x+6y=27
7x-3y=9 por metodo de igualacion

Answer:

The correct option is D.

Step-by-step explanation:

The general exponential regression equations is

[tex]y=ab^x[/tex]                      .... (1)

where, a is initial value and b is growth factor.

Using graph calculator, we get

[tex]a=3.5349151766\approx 3.53[/tex]

[tex]b=4.37391527533\approx 4.37[/tex]

[tex]R^2=0.99878148[/tex]

Put the value of a and b in equation (1), to find the exponential regression equation.

Substitute a=3.53 and b=4.37 in equation (1).

[tex]y=(3.53)(4.37)^x[/tex]

[tex]y=3.53(4.37)^x[/tex]

The exponential regression equations that best fits the data is [tex]y=3.53(4.37)^x[/tex].

Therefore the correct option is D.

Answer:

Step-by-step explanation:

Factorial is used to multiply any natural number with all the numbers smaller than it. It is denoted by n! (n is the natural number)

where n! = n*(n-1)*(n-2)*(n-3)*(n-4) so on....

For example if we take factorial of 5.

Then,

5!= 5*(5-1)*(5-2)*(5-3)*(5-4)

= 5*4*3*2*1

= 120

It is used for the questions which asks us to order a number of things or in how many ways you can arrange something....

Factorial is a key function in mathematics used to calculate permutations and arrangements. It represents the number of ways objects can be arranged within a set number. Factorial is essential in combinatorics and probability theory.

Factorial is a mathematical function denoted as n! and calculated as the product of all positive integers up to n.

The purpose of factorial is to represent the number of ways in which a set of objects can be arranged or permutations can be made within a set number of objects.

Factorial is extensively used in mathematics, especially in combinatorics and probability theory.

1

Answer:

218,900

Step-by-step explanation:

110,000 x 11%= 12,100

12,100 x 9 = 108,900

110,000+108,900= 218,900

The future value of a present investment of $110,000 at an annual interest rate of 11% compounded for 9 years is approximately $278,984.57.

The question is asking for the future value of a present investment of $110,000 at an annual interest rate of 11% compounded for 9 years. For such a calculation, we can use the formula for compound interest:

FV = PV * (1 + r)^n

Where,

Plugging in the values, we get:

FV = $110,000 * (1 + 0.11)^9

After calculating the above expression, we find that the investment will grow to be approximately $278,984.57 after 9 years.

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Answer:

C

Step-by-step explanation:

The center of inscribed circle into triangle is point of intersection of all interior angles of triangle.

The center of circumscribed circle over triabgle is point of intersection of perpendicular bisectors to the sides.

Circumscribed circle always passes through the vertices of the triangle.

Inscribed circle is always tangent to the triangle's sides.

In your case angles' bisectors and perpendicular bisectors intesect at one point, so point A is the center of inscribed circle and the center of corcumsribed circle. Thus, these circles pass through the points X, Y, Z and G, E, F, respectively.

Answer:

The area of the prism: 404 square feet.

Step-by-step explanation:

The idea in this exercise is to find the areas of all the geometric figures, and then add them all.

Notice that we have four consecutive rectangles, two smaller with dimension 6 ft by 8 ft and two larger with dimension 11 ft by 8 ft. Then, combined area of this four rectangles is

A_1 = 6*8 + 6*8 + 11*8+11*8 = 48+48+88+88 = 272.

For the other two rectangles, notice that their bases has the same length (11 ft). Their height can obtained using the characteristics of the prism. In this case must be 6 ft, the same length of the base of the previous smaller rectangles. The, the combined area of this rectangle is

A_2 = 6*11 +6*11 = 66 + 66 = 132.

Finally, adding those two area we get the area of the prism: 404 square feet.

[tex]\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( \sqrt{3} \right)\left( \sqrt[5]{3} \right)\implies \left( \sqrt[2]{3^1} \right)\left( \sqrt[5]{3^1} \right)\implies 3^{\frac{1}{2}}\cdot 3^{\frac{1}{5}}\implies 3^{\frac{1}{2}+\frac{1}{5}}\implies 3^{\frac{5+2}{10}}\implies 3^{\frac{7}{10}}[/tex]

Answer:

5(x + 4)(x - 2)

Step-by-step explanation:

Start by factoring 5 out of all three terms.  We then have

5(x^2 + 2x - 8), or

5(x^2 + 2x - 8), which is in proper quadratic form.

Note that (4)(-2) = 8 and that 4 - 2 = 2, which match the 3rd and 2nd coefficients of x^2 + 2x - 8.

Thus, in completely factored form, we have 5(x + 4)(x - 2)

Answer:

5 (x -2) (x +4)

Step-by-step explanation:

5x^2 + 10x - 40

Factor out a 5

5(x^2 +2x-8)

We can then factor inside the parentheses

What two numbers multiply to -8 and add to 2

-2*4 = -8

-2+4 = 8

5 (x -2) (x +4)

Answer:

Step-by-step explanation:

[tex]\text{The domain:}\\\\(x+3)(x-5)\neq0\iff x+3\neq0\ \wedge\ x-5\neq0\\\\x\neq-3\ \wedge\ x\neq5\\\\========================\\\\f(x)=\dfrac{x(x-2)}{(x+3)(x-5)}\\\\\text{The zeros are for}\ f(x)=0\\\\\dfrac{x(x-2)}{(x+3)(x-5)}=0\iff x(x-2)=0\iff x=0\ \vee\ x-2=0\\\\x=0\in D\ \vee\ x=2\in D[/tex]

Step-by-step explanation:

The political equality of all citizens is an essential principle of democracy. In ademocracy, the just powers of government are based upon the consent of the governed.

D) leaders Must be selected by the citizens rather than inheriting power. (Apex)

Answer:

J. 35 inches

Step-by-step explanation:

Write a proportion:

3 / 5 = 21 / x

Cross multiply:

3x = 105

Divide:

x = 35

The width of the poster is 35 inches.

The width of the poster is 35 inches.

Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios.

A photo with a length of 3 inches and a width of 5 inches is enlarged to poster size.

The poster and the photo are similar. the length of the poster is 21 inches.

Let x be the width of the poster.

The width of the poster is given by;

[tex]\rm \dfrac{Length \ of \ photo}{Width \ of \ photo}=\rm \dfrac{Length \ of \ poster}{Width \ of \ poster}\\\dfrac{3}{5}=\dfrac{21}{x}\\\\3 \times x =21 \times 5\\\\3x=105\\\\x=\dfrac{105}{3}\\\\x=35[/tex]

Hence, the width of the poster is 35 inches.

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Answer:

A(5,3)  ->A'(5,-3)

B(2,1)   ->B'(2,-1)

C(-2,4)  ->C'(-2,-4)

Step-by-step explanation:

If a point is reflected over the x-axis, it ends up on the opposite side of the x-axis with the same distance from the x-axis.

So what that means is the x-coordinate will stay the same and the y-coordinate will be opposite of what it was.

So if we reflect each of your points through the x-axis you will get:

A(5,3)  ->A'(5,-3)

B(2,1)   ->B'(2,-1)

C(-2,4)  ->C'(-2,-4)

Answer:

(5,-3) (2,-1) (-2,-4)

Step-by-step explanation:

When reflection over the x-axis the rule is (x,y) becomes (x, -y)

so your x will stay the same but your y will change

Answer:

1 large truck, 99 small trucks and 180 commercial vans

Step-by-step explanation:

Step 1 : Write the data.

Total amount: 8,000,000

Total trucks needed: 280

Cost of commercial van (x) = $25,000

Cost of small truck (y) = $30,000

Large truck = $40,000 (from my understanding, only 1 large truck has to be bought since the amount given for commercial vans and small trucks is for each of it.

Since they need twice as many vans as small trucks, commercial van will be 2y and small truck will be y

Step 2 : Form two equations

40,000 + 25000(x) + 30000(y) = 8,000,000

25000(x) + 30000(y)  = 7960,000 (equation 1)

1(large truck) + x + y =280

x + y = 279 (equation 2)

Step 3 : Find the value of y

From equation 2:

x = 279 - y

From equation 1:

25000(x) + 30000(y)  = 7960,000

25000(279 - y) + 30000(y)  = 7960,000

-25000y + 30000y + 6975000 = 7960000

5000y = 985000

y= 98.5 rounded off to 99 small trucks

Step 4: Find value of x

x + y = 279

y = 279 - 99

y = 180 commercial vans

Step 5: Answer how many type of each vehicle can they buy.

They can buy:

1 large truck

99 small trucks

180 commercial vans

!!

for this case we have the following equation:

[tex]2x + 5 = -x + 1[/tex]

To resolve:

We add x to both sides of the equation:

[tex]2x + x + 5 = -x + 1 + x[/tex]

[tex]3x + 5 = 1[/tex]

We subtract 5 on both sides of the equation:

[tex]3x + 5-5 = 1-5\\3x = -4[/tex]

We divide between 3 on both sides of the equation:

[tex]x = - \frac {4} {3}[/tex]

Answer:

We add x to both sides of the equation

Answer:

The correct option is C) add one positive x-tile to both sides.

Step-by-step explanation:

Consider the provided equation.

2x + 5 = -x + 1

Now to solve the above equation first isolate the variables.

To isolate the variables add x to the both the side of the equation.

2x + 5 + x = -x + 1 + x

Now add the like terms.

3x + 5 =  1

Here we add the x tiles to the both the side of the equation.

Now consider the options.

The correct option is C) add one positive x-tile to both sides.

If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A and B) = 0.

If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A and B) = 0.

Mutually exclusive events are events that cannot occur at the same time. This means that if event A happens, event B cannot happen, and vice versa. Therefore, the probability of both A and B occurring together is zero.

Answer:

The first one. 4 times square root of 3.

Step-by-step explanation:

The side of the equilateral triangle that represents the height of the triangle will have a length of because it will be opposite the 60o angle. To calculate the area of the triangle, multiply the base (one side of the equilateral triangle) and the height (the perpendicular bisector) and divide by two.

Answer:

Remember:

Triangle area= [tex]\frac{b*h}{2}[/tex]

h of equilateral triangle = [tex]\frac{\sqrt{3}}{2}*a[/tex]

Step-by-step explanation:

b=4yd

a=4yd

h = [tex]\frac{\sqrt{3}}{2}*a[/tex]

h = [tex]\frac{\sqrt{3}}{2}*4yd[/tex]

4/2=2

h= [tex]2\sqrt{3} yd[/tex]

area= [tex]\frac{b*h}{2}[/tex]

area= [tex]\frac{4 yd*2\sqrt{3} yd}{2}[/tex]

2/2=1

Finally

area= [tex]4\sqrt{3} yd^2[/tex]

Answer:

200

Step-by-step explanation:

12% is the same thing of .12

x = the number you are trying to find

.12(x) = 24     ----- This means that 12% of x is 24.

x = 24/.12

x = 200

To solve this you must use a proportion like so...

[tex]\frac{part}{whole} = \frac{part}{whole}[/tex]

12 is a percent and percent's are always taken out of the 100. This means that one proportion will have 12 as the part and 100 as the whole

We want to know out of what number is 24 12% of. This means 24 is the part and the unknown (let's make this x) is the whole.

Here is your proportion:

[tex]\frac{24}{x} =\frac{12}{100}[/tex]

Now you must cross multiply

24*100 = 12*x

2400 = 12x

To isolate x divide 12 to both sides

2400/12 = 12x/12

200 = x

This means that 12% of 200 is 24

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

180

Step-by-step explanation:

According to the table, the relationship between the x and the y value is 20, (4*20 = 80) (5*20 = 100) etc.

The graph with the points has a relationship of 35 (2*35 = 70) (4*35 = 140) etc. Therefore, you can figure out what y-value 12 would have for the table and the graph by multiplying 12 by 20 or 35 respectively.

12*20 = 240

12*35 = 420

420-240 = 180

Answer:

180

Step-by-step explanation:

Answer:

33°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 given angles from 180 for ∠1, that is

∠1 = 180° - (116 + 31)° = 180° - 147° = 33°

The system of inequalities to determine the dimensions and budget of the boxcar, according to the given restrictions in the problem, are: x + 3 >= length, x >= y + 2, and 0.50*x*(x+3) + 4 * 2.25 * y <= 50.

The subject of this question is Mathematics, specifically the topic of inequalities. From the problem, we can create a system of inequalities based on the restrictions specified. We are told that the length of the car must be 3 inches greater than its width, which is represented by x, so one inequality is x+3 >= length. Second, the width of the car must be at least 2 inches greater than the radii of the wheels, represented by y, so we have another inequality, x >= y + 2.

Lastly, we need to account for the monetary constraint. The cost of the base is $0.50 per square inch, so the cost is 0.50*x*(x+3), and the cost of each of the 4 wheels is $2.25 per inch of radius, so the total cost is 4 * 2.25 * y. The total spending must not exceed $50, so our final inequality is 0.50*x*(x+3) + 4 * 2.25 * y <= 50. Therefore, the system of inequalities that can be used to determine the length, width of the car and the radii of the wheels is:

x + 3 >= length
x >= y + 2
0.50*x*(x+3) + 4 * 2.25 * y <= 50

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Answer: B.97

Step-by-step explanation:

When two parallel lines are intersected by a transversal line then the sum of adjacent angles is 180°.

From the given figure , BD is parallel to XY and a transversal intersecting it making a pair of adjacent angles 83° and y°.

[tex]83^{\circ}+y^{\circ}=180^{\circ}\\\\\Rightarrow\ y^{\circ}=180^{\circ}-83^{\circ}=97^{\circ}[/tex]

Hence, the value of y= 97.

Answer:it is 83

Step-by-step explanation:

Answer:

discriminant is zero (0)

Step-by-step explanation:

Actually, you have a double root here:  {6, 6}:  "two real, equal roots."  That tells us immediately that the value of the discriminant was zero (0).

Answer:

The discriminant of the equation is zero.

Step-by-step explanation:

The given graph is a quadratic equation. If x = 6 is the only x-intercept of the graph, then the roots must be equal.

The quadratic equation will have two solutions. Here the two solutions are equal x = 6.

If the roots are equal, then the discriminant is zero.

The factors of the quadratic equation (x - 6) (x - 6)

= [tex]x^2 - 6x - 6x + 36[/tex]

= [tex]x^2 -12x + 36[/tex]

Discriminant = [tex]b^2 - 4ac[/tex]

Here a = 1, b = -12 and c = 36

Discriminant = [tex](-12)^{2} - 4.1.36[/tex]

= 144 - 144

= 0

Therefore, the answer is "The discriminant of the equation is zero."

42 ounces

In this question, it is asking how many ounces of fiber did the Koala eat that day.

In order to solve this question, we would need to gather some important information from the question.

Important Information:

With the information above, we can solve the question.

We know that koalas only absorb 25% of fiber. We also know that a koala absorbed 10.5 ounces of fiber.

This means that the 10.5 ounces is 25% of fiber. This is 1/4 of the fiber it ate.

Now, we just need to find the other 3/4.

We could just multiply 10.5 by 4 to find how much fiber it ate that day.

[tex]10.5*4=42[/tex]

When you multiply, you should get 42.

This means that the Koala ate 42 ounces of fiber that day.

Answer:

42

Step-by-step explanation:

We seek the answer to the question "10.5 ounces is 25% of what number?" If we call the unknown number of ounces x, we have the equation 10.5=0.25x. Dividing both sides by 0.25, we have x=10.5/0.25=42 ounces of fiber.

Answer:

c(p) = 0.59p

Step-by-step explanation:

We multiply the number of pounds of sugar, p, time the cost per pound ,.59, to get the total cost

c(p) = .59*p

Answer: c(p) = 0.59p

Step-by-step explanation:

Answer:

You will need  220 mL of the 60% solution  and  80 mL of pure alcohol.

Step-by-step explanation:

Let 'x' be the amount of 50% alcohol solution and y the amount of pure alcohol.

Therefore:  

(0.5x + y)/300 = 0.65 ⇒ 0.5x + y = 190

x + y = 300

Solving the sistem of equations:

x = 220 and y = 080

Therefore, You will need

220 mL of the 60% solution

and  80 mL of pure alcohol.

Answer:

0.025 $/in.

Step-by-step explanation:

The store bought 300 ft of rope.

1 ft = 12 in.

300 ft * 12 in./ft = 3600 in.

The store bought 3600 inches of rope.

The store sells 40 inches of rope for $1.60. We can find the selling unit price of rope in dollars per inch.

($1.60)/(40 in.) = $0.04/in.

The store sells the rope at a price of $0.04 per inch.

The store sold all the rope at $0.04/in.

3600 in. * $0.04/in. = $144

The store sold all the rope for $144.

The profit was $54 for selling ll the rope.

$144 - $54 = $90

The bought the rope for $90.

The cost is dollars per inch is

($90)/(3600 in.) = 0.025 $/in.

The length of BC in the right triangle with sides 9 and 12 is 15.

In a right triangle, the length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the lengths of the other two sides are given as 9 and 12. Let's label the hypotenuse as BC. We can use the Pythagorean theorem to solve for BC:

a2 + b2 = c2

92 + 122 = c2

81 + 144 = c2

225 = c2

Taking the square root of both sides, we find that the length of BC is 15 units.

Answer:

Step-by-step explanation:

Look at the picture.

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=12ft,\ leg=H,\ hypotenuse=20ft[/tex]

Substitute:

[tex]12^2+H^2=20^2[/tex]

[tex]144+H^2=400[/tex]             subtract 144 from both sides

[tex]H^2=256\to H=\sqrt{156}\\\\H=16\ ft[/tex]

Answer:

16 feet

Step-by-step explanation:

for edg

Answer:

The standard form of the equation is 49t² - 75t + 3 = 0

The solution of the equations are 1.49 and 0.041

Step-by-step explanation:

* Lets explain how to solve the problem

- The standard form of the quadratic equation is ax² + bx + c  = 0,

  where a , b , c are constant and a can not be 0

∵ The quadratic equation is -4.9t² + 7.5t + 1.8 = 2.1

- Lets make the left hand side equal to 0

∵ -4.9t² + 7.5t + 1.8 = 2.1 ⇒ subtract 2.1 from both sides

∴ -4.9t² + 7.5t - 0.3 = 0 ⇒ multiply each term by -10

∴ 49t² - 75t + 3 = 0

* The standard form of the equation is 49t² - 75t + 3 = 0

∵ ax² + bx + c = 0

∴ a = 49 , b = -75 , c = 3

- Lets use the formula [tex]x=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex] to solve

 the equation

∴ [tex]x=\frac{-(-75)+\sqrt{(-75)^{2}-4(49)(3)}}{2(49)}=1.49[/tex]

∴ [tex]x=\frac{-(-75)-\sqrt{(-75)^{2}-4(49)(3)}}{2(49)}=0.041[/tex]

* The solution of the equations are 1.49 and 0.041

Answer:

2.777777 and -7/3

Step-by-step explanation:

2.7182818459 cannot be written in fraction form therefore it is irrational.

2.777777 is rational because it can be written as the fraction 25/9

The square root of 3 is 1.7320508075688772, this number cannot be written as a fraction so it is irrational.

-7/3 is rational because it is already in fraction form.

Answer:

2.777777 and -7/3

Step-by-step explanation:

If a number can be defined in the form of p/q where q≠0, then it is called rational number.

If a decimal number is repeating then it is a rational number because it can be written in the form of p/q.

For example: 1.222, 3/5, 2.5, -1/2, 4.0707007...

All real numbers which are not rational numbers are called irrational numbers.

For example: 0.2357835.., √2, π.

In the given numbers,

Rational numbers = 2.777777,  -7/3

Irrational numbers = 2.7182818459 and √3

Therefore the two rational numbers are 2.777777 and -7/3.

The slope of the line through given two points is [tex]\frac{1}{2}[/tex]

If (x₁, y₁) & (x₂, y₂) are two given points on a line.

Then the slope of the line (m) = [tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]

Given points on a line are (3, 1.5) & (5, 2.5)

∴ Slope of the line (m) = [tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]

                                     = [tex]\frac{2.5-1.5}{5-3}[/tex]

                                     = [tex]\frac{1}{2}[/tex]

So, the required slope is [tex]\frac{1}{2}[/tex]

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