Slope=4; goes through (-3,0)

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.

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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.

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.

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]

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.

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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:

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:

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.

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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

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.

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Answer:

y - 7 =  3/5 (x - 1)

Answer:

962.084375 meters² or 306.25π

Step-by-step explanation:

A diameter is a line that goes straight through the center of the circle. Since it goes through the center, it creates 2 radii. This splits the diameter into 2 separate parts, and since the diameter is 25 meters, that means that the radius will be 25/2 = 17.5 meters.

The formula for the area of a circle is pi • r²

Since we know the radius (17.5), we can solve this expression:

pi • 17.5²

pi • 306.25

If we use 3.1415 for pi, we get962.084375 meters²

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Answer:

please your question is incomplete

Step-by-step explanation:

if....... of a number

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.

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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.

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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

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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]

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.

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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.  

m=2

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

Answer:

5°

Step-by-step explanation:

because: -5°+5°=0° I think

Answer:

5 degrees

Step-by-step explanation:

-5+5=0

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.

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(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.

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The pool is 0.5 centimeters long in the drawing.

The ratio of 1 centimeter to 4 meters means that for every 4 meters in real life, Alice drew 1 centimeter in her drawing.

To find out how long the pool is in the drawing, we need to divide the actual length of the pool by the scale factor.

The scale factor is 4 meters : 1 centimeter, which is the same as 1 meter : 0.25 centimeters.

So to find the length of the pool in the drawing, we need to divide the actual length of the pool by 4 to get the length in meters, and then multiply by 0.25 to convert to centimeters:

Length in drawing = (32 meters / 4) x 0.25 = 2 x 0.25 = 0.5 centimeters

Therefore, the pool is 0.5 centimeters long in the drawing.

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(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           |

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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.

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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.

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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

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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.

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)

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The range οf P-values wοuld be 0.01 < P-value < 0.02

In statistics, a test statistic is a numerical value that is calculated frοm a sample οf data and is used tο determine whether οr nοt tο reject a null hypοthesis in a hypοthesis test.

The chοice οf test statistic depends οn the specific hypοthesis test being perfοrmed and the nature οf the data being analyzed. Fοr example, in a t-test fοr the mean οf a nοrmally distributed pοpulatiοn, the test statistic is the t-value, which is calculated as the difference between the sample mean and the hypοthesized pοpulatiοn mean divided by the standard errοr οf the mean.

Using Table A-3 with n = 38 and a left-tailed test statistic t = 2.714, we find the cοrrespοnding P-value tο be between 0.01 and 0.02. Therefοre, the range οf values fοr the P-value is:

0.01 < P-value < 0.02

Sο the cοrrect respοnse is:

0.01 < P-value < 0.02

Hence, the range οf P-values wοuld be 0.01 < P-value < 0.02

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Complete Question: