Carla is cutting pieces of string that are exactly 24 3/8 inches long. How many pieces can she cut from a ball of string that’s is 100 feet?

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:

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:

0.

Step-by-step explanation:

The nonpermissible replacement of the variable in an expression is the value of x that will make the denominator of the expression zero.

This problem will therefore be written as -5/3y≠0, and it can't be 0, so 0 is your non permissible replacement.

Hope this helps!

Answer:

f(n) = 2 + 3(n-1)

Step-by-step explanation:

Answer:

f(n) = 2 + 3(n-1)

Step-by-step explanation:

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:

Making it the answer A

Step-by-step explanation:

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:

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

[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:

2y + 3x = 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3x + 2y = - 4 into this form

Subtract 3x from both sides

2y = - 3x - 4 ( divide all terms by 2 )

y = - [tex]\frac{3}{2}[/tex] x - 2 ← in slope- intercept form

with slope m = - [tex]\frac{3}{2}[/tex]

• Parallel lines have equal slopes, thus

y = - [tex]\frac{3}{2}[/tex] x + c ← partial equation of parallel line

To find c substitute (4, - 1) into the partial equation

- 1 = - 6 + c ⇒ c = - 1 + 6 = 5

y = - [tex]\frac{3}{2}[/tex] x + 5 ← in slope- intercept form

Multiply through by 2

2y = - 3x + 10 ( add 3x to both sides )

3x + 2y = 10 ← in standard form

The equation of the line parallel to 3x+2y= -4 goes through the point (4,-1).

The general equation of a straight line exists y = mx + c, where m is the gradient, and y = c exists the value where the line cuts the y-axis. This number c is named the intercept on the y-axis. The equation of a straight line with gradient m and intercept c on the y-axis stands y = mx + c.

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3x + 2y = - 4 into this form

Subtract 3x from both sides

2y = - 3x - 4 ( divide all terms by 2 )

y = -  x - 2 ← in slope- intercept form

with slope m = -

• Parallel lines have equal slopes, thus

y = -  x + c ← partial equation of parallel line

To find c substitute (4, - 1) into the partial equation

- 1 = - 6 + c ⇒ c = - 1 + 6 = 5

y = -  x + 5 ← in slope- intercept form

Multiply through by 2

2y = - 3x + 10 ( add 3x to both sides )

3x + 2y = 10 ← in standard form.

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Answer:

-4/3

Step-by-step explanation:

If the lines are parallel, they have the same slope.

Since the red line has a slope of -4/3, the green line will have a slope of -4/3

[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:

[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]\large\boxed{y=-\dfrac{7}{3}x+4}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

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

m - slope

b - y-intercept (0, b)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points:

(0, 4) → b = 4

and (3, -3)

Substitute:

[tex]m=\dfrac{-3-4}{3-0}=\dfrac{-7}{3}\\\\y=-\dfrac{7}{3}x+4[/tex]

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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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:

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:

[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

[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: 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:

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:

-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:

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.

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: 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:

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:

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:

Step-by-step explanation:

When you find the sum of a number you are adding two or more numbers together. therefore the only answer that you could use to get a sum of 5 when your first term is 12 would be -7