Where in the equation of the line passing through the point (2,-14) and having a slope -4

The sum of the two polynomials 4x³+2x²-4x+3 and 7x³-4x² +7x+8 is 11x³-2x²+3x+11.

Algebraic expressions called polynomials include coefficients and variables. For polynomial expressions, we can perform mathematical operations like addition, subtraction, multiplication, and positive integer exponents. Polynomial addition is the process of adding like terms from two or more algebraic equations while maintaining the sign of each term.

Here, given two polynomials 4x³+2x²-4x+3 and 7x³-4x² +7x+8.

First, arrange the given polynomials. The polynomials were already arranged from the increasing to decreasing order of degree. Then,

(4x³+2x²-4x+3)+ (7x³-4x² +7x+8)

Second, group the like terms from both polynomials.

(4x³+7x³)+(2x²-4x²)+(-4x+7x)+(3+8)

Now, simplifying the combining terms, we get,

11x³-2x²+3x+11

The answer is 11x³-2x²+3x+11.

The complete question is -

Add the following polynomials, then place the answer in the proper location on the grid. write the answer in descending powers of x. Find the sum of 4x³+2x²-4x+3 and 7x³-4x² +7x+8.

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Option B is the statement which is  not sufficient to prove the congruence of two triangles.

In all the other options we get to know about three parts of the triangle using which we can prove their congruency .

Option B says ,

Two sides of one triangle are congruent respectively to the two sides of another triangle.

In this statement there is no mention about the third side or a third angle.

Therefore, using option B we cannot prove the congruence of two triangles.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

" ≅ " is the congruence symbol.

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8

x = 6

9

x=7

10

x= 15

see explanation in image

because you know that m and n are parralell you can use the vertical angle theorem as well as the fact that lines in a straight angle add to 180

if you have any questions just comment

The circumcenter of a triangle formed by (4,2), (3,-3) and (2,2) is located at (3, -0.4).

The circumcenter of a triangle is the point of intersection of the three perpendicular bisectors of the sides of a triangle.

Let A = vertex at (4,2)

B = vertex at (3,-3)

C = vertex at (2,2)

Get the midpoint of each side.

midpoint = [(x₂ + x₁)/2 , (y₂ + y₁)/2]

side AB : midpoint = [(3 + 4)/2 , (-3 + 2)/2] = (3.5, -0.5)

side AC : midpoint = [(4 + 2)/2 , (2 + 2)/2] = (3, 2)

side BC : midpoint = [(3 + 2)/2 , (-3 + 2)/2] = (2.5, -0.5)

Get the slope of each side.

slope = (y₂ - y₁) / (x₂ - x₁)

side AB : slope = (-3 - 2) / (3 - 4) = 5

side AC : slope = (2 - 2) / (2 - 4) = 0/-2 = 0

side BC : slope = (2 - -3) / (2 - 3) = -5

Determine the equation of the line of each of the three perpendicular bisectors of the sides of a triangle, that passes through the midpoint and with a slope equal to the negative reciprocal of the slope of the side.

y = mx + b

perpendicular bisector of AB :

-0.5 = -1/5(3.5) + b   ;   b = 0.2   ;   y = -1/5x + 0.2

perpendicular bisector of AC :

since AC is a horizontal line, x = 3

perpendicular bisector of BC :

-0.5 = 1/5(2.5) + b   ;   b = -1   ;   y = 1/5x - 1

Since x is already equal to 3, substitute the value of x in the two other equation and solve for y.

y = -1/5x + 0.2

y = -1/5(3) + 0.2

y = -0.4

y = 1/5x - 1

y = 1/5(3) - 1

y = -0.4

Hence, the circumcenter of the triangle is located at (3, -0.4).

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A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.

Hence, in this problem, the function g(x) is exponential, as when the input x is increased by one, the output g(x) is multiplied by two.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

Hence, in this problem, the function f(x) is linear, as when the input x is increased by one, the output f(x) is increased by a constant of six.

The problem is given by the image shown at the end of the answer.

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The value of [tex]sin^{-1}[/tex](- [tex]\frac{\sqrt{2} }{2}[/tex]) in radians is [tex]-\frac{\pi }{4}[/tex]

The value of  [tex]sin^{-1}[/tex](1) in radians is [tex]\frac{\pi }{2}[/tex]

The value of  [tex]sin^{-1}[/tex](- 1/2) is [tex]-\frac{\pi }{6}[/tex]

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

[tex]sin^{-1}[/tex](- [tex]\frac{\sqrt{2} }{2}[/tex])  is -45 in degress

but [tex]\pi[/tex] rad = 180°

so that - 45° in rad is [tex]\pi[/tex] x - 45/180 which is - [tex]\frac{\pi }{4}[/tex]

[tex]sin^{-1}[/tex](1)  = 90°

but [tex]\pi[/tex] rad = 180°

so that -90° in rad is [tex]\pi[/tex] x 90/180 which is  [tex]\frac{\pi }{2}[/tex]

[tex]sin^{-1}[/tex](- 1/2) = -30°

but [tex]\pi[/tex] rad = 180°

so that - 30° in rad is [tex]\pi[/tex] x - 30/180 which is - [tex]\frac{\pi }{6}[/tex]

In conclusion then values of the sine inverse of the functions are - [tex]\frac{\pi }{4}[/tex],  [tex]\frac{\pi }{2}[/tex], and - [tex]\frac{\pi }{6}[/tex]

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Answer:

So, it will take between 4 and 5 bags of quickrete to fill the tube.

Step-by-step explanation:

To find the volume of the sonotube, you can use the formula for the volume of a cylinder: V = πr^2h, where r is the radius of the tube and h is the height.

First, you need to find the radius of the tube. The diameter of the tube is 10 inches, so you can divide that by 2 to get the radius: r = 10 inches / 2 = 5 inches.

Then, you can plug the radius and height into the formula to find the volume of the tube: V = πr^2h = π(5 inches)^2(48 inches) = about 235.61 inches^3.

To find the number of bags of quickrete you will need to fill the tube, you need to convert the volume of the tube to cubic feet and then divide by the number of cubic feet in a bag of quickrete.

First, you can convert the volume of the tube to cubic feet by dividing by 1728 (the number of cubic inches in a cubic foot): V = 235.61 inches^3 / 1728 inches^3/ft = about 0.14 cubic feet.

Then, you can divide this volume by the number of cubic feet in a bag of quickrete to find the number of bags you need: 0.14 cubic feet / (1 cubic foot / 30-40 bags) = about 4-5 bags.

So, it will take between 4 and 5 bags of quickrete to fill the tube.

Answer:

as you can see on the picture, they both have same rectangle

1st figure is i divide it by 2 and shade 1 to get 1/2

2nd figure is I divide it by 5 and shade 2 to get 2/5

if we use LCD:

1/2 will become 5/10

2/5 will become 4/10

Option (e) SE(u(x)) = 1 is incorrect about the sample correlation coefficient between two random variables X and Y based on a set of bi-variate points (X i , Yi )

The examination of the relationship between two variables is possible using bivariate analysis, which also has many real-world applications. It seeks to determine whether there is a link between the variables and how strong it is.

You can examine an association or causality hypothesis using bivariate analysis. It also aids in the prediction of dependent variable values based on changes in an independent variable.

The correlation coefficient (R) is a numerical value that ranges from -1 to 1. It reveals the strength of the linear relationship between the two specified variables.

The coefficient is referred to as Pearson's correlation coefficient when used to describe a linear regression.

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We can compute Amy's monthly budget for each question using division operations, as follows:

1. Amy's monthly budget for textbooks and course supplies is $100.

2. Amy's monthly budget for rent, utilities, and food is $1,422.

3. Amy's monthly budget for personal and miscellaneous costs is $251.

4. Amy's total monthly budget is $1,825.

The total monthly budget is the total budget divided by the period (nine months).

Division operations can be used to determine the individual monthly budgets for each expense class by dividing the total cost by 9.

Textbooks and Course Supplies =         $900      $100

Rent, Utilities, and Food =                   $12,798   $1,422

Personal & Miscellaneous Expense = $2,259     $251

Transportation =                                      $468       $52

Total non-tuition expenses =             $16,425  $1,825 ($16,425/9)

The number of months for the year = 9 months

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Liam can conclude that the price and monthly rate of both the gyms are equal.

Given, Lian is deciding which of two gyms to join. Each gym charges a monthly rate plus a one-time membership fee.

Lian correctly wrote and solved a system of linear equations by substitution to compare the costs of the memberships. In her work, she substituted an expression for one variable and solved for the other. This resulted in the equation 75 = 75.

we have to mention that what Lian can conclude,

As, substituting the first equation in the second one Liam got the price which is same in both the gyms.

So, Liam can conclude that the price and monthly rate of both the gyms are equal.

Hence, Liam can conclude that the price and monthly rate of both the gyms are equal.

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The values of x and y after solving this system of equations will be 32/35 and -88/105 respectively.

System of equations are a set of two or more equations that contain variables. The values of the variables can be calculated using either method of elimination or substitution. The values of the variables must then satisfy all the equations.

For a set of two equations, in elimination we make the coefficient of any one variable equal to the coefficient of the same variable in the other equation. This can be done by multiplying or dividing the whole equation accordingly. Then we subtract the equations from each other and solve for one variable.

6x - 3y = 8 (multiplying this equation by -2 to make the coefficient of y equal to that of in the equation 23x + 6y = 16)

Now are equations are

-12x + 6y = -16 and 23x + 6y = 16

subtracting eq 1 from eq 2 gives,

35x = 32 (Note that y has now been eliminated)

x = 32/35

Substituting this value of x in any one of the equations will then give the value of y to be -88/105

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Answer:

y = -  [tex]\frac{1}{4}[/tex] x - 1

Step-by-step explanation:

y = mx + b  

Slope:

The m is the slope in the equation.  Look at the two points given.  If you start at the point on the left, you go down 1 and 4 to the right.  1/4

Y-intercept:

The y intercept is the b.  It is where the line crosses the y axis.  It crosses at -1

Answer:

----------------------------------------

Slope- intercept form:

Use two points on the graph:

The first point is a y-intercept, b = - 1

Find the slope:

The line is:

The value of a in the diagram is 24°

a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

From the diagram the three angles of the triangle are a + 36, 3a, 2a

a + 36 + 2a + 3a = 180( sum of angles in a triangle is 180°)

6a + 36 = 180

6a = 180 - 36

6a = 144

a = 144/6

a = 24°

In conclusion the value of a is 24°

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Answer: 32% probability of going to the beach given the information provided in the weather forecast.

Step-by-step explanation:

The probability of going to the beach is equal to the probability of it not raining times the probability of going to the beach if it does not rain. Therefore, the probability of going to the beach is equal to (1 - 0.6) * 0.8 = 0.4 * 0.8 = 0.32.

Answer:

To find the weight of the plane with 77 gallons of fuel in its tank, we can use the linear equation for the weight of the plane in terms of the amount of fuel in its tank. The equation has the form:Weight = m * Fuel + bWhere m is the slope of the line, which is 5.9, and b is the y-intercept, which is the weight of the plane when the amount of fuel is 0. We know that the weight of the plane with 48 gallons of fuel is 2383.2 pounds, so we can use this information to solve for b:2383.2 = 5.9 * 48 + b

b = 2383.2 - 5.9 * 48

b = 2383.2 - 280.8

b = 2102.4Now that we have the value of b, we can plug it back into the equation to find the weight of the plane with 77 gallons of fuel:Weight = 5.9 * 77 + 2102.4

Weight = 456.3 + 2102.4

Weight = 2558.7 poundsSo the weight of the plane with 77 gallons of fuel in its tank is 2558.7 pounds.

Step-by-step explanation:

The equation of the verticallly-oriented ellipse is x²/4 + y²/25 = 1

The equation of a vertically-oriented ellipse centered at the origin with major axis y axis is given by

x²/b² + y²/a² = 1 where a > b

Given that the vertically-oriented ellipse centered at (0,0) with a full major y-axis length of 10 units and a full minor x-axis length of 4 units.

We have that the length of major axis 2a = 10

⇒ a = 10/2

⇒ a = 5

Also, the length of minor axis 2b = 4

⇒ a = 4/2

⇒ a = 2

So, given the equation of the vertically-oriented ellipse,

x²/b² + y²/a² = 1 where a > b

Substituting the values of the variables into the equation, we have that

x²/b² + y²/a² = 1 where a > b

x²/2² + y²/5² = 1

x²/4 + y²/25 = 1

So, the equation is x²/4 + y²/25 = 1

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After 3 seconds will it take for it to fall 112 feet.

What is distance?

Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

Given:

The distance s that an object falls varies directly with the square of the time, t , of the fall.

⇒ D = KT^2

Where D is the distance

T is the time

K is the proportionality constant

As an object falls 16 feet in one second.

⇒  D = 16, T = 1

⇒ 16 = K(1)^2

   16 = K

Therefore, the equation becomes

D = 16T^2

To find the how long will it take for it to fall 112 feet.

Here D = 112 feet

Plug D = 112 in the above equation.

112 = 16T^2

7 = T^2

T = √7

T = 2.65

T ≈ 3

Hence after 3 seconds will it take for it to fall 112 feet.

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The number of roots the polynomial equation 2x⁴ + 5x³ -3x² - 5 have is 4

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

2x^4+5x^3-3x^2-5

Express the polynomial expression properly using proper superscripts

So, we have the following representation

2x⁴ + 5x³ -3x² - 5

The degree of a polynomial is the number of roots in it

This means that

Degree = 4

So, we can conclude that the polynomial equation 2x⁴ + 5x³ -3x² - 5 has 4 roots

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The best course grade your friend can earn is 73.8% the minimum score would your friend would need on the final to earn a 75% for the course is 108%.

Given that,

Before the course's final exam, a friend had an 84% course average. Except for the final, which accounts for 15% of the course grade, everything else is included in that score.

We have to find what is your friend's best possible course grade and What grade on the final must your friend obtain in order to receive a 75% for the course.

We know that,

Best grade = (84%)(0.7) + (100%)(0.15)

Best grade=0.588+0.15

Best grade=0.738 or 73.8%

Now,

Let final = 15% of the grade

Let class work = (110%-15%)=95%

Let your friend minimum score =f

So,

70%(0.84) + 15%(final) = 75%

0.7(0.84) + 0.15f = 0.75

0.588 + 0.15f = 0.75

Collect like terms

0.15f=0.75-0.588

0.15f = 0.162

Divide both side by 0.15f

f=0.162/0.15

f =1.08 or 108%

Therefore, the best course grade your friend can earn is 73.8% the minimum score would your friend would need on the final to earn a 75% for the course is 108%.

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There are 125 participants in this sample. Thus, the margin of error = (1.96) x (0.5/√125) = 0.089

Margin of Error = (Critical value) x (Standard Deviation/Square root of Sample Size)

Critical value = 1.96

Standard Deviation = (30% x 70%)^0.5 = 0.5

Sample Size = 125

Therefore, Margin of Error = (1.96) x (0.5/√125) = 0.089

The margin of error for the survey results described can be calculated using the formula (Critical value) x (Standard Deviation/Square root of Sample Size). A 95% confidence interval's critical value is 1.96.The standard deviation is calculated by taking the square root of the product of the sample proportion (30%) and its complement (70%). There are 125 participants in this sample. Thus, the margin of error = (1.96) x (0.5/√125) = 0.089

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Answer:

h(t) - 94t + 129.

Step-by-step explanation:

Answer:

Step-by-step explanation:

First: You do PEMDAS.

Second: you do what in your parentheses

Answer: 11

Step-by-step explanation:

plug in x where eligible

4(11)-10 and 2(11)+12

both equal 34 and since a triangle's interior angles always equal 180 you can solve for the 3rd angle 32*2= 64 then 180-64= 116

The dimensions of the rectangular garden which minimize the cost is equal to 9.6ft and 14.6ft respectively.

As given in the question,

Cost of brick wall is equal to $40/ft

Cost of metal fencing is equal to $20/ft

Let 'x' and 'y' are the dimensions of the rectangular garden

Area of the rectangular garden = 142 square feet

⇒ 142 = xy

⇒x = 142/y

Costing of four side fencing 'C' = 40x + 20x + 20y + 20y

⇒ C = 60x + 40y

⇒C = 60(142/y) + 40y

⇒C = 8520/y + 40y

Differentiate with respect to y

dC/dy = -8520/ y² + 40

Put dC/dy = 0

-8520/ y² + 40 = 0

⇒y² = 8520/40

⇒y = √213

⇒ y= 14.6 ft

⇒ x= 142/14.6

     = 9.7 ft

Therefore, the dimensions of the rectangular garden with the given area which minimize the cost is equal to 14.6ft and 9.7ft.

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Simplifying an exponential equation can be done by using different laws of exponents.

In this case, we can use the power rule and negative exponent rule

Power rule:

[tex](a^x)^y=a^x^y[/tex]

Negative exponent rule:

[tex]a^-^y=\frac{1}{a^y}[/tex]

1. Use the negative exponent rule

[tex](10x^2)^-^3=\frac{1}{(10x^2)^3}[/tex]

2. Use the power rule and simplify

[tex]10^3=1000[/tex] and [tex](x^2)^3=x^6[/tex]

∴[tex]\frac{1}{1000x^6}[/tex]

Answer:

= 10x⁻⁶

Step-by-step explanation:

2*-3 = -6

then:

[tex]10x^{2^{-3}} = 10x^{-6}[/tex]

= 10x⁻⁶

a) The 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month is given as follows:

(747, 853).

b) The sampling error at the 95% confidence level is of: 35.8.

We have the standard deviation for the population is known, hence the z-distribution is used to calculate the confidence interval.

The equation that gives the bounds of the confidence interval is presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The remaining parameters are given as follows:

[tex]\overline{x} = 800, \sigma = 200, n = 55[/tex]

Then the lower bound of the interval is calculated as follows:

800 - 1.96 x 200/square root of 55 = 747.

The upper bound of the interval is calculated as follows:

800 + 1.96 x 200/square root of 55 = 853.

For a sample size of n = 120, the sampling error is obtained as follows:

Sampling error = 1.96 x 200/square root of 120 = 35.8.

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Answer: Two dimensions.

Straight sides.

Congruent (equal-length) sides.

An interior and exterior.

Equal interior angles.

Equal exterior angles.

Step-by-step explanation:

a) A dollar is 40% of four dimes.

b) 8% of a dollar is equal to 1 nickel and 3 cents.

c) A dollar is equal to 135% of 5 quarters and 1 dime.

A value or ratio stated as a fraction of 100 is known as a percentage in mathematics. Frequently, the percent symbol (%) or the abbreviation "pct" are used to indicate the percentage. The word "percent" derives from "percent," a contraction of "per centum," which meant per hundred.

1 dime equals 10 cents, as we all know. Thus, 4 dimes equal 40 cents. 4 dimes are consequently 40% of a $1.

We are aware that a nickel costs five cents and a penny one cent. Therefore, 8% of a dollar is equal to 1 nickel and 3 cents.

We are aware that a quarter equals 25 cents and a dime equals 10 cents. 5 quarters and 1 dime are therefore 135% of a dollar.

Therefore,

A dollar is 40% of four dimes.

8% of a dollar is equal to 1 nickel and 3 cents.

A dollar is equal to 135% of 5 quarters and 1 dime.

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The complete question is:

"What percentage of a dollar is the value of each coin combination?

a. 4 dimes

b. 1 nickel and 3 pennies

c. 5 quarters and 1 dime"