Please read the photo

Answer:

To solve the system of equations graphically, you can plot the two lines on a coordinate plane and find the point where they intersect, which represents the solution to the system.

First, let's start by rewriting the equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

For the first equation:

3x + y = 15

y = -3x + 15

For the second equation:

3x - 4y = 0

y = (3/4)x

Next, we can plot these two lines on a coordinate plane by using any two points on each line and connecting them with a straight line.

Once the lines are plotted, we can find the point where they intersect, which represents the solution to the system. In this case, the solution is (2, 9), meaning that at x = 2 and y = 9, both equations are satisfied.

So, the solution to the system of equations is (2, 9), which means that the two lines intersect at the point (2, 9).

On solving the provided question, we cans ay that  in this triangle by Pythagorean theorem [tex]A^2 = B^2 + C^2[/tex] => AC = [tex]\sqrt{115}[/tex]

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here, in this triangle by Pythagorean theorem

[tex]A^2 = B^2 + C^2[/tex]

AC = [tex]\sqrt{14^2 - 9^2}[/tex]

AC  = [tex]\sqrt{196 - 81}[/tex]

AC = [tex]\sqrt{115}[/tex]

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Answer:

-1/3

Step-by-step explanation:

Yhe equation 6x^2 + x - 2 has two roots, alpha and beta, that can be found by using the quadratic formula or by factoring.

The sum of the roots (alpha and beta) can be found by using the formula:

-b/a

where a = 6, b = 1 and c = -2

-1/6

The product of the roots (alpha and beta) can be found by using the formula:

c/a

where a = 6, b = 1 and c = -2

-2/6 = -1/3

So, the sum of the roots is -1/6 and the product of the roots is -1/3.

The solution to the equation 2n + 5 = 6( n² - 5 ) is n = ( 1 - √(211 )) / 6 and n = ( 1 + √(211 )) / 6

Given the quadratic equation in the question;

2n + 5 = 6( n² - 5 )

First we simplify the given equation;

2n + 5 = 6( n² - 5 )

2n + 5 = 6n² - 30

6n² - 2n - 5 - 30 = 0

6n² - 2n - 35 = 0

To solve for n, we use the quadratic formula.

n = (-b±√(b² - 4ac)) / (2a)

Compare 6n² - 2n - 35 = 0 to the quadratic equation in its standard form an² + bn + c = 0.

Plug the values into the quadratic formula

n = (-b±√(b² - 4ac)) / (2a)

n = ( -(-2) ±√( (-2)² - 4 × 6 × -35 )) / (2 × 6 ))

n = ( 2 ±√( 4 + 840 )) / ( 12 )

n = ( 2 ±√( 844 )) / ( 12 )

n = ( 2 ±2√(211 )) / ( 12 )

n = ( 1 ± √(211 )) / 6

n = ( 1 - √(211 )) / 6 or n = ( 1 + √(211 )) / 6

Therefore, the values of n are ( 1 - √(211 )) / 6 and ( 1 + √(211 )) / 6.

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A. passenger train 36mph

B. freight train 18mph

What is meant by speed?

Speed is what it means. the speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Given that it just has a direction and no magnitude, speed is a scalar number.

Given that, A freight train departs from a train depot and let us consider it is travelling at an 'x' mph

and An hour later a passenger train departs the same train depot with a speed 'of x+18 mph.

After 2 hours the passenger train overtakes the freight train.

The total distance travelled by both trains when the passenger train overtakes the freight is equal.

Distance travelled by freight train = x*3

Distance travelled by passenger train = (x+18)*2

Now, 3x = 2x + 36

x = 18

and x + 18 = 36

Therefore, The speed of the passenger train and freight train are 36mph, and 18mph respectively

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The volume of the rectangular prism will be 270 cm³. The correct option is B.

The volume of the rectangular prism is defined as the space in three-dimension covered by the rectangular prism having the sides Length, Width, and Height.

The volume of the rectangular prism will be the multiplication of the three parameters which are Length, Width, and Height of the prism.

The volume will be calculated by the formula:-

Volume = L x W x H
Volume = 2 x 9 x 15

Volume = 270 cubic cm

The volume of the rectangular prism will be 270 cm³.

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The complete question is given below and the missing image is attached with the answer below.

A ringtoss toy is composed of a rectangular prism on top of a cylinder.

The rectangular prism is completely filled with water.

The dimensions of the rectangular prism are shown in the diagram.

What is the volume of the rectangular prism in cubic centimeters?

A) 26 cm3

B) 270 cm3

C) 165 cm3

D) 348 cm3

Answer: x =1, y = -1

Step-by-step explanation:

-10x+4y=-14

7x+5y=2

Let's eliminate y.

5(-10x+4y= -14)

4(7x + 5y=2)

[ I multiplied the first equation by the coefficient of y in the second equation and did the same in the second equation].

=> -50x+20y =-70

     28x+20y = 8

Notice how the coefficients of y are the same. We can subtract the 2 equations to eliminate y.

Thus,

-78x = -78 ( y has been eliminated)

∴ x=-78/-78 =1.

Put the value of x in any equation to find y.

7x + 5y =2

=> 7(1) + 5y =2

7+5y=2

5y = 2-7

5y = -5

y = -1.

Hope this helps :)

Check the picture below.

so the polygon is really just a 5x7 rectangle with a triangle that has a base of 7 units(vertically) and a height of 2 units.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{rectangle}{(5)(7)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(7)(2)}}\implies 35~~ + ~~7\implies \text{\LARGE 42}~units^2[/tex]

Answer:

The table that represents a linear function is:

x 0 1 2 3 4

y −2 1 0 1 −2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation: The linear function is a function that has a straight line when plotted on a

graph.

The correct option;

The table of ordered pairs that represent a linear function is the option; x/y  -8/-7  0/0  8/7  16/14

Reasons why the above selection is correct:

Given;

The given data can be presented as follows;

x/y -8/22 0/1 8/22 16/102

x/y -8/-7 0/1 8/9 8/2

x/y -8/-7 0/0 8/7 16/14

x/y -8/-7 0/1 8/5 16/4

Representation of the options in tabular form;

In a tabular format, we have;

Characteristic of linear function;

In a linear function, when the x-values have a constant rate of increase the

the first difference in the y-values is constant.

Selection of the table representing a linear function;

The option that has a constant first difference along with a continuous rate of

increase in the x-value is the option with the following table;

, which is the option x/y -8/-7 0/0 8/7 16/14

Rounding this to the nearest cent, the total amount that was wanted to be saved is $64.29.

To solve this problem, we can set up a proportion using the given information. Let x be the total amount that was wanted to be saved.

We know that the amount saved ($45) is 70% of the total amount that was wanted to be saved. Therefore, we can write:

45 = 0.7x

To solve for x, we can divide both sides by 0.7:

x = 45 ÷ 0.7

x = 64.28571429

The answer to the problem is $64.29, rounded to the nearest cent. This means that the total amount that was wanted to be saved was $64.29, and 70% of this amount is equal to the amount that was actually saved ($45). To check our work, we can multiply 64.29 by 0.7 to see if it equals 45. When we do this, we get:

64.29 x 0.7 = 45.003, which rounds to $45, so our answer is correct.

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The exponential function for the given table will be y=0.01(2)ˣ where x=positive integer.

What exactly are exponential functions?

An exponential function is a mathematical function with the formula f (x) = aˣ, where "x" is a variable and "a" is a constant that is termed the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most often used exponential function basis.

Growth that is exponential

The amount expands extremely slowly at first, then rapidly in Exponential Growth. The rate of change accelerates with time. As time passes, the pace of growth accelerates. The quick expansion is designed to represent a "exponential rise".

The exponential growth formula is: y = a (1+ r)ˣ, where r is the growth percentage.

Now,

as given in the table initial value = 0.01

and it is increasing into multiples of 2ˣ where x=positive integer

Then for the value of y for any value of x will be

y=0.01(2)ˣ where x=positive integer

Hence,

           The exponential function for the given table will be y=0.01(2)ˣ.

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The system of equations that correctly represents the situation of Lina and Sarika's ages are:

A system of equations is two or more equations solved concurrently or at the same time.

A system of equations is called simultaneous equations.

The sum of Lina and Sarika's ages = 31

Lina's age > Sarika's by 5 years

Let Lina's age = L

Let Sarika's age = S

L + S = 31... Equation 1

L - S = 5... Equation 2

2L = 36

L = 18.

Substituting L = 18 into either Equation 1 or 2:

18 + S = 31

S = 31 - 18

S = 13

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Answer: 57

Step-by-step explanation: I recommend learning angle properties, pictures on the internet might help ya out

(i) The probability that the bulb that lang selects will last exactly 9950 hours is 0.3085.

(ii) The probability that the bulb that lang selects will last at most 9950 hours is 0.5

(iii) The probability that the bulb that lang selects will last at least 9950 hours is 0.6915.

(iv) The probability that the bulb that lang selects will last less than 9000 hours or more than 11,500 hours is 0.0668

(v) The probability that the bulb that lang selected will last between 9000 hours and 11,000 hours, inclusively is  0.6826.

(vi) The life length represents the 95th percentile is 11,645

The lifespan of the Lights of America light bulb is normally distributed, with a mean of 10,000 hours and a standard deviation of 1000 hours. This means that the majority of bulbs will last around 10,000 hours, but there will be some that last longer or shorter than this.

(i) To find the probability that the bulb selected by Lang will last exactly 9950 hours, we need to use the normal distribution formula. We know that the mean is 10,000 hours and the standard deviation is 1000 hours. Using these values, we can calculate the z-score (standardized value) for 9950 hours.

z = (9950 - 10000) / 1000 = -0.5

Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. Therefore, the probability that the bulb will last exactly 9950 hours is 0.3085.

(ii) To find the probability that the bulb will last at most 9950 hours, we need to find the area under the normal curve to the left of 9950 hours. We can use the z-score formula to calculate the z-score for 9950 hours as we did in part (i).

z = (9950 - 10000) / 1000 = -0.5

Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. However, since we want the probability of the bulb lasting at most 9950 hours, we need to add the area under the normal curve to the left of -0.5, which is 0.3085 + 0.1915 = 0.5. Therefore, the probability that the bulb will last at most 9950 hours is 0.5.

(iii) To find the probability that the bulb will last at least 9950 hours, we need to find the area under the normal curve to the right of 9950 hours. We can use the z-score formula to calculate the z-score for 9950 hours as we did in part (i).

z = (9950 - 10000) / 1000 = -0.5

Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. However, since we want the probability of the bulb lasting at least 9950 hours, we need to add the area under the normal curve to the right of -0.5, which is 1 - 0.3085 = 0.6915. Therefore, the probability that the bulb will last at least 9950 hours is 0.6915.

(iv) To find the probability that the bulb will last less than 9000 hours or more than 11,500 hours, we need to find the areas under the normal curve to the left of 9000 hours and to the right of 11,500 hours, and add them together. We can use the z-score formula to calculate the z-scores for 9000 hours and 11,500 hours.

For 11,500 hours: z = (11,500 - 10,000) / 1000 = 1.5

Then the corresponding probability from Z table is written as,

=> 0.0668

(v) To find the probability that the bulb will last between 9000 hours and 11,000 hours, inclusively, we need to find the area under the normal curve between the z-scores for 9000 hours and 11,000 hours. We can use the z-score formula to calculate the z-scores for 9000 hours and 11,000 hours.

For 9000 hours: z = (9000 - 10,000) / 1000 = -1

For 11,000 hours: z = (11,000 - 10,000) / 1000 = 1

Using a standard normal distribution table or calculator, we can find the probability of a z-score of -1 (for 9000 hours), which is 0.1587, and the probability of a z-score of 1 (for 11,000 hours), which is 0.8413. Subtracting the area under the normal curve to the left of -1 from the area under the normal curve to the left of 1, we get the probability of the bulb lasting between 9000 hours and 11,000 hours inclusively, which is 0.8413 - 0.1587 = 0.6826.

(vi) To find the lifelength that represents the 95th percentile, we need to find the z-score that corresponds to the 95th percentile of the normal distribution. We can use a standard normal distribution table or calculator to find this value, which is approximately 1.645.

Using the z-score formula, we can solve for the life length that corresponds to a z-score of 1.645:

1.645 = (x - 10,000) / 1000

Multiplying both sides by 1000 and adding 10,000, we get:

x = 11,645

Therefore, the life length that represents the 95th percentile is 11,645 hours, which means that only 5% of bulbs will last longer than this value.

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Answer:

The required measure of Street K between Street C and D is 337.5 ft.

Step-by-step explanation:

have a nice day.

Answer:

CD = 36°

Step-by-step explanation:

the measure of secant angle BFE is half the difference of the measures of the intercepted arcs , that is

[tex]\frac{1}{2}[/tex] (BE - CD) = ∠ BFE

[tex]\frac{1}{2}[/tex] (128 - x) = 46 ( multiply both sides by 2 to clear the fraction )

128 - x = 92 ( subtract 128 from both sides )

- x = - 36 ( multiply both sides by - 1 )

x = CD = 36°

The approximate arc length of one slice of pic is 5.24 inches according to the circle circumference.

Let us assume that the pic is equally cut into 6 pieces. Also given that the diameter of the pie is 10 inches.

Diameter (D)=10.

So the radius will be D/2.

Radius (R)=10/2=5.

The pie's circumference is given by:

C=2πR

C=2π*5

C= 10π (in)

Because the pie is divided into six pieces, the circumference of the pie is divided into six equal-length arcs. So,

Length of Arc (L)= 10π/6

L = 5π/3

L= 5(3.14)/3

L=5.234=5.24

Therefore the approximate arc length of one slice of pie is 5.24 inches.

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Answer: .75 + .25x ≤ 7

Step-by-step explanation: The x equals the amount that you can buy for each item.

The slope of this line is 0.35, which represents the amount that the cost increases for each additional click.

What is equation of straight line ?

Equation of straight line can be as follows, y = mx +b

where m is a slope of line.

Given,

To find , The cost, C, in dollars for advertising on a social networking website is proportional to the number n] of clicks on the advertisement.

When a business is charged $108.50 for 310 clicks on its advertisements.

The cost, C, and number of clicks, n, are related by the equation

C = k * n, where k is the constant of proportionality.

From the given information, we know that C = $108.50 when n = 310. We can use this information to find the value of k:

$108.50 = k * 310

Solving for k:

k = $108.50 / 310

k = $0.35

So, the equation for the relationship between cost and clicks is:

C = $0.35 * n

Therefore, The slope of this line is 0.35, which represents the amount that the cost increases for each additional click.

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Answer:

$90

Step-by-step explanation:

180 - 50% or 180 x .50 = $90

The total volume of the space dome theatre is 41867 m³.

In geometry, a sphere is a three-dimensional solid figure, which is round in shape.

The surface area is 4πr².

The volume is (4/3)πr³.

The diameter is 2×radius of the sphere.

A cylinder is a three-dimensional solid object having two similarly circular bases that are joined by a curving surface that is positioned a certain distance from the center.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

Given, The space dome theatre has a base radius of 20m.

Therefore, The volume of the hemispherical dome is,

= (2/3)π(20)³.

= (2/3)π×8000.

= (16000/3)π m³.

And, As the dome base has a radius of 20 m the cylindrical shape will also have the same.

Therefore, The volume of the cylindrical shape is,

= π(20)²×20.

= 8000π m³.

And, The total volume is the sum of the volumes of two shapes,

= 8000π + (16000/3)π m³.

= [(24000 + 16000)/3]π m³.

= (40000/3)π m³.

= 41867 m³.

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Answer: 151 minutes

Step-by-step explanation:

95.40 - 35 =

60.40

60.40/.40 = 151

Answer:

A formula can help solve problems as it gives the person a step-by-step mini key or guide when needing to actually answer a mathematical or scientific equation or question.

The cost of each order of french Fries is $1.75.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Wendell purchased a hot dog and 3 orders of French fries for $6.00.

If the hot dog cost $2.25.

Then the cost of Hot dog

= 6 - 2.25

= 3.75

and, the cost of each order of French Fries

= 3.75 / 3

= $1.25

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Answer:

x = 3/85

Step-by-step explanation:

log2 (6) - log2 (5x) = log2 ( 34)

We can use the properties of logs.

First subtract log2 (6) from each side.

log2 (6) - log2 (5x) - log2 (6) = log2 ( 34)-log2 (6)

- log2 (5x)  = log2 ( 34)-log2 (6)

Now we know that log a - log b = log a/b

- log2 (5x)  = log2 ( 34/6)

- log2 (5x)  = log2 ( 17/3)

Multiply each side by -1

 log2 (5x)  = -log2 ( 17/3)

We know that  -log (a/b) = log ( b/a)

 log2 (5x)  = log2 ( 3/17)

The terms inside the logs must be the same

5x = 3/17

Divide each side by 5

5x/5 = 3/17 * 1/5

x = 3/85

The probability that there are 30 or fewer successes in 112 trials with a probability of 0.42 of success is  0.874763 rounding to 6 decimaiplaces.

To use the Excel spreadsheet programme to calculate the likelihood that 30 or fewer successes occur in 112 trials with a success probability of 0.42, follow these steps:

In Excel, create a new spreadsheet with the first column labelled "Number of Successes" and the second column labelled "Probability."

Enter "0" in the first row of the "Number of Successes" column.

Enter "1" in the second row of the "Number of Successes" column.

Continue to input numbers in the "Number of Successes" column in ascending order until you reach 30.

Enter the following formula in the field next to the "0" in the "Probability" column: =BINOM.DIST (0,112,0.42,TRUE)

Enter the following formula: =SUM (B1:B31)

The result in the cell where you input the formula in step 8 will be the chance of 30 or fewer successes in 112 trials with a success rate of 0.42.

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