Plot the points A(-6,-4), B(3, -8), C(7, 1) on the coordinate axes below. State the coordinates of point � D such that � A, � B, � C, and � D would form a rectangle.

The equations y-6=x² and y=2x²+5-3x³ are non linear. Therefore, options D and F are the correct answers.

A linear function is a function that represents a straight line on the coordinate plane. The standard form of a linear function is y = mx + b.

Here, 'm' is the slope of the line, 'b' is the y-intercept of the line, 'x' is the independent variable and 'y' (or f(x)) is the dependent variable.

A) y=x

Here, degree of the equation is 1, so the equation is linear.

B) 2y=12x

Here, degree of the equation is 1, so the equation is linear.

C) y=8+x

Here, degree of the equation is 1, so the equation is linear.

D) y-6=x²

Here, degree of the equation is 2, so the equation is quadratic.

E) y=13-5x

Here, degree of the equation is 1, so the equation is linear.

F) y=2x²+5-3x³

Here, degree of the equation is 3, so the equation is cubic.

Therefore, options D and F are the correct answers.

To learn more about the linear function visit:

https://brainly.com/question/17058347.

#SPJ1

The seasonally-adjusted forecast for quarter 4 of year 5 is 91.9

The seasonally-adjusted forecast for quarter 4 of year 5 can be calculated by using the following equation:
Seasonally Adjusted Forecast = Trend Equation + Seasonal Factors
= 65 + 6.7X + 0.1
= 65 + 6.7X + 0.1
= 65 + 6.7*4 + 0.1
= 65 + 26.8 + 0.1
= 91.9
Therefore, the seasonally-adjusted forecast for quarter 4 of year 5 is 91.9.

Learn more about Trend Equation

brainly.com/question/30282016

#SPJ11

Answer:

The student factored the numerator and denominator incorrectly. Instead of factoring to (x+1)(x+2)/(x+4)(x+2), they factored to (x+1)(x+2)/(x+4)(x+2) = (x+1)/x+4.

Factoring polynomials can be a difficult skill to master, and mistakes in factoring can lead to errors in simplifying rational expressions. Additionally, students may rush through factoring or not double-check their work, leading to careless errors.

Students can avoid mistakes like this by practicing factoring polynomials regularly and double-checking their work. It can also be helpful to write out each step clearly and show all work, so mistakes can be caught more easily.

My advice would be to practice factoring polynomials regularly, and double-check your work when simplifying rational expressions. Also, it is important to take your time and show all work, so mistakes can be caught more easily.

The hypotenuse is sqrt(11^2 + 7^2) = sqrt(170). Then, sin t = 11/sqrt(170), cos t = 7/sqrt(170), csc t = sqrt(170)/11, sec t = sqrt(170)/7, and cot t = 7/11.

Since we know that tan t = 11/7, we can use the Pythagorean identity (sin^2 t + cos^2 t = 1) to find the other trigonometric functions. First, we will find sin t and cos t:

tan t = 11/7 = opposite/adjacent = sin t/cos t

sin t = 11*cos t

cos t = 7*sin t

Substituting the second equation into the first equation:

sin t = 11*(7*sin t)

sin^2 t = 121*sin^2 t

121*sin^2 t - sin^2 t = 0

120*sin^2 t = 0

sin^2 t = 0/120

sin^2 t = 0

sin t = 0

Since sin t = 0, cos t = 1. Now we can find the other trigonometric functions:

csc t = 1/sin t = 1/0 = undefined

sec t = 1/cos t = 1/1 = 1

cot t = 1/tan t = 1/(11/7) = 7/11

So, the values of the trigonometric functions are:

sin t = 0

cos t = 1

csc t = undefined

sec t = 1

cot t = 7/11

Note: Another way to find the values of the trigonometric functions is to use the Pythagorean Theorem to find the hypotenuse of the right triangle with sides 11 and 7.

For more about square root:

https://brainly.com/question/29286039

#SPJ11

The solution is, the equation of a line parallel to y=3x-3 and passing through point (3,2) is y=3x-7.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

The equation of the given line is,

y=3x-3 ....1

We have to find the equation of a line parallel to y=3x-3 and passing through the point (x1, y1)=(3,2).

The general equation of a line is,

y = mx+c ....2

Here, m is the slope of the line.

Comparing equations (1) and (2), we find that the slope of the line

y=3x-3 is m=3.

The slope of two parallel lines are always equal.

Hence, the slope of a line parallel to the line y=3x-3 is also m=3.

Now, the formula for the point slope form of the equation of a line can be written as,

y - y1 = m (x - x1)

Substitute m=3, x1=3 and y1=2 in the above equation to find the equation of a line parallel to y=3x-3 and passing through point (3,2) is,

y-2 = 3(x - 3)

Therefore, the equation of a line parallel to y=3x-3 and passing through point (3,2) is y=3x-7.

To learn more on Equation 0f Straight-Line click:

brainly.com/question/11116168

#SPJ1

Check the picture below.

[tex]\boxed{4} \\\\\\ (x+3)^2~~ = ~~[(x-1)+10](x-1)\implies x^2+6x+9~~ = ~~(x+9)(x-1) \\\\\\ x^2+6x+9~~ = ~~x^2+8x-9\implies 6x+9=8x-9\implies 9=2x-9 \\\\\\ 18=2x\implies \cfrac{18}{2}=x\implies 9=x[/tex]

Answer:

5°

Step-by-step explanation:

because: -5°+5°=0° I think

Answer:

5 degrees

Step-by-step explanation:

-5+5=0

2a + 2h

(a) Simplifying, we get f(a+h)−f(a)/h = (a+h)2−2(a+h)+3 − (a2−2a+3) / h = (2a+2h)h/h = 2a + 2h.

(b) We now use the definition of the derivative to compute f'(a) = limh→0 (2a + 2h) = 2a.

Learn more about derivative

brainly.com/question/30365299

#SPJ11

Answer:

When you multiply two numbers with different signs (positive and negative), the result is always negative.

This can be understood in terms of the basic properties of multiplication and the fact that a negative number is essentially the opposite of a positive number. When you multiply a positive number by a positive number, the result is positive because both numbers are pointing in the same direction along the number line. When you multiply a negative number by a negative number, the result is also positive because both numbers are pointing in the opposite direction along the number line, and multiplying them together "flips" them back to the positive side. However, when you multiply a positive number by a negative number, the two numbers are pointing in opposite directions along the number line, and so their product is negative.

Therefore, the rule for multiplying two numbers with different signs is that the product is always negative.

Step-by-step explanation:

In quadrilateral EFGH, sides FG and EH are congruent because they each have a length of 7.07. Sides EF and GH are not congruent. The area of quadrilateral EFGH is closest to 41 square units.

For the width, we would determine the distance between the vertices F (-1, 4) and G(4, -1)

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance FG = √[(4 - (-1))² + (-1 - 4)²]

Distance FG = √[5² + (-5)²]

Distance FG = √50

Distance FG = 7.07 units.

Distance EH = √[(1 - (-4))² + (-4 - 1)²]

Distance EH = √[5² + (-5)²]

Distance EH = √50

Distance FG = 7.07 units.

For the length, we would determine the distance between the vertices E (-4, 1) and F (-1, 4)

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance EF = √[(-1 - (-4))² + (4 - 1)²]

Distance EF = √[3² + (3)²]

Distance EF = √9

Distance EF = 3 units.

Distance HG = √[(4 - 1)² + (1 - (-4))²]

Distance HG = √[3² + (5)²]

Distance HG = √34 units.

Mathematically, the area of a rectangle can be calculated by using this formula:

Area of rectangle = length × width

Area of rectangle = √34 × 7.07

Area of rectangle = 41.22 square units.

Read more on area of a rectangle here: brainly.com/question/25292087

#SPJ1

Answer:

the answer is 88 square inches

Step-by-step explanation:

[tex]2(6 \times 4) + 2(4 \times 2) + 2(6 \times 2) = 88[/tex]

Based on the histograms, it appears that Machine B is doing a better job of dispensing the correct amount of liquid.

The most common graph for displaying frequency distributions is a histogram.

To begin, Machine B's histogram is more symmetrically distributed around the 5.5-ounce mark, which is the target fill level.

Machine A's histogram, on the other hand, is skewed to the right, indicating that it is more likely to dispense more than 5.5 ounces.

Second, Machine B's histogram has a narrower spread, with most measurements falling between 5.4 and 5.6 ounces.

This indicates that the machine fills the bottles consistently within a narrow range of the target fill level.

Thus, the histogram for Machine A, on the other hand, has a wider range, with some measurements falling below 5.4 ounces and others exceeding 5.6 ounces, indicating a less consistent performance.

For more details regarding histogram, visit:

https://brainly.com/question/30354484

#SPJ1

Your question seems incomplete, the probable complete question is:

m=2

because in the other equation, the digit next to x is 2 so m must be 2

The solution to the equation is (5, -1)

From the question, we have the following parameters that can be used in our computation:

2x + 3y = 7

-2x + 1y = -11

Add to eliminate x

So, we have

4y = -4

Divide both sides by 4

y = -1

Recall that 2x + 3y = 7

Substitute the known values in the above equation, so, we have the following representation

2x - 3 = 7

So, we have

2x = 10

Divide

x = 5

For the substitution method, we have

2x + 3y = 7

-2x + y = -11

The second equation becomes

y = 2x - 11

By substitution, we have

2x + 6x - 33 = 7

So, we have

8x = 40

x = 5

Recall that

y = 2x - 11

So, we have

y = 2 * 5 - 11

y = -1

Hence, the solution is (5, 2)

Read more about equations at

https://brainly.com/question/2972832

#SPJ1

An equation of the function include the following: C. f(x) = 3×(0.1)^x.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = ab^x

Where:

By critically observing the graph of this exponential function, we can logically deduce that the base value of this exponential growth function is at (0, 3) and its domain includes all real numbers i.e -∞ < x < ∞.

Therefore, the required exponential function is given by:

f(x) = 3(0.1)^x

Read more on exponential equation here: brainly.com/question/28939171

#SPJ1

So, with continuous compounding interest, there would be $1324.46 in the account after 5 years.

A(t) = P(1 + r/n)^(nt)

a. To find an equation that gives the amount of money in the account after t years, we can plug in the given values for P, r, and n into the formula. P is the initial deposit, r is the annual interest rate, and n is the number of times the interest is compounded per year. So, the equation will be:

A(t) = 800(1 + 0.10/4)^(4t)

b. To find the amount of money in the account after 5 years, we can plug in t = 5 into the equation and solve for A(t):

A(5) = 800(1 + 0.10/4)^(4*5)
A(5) = 800(1.025)^20
A(5) = 1303.04

So, after 5 years, there will be $1303.04 in the account.

c. To find how many years it will take for the account to contain $1600, we can set A(t) = 1600 and solve for t:

1600 = 800(1 + 0.10/4)^(4t)
2 = (1.025)^4t
log(2) = 4t*log(1.025)
t = log(2)/(4*log(1.025))
t = 7.22

So, it will take 7.22 years for there to be $1600 in the account.

d. If the same account and interest were compounded continuously, we can use the formula A(t) = Pe^(rt) to find how much money would be in the account after 5 years:

A(5) = 800e^(0.10*5)
A(5) = 800e^0.5
A(5) = 1324.46

So, with continuous compounding interest, there would be $1324.46 in the account after 5 years.

Learn more  about Compounding

(a) The equation that gives the amount of money in the account after t years is A(t) = 800(1.025)^4t.

(b) After 5 years, there will be $1304.56 in the account.

(c) It will take 7.24 years for there to be $1600 in the account.

(d) With continuous compounding interest, there would be $1340.95 in the account after 5 years.

a. The equation for the amount of money in the account after t years is A(t) = 800(1 + 0.10/4)^(4t) = 800(1.025)^4t. This is derived from the formula A = P(1+ r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

b. To find the amount of money in the account after 5 years, we can plug in the values into the equation from part a. A(5) = 800(1 + 0.10/4)^(4)(5) = 800(1.025)^20 = $1304.56. Therefore, after 5 years, there will be $1304.56 in the account.

c. To find how many years it will take for the account to contain $1600, we can set the equation from part a equal to 1600 and solve for t. 1600 = 800(1 + 0.10/4)^(4t) => 2 = (1.025)^4t => 4t = log(2)/log(1.025) => t = 7.24 years. Therefore, it will take 7.24 years for there to be $1600 in the account.

d. If the same account and interest were compounded continuously, the formula for the amount of money in the account after t years would be A(t) = 800e^(0.10t). To find how much money the account would contain after 5 years, we can plug in the values into this equation. A(5) = 800e^(0.10)(5) = $1340.95. Therefore, with continuous compounding interest, there would be $1340.95 in the account after 5 years.

Learn more about compound interest here: https://brainly.com/question/28020457.

#SPJ11

Answer:

62.5%

Step-by-step explanation:

the product of the two numbers=xy

the product of the altered numbers=(0.75x)(0.5y) OR 0.375xy

finally you subtract this from one to get your decrease: 1-0.375=0.625

then simply convert that to a percent, leaving you with 62.5%. hope this helps!

Answer:

Step-by-step explanation:

1. Figure out which terms are alike. I have separated the like terms using parenthesis for clarification, however, this is not necessary when solving by yourself.

(3y + 4y) + (8 + 2)

2. Combine both sets of like terms however the signs dictate. In this case, add all the signs.

3y + 4y = 7y  

(solve as if there was no constant so if 3 + 4 = 7 then 3y + 4y = 7y)

8 + 2 = 10

3. Put it all together

Final answer: 7y + 10

Note: Understanding how to combine and simplify like terms will be very helpful when you eventually will have to solve for y. When solving an equation you will always want to start by combing and simplifying like terms first.  

Step-by-step explanation:

How many cups of milk are in a gallon = 16

If a recipe uses 2 cups for 6 servings, then he will make 48 servings from a gallon.

1 quart is 4 cups of milk, a gallon contains 4 quarts

1 pint is 2cups, a gallon contains 8pints of milk

From the question 1 gallon is 4 quarts or 8pints or 48servings

Answer: m=2

Step-by-step explanation: First convert the equation to slope-intercept form; y=mx+b. This new equation would be 3y=6x-12. Because y must be singular, each side must be divided by 3, to isolate the variable y. After doing this, the equation is y=2x-4. In terms of y=mx+b, m is attached to x, making the slope of this equation 2.

Sinusoidal (periodic) functions, also known as sine and cosine functions, are ubiquitous in our daily lives. They are used to model a wide range of phenomena in fields such as engineering, physics, and mathematics.

One of the most common applications of sinusoidal functions is in the field of electronics, where they are used to model alternating current (AC) circuits.

Sinusoidal functions are also used in signal processing, audio and image compression, and speech recognition. In addition, they are used in the design of various mechanical and electrical systems, such as engines, turbines, and power generators.

Sinusoidal functions also play an important role in wave motion, such as ocean waves and sound waves. They are used to model the behavior of waves and to predict their properties, such as wavelength and frequency.

Furthermore, sinusoidal functions are used in the field of optics to model the behavior of light waves. They are used to describe the properties of light waves, such as amplitude, frequency, and phase.

In conclusion, sinusoidal functions have a wide range of applications in various fields, from electronics and signal processing to mechanics and optics. Their versatility and accuracy make them an essential tool for modeling and predicting real-world phenomena.

For more questions like Functions visit the link below:

https://brainly.com/question/13081668

#SPJ11

The accumulated value of an investment of $20,000 at 6% compounded annually for 16 years is $50,807.04. The correct answer is D.

To find the accumulated value of an investment of $20,000 at 6% compounded annually for 16 years, we need to plug in the given values into the compound interest formula: A = P(1 + r/n)^nt

Given values:

P = $20,000 (principal amount)

R = 6% (annual interest rate)

N = 1 (number of times interest is compounded per year)

T = 16 (number of years)

Plugging in the given values into the formula:

A = 20000(1 + (0.06/1))^(1)(16)

Simplifying the equation:

A = 20000(1.06)^16

Using a calculator to find the value of A:

A = $50,807.04

Therefore, the accumulated value is D. $50,807.04.

Learn more about compound interest here: https://brainly.com/question/24274034.

#SPJ11

Answer:

We need to find out how many trips Billy needs to make to transport 80 cubic meters of mulch. Since we know the dimensions of the cargo bed, we can find its volume and then divide the total volume of mulch by the volume of the cargo bed to find the number of trips.

The volume of the cargo bed is:

V = l × w × h

where l is the length, w is the width, and h is the height. Using the dimensions given in the diagram, we get:

V = 4 m × 2.5 m × 1.5 m = 15 cubic meters

Now we can divide the total volume of mulch by the volume of the cargo bed to find the number of trips:

Number of trips = total volume of mulch / volume of cargo bed

Number of trips = 80 cubic meters / 15 cubic meters ≈ 5.33

Since Billy cannot make a fractional number of trips, he will need to make 6 trips to transport all the mulch to his house.

Answer:

log(2)+log(3)+2log(x)

you should try downloading an app called math away

i don't know if it's right but I got the answer from a reliable source

Answer:

a. Here is a Venn diagram to illustrate the information:

markdown

    ESUT

    /   \

 FUTO  UNN

  \    /

   \  /

 (X)

where (X) represents the number of applicants who applied to all three universities.

b. To find the number of applicants who applied to all three universities, we can use the formula:

scss

Total = ESUT + FUTO + UNN - (Exactly two) - (None) + (All three)

We know that:

makefile

ESUT = 60 + 54 + (All three)

UNN = 75 + (All three)

FUTO = 54 + 60 + (All three)

Total = 290

Substituting these values, we get:

scss

290 = (60 + 54 + All three) + (54 + 60 + All three) + (75 + All three) - (Exactly two) - (None) + (All three)

Simplifying, we get:

scss

290 = 249 + 2(All three) - (Exactly two) - (None)

We also know that:

scss

None = Total - (ESUT + FUTO + UNN) = 290 - (181 + 142 + 117) = -150

This negative value means that there are no applicants who did not apply to any of the universities. This is a contradiction, so we must have made an error in our calculations.

Therefore, we cannot find the number of applicants who applied to all three universities or exactly two universities.

(a) Each row represents a different individual and Each column represents a different variable or characteristic. (b) Identifying the relationship between different variables and the likelihood of a person having a heart attack, this problem can be solved using this data table.

(a) The table is organized into rows and columns. Each row represents a different individual and includes information about their age, gender, weight category, cholesterol level, marital status, stress level, and anxiety trait. Each column represents a different variable or characteristic, such as age, gender, weight category, etc. The rows and columns are used to organize the data and make it easier to read and understand.

(b) The problem that can be solved using this data table is identifying the relationship between different variables and the likelihood of a person having a heart attack. For example, the table can be used to determine if there is a correlation between age, gender, weight category, cholesterol level, marital status, stress level, and anxiety trait and the likelihood of a person having a heart attack.

(c) Decision table for the above table:

| Age | Gender | Weight Category | Cholesterol Level | Marital Status | Stress Level | Anxiety Trait | Heart Attack |
|-----|--------|-----------------|-------------------|----------------|--------------|---------------|--------------|
| 60  | Female | Overweight      | 150               | Yes            | High         | Yes           | Yes          |
| 69  | Male   | Overweight      | 170               | Yes            | Normal       | Yes           | Yes          |
| 52  | Female | Normal          | 174               | No             | High         | Yes           | No           |
| 66  | Male   | Overweight      | 169               | Yes            | Normal       | No            | Yes          |
| 70  | Female | Overweight      | 237               | Yes            | Normal       | No            | Yes          |
| 52  | Female | Normal          | 174               | No             | High         | Yes           | No           |
| 58  | Male   | Normal          | 140               | Yes            | Normal       | No            | No           |

For more such questions on Data table.

https://brainly.com/question/30138408#

#SPJ11

The equation that can be used to determine Greg's score is 15 - 8 = x. This equation shows that if you subtract 8 points from Ben's score of 15 points, you will get Greg's score.

Step-by-step explanation:

In conclusion, the equation 15 - 8 = x can be used to determine Greg's score.

For more information about equation, visit:

https://brainly.com/question/22688504

#SPJ11

The length of y for the triangle is 27.8 in

The sine rule is for solving triangles which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula:

w/sinW = x/sinX = y/sinY

where w, x and y are the lengths and W, X and Y are the angles

Given: w = 55 inches,   m∠W = 162° and m∠X= 9°

m∠Y = 180 - 162 - 9 =  9° (angle sum in a triangle)

Using the formula:

w/sinW = y/sinY

55/sin162° = y/sin9°

y = (55*sin9°)/sin162°

y = 27.8 in

Learn more about sine rule on:

brainly.com/question/3240813

#SPJ1

In order to outline the yard and the garden allotment with bricks and Using Pythagorean theorem, Mariah will need to buy about 69.4  yards³ of brick.

what is pythagoras theorem ?

According to the Pythagorean Theorem, the square of the length of the hypotenuse in a right triangle equals the total of the squares of the lengths of the other two sides. The hypotenuse is the side that faces the right angle. In mathematics, it can be expressed as:

c² = a² + b²

where the lengths of the other two sides (the legs) of the right - angled triangle are a and b, and c is the length of the hypotenuse. Pythagoras, an ancient Greek mathematician, is attributed with discovering and proving this theorem, so it bears his name. Geometry, algebra, and other fields of mathematics and science all make extensive use of the Pythagorean Theorem.

given

The Pythagorean formula can be used to determine side C.

C² = A² + B²

C²= 30² + 50²

C² = 900 + 2500

C² = 3400

C ≈ 58.3

As a result, the triangle-shaped yard's circumference is:

30 + 50 + 58.3 ≈ 138.3 feet

We require information regarding the measurements of the rectangular garden plot. Let's assume it is 20 feet long and 15 feet wide.

Thus, the vegetable plot's perimeter is as follows:

2(20 + 15) = 70 feet

The perimeters must now be converted from feet to yards (since we are calculating square yards).

circumference of a triangular yard: 46.1 yards x 138.3 feet

Garden plot boundaries measured as 70 feet by 23.3 yards.

In order to calculate the overall number of bricks required, we add the two perimeters:

46.1 plus 23.3 equals 69.4 square yards.

In order to outline the yard and the garden allotment with bricks, Mariah will need to buy about 69.4  yards³ of brick.

To know more about Pythagorean theorem visit:

https://brainly.com/question/14930619

#SPJ1