The product of the polynomials (2ab + b) and (a2 – b2)

Answer:

(0,-3)

(3,0)

Step-by-step explanation:

The solutions to the system of equations are where the two graphs cross

The first is at x=0 and y=-3

The second is at x=3 and y=0

Answer:

x = 3 and -2 are the two solutions.

Step-by-step explanation:

2x^2 -2x -12 = 0

First factor out a 2

2(x^2 - x - 6) = 0

2(x - 3)(x + 2) = 0

2 = 0 x - 3 = 0 x + 2 = 0

2 does not equal zero so this is an extraneous solution

x - 3 = 0 so x = 3

x + 2 = 0 so x = -2

Answer:

a) The first inequality 100+55x>150+51x;

b) The last inequality x>12.5

c) 13 months

Step-by-step explanation:

a) Let x be the number of months.

1. The first phone costs $100 and $55 per month for unlimited usage, then for x months it will cost $55x and in total

$(100+55x)

2. The second phone costs $150 and $51 per month for unlimited usage, then for x months it will cost %51x and in total

$(150+51x)

3. If the second phone must be less expensive than the first phone, then

150+51x<100+55x

or

100+55x>150+51x

b) Solve this inequality:

55x-51x>150-100

4x>50

x>12.5

c) Sal's mother has to keep the second cell phone for at least 13 months (because x>12.5).

Part 1:

The first phone costs $100 and $55 per month for unlimited usage.

Let f(x) be the cost of the first phone and x be the number of months.

Equation forms:

[tex]f(x)=55x+100[/tex]

The second phone costs $150 and $51 per month for unlimited usage.  

Let g(x) be the cost of the second phone and x be the number of months.

Equation forms:

[tex]g(x)=51x+150[/tex]

We have to find the inequality that will determine the number of months, x,  that are required for the second phone to be less expensive, it is given by:

[tex]g(x)<f(x)[/tex]

[tex]51x+150<55x+100[/tex]

Part 2:

The solution to the inequality is:  

[tex]51x+150<55x+100[/tex]

=> [tex]51x-55x<100-150[/tex]

=> [tex]-4x<-50[/tex]

=> [tex]-x<-12.5[/tex]

=> [tex]x>12.5[/tex]

Or rounding off to 13.

Part 3:

Sal’s mother would have to keep the second cell phone plan for at least 13 months in order for it to be less expensive.

Answer:

=6000 m/min

Step-by-step explanation:

There are 60 seconds in 1 minute.

The speed of the race car is 100 m/s. If it covers 100 m in one second,  then in one minute it will cover a longer distance calculated as follows.

100 m/s × 60 second/min = 6000 m/min

Answer: Last Option

6,000 meters per minute

Step-by-step explanation:

We know that 60 seconds is equal to one minute.

Then we use this data as a conversion factor.

The speed of the car is 100 meters per second, this is:

[tex]s = 100\ \frac{meters}{seconds}[/tex]

Now we multiply this amount by the conversion factor in the following way:

[tex]100\ \frac{meters}{second} * \frac{60\ second}{1\ minute}= 6000\ \frac{meters}{minute}[/tex]

The answer is:

6,000 meters per minute

Hello There!

My equation would be 5c + 11d <= 39

C represents cassete tape

D represents disk or the second letter of CD

To solve this I set tapes as X and CDs as Y and then multiplied each variable by the cost, respectively.

Next I set the inequality to be less than or equal to 39, because that is the amount of money you have.

The  expression for g(x) is g(x) = x^3, a cubic function that passes through the origin and is slightly narrower than the graph of f(x) = x^2.

 Certainly! Let's walk through the step-by-step calculation to determine the expression for g(x) based on the given information.

Given Information:

f(x) = x^2 (quadratic function)

Coordinate marked for g(x) is (2, 8)

g(x) is a parabola slightly narrower than f(x)

The curve g(x) passes through the origin

Expression for g(x):

Since g(x) is a parabola, we consider it as g(x) = ax^2 initially.

The coordinate (2, 8) helps determine the value of a.

g(2) = a(2)^2 = 4a = 8

Solving for a, we get a = 2.

So, g(x) = 2x^2 is the initial expression.

Adjusting for Narrowness:

If g(x) is slightly narrower than f(x), we need to make it narrower than 2x^2.

To achieve this, we can use g(x) = x^3.

Verification:

Check the coordinate (2, 8) in g(x) = x^3:

g(2) = 2^3 = 8

The coordinate (2, 8) satisfies the expression.

To solve the given system of equations, one can utilize matrix operations, specifically finding the inverse of the coefficient matrix and multiplying it by the constants matrix to solve for the variables x, y, and z.

Solving a System of Equations

To solve the system of linear equations: 3x+4y+3z=5, 2x+2y+3z=5, and 5x+6y+7z=7, we can use methods such as substitution, elimination, or matrix operations. In this case, matrix operations may be more efficient for finding the values of x, y, and z.

Firstly, we must write the system of equations in matrix form (Ax = b), with A being the coefficient matrix, x the variable matrix, and b the constant terms matrix:

A =
| 3 4 3 |
| 2 2 3 |
| 5 6 7 |,
x =
| x |
| y |
| z |,
b =
| 5 |
| 5 |
| 7 |

Next, we find the inverse of matrix A, if it exists, and then multiply it by b to solve for x:

x = A-1 * b

Through matrix operations, we can find A-1. The existence of an inverse is dependent on the determinant of A not being zero. If the determinant is non-zero, the inverse can be used to compute the variables' values. Therefore, we proceed with calculating the determinant and, if possible, the inverse to solve for x, y, and z.

Finally, we multiply the inverse of A (if it exists) by b to get the values for x, y, and z. This involves algebraic steps and matrix multiplication. If any mistake is made, the process requires careful checking and rechecking.

Answer:

96 units squared

Step-by-step explanation:

Answer:

B. 96 Units^2.

Step-by-step explanation:

Got Correct On Assist.

Answer:

[0, 2, 5]

Step-by-step explanation:

Find z, plug in 5 for every "z" you see, then solve by Elimination to find y and x.

The solution to the given system of linear equations is x = 1, y = 3, z = 5. The problem is resolved by first solving the simplest equation and using its answer to simplify and solve the next, allowing us to find the final answers.

To solve the given system of linear equations, we need to find the values for variables x, y and z that satisfy all the three equations. Start by solving the simplest equation which is '2z = 10'. By dividing both sides by 2, we find that z = 5.

Next, substitute z = 5 into the other two equations. The first equation 'x + 2y + z = 9' becomes 'x + 2y + 5 = 9', which simplifies to x + 2y = 4. The second equation 'x - y + 3z = 13', becomes 'x - y + 3*5 = 13', simplifying to x - y = -2.

We now have two equations with two variables, which we can solve simultaneously. By adding the equations together '(x + 2y = 4) + (x - y = -2)', we get 2x + y = 2, hence, x = 1. Substituting x = 1 into 'x - y = -2' yields y = 3.

Therefore, the solution to the system is x = 1, y = 3, z = 5.

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Answer: Square root of x+3

Step-by-step explanation:

Insert the denominator to 3

ANSWER

The graph of the function starts from (1,4) and moves up right.

EXPLANATION

The given rational function is

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

The base of this function is

[tex]y = \sqrt{x} [/tex]

The -1 under radical sign means the graph of the base function is shifted 1 unit right.

The +4 shows that base function is shifted up by 4 units.

The graph of the function therefore starts from (1,4) and moves up right.

Answer:

20

Step-by-step explanation:

24/3=8

36/3=12

8+12=20

he'll have 20 3' ropes

Answer:

7.5 Miles.

Step-by-step explanation:

3 + 4.5 = 7.5 Miles.

Answer:

The inequality is  [tex]6x+4,885.78\leq 9,750.05[/tex]

[tex]x\leq 810.71\ gal[/tex]

Step-by-step explanation:

Let

x -----> amount of water that can be used by only one family member for the rest of the month

we know that

[tex]6x+4,885.78\leq 9,750.05[/tex]

Solve for x

Subtract 4,885.78 both sides

[tex]6x\leq 9,750.05-4,885.78[/tex]

[tex]6x\leq 4,864.27[/tex]

Divide by 6 both sides

[tex]x\leq 4,864.27/6[/tex]

[tex]x\leq 810.71\ gal[/tex]

Answer:

Each member can use, x = 810.71 gallons of water for the remaining month.

The equation is 6x + 4885.78 [tex]\leq[/tex] 9750.05

Step-by-step explanation:

Total number of members in Green's family = 6

Let one member uses = x gallons of water

Therefore six member will use = 6x gallons of water

Given the Green's family can use only 9750.05 gallons of water in one month. And they have use so far 4885.78 gallons of water.

Therefore the equation becomes

6x + 4885.78 [tex]\leq[/tex] 9750.05

6x [tex]\leq[/tex] 9750.05 - 4885.78

6x [tex]\leq[/tex] 4864.27

x [tex]\leq[/tex] 4864.27 / 6

x [tex]\leq[/tex] 810.71 gallons

Hence, the equation is 6x + 4885.78 [tex]\leq[/tex] 9750.05

and each member can use 810.71 gallons of water for the remaining days of the month.

Answer:

The distance would be 4 units and you would go 4 to the right

I hope this helps :)

Step-by-step explanation:

Answer: First option

Step-by-step explanation:

The distance between two points is calculated using the following formula

[tex]d=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]

In this case we have the following points

W(0, 8) and X(0, 12)

Therefore

[tex]x_1 = 0\\x_2 = 0\\y_1=8\\y_2=12[/tex]

[tex]d=\sqrt{(0-0)^2 +(12-8)^2}[/tex]

[tex]d=\sqrt{(12-8)^2}[/tex]

[tex]d=\sqrt{(4)^2}[/tex]

[tex]d=4[/tex]

Answer: A) [tex]18, 0, -10, -10[/tex]

Step-by-step explanation:

Given the quadratic function [tex]y=x^2-x-12[/tex], you need to substitute each value of "x" into the function to find the corresponding value of "y":

For [tex]x=-5[/tex]:

[tex]y=(-5)^2-(-5)-12\\\\y=18[/tex]

For [tex]x=-3[/tex]:

[tex]y=(-3)^2-(-3)-12\\\\y=0[/tex]

For [tex]x=-1[/tex]:

[tex]y=(-1)^2-(-1)-12\\\\y=-10[/tex]

For [tex]x=2[/tex]:

[tex]y=(2)^2-(2)-12\\\\y=-10[/tex]

The correct option is: A

Answer:  [tex]\bold{\dfrac{1}{(x+1)(x-2)}}[/tex]

Step-by-step explanation:

[tex]\dfrac{x+2}{4x^2+5x+1}\times \dfrac{4x+1}{x^2-4}\\\\\\\text{Factor the quadratics:}\\\dfrac{x+2}{(4x+1)(x+1)}\times \dfrac{4x+1}{(x-2)(x+2)}\\\\\\\text{Simplify - cross out (4x+1) and (x+2):}\\\dfrac{1}{(x+1)(x-2)}[/tex]

Answer:

[tex]\frac{1}{x^2 - x - 2}[/tex]

Step-by-step explanation:

The given expression is

[tex]\frac{x+2}{4x^2+5x+1}\times \frac{4x+1}{x^2-4}[/tex]

Factorize the denominators.

[tex]\frac{x+2}{4x^2+4x+x+1}\times \frac{4x+1}{x^2-2^2}[/tex]

[tex]\frac{x+2}{4x(x+1)+1(x+1)}\times \frac{4x+1}{(x-2)(x+2)}[/tex]             [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]\frac{x+2}{(x+1)(4x+1)}\times \frac{4x+1}{(x-2)(x+2)}[/tex]

Cancel out common factors.

[tex]\frac{1}{(x+1)}\times \frac{1}{(x-2)}[/tex]

[tex]\frac{1}{(x+1)(x-2)}[/tex]

On further simplification we get

[tex]\frac{1}{x^2 - x - 2}[/tex]

Therefore, the simplified form of the given expression is [tex]\frac{1}{x^2 - x - 2}[/tex].

Answer:

Step-by-step explanation:

3 ln(2x) + 7 = 15            Subtract 7 from both sides

3 ln(2x)  = 15 - 7            Combine

3 ln(2x) = 8                    Divide by 3

  ln(2x) = 8/3                Do the division. Take the antilog of both sides.

e^ln(2x) = e^(8/3)

2x = 14.392                   Divide by 2

x = 14.392

x = 7. 196

Answer:

5cm

Step-by-step explanation:

okay what you need to know is that:

1cm:5km

5km times 5 is the distance you traveled, 25km

1cm times 5 is 5

Don't get confused with 5km to 5.

It's totally different.

Using the map scale of 20cm to 100km, it is calculated that 25 kilometers in reality is represented by 5 centimeters on the map. This is determined by setting up a proportion between the distance on the map and the actual distance and solving for the unknown value.

To find out how many centimeters on the map represent 25 kilometers of actual distance, we use the map's scale. The scale given is 20cm:100km, which means that for every 20 centimeters on the map, the actual distance represented is 100 kilometers. To solve the problem, we need to set up a proportion.

First, convert the actual distance you want to find on the map from kilometers to centimeters using the scale. So, for every 100 kilometers, we have 20 centimeters on the map. Hence, for 1 kilometer, the distance on the map would be 20 cm divided by 100 km.

20 cm/100 km = X cm/25 km

To find the value of 'X', our unknown value which represents how far you've travelled on the map, we perform cross-multiplication.

100 km * X cm = 20 cm * 25 km

X = (20 cm * 25 km) / 100 km

X = 500 cm / 100

X = 5 cm

So, you have travelled 5 centimeters on the map.

ANSWER

[tex]c = 5[/tex]

EXPLANATION

A quadratic equation is said to be in standard form when it is in the form

[tex]a {x}^{2} + bx + c = 0[/tex]

where a, b, c are real numbers.

The given quadratic equation is

[tex] - 6 = {x}^{2} + 4x - 1[/tex]

When we add 6 to both sides, we obtain,

[tex]-6 + 6= {x}^{2} + 4x - 1 + 6[/tex]

[tex] \implies \: 0= {x}^{2} + 4x + 5[/tex]

Or

[tex]\implies \: {x}^{2} + 4x + 5 = 0[/tex]

This is what Alexandra got after he wrote the quadratic equation in standard form.

By comparing this equation to

[tex]a {x}^{2} + bx + c = 0[/tex]

we have a=1, b=4 and c=5.

[tex]\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{2^{\frac{3}{4}}}{2^{\frac{1}{2}}}\implies 2^{\frac{3}{4}}\cdot 2^{-\frac{1}{2}}\implies 2^{\frac{3}{4}-\frac{1}{2}}\implies 2^{\frac{3-2}{4}}\implies 2^{\frac{1}{4}}\implies \sqrt[4]{2^1}\implies \sqrt[4]{2}[/tex]

Answer:

=42

Step-by-step explanation:

The expression 8×7×9×49×3 can be written in its simplest factor form as follows.

8=2³

49=7²

9=3²

Thus the expression becomes:2³×7×3²×7²×3

Combine the indices to the same base.

2³×3³×7³

Finding the cube root involves dividing the index by three.

Thus ∛(2³×3³×7³)= 2×3×7

=42

Answer:

y = -3x - 1

Step-by-step explanation:

The slope intercept form of the equation of a line is:

y = mx + b

where m is the slope, and b is the y-intercept.

First, we find the slope of the line using the two given points.

m = slope = (y2 - y1)/(x2 - x1) = (2 - (-7))/(-1 - 2) = (2 + 7)/(-3) = 9/(-3) = -3

Now we plug in the slope we found into the equation above.

y = -3x + b

We need to find the value of b, the y-intercept. We use the coordinates of one of the given points for x and y, and we solve for b. Let's use point (2, -7), so x = 2, and y = -7.

y = -3x + b

-7 = -3(2) + b

-7 = -6 + b

Add 6 to both sides.

-1 = b

Now we plug in -1 for b.

y = -3x - 1

[tex]

\dfrac{8^{3x}}{2^{10}}=\dfrac{4^{2x}}{16} \\

\dfrac{2^{3(3x)}}{2^{10}}=\dfrac{4^{2x}}{4^2} \\

2^{9x-10}=4^{2x-2} \\

2^{9x-10}=2^{2(2x-2)} \\

2^{9x-10}=2^{4x-4} \\

9x-10=4x-4 \\

5x-6=0 \\

5x=6 \\

\boxed{x=\dfrac{6}{5}}

[/tex]

Hope this helps.

r3t40

Answer:

Surface Area = 283

Step-by-step explanation:

Radius = 3

Height = 12

Formula for suface area is SA= 2πrh+2πr^2

let "r" be for radius

let "h" be for height

SA=2*π*3*12+2*π*3^2

SA=282.74

round to the nearest ones spot and that will make the surface area = 283

The surface area of a right cylinder with a radius of 3 and a height of 12 is calculated using the formula S = 2πr(h + r), resulting in S = 90π or approximately 282.6 square units.

The question is asking to calculate the surface area of a right cylinder with a known radius and height. The formula to find the surface area of a cylinder is S = 2πr(h + r), where r is the radius, and h is the height.

To calculate the surface area of the given cylinder with a radius of 3 and a height of 12, we plug in these values into the formula:

S = 2 × π × 3 × (12 + 3)

This simplifies to S = 2 × π × 3 × 15, which further simplifies to S = 2 × π × 45, and hence S = 90π. By multiplying this by the approximate value of π (3.14), we get S = 282.6 square units as the surface area of the cylinder.

The cross-sectional area (base area) of the cylinder is πr², which is the area of a circle with the same radius as the cylinder. The side surface area, which is the area of the rectangle that would be formed if you 'unrolled' the outer surface of the cylinder, is 2πrh. Adding two times the base area and the side surface area gives you the total surface area of the cylinder.

The probability that a first roll is an even number and a second role is a number greater than 4 when a six-sided number cube is rolled twice is 1/6.

The probability of an event is the fractional value determining how likely is that event to take place. If the event is denoted by A, the number of outcomes favoring the event A is n and the total number of outcomes is S, then the probability of the event A is given as:

P(A) = n/S.

When the occurrence of one event, doesn't affect the occurrence of the other event, then the two events are independent of each other.

If we have two independent events A and B, then the probability of A and B is given as:

P(A and B) = P(A) * P(B).

We are informed that a six-sided number cube is rolled twice. We are asked what is the probability that a first roll is an even number and a second roll is a number greater than 4.

Let the event of getting an even number on a first roll be A.

∴Number of outcomes favorable to event A (n) = 3 {2, 4, 6}

Total number of outcomes (S) = 6 {1, 2, 3, 4, 5, 6}

∴ The probability of getting an even number on a first roll is:

P(A) = n/S = 3/6 = 1/2.

Let the event of getting a number greater than 4 on a second roll be B.

∴Number of outcomes favorable to event B (n) = 2 {5, 6}

Total number of outcomes (S) = 6 {1, 2, 3, 4, 5, 6}

∴ The probability of getting a number greater than 4 on a second roll is:

P(B) = n/S = 2/6 = 1/3.

∵ Our two events, A and B, are independent of each other, that is, the occurrence of one doesn't affect the occurrence of the other, the probability that a first roll is an even number and a second roll is a number greater than 4 is given by:

P(A and B) = P(A)*P(B) = (1/2)*(1/3) = 1/6.

∴ The probability that a first roll is an even number and a second role is a number greater than 4 when a six-sided number cube is rolled twice is 1/6.

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Answer:

-6 - x^5+3x^2 is cubic, and trinomial

5x^3 - 8x is cubic, and binomial

1/3x^4 is quartic, and monomial

6/7x + 1 is linear, and binomial

-0.7x^2 is quadratic, and monomial

Step-by-step explanation:

Monomial is 1 term

Binomial is 2 terms

Trinomial is 3 terms

- Exponents don't count as terms btw

Answer:

Step-by-step explanation:

Answer:

x=3/4

Step-by-step explanation:

0=8(8x-7)+8

0=64x-56+8

0=64x-48

48=64x

x=48/64

x=6/8

x=3/4

[tex]8(8x - 7) + 8=0\\64x-56=-8\\64x=48\\x=\dfrac{48}{64}=\dfrac{3}{4}[/tex]

im pretty sure its 85

please correct me if im wrong!

Answer:

x = 4

Step-by-step explanation:

We require to find RT

Since ΔRST is right use the sine ratio to find RT

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2\sqrt{3} }{RT}[/tex]

Multiply both sides by RT

RT × sin60° = 2[tex]\sqrt{3}[/tex] ( divide both sides by sin60° )

RT = [tex]\frac{2\sqrt{3} }{sin60}[/tex] = 4

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

Since ΔRTQ is right use the tangent ratio to find x

tan45° = [tex]\frac{RQ}{RT}[/tex] = [tex]\frac{x}{4}[/tex]

Multiply both sides by 4

4 × tan45° = x, hence

x = 4 × 1 = 4

That is x = 4

Answer: 80 cans

Step-by-step explanation:

The ratio between cups to cans is 1:5

If we have 14 cups, multiply that by 5 and it is equal to 80 cans

[tex]14[/tex] cups is equals to [tex]70[/tex] number of cans.

" Number is defined as the count of any given quantity."

According to the question,

Given,

[tex]2[/tex] cups [tex]=[/tex] [tex]10[/tex] number of cans

[tex]1[/tex] cup [tex]= \frac{10}{2}[/tex] number of cans

Therefore,

[tex]14[/tex] cups [tex]= \frac{10}{2} \times 14[/tex] number of cans

            [tex]= 70[/tex] number of cans

Hence, [tex]14[/tex] cups is equals to [tex]70[/tex] number of cans.

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Answer:

V≈4188.79

Step-by-step explanation:

The formula of the volume of a sphere is V=4/3πr^3