Write into an algebraic expression. Double the sum of 2 and x increased by one-half x squared.

We know that the perimeter is 72 meters, so we have

[tex] y+2x+(2x+6)=72 \iff y+4x+6=72 \iff y=-4x+66 [/tex]

Now we can use the pythagorean theorem: the sum of the squares of the legs is the square of the hypotenuse:

[tex] (2x)^2+(2x+6)^2 = y^2 \iff (2x)^2+(2x+6)^2 = (-4x+66)^2 [/tex]

Expand the squares to get

[tex] 8 x^2 + 24 x + 36 = 16 x^2 - 528 x + 4356 [/tex]

Bring everything to the right hand side to get

[tex] 8 x^2 - 552 x + 4320 = 0 [/tex]

Divide both sides by 8:

[tex] x^2 - 69x + 540 = 0 [/tex]

This equation has solutions [tex] x=9,\ x=60 [/tex]

This solutions would yield the following side lengths:

[tex] x=9\implies\begin{cases} 2x = 18\\2x+6=24\\-4x+66=30\end{cases}[/tex]

[tex] x=60\implies\begin{cases} 2x = 120\\2x+6=126\\-4x+66=-174\end{cases}[/tex]

Since we can't have negative side lengths, we can only accept the solution x=9.

In fact, you can check that 18,24,30 is a pythagorean triplet, i.e.

[tex] 18^2+24^2=30^2 [/tex]

Area of the horizontal rectangle.

A = L *W

L = 8cm

W = 3 cm

Area = 8 * 3 = 24 cm^2

Area of the Vertical Rectangle

The vertical rectangle has the same dimensions

L = 8 cm

W = 3 cm

Area = L * W

Area = 8 * 3

Area = 24 cm^2

Combined Area

Area = 24 + 24

Area = 48 cm^2  <<< Answer

Hey there!!

In order to solve for the area, let's divide this figure into two rectangles.

Area of a rectangle = Length × Breadth

First rectangle at the top - Length = 8 and width = 3

Hence, the area would be = 24cm²

The second triangle measures : Length = 3 and the width = 5

Area = 3 × 5

... 15cm²

Total area = 24cm² + 15cm²

... 24 + 15 cm²

... 39cm²

Hope my answer helps!!

The different forms you can convert 6 2/3 to would be 20/3 and 6.6 but I'd have to say 20/3 would be the simplest form to convert it to. Hope this helps <3

20/3 thats the exact form

Answer:

D.)  (12 + 11 + 20) ÷ 3

Step-by-step explanation:

SOLUTION: The measure of angle 1 is five less than four times the measure of angle 2. If angle 1 are two form a linear pair, what are their measures. Question 345899: The measure of angle 1 is five less than four times the measure of angle 2. If angle 1 are two form a linear pair, what are their measures.

38a) $10.50 To get this answer, you need to multiply $1.50 by 7

38b) $25.50 To get this answer, you need to subtract $10.50 from $36

40) The answer would be $13.7694 and it could be rounded to $13.77. To get this answer .you need to multiply $12.99 by 1.06 since it has a 6% sales tax.

Answer:

x=-39

Step-by-step explanation:

subtract 23 from both sides

-16 - 23= -39

therefore x=-39

Thus, the proportion of female wolves that do not hunt in medium sized packs is 4/10 or 0.4. When expressed as percent, this is 40%.

Let x and y be the two numbers.  

x = y - 4  

2y = 5x - 10  

solve the system of equations:  

2y = 5(y - 4) - 10  

2y = 5y - 20 - 10  

-3y = -30  

y = 10  

x = 10 - 4 = 6

I will try my best...

Let x and y be the two numbers.  

x = y - 4  

2y = 5x - 10  

Now, we solve the system of equations:  

2y = 5(y - 4) - 10  

2y = 5y - 20 - 10  

-3y = -30  

So...

y = 10  

x = 10 - 4 = 6

GCF of 45 and 70 is 5

The answer is about 4 times as many people live in China then in the United States

There are 4.4 times more people living in china than united states as the definition of ratio says "the quantitative relation between two amounts showing the number of times one value contains or is contained within the other".

The indicated quotient of two mathematical expressions is referred to as a ratio. A/B stands for an ordered pair of numbers where B does not equal 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

Here,

To find that how many times as many people live in China then in the United States, we need to divide the population of china by the population of united states.

let x be the value of how many times as many people live in China then in the United States,

so, the population of china=1.325 billions

the population of united states=0.304 billions

x=1.325/0.304

x=4.356

x≈4.4 times

As stated in the definition of ratio, "the quantitative relation between two amounts showing the number of times one value contains or is contained within the other," there are 4.4 times as many people living in China as there are in the United States.

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If we draw the diagonals of the octagonal gazebo, the 4 diagonals divide the octagon into 8 triangles.

Note that each triangle is an isosceles triangle whose equal sides are x, the radius of the circle.

The top angle of each triangle is obtained by dividing the full angle by 8.

So, each top angle = [tex]\frac{360}{8}[/tex]

= 45°

Now, in fig., consider one of the triangles Δ OAB. Draw an altitude OC from O to the opposite side AB.

This altitude OC bisects the top angle 45°.

Therefore, ∠ AOC = 22.5°.

Now, in Δ AOC,

[tex]sin 22.5=\frac{AC}{OA}[/tex]

[tex]=\frac{AC}{x}[/tex]

So, AC = x sin 22.5°

Note that, AB = 2 AC.

Therefore, AB = 2x sin 22.5°.

Also, [tex]cos 22.5=\frac{OC}{OA}[/tex]

[tex]=\frac{OC}{x}[/tex]

So, OC = x cos 22.5°.

Area of Δ AOB = [tex]\frac{1}{2}(AB)(OC)[/tex]

= [tex]\frac{1}{2}[/tex] × (2x sin 22.5°) × (x cos 22.5°)

= [tex]\frac{1}{2} x^{2}[/tex] (2 sin 22.5° cos 22.5°)

= [tex]\frac{1}{2} x^{2}[/tex] sin 45°

= [tex]x^{2}[/tex] / [tex]2\sqrt{2}[/tex]

Area of the octagonal gazebo = 8 × one triangular area

= 8 × ([tex]x^{2}[/tex] / [tex]2\sqrt{2}[/tex])

[tex]=2\sqrt{2} x^{2}[/tex]

[tex]=2.828x^{2}[/tex]

Area required for mulch = circular area - area of the gazebo

[tex]=3.14x^{2} -2.828x^{2}[/tex]

[tex]=0.312x^{2}[/tex]

Now, cost per unit area = $1.50.

Hence, total cost g(m) = area × cost per unit area

Total cost g(m) = [tex]0.312x^{2}[/tex] × 1.5

[tex]=0.468x^{2}[/tex]

Hence, total cost g(m) = [tex]0.468x^{2}[/tex].

Answer:

1.50(piexsqared-2root2xsqared) or on edge A

Step-by-step explanation:

i just did it

First of all remeber that "a number" means we don't know the number or it could be many but not all numbers, so it is represented by x.

5. 1/2x + 6 > 20

6. 12 + 3x < -11  (They asked for the opposite of 11, the opposite of a positive number is always the negative of that number, and the opposite of a negative number is the positive of that number).

7. 2x - 8 < 5

Answers:

5) 1/2n + 6 > 20

6) 12 + 3n < -11

7) 2x - 8 < 5

Hope this helps :-)

we have

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

Combine like terms in both sides

[tex](\frac{3}{5}x+ x)+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x[/tex]

we know that

[tex](\frac{3}{5}x+ x)=(\frac{3}{5}x+ \frac{5}{5}x)=\frac{8}{5}x[/tex]

substitute in the expression above

[tex]\frac{8}{5}x+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x[/tex]-----> equation A        

Multiply equation A by [tex]5*3*2=30[/tex] both sides

[tex]30*(\frac{8}{5}x+\frac{2}{3})=30*(\frac{1}{2}-\frac{1}{5}x)[/tex]

[tex]48x+20=15-6x[/tex] ---------> equation B

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]48x+6x=15-20[/tex]

[tex]54x=-5[/tex] ---------> equation C

Solve for x

[tex]x=-\frac{5}{54} =-0.09[/tex]

We are going to proceed to verify each case to determine the solution.

Case a) [tex]\frac{8}{5}x+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x[/tex]

the case a) is equal to the equation A

so

the case a) have the same solution that the given equation

Case b) [tex]18x+20+30x=15-6x[/tex]

Combine like terms in left side

[tex](18x+30x)+20=15-6x[/tex]

[tex](48x)+20=15-6x[/tex]

the case b) is equal to the equation B

so

the case b) have the same solution that the given equation

Case c) [tex]18x+20+x=15-6x[/tex]

Combine like terms in left side

[tex](18x+x)+20=15-6x[/tex]

[tex](19x)+20=15-6x[/tex]

[tex]19x+6x=15-20\\25x=-5\\x=-0.20[/tex]

[tex]-0.20\neq -0.09[/tex]

therefore

the case c) not have the same solution that the given equation

Case d) [tex]24x+30x=-5[/tex]

Combine like terms in left side

[tex]54x=-5[/tex]

the case d) is equal to the equation C

so

the case d) have the same solution that the given equation

Case e) [tex]12x+30x=-5[/tex]

Combine like terms in left side

[tex]42x=-5[/tex]

[tex]x=-5/42=-0.12[/tex]

[tex]-0.12\neq -0.09[/tex]

therefore

the case e) not have the same solution that the given equation

therefore

the answer is

case a) [tex]\frac{8}{5}x+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x[/tex]

case b) [tex]18x+20+30x=15-6x[/tex]

case d) [tex]24x+30x=-5[/tex]

Answer:

Option (a) , (b) and ( d) are equivalent to given expression [tex]\frac{3}{5}x+\frac{2}{3}+x= \frac{1}{2}- \frac{1}{5}x[/tex]

Step-by-step explanation:

 Given equation :  [tex]\frac{3}{5}x+\frac{2}{3}+x= \frac{1}{2}- \frac{1}{5}x[/tex]

We have to use  properties to rewrite the given equation and check which are correct from thee given options,

Consider the given equation,

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

Applying commutative property of addition , [tex]a+b=b+ a[/tex]

Equation becomes,

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

Now adding x terms on right side , we get,

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

[tex]\Rightarrow \frac{8}{5}x+\frac{2}{3}= \frac{1}{2}- \frac{1}{5}x[/tex]

Thus, obtained option (a).

Again consider given equation ,

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

Taking LCM both sides, we get,

[tex]\frac{9x+10+15x}{15}= \frac{5-2x}{10}[/tex]

Solving , we get,

[tex]\frac{9x+10+15x}{3}= \frac{5-2x}{2}[/tex]

Cross multiply, we get,

[tex]2\times (9x+10+15x)=3\times(5-2x)[/tex]

[tex]18x+20+30x=15-6x[/tex]

Thus, obtained option (b).

Taking like terms together,

[tex]18x+6x+30x=15-20[/tex]

[tex]\Rightarrow 24x+30x=-5[/tex]

Thus, obtained option (d).

Thus, Option (a) , (b) and ( d) are equivalent to given expression [tex]\frac{3}{5}x+\frac{2}{3}+x= \frac{1}{2}- \frac{1}{5}x[/tex]

Answer:

C) x also increases 5 times its original value

35/5=7

70/10=7

Step-by-step explanation:

Answer:

2

Step-by-step explanation:2+2

The side lengths of a square in which the perimeter of a square is greater than its area is 1 unit, 2 units, and 3 units.

A square is a 2D figure of which all sides are equal.

We know that the perimeter of a square is the sum of the lengths of all the sides and the area of a square is (side)².

Assuming a square has a side length of 4 units.

Therefore the perimeter of the square is 4×side = 4×4 = 16 units.

Now the area of the square will be (4)² = 16 sq units.

Now assuming the side length of the square is 2 units.

The area of the square is (2)² = 4 units and the perimeter is (2×4) = 8 units.

∴ The side length which provides a counter-example is 2 units.

Basically, we have to determine the numbers that when multiplied by 4 are greater than it's square such numbers are 1, 2, 3.

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Answer:

A. consume food

Step-by-step explanation:

The food they eat has energy. One eaten the energy the food had is passed along to the animal.

There are no graphs shown, but the vertical line test is something you can use to find out if a function works. If you make a vertical line anywhere on one of the graphs, it should only pass through one point. For example, a regular straight line almost always passes the vertical line test. If it's a sideways parabola, it will not.

Answer:

She did not get the correct answer because she did not put the decimal in the correct spot. The correct answer should be 428.206.

Step-by-step explanation:

17.06×25.1=428.206

ANSWER

ANSWER TO QUESTION 1.

If you give [tex]x[/tex] surfing lessons, then you will earn $ [tex]25x[/tex]

If you are charged $200 for using the place, then your profit will reduce by $200.

The profit function is given by

[tex]P(x)=25x-200[/tex] dollars.

The y-intercept is  [tex]-200[/tex]. It is negative because it is a cost which is a liability. So it does not add to your profit.

ANSWER TO QUESTION 2.

The slope is [tex]25[/tex]. It is positive because as the number of hours increases, the profit earned also increases. In other words there is a direct relation between the number of hours worked and the profit earned.

ANSWER TO QUESTION 3.

The slope intercept form is when an equation is written in the form;

[tex]y=mx+c[/tex],

where [tex]m[/tex] is the slope and [tex]c[/tex] is the y-intercept. The profit function in slope intercept form is

[tex]P(x)=25x-200[/tex]

ANSWER TO QUESTION 4.

If you break even, then the difference between the revenue and cost is zero. So we equate the profit function to zero.

[tex]25x-200=0[/tex]

[tex]25x=200[/tex]

[tex]x=8[/tex]

Therefore you need to give 8 different lessons to break even.

ANSWER TO QUESTION 5.

If you give 20 lessons, the [tex]x=20[/tex]. We need to substitute

[tex]x=20[/tex] in to the profit function to calculate the profit made after 20 lessons.

[tex]P(20)=25(20)-200[/tex]

[tex]P(20)=500-200[/tex]

[tex]P(20)=300[/tex].

ANSWER TO QUESTION 6.

If the new price is $75, then the new profit function becomes

[tex]P(x)=75x-200[/tex]

ANSWER TO QUESTION 7.

To find the number of lessons that lets you break even, we equate the new profit function to zero.

[tex]75x-200=0[/tex]

We solve for x by adding 200 to both sides of the equation.

[tex]\Rightarrow 75x=200[/tex]

We now divide through by 75

[tex]\Rightarrow x=\frac{200}{75}[/tex]

[tex]\Rightarrow x=2\frac{2}{3}[/tex]

Therefore you would have to 2\frac{2}{3} lessons to break even. That is approximately 3 lessons.

ANSWER TO QUESTION 8.

If you give 20 lessons and we want to find the profit you made with this new profit function, then we have to plug in [tex]x=20[/tex] in to [tex]P(x)=75x-200[/tex].

That is,

[tex]P(20)=75(20)-200[/tex]

[tex]P(20)=1500-200[/tex]

[tex]P(20)=1300[/tex] dollars

The perimeter is adding all the outside edges together:

4 + 1 +4 +1 + 3 + 1 = 14 cm.

4/10 Probability

-Hiadamcom

Answer:

2/5

Step-by-step explanation:

4 ÷ 10= 2/5

(4 ÷10 is for 4/10 which is red marbles to the total marbles)

The probability of the compliment is 3/5(for edge students)

If you plug in h, the answer would be 13-9 which is 4.

h(13)=13-9=4,inlocuiesti x cu 13 si calculezi.

3.- 5x-6=y

First you leave the variable alone along with 5 and you pass to the other side number 6 with the opposite sign

5x=y+6

then as 5 is multiplying you pass it dividing

         y+6                                                                                                                                                                    x=        5

4.-2x-3y=8

First you leave the variable with 3 alone and you pass the 2x to the other side subtracting

-3y=8-2x

Then as -3 is multiplying you pass it dividing

y= 8-2x/-3

12.-7x-y=14

First you leave the variable with the 7 alone and you pass the -y to the other side adding

7x=14+y

then as 7 is multiplying you pass it dividing

x=14+y/7

18.-12x-4y=20

First you leave the variable y with the -4 alone and you pass the 12x to the other side subtracting

-4y=20-12x

Then as -4 is multiplying you pass it dividing

y= 20-12x/-4

20.- R-C/N=P

First you leave the R and the C alone and as N is dividing you pass it multiplying

R-C=PxN

Then as C is subtracting you pass it adding

R= (PxN)+C

I haven't done these types of problems in forever, so I did a few of the easier ones before I went onto a few of the harder ones. Sorry if 20 is incorrect, I wasn't too sure.

the answer is B. hope i helped!

x² + 3x + 2 = (x + 2)(x + 1)

consider the factors of the constant term ( + 2 ) which sum to give the coefficient of the x- term ( + 3)

These are + 2 and + 1

x² + 3x + 2 = (x + 2 )(x + 1)

Jasmine is 23 years old. Three years less, 20, half is 10. If I am correct, George is 10.

Answer:

a=43

Step-by-step explanation:

90+47=137    180-137=43

Answer:

Step-by-step explanation:

The lines can be related in following three ways

Now three real life examples of above three scenarios are described below:

Answer:

1. KI

2. HI and DF

3. 8

4. 4 and 7

Step-by-step explanation: