rearranging familiar formulas the area A of rectangle is 25 in in formula for area is A=lw if the width w is 10 inches what is the lengh l

Answer:

30

Step-by-step explanation:

To find the area of a triangle you need to multiply base times height. Which in this case is 6 times 10 equals 60. Then you just need to simplify it and it equals 30.

Answer:

[tex]4x^2+34x-28=0[/tex]

x = 0.76

Step-by-step explanation:

We can write the area of steel before it is cut as:

Area = [tex](11+2x)*(6+2x)cm^2[/tex]

Expanding it by multiplying the brackets to get:

Area = [tex]4x^2+22x+12x+66[/tex]

Area  area of steel before cutting = [tex]4x^2+34x+66[/tex]

Then we need the area of steel after 11*6 inside dimensions are cut out:

[tex]4x^2+34x+66-(11*6)=4x^2+34x[/tex]

This area should be close to 28 cm[tex]^2[/tex], hence the equation becomes:

[tex]4x^2+34x-28=0[/tex]

Moreover, plotting the graph gives us a value of x = 0.76.

Answer:

Step-by-step explanation:

4x2+34x-28

0.76cm

plato

Answer:

x = -2, y = 0

Step-by-step explanation:

This is a systems of equations. Using substitution, we solve for a single variable, plug it in to solve for the other, and solve that one back in to solve for the original. Let's solve it.

5x + y = -10

Subtract 5x from both sides.

y = -5x - 10

Now that we have y isolated, we can plug it in to the other equation.

4x - 7(-5x-10) = -8

Distribute.

4x + 35x + 70 = -8

Subtract 70 from both sides and simplify.

39x = -78

Divide both sides by 39.

x = -2

Now that we have x as -2, we plug it in to the original.

5(-2) + y = -10

Simplify.

-10 + y = -10

Add 10 to both sides.

y = 0

x = -2, y = 0

[tex]\left\{\begin{array}{ccc}5x+y=-10&|\text{subtract 5x from both sides}\\4x-7y=-8\end{array}\right\\\left\{\begin{array}{ccc}y=-5x-10&|\text{substitute to the second equation}\\4x-7y=-8\end{array}\right\\\\4x-7(-5x-10)=-8\qquad\text{use distributive property}\\\\4x+(-7)(-5x)+(-7)(-10)=-8\\\\4x+35x+70=-8\qquad\text{subtract 70 from both sides}\\\\39x=-78\qquad\text{divide both sides by 39}\\\\\boxed{x=-2}\\\\\text{Put the value of x to the first equation}\\\\y=-5(-2)-10\\\\y=10-10\\\\\boxed{y=0}[/tex]

[tex]Answer:\ \boxed{x=-2\ and\ y=0}[/tex]

Answer:

let x be the Robert piece

y Maria's piece

x+y=10

0,5*x ( half of Robert piece)= 2/3 y( 2 thirds)

2 equations then

x+y= 10 then x= 10-y

0,5x= 0,67 y  then we replace x by 10-y on the second equation and it gives

0,5(10-y)= 5-0,5y=0,67y

5= 1,17 y so y= 4,27    and then x= 10-y= 5,73

the question asks how much Robert wire is longer than Maria's wire

so we get x-y= 1,46

Robert's wire is longer [tex]\frac{4}{3}[/tex] times than Maria's wire and also   it [tex]\frac{10}{7}[/tex] longer than Maria's wire

A wire is a single, usually cylindrical, flexible strand or rod of metal. It are used to bear mechanical loads or electricity and telecommunications signals.  

Half of Robert's wire = 2 thirds of Maria's wire, so

[tex]\frac{1}{2} *[/tex]  Robert's wire = [tex]\frac{2}{3} * Maria's wire[/tex]

The total length of their wires = 10 feet

10 feet =  Robert's wire + Maria's wire

10 feet =  [tex]\frac{4}{3} * Maria's wire[/tex] + Maria's wire

10 feet =  [tex]\frac{7}{3} * Maria's wire[/tex]

Maria's wire =  [tex]\frac{30}{7}[/tex]  feet

 [tex]\frac{1}{2} *[/tex]   Robert's wire = [tex]\frac{2}{3} * Maria's wire[/tex]

Robert's wire = [tex]\frac{4}{3} * \frac{30}{7} [/tex]

Robert's wire =  [tex]\frac{120}{21} feet[/tex]

Robert's wire = [tex] \frac{40}{7} feet[/tex]

If we draw the piece, we get the information that

7 units = 10 feet

1 unit = [tex]\frac{10}{7}[/tex] feet

Hence the  Robert's wire is [tex]\frac{10}{7}[/tex] longer than Maria's wire because

Robert's wire - Maria's wire =   [tex]\frac{40}{7} - \frac{30}{7} feet = \frac{10}{7} feet[/tex]

Grade:  5

Subject:  math

Chapter:  wire

Keywords:  

wire, feet,  piece of wire, piece, wires

The answer is George Washington.

Answer:

The first president was George Washington. Hope this helps you out.

Step-by-step explanation:

Answer:

The difference of given expressions is [tex]\frac{x^2+7x+10}{x^3-9x}[/tex].

Step-by-step explanation:

The given expression is

[tex]\frac{2x+5}{x^2-3x}-\frac{3x+5}{x^3-9x}-\frac{x+1}{x^2-9}[/tex]

Find factors of denominators.

[tex]\frac{2x+5}{x(x-3)}-\frac{3x+5}{x(x^2-9)}-\frac{x+1}{x^2-9}[/tex]

Use [tex]a^2-b^2=(a-b)(a+b)[/tex]

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

Take  [tex]x(x+3)(x-3)[/tex] as LCD.

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

[tex]\frac{(2x^2+5x+6x+15)-3x-5-x^2-x}{x(x^2-3^2)}[/tex]

[tex]\frac{2x^2+5x+6x+15-4x-5-x^2}{x(x^2-9)}[/tex]

[tex]\frac{x^2+7x+10}{x^3-9x}[/tex]

Therefore the difference of given expressions is [tex]\frac{x^2+7x+10}{x^3-9x}[/tex].

Answer:

(x+5)(x+2)/x^3-9x

Step-by-step explanation:

For short if taking on edgen then option A is correct.

Answer: k = -12

The mixed number -1 & 1/3 converts to the improper fraction -4/3

Let r be the common ratio. To go from one term to the next, we multiply by this common ratio. So,

second term = (first term)*(common ratio)

4 = (-4/3)*r

3*4 = 3*(-4/3)*r

12 = -4r

-4r = 12

r = -3

We multiply each term by -3 to get the next term. The third term is therefore,

third term = (second term)*(common ratio)

third term = 4*r

third term = 4*(-3)

third term = -12

and if we keep going...

fourth term = (third term)*(common ratio)

fourth term = -12*(-3)

fourth term = 36

So it matches up

If a, b, c are the geometric sequence, then

[tex]ac=b^2[/tex]

We have a = 4, b = k, c = 36. Substitute:

[tex](4)(36)=k^2\\\\k^2=144\to k=\pm\sqrt{144}\to k=-12\ \vee\ k=12[/tex]

First term is negative, therefore it's the alternating sequence. Therefore your answer is

Slope-intercept form:

y = mx + b   "m" is the slope, "b" is the y-intercept

For lines to be perpendicular, their slopes have to be the opposite/negative reciprocal (flipped sign and number)

For example:

slope is 2

perpendicular line's slope is -1/2

slope is -3/4

perpendicular line's slope is 4/3

#1: The slopes are the same, meaning they are parallel lines

#2: First isolate the "y" in the first equation

-4x + 5y = -5

5y = -5 + 4x

y = -1 + 4/5x   They are not perpendicular because the slopes are 4/5 and -4/5

#3: Isolate "y" in the second equation

8y = 3x - 32

y = 3/8x - 4         They are perpendicular

#4: Isolate "y" is the 1st equation

10y = -9x

y = -9/10x     They are parallel lines

The 3rd choice is your answer

(a) <TOR=pi/3 radians

To determine <TOR we use the fact that in the right-angled triangle ORT we know two sides:

|OT|=radius=8cm and |OR|=radius/2=4cm

and can use the sine:

[tex]\sin \angle OTR=\frac{r/2}{r}=\frac{1}{2}\implies \angle OTR =\frac{\pi}{6}[/tex]

and since <TRO=pi/2, it must be that

[tex]\angle TOR =\pi-\frac{\pi}{2}-\frac{\pi}{6}=\frac{\pi}{3}[/tex]

(b) The arc length is approximately 7.255 cm

In order to calculate the arc length QT, we need to first determine the length |ST| and the angle <OST.

Towards determining angle <OST:

[tex]\angle SOT = \pi - \angle TOR = \pi - \frac{\pi}{3} = \frac{2}{3}\pi[/tex]

Next, draw a line connecting P and T. Realize that triangle PTS is right-angled with <PTS=pi/2. This follows from the Thales theorem. Since R is a midpoint between P and O, it follows that the triangles ORT and PRT are congruent. So the angles <PTR and <OTR are congruent. Knowing <PTS we can  determine angle <OTS:

[tex]\angle OTR \cong \angle PTR=\frac{\pi}{6}\implies\angle OTS=\angle PTS -\angle PTR -\angle OTR\\\angle OTS = \frac{\pi}{2}-\frac{\pi}{6}-\frac{\pi}{6}=\frac{\pi}{6}[/tex]

and so the angle <OST is

[tex]\angle OST = \pi - \angle TOS - \angle OTS = \pi -\frac{2}{3}\pi - \frac{1}{6}\pi=\frac{\pi}{6}[/tex]

Towards determining |TS|:

Use cosine:

[tex]\cos \angle OST =\frac{|RS|}{|ST|}\implies |ST|=\frac{\frac{3}{2}r}{\cos \frac{\pi}{6}}=\frac{12\cdot 2}{\sqrt{3}}=8\sqrt{3}cm[/tex]

Finally, we can determine the arc length QT:

[tex]QT = {\angle OST}\cdot |ST|=\frac{\pi}{6}\cdot 8 \sqrt{3}=\frac{4\pi}{\sqrt{3}}\approx 7.255cm[/tex]

Answer:

EACH TIE COSTS 7.43

Step-by-step explanation:

If 13.35x13=173.55 then that means the ties total is 189.46 now devide that by 22 it equals 13.35

The cost calculation of a tie can be done by subtracting the total cost of the shirts from the total cost. The remainder is then divided by the number of ties bought, resulting in the price of a tie, about $7.43.

To find the cost of a tie, we'll first determine the total cost of the shirts and then subtract this from the total spent. Firstly, we need to calculate the total cost of the shirts by multiplying the cost of one shirt by the number of shirts purchased. That is 13 shirts * $15.35/shirt = $199.55.

Next, we subtract the total cost of the shirts from the total spent to find out how much was spent on ties: $363.01 (total spent) - $199.55 (total spent on shirts) = $163.46 (total spent on ties).

Now, to find the cost of one tie, we divide the total spent on ties by the number of ties purchased. That is: $163.46/22 ties = $7.43/tie. Therefore, each tie costs approximately $7.43.

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Answer:

$0.13 (this is a rounded answer)

Step-by-step explanation:

The unit cost is the cost of a 1 ounce bottle so you would divide the cost by the total number of ounces:

$2.00 divided by 16 is 0.125 but you would round because you need a cost not a decimal.

So your final answer would be $0.13 per ounce.

Answer:

$.13 per fl oz

Step-by-step explanation:

To find the unit cost, we take the cost and divide by the number of units

$2.00/16

$.125 per fl oz

Since this is money we round to the nearest cent.

$.13 per fl oz

Answer:

Correct answer is C.

Step-by-step explanation:

Note that graph in the diagram has period [tex]\pi.[/tex]

Consider the function [tex]y=-2\cos (2(x+\pi ))-1.[/tex]

This function has a period [tex]T=\dfrac{2\pi}{2}=\pi.[/tex] Functions in another options have period that differes from [tex]\pi.[/tex]

The graph of this function passes through the point (0,-3), because

[tex]y(0)=-2\cos (2(0+\pi ))-1=-2\cos 2\pi-1=-2\cdot 1-1=-3.[/tex]

Answer:

[tex]y=-2cos (2(x+\pi ))-1[/tex]

Step-by-step explanation:

We are a given a graph from which we can clearly see that y = -1 when x  = 0.

Next, we will find out which of the options is the equation of the given graph and for that we need to set our calculator to the radian mode and then put the value of x to be 0.

1. y = -2 cos (4(x + pi)) - 1 = -2 cos (4(0 + pi)) - 1  = 3

2. y = 2 cos(x + pi) = 2 cos(0 + pi) = -1

3. y = -2 cos (2(x + pi)) - 1 = -2 cos (2(x + pi)) - 1 = -3

We get y = -1 when x = 0 in equation number 3, y = -2 cos (2(x + pi)) - 1, so that is the equation of the given graph.

Find the volume of the bath tub by multiplying all the dimensions together:

18 inches = 1.5 feet:

5 ft x 3 feet x 1.5 feet = 22.5 cubic feet.

The tub is 3/4 full so multiply the volume by 3/4 to find the amount of water in the tub:

22.5 x 3/4 = 16.875 cubic feet of water.

The tub drains at 1 cubic foot per minute, so it would take about 17 minutes to drain.    (16.875 rounded to the nearest whole minute).

Answer:

A) 2(6x + 13)

Step-by-step explanation:

2(5 + 8 + 6x)

= 2(13 + 6x)

= 2(6x + 13)

Answer:

2(6x + 13)

Step-by-step explanation:

Answer:

-4r

Step-by-step explanation:

r + (-5r)

1r + (-5r)

Factor out an r

r( 1 -5)

One minus 5 is negative 4.   If you have one dollar and you borrow five dollars,  how much did you borrow?  4  but that 4 is borrowed so it is negative

r (-4)

-4r

Question

6v²+ 4v²  please solve this equation

Answer:

Step-by-step explanation:

6v²+ 4v² =

(6 + 4)v² =

10v²

There are a few ways to solve this, the simplest of which is probably factoring. Start by finding factors of C (10) that add up to be B (-2).

fac(10) { -10, 1 ; -5, 2 }

Well, there are no factors of 10 that can add to b - so we will use the quadratic formula.

(-b +- sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -2, c = 10

b^2 - 4ac = (-2)^2 - 4(1)(10) = 4 - 40 = -36

-b +- sqrt(-36) / 2a

(2 +- sqrt(-36)) / 2

sqrt(-36)

sqrt(-1 * 36)

sqrt(-1) * sqrt(36)

i * 6

6i

2 + 6i / 2 ; 1 + 3i

2 - 6i / 2 ; 1 - 3i

Solutions: 1 + 3i, 1 - 3i

Answer:

x = 1± 3i

Step-by-step explanation:

x^2-2x+10=0

We can complete the square to solve by subtracting 10 from each side

x^2-2x+10-10=-10

x^2 -2x = -10

We need to add (2/2) ^2  to each side or 1

x^2 -2x+1 = -10 +1

x^2 -2x+1 = -9

The left side factors into (x- (2/2) ) ^2

(x-1) ^2 = -9

Take the square root of each side

sqrt((x-1) ^2 =± sqrt(-9)

x-1 = ±sqrt(-1) sqrt(3)

Remember the sqrt(-1) = i

x-1 = ± 3i

Add 1 to each side

x-1+1 = 1± 3i

x = 1± 3i

ANSWER: The length of the entire dash is 700 meters.

EXPLANATION:

Because 20% of the dash equals 140 meters, we can use a variable to figure out the length of the entire dash.

Let x be the length of the entire dash.

[tex].2x = 140\\\\x = 700[/tex]

The length of the entire dash is 700 meters.

Answer:

15/216 (6.944%)

Tienes suerte, me tomé 5 años de español! Hoep me ayudó!

Answer:

Suceso A= (6;4) (5;5) (4;6)

n(A)= 3

Suceso B= (5;5)

n(B)= 1

P(AnB)= (5;5)= 1

Espacio muestral= 36

P(B/A)= 1/36 / 3/36= 0.33= 33%

Suceso C= (4;6) (6;4)  

n(C)= 2

P(AnC)= (4;6) (6;4)

P(AnC)= 2

P(C/A)=2/36 / 3/36= 2/3= 0.66= 66%

x = number of hours after 9 am (eg: x = 1 means 1 hr after 9 am, so 10 am)

f(x) = population count x hours after 9 am

f(1) = population count at 10 am (1 hour later)

f(2) = population count at 11 am (2 hrs after 9 am)

f(2) - f(1) represents the difference in population counts from 10 am to 11 am, or put another way, how much the population increased during that time interval.

f(2)-f(1) represents the change in the population of bacteria from the first to the second hour after 9 a.m., giving us the rate of population growth over that one-hour period.

The expression f(2)-f(1) in the function f(x), where x represents the hours after 9 a.m., illustrates the change in the population of the bacteria between the first and second hour after 9 a.m. Population growth in bacteria usually follows a logarithmic scale where it doubles every given time period, typically every hour. Thus, by calculating the difference between the population at the second hour (f(2)) and the first hour (f(1)), we can get the increase in the population of bacteria over that one-hour period.

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Answer:

$2

Step-by-step explanation:

$40 * 0.02 = 5

Answer: 9 gallons

Step-by-step explanation:

Set up the proportion, then multiply to solve for the variable.

[tex]\dfrac{\frac{1}{2}\ \text{gallon}}{4\ \text{pints}}=\dfrac{x}{72\ \text{pints}}[/tex]

[tex](72\ \text{pints})\dfrac{\frac{1}{2}\ \text{gallon}}{4\ \text{pints}}=(72\ \text{pints)}\dfrac{x}{72\ \text{pints}}[/tex]

[tex]\dfrac{36\ \text{gallons}}{4}=x}[/tex]

9 gallons = x

To convert pints to gallons, divide the number of pints (72) by the number of pints in a gallon (8), resulting in 9 gallons.

To determine how many gallons are the equivalent of 72 pints, we use the conversion factor that 1 gallon is equivalent to 8 pints.

First, we divide the given number of pints by the number of pints in a gallon:

Therefore, 72 pints is equivalent to 9 gallons.

Answer:

speed = 67/6 miles per hour

Step-by-step explanation:

To find the average speed, we divide the distance by the time

d/t = 134 miles/ 12 hours

speed = 134/12 miles per hour

We can simplify this fraction  by dividing the top and bottom by 2

speed = 67/6 miles per hour

Answer:

11.16 mph

Step-by-step explanation:

You divide Distance by Time to get the speed.

134/12= 11.1667

3=x/100*12

x/25*3=3

x=3:3/25

x=25

The answer is 25%. Hope this helps! <3

Answer:

3 is 25% of 12

Step-by-step explanation:

Answer:

10 is 5,650

9 is 18.5

11 is 71.24

Step-by-step explanation:

11 .2.74  x25

Answer:

295.16 feet

Step-by-step explanation:

We need to find the length of the diagonal of a right angled triangle with equal length legs.

Length of each leg = √(43560)

Using the Pythagoras theorem:-

x^2 = (√(43560))^2 + (√(43560))^2    (where x = length of the diagonal)

x^2 = 43560 + 43560

x = √(87120) = 295.16 feet

Answer:

distance from corner to corner = 295.16 ft

Step-by-step explanation:

Given the land is square, then its area is computed as:

Area = (length of a side)^2

Replacing with area = 1 acre =  43560 sq. ft.

43560 = (length of a side)^2

length of a side = √43560

length of a side = 208.71 ft

The distance from corner to corner and two sides of the square form a right triangle, where the distance from corner to corner is the hypotenuse and the square sides are the legs. From Pythagorean theorem:

(distance from corner to corner)^2 = 208.71^2 + 208.71^2

distance from corner to corner = √(208.71^2 + 208.71^2)

distance from corner to corner = 295.16 ft

Answer:

Step-by-step explanation:

Factor out 6

I assume you mean 6x^2+30x+36, because that makes far more sense

6(x^2+5x+6) = 6(x^2 + 2x +3x +6)

(To find that it is 2x and 3x: 2 +3 = 5, 2 * 3 = 6)

Factor by grouping:

6* x(x+2) +3(x+2) = 6(x+3)(x+2)

For binomials, it could be either (6x+18) (x+2) or (x+3) (6x+12), depending on where you multiply the 6.

Answer:x+2

Step-by-step explanation:

Answer:

y^2 +8y + 16

Step-by-step explanation:

 6y^2 +2y +5  - (5y^2 -6y -11)

I distribute the minus sign

6y^2 +2y +5  - 5y^2 +6y +11

Then I put them vertical.

6y^2 +2y +5  

-5y^2 +6y +11

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

y^2 +8y + 16

This is in standard from since the exponential decreases.