If 100 mL of a solution contains 20 g, how many milligrams will 20 mL contain?

[tex]\dfrac{16}{7x+4}+A=\dfrac{49x^2}{7x+4}\\\\A=\dfrac{49x^2}{7x+4}-\dfrac{16}{7x+4}\\\\A=\dfrac{49x^2-16}{7x+4}\\\\A=\dfrac{(7x-4)(7x+4)}{7x+4}\\\\A=7x-4[/tex]

[tex]\bf \stackrel{~~~~~~~~\textit{is equivalent}}{\cfrac{16}{7x+4}+A~~=~~\cfrac{49x^2}{7x+4}}\implies \stackrel{\textit{cross-multiplying}}{\cfrac{16~~\begin{matrix} (7x+4) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 7x+4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}+A(7x+4)=49x^2} \\\\\\ 16+A(7x+4)=49x^2\implies A(7x+4)=49x^2-16\implies A=\cfrac{49x^2-16}{7x+4}[/tex]

[tex]\bf A=\cfrac{7^2x^2-4^2}{7x+4}\implies A=\cfrac{\stackrel{\textit{difference of squares}}{(7x)^2-4^2}}{7x+4}\implies A=\cfrac{(7x-4)~~\begin{matrix} (7x+4) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 7x+4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A=7x-4~\hfill[/tex]

Answer: 2x^2-y^2+5xy-2y

a. There is four terms in the simplified expression.

b. Two terms in the simplified expression are negative.

Step-by-step explanation:

Write the expression like an addition/ subtraction problem.

-3x²+2y²+5xy-2y

+5x²-3y²

_________

This makes it easier to identify what to combine for like terms.

Final answer:

The simplified expression is 2x² - y² + 5xy - 2y. There are two negative terms in the simplified expression: -y² and -2y.

Explanation:

To simplify the expression -3x² + 2y² + 5xy - 2y + 5x² - 3y², we need to combine like terms. The like terms are the ones that contain the same variables to the same power. Here’s a step-by-step explanation:

The simplified expression is 2x² - y² + 5xy - 2y.

Now, to answer the question about the number of negative terms: in the simplified expression, there are two negative terms, which are -y² and -2y. A term is considered negative if it has a minus sign in front of it, indicating that it is less than zero when all other variables are considered to be positive.

The correct option that shows the values of the two 3s in the price $3,435 is D) 3,000; 30

In the given price, $3,435, the first 3 represent the thousand place value, while the second 3 represents the one's place value.

The comma in option D indicates the separation of thousands, so it correctly represents the first 3 as part of the thousands place value.

The number 30 in option D represents the second 3 as part of the one's place value.

Therefore, option D) 3,000; 30 is the choice that correctly shows the values of the two 3s in the price $3,435.

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Answer:

[tex]\large\boxed{\dfrac{x+5}{x^2}-\dfrac{2}{5x}=\dfrac{3x+25}{5x^2}}[/tex]

Step-by-step explanation:

[tex]\dfrac{x+5}{x^2}-\dfrac{2}{5x}=\dfrac{5(x+5)}{5x^2}-\dfrac{2x}{5x^2}\qquad\text{use the distributive property}\\\\=\dfrac{5x+25}{5x^2}-\dfrac{2x}{5x^2}=\dfrac{5x+25-2x}{5x^2}=\dfrac{3x+25}{5x^2}[/tex]

The difference between the rational expressions below will be,[tex]\frac{3x+25}{5x^2}[/tex]

Arithmetic is an area of mathematics involving the study of numbers and the different operations that can be performed on them.

The difference in the rational expression is found as;

[tex]=\frac{x+5}{x^2} -\frac{2}{5x} \\\\=\frac{5(x+5)}{x^2} - \frac{2x}{5x^2} \\\\\ = \frac{5x+25}{5x^2} -\frac{2x}{5x^2 }\\\\\ = \frac{5x+25-2x}{5x^2} \\\\ = \frac{3x+25}{5x^2}[/tex]

The difference between the rational expressions below will be,[tex]\frac{3x+25}{5x^2}[/tex].

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Answer:

Making it the answer A

Step-by-step explanation:

For this case we have the expression:

"the square root of 4" is represented algebraically as:

[tex]\sqrt {4}[/tex]

Then, we can express the given statement as:

[tex]3 \sqrt {4} -2 \sqrt {4} =[/tex]

They are similar terms, we can subtract:

[tex]3 \sqrt {4} -2 \sqrt {4} = \sqrt {4} = \sqrt {2 ^ 2}[/tex]

By definition of power properties we have that:

[tex]\sqrt [n] {a ^ n} = a ^ {\frac {n} {n}} = a[/tex]

Then the expression is reduced to:

[tex]\sqrt {2 ^ 2} = 2[/tex]

Answer:

[tex]3 \sqrt {4} -2 \sqrt {4} = 2[/tex]

Answer:

Volume = 784*pi

Step-by-step explanation:

We are given the height and radius of cylinder

So,

Radius = r = 7

Height = h = 16

The formula for finding volume of cylinder is:

[tex]Volume=\pi r^{2} h\\Putting\ in\ the\ values\ of\ r\ and\ h\\Volume=\pi *(7)^{2}*16\\V=\pi *49*16\\V=784\pi [/tex]

Answer:

Volume of cylinder = 784 cubic units

Step-by-step explanation:

Points to remember

Volume of cylinder =  πr²h

Where r - Radius of cylinder and

h - Height of cylinder

To find the volume of cylinder

It is given that,

radius r = 7 units and height h = 16 units

Volume of cylinder =  πr²h

 = π * 7² * 16

 = 784 cubic units

Therefore Volume of cylinder = 784 cubic units

Answer:

x + y - 2 = 0

Step-by-step explanation:

First, set the equation equal to 2 by moving 2 to the other side of the equation to get x + y = 2, then move -x over to the other side to end up with y = -x + 2. The reason being is because the rate of change [slope] is -1. Simply do rise\run until you hit another endpoint, starting from your y-intercept. As you can see, you go two blocks south, then go two blocks over east. Now, if when you look carefully, you will see that -2\2 = -1. This is the simplification of the slope. Do you understand?

Answer:

[tex]\frac{1}{2}[/tex] , or the first option

Step-by-step explanation:

The formula to find the slope of a line is [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]. It doesn't matter which set of coordinates is (x₁,y₁), as long as you make sure you put them in the right places.

(x₁,y₁) = (1,2)

(x₂,y₂) = (5,4)

[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]   Plug in your numbers

[tex]\frac{4 - 2}{5 - 1}[/tex]   Simplify

[tex]\frac{2}{4}[/tex]   Simplify

[tex]\frac{1}{2}[/tex]

Answer:

slope = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (5, 4)

m = [tex]\frac{4-2}{5-1}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

ANSWER

[tex]y = \frac{1}{4}x+1[/tex]

EXPLANATION

The slope-intercept equation of a straight line is of the form

[tex]y = mx + b[/tex]

Where 'm' is the slope and 'b' is the y-intercept.

From the question we have slope to be

[tex]m = \frac{1}{4} [/tex]

We substitute the slope into the slope-intercept equation and obtain:

[tex]y = \frac{1}{4}x + b[/tex]

To find the value of 'b' we plug in the point (-8,-1) into our current equation.

[tex] - 1= \frac{1}{4}( - 8)+ b[/tex]

[tex] - 1= - 2+ b[/tex]

[tex] - 1 + 2 = b[/tex]

[tex]1 = b[/tex]

[tex]b =1 [/tex]

The complete equation is

[tex]y = \frac{1}{4}x + 1[/tex]

ANSWER

[tex]x = - 3[/tex]

EXPLANATION

When a quadratic equation is in the vertex form,

[tex]f(x) = a {(x - h)}^{2} + k[/tex]

the equation of axis of symmetry is simply

[tex]x = h[/tex]

The given quadratic equation is

[tex]f(x) = {(x + 3)}^{2} - 8[/tex]

We can rewrite this as

[tex]f(x) = {(x - - 3)}^{2} - 8[/tex]

We now compare to

[tex]f(x) = a {(x - h)}^{2} + k[/tex]

We have

[tex]h = - 3 \: \: \: and \: \: k = - 8[/tex]

Therefore equation of axis of symmetry is:

[tex]x = - 3[/tex]

Answer:

B) {-5x + 4y = 8

{-x + 5y = 10

Step-by-step explanation:

Add like it said, and you will see your answer.

Answer:

Option B

[tex]-5x+4y=8[/tex]

[tex]-x+5y=10[/tex]

Step-by-step explanation:

We are given that

System of equations

[tex]-5x+4y=8[/tex]

[tex]4x+y=2[/tex]

We have to find an equivalent system of equations using sum of system and first equations

Sum of system of equations

[tex]-5x+4y+4x+y=8+2[/tex]

[tex]-x+5y=10[/tex]

Therefore, option B is true.

Answer:

72

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

Absolute value is the distance a number is from 0.

For example, look at the following number line.

<-|-------|--------|---------|---------|----------|---------|->

 -6      -5       -4       -3        -2         -1         0

The absolute value of -6 is 6 since the number -6 is 6 digits away from 0.

So likewise if:

|-6| = 6

[keep in mind that this symbol ---> |  | is the absolute value symbol]

then:

|-72| = 72

Since -72 is 72 digits away from 0.

I hope this helps! :)

Answer:

2p

Step-by-step explanation:

Take a trip back to simple division. What's 12/6? If you put 12 p's evenly into 6 piles, how many p's are in each pile?

2

Therefore, the answer is 2p.

Answer:

-6x^2 y^3 = B

Step-by-step explanation:

42x^5y^4=(-7x^3y)(B)​

Solve for B

Divide by -7

42x^5y^4/-7=(-7x^3y)(B)/-7

-6 x^5 y^4 = x^3 y B

Divide by x^3

-6 x^5 y^4/x^3 = x^3 y B​/x^3

-6 x^5/x^3 y^4 = By

-6 x^2 y^4

Divide by y

-6x^2 y^4/y = By/y

-6x^2 y^3 = B

Answer:

[tex]\frac{16x^2+48x}{8x} = 2x+6\\\frac{56x^2-14x}{7x} = 8x-2\\\frac{18x^2+15x}{3x}=6x+5\\\frac{20x^2-32x}{4x}=5x-8[/tex]

Step-by-step explanation:

We will solve the division one by one:

[tex]\frac{16x^2+48x}{8x} = \frac{8x(2x+6)}{8x} = 2x+6\\\frac{56x^2-14x}{7x}=\frac{7x(8x+2)}{7x}=8x+2\\\frac{18x^2+15x}{3x} =\frac{3x(6x+5)}{3x} = 6x+5\\\frac{20x^2-32x}{4x}=\frac{4x(5x-8)}{4x}=5x-8[/tex]

a)

[tex]\dfrac{16x^2+48x}{8x}[/tex]

Since, both the terms in the numerator have a common factor as: 8x.

Hence, we take out common 8x from the numerator term and hence it could be written as:

[tex]\dfrac{8x(2x+6)}{8x}[/tex]

i.e.

[tex]=2x+6[/tex]

b)

[tex]\dfrac{56x^2-14x}{7x}[/tex]

Since, both the terms in the numerator have a common factor as: 14x.

Hence, we take out common 14x from the numerator term and hence it could be written as:

[tex]=\dfrac{14x(4x-1)}{7x}\\\\=2(4x-1)\\\\=8x-2[/tex]

c)

[tex]\dfrac{(18x^2+15x)}{3x}[/tex]

Since, both the terms in the numerator have a common factor as: 3x.

Hence, we take out common 3x from the numerator term and hence it could be written as:

[tex]=\dfrac{3x(6x+5)}{3x}\\\\=6x+5[/tex]

d)

[tex]\dfrac{20x^2-32x}{4x}[/tex]

Since, both the terms in the numerator have a common factor as: 4x.

Hence, we take out common 4x from the numerator term and hence it could be written as:

[tex]=\dfrac{4x(5x-8)}{4x}\\\\=5x-8[/tex]

Answer: B. 2=3x+10x^2

Step-by-step explanation:

The expression means the quadratic function equation.

B = 10x^2 + 3x -2 = 0

the equation is [-b ±√(b^2 -4ac)]/2a

b should be +3 to become -3 when it is plugged into the equation, and 'a' should be 10, and c should be -2.

Answer:B

Step-by-step explanation:

Ye you know me keep it a buck like 123 ye 2022 baby

Answer:

Because the negative in the front cancels out the other neg.

Step-by-step explanation:

Answer:

-(3 - 2x ) = -3 + 2x = 2x - 3

Step-by-step explanation:

If you expand the brackets in -(3 - 2x) by multiplying all numbers by -1 (the negative symbol in front of the brackets represents negative 1 just without the 1)

Thus you get -3 + 2x.

Then rearranging the equation by swapping the 2x with the -3 you get 2x - 3.

Answer:

The solutions are: x=6. x=-4 and x=-8.

Step-by-step explanation:

The solution to the system of the equation is going to be given by the points where the graphs of:

y = x3 + 6x2 - 40x AND y = 192 intercept.

By looking at the graph, we can deduce they intercept at three points:

(-8, 192), (-4, 192) and (6, 192).

Another way to verify this, is by solving the following system of equations:

x3 + 6x2 - 40x - 192 = 0

Factorizing, we get:

(x-6)(x+4)(x+8) = 0

Where we can clearly see that the solutions are: x=6. x=-4 and x=-8.

Answer:

A -8

B -4

D 6

Step-by-step explanation:

Correct on EDGE

Answer:

The formula is a^2+2a+ sqrt a^2+h^2

Step-by-step explanation:

a=base edge

h=height

Answer:

The formula is A=a²+2a(√a^2 )/4+h²

Step-by-step explanation:

[tex](x+3)(x+5) =x^2+5x+3x+15=x^2+8x+15[/tex]

[tex]x^2+8x+15[/tex]

Use the FOIL method of multiplying binomials.

First term in each binomial: [tex]x*x=x^2[/tex]

Outside terms: [tex]x*5=5x[/tex]

Inside terms: [tex]3*x=3x[/tex]

Last term in each binomial: [tex]3*5=15[/tex]

Add them all together. [tex]x^2+5x+3x+15[/tex]

Simplify. [tex]x^2+8x+15[/tex]

Answer:  A) 7 o---------------→

Step-by-step explanation:

[tex]\dfrac{2}{9}x+3>4\dfrac{5}{9}\\\\\\\text{Subtract 3 from both sides:}\\\\\dfrac{2}{9}x>1\dfrac{5}{9}\\\\\\\text{Convert the mixed number into an improper fraction:}\\\\\dfrac{2}{9}x>\dfrac{14}{9}\\\\\\\text{Multiply both sides by }\dfrac{9}{2}\text{ to isolate x:}\\\\x>\dfrac{14}{9}\times \dfrac{9}{2}\\\\\\\text{Simplify (cancel out the 9's and factor out a 2:}\\\\x>7[/tex]

The graph will have an open dot at 7 and the arrow will point to the right.

7 o--------->

Answer:

A

Step-by-step explanation:

EDGE 23

Answer:

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

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

step 1

Find the value of k

we have

the point (9,-12)

x=9, y=-12

[tex]k=y/x[/tex]

substitute

[tex]k=-12/9=-4/3[/tex]

step 2

Find the equation

[tex]y=kx[/tex]

so

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

Answer:

d. 36 sq. ft​

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh  where b is the base and h is the height

A = 1/2 (12) * 6

A = 36 ft^2

Answer:

area = 50.27 sq inches

circumference = 25.14 in

Step-by-step explanation:

given radius r = 4 in

area = πr² = 3.142 x 4² = 50.27 square inches

circumference = 2πr = 2 x 3.142 x 4 = 25.14 inches

Hey there! :)

-4c + 3d = 8e ; solve for d.

In order to solve for d, you must isolate it (get it onto its own side). So, let's start off by adding 4c to both sides.

-4c + (-4c) + 3d = 8e + (-4c)

Simplify.

3d = 8e - 4c

Then, divide both sides by 3.

3d ÷ 3 = (8e - 4c) ÷ 3

Simplify.

d = 8/3e - 4/3c

Therefore, [tex]d = \frac{8}{3} e  -\frac{4}{3} c[/tex]

Answer:

Hundreds

Step-by-step explanation:

The value of 5 is given based on the place value in which it is located.

The 5 is located in the "hundreds" place value, and so Hundreds is your answer.

Place value:

3: Thousands

5: Hundreds

9: Tens

0: Ones

Answer:

24

-560

Step-by-step explanation:

(1) (-2) * 3 * (-4)

A negative time a negative is a positive

2*3*4 = 24

(iv) 8 x 7*(-10)

This result will be negative since there are positive times negative

8*7 =56* 10 = 560

8*7* (-10) = -560

Answer: 4 seconds

Step-by-step explanation:

We have the equation that models the height of the golf ball in feet after being hit.

When the ball reaches the ground its height is equal to zero.

Then to solve this problem you must equal h to zero and solve the equation for the variable t

[tex]h = -16t^2 + 64t=0[/tex]

[tex]-16t^2 + 64t=0[/tex]

Take 16t as a common factor

[tex]-16t(t - 4)=0[/tex]

The equation is equal to zero when t = 0 and when t = 4

t = 0 is at the instant in which the ball has just been hit and t = 4 seconds is the instant in which the ball touches the ground.

Then the answer is t=4 seconds

Answer:

Step-by-step explanation:

x= 6± √(6)^2-4(1)(6)   /2(1)

=6± √12   /2

=6± 2√3   /2

=3± √3

Answer:  The required solution of the given quadratic equation is

x = 3 + √3  and  x = 3 - √3.

Step-by-step explanation:  We are given to solve the following quadratic equation using quadratic formula :

[tex]x^2-6x+6=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Quadratic formula :  The solution of a quadratic equation of the form [tex]ax^2+bx+c=0,~a\neq 0[/tex] is given by

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

For the given quadratic equation (i), we have

a = 1,  b = -6   and   c = 6.

Therefore, the solution of equation (i) is given by

[tex]x\\\\\\=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\=\dfrac{-(-6)\pm\sqrt{(-6)^2-4\times 1\times6}}{2\times1}\\\\\\=\dfrac{6\pm\sqrt{36-24}}{2}\\\\\\=\dfrac{6\pm\sqrt{12}}{2}\\\\\\=\dfrac{6\pm2\sqrt{3}}{2}\\\\=3\pm\sqrt3.[/tex].

Thus, the required solution of the given quadratic equation is

x = 3 + √3  and  x = 3 - √3.