Ingredients for 16 brownies:

2/3 cup butter, 5 ounces unsweetened chocolate, 1 and 1/2 cups sugar, 2 teaspoons vanilla, 2 eggs, 1 cup

How much of each ingredient is needed to make 12 brownies?

Answer:

x  = - 2 is confirmed to be the real solution of the equation.

Step-by-step explanation:

We are tasked with the following activities

Conjecture: How many solutions do [tex]x^3 - 5x^2 + 28 = 0[/tex]  have?

Find the real solution(s) of the equation.

Then use polynomial long division to find the other solution(s).

To start with the how many solutions that  [tex]x^3 - 5x^2 + 28 = 0[/tex]  have

suppose that -2 happens to be a root of the equation, we can easily replace x = - 2 in the given equation. Then , we will have :

[tex](-2)^3 - 5(-2)^2 + 28 = 0[/tex]

[tex]-8 - 5\times 4 + 28 = 0[/tex]

-8 - 20  + 28 = 0

-28 - 28 = 0

0 = 0

The equation resulted to 0 = 0 when x = -2 , as such -2 happens to be one root of the equation

So , as x = - 2

x + 2 = 0  

x  = - 2 is confirmed to be the real solution of the equation.

A picture showing the polynomial long division method used for solving the polynomial equation and other solution(s) can be found in the attached file below.

Answer:

r = -7

Step-by-step explanation:

Solve for r:

8 r + 9 = -4 (3 - r) - 7

-4 (3 - r) = 4 r - 12:

8 r + 9 = 4 r - 12 - 7

Grouping like terms, 4 r - 12 - 7 = 4 r + (-7 - 12):

8 r + 9 = 4 r + (-7 - 12)

-7 - 12 = -19:

8 r + 9 = 4 r + -19

Subtract 4 r from both sides:

(8 r - 4 r) + 9 = (4 r - 4 r) - 19

8 r - 4 r = 4 r:

4 r + 9 = (4 r - 4 r) - 19

4 r - 4 r = 0:

4 r + 9 = -19

Subtract 9 from both sides:

4 r + (9 - 9) = -9 - 19

9 - 9 = 0:

4 r = -9 - 19

-9 - 19 = -28:

4 r = -28

Divide both sides of 4 r = -28 by 4:

(4 r)/4 = (-28)/4

4/4 = 1:

r = (-28)/4

The gcd of -28 and 4 is 4, so (-28)/4 = (4 (-7))/(4×1) = 4/4×-7 = -7:

Answer:  r = -7

Answer:

C' ( -10 , 4)

D' (-10 , 6)

E' (-8 , 6)

F' (-8 , 4)

Answer:

Step-by-step explanation:

4. when bases are equal ,powers are also equal.

x+4=3x-1

3x-x=4+1

2x=5

x=5/2=2.5

Answer:

x  = 24  minutos

Step-by-step explanation:

Llamaremos  "y" el costo fijo mensual y "x" la cantidad de minutos consumidos al mes, según lo cual:

El enunciado del problema establece que la facturación en pesos es igual a un costo fijo  y   más el consumo en minutos del mes, entonces

En Abril    52,50  =  y  +  b*x     ⇒   52,5  =  y  +  69*b

y en Mayo   32   =  y  +  b*x      ⇒   32  =  y  + 28*b

Así obtuvimos un sistema de dos ecuaciones con dos incógnitas, que resolveremos y obtendremos los valores de b y de y

y  =  52,50  -  69*b

32 = ( 52,50  -  69*b ) + 28*b

- 20,50  =  - 41*b

b  =  0,5

y    y  =  52,5  - 69*0,5

y =  18

Entonces la ecuación de facturación es :

F(x) = 18  + 0,5*x

Para pagar como máximo 30 pesos en el mes siguiente

F(x) =  30  =  18 + 0,5*x

30 -  18  =  0,5*x

x  = 24  minutos

Answer:

Step-by-step explanation:

(6 x 10^5) + (4 x 10^4) + (5 x 10^3) + (3 x 10^2)

Answer:

B. ZJ = 85

C. KH = 68

Step-by-step explanation:

Given that ZK, ZL, ZM are perpendicular bisectors of ∆GHJ, they form a circumcenter which is equidistant from the vertices of ∆GHJ. According to the circumcenter theorem, ZH = ZG = ZJ = 85.

Also each median formed is equal. This means: KH = GH, LH = LJ, MG = MJ

Since HG = 136, KH = ½ of 136 = 68.

The two options that are true are:

B. ZJ = 85

C. KH = 68

Answer:

Step-by-step explanation:

See attachment

Answer:

83

Step-by-step explanation:

.179 of x = 14.857

x = 14.857/.179

x = 83

Answer:

1) [tex]a=\dfrac{F}{m}[/tex]

2) [tex]m=\dfrac{p}{v}[/tex]

Step-by-step explanation:

1) The given equation is

[tex]F=ma[/tex]

We need to solve this for a.

In the given triangle place single variable i.e., F, on the top and variables in the product in the bottom (order of m and a does not matter) as shown in the below figure.

Using the triangle and the operations (× and ÷), we get

[tex]F=ma[/tex]

[tex]a=\dfrac{F}{m}[/tex]

[tex]m=\dfrac{F}{a}[/tex]

Therefore, the required answer is [tex]a=\dfrac{F}{m}[/tex].

2) The given equation is

[tex]p=mv[/tex]

We need to solve this for m.

In the given triangle place single variable i.e., p, on the top and variables in the product in the bottom (order of m and v does not matter) as shown in the below figure.

Using the triangle and the operations (× and ÷), we get

[tex]p=mv[/tex]

[tex]m=\dfrac{p}{v}[/tex]

[tex]v=\dfrac{p}{m}[/tex]

Therefore, the required answer is [tex]m=\dfrac{p}{v}[/tex].

Answer:

Is the number rational or irrational?

30‾‾‾√

rational

irrational

Step-by-step explanation: help ;-;

Option (3) the product of two irrational numbers is a rational number is a correct option.

"Rational numbers are numbers that can be expressed as a fraction or part of a whole number. It includes the integers, plus all fractions, or terminating decimals and repeating decimals".

"Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers".

For the given situation,

We need to analyze the all options.

Option 1:

The sum of a rational number and an irrational number is an irrational number.

Option 2:

The product of a rational number and an irrational number is an irrational number.

Option 3:

The product of two irrational numbers is a rational or an irrational number based on the numbers taken.

Option 4:

The sum of two irrational numbers is an irrational number.

Hence we can conclude option(3), the product of two irrational numbers is a rational number is a correct option.

Learn more about rational numbers here

https://brainly.com/question/24540810

#SPJ2

Answer:

Probabilty= 7.66*10^-3

Step-by-step explanation:

A box contains 65 balls numbered from 1 to 65.

9 balls are drawn with replacement.

Probabilty of selecting a number = 1/65

Probabilty of selecting a number

= 0.0154

Probabilty of at least 2 numbers out of 9 selected to have Same number

Probabilty= 9C2(0.0154)^2(0.9846)^7

Probabilty= 7.66*10^-3

Answer:

plz give hlamberttx the brainliest!

Step-by-step explanation:

he saved my grade and helped me sooo much with this question. he is 100% correct i got an 100 on my usa test prep

Answer:

well basically for the first question it gives you

The rate that increases. which is 0.03 per second

And that R = 48 inches at time.

and T= 0.

The question wants you to determine the volume of the balloon at the time and find the volume when t= 300 seconds. so just replace 0 to 300.

Answer:

Answer: 13m

Step-by-step explanation:

Use Pythagorean theorem: a²+b²=c²

5²+12²=c²

25+144=c²

c²=169

c=13 (even if it is true that there are positive and negative solution, but length cannot be negative)

Given:

To Find:

Concept Used:

Answer:

Here given

Here the length of ladder is equal to hypotenuse of ∆ so formed.

Now in a right angled ∆ ,

=> (hypotenuse)² = (pependicular)²+(base)².

=> h ² = (12m)²+(5m)²

=> h² = 144m² + 25m².

=> h² = 169m².

=> h = √169m².

=> h = 13m.

Hence the required answer is 13m.

Answer:

-15 > -19

Step-by-step explanation:

-15 > -19

-15 is closer to 0 than -19 so it is greater than

Answer:

[tex] \boxed{\sf Area \ of \ rectangle = 10x^3} [/tex]

Given:

Length of rectangle = 5x²

Width of rectangle = 2x

To Find:

Area of rectangle

Step-by-step explanation:

[tex]\sf Area \ of \ rectangle = Length \times Width[/tex]

[tex] \sf = 5 {x}^{2} \times 2x[/tex]

[tex] \sf = 5 \times 2 {x}^{2 + 1} [/tex]

[tex] \sf = 5 \times 2 {x}^{3} [/tex]

[tex] \sf = 10 {x}^{3} [/tex]

Answer:

[tex]\huge\boxed{Area\ of\ Rectangle = 10x\³}[/tex]

Step-by-step explanation:

Area of Rectangle = Length * Width

Where Length = 2x and Width = 5x²

Area of Rectangle = (2x)(5x²)

Area of Rectangle = 10x³

Answer:

c = 72

Step-by-step explanation:  

8        

        x   ___c__     =   9  x   8

                   8

c = 72

Hi there! Hopefully this helps!

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

[tex]\frac{c}{8} = 9[/tex]

Multiply both sides by 8.

[tex]c = 9 \times 8[/tex]

Answer:

Jane is correct

Step-by-step explanation:

100 divide by 3 is 33.333 recurring

100 divided by 8 is 12.5

Answer:

59

Step-by-step explanation:

I think your equation is supposed to look like this:

(7 + 1)² - (11 + 3²)/4

Follow PEMDAS to solve (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)

(7 + 1)² - (11 + 9)/4

(8)² - (20)/4

64 - (20)/4

64 - 5

59

Answer:

Chances of both even number = 30 times

Step-by-step explanation:

Given:

Chances of both even number = 1/4

Total number of tosses = 120

Find:

How many times both dice show even number

Computation:

Chances of both even number = [Chances of both even number][Total number of tosses]

Chances of both even number = 1/4 [120]

Chances of both even number = 30 times

Answer:

24 - 3y

Step-by-step explanation:

Since the sum of the two numbers is 8, the larger number is 8 - y.

Three times the larger number: 3 (8 - y).

Simplify using Distributive property: 3 (8 - y) = 24 - 3y.

So the answer is 24 - 3y

Answer:

56

Step-by-step explanation:

First, convert the 70% so that we can use it with the 80 cups. To do this, convert the percent to a decimal by moving the decimal 2 spaces to the left:

70% → 70.00 → 0.70 → 0.7

70% percent can be seen as 0.7. Multiply this by 80:

[tex]80*0.7=56[/tex]

So, 70% of 80 is 56. Desmond sold 56 cups on the second Saturday.

:Done

Answer:

Step-by-step explanation:

Hello, first we can develop (x+a)(x+b)

[tex](x+a)(x+b)=x(x+b)+a(x+b)=x^2+bx+ax+ab=x^2+(a+b)x+ab[/tex]

We know that this should be equal to

[tex]x^2+x-72[/tex]

So, we can identify the coefficients of the like terms

1 = 1 (terms in [tex]x^2)[/tex]

1 =  a + b (terms in x)

-72 = ab (constant term)

72 is 8 * 9 so, -72=9*(-8)

and we have 9 - 8 =1

so, a = 9 and b = -8

[tex]\Large \boxed{\sf \bf \ x^2+x-72=(x+9)(x-8) \ }[/tex]

Thank you

We are to consider the given expression:

x² + x - 72

The above expression is a quadratic expression and the objective is to determine its roots in form of (x + a) (x + b)

In form of (x + a) (x + b), the values of the expression x² + x - 72 in form of (x + a) (x + b) are 9 and -8 respectively.

From the given expression;

x² + x - 72

So; we will look for two factors of 72 in such a way that if those factors are multiplied together; they will give -72 and the addition of those two numbers will give +1.

So, the factors of 72 are:

From the above factors;

∴

Our factors are:  (-8)  and (9)

From  x² + x - 72, we have:

x² + (-8x) + (9x) - 72 = 0

(x² - 8x) + (9x -72) = 0

Opening the brackets by factorization;

x(x -8) + 9(x -8) = 0

(x + 9) or (x - 8) = 0

(x + 9) (x - 8) = 0

Recall that, we are to replace the values of a and b with the roots derived from the expression x^2 + x - 72.

Therefore, we can conclude that the values of a and b are 9 and -8 respectively.

Learn more about quadratic equations here:

https://brainly.com/question/17177510?referrer=searchResults

Answer:y=0 So its A

Step-by-step explanation:3(-y+7)=3(y+5)+6

We move all terms to the left:

3(-y+7)-(3(y+5)+6)=0

We add all the numbers together, and all the variables

3(-1y+7)-(3(y+5)+6)=0

We multiply parentheses

-3y-(3(y+5)+6)+21=0

We calculate terms in parentheses: -(3(y+5)+6), so:

3(y+5)+6

We multiply parentheses

3y+15+6

We add all the numbers together, and all the variables

3y+21

Back to the equation:

-(3y+21)

We get rid of parentheses

-3y-3y-21+21=0

We add all the numbers together, and all the variables

-6y=0

y=0/-6

y=0

Answer:

y = 0

Step-by-step explanation:

Answer:

C, (6, ∞)

Step-by-step explanation:

The x intercept is 6, and it continues downward for infinity. :) I had this question on my assignment today and it was right!

Interval of the domain for which function is negative is equals to ( 6, ∞).

" Function is defined as relation between two variable is such that for all the inputs there is exactly one output."

Standard equation of the line

y = mx + b

b = y-intercept

m = slope

According to the question,

For the given line in graph,

y- intercept = 4

x- intercept = 6

Therefore ,

For the function y = mx + b  we have,

b = 4

y = mx + 4

Substitute the value of x- intercept in the function y = mx +4 we get,

when x = 6 , y= 0

[tex]0 = m(6) + 4\\\\\implies m= \frac{-4}{6}\\ \\\implies m= \frac{-2}{3}[/tex]

Function [tex]y = \frac{-2}{3}x+ 4[/tex]

Interval of the domain is function is  negative.

[tex]y < 0 \\\\\implies \frac{-2}{3}x+ 4 < 0\\\\\implies -2x + 12 < 0\\\\\implies -2x < -12\\\\\implies 2x > 12\\\\\implies x > 6[/tex]

Interval of the domain is function is  negative is ( 6, ∞).

Hence, Option (C) is the correct answer.

Learn more about function here

https://brainly.com/question/12431044

#SPJ2

Answer:

Step-by-step explanation:

Parallel lines