What are the solutions of this system of equations?
The first three steps in determining the solution set of the
system of equations algebraically are shown.
y = x2 - x-3
y=-3x + 5
(-2, -1) and (4, 17)
(-2, 11) and (4, -7)
(2, -1) and (-4, 17)
(2, 11) and (-4,-7)
Step
1
2
Equation
x– X-3 = -3x +5
0 = x² + 2x - 8
0 = (x-2)(x+4)
3

Answer:

cost of system is $175 and cost of the games is $525

Step-by-step explanation:

Let us take the cost of the system to be X.The games cost 3 times as much as the system and are therefore given 3X. The total cost of the system and the games is $700.Therefore,we form the equation 3X+X=$700.Meaning that 4X=$700 and X is equal to $175.The cost of the system is X therefore it is $175 and the cost of the games is 3X and is therefore $525.

The cost of the video game system is $175, while the cost of the games is $525,.

The student is asking to find the cost of a video game system and the games sold with it, given that the total cost is $700 and that the cost of the games is three times as much as the cost of the system.

Let's define the cost of the system as 'x'.

The cost of the games would then be '3x'.

The total cost is given as $700, so we can write the equation as:

x + 3x = 700

Combining like terms, we get:

4x = 700

x = 700 / 4

x = $175

So, the cost of the system is $175,

and the cost of the games is three times that, which is:

3 × $175 = $525

Answer:

D. :)

Step-by-step explanation:

Answer:

A linear function is in the form y = mx + b or f(x) = mx + b, where m is the slope or rate of change and b is the y-intercept or where the graph of the line crosses the y axis. ... if your first diffs are the same it is linear. if not it is not linear.

a LINEar equation is an equation with a polynomial of degree 1 and is the graph of a LINE, let's look at this one, y = x² - 3, notice the exponent of ², meaning is a 2nd degree equation, and is a parabola, so is namely a quadratic, not a linear one.

Answer:

A. A number divided by three minus fifteen.

A number is divided by three minus fifteen best describes the given algebraic expression [tex]\frac{x}{3}-15[/tex].

Option A is correct.

An algebraic expression is a variable expression described using its terms, and operations on the terms. For example, x + 3 can be described as "3 more than x".

Given algebraic expression

[tex]\frac{x}{3}-15[/tex]

[tex]\frac{x}{3}[/tex] means a number is divided by three and [tex]\frac{x}{3}-15[/tex] means a number is divided by three minus fifteen.

A number is divided by three minus fifteen best describes the given algebraic expression [tex]\frac{x}{3}-15[/tex].

Option A is correct.

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Answer:

√55x\11x⁸y⁵

Step-by-step explanation:

Factor the numerator and denominator and cancel the common factors.

Answer: C

Explanation:

√55x⁷y⁶/11x¹¹y⁸

→ 55/11 = 5

→ x⁷/x¹¹= x⁷⁻¹¹= x⁻⁴

→ y⁶/y⁸= y⁶⁻⁸= y⁻²

→ √5/x⁴y²

→ √5/x²y

If the exponent is a negative, the base is the reciprocal of itself with a positive exponent.

Ex: 6⁻² = 1/6² = 1/36

The square root of an exponent with a positive, even power is half of that power.

Ex: √x⁴ = x²

Answer:

p = 3

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :  

                    p-(3000*(1/1000))=0  

Step by step solution :

Step  1  :

             1  

Simplify   ————

           1000

Equation at the end of step  1  :

                1  

 p -  (3000 • ————)  = 0  

              1000

Step  2  :

Equation at the end of step  2  :

 p - 3  = 0  

Step  3  :

Solving a Single Variable Equation :

3.1      Solve  :    p-3 = 0  

Add  3  to both sides of the equation :  

                     p = 3

Please mark brainliest and have a great day!

Answer:

5000 g

Step-by-step explanation:

5000 g = 11.02311 lb

10 lb​ = 4535.92

Answer:

[tex]y=2x^{2}+1[/tex]

Step-by-step explanation:

we know that

The graph is a vertical parabola open upward

The vertex is the point (0,1)

The equation of a vertical parabola in vertex form is equal to

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

substitute the vertex in the equation

[tex]y=a(x-0)^{2}+1[/tex]

[tex]y=a(x)^{2}+1[/tex]

Find the value of coefficient a

Observing the graph

For x=1, y=3

substitute in the equation

[tex]3=a(1)^{2}+1[/tex]

[tex]a=3-1=2[/tex]

The equation on the graph is equal to

[tex]y=2x^{2}+1[/tex]

Answer:

[tex]\displaystyle y' = -4e^{-4x}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                          [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Basic Power Rule:

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = e^{-4x}[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

The derivative of y = e^-4x is -4e^-4x.

To find the derivative of y = e-4x, we can use the power rule for derivatives. The power rule states that if we have a function of the form y = axb, then the derivative is given by dy/dx = abxb-1. Applying this rule to the given function, we have dy/dx = -4e-4x. Therefore, the derivative of y = e-4x is -4e-4x.

Answer:

f(x) +g(x)  = -1.3 - 1.75x

Step-by-step explanation:

f(x) +g(x) is simply obtained by adding the two given functions, f(x) and g(x). We are given that;

F(x)= 3.7-2x and g(x)= 0.25x-5

f(x) +g(x)  = 3.7-2x + (0.25x-5)

f(x) +g(x)  = 3.7 -5 + 0.25x - 2x

f(x) +g(x)  = -1.3 - 1.75x

For this case we have the following functions:

[tex]f (x) = 3.7-2x\\g (x) = 0.25x-5[/tex]

We must find[tex]f (x) + g (x):[/tex]

We have to:

[tex]f (x) + g (x) = 3.7-2x + (0.25x-5)\\f (x) + g (x) = 3.7-2x + 0.25x-5[/tex]

We add similar terms:

[tex]f (x) + g (x) = - 1.75x-1.3[/tex]

Thus, the result is:[tex]-1.75x-1.3[/tex]

Answer:

[tex]-1.75x-1.3[/tex]

Answer:

Mia multiplied one side of the equation by 5/3 and the other side by 3/5. This makes the equation unbalanced and untrue. x should be 50

Step-by-step explanation:

Mia made an error when setting up the equation to determine the total time allotted for the math section of the exam. She incorrectly set up the equation as 30 = (1/4) * x, instead of 30 = (1/4) * x. The correct solution is x = 120.

Mia made an error when setting up the equation to determine the total amount of time allotted for the math section of the exam. Since Mia spent 30 minutes answering the math questions, which was 1/4 of the total time, the correct equation should be:

30 = (1/4) * x

To solve for x, we need to multiply both sides of the equation by 4 to undo the division:

4 * 30 = x

x = 120

Therefore, the total amount of time allotted for the math section of the exam is 120 minutes, not 30 minutes as Mia mistakenly calculated.

The taxicab, after all its movements, is about 3.16 blocks away from its starting position. It ends up 3 blocks west and 1 block north from where it initially started.

The question asks us to determine the final position of a taxicab relative to its starting position after following a series of movements. The taxicab's starting position in this case is at the coordinate (1, -2).

Initially, it goes 4 blocks south (downwards in the grid, which we'll regard as negative) and 3 blocks east (to the right on the grid, which we'll regard as positive). Therefore, it moves to a point that is (+3, -4) relative to its starting position.

Next, it goes 6 blocks west (left on the grid, which is negative) and 5 blocks north (up on the grid, which is positive). So, this movement's relative position is (-6, +5).

To find out the final position of the taxicab relative to its starting position, we need to add up these movements' relative positions. The final relative position will be (+3-6, -4+5), which equals (-3, 1).

Hence, in terms of blocks, the taxicab is 3 blocks west and 1 block north of its starting position. The direct distance to the start would then be determined using the Pythagorean theorem, where the total distance is the square root of the sum of the squares of the movements in each direction (x and y coordinates). That forms the equation √((-3)² + 1²) = √10 ≈ 3.16 blocks.

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Answer:

a

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Rearrange 3x - y = 4 into this form ( add y to both sides )

3x = y + 4 ( subtract 4 from both sides )

3x - 4 = y OR y = 3x - 4 → a

Final answer:

The equation 3x - y = 4 is rewritten in slope-intercept form as y = 3x - 4, where the slope is 3 and the y-intercept is -4, corresponding to answer option A.

Explanation:

To rewrite the equation 3x - y = 4 in slope-intercept form (y = mx + b), we need to solve the equation for y.

Here are the steps:

Add y to both sides of the equation: 3x = y + 4.

Subtract 4 from both sides of the equation: y = 3x - 4.

Therefore, the equation in slope-intercept form is y = 3x - 4. This represents a line with a slope of 3 and a y-intercept of -4. So the correct answer is option A: y = 3x - 4.

Answer:

The quotient is: m^2-10m-6

The remainder is: 0

Step-by-step explanation:

We need to divide m^3-13m^2+24m+18 ÷ m-3 using synthetic division

The division is shown in the figure below.

The quotient is: m^2-10m-6

The remainder is: 0

Answer:

Step-by-step explanation:

The formula of an area of a parallelogram:

A = bh

b - base

h - height

We have A = 140 units², and h = 10 units. Substitute:

140 = 10b           divide both sides by 10

14 = b → b = 14 units

Answer:

amplitude = 3

Step-by-step explanation:

given a cosine function in standard form, that is

y = acosx, then

amplitude = | a |

Hence for f(x) = 3cosx, amplitude = | 3 | = 3

Final answer:

The amplitude of the function f(x) = 3cosx is 3, as the amplitude is the coefficient in front of the cosine function.

Explanation:

The amplitude of a trigonometric function like f(x) = 3cosx can be found by looking at the coefficient in front of the cosine function. In this case, the function f(x) = 3cosx has an amplitude of 3. This is because the amplitude of cosx or sinx is the absolute value of the coefficient multiplied by the cosine or sine function, which dictates how much the wave's peak or valley deviates from the center line of the graph. For example, if the function was f(x) = A cosx, the amplitude would be the absolute value of A. Since there is no negative sign or other function manipulating the 3 in f(x) = 3cosx, the amplitude is simply 3.

Answer:

Part 1) The quadratic equation is [tex]x^{2}-5x-50=0[/tex]

Part 2) The length of rectangle is 10 in and the width is 5 in

Step-by-step explanation:

Part 1)

Find the quadratic equation

Let

x -----> the length of rectangle

y ----> the width of rectangle

we know that

The area of rectangle is equal to

[tex]A=xy[/tex]

[tex]A=50\ in^{2}[/tex]

so

[tex]50=xy[/tex] -----> equation A

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

[tex]y=x-5[/tex] -----> equation B

substitute equation B in equation A

[tex]50=x(x-5)\\50=x^{2} -5x\\ x^{2}-5x-50=0[/tex]

Part 2) Find the length of the rectangle

[tex]x^{2}-5x-50=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]x=10\ in[/tex]

see the attached figure

Find the value of y

[tex]y=10-5=5\ in[/tex]

therefore

The length of rectangle is 10 in and the width is 5 in

Answer:

Quadratic equation: [tex]x^{2} +5x-50=0[/tex]

Length of the rectangle: 10 inches.

Step-by-step explanation:

In order to solve this you just have to factorize the equation to solve the different values for X:

[tex]x^{2} +5x-50=0\\(x+10)(x-5)=0[/tex]

So the only possible answer for the problem would be 5, so if the width is equal to X and the length is x+5 then the length of the rectangle would be 5+5 and that would be 10.

Answer:

The number in the square root is 50.

Step-by-step explanation:

Using the pythagorean theorem, we know that c is 10, so we plug in 2a^2=100, since we know that both of the leg lengths are the same.

Simplifying this equation gives a^2=50, which square rooting both sides gives

a = sqrt(50)

Hope this helps!

Choice #1 is better

To find the solution to this problem, we have to compute the are in each case, and divide each value by the corresponding cost in order to find the cost per square. The lower the cost, the better the offer because it will give you more pizza for your money Thus:

CHOICE 1:

Here the offer of Big Bob’s Pizza gives one slice of pizza from a pizza with a 22 inches diameter (then the radius is 11 inches) and is cut into 8 slices, so the area for the first entire pizza is:

[tex]A_{1}=\pi r^2=\pi(11)^2 \\ \\ A_{1}=121 \pi in^2[/tex]

Each slice has an area of:

[tex]A_{slice}=\frac{121 \pi}{8} \\ \\ A_{slice}=47.51in^2[/tex]

Finally, the cost per square inch is:

[tex]C=\frac{4.95\$}{47.51in^2}=0.10\$[/tex]

CHOICE 2:

Here the offer of Big Bob’s Pizza gives: An entire personal-size pizza that has a diameter of 6 inches (then the radius is 3 inches), so the area for the entire pizza is:

[tex]A_{2}=\pi r^2=\pi(3)^2 \\ \\ A_{2}=28.27 in^2[/tex]

Finally, the cost per square inch is:

[tex]C=\frac{3.75\$}{28.27in^2}=0.13\$[/tex]

CONCLUSION: Choice #1 gives you more pizza for your money because the cost per square inch is less than the other option.

The special at Big Bob's Pizza which will give you more pizza for your money is Choice #1. Per square inch, Choice #1 will cost less and give more overall pizza at $0.10 a square inch then Choice #2 at $0.13 per square inch. You can find more pizza for your money, by using the area formula for a circle for each pizza and finding the price per square inch of each serving. This is called a unit rate and is the cost per unit.

a. Find the radius of each pizza.

Since a pizza is a circle shape, it has a diameter and radius. The diameter is the distance across the pizza and the radius is half the diameter. We use the radius to find the area.

b. Find the area of each pizza using [tex]A = \pi r^{2}[/tex].

       [tex]A = \pi r^{2} \\A = \pi (11)^{2} \\A = 121\pi \\A= 379.94[/tex]

       The area of one slice is [tex]\frac{379.94}{8} = 47.49.[/tex]

       [tex]A = \pi r^{2} \\A = \pi (3)^{2} \\A = 9\pi \\A= 28.26[/tex]

c. Divide each area by the price.

        [tex]\frac{4.95}{47.49} = 0.10[/tex]

       [tex]\frac{3.75}{28.26} = 0.13[/tex]

Grade: 8th Grade

Subject: Geometry

Chapter: Applications for Area of Shapes

Keywords: circle, area, radius, diameter, cost, unit rate

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Answer: Option  C

(C ) 96

Step-by-step explanation:

The correct answer would be C, which is 96.

                         You're Welcome!

[tex]1350\sqrt{3}[/tex] square units (approximately 2338.26859)

The formula for finding the area of a regular hexagon when you know its side length is [tex]A=\frac{3\sqrt{3}*s^2}{2}[/tex], where [tex]A[/tex] is the area and [tex]s[/tex] is the side length.

[tex]1350\sqrt{3}[/tex] is as simple as the solution can get without estimating, but you can estimate with a calculator to find that it is approximately 2338.26859.

Answer:

1. (2, -9)

2.  ( 0,-5)

Answer:

Option A is correct.

Step-by-step explanation:

Given terms,

1 , 4 , 16 , 64 , 256.

If we observe the equation, we can easily say that the terms are getting multiplied by 4 to get the next one.

Since this equation has a common ratio, this can be solved by using the properties of geometric progressions.

From the properties of geometric progressions :

Here,

Common Ratio ( or r ) = any term( except first ) / previous terms = 64 / 16 = 16 / 4 = 4

First terms = 1

Therefore,

= > Next term should be : 1 x ( 4 )^( 6 - 1 ) { Since next term will be 6th term }

= > Next term = 1 x 4^5

= > Next term = 1024

Hence the required next term is 1024.

Option A is correct.

Or

Here we can see that the terms are written in the form of 4^n where n is any whole number.

Since 246 is 4^4 , and terms are increasing in order of 1, next term should be 4^5 i.e. 1024 .

Thus, option A is correct.

Answer:

A

Step-by-step explanation: you times each one by 4

Answer:

11.6%

Step-by-step explanation:

On the first selection, there are 20 red pencils out of 42 total pencils.

On the second selection, there are 10 green pencils out of 41 pencils left over.

So the probability is:

(20/42) (10/41)

100/861

≈11.6%

Answer:

The function rule is y = (2/3)x - 5.

Step-by-step explanation:

Let's assume for now that the function is a linear one.  Then y = mx + b.

As we move from (0, -5) to (3, -3), x increases by 3 and y increases by 2.

Thus, the slope of this line is m = rise / run = 2/3.

Then our y = mx + b becomes  y = (2/3)x + b, or -5 = (2/3)(0) + b.

Thus, b = -5, and the equation is y = (2/3)x - 5.

Now let's check this result.  When x = 6, does the equation predict y = -1?

y = (2/3)(6) - 5 = 4 - 5 = -1.  YES

The function rule is y = (2/3)x - 5.

First you must distribute the 2 to the numbers inside the parentheses, which would be 1 and -x...

(2 * 1) + (2 * -x) > 2x

2 + (-2x) > 2x

2 - 2x >2x

Add 2x to both sides (what you do on one side you must do to the other). Since 2x is being subtracted, addition (the opposite of subtraction) will cancel it out (make it zero) from the left side and bring it over to the right side.

2 - 2x + 2x > 2x + 2x

2 + 0 > 4x

2 > 4x

Next divide 4 to both sides to finish isolating x. Since 4 is being multiplied by x, division (the opposite of multiplication) will cancel 4 out (in this case it will make 4 one) from the right side and bring it over to the left side.

2/4 > 4x / 4

1/2 > x

or

x < 1/2

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

x<1/2

Step-by-step explanation:

Expand.

 ↓

2(1-x)=2-2x

2-2x>2x

First, subtract by 2 from both sides of equation.

2-2x-2>2x-2

Simplify.

-2x>2x-2

Then subtract by 2x from both sides of equation.

-2x-2x>2x-2-2x

Simplify.

-4x>-2

Multiply by -1 from both sides of equation.

(-4)(-1)<(-2)(-1)

Simplify.

4x<2

Divide by 4 from both sides of equation.

4x/4<2/4

Simplify, to find the answer.

2/4=1/2

X<1/2 is the correct answer.

Answer:

The answer is 337.5.

Step-by-step explanation:

Srry Im late. :(

Answer: C. 337.5

Hope this helps!

To find the 4th term of (x-2y)^6, you can use the binomial expansion formula. The 4th term is 240x^2y^4.

Therefore, the 4th term of (x-2y)^6 is 15 * x^2 * (-2y)^4, which simplifies to 15x^2 * 16y^4 = 240x^2y^4.

To find the 4th term of (x - 2y)^6, we can use the binomial expansion formula.

To find the 4th term of (x - 2y)^6, we can use the binomial expansion formula.

The formula is: (a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nCn * a^0 * b^n

Where nCk represents the binomial coefficient, which can be calculated as n! / (k! * (n-k)!)

In this case, a = x and b = -2y.

The exponents will go from 6 down to 0, and we need to find the term with k = 4.

Let's substitute these values into the formula:

(x - 2y)^6 = 6C0 * x^6 * (-2y)^0 + 6C1 * x^5 * (-2y)^1 + 6C2 * x^4 * (-2y)^2 + 6C3 * x^3 * (-2y)^3 + 6C4 * x^2 * (-2y)^4 + 6C5 * x^1 * (-2y)^5 + 6C6 * x^0 * (-2y)^6

To find the 4th term, we look at the term with k = 4. Using the binomial coefficient:

6C4 = 6! / (4! * (6-4)!)

= 15

Substituting this back into the formula, we get:

15 * x^2 * (-2y)^4

Answer:

C

Step-by-step explanation:

note that - (- 19) = + 19

Given

y - (- 19) = 25, that is

y + 19 = 25 ( subtract 19 from both sides )

y = 6 → C

Answer:

Answer is C. 6

Step-by-step explanation:

Because:

y -(-19) = 25 (well i always put a 1 infront of parenthesis) so,

y -1(-19) =25 distribute the 1 in the parenthesis and you would get

19=25 minus 19 on both sides and you get y= 6

Hope my answer has helped you!

Answer: sorry i meant 7.5 would be incorrect

Step-by-step explanation: she wouldn't be able to do it if it goes over 6 so that is incorrect

Answer:

Teagan is correct.

Step-by-step explanation:

We are given the following information in the question:

Number of friends = 6

Pizza eaten by all friends = [tex]\frac{4}{5}[/tex]

Now, in order to find pizza eaten by each friend, Teagan need to divide pizza eaten by total number of friends.

Formula:

[tex]\text{Pizza eaten by each friend} = \displaystyle\frac{\text{Total pizza eaten}}{\text{Number of friends sharing the pizza}}\\\\= \displaystyle\frac{\frac{4}{5}}{6} = \displasystyle\frac{4}{30} = \displaystyle\frac{2}{15}[/tex]

Thus, each friend had  [tex]\frac{2}{15}[/tex] of a pizza.