How can one thirdx − 2 = one fourthx + 11 be set up as a system of equations?

Answer:

[tex]\large\boxed{\dfrac{1}{36a^4b^{10}}}[/tex]

Step-by-step explanation:

[tex]\left(\dfrac{\left(2a^{-3}b^4\right)^2}{\left(3a^5b\right)^{-2}}\right)^{-1}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\=\dfrac{\left(3a^5b\right)^{-2}}{\left(2a^{-3}b^4\right)^2}\qquad\text{use}\ (ab)^n=a^nb^n\\\\=\dfrac{3^{-2}(a^5)^{-2}b^{-2}}{2^2(a^{-3})^2(b^4)^2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{3^{-2}a^{(5)(-2)}b^{-2}}{4a^{(-3)(2)}b^{(4)(2)}}=\dfrac{3^{-2}a^{-10}b^{-2}}{4a^{-6}b^8}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}[/tex]

[tex]=\dfrac{3^{-2}}{4}a^{-10-(-6)}b^{-2-8}=\dfrac{3^{-2}}{4}a^{-4}b^{-10}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{3^2}\cdot\dfrac{1}{4}\cdot\dfrac{1}{a^4}\cdot\dfrac{1}{b^{10}}=\dfrac{1}{36a^4b^{10}}[/tex]

Answer:

1 / 36a^4 b^10

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

xy^2 =  k*k y^2            x = k * k so x has to be a perfect square.

xy is a perfect square which means that since x is a perfect square (see above) then y will have to be as well

There is nothing that prohibits x = 4 and y = 4 as being the answer where x = y.

I think the smallest possible value for x + y is 8.

This excludes any possibility of 1 or 0 in some combination, although I would look into 1.

(9 - 4i)(2 + 5i)

To solve this question you must FOIL (First, Outside, Inside, Last) like so

First:

(9 - 4i)(2 + 5i)

9 * 2

18

Outside:

(9 - 4i)(2 + 5i)

9 * 5i

45i

Inside:

(9 - 4i)(2 + 5i)

-4i * 2

-8i

Last:

(9 - 4i)(2 + 5i)

-4i * 5i

-20i²

Now combine all the products of the FOIL together like so...

18 + 45i - 8i - 20i²

***Note that i² = -1; In this case that means -20i² = 20

18 + 45i - 8i + 20

Combine like terms:

38 - 37i

^^^This is your answer

Hope this helped!

~Just a girl in love with Shawn Mendes

Final answer:

The width of the rectangle frame with a total area of 160 square inches, and expressions for length (2x + 8) and width (2x + 6), is found to be 10 inches.

Explanation:

To solve for the width of the rectangle frame with an area of 160 square inches, where the length is represented by 2x + 8 and the width by 2x + 6, we need to set up an equation using the formula for the area of a rectangle, which is length × width. With the given area of 160 square inches, the equation is:

(2x + 8)(2x + 6) = 160

Let's expand this and solve for x:

4x² + 12x + 16x + 48 = 160

4x² + 28x + 48 = 160

4x² + 28x - 112 = 0

Divide everything by 4 to simplify:

x²+ 7x - 28 = 0

Factor this quadratic equation:

(x + 14)(x - 2) = 0

x = -14 or x = 2

Since a width cannot be negative, x = 2

Now, to find the width, replace x in the width expression:

Width = 2x + 6

Width = 2(2) + 6 = 4 + 6 = 10 inches

Thus, the width of the rectangle frame is 10 inches.

Answer:

B. One of the sides, or legs, that make up the right  angle.

Step-by-step explanation:

The Pythagoras Theorem applies to the right-angled triangles. It is basically a relationship between the sizes of the all lengths of the triangle. The Pythagoras Theorem is given by:

C^2 = A^2 + B^2; where A and B are perpendicular and base respectively, and C is the hypotenuse. It is interesting to note that A can either be the perpendicular or the base of the right angled triangle. Same goes for B; it can be either the perpendicular or the base. Both the perpendicular and the base intersect at 90 degrees. But both cannot be the hypotenuse. Therefore, the variable A in the Pythagoras Theorem is one of the sides, or legs, that make up the right  angle, i.e. Option B is the correct answer!!!

Answer:

obtuse, isosceles

Step-by-step explanation:

We have two angles that have the same measure  - that means two sides are equal length.  That means the triangle is isosceles

We have one angle that is greater than 90 degrees  - that tells us the triangle is obtuse

Answer:

The perimeter of the triangle is equal to 36 cm

Step-by-step explanation:

we know that

The inscribed circle contained in the triangle BCA is tangent to the three sides

we have that

BF=BH

CF=CG

AH=AG

step 1

Find CG

we know that

CF=CG

so

CF=7 cm

therefore

CG=7 cm

step 2

Find AG

we know that

CA=AG+CG

we have

CA=15 cm

CG=7 cm

substitute

15=AG+7

AG=15-7=8 cm

step 3

Find AH

Remember that

AG=AH

we have

AG=8 cm

therefore

AH=8 cm

step 4

Find BF

Remember that

BF=BH

BH=3 cm

therefore

BF=3 cm

step 5

Find the perimeter of the triangle

P=AH+BH+BF+CF+CG+AG

substitute the values

P=8+3+3+7+7+8=36 cm

The perimeter of  ΔBCA (triangle BCA) is 36 cm

The perimeter of a triangle is the sum of the length of the three sides.

The inscribed circle contained in the triangle BCA is tangent to the three sides

Therefore,

BF = BH = 3 cm

CF = CG = 7 cm

AH = AG = 15 - 7 = 8 cm

Therefore,

perimeter = CA + BC + BA

perimeter = 15 + 3 + 7 + 3 + 8

Therefore,

perimeter = 15 + 10 + 11

perimeter = 15 + 21

perimeter = 36 cm

learn more on perimeter here: https://brainly.com/question/15450681

Answer:

f(8) = 8.25(1.1)^7; f(8) = 16.077

Step-by-step explanation:

In order to calculate the explicit formula we need to look at the y coordinates. All the options list the formula of a Geometric Sequence, so we will find which sequence defines the given coordinates:

The sequence is:

8.25, 9.075, 9.9825, 10.98075

f(1) = First term of the Sequence = 8.25

r = Common Ratio = Ratio of two consecutive terms = [tex]\frac{9.075}{8.25}[/tex] = 1.1

The explicit formula for a geometric sequence is:

[tex]f(n)=f(1)(r)^{n-1}[/tex]

Using the values, we get:

[tex]f(n)=8.25(1.1)^{n-1}[/tex]

For 8th term, we have to replace n by 8:

[tex]f(8)=8.25(1.1)^{8-1}\\\\ f(8)=8.25(1.1)^{7} \\\\ f(8)=16.077[/tex]

So, second option gives the correct answer: f(8) = 8.25(1.1)^7; f(8) = 16.077

Answer:

B // f(8) = 8.25(1.1)^7; f(8) = 16.077

Step-by-step explanation:

I'm Pretty Sure She's Got It ^^^

Answer:

C

step-by-step explanation:

you just have to subtract them 9/16-1/4=8/12

Answer:

[tex]2*10^{9}[/tex]

Step-by-step explanation:

we know that

One billion is equal to  one thousand million

1 billion is equal to 1,000,000,000

so

Multiply by 2

2 billion is equal to  2,000,000,000

Remember that

In scientific notation, a number is rewritten as a simple decimal multiplied by 10  raised to some power, n

n is simply the number of zeroes in the  full written-out form of the number  

In this problem n=9  

so

[tex]2,000,000,000=2*10^{9}[/tex]

Answer:

1) [tex]3 a^3 + 8 a^2 b - b^3[/tex]

2) 93 inches

Step-by-step explanation:

1) We know that the lenghts are given by these expressions:

[tex]2ab(a - b)\\\\3a^2(a + 2b)\\\\b^2(2a - b)[/tex]

Then, we need to add them in order to find the expression that represents the total length of the rope:

- Apply Distributive property.

- Add the like terms.

Then:

[tex]=2ba^2-2ab^2+3a^3+6ba^2+2ab^2-b^3\\\\=3 a^3 + 8 a^2 b - b^3[/tex]

2) Knowing that:

[tex]a=2in\\\\b=3in[/tex]

We must substitute these values into [tex]3 a^3 + 8 a^2 b - b^3[/tex] in order to caculate the total lenght of the rope. This is:

 [tex]3 (2in)^3 + 8 (2in)^2 (3in) - (3in)^3=93in[/tex]

Answer:

100/9

Step-by-step explanation:

(7*5*2/7*3)² * (5^0/2^-3)³ * 2^-9

Solution:

We know that any number with power 0 = 1

(7*5*2/7*3)² * (1/2^-3)³ * 2^-9

Now cancel out 2 by 2

= (7*5*2/7*3)² * (1/1^-3)³ * 1^-9

=(70/21)² * (1)³/(1^-3)³ * 1^-9

=(10/3)^2 * 1/1^-1 * 1/1^9

=100/9 *1 *1

=100/9....

Answer:

[tex]\large\boxed{(2x^4y^3)(6x^3y^2)=6x^7y^5}[/tex]

Step-by-step explanation:

[tex](2x^4y^3)(6x^3y^2)\\\\=(2)(3)(x^4x^3)(y^3y^2)\qquad\text{use}\ a^na^m=a^{n+m}\\\\=6x^{4+3}y^{3+2}\\\\=6x^7y^5[/tex]

Answer:

1

Step-by-step explanation:

Your equation may be written as follows:

[tex]\frac{1}{5} +2n=3n-\frac{4}{5}[/tex]

Start by multiplying both sides by 5 to clear your fractions.

[tex]\frac{1}{5} +2n=3n-\frac{4}{5} \\1+10n=15n-4[/tex]

Next, subtract 10n from both sides.

[tex]1+10n=15n-4\\1=5n-4[/tex]

Add 4 to both sides.

[tex]1=5n-4\\5=5n[/tex]

Divide both sides by 5 to solve for n.

[tex]5=5n\\1=n[/tex]

Final answer:

By setting up an equation 1/5 + 2x = 3x - 4/5 and solving for x, we find that the number is 1.

Explanation:

The problem involves finding a number when given a relationship involving fractions and that number. The relationship is: the sum of 1/5 and twice a number is equal to 4/5 subtracted from three times the number. To find the number, we set up an equation and solve for the variable, which represents the number.

Let's denote the number as x. Our equation can be written as:

1/5 + 2x = 3x - 4/5

We bring all the x terms on one side and the constants on the other to solve for x:

2x - 3x = -4/5 - 1/5

-x = -1

x = 1

Answer:

60 nickles and 30 dimes

Step-by-step explanation:

60 $0.05=3.00

30 $.10=3.00

60+30=90

In the box, there are 30 dimes and 60 nickels, as determined by solving a system of equations based on the total number of coins and their value.

The box contains both dimes and nickels, totaling an amount of money of $6.00. Because a dime is worth $0.10 and a nickel is worth $0.05, we can set up a system of equations to solve this problem.

Let's denote the number of dimes as x and the number of nickels as y. Thus, our equations are x + y = 90 (since the total number of coins is 90) and 0.10x + 0.05y = 6 (since the total value of the coins is $6.00).

Solving these equations will give us the number of dimes and nickels in the box. Doubling the second equation gives us 0.20x + 0.10y = 12. We can subtract the first equation from this to solve for x, giving us x = 30. Substituting x=30 into the first equation, y = 90 - 30, so y = 60. So, there are 30 dimes and 60 nickels in the box.

https://brainly.com/question/35467992

#SPJ2

Answer:

[tex]3r^{4}s^{5}\\-r^{4}s^{6}[/tex]

Step-by-step explanation:

The standard form of a polynomial is when its term of highest degree is at first place.

In this case, we have two variables. The grade of each term is formed by the sum of its exponents. That means both given terms have a degree of six. So, the right answers must have a higher degree.

Therefore, the right answers are the second and third choice, because their degrees are 9 and 10 respectively.

Answer:

[tex]\large\boxed{y=-\dfrac{8}{5}x+\dfrac{31}{5}}[/tex]

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept[/tex]

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\--------------------------[/tex]

[tex]\text{We have:}\\\\y=\dfrac{5}{8}x-4\to m_1=\dfrac{5}{8}\\\\\text{The slope of a perpendicular line:}\ m_2=-\dfrac{1}{\frac{5}{8}}=-\dfrac{8}{5}\\\\\text{The equation:}\\\\y=-\dfrac{8}{5}x+b\\\\\text{Put the coordinates of the point (2, 3) to the equation:}\\\\3=-\dfrac{8}{5}(2)+b\qquad\text{solve for}\ b\\\\3=-\dfrac{16}{5}+b\qquad\text{add}\ \dfrac{16}{5}\ \text{to both sides}\\\\\dfrac{15}{5}+\dfrac{16}{5}=b\to b=\dfrac{31}{3}\\\\\text{Finally:}\\\\y=-\dfrac{8}{5}x+\dfrac{31}{5}[/tex]

Answer:

1980.

Step-by-step explanation:

John was born in  1995 - 40 = 1955.

His father was born in 1995 - 65 = 1930.

Let x  be Johns age and his father 2x

1955 + x = 1930 + 2x

1955 - 1930 = 2x - x

x =  25

So the year is 1955 + 25 = 1980..

In that year John was 25 and his father was  50.

Answer:

=6√3 the third option.

Step-by-step explanation:

We can use the Pythagoras theorem to find the value of y. We need two equations that include y.

a²+b²=c²

c=9+3=12

x²+y²=12²

x²=144 - y².........i (This is the first equation)

We can also express it in another way but let us find the perpendicular dropped to c.

perpendicular²= x²-3²=x²-9 according to the Pythagoras theorem.

y²=(x²-9)+9²

y²=x²+72

x²=y²-72....ii( this is the second equation

Let us equate the two.

y²-72=144-y²

2y²=144+72

2y²=216

y²=108

y=√108

In Surd form √108=√(36×3)=6√3

y=6√3

Answer:

385.5 USD

Step-by-step explanation:

If an average car is sold for 25,700 USD, and the sales person gets 1.5% commission of it, we can easily get to the amount of money that the sales person managed to get from each sale.

The 25,700 should be divided by 100, as that is number of total percentage:

25,700 / 100 = 257

So we have 1% being 257 USD, but we need 1.5%, so we should multiple the 257 USD by 1.5%:

257 x 1.5 = 385.5

So we get a result of 385.5 USD, which is the amount the sales person makes from commissions on average per sold car.

Neither of those two graphs do the trick, but if I saw the rest of the answer choices, then I would be happy to assist you.

Answer:

The answer is B, given the module of a number has always a positive value

Answer:

Answer is B.

SECOND NUMBER LINE

Step-by-step explanation:

Answer:

[tex]f^{-1}(x)=-2x+6[/tex].

Step-by-step explanation:

[tex]y=f(x)[/tex]

[tex]y=3-\frac{1}{2}x[/tex]

The biggest thing about finding the inverse is swapping x and y.  The inverse comes from switching all the points on the graph of the original.  So a point (x,y) on the original becomes (y,x) on the original's inverse.

Sway x and y in:

[tex]y=3-\frac{1}{2}x[/tex]

[tex]x=3-\frac{1}{2}y[/tex]

Now we want to remake y the subject (that is solve for y):

Subtract 3 on both sides:

[tex]x-3=-\frac{1}{2}y[/tex]

Multiply both sides by -2:

[tex]-2(x-3)=y[/tex]

We could leave as this or we could distribute:

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

The inverse equations is [tex]y=-2x+6[/tex].

Now some people rename this [tex]f^{-1}[/tex] or just call it another name like [tex]g[/tex].

[tex]f^{-1}(x)=-2x+6[/tex].

Let's verify this is the inverse.

If they are inverses then you will have that:

[tex]f(f^{-1}(x))=x \text{ and } f^{-1}(f(x))=x[/tex]

Let's try the first:

[tex]f(f^{-1}(x))[/tex]

[tex]f(-2x+6)[/tex]  (Replace inverse f with -2x+6 since we had [tex]f^{-1})(x)=-2x+6[/tex]

[tex]3-\frac{1}{2}(-2x+6)[/tex]  (Replace old output, x, in f with new input, -2x+6)

[tex]3+x-3[/tex]  (I distributed)

[tex]x[/tex]

Bingo!

Let's try the other way.

[tex]f^{-1}(f(x))[/tex]

[tex]f^{-1}(3-\frac{1}{2}x)[/tex] (Replace f(x) with 3-(1/2)x since [tex]f(x)=3-\frac{1}{2}x[/tex])

[tex]-2(3-\frac{1}{2}x)+6[/tex] (Replace old input, x, in -2x+6 with 3-(1/2)x since [tex]f(x)=3-\frac{1}{2}x[/tex])

[tex]-6+x+6[/tex] (I distributed)

[tex]x[/tex]

So both ways we got x.

We have confirmed what we found is the inverse of the original function.

Answer:

[tex]\laege\boxed{f^{-1}(x)=-2x+6}[/tex]

Step-by-step explanation:

[tex]f(x)=3-\dfrac{1}{2}x\to y=3-\dfrac{1}{2}x\\\\\text{Exchange x to y and vice versa:}\\\\x=3-\dfrac{1}{2}y\\\\\text{Solve for}\ y:\\\\3-\dfrac{1}{2}y=x\qquad\text{subtract 3 from both sides}\\\\-\dfrac{1}{2}y=x-3\qquad\text{multiply both sides by (-2)}\\\\\left(-2\!\!\!\!\diagup^1\right)\cdot\left(-\dfrac{1}{2\!\!\!\!\diagup_1}y\right)=-2x-3(-2)\\\\y=-2x+6[/tex]

Answer:

10,000 m/square

Step-by-step explanation:

we know that

A hectare is a unit of area equal to [tex]10,000\ m^{2}[/tex]

The symbol is Ha

Verify each case

case 1) 10,000 m/square

The option is true

case 2) 100 m/square

The option is false

case 3) 100,000 m/square​

The option is false

Please see attached image for complete answer and steps in detail.

Answer:

The result is 150 + 1.5d

Step-by-step explanation:

We want to translate the wordings into algebraic expression.

Firstly, we increase 120 by d%

d% = d/100

So increasing 120 by d % means;

120 + (d/100 * 120)

= 120 + 1.2d

Then increase this by 25%

= (120 + 1.2d) + 25/100(120 + 1.2d)

= 120 + 1.2d + (120+1.2d)/4

= 120 + 1.2d + 30 + 0.3d

= 120 + 30 + 1.2d + 0.3d

= 150 + 1.5d

Answer:

[tex]\large\boxed{\dfrac{a^{-3}}{a^{-2}b^{-5}}=a^{-1}b^5}[/tex]

Step-by-step explanation:

[tex]\dfrac{a^{-3}}{a^{-2}b^{-5}}=a^{-3}\cdot\dfrac{1}{a^{-2}}\cdot\dfrac{1}{b^{-5}}\qquad\text{use}\ x^{-n}=\dfrac{1}{x^n}\\\\=a^{-3}\cdot a^2\cdot b^5\qquad\text{use}\ x^n\cdot x^m=x^{n+m}\\\\=a^{-3+2}b^5=a^{-1}b^5[/tex]

Answer:

(2,2)

Step-by-step explanation:

Answer:

Equation of the parabola: [tex]y = 2x^{2} + 4x - 3[/tex].

Axis of symmetry: [tex]x= -1[/tex].

Coordinates of the vertex: [tex]\displaystyle \left(-1, -5\right)[/tex].

Step-by-step explanation:

The axis of symmetry and the coordinates of the vertex of a parabola can be read directly from its equation in vertex form.

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

The vertex of this parabola will be at [tex](h, k)[/tex]. The axis of symmetry will be [tex]x = h[/tex].

The equation in this question is in standard form. It will take some extra steps to find the vertex form of this equation before its vertex and axis of symmetry can be found. To find the vertex form, find its coefficients [tex]a[/tex], [tex]h[/tex], and[tex]k[/tex].

Expand the square in the vertex form using the binomial theorem.

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

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

By the distributive property of multiplication,

[tex]y = (ax^{2} - 2ahx + ah^{2}) +k[/tex].

Collect the constant terms:

[tex]y = ax^{2} - 2ahx + (ah^{2} +k)[/tex].

The coefficients in front of powers of [tex]x[/tex] shall be the same in the two forms. For example, the coefficient of [tex]x^{2}[/tex] in the given equation is [tex]2[/tex]. The coefficient of [tex]x^{2}[/tex] in the equation [tex]y = ax^{2} - 2ahx + (ah^{2} +k)[/tex] is [tex]a[/tex]. The two coefficients need to be equal for the two equations to be equivalent. As a result, [tex]a = 2[/tex].

Similarly, for the term [tex]x[/tex]:

[tex]-2ah = 4[/tex].

[tex]\displaystyle h = -\frac{2}{a} = -1[/tex].

So is the case for the constant term:

[tex]ah^{2} + k = -3[/tex].

[tex]k = -3 - ah^{2} = -5[/tex].

The vertex form of this parabola will thus be:

[tex]y = 2(x -(-1))^{2} + (-5)[/tex].

The vertex of this parabola is at [tex](-1, -5)[/tex].

The axis of symmetry of a parabola is a vertical line that goes through its vertex. For this parabola, the axis of symmetry is the line [tex]x = -1[/tex].