the points (16, 12) and (12, 9) fall on a particular line. what is its equation in slope-intercept form?

Answer:

Below

Step-by-step explanation:

The area is just the two side lengths multiplied together

area = (4x+13)(5x-2) = 20x^2 +57x -26   units^2

Answer:

x = 3 or x = -1/2

Step-by-step explanation:

Solve for x:

2 x^2 - 5 x - 3 = 0

The left hand side factors into a product with two terms:

(x - 3) (2 x + 1) = 0

Split into two equations:

x - 3 = 0 or 2 x + 1 = 0

Add 3 to both sides:

x = 3 or 2 x + 1 = 0

Subtract 1 from both sides:

x = 3 or 2 x = -1

Divide both sides by 2:

Answer: x = 3 or x = -1/2

The amount of money in the account after 14 years is $20248.59

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

Also from the question, we have

V = Pe^{rt}

Where

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

V = 8620 * e^(6.1% * 14)

Evaluate the products

So, we have the following representation

V = 8620 * e^(0.854)

Evaluate the exponent

So, we have the following representation

V = 8620 * 2.34902418149

Lastly, evaluate the products

So, we have the following representation

V = 20248.5884444

Approximate

V = 20248.59

This means that the value after 14 years is $20248.59

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In Japan, the average cost is $17.61 and in Switzerland, the average cost is $13.55.

An equation is a relationship between two or more variables expressed in equal to form. The equation of two variables look like ax + by=c. It is solved to find the value of variables.

According to the question, the equation are as under:

3x+2y=79.93----------------1

2x+3y=75.87 ----------------2

Multiply equation 1 by 2 and equation 2 by 3 and subtract the result from equation 2 from the result coming from equation 1.

6x+4y=159.86

6x+9y=227.61

Subtracting

6x+4y-6x-9y=159.86-227.61

-5y=-67.75

y=13.55

Put the value of y=13.55 in 3x+2y=79.93

3x+2(13.55)=79.93

3x+27.10=79.93

3x=79.93-27.10

3x=52.83

x=52.83/3

x=17.61

Hence the average cost in Japan is $17.61 and the average cost in Switzerland is $13.55.

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Answer: 40

Step-by-step explanation:

Answer: 20

Step-by-step explanation:
5x^2

5 ( 2 )^2 (substituting the value of x)

5 ( 2 x 2) (working out the exponents of x)

5 (4) (solving the brackets)

20

Answer: 0.6

Step-by-step explanation:

9/15 = 0.6

$9 / 15 cookies = $0.6 cents per cookie

Noah is using the 50/30/20 budgeting money management strategy

What is money management?

Money management in mathematics is the application of mathematical principles and techniques to the management of personal or corporate money. It entails the use of mathematical tools like equations, graphs, and statistics to analyse financial data and make educated decisions about budgeting, saving, investing, and spending. Mathematicians also use probability and risk analysis to manage money by estimating the likelihood of different financial events and making decisions based on the benefits and dangers of various financial options. Overall, mathematicians' understanding of money management enables people and organisations to better manage their financial resources and reach their financial objectives.

Noah is using the 50/30/20 budgeting money management strategy because he is using 50% of his income for his basic needs, 30% for entertainment, and 20% for savings and debt repayment.

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Answer:

Questions and answers

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Question

The perimeter of a shape is 25.71 cm calculate the value of the radius X takes pie to be 3.142

Answer · 15 votes

Answer:5 cmStep-by-step explanation:Given a semicircle with perimeter 25.71 cm, we are required to find the radius of the circle.Circumference of a Semicircle=Length of the Circular part+Length of the diameter[tex]=\pi r+2r[/tex][tex]If \: \pi=3.142, C=25.71\Then:\25.71=3.142r+2r (3.142+2)=25.71\5.142r=25.71 =25.71 \div5.142 =5cm[/tex]

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Question

The perimeter of the semicircle is 25.71 cm. Calculate the value

Answer:

- 2

Step-by-step explanation:

the factors of a difference of square are

a² - b² = (a + b)(a - b)

(1 + [tex]\sqrt{3}[/tex] )(1 - [tex]\sqrt{3}[/tex] ) ← are the factors of a difference of squares , then

(1 + [tex]\sqrt{3}[/tex] )(1 - [tex]\sqrt{3}[/tex] )

= 1² - ([tex]\sqrt{3}[/tex] )²

= 1 - 3

= - 2

Reject the null hypothesis because [tex]$p$[/tex]-value [tex]$=0.0045$[/tex] is less than the Significance level x=0.025.

The null hypothesis is a widely used statistical theory that states that for any given single observable variable, there is no statistical relationship or significance between any two sets of observed data and measured events.

According to the given information

[tex]& H_0: \mu=57 \\[/tex]

[tex]& H_a ; \mu > 57 \\[/tex]

[tex]& \alpha=0.025 \\[/tex]

[tex]& \text { Test Statistic }=2.61[/tex]

So,

This is right tailed test

[tex]& \text { Using } z \text { table } \\[/tex]

[tex]& p(z > 2.61) \\[/tex]

[tex]&= 1-p(z < 2.61) \\[/tex]

[tex]&= 1-0.9955 \\[/tex]

[tex]& p \text {-value }= 0.0045[/tex]

Reject the null hypothesis because [tex]$p$[/tex]-value [tex]$=0.0045$[/tex] is less than the Significance level x=0.025.

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The correct answer is boosting.

Given that,

The four tree-based techniques are boosting, bagging, random forests, and decision trees. Which method uses bootstrapped samples, or the process of repeatedly obtaining random samples from training data and replacing them?

Boosting is an emsemble machine learning approach, where we use bootstrapping sampling technique to get the required samples. It helps in the reduction of variance and thus bring in less bias in the sampling approach. Therefore boosting is the correct answer here.

In order to gather the necessary samples for boosting, we employ the bootstrapping sampling technique. It aids in lowering variance, which reduces bias in the sampling strategy. Thus, boosting is the appropriate response in this case.

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The value of (1 + i)^8 is 16. De Moivre's describes how the power of a complex number can be calculated using the properties of its modulus and argument.

De Moivre's theorem states that for any complex number z = r * (cos(θ) + i * sin(θ)) and any integer n, we have:

zⁿ = rⁿ * (cos(n * θ) + i * sin(n * θ))

To use this theorem, we need to first express the complex number (1 + i) in terms of its magnitude and angle. We can do this by using the Pythagorean theorem to find the magnitude of the complex number, which is the square root of the sum of the squares of the real and imaginary parts.

In this case, the magnitude is the square root of 1^2 + 1^2, or √2.

The angle of the complex number can be found using the inverse tangent function. In this case, the angle is 45 degrees, since the tangent of 45 degrees is 1. Now that we have the magnitude and angle of the complex number, we can use De Moivre's theorem to find the value of (1 + i)^8. Substituting the values we found into the formula above, we get:

(1 + i)^8 = √2^8 * (cos(8 * 45) + i * sin(8 * 45))

        = 2^4 * (cos(360) + i * sin(360))

        = 16 * (1 + i * 0)

        = 16

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Answer:

d. [tex]5x^3[/tex] is a monomial

Step-by-step explanation:

⭐What is a monomial?

D is correct because the expression [tex]5x^3[/tex] consists of 1 term only.

⭐What is a linear polynomial?

⭐What is the degree of a polynomial?

A is incorrect because the largest exponent in the expression [tex]x^2 + 5x -3[/tex] is 2, which makes expression A a quadratic polynomial.

⭐What is a binomial?

B is incorrect because the expression [tex]x^2 + 4x - 1[/tex] consists of 3 terms, not 2 terms. B is a trinomial.

C is incorrect because the expression [tex]x+1[/tex] consists of 2 terms, not 1 term. C is a binomial.

⭐if this response helped you, please mark it the "brainliest"!⭐

Answer:

x = 65 degrees

Step-by-step explanation:

Let's say z=the angle adjacent (next to) to the 145 degrees angle.

80 + x + z = 180  ==> 180 is the total number of degrees in a triangle

z + 145 = 180  ==>   In addition, if you add up Angle z and 145

                               degrees, you get a straight line which totals to 180

                               degrees

z + 145 - 145 = 180 - 145  ==> solve for z

z = 35 degrees

80 + x + z = 180

80 + x + 35 = 180  ==> plug in 35 for z

80 + 35 + x = 180

115 + x = 180  ==> solve for x

115 - 115 + x = 180 - 115 ==> simplify

x = 65 degrees

Answer:

(1, -1)

Step-by-step explanation:

we isolate y in the first equation

2x+y=1

-2x.  -2x

y=1-2x

and now we fill y into second equation

4x-2(1-2x)=6

4x-2+4x=6

8x-2=6

   +2 +2

8x=8

/8 /8

x=1

and now to find y we insert x

2(1)+y=1

2+y=1

-2.   -2

y= -1

hopes this helps

Step-by-step explanation:

The spherical and Cartesian coordinates are related by the equations,

x = ρ sin(φ) cos(θ)

y = ρ sin(φ) sin(θ)

z = ρ cos(φ)

Here, x, y and z represent the coordinates of the center of the sphere on x, y and z axes respectively.

Now, multiply the given surface equation by ρ.

ρ² = ρsin(θ) sin(φ)

We have, ρ² = x² + y² + z².

Substitute this value in above equation and also replace the RHS by y coordinate.

x² + y² + z² = y

Now, simplify the above equation.

x² + y² - y + z² = 0

x² + y² - 2y½ + (1/2)² + z² = (1/2)²

x² + (y - 1/2)² + z² = (1/2)² ...(1)

The general form of equation of sphere is,

(x - a)² + (y - b)² + (z - c)² = r²

Here, a, b, c are the coordinates of the center of the sphere on x, y, z axes respectively and r is the radius of the sphere.

Compare equation (1) with the general form of equation of sphere. Therefore we get,

Therefore, the radius of the sphere is 1/2 and center of sphere is at (0, 1/2, 0).

Thus, The given equation represents - a sphere of radius 1/2 centers at (0, 1/2, 0).

The solution for the expression 2^(x) − 2^(−x) = 5 is x = log2(10)

Substitute 2^(−x) for 5 and solve for x, which is log2(10).

The given expression ,

2^(x) − 2^(−x) = 5

2^(x) = 5 + 2^(−x)

2^(2x) = (5 + 2^(−x))^2

2^(2x) = 25 + 10*2^(−x) + 2^(−2x)

25 + 10*2^(−x) + 2^(−2x) = 2^(2x)

25 − 2^(2x) = 10*2^(−x) − 2^(−2x)

25 − 2^(2x) = 10*2^(−x) − 2^(−2x) + 2^(2x)

25 = 10*2^(−x) + 2^(2x) − 2^(−2x)

25 = 10*2^(−x) + 2^(−2x) (2^(2x) - 2^(−2x))

25/(2^(−2x) (2^(2x) − 2^(−2x))) = 10*2^(−x)

25/(2^(2x) − 2^(−2x)) = 10*2^(−x)

2^(x) = 10

x = log2(10)

Substitute 2^(−x) for 5 and solve for x, which is log2(10).

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The length of the Antenna will be;

⇒ h = 18 meters

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

Tyler is 1.8 meters and his shadow is 6 meters.

And, Tyler is standing 54 meters from the antenna.

Now,

Since, Tyler is 1.8 meters and his shadow is 6 meters.

And, Tyler is standing 54 meters from the antenna.

Let the length of the Antenna = x

Hence, We get by definition of proportional, we get;

⇒ 1.8 / 6 = h / (54 + 6)

⇒ 0.3 = h / 60

⇒ h = 0.3 × 60

⇒ h = 18 meters

Thus, The length of the Antenna will be;

⇒ h = 18 meters

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The value of angle x in the triangle is 130 degrees

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

Lines = parallel lines

Shapes = Triangles

By the alternate interior angle, the third angle in the bottom triangle has the  same measure as 60 degrees

This means that

x = 70 + 60 -- by the alternate exterior angle throrem

Evaluate the sum

x = 130

Hence, the value of x is 130

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The circumference of a circle with a radius of 11 is 68.1

The route or boundary that encircles any shape in mathematics is defined by the shape's circumference. In other terms, the circumference is also known as the perimeter, which aids in determining how long a shape's outline is.

The formula to calculate the circumference of a circle is C=2[tex]\pi[/tex]r where r is the radius of the circle.

The problem tells us that r= 11, substituting that in the equation and solving:

C=2[tex]\pi[/tex]r =2[tex]\pi[/tex](11) = 22[tex]\pi[/tex]

The value of [tex]\pi[/tex] is approximately 3.14, putting the value of  [tex]\pi[/tex] in the equation:

C= 22(3.14) = 68.08→ 68.1

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The number of the students in the sixth grade will be 132 students.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The proportion of sixth and seventh graders is 11 to 9. In the event that there were 108 seventh graders.

The ratio of the number of students in the sixth and seventh will remain constant.

Let 'x' be the number of students in sixth grade. Then the equation is given as,

x / 108 = 11 / 9

Simplify the equation, then we have

x / 108 = 11 / 9

x = 108 × 11 / 9

x = 12 × 11

x = 132

The number of the students in the sixth grade will be 132 students.

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Answer: 74

Step-by-step explanation:

Answer:

74

Step-by-step explanation:

Got it right on the test.

The number of people died from aids in U.S. in 2005 are 2,30,68,96,671

Given, diseases tend to spread according to the exponential growth model.

In the early days of aids, the growth factor (i.e. common ratio; growth multiplier) was around 1.9.

In 1983, about 1700 people in the U.S. died of aids.

we have to find the number of people died from aids in 2005.

Let the exponential function, be

P(x) = AB^x

where, A is the initial population of people died of aids in U.S.

B is the growth factor of aids in U.S.

as, B = 1.9

In 1983, x = 0

P(0) = AB^0

1700 = A

Now, P(x) = 1700(1.9)^x

and the number of years from 1983 to 2005 are, 22 years

The number of people died from aids in 2005 be,

P(22) = 1700(1.9)^22

P(22) = 2,30,68,96,671

So, 2,30,68,96,671 people died from aids in 2005.

Hence, 2,30,68,96,671 people died from aids in 2005.

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The distance of the reaction as Jerry drives at a rate of 35 mph is 11.73 m.

Distance is the total movement of an object without any regard to direction.

To calculate the approximate reaction distance, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitiute these values into equation 1

Hence, the distance of the reaction is 11.73 m.

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The percent increase of the trees is 50%

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

Initial = 2 feet

Final = 3 feet

The percent increase can then be calculated using

Percentage increase = (Final length - Initial length)/Initial length * 100%

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

Percentage increase = (3 - 2)/2 * 100%

Evaluate

Percentage increase = 50%

Hence, the percentage increase is 50%

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The smallest degree of rotation that will map a regular 16-agon onto itself is 22.5 degrees.

What is a degree?

A degree is a unit of measurement used to express angles. It is defined as 1/360th of a full rotation, or 1/2π radians.

To see this, note that a regular 16-agon has 16 sides, and each angle between sides measures 180(16-2)/16 = 135 degrees. Therefore, to rotate the 16-agon so that it maps onto itself, we must rotate it an integer multiple of 135 degrees.

However, we want the smallest such angle, so we must find the smallest integer multiple of 135 degrees that is greater than or equal to 360 degrees (since a full rotation maps the figure onto itself). The smallest such multiple is 2, which is equal to 270 degrees.

The smallest degree of rotation that will map the 16-agon onto itself is 270 degrees / 2 = 135 degrees / 2 = 22.5 degrees.

Hence, The smallest degree of rotation that will map a regular 16-agon onto itself is 22.5 degrees.

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Answer: $79.79

Step-by-step explanation:

First, take 899 divided by 100% = 8.99

Then take 8.99 times 8.875 = $79.79

Answer:

Below

Step-by-step explanation:

8.875 % is .08875 in decimal form:

899 * .08875 = 79.79 dollars

D) none of these choices are correct