Lena decides to make 1 batch of mac-and-cheese
and 3 pizzas. How many tablespoons of basil does
she need?

Answer:

Answer:

the modulus of a complex number z = a + bi is:

Izl= √(a²+b²)

The fact that n is complex does not mean that n doesn't has a real part, so we must write our numbers as:

m = 2 + 6i

n = a + bi

Im + nl = 3√10

√(a² + b²+ 2²+ 6²)= 3√10

√(a^2 + b^2 + 40) = 3√10

squaring both side

a²+b²+40 = 3^2*10 = 9*10 =90

a²+b²= 90 - 40

a²+b²=50

So,

|n|=√(a^2 + b^2) = √50

The modulus of n must be equal to the square root of 50.

now

values a and b such

a^2 + b^2 = 50.

for example, a = 5 and b = 5

5²+5²=25+25= 50

Then a possible value for n is:

n = 5+5i

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]5x+4y=16\implies 4y=-5x+16\implies y=\cfrac{-5x+16}{4} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{5}{4}}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is -5/4 and it passes through (8 , -7)

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{- \cfrac{5}{4}}(x-\stackrel{x_1}{8}) \implies y +7= -\cfrac{5}{4} (x -8) \\\\\\ y+7=-\cfrac{5}{4}x+10\implies {\Large \begin{array}{llll} y=-\cfrac{5}{4}x+3 \end{array}}[/tex]

Answer:

This equation involves three variables: a, b, and c. Each variable is multiplied by a coefficient and then added together to equal a constant. To solve the equation, we must first determine what the value of the three variables are. To do this, we must use the coefficients to isolate each variable. We can start by isolating c. Divide both sides of the equation by 4 to get 2a + 9b = c. Now we can isolate b by subtracting 2a from both sides to get 9b = c - 2a. Divide both sides by 9 to get b = (c - 2a)/9. Finally, we can isolate a by subtracting 9b from both sides to get 2a = 4c - 9b. Divide both sides by 2 to get a = (4c - 9b)/2. Once we have the values of the three variables, we can substitute them into the original equation to check our work.

Step-by-step explanation:

Answer:

a=\frac{4c-9b}{2}

Answer:

12.9

Step-by-step explanation:

cos 72 = 4/x

x = 4/cos72

x = 12.9

Answer:

2

Step-by-step explanation:

Answer:

5 (x + 4)

Step-by-step explanation:

5x = 5 * x

20 = 5 * 4

5 is the only thing thye have in common, so we put 5 in front and add x + 4

5 (x + 4)

5(x+4) is the correct answer

Answer:

Step-by-step explanation:

a. we konw triangle have 180°

b. A straight line have 180°， so

∠abc=180-5x-12=168-5x,

∠bca=180-10x+37=217-10x

∠cab=180-9x-1=179-9x

then  add them all 564 - 24x = 180

c.384=24x, x=16

d.so ∠bca=217-10·16=57.

Answer:

-------------------------------------------

Sum of exterior angles is 360°:

The exterior angle at vertex C is:

The ∠BCA is the linear pair with 123°:

Answer:

Your right

Step-by-step explanation:

Answer:

(-5, -1)

Step-by-step explanation:

Equation Form:

x = -5

y = -1

Answer:

Solve the System of Equations

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(−5,−1)

Equation Form:

x= −5, y= −1

The missing side of a right triangle without using a calculator can be found by using the Pythagoras theorem .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the square of the hypotnuse (longest side) is equal to the sum of the square of the perpendicular and base .

that means : [tex]Hypotnuse^{2} = Perpendicular^{2} + Base^{2}[/tex]  ;

let the missing side of the right triangle  be the hypotnuse ;

So , missing side can written as :  [tex]Hypotnuse = \sqrt{Perpendicular^{2} + Base^{2}}[/tex] .

For Example : Let the right triangle has sides lengths as perpendicular = 6 and hypotnuse = 10

The length of side "base" is unknown.

So ,  to find length of side b, we put the known values into theorem:

[tex]10^{2} = 6^{2} + Base^{2}[/tex] ;

[tex]base^{2} = 100 - 36[/tex] ;

So , the missing side "base" = 8 ;

Therefore , the missing side without using calculator can be found by the Pythagoras Theorem .

The given question is incomplete , the complete question is

How do you find the missing side of a right triangle without a calculator when the other two sides are given ?

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The time taken for 21,000 spectators to vacate the stadium, if only 15 exits are functional is 28 minutes

A variation is a relation between a set of values of one variable and a set of values of other variables

Let E, N and T represent the number of exits, the number of spectators and the time taken to exit the stadium respectively

We can write the variation as:

T α N/E

T = kN/E  (where k is constant of proportionality)

when N = 25,000, E = 25, T = 20:

T = kN/E

k = TE/N

k = (20×25)/25000 = 0.02

when N = 21,000 and E = 15:

T = kN/E

T = (0.02×21,000)/15 = 28 minutes

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Answer:

A. 10 points

Step-by-step explanation:

The average test score for studying 3 hours is 75, while the average test score for studying 4 hours is 85. Therefore the average rate of increase of test scores between 3 and 4 hours studied is 10 points, since 85-75=10.

Answer:

[tex]11 \: minutes = 99 \: gallons \\ 1 \: minute = (\frac{1 \times 99}{11} ) \: gallons \\ = 9 \: gallos \: per \: minute[/tex]

Oscar Wilde creates a hilarious tone by using puns, situational irony, dramatic irony, satire, and epigrams.

Oscar Fingal O'Flahertie Wills, an Irish poet, and playwright, lived from 16 October 1854 to 30 November 1900.

He wrote in a variety of genres throughout the 1880s before becoming one of London's most well-known playwrights in the early 1890s.

The Picture of Dorian Gray, his plays and epigrams, as well as the circumstances surrounding his meningitis-related early death at age 46 and criminal conviction for gross indecency for consensual homosexual activities in "one of the earliest celebrity trials," is what people will remember him for most.

Using puns, situational irony, dramatic irony, satire, and epigrams, Oscar Wilde establishes a humorous tone.

Therefore, Oscar Wilde creates a hilarious tone by using puns, situational irony, dramatic irony, satire, and epigrams.

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Answer:

Vertex (2, 3)

Axis of Symmetry: x = 2

Step-by-step explanation:

You can look at the labeling from my last answer, the parabola is just upside down but it is still the same label.

Hope it makes sense :)

Answer:

Axis of Symmetry:  x = 2

Vertex:  (2, 3)

Step-by-step explanation:

find axis of symmetry:  x = -b/2a

x = -8 ÷ 2(-2)

x = 2

find vertex by substituting 2 for 'x':

y = -2(2²) + 8(2) - 5

y = -8 + 16 - 5

y = 8 - 5

y = 3

Vertex:  (2, 3)

Answer:

477

Step-by-step explanation:

Answer:

half of 8 is 4

4^4 = 16

16 x 3.14 = 50.24 (area of a circle)

Now we multiply it by the height:

50.24 x 19 = 954.56 rounded to the nearest hundredths place is:

954.56 yd3 is your answer.

Answer:

165 students or the sophomore class of 220 are not athletic.

Step-by-step explanation:

60/240 = .25 This means that 25% of the class is athletic.  That would mean and .75 or 75% are not athletic.

220 x .75 = 165

Step-by-step explanation:

[tex]P( - 2 \leqslant x \leqslant 2) = 0.33 + 0.16 + 0.11 \\ = 0.6[/tex]

Answer: 375

Step-by-step explanation:

Since we are given the information that there are 250 bricks used to build a wall 20 feet high, the number of brick used per feet will be:

= 250/20

= 12.5 bricks per feet.

Therefore, the number of bricks that will be used to buld a wall that is 30 fet high will be:

= 12.5 × 30

= 375 bricks.

Therefore, 375 bricks would be used.

Answer:

y-intercept is -9

Step-by-step explanation:

g(0) = -3(0)² - 5(0) - 9

g(0) = 0 - 9

g(0) = -9

Answer:

22% decrease

Step-by-step explanation:

(1100-900)/900 = .22

Answer:

For the first line its distributive property
The 2nd is combining like terms

4th is simplifying it

Im not sure about the last one since its just the answer of the problem

Step-by-step explanation:

Answer:

B. 1

Because of the shape you can have only one line of symmetry

Answer:

1408 yards

Step-by-step explanation:

A horse walks 4224 feet in 12 minutes, so to find out how many yards the horse walks in twelve minutes, we need to convert 4224 feet to yards. Since there are 3 feet in a yard, we can divide 4224 by 3 to find the number of yards:

4224 feet / 3 feet/yard = 1408 yards

So a horse walks 1408 yards in 12 minutes.

Answer:

1. A=bh/2

2. I don’t know, I‘m sorry :(((( but if I had to guess I’d pick A = s x s

3. A = πr² (might be wrong, i’m so sorry)

Step-by-step explanation:

1.  The formula for area of a triangle is A = bh/2

2. The formula for area of a square is s x s.

3. The formula for area of a circe is A = πr².

The formula used in getting the area of the shaded region is (1/2)bh, s * s and  πr²

An area is the amount of space occupied by a two dimensional shape or object.

1) The area of a triangle = (1/2) * base (b) * height (h) = (1/2)bh

2) Area of square = side (s) * side(s) = s * s

3) Area of circle = π * radius (r)²= πr²

The formula used in getting the area of the shaded region is (1/2)bh, s * s and  πr²

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