As part of a chemistry experiment, Barry is making a mixture of two solutions. He uses 4 cups of solution A for every 2 cups of solution B. The table below shows the numbers of cups he uses of solution A and solution B. Solution A (cups) Solution B (cups) 4 2 8 4 12 6 16 8 Using the information from the table, choose the correct statement. A. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3. B. The ratio of the number of cups of solution A to the total number of cups of the mixture is 3:2. C. There are 3 cups of solution A for every 6 cups of mixture. D. For each cup of solution A, there are 2 cups of solution B.

1. (ab + bc) (ab – bc) + (bc + ca) (bc – ca) + (ca + ab) (ca – ab) = 0

We know that (a+b)(a-b) = a²-b²

(ab + bc)(ab -bc) can be written as a²b² - b²c²

(bc + ca)(bc -ca) can be written as b²c² - c²a²

(ca + ab)(ca - ab) can be written as c²a² - a²b²

→ a²b² - b²c² + b²c² - c²a² + c²a² - a²b²

→ a²b² - a²b² - b²c² + b²c² - c²a² + c²a²

→ 0

2. (a + b + c) (a² + b² + c² – ab – bc – ca) = a³ + b³+ c³ – 3abc

→ a³ + ab² + ac² -a²b - abc -ca² + a²b + b³ + bc² - ab² - b²c - abc + a²c + b²c + c³ - abc - bc² - c²a

→ a³ + b³+ c³ + (- abc - abc - abc) + (ab² - ab² )+ (ac² - ca² ) -(a²b + a²b )+ (bc² - bc² )+ (a²c - c²a) + (b²c - b²c)

→ a³+b³+c³ - 3 abc .

3. (p – q) (p² + pq + q²) = p³ – q³.

→ p³ + p²q + pq² - p²q - pq² - q³

→ p³ - q³ +(p²q - p²q) + (pq² - pq²)

→ p³ - q³

Step-by-step explanation:

Hello,

Firstly just look to triangle BDE,

Here, you will find that,

140° = y+80° {the exterior and opposite interior angle of a triangle is equal}.

or, y= 140°-80° {shifting 80° to another side and subtracting it.}

Therefore, the value of y is 60°.

now, let's simply work with line EB or EG. we get;

angle GEF + y=180° { being a linear pair}.

or, angle GEF + 60°= 180°

or, angle GEF = 180°-60°

Therefore, the value of angle GEF = 120°.

now, looking in triangle EFG, we get;

angle GEF + 35°+x= 180° { the sum of interior angle of a triangle is 180°}.

or, 120°+35°+ x= 180°

or, x= 180°- 155°

Therefore, the value of x is 25°.

now, lastly finding the value of "z"

We find that x= z {being vertical opposite angle}

or, z =25°

Therefore, the value of z is 25°.

So, the values are,

x=25°

y=60°

and z= 25°

Hope it helps...

6 cm from what im seeing

Answer: 7 cm

Step-by-step explanation:

Answer:

(3x-1) (x+1)

Step-by-step explanation:

3x^2 + 2x − 1

3x^2 factors into 3x and x

-1 factors into -1 and 1

We want a postive 2x

(3x-1) (x+1)

Answer:

(3x-1)(x+1)

Step-by-step explanation:

3x² + 2x − 1

when factorizing , first look at the constant number( in this case it is 1 prime number), then find the GCF if found.

(3x        )(x      )     first step : 3x*x=3x^2

(3x-      ) (x+   )      the sign for the constant is minus so the factoring has to be minus and plus on each side

(3x-1)(x+1)   look at the 2x it has positive sign, means the sign is plus:

3x-1

x+1

                        regular standard multiplication

3x(x)-1(x)+1(3x)-1

3x²+2x-1

Answer:

x = -1

Step-by-step explanation:

the line of the simetry is x = -1

Answer:

Its x = -1 because it splits the diamond shape perfectly at x -1

Step-by-step explanation:

Answer:

prime

Step-by-step explanation:

3x^2 + 5x + 1

it can't be factorizes with rational numbers

Answer:

Prime

Step-by-step explanation:

3x^2 + 5x + 1

3x^2  factors in to 3x and x

1 factors into 1 and 1

( 3x   + 1) ( x+1)

We need to verify the middle is 5

3x+1x = 4x

so this is not true

We cannot factor this so it is prime

Answer:

D

Step-by-step explanation:

Since this is a right triangle, and we are given that one of the other angles is 30°, we have a 30°, 60°, 90° triangle.

In a 30°, 60°, 90° triangle, the side lengths are all related as shown below.

We should determine a first. a is the measure of the side opposite to the 30° angle. Thus:

[tex]a=11[/tex]

The side opposite to the 60° angle is given by a√3. Since a = 11, the side opposite to the 60° angle or x is:

[tex]x=(11)\sqrt{3}=11\sqrt3[/tex]

Finally, the hypotenuse will be 2a. Since a = 11, the hypotenuse or y will be:

[tex]y=2(11)=22[/tex]

Hence, x = 11√3 and y = 22.

Our answer is D.

=================================================

Explanation:

The graph goes on forever to the left and right. This means any real number x can be plugged into the function to get some output y. The domain is the set of all real numbers. In interval notation, we would say [tex](-\infty, \infty)[/tex] which is another way of saying [tex]-\infty < x < \infty[/tex]

The range is y > -100 because the exponential graph steadily approaches this horizontal asymptote. Think of it like an electric fence you cannot touch. Since we never actually get to this y value, this means y = -100 is not part of the range. Your teacher made a typo when they wrote [tex]y \ge -100[/tex] and instead they should have written [tex]y > -100[/tex]. So basically y can be anything larger than -100. The graph may look like it eventually reaches y = -100 itself, but it's actually just getting closer and closer to this y value. To write the range in interval notation, we would say [tex](-100, \infty)[/tex]

This function is exponential because it has the general shape all exponential growth functions do. We have a fairly flat part with very slow growth at first, but then as time goes on, the growth rate increases dramatically resulting in the very steep curve.

Quartic polynomials are 4th degree polynomials. They have the same end behavior as quadratic functions do, since both are even degree polynomials. We don't have a quartic here because the left end behavior isn't going off to positive infinity as the right end behavior is.

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]a = b[/tex]

Required

Match proper type of equality

Each of the equality properties can easily be identified with their names; For multiplication property of equality, same term must be multiplied on both sides;

For addition, same term  must be added on both sides;

Same thing implies for division and subtraction

Multiplication:

[tex]a(c) = b(c)[/tex]

Subtraction

[tex]a - c = b - c[/tex]

Addition

[tex]a + c = b + c[/tex]

Division

[tex]a/c = b/c[/tex]

Answer:

Toni's Tiles and Bob's Bathrooms are in a proportional relationship as they have the same unit rate

Step-by-step explanation:

The given parameters are;

,                                           Area Tiled (ft²)                                    Time (Hr:min)

,                                            

Toni's Tiles,                                   803                               2:12

Bob's Bathrooms,                         1,460                             4:00

Rhonda's Restroom Redos          753                                1:30

The unit rate for each tiler

Toni's Tiles = 803/2:12 = 803/(2×60 + 12) =  6.083 ft²/min

Bob's Bathrooms = 1460/(4×60) =  6.083 ft²/min

Rhonda's Restroom Redos  = 753/(60 + 30) = 8.37 ft²/min

Therefore we have;

The rates at which Toni's Tiles and Bob's Bathrooms tile are to one another = 6.083 to 6.083  = 1:1

The rates at which Toni's Tiles and Rhonda's Restroom Redos tile are to one another = 73/12×30/251 = 365:502

The rate at which Bob's Bathrooms  and Rhonda's Restroom Redos tile are to one another = 73/12×30/251 = 365:502

Therefore, Toni's Tiles and Bob's Bathrooms are in a proportional relationship as they have the same unit rate.

Answer:

21 squares

Step-by-step explanation:

Here in this question, we are given a pattern and we want to determine what the values in that pattern will be at a specific step.

We proceed as follows;

What we can see in this pattern is that the difference in number of squares between a pattern and the next pattern increases by the addition of the next integer to the number of squares we have in the last pattern.

Thus for step 5, we shall be adding the next integer( 5) to the number of squares ;

That would be 10 + 5 = 15 squares

For step 6, we shall be adding the next integer (6) to the number of squares in step 5.

That would be 15 + 6 = 21 squares

How we got the initial next integer?

step 1 = 1 square

step 2 = 3 squares ( integer difference of 2)

step 3 = 6 squares ( integer difference of 3)

step 4 = 10 squares ( integer difference of 4)

so;

step 5 = 15 squares ( integer difference of 5)

step 6 = 21 squares( integer difference of 6)

Answer:

B. 2.7 g

Step-by-step explanation:

The half life of a substance is the time taken for the substance to reduce to half of its original amount. It is given by:

[tex]A=A_o*(\frac{1}{2})^\frac{t}{t_{1/2}}\\ Where\ A\ is \ the \ amount \ of \ substance\ remaining\ after\ t\ years, \\A_o \ is \ the\ initial\ value\ of \ the\ substance,\ t_{1/2} is\ the\ half\ life\ and\\t\ is\ the\ years\ spent[/tex]

Given that:

Ao = 4 g, t = 3 years, t(1/2) = 5.26 years. Therefore:

[tex]A=A_o*(\frac{1}{2})^\frac{t}{t_{1/2}}\\A=4*(\frac{1}{2} )^\frac{3}{5.26}=4*0.6735=2.7\\ A=2.7\ g[/tex]

Answer:

[tex] 0.88^x [/tex]

Step-by-step explanation:

Exponential decay formula is given as [tex] a(1 - r)^x [/tex], where,

a is the initial amount

r is the decay rate

x is the time interval

Therefore, the multiplier that corresponds to 12% decay is [tex] (1 - r)^x = (1 - \frac{12}{100})^2 = (1 - 0.12)^x = 0.88^x [/tex]

[tex]2x \times x + 2x \times 5 - 9 \times x - 9 \times 5[/tex]

[tex] {2x }^{2} + 10x - 9x - 45 [/tex]

[tex] {2x}^{2} + x - 45 [/tex]

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

[tex]\boxed{x=14}[/tex]

Reorder the terms:

[tex]-9 + 2x = 5 + x[/tex]

Solving

[tex]-9 + 2x = 5 + x[/tex]

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.

[tex]-9 + 2x + -1x = 5 + x + -1x[/tex]

Combine like terms: [tex]2x + -1x = 1x[/tex]

[tex]-9 + 1x = 5 + x + -1x[/tex]

Combine like terms: [tex]x + -1x = 0[/tex]

[tex]-9 + 1x = 5 + 0\\-9 + 1x = 5[/tex]

Add '9' to each side of the equation.

[tex]-9 + 9 + 1x = 5 + 9[/tex]

Combine like terms: [tex]-9 + 9 = 0[/tex]

[tex]0 + 1x = 5 + 9\\1x = 5 + 9[/tex]

Combine like terms: [tex]5 + 9 = 14[/tex]

[tex]1x = 14[/tex]

Divide each side by '[tex]1[/tex]'.

[tex]x = 14[/tex]

Simplifying

[tex]x = 14[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

Answer:  x = 4/5

Step-by-step explanation:

[tex]\tan\ y=\dfrac{\text{side OPPOSITE y}}{\text{side ADJACENT to y}}=\dfrac{1}{6}\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \dfrac{x}{x+4}=\dfrac{1}{6}\\\\\\\text{Cross multiply, distribute, and solve for x:}\\6(x)=1(x+4)\\6x=x+4\\5x=4\\\\\large\boxed{x=\dfrac{4}{5}}[/tex]

Answer:

Step-by-step explanation:

[tex]x^{2} -x-x<[/tex] 0

[tex]x^{2} -2x[/tex] < 0

x^2-2x+1<1

(x-1）^2<1

-1<x-1<1

0<x<2

[tex](x-1)^{2}[/tex][tex](x-1)^{2}[/tex]

Answer:

47

Step-by-step explanation:

Using the follwing property

[tex]x^{2} -y^2=(x+y)(x-y)[/tex]

in which x=24 and y=23

so

[tex]24^2-23^2=(24-23)(24+23)\\=1(47)\\=47[/tex]

Answer:

47

Step-by-step explanation:

Lets say 24 is x and 23 is y.

the equation would be x^2 - y^2

this is = to (x-y)(x+y)

substitute the numbers in

(24-23)(24+23)

which simplifies to

(1)(47)

which equals 47

Answer:

Linear f(x) = 2·x + 3

Quadratic f(x) = x² + 2·x - 3

Exponential f(x) = 3ˣ - 2

Step-by-step explanation:

1) Linear function

The general form of the linear equation is of the form, f(x) = y = m·x + c

Where;

m = The slope

c = y-intercept (Constant)

The linear function is therefore, f(x) = 2·x + 3

2) Quadratic function

The general form of the quadratic function is f(x) = a·x² + b·x + c

Where;

a, and b are the coefficients of x² and x respectively and c is the constant term

Therefore,  f(x) = x² + 2·x - 3, is a quadratic function, with a = 1, b = 2, and c = -3

3) Exponential function

The general form of the exponential function is f(x) = a·bˣ + k

Where;

a = The initial

b = The multiplier (growth or decay value)

k = vertical shift

Therefore, the function f(x) = 3ˣ - 2 is an exponential function with the initial = 1, b= 3, and k = -2

Answer:

Man's present age: 32 years

Older son's present age: 8 years

Younger sons present age: 4 years

Step-by-step explanation:

Let their present ages be represented by:

Man = a

Older boy = b

Younger boy = c

A man has two sons, one twice as old as the other:

b = 2 × c

b = 2c......... Equation 1

The man is four times as old as the older boy:

a = 4 × b

a = 4b.......Equation 2

In three years he will be five times as old as the younger boy:

a + 3 = 5 (c + 3)

a + 3 = 5c + 15........Equation 3

Since b = 2c and a = 4b

Subtitute 2c for b in Equation 2

a = 4b

a = 4 × 2c

a = 8c

Subtitute 8c for a in Equation 3

a + 3 = 5c........Equation 3

8c + 3 = 5c + 15

Collect like terms

8c - 5c = 15 - 3

3c = 12

c = 4

Therefore since c, represents the present age of the younger son, the younger son is 4 years old

b = 2c

b = 2 × 4

b = 8

Since b is the present age of the older son, the older son is 8 years old

a = 4b

b = 8

a = 4 × 8

a = 32

Since a is the present age of the man, the man is 32 years old

Therefore,

Man's present age: 32 years

Older son's present age: 8 years

Younger sons present age: 4 years

Answer:

10 centimeters

Step-by-step explanation:

formula for volume of a cylinder = πr² · h

1. Set up the equation

(3.14)(r²)(14) = 4,396

2. Simplify

(43.96)(r²) = 4,396

3. Solve

r² = 100

√r = √100

r = 10

Answer:

Graph C.

Step-by-step explanation:

Hi there!

Well let’s first put,

7x + 2y < 8

We need to single out y.

7x + 2y < 8

-7x to both sides

2y < -7x + 8

Divide everything by 2,

y < -7/2x + 4

Well the shade on the graph should be going down because it is y is less than,

And the y intercept should be at 4 with a dotted line and a slope of -7/2.

So graph C. Is correct.

Hope this helps :)

The graph that represents the inequality 7x + 2y < 8 will be graph C.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The inequality is given as,

7x + 2y < 8

Simplify the equation in slope-intercept form, then we have

7x + 2y < 8

2y < 8 - 2x

y < (8 - 2x) / 2

The value of the variable 'y' is less. Then the graph that represents the inequality 7x + 2y < 8 will be graph C.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ2

Answer:

Anthropologists study human societies and cultures and the development of them from the past and present. They study this to analyze the differences and evolutions that us as humans have.

Answer:

[tex]\boxed{10}[/tex]

Step-by-step explanation:

[tex]2x+5=8x[/tex]

[tex]\sf Subtract \ 8x \ from \ both \ sides.[/tex]

[tex]2x+5-8x=8x-8x[/tex]

[tex]-6x+5=0[/tex]

[tex]\sf Subtract \ 5 \ from \ both \ sides.[/tex]

[tex]-6x+5-5=0-5[/tex]

[tex]-6x=-5[/tex]

[tex]\sf Divide \ both \ sides \ by \ -6.[/tex]

[tex]\displaystyle \frac{-6x}{-6} =\frac{-5}{-6}[/tex]

[tex]\displaystyle x =\frac{5}{6}[/tex]

[tex]\sf Evaluate \ 12x.[/tex]

[tex]\displaystyle 12 \cdot \frac{5}{6} =\frac{60}{6} =10[/tex]

Answer:

10

Step-by-step explanation:

2x+5=8x: First, you are going to subtract 2x from both sides of the equation.

5=6x: Now divide 6x from each side of the equation.

x=5/6: now plug in 5/6 by multiplying this number by 12.

Your final answer should be 10.

[tex]\text{Solve for y:}\\\\-4.1=8(y-5)\\\\\text{Use the distributive property}\\\\-4.1=8y-40\\\\\text{Add 40 to both sides}\\\\35.9=8y\\\\\text{Divide by 8}\\\\\boxed{4.4875=y}\\\\[/tex]

Answer:

Hey there!

4^2-2(3(5)+1)

16-2(15+1)

16-2(16)

-16

C is correct.

Let me know if this helps :)

Answer:

Step-by-step explanation:

[tex] \mathsf{ {4}^{2} - 2(3 \times 5 + 1)}[/tex]

Evaluate the power

⇒[tex] \mathsf{16 - 2(3 \times 5 + 1)}[/tex]

Multiply the numbers

⇒[tex] \mathsf{16 - 2(15 + 1)}[/tex]

Calculate the sum

⇒[tex] \mathsf{16 - 2 \times 16}[/tex]

Multiply the numbers

⇒[tex] \mathsf{16 - 32}[/tex]

Calculate

⇒[tex] \mathsf{ - 16}[/tex]

Hope I helped!

Best regards!

Answer:

90

Step-by-step explanation:

90 has 0 ones so it is already rounded.

Answer:

90

Step-by-step explanation:

Hey there!

Well 90.000 to the nearest tenth is just 90 because there is decimal places to round.

Hope this helps :)

Answer:

100.5 ft^2

Step-by-step explanation:

First find the area of the rectangle

A = l*w

A = 12.16 * 6

A =72.96 ft^2

Then find the area of the triangle

A = 1/2 bh

The base is 12 ft - 6ft = 6ft

The height is 9.16 ft

A = 1/2 ( 9.16) * 6

A = 27.48 ft^2

Add them together

27.48+72.96

100.44 ft^2

Round to the nearest tenth

100.5 ft^2

Answer:

[tex]\huge \boxed{\mathrm{100.4 \ ft^2 }}[/tex]

Step-by-step explanation:

To find the area of the shape, we can add the area of the rectangle with the area of the triangle.

Area of rectangle :

base × height

6 ft × 12.16 ft

72.96 ft²

Area of triangle :

base × height × 1/2

(12 ft - 6 ft) × 9.16 ft × 1/2

6ft × 9.16 ft × 1/2

27.48 ft²

Adding the areas.

72.96 ft² + 27.48 ft²

100.44 ft²

≈ 100.4 ft² (rounded to nearest tenth)

Answer:

C(x)=3x³+4x²-11x-8

Step-by-step explanation:

The water usage is modeled by the equation W(x) = 4x³ + 6x² − 11x + 7

The amount of decrease in water used is modeled by D(x) = x³ + 2x² + 15

C(x)= W(x)-D(x)

C(x)=4x³ + 6x² − 11x + 7-(x³ + 2x² + 15)

C(x)=4x³ + 6x² − 11x + 7-x³-2x²-15

c(x)=3x³+4x²-11x-8

Answer:

the second option

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Let x be the measure in degrees

● x/180 = 1.2/Pi

Cross multiply the values

● x*Pi = 180×1.2

● x = 216/Pi

Take Pi = 3.14

● x = 68.78 wich is approximatively 69°

Answer:

i couldnt find a solution to the equation all i could get is u +v

Step-by-step explanation:

what were you trying to say when you said "let u="

Answer:

4.8

Step-by-step explanation:

(-3,4) + (8,2) = 4.8