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Answer:

a(a - b)

Step-by-step explanation:

given polynomial:  a²- ab - 8a + 8a

We can first simplify this answer by removing like terms,

- 8a + 8a = 0

so we have a²- ab in. the simplest form

we can take this one step further and factor out the a (not simplest form)

a time a = a²

a times b = ab

hence, a(a - b)

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Answer:

[tex](x^2+y^2+xy)(x^2+y^2-xy)[/tex]

Step-by-step explanation:

Rewrite the middle term.

[tex]x^4+2x^2y^2-x^2y^2+y^4[/tex]

Rerrange terms.

[tex]x^4+2x^2y^2+y^4-x^2y^2[/tex]

Factor first three terms by perfect square rule.

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

Rewrite [tex]x^2y^2[/tex] as [tex](xy)^2[/tex].

[tex](x^2+y^2)^2-(xy)^2[/tex]

Since both terms are perfect squares, factor using the difference of squares formula, [tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=x^2+y^2[/tex] and [tex]b=xy[/tex].

[tex](x^2+y^2+xy)(x^2+y^2-(xy))[/tex]

Remove parentheses.

[tex](x^2+y^2+xy)(x^2+y^2-xy)[/tex]

Answer: [tex]20x^2 + 47x+24[/tex]

Step-by-step explanation:

We just multiply the values on the edges like we are finding the area of a square, L * L = area.

4x * 5x = 20x^2

4x * 8 = 32x

3 * 8 = 24

3 * 5x = 15x

Next add the answers together

20x^2 + 47x + 24

Answer:

option 3

Step-by-step explanation:

you need to times (4x+3) by (5x+8)

so you basically need to expand the brackets and collect like terms

Answer:

shorter side: 5 km

longer side: 27 km

Step-by-step explanation:

So you're already given the formula for the area of a rectangle, the next thing to do is assign length and width in terms of some unknown variable, which for convenience, I'll just say is x. So let's say one of the sides is x, the one that's the shorter side, since the longer side can be related to the shorted side, which is x. The longer side is 12km longer than 3 times the other side, so since the other side is x, it's length is (3x+12). So we simply multiply this by x, to get the area which is 135

"Known" Values: one side=x, other side=3x+12, area=135 km^2

[tex]135=x(3x+12)[/tex]

Distribute the x

[tex]135=3x^2+12x[/tex]

Subtract 135 from both sides

[tex]0=3x^2+12x-135[/tex]

Now since the equation is equal to zero, we can use the quadratic equation. In this case a=3, b=12, and c=-135

[tex]x=\frac{-12\pm\sqrt{12^2-4(3)(-135)}}{2(3)}[/tex]

Simplify denominator and multiply inside of the radical

[tex]x=\frac{-12\pm\sqrt{144+1,620}}{6}[/tex]

If you're confused where the negative went in the radical, it canceled out when multiply -4 by -135. Now add the stuff in the radical

[tex]x=\frac{-12\pm\sqrt{1,764}}{6}[/tex]

Simplify the radical

[tex]x=\frac{-12\pm 42}{6}[/tex]

Now you might think there are two solutions to this equation, but the thing is that one of the sides simply cannot have a "negative length", because in this context, x must be positive. So it's easy to see you have to use the positive sign, since using the negative sign would result in -12-42 over 6 which is certainly negative. So we can ignore that solution as it doesn't mean anything in this context. We only need the positive solution

[tex]x=\frac{-12+42}{6}[/tex]

Add values

[tex]x=\frac{30}{6}[/tex]

Divide

[tex]x=5[/tex]

Since the shorter side was 5, that's the solution to the shorter side, now to find the longer side we plug in 5 into the equation: [tex]3x+12[/tex] which becomes 3(5) + 12 = 15+12 = 27. This means the two lengths are 5 and 27

Step-by-step explanation:

let x = length of shorter side

[tex](3x + 12)(x)= 135[/tex]    This is the equation

[tex]3x^2+12x=135[/tex]        use distributive property to multiply out

[tex]3x^2+12x-135=0[/tex]   subtract 135 from both sides to get in position to factor

[tex]3(x^2+4x-45)[/tex]           factor out a 3

[tex]3(x-5)(x-9)[/tex]           factor the resulting expression

[tex]x=5,9[/tex]                       two answers (we want one so see which one works)

Check both values of x

[tex]5*3+12=27[/tex]

[tex]27*5=135[/tex]

Therefore, we know the shorter side is 5 km and the longer side is 27 km.

At this point, we do not even need to check x=9

Answer:

The last option

Step-by-step explanation:

When you plug in 1 for the x and 2 for y, the answer is -5 for the first equation and is 12 for the second equation. I hope that helps!

Answer:

[tex]\tt x = 16[/tex]

Step-by-step explanation:

[tex]\tt 4x-64=0[/tex]

Add 64 to both sides.

[tex]\tt 4x - 64 + 64 = 0+ 64[/tex]

Simplify.

[tex]\tt 4x = 64[/tex]

Divide both sides by 4.

[tex] \tt \cfrac{4x}{4} = \cfrac{64}{4} [/tex]

Simplify.

[tex]\tt x = 16[/tex]

Done!!!

[tex]\Large\maltese\star\underline{\textbf{What is Asked}}\star\maltese[/tex]

[tex]\Large\maltese\star\underline{\textbf{The required answer is below -:}}\star\maltese[/tex]

First we need to add 64 to both sides. That way, we will be one step closer to solving this in terms of x.

[tex]\bf{4x-64+64=0+64}[/tex] | on the left side the 64's sum to zero

[tex]\bf{4x=0+64}[/tex] | the right side is now 64

[tex]\bf{4x=64}[/tex] | divide the equation by 4

[tex]\bf{x=16}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\gray\star\bf{Result / Required\;Answer:}[/tex]

                  [tex]\star\blacksquare\Large\boxed{\boxed{\bf{X=16.}}}\blacksquare\star[/tex]

When you're solving an equation in terms of x, or any other variable, use inverse operations to solve it. For instance, if something is added to x, use subtraction. If something is subtracted to x, use addition.

If x is multiplied by something, use division. If x is divided by something, use multiplication.

[tex]\infty\LARGE\boxed{\bf{\brace aesthetic\not1\theta\ell}}\infty[/tex]

Step-by-step explanation:

general form of a parabola :

y = ax² + bx + c

we have 3 points of the parabola to calculate the 3 variables :

the 2 intercepts are actually

(-2, 0)

(6, 0)

and then

(8, 6)

so, we get the 3 equations

0 = a(-2)² + b×-2 + c = 4a - 2b + c

0 = a×6² + b×6 + c = 36a + 6b + c

6 = a×8² + b×8 + c = 64a + 8b + c

from the 1st equation we get

c = -4a + 2b

using that in the 2nd equation we get

0 = 36a + 6b - 4a + 2b = 32a + 8b = 4a + b

b = -4a

therefore,

c = -4a + 2b = -4a + 2×-4a = -4a - 8a = -12a

using all that in the 3rd equation we get

6 = 64a + 8×-4a + -12a = 64a - 32a - 12a = 20a

a = 6/20 = 3/10 = 0.3

b = -4a = -4×3/10 = -12/10 = -1.2

c = -12a = -12×3/10 = -36/10 = -3.6

so, we have

y = 3/10 x² - 12/10 x - 36/10 = 3/10 × (x² - 4x - 12)

The expression that is equivalent to the given expression is 16⁴

From the question, we are to determine the expression that is equivalent to the given expression

The given expression is

[tex](\frac{1}{16} )^{-4}[/tex]

Evaluating

[tex](\frac{1}{16} )^{-4}[/tex]

[tex]= (16^{-1} )^{-4}[/tex]

[tex]= 16^{-1 \times -4}[/tex]

[tex]= 16^{4}[/tex]

Hence, the expression that is equivalent to the given expression is 16⁴

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The distance between the ships is 26.65.

Based on the information given, after 3 hours, the distance of ship B will be:

= 20 + (17 × 3)

= 71.

A = 21 × 3 = 63

Well calculate the square root which will be:

A² + B² = 71² + 63²

= 5041 + 3969

= 9010

Therefore, ✓9010 = 94.92

Finally, the distance will be:

= (63 × 21) + (71 × 17) / 94.92

= (1323 + 1207)/94.92

= 26.65

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Answer:

35mph

Step-by-step explanation:

divide 140/4=35

The System of Equations 1, 2, 3, and 4 have solutions corresponding to the option B, A, C, and D.

A system of equations is a set of equations that have a common solution.

The first system of equations is

y+12 = x² +x

x+y = 3

To determine the solution, the equations are plotted on the graph and the intersection of the equations gives the solution.

The solution is (-5,8) (3,0)

The second system of equation is

y-15 = -x² +4x

x+y = 1

The solution to the system is (7,-6) (-2,3)

The third system of equation is

y+5 = x²-3x

2x+y = 1

The solution to the system is (3,-5) (-2,5)

The fourth system of equation is

y-17 = x²-9x

-x+y =1

The solution to the system is (2,3) , (8,9)

Therefore, the System of Equations 1, 2, 3, and 4 have solutions corresponding to the option B, A, C, and D.

The graphs are attached with the answer.

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The height of the flagpole with an angle of elevation to the top of the pole of 31° is 60.086 feet

An equation is an expression that shows the relationship between two or more numbers and variables.

Trigonometric ratio is used to show the relationship between the sides and angles of a triangle.

Let h represent the height of the flagpole, hence:

tan(31) = h/100

h = 60.086 feet

The height of the flagpole with an angle of elevation to the top of the pole of 31° is 60.086 feet

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The average rate of change in attendance from 2011-2021 is 1.132 per year

From the graph, we have:

The average rate of change is then calculated as:

Rate = (58.77 - 47.45)/(2021 - 2011)

Evaluate

Rate = 1.132

2022 is 11 years from 2011.

So, the predicted annual attendance for 2022 is;

Attendance = 47.45 + 1.132 * 11

Attendance = 59.90

The years with unusual growth are 2020 and 2021.

This is so because they have the same attendance.

The factor that might have contributed to the anomalous growth include

In (a), we have:

Attendance = 47.45 + 1.132 * 11

Express as a function

y(t) = 47.45 + 1.132(t)

2025 is 14 years from 2011.

So, we have:

y(14) = 47.45 + 1.132(14)

y(14) = 63.298

2030 is 19 years from 2011.

So, we have:

y(19) = 47.45 + 1.132(19)

y(19) = 68.958

The factors include:

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Answer:

955,500,000,000,000,000,000,000,000,000,000,000,000

or 9.555 x 10^38

Step-by-step explanation:

multiply 245 x 39 first and then add all the zeros from both numbers after

The triangle is Obtuse and scalene , Option C is the correct answer.

A triangle is a polygon with three sides , three angles and three vertices.

A triangle can be classified as Acute , Right or Obtuse on the basis of the angle in a Triangle .

and it is classified as scalene , equilateral and isosceles on the basis of the length of the sides of a triangle.

The triangle given in the question has all the sides different , so it is a scalene triangle.

One of the angle is obtuse angle and so it can be classified as a Obtuse Angle Triangle.

Therefore , Option C is the correct answer.

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Answer:

right angle

Step-by-step explanation:

Translating shape A by the vector [tex](^1_4)[/tex] means translating 1 unit right and 4 unit up to get A'(4, 7), B'(7, 7), C'(7, 5) and D'(4, 5)

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

Let us assume that the vertices of shape A is at A(3, 3), B(6, 3), C(6, 1) and D(3, 1)

Translating shape A by the vector [tex](^1_4)[/tex] means translating 1 unit right and 4 unit up to get A'(4, 7), B'(7, 7), C'(7, 5) and D'(4, 5)

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The expression that is a sum of cubes is given as follows:

[tex]-27a^3b^6 + 8a^9b^12[/tex]

An expression that is a sum of cubes is given as follows:

a³ + b³.

For the sum, all numeric factors have to be powers of 3, while all exponents have to be multiples of 3. Hence the expression that is a sum of cubes is given as follows:

[tex]-27a^3b^6 + 8a^9b^12[/tex]

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[tex]2x - 7x + 2 + 1 - 2[/tex]

[tex]2x - 7x + 3 - 2[/tex]

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

Answer:

162, 163, and 164.

Step-by-step explanation:

Here we will use algebra to find three consecutive integers whose sum is 489. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 489. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 489

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 489

3X + 3 = 489

3X + 3 - 3 = 489 - 3

3X = 486

3X/3 = 486/3

X = 162

Which means that the first number is 162, the second number is 162 + 1 and the third number is 162 + 2. Therefore, three consecutive integers that add up to 489 are 162, 163, and 164.

162 + 163 + 164 = 489

We know our answer is correct because 162 + 163 + 164 equals 489 as displayed above.

Answer:

161, 163, 165

Step-by-step explanation:

x + x+2 + x +4 =489.

This is how we calculate three consecutive odd integers!

Combine like terms:

3x+6=489

3x=483

x=161

Three numbers are:

161, 161+2, 161+4.

161, 163, 165

Answer:

84π m^3

Step-by-step explanation:

1. The formula of a cone is: (1/3) · π · r^2 · h

2. The radius is 6m. (Diameter / 2)

3. (1/3) * π * (6^2) * 7

4. Multiply all numbers besides pi to get the answer in terms of pi

5. (36 / 3 ) = 12 * 7 = 84

6. 84π

[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Given...}}}}} \: [/tex]

[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{To \: Find ...}}}}} \: [/tex]

[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Formula \: Using ...}}}}} \: [/tex]

[tex]\Large❏ \: \Large\begin{gathered} {\underline{\boxed{ \sf {{\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {r}^{2} h}}}}}\end{gathered}[/tex]

Where,

[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Solution ...}}}}} \: [/tex]

Substituting the given values in formula.

[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {r}^{2} h[/tex]

[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {(6)}^{2} \: \times \: 7[/tex]

[tex] \large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{ \cancel3}\pi \: \times \: \cancel{ 36} \: \: ^{ \pink{12}} \: \times \: 7 \\ [/tex]

[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \:\pi \: \times \: 12 \: \times \: 7 \\ [/tex]

[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: 84 \pi \: {m}^{3} [/tex]

Hence , option b is the correct answer

The graph of the solution set for the inequality can be seen below.

Here we have the inequality:

3x - 2y < -12

If we isolate y, we get:

3x + 12 < 2y

(3x + 12)/2 < y

(3/2)x + 6 < y

Now, we just need to graph the line y = (3/2)x + 6 with a dashed line (because the points on the line are not solutions).

And then we need to shade the region above the line.

The graph of the solution set can be seen below.

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Answer:

#of advanced tickets (x) = 30

#of same-day tickets (y) = 20

Step-by-step explanation:

x-#of advanced tickets

y-#of same-day tickets

[tex]x+y=50,\\35x+30y=1650[/tex]

5x+30(x+y)=1650

5x+30(50)=1650

5x=150

x=30

y=20

The equations of the transformed graphs are [tex]f(x) = \frac 23\sqrt{x - 3}[/tex], [tex]f(x) = 8\sqrt{x }-3[/tex], [tex]f(x) = \sqrt{\frac x7} + 5[/tex] and [tex]f(x) = \sqrt{-x} - 10[/tex]

The function #1

The function is given as::

[tex]f(x) = \sqrt{x}[/tex]

It is shifted right by 3 units.

So, we have:

[tex]f(x) = \sqrt{x - 3}[/tex]

It is shrunk vertically by a factor of 2/3

[tex]f(x) = \frac 23\sqrt{x - 3}[/tex]

Hence, the equation of the transformed graph is [tex]f(x) = \frac 23\sqrt{x - 3}[/tex]

The function #2

The function is given as::

[tex]f(x) = \sqrt{x}[/tex]

It is stretched vertically by a factor of 8

[tex]f(x) = 8\sqrt{x }[/tex]

It is shifted down by 3 units.

So, we have:

[tex]f(x) = 8\sqrt{x }-3[/tex]

Hence, the equation of the transformed graph is [tex]f(x) = 8\sqrt{x }-3[/tex]

The function #3

The function is given as::

[tex]f(x) = \sqrt{x}[/tex]

It is stretched horizontally by a factor of 7

[tex]f(x) = \sqrt{\frac x7}[/tex]

It is shifted up by 5 units.

So, we have:

[tex]f(x) = \sqrt{\frac x7} + 5[/tex]

Hence, the equation of the transformed graph is [tex]f(x) = \sqrt{\frac x7} + 5[/tex]

The function #4

The function is given as::

[tex]f(x) = \sqrt{x}[/tex]

It is reflected across the y-axis

[tex]f(x) = \sqrt{-x}[/tex]

It is shifted down by 10 units.

So, we have:

[tex]f(x) = \sqrt{-x} - 10[/tex]

Hence, the equation of the transformed graph is [tex]f(x) = \sqrt{-x} - 10[/tex]

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Based on the calculations, the equation for the locus of these points is equal to x² + y² = 9.

First of all, we would determine the distance between points A and B as follows:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(-3 - 3)² + (0 - 0)²]

Distance = √[-9² + 0]

Distance = √81

Distance = 9.

Four (4) times the distance between points A and B​ is given by:

Distance = 9 × 4

Distance = 36.

Translating the word problem into a mathematical expression, we have:

a² + b² = 36

Also, from the distance formula we have:

a = √[(h + 3)² + (k - 0)²]

a² = h² + 6h + 9 + k²    

Similarly, b² is given by:

b = √[(h - 3)² + (k - 0)²]

b² = h² - 6h + 9 + k²

Equating the equations, we have:

a² + b² = 36

h² + 6h + 9 + k² + h² - 6h + 9 + k² = 36

2h² + 2k² = 36 - 18

2h² + 2k² = 18

Dividing both sides by 2, we have:

h² + k² = 9   ⇒ x² + y² = 9.

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Answer: 290.6

Step-by-step explanation:

The volume of the cone is [tex]\frac{1}{3}(\pi)(5.6^{2})(13.8-7)=\frac{26656}{375}\pi[/tex].

The volume of the cylinder is [tex](\pi)(5.6^2)(7)=219.52\pi[/tex].

Adding these together gives the exact volume to be [tex]\frac{108976}{375}\pi[/tex], which is 290.6 to the nearest tenth.

Answer:

x = 27°

Step-by-step explanation:

Hello!

Complementary angles add up to 90°.

Since angles A and B are complementary, we can sum up the equations to 90° and solve for x.

The value of x is 27°.

Answer:

14 inches

Step-by-step explanation:

If you think about it, if you were to shift the side DC to the left until it aligns with FE, you would get a straight line. This line would be parallel, and equal to AB, which can be determined by using the right angles, which are given. So AB = FE + DC, and the value of AB is given as well as the value of DC. So plugging in the known values you get 20 = FE + 6. Now subtract 6 from both sides and you get 14 = FE. So FE is 14 inches

Answer:

Step-by-step explanation:

Please help. I just need to know what the missing side is.

from the question you are looking for EF

EF + CD = 20 in (from AB misure)

so

20 - 6 = 14 = EF

The addition is one of the four fundamental mathematical operations. Jenny can have dinner at 7 pm and 7.5 mins.

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

The time can be calculated as,

Flight lands at 4 pm

Jenny has bought a 2.4kg chicken. It takes 35-45 minutes per kg plus an additional 30 minutes to cook the chicken. Time needed for cooking the chicken = (2.5×45 + 30) = 142.5 min

⇒ 15+25+5+142.5 min

Thus, the total time it takes for Jenny to cook the food starting when the flight lands are ⇒ 187.5 mins = 3 hours 7.5 mins

Since the flight lands at 4 pm

⇒ 4 pm + 3 hours 7.5 mins

⇒ 7 pm and 7.5 mins

Hence, Jenny can have dinner at 7 pm and 7.5 mins.

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Answer: x-axis

Step-by-step explanation:

If you visualize the line of reflection, it must be vertical. Option A is the only option that has a vertical line.