Find the area of a parallelogram who vertices ate (2,1), (7,1), (9,5) and (4,5)

Some factoring lets us write

[tex]a^{2b}-\dfrac1{a^b}=a^{2b}-a^{-b}=a^{-b}(a^{3b}-1)[/tex]

Then

[tex]8a^{3b}=1\implies a^{3b}=\dfrac18[/tex]

[tex]a^{2b}-\dfrac1{a^b}=a^{-b}\left(\dfrac18-1\right)=-\dfrac78a^{-b}=-\dfrac7{8a^b}[/tex]

Taking the cube root to solve for [tex]b[/tex], we find

[tex]\sqrt[3]{a^{3b}}=\sqrt[3]{\dfrac18}\implies a^b=\dfrac12[/tex]

so ultimately

[tex]a^{2b}-\dfrac1{a^b}=-\dfrac7{8\cdot\frac12}=-\dfrac74[/tex]

Answer:

The value of the given expression is    1 - 1 = 0

Step-by-step explanation:

8a^{3b} = 1   can be rewritten as (8a³)^b = 1 = (8a³)^0, which indicates that b = 0.  If b= 0, then 2b = 2(0) = 0.

Then a^(2b) = a^0 = 1, and 1/a^b = 1/1 = 1.

Thus, the value of the given expression is    1 - 1 = 0

2x-10=2. (Answer=6)

2x=12 (you move the -10 to the other side of the equation to make it positive)

Then you divide by 2

2x divided by 2 equals x 12 divided by 2 is 6

So your number is 6. x=6

And you can check this by redoing the equation but putting 6 instead of x

2(6)-10=2

12-10=2

2=2

This equation is true therefore, your unknown number is 6

Final answer:

The problem is solved by setting up an equation where the larger number (2x) is diminished by 10 equals the smaller number (x) plus 2. Solving for x reveals that the smaller number is 12 and the larger number is therefore 24.

Explanation:

Let's denote the smaller number as x and the larger number as 2x since one number is twice another number. The problem states that if the larger number is diminished by 10, the result, which is 2x - 10, is 2 more than the smaller number. Therefore, we can write the equation:

2x - 10 = x + 2.

To solve for x, we first add 10 to both sides of the equation:

2x = x + 12.

Then, we subtract x from both sides:

x = 12.

Now that we know the smaller number is 12, the larger number is twice that, which means the larger number is 24.

In conclusion, the two numbers in question are 12 and 24.

I am pretty sure it is x^2 - 37x

but i am not completely sure

let x=length

let y=width

x/y=5/2

y=2x/5

area=length*width

area=x*y=x(2x/5)=2x^2/5

2x^2/5=360

2x^2=1800

x^2=900

x=30

y=60/5=12

length= 30 inches

width= 12 inches

there you go!

The dimensions of the rectangle are 20 inches in length and 8 inches in width.

The rectangle has an area of 160 square inches, and the length ratio to the width is 5:2. Let's denote the length as 5x and the width as 2x. The equation for the area of a rectangle is width * length, so we set up and solve the following equations:

Then, we multiply 'x' with the respective parts of the ratio (5 and 2) to find the length and width:

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Answer:

Yes, because these widths result in a positive value for area.

Step-by-step explanation:

in imagine math it is c or the bottom left one for me

The question involves using a quadratic function to model the area of a rectangle with a given perimeter. The function is not applicable to a width of 100 feet since it exceeds the logical constraints of the rectangle's perimeter.

The student is asking about determining the dimensions of a rectangular area given a fixed perimeter and using a function to find the area for a given width, w. The function provided, A(w)=24w−w^2, is a quadratic function that models the area of a rectangle with a fixed perimeter of 144 feet. When the width is defined as w=100 feet, we cannot use this particular function to find the area because it would imply an unrealistic negative length for the remaining side, given the fixed perimeter constraint. Therefore, the function can only model the situation over the interval where 0 < w < 24, as the width must be less than half of the perimeter for a rectangle.

Answer:

it is already fikled ok

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The horizontal asymptote is found by considering the ratio of the coefficients of the highest degree terms on the numerator and denominator, that is

coefficient of 6x² on the numerator ⇒ 6

coefficient of 9x³ on the denominator ⇒ 9

The horizontal asymptote is

y = [tex]\frac{6}{9}[/tex] ⇒ y = [tex]\frac{2}{3}[/tex] → D

Answer:

B  1/3

Step-by-step explanation:

3^-3 * 3^8

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

3^6

We know that a^b * a^c = a^(b+c)

3^(-3+8)

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

3^6

3^(5)

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

3^6

We know that a^b divide by a^c = a^(b-c)

3^(5-6)

3^-1

A negative exponent means it goes in the denominator of the fraction

1/3^1

1/3

Answer:

The correct answer is D) f(x) = (x^2 - 2)/3

Step-by-step explanation:

To find an inverse function, swap x and f(x) and then solve for the new f(x). That will be the new inverse function.

f(x) = √3x+2

x = √3f(x)+2

x - 2 = √3f(x)

x^2 - 2 = 3f(x)

(x^2 - 2)/3 = f(x)

Answer:

True

Step-by-step explanation:

The formula for an area of a circle is a = pi times radius squared

Answer:

True.

Step-by-step explanation:

To calculate the area of a circle you have to use the formula Area = PI times radius squared.

yes It has at least one set of parallel lines

[tex] \frac{8}{7} = 114\%[/tex]

A faction who's numerator is larger than it's denominator will always produce an equivalent percentage larger than 100%

Answer:

Step-by-step explanation:

12/24 reduces to 1/2, whereas 3/4 does not reduce.  This pair of ratios does not form a proportion.

If both ratios reduced to the same common value, that would represent a proportion.  

Answer:

Step-by-step explanation:

12/24 reduces to 1/2, whereas 3/4 does not reduce. This pair of ratios does not form a proportion.

If both ratios reduced to the same common value, that would represent a proportion.

Answer:

The mean shall be 10.67 and the standard deviation shall be 6.09

Step-by-step explanation:

There are calculators online that can help u with problems like these :)

Answer:

see explanation

Step-by-step explanation:

given

x + 4 > - 8 ( subtract 4 from both sides )

x > - 12 ← solution

The step to use is subtract 4 from both sides

The value of x is -12

x + 4 > -8

Subtract 4 from both sides

x + 4 -4 > -8 -4

x > -12

The radius of the ring is 1 meter.

Given a ring of fire has a diameter of 2 meters for which a leopard has been trained to jump through.

As we know that in a circle that has a diameter 'd', the radius 'r' is equal to half of the diameter. This means,

[tex]r = \frac{d}{2}[/tex]

Also, the perimeter of this circle is given by

[tex]2\pi r[/tex]

Now,

As given in the question, we have,

The diameter of the ring of fire = 2 meters

So,

The radius of a ring of fire

[tex]= \frac{2}{2}[/tex]

[tex]= 1 meter[/tex]

Hence, the radius of the ring of fire is 1 meter.

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The radius of a circle with a diameter of 2 meters is 1 meter. The radius is found by dividing the diameter by two.

The question pertains to determining the radius of a circle when the diameter is given. The ring through which a leopard jumps in the circus has a diameter of 2 meters.

The formula for the diameter of a circle is d = 2r, where d is the diameter and r is the radius of the circle. To find the radius, we simply divide the diameter by 2.

Therefore, the radius of the ring is 1 meter, as r = d / 2 and thus, r = 2 meters / 2.

Answer:

[tex]\large\boxed{(f+g)(x)=x^2+3x-3}[/tex]

Step-by-step explanation:

[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=3x-5,\ g(x)=x^2+2\\\\\text{Substitute:}\\\\(f+g)(x)=(3x-5)+(x^2+2)=3x-5+x^2+2=x^2+3x+(-5+2)=x^2+3x-3[/tex]

Final answer:

To find (f+g)(x) for the given functions f(x)=3x-5 and g(x)=x²+2, you simply add the two functions to get (f+g)(x) = x²+ 3x - 3.

Explanation:

Adding Functions f(x) and g(x)

To find (f+g)(x), you simply need to add the values of f(x) and g(x) together for any value of x. Given that f(x)=3x-5 and g(x)=x²+2, the sum (f+g)(x) is obtained as follows:

Take the expression for f(x) and g(x):

f(x) = 3x - 5

g(x) = x² + 2

Add the two expressions together:

(f+g)(x) = f(x) + g(x)

(f+g)(x) = (3x - 5) + (x² + 2)

Combine like terms:

(f+g)(x) = x² + 3x - 3

The resulting function (f+g)(x) = x² + 3x - 3 is the sum of the two functions f(x) and g(x).

Answer:

Option B:  g(x) = −5x + 8

Step-by-step explanation:

If we have a function f(x) and wish to make a function g (x) that is equal to the reflection of the function f(x) on the y-axis, then we must make the following transformation to f(x):

[tex]g(x) = f(-x)[/tex]

In this case:

[tex]f(x) = 5x +8[/tex].

So when applying the transformation we obtain:

[tex]g(x) = f(-x) = 5(-x) + 8[/tex]

Finally we have that

[tex]g(x) = -5x +8[/tex]

Answer:

Your answer would be: B

Step-by-step explanation:

Answer:

(1/2, ∞ ).  This corresponds to Answer B

Step-by-step explanation:

Important:  enclose that negative exponent (-2/3) inside parentheses:

1/3e^(x- 2/3) + 1/2

and also that coefficient, 1/3:

(1/3)e^(x- 2/3) + 1/2

The range of the exponential function y = e^x is (0, ∞ ); that is, y is always positive, never zero or negative.  

The function of that "1/2" is to shift the entire graph 1/2 unit up.

Thus, the range   (0, ∞ )  becomes  (1/2, ∞ ).  This corresponds to Answer B.

Answer:

Answer is B for plato or edmentum

Step-by-step explanation:

[tex]b = - 7 \: y = 7[/tex]

[tex]b - 4y[/tex]

[tex]( - 7) - 4(7)[/tex]

[tex] - 7 - 28[/tex]

[tex] = - 35[/tex]

Answer:

-35

Step-by-step explanation:

b-4y

We know b = -7 and y =7

-7 - 4(7)

Multiply

-7 -28

Add

-35

Answer:

A

Step-by-step explanation:

A, because just read the three letters in any order but with the origin in the middle

Answer:

140 pigs and 120 cows

Step-by-step explanation:

20+50=70

70x2=140(number of pigs)

140-20=120(number of cows)

Answer:

12

Step-by-step explanation:

The correct answer is 12

Answer:

B. 990<s<1,850

seal dive, s is greater than 990ft and less than 1850 ft

=》 990<s<1850

she could feed 20 people. To find the answer put 22/8 simplify to get 11/4 then multiply by 5/5

Answer:

22/8 simplify to get 11/4 then multiply by 5/5

Step-by-step explanation:

Answer: 2/5y

Step-by-step explanation:

[tex]\frac{8x^{2}y^{2} }{10x^{2}2y^{3}} = \frac{(2)(2)(2)xxyy}{(5)(2)(2)xxyyy}[/tex]

remove common factors on top and bottom

= 2/5y

Answer:

the printer prints 8.5 pgs per minute

Step-by-step explanation:

34 ÷ 4 = 8.5

There are 3.4 pages does it print per minutes.

The unitary method is a fundamental concept of Mathematics and makes it convenient to solve various sums.

Let, x be the number of prints print per minute.

A printer prints 34 pages in 4 minutes. How many pages does it print per minutes?

The number of pages prints per minute is given by;

[tex]\rm Per \ minute \ print \ Pages=\dfrac{Total \ number \ of \ print \ pages}{Print \ in \ minutes}\\\\ Per \ minute \ print \ Pages=\dfrac{34}{4}\\\\ Per \ minute \ print \ Pages=8.5[/tex]

Hence, there are 3.4 pages does it print per minutes.

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The original area of the garden is 1,000 square feet. When the garden is reduced to 2/5 of its original size, the new area becomes 400 square feet. Therefore, the scale of the new drawing is 2:5.

The original area of the rectangular garden is 100 feet by 10 feet which equals 1,000 square feet. Next season, the garden is decreased to 2/5 of its size. To find the new area of the garden, you multiply the original area by 2/5.

1,000 square feet * 2/5 = 400 square feet.

Therefore, the size of the garden is reduced to 400 square feet which reflects a scale of 2:5 (2 represents the new size, 5 represents the original size) in the new drawing.

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The scale of the new drawing after the garden is decreased to 2/5 of its original size is 2/5.

In this problem, we are given the dimensions of a rectangular garden: 100 feet by 10 feet. We need to find the scale of the new drawing after the garden is decreased to 2/5 of its original size.

To find the scale, we can use the proportionality of the areas to the squares of the distances. The original area of the garden is 100 feet * 10 feet = 1000 square feet.

When the garden is decreased to 2/5 of its original size, the new area becomes 1000 square feet * 2/5 = 400 square feet.

In terms of the scale, the new area is 400 square feet, which is 2/5 of the original area. Therefore, the scale is 2/5.

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Answer:

[tex]y+6=-4(x+2)[/tex]

Step-by-step explanation:

Perpendicular lines are lines which have negative reciprocal slopes. The slope of the equation is 1/4. This means the perpendicular slope is -4. Substitute m = 4 and (-2,-6) into the point slope formula.

[tex]y - y_1 = m(x-x_1)\\y --6=-4(x--2)\\y+6=-4(x+2)[/tex]

Answer:

8

Step-by-step explanation:

2+6+8+12+12 is 40 divide that by 5 and it gives you 8