Graph the line.
y= 1/2x - 5

The solution to the system of equations is:x = -3 and y = 2.

To solve the following system of equations using matrix inverse:4x + 5y = 143x - 2y = -1

Using the matrix inverse, we can rewrite the system of equations into a matrix equation:

AX = B

where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

The variable matrix X can be found by multiplying the inverse of A to the constant matrix B, which is:X = A⁻¹B

To use matrix inverse, let us first obtain the coefficient matrix A, constant matrix B, and inverse of matrix A.

Then we will use these matrices to obtain the variable matrix X.

A = [4 5; 3 -2]

B = [14; -1]

A⁻¹ = (1/22) [-2 -5; -3 4]

X = A⁻¹BX = (1/22)[-2 -5; -3 4][14; -1]= [-3; 2]

Learn more about matrix at

https://brainly.com/question/32268282

#SPJ11

The centroid of an octant of a solid sphere is located at the point (r/3, r/3, r/3), where r is the radius of the sphere.

An octant is one-eighth of a solid sphere, so it is formed by cutting the sphere into eight equal parts along the x, y, and z axes. The centroid of a solid is the point at which the mass of the solid is evenly distributed, and for an octant of a sphere, this point is located at (r/3, r/3, r/3).

This can be determined by using the formula for the centroid of a solid, which is the average of the x, y, and z coordinates of all the points in the solid. For an octant of a sphere, the x, y, and z coordinates all range from 0 to r, so the average of these coordinates is r/3.

In conclusion, the point representing the centroid is (r/3, r/3, r/3).

See more about centroid at https://brainly.com/question/7644338.

#SPJ11

Answer:

Step-by-step explanation:

Shawn will have:

Mark will have:

Together their target is 225:

Correct choice is D

Now they will have eq.,

→ Shawn = 16 + 10x

→ Mark = 22 + 7x

They togetherly get their target,

→ 16+ 10x + 22 + 7x = 225

→ 38 +17x = 225

Hence, option (D) is the answer.

The missing terms in the blanks  and number of terms  are determined below.

The missing terms in the blanks for the pattern and number of terms  can be determined as follows:

1. 32, 30, 28, 26, 32__________________________, 0

The difference is 2. Thus, subtract 2 till you reach 0. That is:

32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0

Number of terms: 16

2. 75, 70, 65, 60, 55, 50, ____________________, 0

The difference is 5. Thus, subtract 5 till you reach 0. That is:

75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5, 0

Number of terms: 15

3. 30, 27, 24, 21, ___________________________, 0

The difference is 3. Thus, subtract 3 till you reach 0. That is:

30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0

Number of terms: 10

4. 81, 72, 63, ______________________________, 0

The difference is 9. Thus, subtract 9 till you reach 0. That is:

81, 72, 63, 54, 45, 36, 27, 18, 9, 0

Number of terms: 9

5. 48, 44, 40, 36, __________________________, 0

The difference is 4. Thus, subtract 4 till you reach 0. That is:

48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0

Number of terms: 12

Learn more about number patterns on:

https://brainly.com/question/28580633

#SPJ1

f(x) = 2x + 10 is the equation in function notation given that an equation for measuring height of a balloon versus time is h=2t+10, where the variables h and t represents height and time respectively. This can be obtained by understanding what function notation is.

Here is an example of function notation and its meaning,

⇒ f(x) = x²

the name of the function is f, the input variable is x, the formula is x²

We can evaluate this function for a particular value of x

Here in the question it is given that,

We have to find the equation in function notation.

Let the name of the function be f, the input variable be x and the given formula will be 2x + 10.

Then the function notation can be written as,

f(x) = 2x + 10

Hence f(x) = 2x + 10 is the equation in function notation given that an equation for measuring height of a balloon versus time is h=2t+10, where the variables h and t represents height and time respectively.

Learn more about function notation here:

brainly.com/question/20755259

#SPJ9

Answer:

C and D.

Step-by-step explanation:

I am guessing that he wants to find if 2 is a rational number by comparing it to  the fraction \(\frac{\sqrt {2}}{1}\)

There are a couple of reasons why Mark is not correct:

1. A number is rational only if it can be written as a fraction made up of the numerator and denominator as integers.

2. The fraction \(\frac{\sqrt {2}}{1}\) is not equal to 2, so, he is wrong.

So, C and D would be correct.

NOTE: In case I misinterpreted the question, use 1. to judge if it is rational or not, you should get your answer.

Answer:

Mark is not correct because a fraction is rational only if the numerator and the denominator are both integers.​

Step-by-step explanation:

This is the correct answer

brainliest pls

We have two fractions being divided. When we divide two fractions, we flip the second fraction and multiply

1/12 divided by 1/6 = 1/12 * 6/1

-------

From here we multiply straight across.

The numerators multiply to get 1*6 = 6

The denominators multiply to 12*1 = 12

We end up with 6/12 which reduces to 1/2 when you divide both parts by the GCF 6

Answer:

d

Step-by-step explanation:

is that the answer is yes then

The z-values for the given situations are approximate:

a. The area to the left of z is 0.1827. z = -0.90

b. The area between −z and z is 0.9830. z = 2.17

c. The area between −z and z is 0.2148. z = 0.85

d. The area to the left of z is 0.9997. z = 3.49

e. The area to the right of z is 0.6847. z= -0.48

a. For an area of 0.1827 to the left of z, the corresponding z-value can be found using a standard normal distribution table or a statistical calculator. The z-value is approximately -0.90.

b. To find the z-value for an area between -z and z equal to 0.9830, we need to find the value that corresponds to (1 - 0.9830)/2 = 0.0085 in the upper tail of the standard normal distribution. Using the table or calculator, the z-value is approximately 2.17.

c. Similarly, for an area between -z and z equal to 0.2148, we find the value that corresponds to (1 - 0.2148)/2 = 0.3926 in the upper tail. The z-value is approximately 0.85.

d. For an area of 0.9997 to the left of z, we find the value that corresponds to 0.9997 in the upper tail. The z-value is approximately 3.49.

e. To find the z-value for an area to the right of z equal to 0.6847, we find the value that corresponds to 1 - 0.6847 = 0.3153 in the upper tail. The z-value is approximately -0.48.

In summary, the z-values for the given situations are approximate:

a. -0.90

b. 2.17

c. 0.85

d. 3.49

e. -0.48

These values can be used to determine the corresponding percentiles or probabilities for the standard normal distribution. The values are typically found using standard normal distribution tables or statistical calculators that provide the cumulative probability distribution function (CDF) for the standard normal distribution.

For more such answers on z-values

https://brainly.com/question/28000192

#SPJ8

Answer: To differentiate this function, we need to use the product rule and the chain rule.

First, we will simplify the function:

f(y) = (1/y^2 - 3/y^4) * y(y + 9y^3)

f(y) = (y + 9y^3) / y^3 - (3y + 27y^3) / y^5

f(y) = y^-3 * (y^4 + 9y^6 - 3y^4 - 27y^6)

f(y) = 6y^4 / y^3

f(y) = 6y

Now we can differentiate:

f'(y) = 6

Therefore, the derivative of f(y) is 6.

Using product rule and power rule of differentiation, the derivative of the function f(y) = 1/y² - 3/y⁴ * (y + 9y³) is f'(y) = 12/y⁷ - 6/y⁶ - 54/y⁵.

To differentiate the given function,

We need to use product rule and the power rule of differentiation

use product rule to differentiate two terms in the function;

Let's consider the first term: 1/y²

The derivative of 1/y² with respect to y is:

d(1/y²)/dy = -2/y³

Now, let's consider the second term: -3/y⁴ * (y + 9y³)

The derivative of -3/y⁴ with respect to y is:

d(-3/y⁴)/dy = 12/y⁵

The derivative of (y + 9y³) with respect to y is:

d(y + 9y³)/dy = 1 + 27y²

Let's use product rule to differentiate the expression

Using the product rule, the derivative of the entire expression f(y) = 1/y₂- 3/y⁴ * (y + 9y³) is:

f'(y) = (1/y²) * (d(-3/y⁴ * (y + 9y³))/dy) + (-3/y⁴ * (y + 9y³)) * (d(1/y²)/dy)

Let's plug the value into the previous expression

f'(y) = (1/y²) * (12/y⁵) + (-3/y⁴* (y + 9y³)) * (-2/y³)

Simplifying further:

f'(y) = 12/y⁷ - 6(y + 9y³)/y⁷

      = 12/y⁷ - 6(y/y⁷ + 9y³/y⁷)

      = 12/y⁷ - 6/y⁶ - 54y²/y⁷

      = 12/y⁷ - 6/y⁶ - 54/y⁵

Learn more on product rule here;

https://brainly.com/question/847241

#SPJ4

Answer:

1888 × \(10^{8}\)

or

188.8 × \(10^{9}\)

or

18.88 × \(10^{10}\)

Step-by-step explanation:

Lets look at this in a more simple way:

\((5.9\) × \(10^{6} )\) × \((3.2\) × \(10^{4} )\)

First, let's move \(10^{6}\) and switch it's places with 3.2:

(5.9 × 3.2) × (\(10^{6}\) × \(10^{4}\))

Then, let's simplify:

18.88 × \(10^{10}\)

Finally, Celebrate! WooHoo! You just learned how to do this!

Pls Brainliest! It would mean and help a lot! ;)

Thanks! Have a nice day! Please Thanks this, Vote 5, and Go to my Profile and Thanks me!

Step-by-step explanation:

Step 1:  Answer the question

They are independent because the cards are always going to stay the same.  If each card that was picked and discarded, that would alter the future which would make it dependent.  But... since it doesn't change the cards, it is independent.

Answer: independent

Answer:

Independent

Step-by-step explanation:

Since the second selection is made after replacement, the options are exactly the same as the first selection. Therefore the second selection doesn't depend on the first one. Hence, they are independent

If it was without replacement, they would have been dependent

B. discrete quantitative data is correct answer.

Because shoe size may only take on specific values, such as 5, 5.5, 6, 6.5, etc., it is a discrete type of quantitative data.

Discrete refers to anything unique or separate. The values that fall under integers or whole numbers are contained in the discrete data. Discrete data include things like the overall number of students in the class. There is no way to convert these data into decimal or fractional values. The discrete data cannot be subdivided because they are countable and have finite values. Typically, a bar graph, number line, or frequency table is used to depict these data.

The number of needle sticks, the number of pregnancies, and the number of hospitalizations are a few examples of discrete quantitative variables.

know more about quantitative data here

https://brainly.com/question/14810759#

#SPJ4

Option (A): "As the degrees of freedom increases the shape of the Chi-Square Distribution becomes more skewed" is a false statement.

Now, amongst the considered options, "As the degrees of freedom increases the shape of the Chi-Square Distribution becomes more skewed." (Option A) is not true, because:

As the degrees of freedom increases, the shape of the Chi-Square Distribution approaches a normal distribution and the graph of the Chi-Square Distribution looks more symmetrical.

To learn more about Chi-Square Distribution, refer to the link: https://brainly.com/question/4543358

#SPJ4

Answer: the eight term is 8/243

Step-by-step explanation:

Each term in this geometric sequence is equal to the previous term, divided by 3.

72,24, 8

a = 72, r = 1/3

a = first term, r is common ratio

tn = ar^n-1

t8 = 72÷ 3^8–1

t8 = 72÷ 3^7

= 72/ 3^7

= 8/243

The symbols d and sd represent:

The differences in the mean of the paired data entries in the dependent samples.

What is the standard deviation?

A measure of a set of values' variance or dispersion is called the standard deviation.

Here,

d: the difference between paired data in the dependent samples.

sd:  standard deviation.

The dependent samples' dependent samples' standard deviation for the variance between the means of the paired data items.

Hence, the differences in the mean of the paired data entries in the dependent samples.

To learn more about the standard deviation from the given link

https://brainly.com/question/475676

#SPJ4

A percentage is a way to describe a part of a whole. The regular selling price of the computer notebook will be $937.5.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Let the selling price of the computer notebook be represented by x.

Now, if Sara buys the computer this week, the selling price of the computer will be (100%-16%)x = 0.84x.

Also, the saving she made by buying this week will be $150, therefore, we can write,

x-0.84x = $150

0.16x = $150

x = 937.5

Hence, the regular selling price of the computer notebook will be $937.5.

Learn more about Percentages:

https://brainly.com/question/6972121

#SPJ1

The area of rectangular region r is = 12.

Given:

each diagonal of r has length 5. the perimeter of r is 14.

Let l and b be the length and breadth of a rectangle.

we know that

perimeter of rectangle = 2 ( l + b )

2 ( l + b ) = 14

divide by 2 on both sides

( l + b ) = 14/2

l + b = 7

l = 7 - b

l^2 + b^2 = d^2

( 7 - b )^2 + b^2 = 5^2

7^2 + b^2 - 2 * 7 * b  + b^2 = 25

49 + 2b^2 - 14b = 25

2b^2 - 14b + 24 = 0

on solving b = 4,3

Take any one value

b = 4

l = 7 - 4

l = 3

Area of rectangle = l * b

= 4 * 3

= 12

Learn more about the area here:

https://brainly.com/question/27683633

#SPJ4

Answer:

\(\angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

Step-by-step explanation:

\(\frac{\sin(\angle BAC)}{13}=\frac{\sin 23^{\circ}}{6} \\ \\ \sin \angle BAC=\frac{13\sin 23^{\circ}}{6} \\ \\ \angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

The midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is 9980

The midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is calculated by summing the area of each subinterval under the midpoint of the interval.

The formula for the midpoint Riemann sum is given by:

Sum = (width of interval) * (height of midpoint)

For this problem, since the width of each interval is 16/4 = 4, the midpoint Riemann sum is calculated by:

Sum = 4 * (1 + (16/4)^3 + (32/4)^3 + (48/4)^3)

Substituting the values for each midpoint, we get the following equation:

Sum = 4 * (1 + 4^3 + 8^3 + 12^3)

This simplifies to:

Sum = 4 * (1 + 64 + 512 + 1728)

Therefore, the midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is:

Sum = 4 * (2495)

Sum = 9980

Learn more about Riemann sum here:

https://brainly.com/question/30241844

#SPJ4

Percentage is represented by '%' symbol. The final cost of the bike will be equal to $490.

A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.

Given to us

The initial cost of the bike, P = $950

Additional coupon = 30%

Marked down = $200

We know the original cost of the bike which is $950. therefore, when the price of the bike was marked down, its cost will be,

$900 - $200 = $700

Thus, the marked-down cost of the bike will be $700.

As it is given that we have an additional 30% off after the markdown, therefore, cost of the bike will be 70% of the marked price,

\(70\%\ of\ \$700\\\\ = 0.70 \times 700\\\\= \$490\)

Hence, the final cost of the bike will be equal to $490.

Learn more about Percentage:

https://brainly.com/question/6972121

Answer:

D

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

Work Shown:

Use the slope formula

m = (y2 - y1)/(x2 - x1)

m = (3-3)/(2-10)

m = 0/(-8)

m = 0

The slope of any horizontal line is always zero due to the fact all y coordinates on this line are the same. When we pick two points from the line, the same y coordinates subtract to 0. We can have 0 in the numerator, but not in the denominator.

As the slope formula shows, we basically subtract the y coordinates together, and do the same for the x coordinates as well in the same order. Then we divide the differences.

Answer:

D because it costs less for 7 hours

Answer:

The company that would give you the best deal would be Company D.

Step-by-step explanation:

Company A:

First you set up as an equation.

y=25x+50

I used 25x because 25 represents the hourly rate and x represents the hour it increases.

y=25(7)+50

We have to substitute 7 in for x because it says "If you had planned for 7 hours".

Multiply 25 and 7. You should get 175.

y=175+50

Add 175 and 50. You should get 225.

y=225.

You do the same thing for the rest of the problems.

Company B:

y=30x+40

y=30(7)+40

y=210+40

y=250

Company C:

y=20x+60

y=20(7)+60

y=140+60

y=200

Company D:

y=5x+150

y=5(7)+150

y=35+150

y=180

The company that would give you the best deal would be Company D.

Answer:

6.5 inches

Step-by-step explanation:

Divide 26 by 4

26/4=6.5

The length of one side of the poster to the nearest tenth of an inch is 5.1 inches.

The area of a square can be calculated as the square of the sides of a given figure.

The area of a square = side x side

Given; The area of a square poster 26 inch

We need to find the length of one side of the poster to the nearest tenth of an inch.

The area of a square would be S^2

26 = S^2

s = sqrt(26) = 5.099

Then rounded to nearest tenth = 5.1 inches

Hence, the length of one side of the poster to the nearest tenth of an inch is 5.1 inches.

Learn more about the area here;

https://brainly.com/question/1658516

#SPJ2

Answer:

15%

Step-by-step explanation:

Price of daily tickets entrance

Adult=£55

Children=£45

Family (2 adults and 2children)=£170(discount price)

Let

price for adults=a

Price for Children=c

Price of tickets without discount for 2 adults and 2 children=2(a+c)

=2(55+45)

=2(100)

=£200

Percentage discount offered with the family tickets=difference in price/original price×100

=£200-£170/200×100

=30/200×100

=30/2

=15%

The Percentage discount offered with the family tickets=15%

Answer:

y = |x| - 1

Step-by-step explanation:

The difference between the parent function (y=|x|) and the graph, is that the graph is 1 unit down. y = |x| -1 has the parent function 1 unit down

Answer:

C. y = |x| - 1

Step-by-step explanation:

y = |x| Is the same graph, but with the vertex on point (0,0)

y = |x+1| Moves graph to the left 1

y = |x| + 1 Moves the graph up 1

y = |x| - 1 moves the graph down 1

y = |x-1| moves the graph right one

Therefore, y = |x| - 1 is the answer.

To further explain it, you can write down a table of values for proof. For y = |x| when x = 0, y = 0. When x = 1, y = 1 and so on. When x = -1, y = 1 and so on in that direction.

If we look at the choices and plug in numbers, we get for A when x = 0, y = 1, which if we look at the graph given does not fit.

For B, when x = 0, we get y = 1, which again does not work.

For C, when x = 0, y = -1, which is the answer we need, but to make sure, I am going to do D.

For D, when x = 0, y = 1. Therefore, C is the only possible answer.