Write an augmented matrix for the following system of
equations.
-2x + 8y = 9
2x - 2y = 4
The entries in the matrix are:
_ _ | _
_ _ | _

Answer:

D

Step-by-step explanation:

If you dilate the figure with the center at (0,0), the sides of the triangle will be twice as long.  Then You translate the figure 7 units to the right.  

Helping in the name of Jesus.

The correct statement is,

⇒ A dilation by a scale factor of 2, centered at the origin, followed by

the translation (x, y) → (x + 7, y)

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Since, Scale Factor is defined as the ratio of the size of the new image to the size of the old image.

If the scale factor is more than 1, then the image stretches.

If the scale factor is between 0 and 1, then the image shrinks.

If the scale factor is 1, then the original image and the image produced are congruent.

And, The only change in the dilation process is that the distance between the points changes.

It means that the length of the sides of the original image and the dilated image may vary.

Here, By dilation with factor 2 to the small triangle, its sides becomes equal as big triangle.

Now, center the small triangle at origin (0,0).

Then, transform the small triangle to (x + 7, y) i.e., it exactly gets the coordinates of the big triangle.

There are same in terms of sides length and coordinates.

Learn more about Scale factor and dilation here:

brainly.com/question/12233914

#SPJ5

To show that the total charge contained in the charge distribution is Q, we integrate the charge density over the entire volume. The charge density is given by:

ρ(r) = ρ₀(1 - r/R) for r ≤ R,

ρ(r) = 0 for r > R,

where ρ₀ = 3Q/πR³.

To find the total charge, we integrate ρ(r) over the volume:

Q = ∫ρ(r) dV,

where dV represents the volume element.

Since the charge density is spherically symmetric, we can express dV as dV = 4πr² dr, where r is the radial distance.

The integral becomes:

Q = ∫₀ᴿ ρ₀(1 - r/R) * 4πr² dr.

Evaluating this integral gives:

Q = ρ₀ * 4π * [r³/3 - r⁴/(4R)] from 0 to R.

Simplifying further, we get:

Q = ρ₀ * 4π * [(R³/3) - (R⁴/4R)].

Simplifying the expression inside the parentheses:

Q = ρ₀ * 4π * [(4R³/12) - (R³/4)].

Simplifying once more:

Q = ρ₀ * π * (R³ - R³/3),

Q = ρ₀ * π * (2R³/3),

Q = (3Q/πR³) * π * (2R³/3),

Q = 2Q.

Therefore, the total charge contained in the charge distribution is Q.

To show that the electric field in the region r > R is identical to that created by a point charge Q at r = 0, we can use Gauss's law. Since the charge distribution is spherically symmetric, the electric field outside the distribution can be obtained by considering a Gaussian surface of radius r > R.

By Gauss's law, the electric field through a closed surface is given by:

∮E · dA = (1/ε₀) * Qenc,

where ε₀ is the permittivity of free space, Qenc is the enclosed charge, and the integral is taken over the closed surface.

Since the charge distribution is spherically symmetric, the enclosed charge within the Gaussian surface of radius r is Qenc = Q.

For the Gaussian surface outside the distribution, the electric field is radially directed, and its magnitude is constant on the surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q,

Simplifying:

E = Q / (4πε₀r²).

This is the same expression as the electric field created by a point charge Q at the origin (r = 0).

To derive an expression for the electric field in the region r ≤ R, we can again use Gauss's law. This time we consider a Gaussian surface inside the charge distribution, such that the entire charge Q is enclosed.

The enclosed charge within the Gaussian surface of radius r ≤ R is Qenc = Q.

By Gauss's law, we have:

∮E · dA = (1/ε₀) * Qenc.

Since the charge distribution is spherically symmetric, the electric field is radially directed, and its magnitude is constant on the Gaussian surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q.

Simplifying:

E = Q / (4πε₀r²).

This expression represents the electric field inside the charge distribution for r ≤ R.

Learn more about charge here:

https://brainly.com/question/18102056

#SPJ11

Answer:

0

Step-by-step explanation:

10(x-2)=-20

10x-20=-20

10x=0

x=0

Answer:

C is the answer you are looking for! :)

Step-by-step explanation:

Answer: C

Step-by-step explanation:

it was correct on edge 2022

Since angle y and angle x form vertical angles, the measure of angle x is equal to 50°.

In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

Furthermore, the sum of the angles on a straight line is equal to 180. Therefore, we would sum up all of the angles as follows;

60° + 70° + y = 180°

130° + y = 180°

y = 180° - 130°

y = 50°

Since both angle x and angle y are vertical angles, we can logically deduce that they are congruent and as such the magnitude of angle x is equal to 50°.

Read more on vertical angles theorem here: brainly.com/question/17876852

#SPJ1

Answer:

16

Step-by-step explanation:

Hello, do you remember that result?

For any a and b real numbers,

\((a+b)^2=a+2\cdot a \cdot b+b^2\)

In this example, we have.

\(u^2+8u=u^2+2\cdot 4 \cdot u\\\\\text{ This is the beginning of ... } u^2+8u+4^2=u^2+8u+16\\\\\text{ So, we need to add 16 to make a perfect square}\\\\u^2+8u+\boxed{16}=u^2+2\cdot 4\cdot u +4^2=(u+4)^2\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

the question?

Step-by-step explanation:

Answer:

Fatima paid $649.75

Step-by-step explanation:

Simply multiply 129.95 times 5, since each pallet was $129.95 and they purchased 5.

The probability distribution that would be used to determine the probability that in a given year, there will be at most five recalls for a leading car manufacturer is the Poisson distribution.

The Poisson distribution is commonly used to model the number of rare events occurring over a fixed interval of time or space. In this case, the mean number of recalls in a year is given as seven, which satisfies the conditions for the Poisson distribution. By using the Poisson distribution, we can calculate the probability of having at most five recalls in a given year.

The Poisson distribution is a discrete probability distribution that models the number of events that occur in a fixed interval of time or space, given that these events occur independently and with a constant rate λ. The Poisson distribution is often used to model rare events, such as the number of defects in a production process, the number of accidents in a given day, or the number of customers arriving at a store in a given hour.

To learn more about probability, click here:

https://brainly.com/question/30034780

#SPJ11

The critical t-value is approximately 1.753.

To find the critical value for a 96% confidence interval with a sample size of 15, we need to determine the t-value from the t-distribution table. The t-distribution table is a statistical tool used to determine the probability of a t-value given the degrees of freedom (df) and the desired level of significance (α).

In this case, we have a sample size of 15, which means our degrees of freedom are 14 (n - 1). Looking at a t-distribution table for 14 degrees of freedom and a 96% confidence interval.

This means that if we were to construct a confidence interval from a sample size of 15, the margin of error would be calculated by multiplying the critical t-value of 1.753 by the standard deviation of the sample and dividing by the square root of the sample size. The resulting interval would contain the population mean with 96% confidence.

It's essential to note that the critical value will change as the sample size and confidence level change. Therefore, it's crucial to use the correct table to find the corresponding critical values for a given dataset's sample size and confidence level.

For such more questions on critical

https://brainly.com/question/30459381

#SPJ8

This student performed better than 68% of the other test-takers in the verbal part and better than 27% in the quantitative part.

Given,

Test-taker scored at the 68th percentile for their verbal grade and at the 27th percentile for their quantitative grade .

Now,

68% percentile : 68% scores equal or less .

27% percentile : 27^ scored equal or less .

Thus option D

This student performed better than 68% of other test taker in verbal and better than 27% in quantitative part .

Know more about percentile,

https://brainly.com/question/2416601

#SPJ12

The value of a Chi-Square goodness-of-fit test at a 5% significance level is 13.45

We need to perform a Chi-Square goodness-of-fit test at a 5% significance level.

First we need to calculate the expected count

expected value = ∑(x)/n

= (40 + 33 + 35 + 32 + 60)/5

= 200/5

= 40

Now we need tocalculate the test statistic value

Observed  expected  O - E    (O - E)^t/E       %

40                40             0            0                   0

33                40             -7          1.225          9.11

35                40             -5          0.625         4.65

32                40             -8         1.6                11.90

60                40             20        10                 74.35

Chi square test is 13.45

Therefore, the value of test statistics is 13.45.

To learn more about test staistics refer here

https://brainly.com/question/15980493

#SPJ4

Answer:

A. 2 units

Step-by-step explanation:

took the test and got it right

The radius of the circle is r = 2 units

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the equation of the circle be represented as A

Now , the value of A is

( x - 7 )² + ( y - 10 )² = 4

The equation ( x - 7 )² + ( y - 10 )² = 4 represents a circle in standard form, where the center of the circle is located at the point (7, 10) and the radius is the square root of the number on the right side of the equation

Taking the square root of 4, we find that the radius of the circle is 2 units

Hence , the radius is r = 2 units

To learn more about circle click :

https://brainly.com/question/28391204

#SPJ7

The formula for calculating the required sample size to estimate the population mean with a 90% confidence level is given by:

n = ((z_(α/2)×σ) / E)²Here, z_(α/2) is the z-value for the given level of confidence (90% in this case), σ is the population standard deviation (6.8 in this case), and E is the maximum error we can tolerate (0.02 in this case).

Substituting the given values in the formula, we get:

n = ((z_(α/2)×σ) / E)²n = ((1.645×6.8) / 0.02)²n = 1910.96

Rounding up to the nearest whole number, we get the required sample size to be 1911.

Therefore, a sample size of 1911 is required to estimate the population mean with a 90% confidence level and an error of less than 0.02.

To know more about sample size visit:

https://brainly.com/question/30100088

#SPJ11

ANSWER

It is given that ABCD is a cyclic quadrilateral  

(∠B−∠D)=60  

o

......(1)

(∠B+∠D)=180  

o

.....(2)

By adding both the equations

∠B−∠D+∠B−∠D=60  

o

+180  

o

So we get  

2∠B=240  

o

By division

∠B=120  

o

By substituting equation it in equation (1)

(∠B−∠D)=60  

o

120  

o

−∠D=60  

o

On further calculation  

∠D=120  

o

−60  

o

by subtraction  

∠D=60  

o

Therefore, the smaller of the two angles ∠D=60  

o

.

Step-by-step explanation:

Answer:

I think the most upright answer would be D

Step-by-step explanation:

Answer:

Step-by-step explanation:

19?

Answer:

5 km

Step-by-step explanation:

Answer:

The values of x that make the triangles congruent.

x = 6 and x = 3

Step-by-step explanation:

Given

Given that the triangles are congruent.

According to the SAS (Side-Side-Side)

AC = DC

AB = DB

so

AC = DC

substituting AC = 5x-2 and DC = 3x+10

5x-2 = 3x+10

5x-3x = 10+2

2x = 12

divide both sides by 2

2x/2 = 12/2

x = 6

and

AB = DB

substituting AB = 5x and DB = 4x+3

5x = 4x+3

5x-4x = 3

x = 3

Therefore, the values of x that make the triangles congruent.

x = 6 and x = 3

The chilled dough is shaped into crescent shapes or other desired forms, proofed to allow for final fermentation, and then baked in a hot oven until golden brown and beautifully puffed.

Croissants, a delicious French pastry, are crafted through a process that involves layering butter between two layers of dough and then folding the dough repeatedly to create multiple layers.

The process of making croissants begins with a dough made from flour, water, yeast, sugar, salt, and sometimes milk. This dough is typically enriched to create a flaky and buttery texture. Once the dough is prepared, it is rolled out into a thin, rectangular shape.

Next comes the crucial step that gives croissants their distinct flaky layers: the incorporation of butter. A block of chilled butter is placed in the center of the rolled-out dough. The dough is then folded over the butter, completely enveloping it. This layering technique is what sets croissants apart from other pastries.

After enclosing the butter, the dough is carefully rolled out again, elongating it into a rectangular shape. The goal here is to evenly distribute the butter within the layers of dough. It's important to maintain the integrity of the butter layers to achieve the desired flakiness.

The rolling and folding process is repeated several times to create even more layers. This step, known as "turns," involves folding the dough into thirds, similar to folding a letter. Each turn multiplies the number of layers, resulting in a light and airy pastry. Traditionally, croissants undergo a minimum of three turns, but some recipes may require more.

Once the desired number of turns is completed, the dough is usually chilled to firm up the butter and allow the gluten to relax. This resting period helps the croissants retain their shape during baking and promotes further flavor development.

Finally, the chilled dough is shaped into crescent shapes or other desired forms, proofed to allow for final fermentation, and then baked in a hot oven until golden brown and beautifully puffed.

The labor-intensive process of layering butter between two layers of dough and folding repeatedly is what gives croissants their signature flaky texture and buttery taste. This meticulous technique has been perfected by French bakers over the years and has made croissants one of the most beloved pastries worldwide.

Learn more about fermentation here

https://brainly.com/question/29610001

#SPJ11

Based on the lengths provided, the triangles can be classified as follows:

1. 9 ft, 20 ft, 14 ft = Obtuse

2. 15 cm, 8 cm, 17 cm = Right Triangle

3. 12 in, 10 in, 8 in = Acute

4. 20 m, 8 m, 19 m = Acute

5. 16 ft, 30 ft, 34 ft = Right Triangle

6. 80 ml, 78 ml, 5 ml= Obtuse

In order to determine the type of triangle, the writer ought to note that obtuse triangles are those in which the squares of the smaller lengths are less than that of the largest length.

Also, the right triangle has squares of smaller lengths equal to the length of the largest length. Finally, the squares of the smaller lengths of an acute triangle are greater than the square of the largest. With this knowledge we can arrive at the following:

1. 9² + 14² = 20²

277 less than 400

Therefore, the triangle is Obtuse.

2. 15² + 8² = 17²

289 equal 289

Therefore, the triangle is a Right triangle

3. 10² + 8² = 12²

164 is greater than 144

Therefore, the triangle is Acute.

4. 8² + 19² = 20²

425 is greater than 400

Therefore,the triangle is Acute.

5. 16² + 30² = 34²

1156 is equal to 1156

6. 78² + 5² = 80²

6109 is less than 6400

Therefore, the triangle is Obtuse.

Learn more about triangles here:

https://brainly.com/question/17335144

#SPJ1

Answer:

Step-by-step explanation:

hello : an equation is :

x²+y²=64

Answer:

C or $463.99

Step-by-step explanation:

did the quiz... also i hate how i did what you did and took a question from a quiz and IM the one who gets the question deleted cause everyone does what we did, taking the question from the quiz

463.99 is the the reconciled bank statement

What is mathematical expression?

A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given,

starting balance is $324.11

purchased items at CVS = -33.56

Deposit = +250

ATM Withdrawal = -80

Dinner at Taco Bell = -31.56

Deposit = +35

Adding the above values we get = 139.88

Adding with starting balance = 139.88 + 324.11

= 463.99

Therefore, the reconciled bank statement and his personal records have a current balance of 463.99

Read more about addition here :

https://brainly.in/question/10133124

#SPJ2

Answer:

False

Step-by-step explanation:

4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10

Answer:

You can't solve for f since f is eliminated from the equation.

Step-by-step explanation:

f = d + e + f

Subtract f from both sides.

0 = d + e

You can't solve for f since f is eliminated from the equation.

A point on the edge of a 45 rpm record is moving 0.18 ft/sec faster than a point on the edge of a 33 rpm record.

To compare the speeds of the two records, we need to find the linear velocity of a point on the edge of each record. The linear velocity is the distance traveled by a point on the edge of the record in a given time.

For the 45 rpm record, the diameter is 7 inches, which means the radius is 3.5 inches (7/2). The circumference of the record is then 2πr = 2π(3.5) = 22 inches. To convert this to feet, we divide by 12 to get 1.83 feet.

The linear velocity of a point on the edge of the 45 rpm record is then:

V45 = 1.83 ft/circumference x 45 rev/min x 1 min/60 sec = 1.91 ft/sec

For the 33 rpm record, the diameter is 12 inches, which means the radius is 6 inches (12/2). The circumference of the record is then 2πr = 2π(6) = 37.7 inches. To convert this to feet, we divide by 12 to get 3.14 feet.

The linear velocity of a point on the edge of the 33 rpm record is then:

V33 = 3.14 ft/circumference x 33 rev/min x 1 min/60 sec = 1.73 ft/sec

The difference in speeds between the two records is then:

V45 - V33 = 1.91 ft/sec - 1.73 ft/sec = 0.18 ft/sec

Therefore, a point on the edge of a 45 rpm record is moving 0.18 ft/sec faster than a point on the edge of a 33 rpm record.

for such more question on speeds

https://brainly.com/question/23377525

#SPJ11

In a case whereby the sum of two consecutive numbers is 25 the largest of the consecutive numbers is 13.

Given that sum of two consecutive numbers is 25 , ans we were required to locatye the  largest of the consecutive numbers. The we can represent the consecutive numbers as x and x+1. According to the problem, the sum of these two consecutive numbers is 25:

x + (x+1) = 25

Simplifying the left side of the equation:

2x + 1 = 25

2x = 24

Dividing both sides by 2:

x = 12

So the first consecutive number is 12. The second consecutive number is 12 + 1 = 13. Therefore, the largest of the consecutive numbers is 13.

Learn more about consecutive numbers at:

https://brainly.com/question/26352026

#SPJ1

Answer:

it is 23

Step-by-step explanation:

i got it right

Using the given function, it is found that the snowball traveled 4 feet when the height is 20 feet.

The height when x feet are traveled is given by:

h(x) = -0.5x² + 6x + 4.

When the height is of 20 meters, we have that h(x) = 20, hence:

20 = -0.5x² + 6x + 4.

0.5x² - 6x + 16 = 0

x² - 12x + 32 = 0

(x - 8)(x - 4) = 0

For the first time: x - 4 = 0 -> x = 4.

The snowball traveled 4 feet when the height is 20 feet.

More can be learned about functions at https://brainly.com/question/25537936