considered continuous data.

The variable is given as:

Distance

The distance travelled can take any value between 0 and the length of the track.

Take for instance;

The distance travelled can be 1km and it can also be 1.67 km

This means that the distance is continuous

Hence, the statement that completes the blank is (c) continuous

Read more about variables at:

https://brainly.com/question/24315217

#SPJ1

Answer:

TW = 31

Step-by-step explanation:

the midsegment TW is half the length of the side UV , that is

TW = \(\frac{1}{2}\) × 62 = 31

Answer:

200 minutes

Step-by-step explanation:

In order to find the range, you have to subtract the greatest number to the lowest number. In this case, 400 is the smallest number, and 600 is the greatest number. 600-400 is 200 minutes.

Answer:

$6.48

Step-by-step explanation:

It would be $6.48 because 1.60 times 4 1/2 is 7.2 and if you do 10% of 7.2 you get B.

Answer:

The formula for solving surface area is LxWxH (LengthxWidthxHeight)

And the formula for solving area is LxW (LenghtxWidth)

Step-by-step explanation:

I hope this helps. I didnt really see any pictures for this.

Answer: 1. 60 square centimeters and the volume was 24 cm3

2. Yes, because if you have length, width and height, that's really all the information you need to find out the area, volume, perimeter, surface area, ect!

Step-by-step explanation: Hope this helps! :)

(I had the same question btw)

After 0.5 seconds, the car's speed would be 45 ft/s forward. This is because when the car slams on the brakes, it decelerates at a rate of -30 ft/s^2. Therefore, after 0.5 seconds, the car would have slowed down by (0.5 seconds) x (-30 ft/s^2) = -15 ft/s.

Starting from the initial speed of +60 ft/s, this means the car's new speed would be 60 ft/s - 15 ft/s = 45 ft/s forward.

After slamming the brakes, the car decelerates at a rate of -30 ft/s. To find the speed of the car after 0.5 seconds, you can use the formula: final speed = initial speed + (acceleration × time). In this case:

Final speed = 60 ft/s + (-30 ft/s × 0.5 s)

Final speed = 60 ft/s - 15 ft/s

Final speed = 45 ft/s

After 0.5 seconds, the car is going 45 ft/s forward.

Visit here to learn more about decelerates  brainly.com/question/13802847

#SPJ11

The probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

If the average number of units rented per week is 2.3 and the distribution is Poisson, then the parameter lambda is also equal to 2.3.

The probability of renting exactly three apartments in a week is given by the Poisson probability function:

\(P(X = 3) = (e^(-lambda) * lambda^x) / x!\)

Substituting the values, we get:

\(P(X = 3) = (e^(-2.3) * 2.3^3) / 3!\)

P(X = 3) = (0.09963 * 12.167) / 6

P(X = 3) = 0.2018

Therefore, the probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

To know more about probability refer to-

https://brainly.com/question/30034780

#SPJ11

Answer:

4x+12+mx+3m

You use the FOIL method.

Answer:

(4+m)(x+3)

Step-by-step explanation:

x+3 is a common factor, so you can convert this to put the other 2 parts in a bracket. This results in (4+m)(x+3).

An example of how this works is if you made m=1 and x=2. This would make the original expression 4(2+3)+1(2+3), or 4×5+1×5, which is 5×5 or 25. (1+4)(2+3) also equals to 5×5.

**You may want to revise factorising algebraic equations. I'm always happy to help!

Answer

Explanation:

Volume of a cylinder is expressed as;

If the radius is doubled and the height is unchanged, then;

r2 = 2r

h2 = h

Get the volume of the new cylinder

Karen that has a piece of fabric that is 1 187/240 yards long needs to trim 227/240 yards

Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.

To solve this problem we must perform the corresponding algebraic operations with mixed fraction.

Data of the problem:

A mixed operation is solved as follows:

For the denominator: the same denominator is placed.

For the numerator:

The value of the denominator is multiplied by the integer component.

The result is added to the numerator of the fraction.

We transform the mixed fractions into improper fractions and we have:

1 187/240 =

[(240*1) + 187)] /240=

[240+ 187] /240=

427/240

Calculating how many yards should she trim:

Yards to trim: 427/240 - 5/6

Yards to trim: (427 - 200) / 240

Yards to trim: 227/240

Learn more about fraction at: brainly.com/question/11562149

#SPJ4

After considering the given data we conclude that the answer for the sub questions are
a) Jeff consumes 33.33 units of good x.
b) the compensating variation is:
\(CV=W'-W=2(50)-200=-100CV\)
c) The income effect is negative, indicating that Jeff will consume less of good x due to the decrease in purchasing power caused by the price increase.

a. To find Jeff's demand function for good x, we can use the following equation:
\(\frac{\partial U}{\partial x}=\frac{1}{x}=\frac{p_x}{p_y}=\frac{1}{2}\)
Solving for x, we get:
\(x=\frac{1}{2}y\)
Substituting the given values, we get:
\(x=\frac{1}{2}(200/3)=33.33\)
Therefore, Jeff consumes 33.33 units of good x.
b. If Px increases to 2, the new demand function for good x is:
\(x'=\frac{1}{2}y'\)where y'  is the amount of good y consumed at the new prices and income. To find the compensating variation, we need to find the amount of income Jeff would need at the original prices to achieve the same level of utility as he does at the new prices. We can use the following equation:
\(W'=W+CV\) where W is the original income, W' is the new income, and CV is the compensating variation.
Substituting the given values, we get:
\(8.51=\ln(33.33)+\ln(66.67)8.51=ln(33.33)+ln(66.67)\)
\(y'=\frac{W'}{2}\)
\(x'=\frac{1}{2}y'\) Solving for y', we get:
y'=100
Solving for x', we get:
x'=50
Therefore, the compensating variation is:
\(CV=W'-W=2(50)-200=-100CV\)
c. To calculate the total effect, substitution effect, and income effect of the price change, we can use the following equations:
\(TE=\frac{\Delta U}{U_0}\)
\(SE=\frac{\Delta x_s}{x_0}\)
\(IE=\frac{\Delta x_i}{x_0}\)where \(\Delta U\)is the change in utility, \(U_0\) is the initial utility,\(\Delta x_s\) is the change in consumption due to the substitution effect, \(x_0\) is the initial consumption, and \(\Delta x_i\) is the change in consumption due to the income effect.
The change in consumption due to the price change can be calculated as:
as:
\(\Delta x=x'-x_0=\frac{1}{2}y'-\frac{1}{2}y_0\)
where \(y_0=2x_0\) and \(y'=2x'\)
Substituting the given values, we get:
\(\Delta x=x'-x_0=50-33.33=16.67\)
The substitution effect can be calculated as:
\(SE=\frac{\Delta x_s}{x_0}=\frac{x_s'-x_0}{x_0}=\frac{1}{2}\frac{y_0-y_s'}{x_0}=\frac{1}{2}\frac{p_x}{p_y}\frac{y_0}{x_0}\)
Substituting the given values, we get:
\(SE=\frac{1}{2}\frac{1}{2}\frac{2x_0}{4x_0}=\frac{1}{4}\)
The income effect can be calculated as:
\(IE=\frac{\Delta x_i}{x_0}=\frac{\Delta W}{W_0}=\frac{CV}{W_0}\)
Substituting the given values, we get:
\(IE=\frac{-100}{200}=-0.5\)
The total effect can be calculated as:
\(TE=SE+IE=\frac{1}{4}-0.5=-0.25\)
Therefore, the total effect of the price change is negative, indicating that Jeff will consume less of good x as a result of the price increase. The substitution effect is positive, indicating that Jeff will consume more of good x due to the relative price change. The income effect is negative, indicating that Jeff will consume less of good x due to the decrease in purchasing power caused by the price increase.
To learn more about income effect
https://brainly.com/question/15300267
#SPJ4

The area of the parallelogram is approximately 210 square units.

To find the area of a parallelogram, we multiply the length of the base by the length of the corresponding altitude. In this case, the length of the base (segment AD) is 14.5 units, and the length of the altitude (segment BE) is also 14.5 units.  By applying the formula for the area of a parallelogram (Area = base × altitude), we get:

Area = 14.5 units × 14.5 units = 210.25 square units

Rounding to the nearest unit, the area of the parallelogram is approximately 210 square units.

learn more about parallelograms here:

https://brainly.com/question/28854514

#SPJ11

The statement that best describes "willing suspension of disbelief" is: A dynamic in which the audience agrees to accept the fictional world of the play on an imaginative level while knowing it to be untrue.

The concept of "willing suspension of disbelief" is an essential element in experiencing and appreciating works of fiction, particularly in theater, literature, and film. It refers to the voluntary act of temporarily setting aside one's skepticism or disbelief in order to engage with the fictional narrative or performance. It involves consciously accepting the imaginative world presented by the creator, even though it may contain unrealistic or fantastical elements. By willingly suspending disbelief, the audience allows themselves to become emotionally invested in the story and characters, making the experience more enjoyable and meaningful. This dynamic acknowledges the inherent fictional nature of the work while acknowledging that the audience is aware of its fictional status. It creates a mutual understanding between the audience and the creators, enabling the audience to fully immerse themselves in the narrative and connect with the intended emotions and themes of the work.

Learn more about fictional world here:

https://brainly.com/question/2516102

#SPJ11

The test statistic for this sample is z = (0.254 - 0.203) / (p_hat * (1 - p_hat) * (1/n1 + 1/n2))

Based on the given information, we can set up the hypotheses as follows:

Null hypothesis: p1 - p2 = 0
Alternative hypothesis: p1 - p2 > 0

where p1 represents the proportion of successes in the first population and p2 represents the proportion of successes in the second population.

Since the sample sizes are large (n1 and n2 are not given, but we can assume they are large enough for the normal approximation to hold), we can use the normal distribution to approximate the sampling distribution of the difference in sample proportions.

The test statistic for this sample can be calculated as follows:

z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))

where p_hat = (x1 + x2) / (n1 + n2), x1 and x2 are the number of successes in the two samples respectively.

Plugging in the given values, we get:

p_hat = (0.254n1 + 0.203n2) / (n1 + n2)
z = (0.254 - 0.203) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))

Since the significance level is not given, we cannot determine the critical value for the test. However, we can use the test statistic to calculate the p-value for the test, which is the probability of observing a difference in sample proportions as extreme as the one we observed (or more extreme) under the null hypothesis.

Once we have the p-value, we can compare it to the significance level to make a decision about whether to reject or fail to reject the null hypothesis.

Note: It is important to mention that using the normal approximation without the continuity correction may not always be accurate, especially when the sample sizes are small or the proportion of successes is close to 0 or 1. In such cases, it is recommended to use other methods (such as exact tests or simulation) that do not rely on the normal approximation.

More on test-statistic: https://brainly.com/question/16244531

#SPJ11

The variables for the tree diagram involving the probabilities in this problem are given as follows:

A probability is calculated as the number of desired outcomes divided by the number of desired outcomes.

For nodes a and b, they are relative to the first ball, hence:

If the first ball is green, 6 out of the remaining 9 balls are green and the probabilities of the second ball are given by nodes c and d, as follows:

If the first ball is not green, 7 out of the remaining 9 balls are green and the probabilities of the second ball are given by nodes e and f, as follows:

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Let Xk be independent and normally distributed with common mean 22 and standard deviation 11 (so their common variance is 1.1.). The value of p(-[infinity] ≤ ∑k=181 Xk ≤ 172.89) ≈ 0.0265.

The common variance of independent and normally distributed random variables with a common mean can be computed with the formula

σ² = Var[Xk]

= 1.1.

This can be solved by finding the standard deviation, which is equal to the square root of the variance as

σ = sqrt(1.1)

= 1.0488.

The sum of the independent and identically distributed normal random variables can be expressed as a normal random variable with a mean equal to the sum of the individual means and a variance equal to the sum of the individual variances.

Thus, we can express this random variable as ∑k=181 Xk ~ N(22 * 181, 1.1 * 181).

To solve the given problem, we need to compute the probability that the sum of the random variables lies between -infinity and 172.89.

Since the sum of normal random variables follows the normal distribution, we can standardize the sum by subtracting the mean and dividing by the standard deviation.

Let Z be the standardized random variable.

Then Z = (X - μ)/σ

Z = (∑k=181 Xk - μ)/σ, where μ = 22 * 181 and σ = sqrt(1.1 * 181).

We need to compute P(-infinity ≤ Z ≤ (172.89 - μ)/σ) = P(Z ≤ (172.89 - μ)/σ) .

Since the standard normal distribution is symmetric about zero.

This can be solved using standard normal tables or a calculator to obtain P(Z ≤ -1.9309) ≈ 0.0265 (rounded to four decimal places).

Therefore, p(-[infinity] ≤ ∑k=181 Xk ≤ 172.89) ≈ 0.0265 (rounded to four decimal places).

To know more about standard deviation, visit:

https://brainly.com/question/29115611

#SPJ11

Answer:

its D/ 56.25

Step-by-step explanation:

because the other numbers are too small

The regression equation to predict the number of cans sold on a day that is 90°F will be 871.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

A convenience store manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in the table, shown above. Use technology to find the equation of the least-squares regression line.

Then the regression line will be passing through (55, 340) and (84, 780). Then we have

y - 340 = 15.17(x - 55)

Then the regression equation to predict the number of cans sold on a day that is 90°F will be

y - 340 = 15.17 (90 - 55)

         y = 871

More about the linear system link is given below.

https://brainly.com/question/20379472

#SPJ1

The number of people who owned both a cat and a dog is 73.

We need to calculate how many people owned both a cat and a dog. The number of people who owned a dog and/or a cat is:

Total = dog-only + cat-only + dog-and-cat + neither

Total = 145 + 60 + dog-and-cat + 71

Total = 276 + dog-and-cat

So, the number of people who owned both a cat and a dog (dog-and-cat) is:

dog-and-cat = Total - 276

dog-and-cat = 349 - 276

dog-and-cat = 73

However, this number is the total of those who own both. The answer to the question asks how many owned both a cat and a dog.

So:

dog-and-cat = dog-only + cat-only + dog-and-cat

dog-and-cat = 145 + 60 + dog-and-cat

73 = 145 + 60 + dog-and-cat

dog-and-cat = 73 - 205

dog-and-cat = -132

Hence, 132 people neither own a dog nor a cat. So, the number of people who owned both a cat and a dog is:

dog-and-cat = Total - (dog-only + cat-only + neither)

dog-and-cat = 349 - (145 + 60 + 71)

dog-and-cat = 349 - 276

dog-and-cat = 73

Therefore, the number of people who owned both a cat and a dog is 73.

Learn more about addition operations at

https://brainly.com/question/15379898

#SPJ11

Answer:

(3,-2)

Step-by-step explanation:

See attached image.

Answer:

thirty thousand, six hundred and eighty-two!

Step-by-step explanation:

Answer:

thirty thousand six hundred eighty two

Answer: B:81

Step-by-step explanation:

i took the test

The value should be placed in the blank space is 9 to make the perfect square option (B) 81 is correct.

Any equation of the form  \(\rm ax^2+bx+c=0\) where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

\(\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}\)

It is given that:

The quadratic equation:

x² - 18x + _ = 4 + _

As we know,

(a - b)² = a² - 2ab + b²

x² - 2(9)(x) + _ = 4 + _

To make the above quadratic equation a perfect square plug 9 in the blank space:

x² - 2(9)(x) + 81 = 4 + 81

x² - 2(9)(x) + 9² = 4 + 9²

(x - 9)² = 4 + 81

(x - 9)² = 85

Thus, the value should be placed in the blank space is 9 to make the perfect square option (B) 81 is correct.

Learn more about quadratic equations here:

brainly.com/question/2263981

#SPJ5