A triangle has a perimeter of 8x + 7. The first side of the triangle has a length of 4x, and the second side has a length of 2x − 3. What is the length of the third side of the triangle?

14x + 4
6x − 3
2x + 10
x + 10

Hello:

 --> this question asks for the 100th term

Let's us first write out a formula for an arithmetic term to calculate a nth term:

  [tex]\text{Formula: }a_n=a_1+(n-1)d\\\text{}[/tex]

     -a1: first term in the sequence                         --> -10

     -n: position of the [tex]a_n[/tex] term                                --> 100th term

     -d: common difference between each term --> -5

Let's plug in our values to calculate the 100th term:

  [tex]a_{100}=-10+(100-1)(-5)=-10+99*(-5)=-10+-495=-505[/tex]

Answer: - 505

The equation to represent the percent h the day he spent doing homework on Monday is [tex]\frac{h}{100} = \frac{3}{24}[/tex]

David spent 3 hours doing his homework on Monday. The equation that can be used  to find h, the percent of the day he spent doing homework on Monday can be found as follows:

We have 24 hours in a day. So, on Monday she uses 3 hours for her homework.

Therefore, the equation to represent the percentage h is as follows:

h = 3 / 24 × 100

h = 300 / 24

24h = 300

h = 300 / 24

h = 12.5%

Hence, the equation is as follows;

[tex]\frac{h}{100} = \frac{3}{24}[/tex]

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Answer:6.5 7.5

Step-by-step explanation:

I know you can do this if you need help you can contact me

Answer:

  (18π +4) cm ≈ 60.55 cm

Step-by-step explanation:

You want the perimeter of a figure bounded by two semicircles and a straight line segment.

The perimeter of the figure is the sum of the lengths of the curves and lines that form its boundary. Here, one boundary is a semicircle of diameter 16 cm, another boundary is a semicircle of diameter 20 cm, and a straight line forms the remaining boundary.

The length of a semicircle is half the circumference of a full circle of the same diameter:

  boundary length = 1/2(πd)

The smaller semicircle has a length of ...

  boundary length (small) = 1/2π(16 cm) = 8π cm

The larger semicircle has a length of ...

  boundary length [large] = 1/2π(20 cm) = 10π cm

The length of the line segment is the difference of the diameters:

  line segment length = (20 cm) -(16 cm) = 4 cm

The perimeter is the sum of these lengths:

  P = boundary length (small) + boundary length (large) + line segment length

  P = (8π +10π +4) cm = 18π +4 cm ≈ 60.55 cm

The perimeter of the figure is about 60.55 cm.

__

Additional comment

The perimeter is closer to 60.549 cm, so rounds to 60.5 cm.

Answer:

A- The point-slope form of a line parallel to another line is given by y - y1 = m(x - x1), where m is the slope of the original line. The slope of the line x+2y=6 is -1/2. So, the equation of the line parallel to x+2y=6 through (8,3) is y - 3 = -1/2 (x - 8), which can be written in standard form as -2x + y = -11.

B- The point-slope form of a line perpendicular to another line is given by y - y1 = -1/m(x - x1), where m is the slope of the original line. The slope of the line x+2y=6 is -1/2. So, the equation of the line perpendicular to x+2y=6 through (8,3) is y - 3 = 1/2 (x - 8), which can be written in standard form as 2x + y = 15.

C- To graph the three lines, we can plot the x- and y-intercepts of each line and then draw a line through the points.

The x-intercepts are (-11/2,0), (0,-15), (0,-11) and the y-intercepts are (0,3), (0,7.5) and (0,5.5) respectively.

For a more detailed graph you can use a graphing software or calculator.

0.53 is the probability of a patient being over 65, and 0.47 is the probability of a patient being under 65 and calculated as the sum of the probabilities of 0, 1, 2, 3, and 4 patients being over 65:

P(X < 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4).

a) The probability of exactly 9 out of 15 patients being over 65 can be calculated using the binomial distribution:

P(X=9) = (15 choose 9) * (0.53)^9 * (0.47)^6

where (15 choose 9) is the binomial coefficient, 0.53 is the probability of a patient being over 65, and 0.47 is the probability of a patient being under 65.

b) The probability of less than 5 patients being over 65 can be calculated as the sum of the probabilities of 0, 1, 2, 3, and 4 patients being over 65:

P(X < 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)

Therefore, 0.53 is the probability of a patient being over 65, and 0.47 is the probability of a patient being under 65 and calculated as the sum of the probabilities of 0, 1, 2, 3, and 4 patients being over 65:

P(X < 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4).

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0.53 is the probability of a patient being over 65, and 0.47 is the probability of a patient being under 65 and calculated as the sum of the probabilities of 0, 1, 2, 3, and 4 patients being over 65:

P(X < 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4).

a) The probability of exactly 9 out of 15 patients being over 65 can be calculated using the binomial distribution:

P(X=9) = (15 choose 9) * (0.53)^9 * (0.47)^6

where (15 choose 9) is the binomial coefficient, 0.53 is the probability of a patient being over 65, and 0.47 is the probability of a patient being under 65.

b) The probability of less than 5 patients being over 65 can be calculated as the sum of the probabilities of 0, 1, 2, 3, and 4 patients being over 65:

P(X < 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)

Therefore, 0.53 is the probability of a patient being over 65, and 0.47 is the probability of a patient being under 65 and calculated as the sum of the probabilities of 0, 1, 2, 3, and 4 patients being over 65:

P(X < 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4).

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Simplest radical form is x = [tex]\sqrt{7}[/tex]/30 Simply put, the algebraic statement or number in its radical form.

Explanation:

x = [tex]\sqrt{7}[/tex]/30.            

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Answer:

x = -13

Step-by-step explanation:

Multiply:

1x+16=31

+16=3

Subtract them

x+16=3

+16 - 16 = 3 - 16

Simplifying:

x+16−16=3−16

x = 3 - 16 =

-13.

Answer x = - 13

Good or bad?

The system of equations models is

x=4+3y

x+y=24

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Batman  obstacles  = x

Superman obstacles  = y

Batman completed 4 more than three times

the number of obstacles that Superman

completed.

=> x=4+3y

. They completed a total of 24

obstacles.

=> x+y=24

The system of equations models is

x=4+3y

x+y=24

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The area of the shaded region is 42cm².

Here we have the side of the square as 7 + 7 = 14cm

We know that the area of the square formula is a² and the area of the quadrant is πr²/4.

We can now subtract the area of the square from the area of the 4 quadrants, and we get

Area of shaded region = Area of the square – Area of 4 quadrants.

                                      = (7)² - 4× π(7)²/4

We can now solve the above steps, we get

Area of shaded region = 14×14 - 22/7 ×7×7 = 196-154 = 42cm².

The location is the degree of a place's size on a floor. The area of a plane vicinity or aircraft region refers to the place of a shape or planar lamina, even as floor area refers back to the location of an open surface or the boundary of a 3-dimensional object. The place may be understood as the amount of fabric with a given thickness that could be vital to fashion a model of the form or the amount of paint necessary to cover the floor with an unmarried coat. it's far the two-dimensional analog of the period of a curve (a one-dimensional concept) or the extent of a solid (a three-dimensional concept).

There are several well-known formulations for the areas of easy shapes including triangles, rectangles, and circles. using these formulas, the location of any polygon may be observed by means of dividing the polygon into triangles. For shapes with curved boundaries, calculus is typically required to compute the location. certainly, the trouble of figuring out the location of aircraft figures changed into a prime motivation for the ancient improvement of calculus.

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If the Zip line is from top of the 130 feet building and to the top of 30 feet building , then the estimated length of Zip Line is (a) about 123.2 ft .

The height of the bigger building is = 130 feet ;

the height of the shorter building is = 30 feet ;

the distance between the two buildings is = 72 feet ,

let the length of the zip line be =  x feet ;

the given situation form as right triangle , where the Zip length is represented by the hypotnuse , the base is 72 feet , and the perpendicular side is = 130 - 30 = 100 ft ;

By Pythagoras Theorem ,

we get ;

⇒ [tex]x^{2} = 100^{2} +72^{2}[/tex] ;

⇒ [tex]x^{2} = 10000 +5184[/tex] ;

⇒ [tex]x^{2} = 15184[/tex]

⇒ [tex]x = \sqrt{15184}[/tex] , the value is approx. 123.2233  .

Therefore , the estimated length of the zip line is 123.2 feet .

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The time taken for a train distance 100 m long to pass a specific telegraph at a speed of 36 km/h is 11.11 seconds.

Distance = 100 m

Speed = 36 km/h

Convert km/h to m/s = (36 km/h) * (1000 m/1 km) * (1 h/3600 s) = 10 m/s

Time = Distance/Speed = 100 m/10 m/s = 11.11 s

The time taken for a train 100 m long to pass a specific telegraph at a speed of 36 km/h can be calculated by using the formula Distance/Speed. First, we need to convert the speed in km/h to m/s. This can be done by multiplying the speed in km/h with 1000 m/1 km and then with 1 h/3600 s. The resulting speed in m/s is 10 m/s. Then, we can calculate the time taken by the train to pass the telegraph by dividing the distance (100 m) by the speed (10 m/s). This yields a time of 11.11 seconds. Thus, a train 100 m long at a speed of 36 km/h will take 11.11 seconds to pass a specific telegraph.

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The volume of an an office cubicle measures 7 feet by 8 feet with a 5 feett wall is 280 cubic feet.

What is Geometry?

It deals with the dimensions, regions, and densities of the various 2D and 3D shapes.

2D shapes

Flat geometry is a subset of 2D shapes, which comprises flat shapes like squares, circles, and triangles. These forms simply have two dimensions: length and width.

3D shapes

3D shapes are solid figures or objects with three dimensions—length, breadth, and height—that are referred to as three-dimensional shapes. In contrast to two-dimensional shapes, three-dimensional shapes include thickness or depth.

A five-foot wall separates an office cubicle's seven by eight feet of space.

Then the volume of the cubicle office will be

The volume is given as

Volume = length x width x height

We have

Volume = 7 x 8 x 5

Volume = 280 cubic feet

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The building is 141 cm tall when a pole that is 3.1 m tall casts a shadow that is 1.68 m long.

What is ratio ?

ratio can be defined as the given value divided by the total value, called as the ratio.

Given,

A pole that is 3.1 m tall casts a shadow that is 1.68 m long.

At the same time, a nearby building casts a shadow that is 48.25 m long

to solve this, use proportions. The height of the pole corresponds to the height of the building; the shadows are corresponding:

3.1/ x = 1/45.5

x = 3.1* 45.5

x = 141.05

Hence, the building is 141 cm tall when a pole that is 3.1 m tall casts a shadow that is 1.68 m long.

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Answer: To calculate the time it will take Donald Duck to travel from Disneyworld to Antarctica in his super-advanced car, we need to know the distance and the speed of the car. In this case, the distance is 8,563 miles and the speed is 800 mph.

We can use the equation:

Time = Distance / Speed

Where Time is measured in hours, Distance is measured in miles and Speed is measured in miles per hour.

We can plug in the values for distance and speed into the equation:

Time = 8,563 / 800

Time = 10.70375

So, it will take Donald Duck approximately 10.70375 hours to travel from Disneyworld to Antarctica in his super-advanced car, traveling at 800 mph the entire trip.

Step-by-step explanation:

Option B is Correct. Determine the number of solutions to a quadratic equation using the discriminant, b^2-4ac. We utilise the condition as follows for a quadratic equation of the form ax^2+bx+c=0.a=0. There is only one solution to the equation if b^2 - 4ac = 0.

Keeping in mind that a, b, and c are the coefficients of your quadratic in standard form, the discriminant is calculated using the formula b squared minus 4ac. It reveals how many possible answers there are to a quadratic problem.

There are two solutions if the discriminant is bigger than zero. The square root's input (i.e., its contents), which is the phrase b^2 = 4ac, is known as the "discriminant" because using its value, you may "discriminate" between (i.e., be able to distinguish between) the different solution types.

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Yes, Y = 2x + 1 is a linear function.

A linear function is a function whose graph is a straight line. The equation of a linear function is of the form y = mx+  b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). The graph of a linear function is a straight line, the slope of the line is constant, and the y-intercept is a single point.

Y = 2x + 1 is a linear function because it is in the form y = mx + b, where m is the slope of the line which is 2 and b is the y-intercept which is 1. This means that the slope of the line is 2 and the y-intercept is (0,1).

So the graph of this function will be a straight line and it will pass through the point (0,1).

Therefore, Y = 2x + 1 is a linear function.

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The zeroes of the given quadratic equation will be ±11i.

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given quadratic equation is 2x² + 18 - 2 = 6 - 12. The equation can be solved as:-

2x² + 18 - 2 = 6 - 12.

2x² + 16  = -6

2x² + 22 = 0

x² + 11 =0

x²  = - 11

x = √-11

x = ±11i

Hence, the solution of the quadratic equation is x = ±11i.

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Answer:

94

Step-by-step explanation:

The sum of all angles in a trapezoid is 360 degrees

Therefore,

x = 360 - 130 - 87 - 49

x = 94

Answer:

didn't I helped you out with that question?

The solution to the given linear inequality is given in the graph.

What is linear inequality?

Inequality denotes a mathematical expression in which neither side is equal. An inequality occurs when a connection produces a non-equal comparison between two expressions or two integers.

The equal sign "=" in the phrase is substituted by any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to a symbol (≥), less than or equal to a symbol (≤), or not equal to a symbol (≠).

In mathematics, there are three types of inequalities: polynomial inequalities, rational inequalities, and absolute value inequalities.

The symbols "< and '>' represent strict inequalities, whereas  ‘≤’ and ‘≥’ represent slack inequalities.

A linear inequality appears to be a linear equation, however, there is a difference in the formula.

Graph for |2x + 2| ≤ 6 is in the image attached below.

Hence, The solution to the given linear inequality is given in the graph.

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The roots of equation 2x² -5x +3 = 0 are 3/2 or 1.

Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term. Quadratic equations are another name for it. The general form of the quadratic equation is:  ax² + bx + c = 0,

where x is an unknown variable and a, b, c are numerical coefficients.

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics.

Given that,

2x² -5x +3 = 0

=> 2x² -2x - 3x +3 = 0 = 0

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

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

x = 3/2 or 1 are the two roots of the equation.

Thus, The roots of the equation 2x² -5x +3 = 0 are 3/2 or 1.

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Answer:  I do believe the answer is p=12

2/3 = 8/p

3p. 2/3 = 3p. 8/p

Using Pascal's triangle the expansion of the expression [tex](5x+5)^3[/tex] is [tex]125x^3+375x^2+375x+125[/tex].

What is Pascal's triangle?

The triangle can be used to calculate the coefficients of the expansion of  [tex](a+b)^n[/tex] by taking the exponent n and adding 1. The coefficient will correspond with line n+1 of the triangle.

Here for [tex](5x+5)^3[/tex] , n= 3 so the coefficient of the expansion will correspond with line 4.

The expansion follow the rule ,

[tex](a+b)^n=c_{0}a^nb^0+c_{1}a^{n-1}b^1+c_{n-1}a^1b^{n-1}+c_{n}a^0b^n[/tex]

The values of the coefficients, from the triangle, are 1-3-3-1.

=> [tex]1a^3b^0+3a^2b+3a^1b^2+1a^0b^3[/tex]

Here substitute a=5x and b=5 then,

=> [tex]1(5x)^35^0+3(5x)^25+3(5x)^25^2+1(5x)^15^3[/tex]

=> [tex]125x^3+375x^2+375x+125[/tex]

Hence the expansion of the expression [tex](5x+5)^3[/tex] is [tex]125x^3+375x^2+375x+125[/tex].

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Answer:

y = 6

Step-by-step explanation:

the total horizontal length of the figure ( base ) is 16

the 2 horizontal lengths of 5 and 5 are then subtracted from 16 to give the length of y , that is

y = 16 - 5 - 5 = 16 - 10 = 6

The probability that the sample mean time is up to 24.4 minutes is 0.97725.

The probability that the sample mean time is up to 24.4 minutes is calculated using the central limit theorem.

According to the central limit theorem, the sample mean of a random variable, in this case the time a student spends traveling to school, will be approximately normally distributed for large sample sizes, regardless of the distribution of the underlying variable. Since the sample size of 100 students is considered large, we can assume that the sample mean time will be normally distributed.

The mean of the sample mean time is equal to the population mean, which is 22 minutes, and the standard deviation of the sample mean is equal to the population standard deviation divided by the square root of the sample size, which is 12 minutes / sqrt(100) = 1.2 minutes.

So, the probability that the sample mean time is up to 24.4 minutes can be calculated using the standard normal distribution table or using a calculator that can calculate the probability of a standard normal distribution (or Z-score).

Using the standard normal distribution table or calculator, we can find that the Z-score for 24.4 minutes is

z = (24.4 - 22) / 1.2

z = 2

The probability that a Z-score is less than or equal to 2 is 0.97725.

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The distance of the grain bin is 40 feet if the radius is 20 feet.

A cylinder is a three-dimensional figure that has a radius and a height.

The volume of a cylinder is given as:

Example:

The volume of a cup with a height 5 cm and a radius 2 cm is

Volume = 3.14 x 2 x 2 x 5 = 62.8 cubic cm

We have,

The grain bin is similar to the shape of a cylinder.

Radius = 20 feet

The distance of the grain bin = Diameter of the grain bin

Now,

Diameter = 2 radius

= 2 x 20

= 40 feet

Thus,

The distance of the gain bin is 40 feet.

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The six trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

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 trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.

sine: Sine of an angle is defined as the ratio of the side opposite(perpendicular side) to that angle to the hypotenuse.

cosine: Cosine of an angle is defined as the ratio of the side adjacent to that angle to the hypotenuse.

tangent: Tangent of an angle is defined as the ratio of the side opposite to that angle to the side adjacent to that angle.

cosecant: Cosecant is a multiplicative inverse of sine.

secant: Secant is a multiplicative inverse of cosine.

cotangent: Cotangent is the multiplicative inverse of the tangent.

Thus, The six trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

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(a), The equation of the line that is perpendicular to this line and passes through the point (7, 6) is y = 7/8x - 1/8.

(b), The equation of the line that is parallel to this line and passes through the point (7, 6) is y = -8/7x - 1/8

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the equation is -8x - 7y = 1.

a) For perpendicular lines the slope will be inverse and opposite of the given equation.

y = mx + c

-8x - 7y = 1.

y = -8/7x - 1/7

The equation can be written as,

y = -8/7x - 1/7

6 = ( 7/8 ) x ( 7 ) + c

c = ( -1 / 8 )

The equation can be written as,

y = 7/8x  - 1/8.

b) For the parallel lines the slope will remain the same,

y = -8/7x - 1/7

y = -8/7x + c

6 = (-8/7 x 7 ) + c

c = 6 + 8

c = 14

The equation can be written as,

y = (-8/7)x + 14

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After simlplify of ^8sqrt200-^3sqrt162 is  53[tex]\sqrt{}[/tex] (2)

Simply factoring out any perfect squares from the radicand, shifting them to the left of the radical symbol, and keeping the other factor inside the radical symbol is the simplest way to simplify a square root. Once you write down the number's root, the radical sign will vanish if it is a perfect square.

Write the radicand in exponential form after factoring: 8 10 angle *2 angle *2 sqrt(9)

Put the following phrase in Vaba b:

8√102 × √√2-3√92 × √2 X

Reduce the radical's complexity: * 10sqrt(2) (2) - 3 * 9sqrt(2) (2)

Change the wording to:

(8 x 10) × √2 (3 × 9) × √2 -

Determine the quotient or product: 80square(2) - (3 * Nine) Square (2)

Determine the quotient or product. 80sqrt(2) - 27sqrt(2) (2)

combining similar terms 53sqrt(2)

Response: 53[tex]\sqrt{}[/tex] (2)

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