1.)
What is the solution to the system of equations below?
y = 2x + 8
3(-2x + y) = 19

For this case we have that by definition, the discriminant of a quadratic equation [tex]ax ^ 2 + bx + c = 0[/tex], is given by:

[tex]d = b ^ 2-4 (a) (c)[/tex]

[tex]d> 0[/tex]: Two different real roots

[tex]d = 0[/tex]: Two equal real roots

[tex]d <0[/tex]: Two different complex roots

If we have [tex]9x ^ 2 + 12x + 4 = 0[/tex], then:

[tex]a = 9\\b = 12\\c = 4[/tex]

Substituting the values:

[tex]d = 12 ^ 2-4 (9) (4)\\d = 144-144\\d = 0[/tex]

Thus, we have two equal real roots.

ANswer:

We have two equal real roots.

Answer:

c=8+15h

Step-by-step explanation:

Final answer:

To calculate the population after 5 years at a 2% growth rate, you apply the formula for exponential growth, resulting in an estimated population of 5512 to the nearest whole number.

Explanation:

To calculate the population of a town after 5 years with a 2% annual growth rate, you would use the formula for exponential growth. In this case, the initial population is 5000 and the growth rate is 0.02 (2%). The population after n years is given by the formula P(n) = P(0) × (1 + r)ⁿ, where:

After 5 years, the formula will look like this:

P(5) = 5000 × (1 + 0.02)⁵

Calculating the above:

To the nearest whole number, the population of the town after 5 years will be 5512.

Answer:

18 yards

Step-by-step explanation:

6+5+3+4= 18

Answer:

=2x^3+5x+2

Step-by-step explanation:

hope this helps

Answer: 2-1 / y times y/ 3+1

Step-by-step explanation:

In dividing fractions, it is possible to change the sign to multiplication sign by swapping positions of the numerator and denominator.

For example given,

a/b divided by c/d,

We can write this as

a/b times d/c

To simplify the given complex fraction [tex]\(\frac{{2 - \frac{1}{y}}}{{3 + \frac{1}{y}}}\),[/tex]we'll first rationalize the fractions in the numerator and denominator.

For the numerator:

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

For the denominator:

[tex]\[3 + \frac{1}{y} = \frac{3y}{y} + \frac{1}{y} = \frac{3y + 1}{y}\][/tex]

So, the original complex fraction becomes:

[tex]\[\frac{\frac{2y - 1}{y}}{\frac{3y + 1}{y}} = \frac{2y - 1}{3y + 1}\][/tex]

Therefore, the equivalent expression to the given complex fraction is option d. (2y-1)(3y+1).

Answer:

Step-by-step explanation:

As the two figure are the image and pre-image of a dilation.

Considering the left sided triangle is original and right sided triangle ( smaller one) is the image.

As one of the sides of the left triangle (original figure) is 4 in. And the corresponding length of the side on the right triangle (image of the figure) is 2 in.

It means the image of the side (2 in) is obtained when the side (4 in) of the original object is dilated by a scale factor of 1/2. In other words, the side of the image (2 in) is obtained multiplying the side (4 in) of original figure by 1/2. i.e. 4/2 = 2 in

Lets determine the missing side of the right side triangle by the same rule.

As the original object has one of the sides is 5 in and the corresponding side of the image has x in. As the original figure is dilated by a scale factor of 1/2. so the missing side of x will be: x = 5/2 = 2.5

So, the value of x will be 2.5

Similarly, the original object has one of the sides with length (y + 1 in). As the As the original figure is dilated by a scale factor of 1/2. As the corresponding length of the side of the image triangle is 3 in.

so

y + 1 = 2(3)         ∵ 3 in (image side) is multiplied by 2

y + 1 = 6

y = 6 - 1

y = 5

So, the value of y = 5

Therefore,

Answer:5.5

6

Step-by-step explanation:

Answer: Below

Step-by-step explanation:

If you don't know Trigonometry, in a 30-60-90 triangle, the hypotenuse is always twice as long as the side opposite the 30° angle and the side opposite the 60° angle is √3 times as long as the side opposite the 30° angle.  

So, since the hypotenuse has length 12 cm,  

    side opposite 30° angle (shorter leg) = 6 cm

    side opposite 60° angle (longer leg) = 6√3 cm

The possible lengths of the legs are 6 and 6√3

The triangle is given as:

30-60-90 triangle

And we have:

Hypotenuse = 12 cm

A 30-60-90 triangle is a unique triangle with the following parameters

Opposite = Hypotenuse/2

Adjacent = Hypotenuse/2 * √3

So, we have:

Opposite = 12/2

Adjacent = 12/2 * √3

Opposite = 6

Adjacent = 6√3

Hence, the possible lengths of the legs are 6 and 6√3

Read more about right triangles at:

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Explanation:

Answer:

Everything except lawn care.

Answer:

Step-by-step explanation:

r=√((4-1)²+(2+2)²)=√(9+16)=5

area of circle=π r²=3.14×5²=78.50=78.5

The area of the circle is found by calculating the radius using the distance formula and then applying the formula A = πr². Using the common approximation of π as 3.14, the area is found to be approximately 78.5 square units when rounded to the nearest tenth.

The first step in finding the area of the circle is to determine its radius. The radius can be found by calculating the distance between the center of the circle, C (1, -2), and a point on the circle, (4, 2). Using the distance formula, we get the radius r = √((4-1)² + (2-(-2))²)} = √{(3)² + (4)²} = √{9 + 16} = √{25} = 5 units. Next, we use the formula for the area of a circle, which is A = πr². Substituting the radius in, we find A = π(5)² = 25π. The approximation on the circle for π is 3.14, thus the area of the circle is approximately A = 25 * 3.14 = 78.5 square units, which should be rounded to the nearest tenth.

It is also noteworthy that any approximation on the circle may vary slightly depending on the value chosen for π, but using 3.14 is commonly accepted for most calculations. So our final answer is, rounding to the nearest tenth, the area of the circle is approximately 78.5 square units.

We want to find the total capacity of the mug given that we know how much liquid there is in a 2/3 full mug.

We will find that the capacity of the mug is 1.25 cups.

We know that when the mug is 2/3 full, it has 5/6 cups.

Then if we define C as the total capacity of the mug, we can write:

(2/3)*C = 5/6 cups.

Now we can solve the above equation for C:

C = (3/2)*(5/6) cups = 1.25 cups.

The capacity of the mug is 1.25 cups.

If you want to learn more, you can read:

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Answer:

8.166666666666666666666666666666666666666666

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]3\frac{1}{4}+2\frac{1}{6}=3+2+\frac{1}{4}+\frac{1}{6}\\\\=5+\frac{1}{4}+\frac{1}{6}\\\\LCM(4,6)=12\\\\\frac{1*3}{4*3}=\frac{3}{12}\\\\\frac{1*2}{6*2}=\frac{2}{12}\\\\5+\frac{1}{4}+\frac{1}{6}=5+\frac{3}{12}+\frac{2}{12}\\\\=5+\frac{3+2}{12}=5+\frac{5}{12}\\\\=5\frac{5}{12}[/tex]

Answer:

[tex]5\frac{5}{12}[/tex]

Step-by-step explanation:

Simplify the expression

Exact form: [tex]\frac{65}{12}[/tex]

Decimal Form: 5.416 (The six has a line on top indicating that it goes one forever basically)

Mixed Number form: [tex]5\frac{5}{12}[/tex]

Hopefully this helps

Also Give me your heart ;)

Answer:

B

Step-by-step explanation:

This is very simple if we understand a point of linear and exponential functions.

First of all, a linear growing function increases.

An exponential growing function increases as well.

But, linear function, no matter what the slope is, grows at a CONSTANT RATE. But,

Exponential function grows at a COMPOUND RATE.

So, if there are 2 functions, linear and exponential, the exponential will always exceed the linear, AT SOME POINT EVENTUALLY because of the growth factor (no matter growth factor of linear and exponential -- whatever they are).

So,

B is the correct answer.

Growth factor of each (both) doesn't matter. Exponential will always win!

Answer:

b

Step-by-step explanation:

The exponential function will always exceed the linear function.A quantity increasing exponentially eventually exceeds a quantity increasing linearly.

Answer:

A

Step-by-step explanation:

y = log3(x) – 1

I don't know why but this is the correct answer.

[tex]y = \log_{3}x - 1[/tex] is the equation with real zeros corresponding to the x-intercepts of the graph.

According to the statement, we must find a function such that all values of [tex]x[/tex] so that [tex]y(x) = 0[/tex] and are the same of the graph. A quick approach consists in solving on each expression:

[tex]\log_{3}x-1 = 0[/tex]

[tex]\log_{3}x = 1[/tex]

[tex]x = 3[/tex]

[tex]3\cdot x - 3 = 0[/tex]

[tex]3\cdot x = 3[/tex]

[tex]x = 1[/tex]

[tex]-3\cdot (x-1) + 3 = 0[/tex]

[tex]-3\cdot x +6 = 0[/tex]

[tex]x = 2[/tex]

[tex]\log_{3}2x - 2 = 0[/tex]

[tex]\log_{3}2x = 2[/tex]

[tex]2\cdot x = 9[/tex]

[tex]x = \frac{9}{2}[/tex]

Hence, we conclude that [tex]y = \log_{3}x - 1[/tex] is the equation with real zeros corresponding to the x-intercepts of the graph. [tex]\blacksquare[/tex]

The graph is missing and all functions are poorly formatted. Correct statement is shown below:

Which equation has real zeros corresponding to the x-intercepts of the graph?

A. [tex]y = \log_{3} x - 1[/tex]

B. [tex]y = 3\cdot x -3[/tex]

C. [tex]y = -3\cdot (x-1) + 3[/tex]

D. [tex]y = \log_{3}2x -2[/tex]

To learn more on logarithms, we kindly invite to check this verified question: https://brainly.com/question/7302008

To find the value of k that makes the equation true, we can start by expanding both sides of the equation. Then, rearrange the equation to isolate the terms with a on one side and the terms with b on the other side. Finally, solve for k to find the value that makes the equation true.

To find the value of k that makes the equation true, we can start by expanding both sides of the equation:

12a + 9b = k(2a + 32b)

12a + 9b = 2ka + 32kb

Next, we can rearrange the equation to isolate the terms with a on one side and the terms with b on the other side:

12a - 2ka = 32kb - 9b

This simplifies to:

(12 - 2k)a = (32k - 9)b

To make this equation true, the coefficient of a must be equal to the coefficient of b. Therefore, we can set up an equation:

12 - 2k = 32k - 9

Solving for k:

12 + 9 = 32k + 2k

21 = 34k

k = 21/34

Therefore, the value of k that makes the equation true is 21/34.

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Answer: 4/52 or 1/13 (simplified)

Step-by-step explanation: There are 52 cards in a deck and 4 aces

Answer:

1/13

Step-by-step explanation:

There are 13 types of cards in a deck and there are 4 cards in each. So if you wanted to pull a ace or jack from the deck it would be 1/13

Answer:

its The first one  

Step-by-step explanation:

Ok so to do an average, you add all number together (48) then you Divide by the number of items added (4 games) then it's the first one. Hope this helps, sorry if someone then answer it.  

Answer:

A

Step-by-step explanation:

I took the test

Answer:

59,000

Step-by-step explanation:

That is scientific notation, as used in a calculator, for example, to mean

5.9 * 10^4

5.9 * 10^4 = 5.9 * 10,000 = 59,000

Answer:

Step-by-step explanation:

x/5=6/3

3x=30

x=10

Answer:

x=10

Step-by-step explanation:

x*1/5 = 6/3

Simplify 6/3 =2

1/5x = 2

Multiply each side by 5

1/5x *5 = 2*5

x = 10

Answer:

K = 4

Step-by-step explanation:

If y varies directly as x

y = k x

Divide both sides by by x

K = y/x

When y = 32 and

x = 8

K = 32/8

K = 4

Answer:

bruh bruh bruh bruh bruh

Step-by-step explanation:

cringe

Answer:9

Step-by-step explanation:

multiply the 5.4 by 10 and the 0.6 by ten, then divide the 54 by 6

You get 9, then multiply that by 0.6, and you get 5.4

you multiply because the statement includes "of" which means multiplication

Answer:

-(a-8)*(a+10)

Step-by-step explanation:

Step-by-step explanation:

dy/dt = (A − Be^(-t/5)) y

(a) Find the general solution by separating the variables and integrating.

dy / y = (A − Be^(-t/5)) dt

dy / y = [A + 5B (-⅕ e^(-t/5))] dt

ln |y| = At + 5B e^(-t/5) + C

y = e^(At + 5B e^(-t/5) + C)

y = Ce^(At + 5B e^(-t/5))

(b) As t approaches infinity, dy/dt approaches Ay.  The rate of growth, A, is triple the initial rate of growth 0.02, so A = 0.06.

When t = 0, dy/dt = (A − B)y.  The rate of growth, A−B, is 0.02.  We know A = 0.06, so B = 0.04.

(c) Given that A = 0.06, B = 0.04, and y(0) = 50×10⁶ − 10×10⁶ = 40×10⁶:

40×10⁶ = Ce^(0.06(0) + 5(0.04) e^(-0/5))

40×10⁶ = Ce^(0.2)

C = 40×10⁶ e^(-0.2)

y = 40×10⁶ e^(-0.2) e^(0.06t + 0.2 e^(-t/5))

y = 40×10⁶ e^(-0.2 + 0.06t + 0.2 e^(-t/5))

(d) If A = 0.02 and B = 0, and there is no transformation (y(0) = 50×10⁶), then:

50×10⁶ = Ce^(0.02(0) + 0)

50×10⁶ = C

y = 50×10⁶ e^(0.02t)

Comparing to the answer from part (c):

40×10⁶ e^(-0.2 + 0.06t + 0.2 e^(-t/5)) = 50×10⁶ e^(0.02t)

e^(-0.2 + 0.04t + 0.2 e^(-t/5)) = 5/4

-0.2 + 0.04t + 0.2 e^(-t/5) = ln(5/4)

-5 + t + 5e^(-t/5) = 25 ln(5/4)

t + 5e^(-t/5) = 5 + 25 ln(5/4)

Solve with a calculator:

t = 9.886

The transformed economy surpasses the untransformed economy in the 10th year.

(e) In year t=5, the size of the transformed economy is:

y = 40×10⁶ e^(-0.2 + 0.06(5) + 0.2 e^(-5/5))

y = 47.6×10⁶

The percent growth is:

(47.6×10⁶ − 40×10⁶) / 40×10⁶ × 100% = 19%

The growth rate is greater than 4%, so the current government can expect to be reelected.

Answer:

4

Step-by-step explanation:

10= 6 + 4

Carry over the 6 to the 10 and make e the subject on the right hand side of the equation as shown below:

10 - 6 = e

4= e

Therefore e is 4.

Answer:

e = 4

Step-by-step explanation:

Check the answer by subtraction.

10 - 6 = 4

Or use fact families to check the answer

6 + 4 = 10

4 + 6 = 10

10 - 6 = 4

10 - 4 = 6

Answer:

119

Step-by-step explanation:

Hope this helps! Brainliest is appreciated.

Answer:

24

Step-by-step explanation:

24 cubes. Reasoning varies. Sample reasoning: The length of the box

can fit or 5/4 : 5/12 =3 cubes. The width of the box can fit or 5/3 : 5/12 = 4 cubes.  The height of the box can fit 5/6 : 5/12 = 2 cubes. The box can fit

or 24 cubes.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Length of the box = 5/6 ft

Width of the box = 5/4 ft

Height of the box = 5/3 ft

Sides of the cube salt lick = 5/12 ft

Number of salt lick in the box (length) = 5/6 ÷ 5/12

= 2 cubes.

Number of salt lick in the box (width) = 5/4 ÷ 5/12

= 3 cubes.

Number of salt lick in the box (length) = 5/3 ÷ 5/12

= 4 cubes.

Total number of salt lick = 4 × 3 × 2

= 24 cubes.

Answer:

a) y = 50x + 0

b) y = 35x + 300

Step-by-step explanation:

a) The price is $50 (per person), so you multiply 50 by the number of people going (which is x).

b) The price is $35 dollars (per person), so you multiply 35 by the number of people (which again would be x). There is also an extra cost of $300.

Hope this helps! :)

Answer:1 5/12

Step-by-step explanation:

3 4/6 - 2 1/4

Change to improper fraction we have

22/6 - 9/4

(2x22-3x9)/12

(44-27)/12

17/12=1 5/12

Answer:

1 5/12

Step-by-step explanation:

3 4/6 - 2 1/4

3 2/3 - 2 1/4

11/3 - 9/4

Lcm is 12

(11×4 - 9×3)/12

(44 - 27)/12

17/12

1 5/12