20 POINTS WILL MARK BRAINLIEST PLEASE EXPLAIN

1) I put them in two separate brakets.

2) I solved it by equating both of them.

Answer:

  1. Substitute for y in the first equation. Solve for x by completing the square. Substitute for x in the first equation to find y.

  2. (x, y) = (2+2√2, -2√2) and (2-2√2, 2√2)

Step-by-step explanation:

The first equation is a linear equation in standard form. The second equation is a quadratic equation giving an expression for y. The system can be solved by using the second equation to substitute for y in the first equation. After the resulting equation is put in suitable form, the irrational solutions can be found by completing the square. Then the y-values can be found by substituting the x-values into either of the given equations. Usually, it is easiest to substitute into the linear equation.

__

Substituting for y in the first equation:

  x +(-1/4x^2 +3) = 2

Multiplying by -4 to eliminate the fraction and make the leading coefficient 1, we have ...

  -4x +x^2 -12 = -8

  x^2 -4x = 4 . . . . . . add 12

  x^2 -4x +4 = 8 . . . . add 4 to complete the square

  (x -2)^2 = 8 . . . . . . write as a square

  x -2 = ±√8 = ±2√2 . . . . take the square root

  x = 2 ±2√2 . . . . . . add 2

Solving the first equation for y, we get ...

  y = 2 -x

Substituting the values of x we found gives ...

  y = 2 -(2 ±2√2) = ∓2√2

Solutions are ...

  (x, y) = (2+2√2, -2√2) and (2-2√2, 2√2)

The ordered pair we are looking for is the values of the variables \(x\) and \(y\), or \((x, y).\)  We are given that \(x=2\), and that the formula to evaluate \(y\) is \(y = 5^x\). Note we are given \(x\) so we can evaluate \(y\) as \(y = 5^2 = 25\). Now, we have both the values of \(x\) and \(y\), so our ordered pair is thus \((x,y) = (2,25).\)

Answer:

That'll be the answer choice B

Step-by-step explanation:

-3(4-12)

Distribute :D

-3(4) - -3(12)

A subtraction sign and a negative sign cancel into a plus sign

-3(4) + 3(12)

Multiply!!

-12 + 36

Answer: I believe it would be B.-12+36

Answer:

-3/5

Step-by-step explanation:

Answer: 75%

Step-by-step explanation: 0.15/0.2=0.75

The probability that a customer ordered Vanilla ice cream given they ordered a Sundae is 0.75 or 75%

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

Pedro observed what customers ordered at his ice cream shop and found the following probabilities:

P(Vanilla) = P(V) = 0.3

P(Sundae) = P(S) = 0.2

P(Vanilla and Sundae) = P(V and S) = 0.15

To find the probability that a customer ordered Vanilla ice cream given they ordered a Sundae:

P(V|S) = P(V and S)/P(S)

P(V|S) = 0.15/0.2

P(V|S) = 0.75 or 75%

Thus, the probability that a customer ordered Vanilla ice cream given they ordered a Sundae is 0.75 or 75%

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The equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.

We know that the method to find the axis of the symmetry of the parabola is given by:

x = - b / 2 a

We have the general equation of the parabola as:

y = a x² + b x + c

We have the equation of the parabola as:

y = - 4 x² + 24 x - 35

Comparing from this equation, we get that:

a = - 4

b = 24

c = - 35

Now, substituting the values, we get that:

x = - 24 / 2 (- 4)

x = - 24 / - 8

x = 24 / 8

x = 3

Therefore, the equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.

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The total cost of the hotel for 4 nights with a 12% tip for housekeeping is $891.52.

The cost of the hotel room for 4 nights is:

$199/night * 4 nights = $796

To calculate the tip for housekeeping, we first need to find the amount of the bill before the tip.

This is just the cost of the hotel room:

Bill before tip = $796

To find the amount of the tip, we multiply the bill before tip by the tip percentage as a decimal:

Tip = 0.12 * $796 = $95.52

To find the total cost of the hotel, we add the bill before tip and the tip:

Total cost = Bill before tip + Tip

Total cost = $796 + $95.52

Total cost = $891.52

Therefore, the total cost of the hotel for 4 nights with a 12% tip for housekeeping is $891.52.

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The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.

Let's denote the missing terms as A and B.

The given sequence is: 3/k, A, B, 9/2k.

The common difference can be found by subtracting 3/k from A or B. Therefore:

A - 3/k = B - A = 9/2k - B.

To simplify, we can equate the two expressions for the                     common difference:

A - 3/k = 9/2k - B.

Next, we can solve for A and B using this equation.

Adding 3/k to both sides gives:

A = 3/k + 9/2k - B.

Now, we can substitute the value of A into the equation:

3/k + 9/2k - B - 3/k = 9/2k - B.

Simplifying further, we have:

9/2k - 3/k = 9/2k - B.

Cancelling out the common terms, we find:

-3/k = -B.

Multiplying both sides by -1, we get:

3/k = B.

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The cost of the molding is given as follows:

$119.30.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The parameters for this problem are given as follows:

d = 9 -> r = 4.5.

(as the radius is half the diameter)

Hence the circumference is given as follows:

C = 2 x π x 4.5

C = 28.27 ft.

The cost is of $4.22 per ft, hence the total cost is given as follows:

4.22 x 28.27 = $119.30.

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The transformations taking place in the given function is a horizontal left ward shift of 9 units and 1 unit upward vertical shift.

A Transformation in Math is a process of moving an object (two-dimensional shape) from its original position to a new position.

Given that, a function f(x) undergo some transformations to become f(x+9)-1,

We know that,

Vertical Shifting:

Adding a constant to a function will shift its graph vertically (i.e. y = f (x) + c). Adding a positive constant c will shift the graph upward c units, while adding a negative constant c will shift it downward c units.

Horizontal Shifting:

Horizontal shifts are inside changes that affect the input (x-) axis values and shift the function left or right. Combining the two types of shifts will cause the graph of a function to shift up or down and right or left.

Therefore, there is transformation of a horizontal and vertical shift.

Hence, the transformations taking place in the given function is a horizontal left ward shift of 9 units and 1 unit upward vertical shift.

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Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Answer

The store bought 98 half gallon milks

Explanation

Let the number of half gallon nilks they bought be x

They bought each half gallon milk at a rate of 2.2 dollars each

13 half gallons got spoilt.

They then sold the rest of the half gallone (x - 13) gallons at 3.96 dollars per half gallon

Profit = Revenue - Cost

Revenue = (Amount of half gallons sold) × (Price of each one)

Revenue = (x - 13) × 3.96

Revenue = (3.96x - 51.48)

Cost = (Amount of half gallons bought) × (Price of each one)

Cost = x × 2.20

Cost = 2.20x

Profit = 121 dollars

Profit = Revenue - Cost

121 = (3.96x - 51.48) - 2.20x

121 = 3.96x - 51.48 - 2.20x

121 = 1.76x - 51.48

1.76x - 51.48 = 121

1.76x = 121 + 51.48

1.76x = 172.48

Divide both sides by 1.76

(1.76x/1.76) = (172.48/1.76)

x = 98 half gallon milks

Hope this Helps!!!

The value of h such that the matrix is the augmented matrix of a consistent linear system is -2

From the question, we have the following parameters that can be used in our computation:

6 -3 h

-12 6 4

For a consistent system of linear equation, the equations are the equivalent

So, we have

6x - 3y = h

-12x + 6y = 4

Divide the second equation by -2

6x - 3y = -2

By comparing the equations, we have

h = -2

Hence, the solution of h is -2

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Note that the Polynomial Expression for to represent the total surface area of the two drums is: 4πrh + 4hr².

A polynomial expression is any expression that consists of variables, constants, and exponents and is combined using mathematical operators such as addition, subtraction, multiplication, and division.

According to the number of terms in the expression, polynomial expressions are classed as monomials, binomials, or trinomials.

Given that the total surface area of one cylinder is:

2πrh + 2πr²,

The total surface area of two drums will therefore be:

(2πrh + 2πr²) * 2

⇒ 4πrh + 4hr²

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The restrictions on the width is that it must be between 14.1 yards and 17.3 yards

From the question, we have the following parameters that can be used in our computation:

Area = between 240 yd² and 360 yd²

Also, we have

Length = 1.2 times the width

This means that

l = 1.2w

The area is then calculated as

Area = lw

So, we have

Area = 1.2w²

This means that

240 < 1.2w² < 360

Divide through by 1.2

200 < w² < 300

Take the square roots

14.14 < w < 17.32

Approximate

14.1 < w < 17.3

Hence, the width must be between 14.1 yards and 17.3 yards

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Answer:

Option C. 1020

Step-by-step explanation:

From the question given above,

512 + 256 +... + 4 =?

We'll begin by calculating the number of terms in the sequence. This can be obtained as follow:

First term (a) = 512

Common ratio (r) = 2nd term / 1st term

Common ratio (r) = 256 /512

Common ratio (r) = 1/2

Last term (L) = 4

Number of term (n) =?

Tₙ = arⁿ¯¹

L = arⁿ¯¹

4 = 512 × (1/2)ⁿ¯¹

Divide both side by 512

4 / 512 = (1/2)ⁿ¯¹

1/128 = (1/2)ⁿ¯¹

Express 128 in index form with 2 as the base

1/2⁷ = (1/2)ⁿ¯¹

(1/2)⁷ = (1/2)ⁿ¯¹

Cancel 1/2 from both side

7 = n – 1

Collect like terms

7 + 1 = n

n = 8

Thus, the number of terms is 8

Finally, we shall determine the sum of the series as follow:

First term (a) = 512

Common ratio (r) = 1/2

Number of term (n) = 8

Sum of 8th term (S₈) = ?

Sₙ = a[1 – rⁿ] / 1 – r

S₈ = 512 [1 – (½)⁸] / 1 – ½

S₈ = 512 [1 – 1/256] ÷ ½

S₈ = 512 [255/256] × 2

S₈ = 2 × 255 × 2

S₈ = 1020

Thus, the sum of the series is 1020.

Number of cups are 32.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A dietitian prepares a high-protein drink for 24 residents.

And, Each drink measures 3/4 cup.

Let number of cups of the drink will she prepare = x

So, We get;

⇒ 3/4 × x = 24

⇒ x = 24 × 4 / 3

⇒ x = 32 cups

Thus, There are 32 total cups of the drink will she prepare.

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The end behavior of the polynomials are as follows;

(a) y = x³ - 9·x² + 8·x - 14

End behavior; y → ∞ as x → ∞

\({}\)                        y → -∞ as x → -∞

(b) y = -8·x⁴ + 13·x + 800

End behavior; y → -∞ as x → -∞

\({}\)                        y → -∞ as x → ∞

The end behavior of a polynomial is the characteristics of the graph of the polynomial as the input (x-values), tends to plus and minus infinity.

The factors that effect the end behavior of a polynomial are;

The degree of the polynomial, (even or odd)

The sign of the leading coefficient of the polynomial (positive or negative)

The leading coefficient is the coefficient of the term with the highest degree.

(a) The polynomial, function, y = x³ - 9·x² + 8·x  - 14

The specified polynomial is a third degree polynomial, with a positive leading coefficient of 1, the end behavior is therefore;

y tends to positive infinity as x tends to positive infinity

y tends to negative infinity as x tends to negative infinity

End behavior;

y → ∞ as x → ∞

y → -∞ as x → -∞

(b) The polynomial function can be expressed as follows;

y = -8·x⁴ + 13·x + 800

The above polynomial of degree 4 is an even degree polynomial

The leading coefficient of the polynomial is -8, therefore, the leading coefficient is negative

The shape of the graph of the polynomial is therefore ∩ shaped, such that the end behavior is as follows;

y-values approaches negative infinity as x approaches negative infinity

y-values approaches negative infinity as x approaches positive infinity

End behavior;

y → -∞ as x → -∞

y → -∞ as x → ∞

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Answer:

It is 90º

Step-by-step explanation:

Looking at the picture, we realize that the angle direcly beside it, EGD, is 90º. Now, both angles form a straight line, which equals 180º. 180-90= 90º.

Answer: A 40 B 50 C 90 D 130

where they go: B goes under A, D goes under the whole thing, just like E (although that doesn't want to be answered) and C goes under B

hope this helped

Answer:

It would cost $30 to buy 10 ice creams.

Step-by-step explanation:

1 ice cream costs $3

10*3=30

Answer:

No it is 12

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

6 ÷ 1/2 = 12

(1/2 = 0.5)

6 ÷ 0.5 = 12

Check you answer.

0.5 x 12 = 6

So Jordan is incorrect.

The correct answer is 12

Hope this helped :)

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We can use the concept of Line Intercept form . She should count up 2 and right 1 . So the correct option is D.

When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula. We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable. Set x = 0 and then solve for y to find the y-intercept.

  y=mx+b is the slope intercept formula

The given equation is y=2x-7.

By comparing to slope intercept formula y=mx+b,

   m=2 and b=-7.  

   So the slope of the given equation is 2 and y-intercept is (0,-7).

we know that,

             m=rise/run

             so rise=2 and run=1 that means Sam needs to count up 2 and right 1 to graph the equation using the given slope.

We can use the concept of Line Intercept form . She should count up 2 and right 1 . So the correct option is D.

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Podras comprar un total de 8 docenas, y sobrara $1.30

Sabemos que una docena de bananos cuesta $2.65, y queremos ver cuantas docenas se peden comprar con $22.50, para ver esto, debemos tomar el cociente entre la cantidad de dinero que tenemos y el precio de una docena.

Obtendremos:

$22.50/$2.65 = 8.49

Redondenado al proximo numero entero obtenemos 8, es decir, se pueden comprar 8 docenas.

La cantidad que sobra es:

$22.50 - 8*$2.65 = $1.30

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The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Take a look at the attachment below. It fills in for the attachment that wasn't provided in the question -

An oblique pyramid is one that has a top not aligned with the base. Due to this, the height of the pyramid connects with two vertices at its ends to form a right angle present outside the pyramid, knowing that it is always perpendicular to the base. There is no difference between the calculations of the volume of an oblique pyramid and a pyramid however -

\(\\Base Area = 2 cm * 2 cm = 4 cm^2,\\Volume ( Pyramid ) = 1 / 3 * ( Base Area ) * ( Height ),\\Volume = 1 / 3 * ( 4 ) * ( 3.75 ),\\-------------------------\\Volume = 5 cm^3\)

And thus, you're solution is 5 cm^3, or in other words option b!

Answer:

The answer is B

Step-by-step explanation:

C

y=e^x

x=log base e

same as

16=2^x

x=log 16 base 2

Answer:

C

Step-by-step explanation:

You have to convert them from logarithm to exponential.

The first one becomes x = 2^16

The second one becomes 2 = 16^x

The third one becomes 16 = 2^x

The fourth one becomes x = 16²

The third one is your answer.

Answer: 0.3063 * 10^-1

Step-by-step explanation: hope this helps!

Answer: The expression for the absolute value of x+2 when x is less than 2 is -(x+2).

Step-by-step explanation: When x is less than 2, x+2 is a negative number. The absolute value of a negative number is its opposite with the negative sign, so the absolute value of x+2 is -(x+2). Therefore, when x is less than 2, the expression for the absolute value of x+2 is -(x+2).