Select all of the following that are quadratic equations.
5x-1=3x+8
5 x- 3 = 0
x²-2x = 4x+1
2x²+12 x = 0
x³-6x² + 8 = 0
9x²+6x-3=0

Solving a system of equations we will see that we need to use 40 liters of the 80% acid solution, and the other 20 liters are of the 35% acid solution.

First, we need to define the variables:

We know that we want to produce 60 liters of 65% acid, then we have the system of equations:

x + y = 60

x*0.35 + y*0.80 = 60*0.65

(in the second equation we wrote the percentages in decimal form).

To solve this we need to isolate one of the variables in one equation and then replace it in other one, isolating x we get:

x = 60 - y

Replacing that in the other equation:

(60 - y)*0.35 + y*0.80 = 60*0.65

y*(0.80 - 0.35) = 60*(0.65 - 0.35)

y*0.45 = 60*0.30

y = 60*0.30/0.45 = 40

So we need to use 40 liters of the 80% acid solution, and the other 20 liters are of the 35% acid solution.

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Answer: 22/85

Step-by-step explanation:

Answer:

22/85

Step-by-step explanation:

Answer:

100 pi = about 314.16

Step-by-step explanation:

the surface area of a cylinder: SA = 2πrh+2πr^2

we plug in the values of r and h, and get

SA = 50pi + 50pi = 100 pi, which is approximately 314.16

Answer:

[tex]3(2x + 5)(3x - 1)[/tex]

Step-by-step explanation:

Hello!

We can first factor out the greatest common factor between the coefficients: 3.

Now, let's work with what we have inside the brackets.

Standard form of a quadratic: [tex]ax^2 + bx+ c = 0[/tex]

Given our equation: [tex]6x^2 + 13x - 5[/tex]

We need to find two numbers that add up to b (13) and multiply to ac (-30).

The two numbers are 15 and -2. Expand 13x to 15x and -2x and factor by grouping.

Now, we simply add the other factor, 3, to the final factored form.

Factored Solution: [tex]3(2x + 5)(3x - 1)[/tex]

Answer:

Step-by-step explanation:

The amount of tin used to make the can is about 478 cm².

To find the amount of tin used to make the can, we need to calculate the total surface area of the can. A can is a cylinder, so we can use the formula for the total surface area of a cylinder to calculate it:

Surface area = 2πr² + 2πrh

Where r is the radius of the can and h is the height of the can.

Given that the height of the can is 12.4 cm, we can use the information that the dashed line across the top of the can is labeled 9 cm to calculate the radius of the can.

r = dashed line / 2 = 9cm / 2 = 4.5 cm

Now we can substitute the values of r and h in the formula:

Surface area = 2π (4.5 cm)² + 2π (4.5 cm) (12.4 cm) = 477.594 cm²

Rounding to nearest square centimeter: 478 cm²

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Answer:

2125 lbs

Step-by-step explanation:

1 gallon = 8.5 lbs

we know 1 gallon * 250 = 250 gallons

multiply both sides by 250 to get 250 gallons on one side

250 gallons = 8.5* 250 lbs = 2125 lbs

The equation of the ellipse is [tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]

The given parameters are:

The above means that:

c = 4 and

The semi-major axis, a = 7 i.e 14/2

Calculate b using

[tex]b = \sqrt{c^2 + a^2[/tex]

So, we have:

[tex]b = \sqrt{4^2 + 7^2[/tex]

[tex]b = \sqrt{65[/tex]

Square both sides

[tex]b^2 = 65[/tex]

The standard form of the ellipse is represented as:

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]

This gives

[tex]\frac{x^2}{7^2} + \frac{y^2}{65} = 1[/tex]

Evaluate

[tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]

Hence, the equation of the ellipse is [tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]

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Answer:

Diameter of sphere = 18 cm

Step-by-step explanation:

     Diameter = 18 cm

                  r = 18÷ 2 = 9 cm

                 h = 12 cm

[tex]\sf \boxed{\bf Volume \ of \ cylinder = \pi r^2h}[/tex]

                                    = π * 9 * 9 * 12 cm³

  [tex]\sf \boxed{\text{\bf Volume of sphere = $\dfrac{4}{3} \pi r^3$}}[/tex]

Solid cylinder is melted and turned into a solid sphere.

Volume of sphere = volume of cylinder

 [tex]\sf \dfrac{4}{3}\pi r^3 = \pi *9*9*12[/tex]

      [tex]\sf r^{3}= \dfrac{\pi *9*9*12*3}{4*\pi }\\\\ r^{3}=9 * 9 *3 *3\\\\\\r = \sqrt[3]{9*9*9}\\\\ r = 9 \ cm\\\\diameter = 9*2\\\\\boxed{diameter \ of \ sphere = 18 \ cm}[/tex]

The value of the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex] after substituting y = 7 is 108

The given expression is:

[tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex]

Simplifying the expression, we have:

[tex]2+4+y^2+4+y^2\\\\2y^2+10[/tex]

Substitute y = 7 into the simplified expression

[tex]2(7)^2+10\\\\=2(49)+10\\\\=98+10\\\\=108[/tex]

Therefore, after substituting y = 7, into the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex], the resulting value is 108

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Answer: -1

Step-by-step explanation: khan academy

(a) The number of cases on May 1, 2014, was approximately 188.59.

(b) The number of cases on November 24, 2014, was approximately 27107.76.

(c) C(92) = 1715.70.

This means that on the 92nd day from May 1, 2014, the number of Ebola cases in Africa was approximately 1715.70.

Computed using the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].

We are given that the spread of the Ebola virus in Africa in 2014 could be modeled by the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex], where C represents the number of cases and t represents the number of days since May 1, 2014.

(a) In the question, we are asked for the approximate number of cases on May 1, 2014.

Since, the date is May 1, 2014, t = 0.

Thus, the number of cases, C, can be calculated by putting t = 0, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].

[tex]C(0) = 188.59e^{0.024*0}\\\Rightarrow C(0) = 188.59e^0\\\Rightarrow C(0) = 188.59[/tex]

Thus, the number of cases on May 1, 2014, was approximately 188.59.

(b) In the question, we are asked for the approximate number of cases on November 24, 2014.

Since, the date is November 24, 2014, t = 207.

Thus, the number of cases, C, can be calculated by putting t = 207, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].

[tex]C(207) = 188.59e^{0.024*207}\\\Rightarrow C(207) = 188.59e^{4.968}\\\Rightarrow C(207) = 188.59*143.739121458\\\Rightarrow C(207) = 27107.76[/tex]

Thus, the number of cases on November 24, 2014, was approximately 27107.76.

(c) We are asked to find C(92).

This can be found by putting t = 92, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].

[tex]C(92) = 188.59e^{0.024*92}\\\Rightarrow C(92) = 188.59e^{2.208}\\\Rightarrow C(92) = 188.59*9.09750317953\\\Rightarrow C(92) = 1715.70[/tex]

Thus, C(92) = 1715.70.

This means that on the 92nd day from May 1, 2014, the number of Ebola cases in Africa was approximately 1715.70.

The complete question is:

"The spread of the Ebola virus in Africa in 2014 could be modeled by [tex]C(t) = 188.59e^{0.024t}[/tex] where C represents the number of cases and t represents the number of days since May 1, 2014. (source: http://www.geert.io/exponential-growth-of-ebola.html)

a. [3 pts] Approximately how many cases were there on May 1, 2014?

b. [3 pts] How many cases were projected by November 24, 2014?

c. [4 pts] Find C(92) and explain what it means in the context of the problem.

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There are $2224.12 need to deposit in an account in order to have $3000 in five years.

What is future value?

Future value is the worth of a financial asset or investment on a specific future date. In other words, future value is the amount of money an investment will be worth, assuming a specific rate of return, after a specific amount of time (interest rate).

Given:

Future value = FV = $3000

Number of years = t = 5

Interest rate = r = 6% = 0.06

Compounding period = n = 12

We have to find the present value form given problem.

Consider, the Future value formula,

[tex]FV = PV(1 + \frac{r}{n})^n^*^t[/tex]

Plug the values in the above formula.

[tex]3000 = PV(1+\frac{0.06}{12})^1^2^*^5\\ 3000 = PV(1+0.005)^6^0\\3000 = PV(1.005)^6^0\\PV = 2224.11658[/tex]

PV = $2224.12

Hence, there are $2224.12 need to deposit in an account in order to have $3000 in five years.

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Answer:

The offers are equal at $7,000, after $7,000 more money will be made with a straight commission.

Step-by-step explanation:

.05x = .02x + 210  Subtract .02x from both sides.

.03x  = 210   Divide both sides by .03

x  = $7,000.

Watthours are the units used to measure the amount of electricity used over time.

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Answer:

Step-by-step explanation:

Answer:

If you start at (-4,3) and move 8 units to the right and 10 units down, you would end up at the point (4,-7).

The point is located in the 3rd quadrant, where the x-coordinates are negative and the y-coordinates are negative.

It's important to note that moving 8 units to the right means moving to the positive direction on x-axis and moving 10 units down means moving to the negative direction on y-axis.

Answer: 5(5 + 9). This expression can be solved by multiplying 5 by both the addends. So, 5(5) + 5(9) = 25 + 45 = 70.

Step-by-step explanation:

Answer:

Step-by-step explanation:

7/20 + 3/16 = x

x = 7/20 + 3/16

LCM of 20 and 16 = 80

x = 28/80 + 15/80

x =  43 /80

Answer:

x = 0.5375

Step-by-step explanation:

=7/20 + 3/16 = x

=LCM = 80

=80×7/20 + 80×3/16 = x × 80

=4×7 + 5×3 = x × 80

=28 + 15 = 80x

=43 = 80x

=43/80 = 80x/80

=43/80 = x

=0.5375 = x.

Sorry but I don't know how to use the slash mark (/).

Answer:

B. More than 90

Step-by-step explanation:

Hope this helps!

Answer: 140

Step-by-step explanation:

20+10+10+50+35+15

50+20+35+10+15=130

           -

Answer:4

Step-by-step explanation: 9y-8y+2, when y=2

9(2)-8(2)+2=

18-16+2

=4

The given differential equation has the answer C₁ +C₂ 1/81 -x⁹ +1/9 x⁹ln(x). It has been solved using the variation of parameters method below.

We have the differential equation xy'' − 8y' = x^8.  In order to solve any differential equation using the variation of parameters method, we first write the equation as and solve -

= xy'' − 8y' = 0

After solving this, we get the Auxiliary equation-

so CF is y = 1/9 x⁹ +  C₁ +C₂

Now, we write -

y1 (x) =  1/9 x⁹

y2 (x) = 1

y1'(x) = x^8

y2'(x) = 0

now, using wronskian formula

= W = -x^8

Now, applying the formulas -

= u =  [tex]- \int{\frac{f(x)y2(x)}{W(x)} } \, dx[/tex] and v = [tex]\int{\frac{f(x)y1(x)}{W(x)} } \, dx[/tex]

= u = log(x) and v = -x⁹/81

now particular integrals are

PI = 1/81 -x⁹ +1/9 x⁹ln(x)

total solution

y = C.F+P.I

y = C₁ +C₂ 1/81 -x⁹ +1/9 x⁹ln(x)

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Using the normal distribution, the z-scores are given as follows:

a) Z = 2.8.

b) Z = 2.8.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Item a:

The parameters are:

[tex]\mu = 15, \sigma = 2.5[/tex]

Hence the z-score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{22 - 15}{2.5}[/tex]

Z = 2.8.

Item b:

The parameters are:

[tex]\mu = 38.1, \sigma = 6.35[/tex]

Hence the z-score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55.88 - 38.1}{6.35}[/tex]

Z = 2.8.

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The graph is shown in the attached image.

The probability of E and F expressed as P(E and F) equals;0.12

We are given;

P(E) = 0.2

P(F|E) = 0.6

Now, P(F/E) is known as conditional probability and it means the probability of event F given the probability of another event E. This can be expressed as; P(F|E) = P(E and F)/P(E)

Thus;

P(E and F) = 0.2 * 0.6

P(E and F) = 0.12

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The coordinates of point C are (-9, 1)

The points are given as:

A = (-21, -7)

B = (-6, 3)

m : n = 4 : 1

The coordinates of point C is calculated as:

[tex]C = \frac{1}{m+n} *(mx_2 + nx_1, my_2+ ny_1)[/tex]

So, we have:

[tex]C = \frac{1}{4+1} *(4 * -6 + 1 * -21, 4 * 3+ 1 * -7)[/tex]

This gives

[tex]C = \frac{1}{5} *(-45, 5)[/tex]

This gives

C = (-9, 1)

Hence, the coordinates of point C are (-9, 1)

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Answer:

270 uits

Step-by-step explanation:

The pairs of prime numbers (p,q) such that  p^2-p=37q^2-q is (43, 7)

The expression is given as:

p^2 - p=37q^2 - q

The boundary or range of numbers of p and q is not given.

So, we make use of numbers between 2 (because 1 is not a prime number) and a very large number (say 1000000)

i.e. 2 ≤ p ≤ 1000000 and 2 ≤ b ≤ 1000000

Using the above range, we have the following program to determine the pairs of prime numbers (p, q).

for a in range(2,1000000):

  for b in range(2,1000000):

      if ((a* *2) - a) == (37 * (b* *2) - b):

          print(str(a)+","+str(b))

The output of the above program is:

(43, 7)

The above represent all pairs of prime numbers (p,q) such that p^2 - p=37q^2 - q

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Answer:

BC = 18 cm

Step-by-step explanation:

As we can see from the diagram:

AB + BC + CD = AD

⇒ 10 cm + BC + 11 cm = 39 cm

⇒ BC + 21 cm = 39 cm

⇒ BC = 39 cm - 21 cm

⇒ BC = 18 cm