The area of a rectangle is 42 ft squared, and the length of the rectangle is 5 ft more than twice the width. Find the dimensions of the rectangle. length and width.​

Answer:

301.59

Step-by-step explanation:

your answer was almost right you just forgot to multiply by 9

Answer:

Transformed   [tex]\,\,f(x)= -3\,(x-1)^2[/tex]

Step-by-step explanation:

The process of shifting the graph of the function 1 unite to the right can be obtained by subtracting 1 to the x-coordinate in the expression of the function:

[tex]f(x)=x^2\\new\,f(x) =(x-1)^2[/tex]

The process of stretching vertically the function, would be accomplished by multiplying now the full function by "3":

[tex]new \,\,f(x)= 3\,(x-1)^2[/tex]

the reflection over the x-axis is obtained by multiplying the full function by the constant "-1":

[tex]new \,\,f(x)= -3\,(x-1)^2[/tex]

Answer:

  B(-6, 0)

Step-by-step explanation:

You want to find B such that ...

  (B -A) = (3/4)(C -A) . . . . the required distance relation

  4(B -A) = 3(C -A) . . . . . . multiply by 4

  4B = 3C +A . . . . . . . . . . add 4A, simplify

Now, we can solve for B and substitute the given coordinates:

  B = (3C +A)/4 = (3(-6, -2) +(-6, 6))/4 = (-24, 0)/4 = (-6, 0)

The coordinates of point B are (-6, 0).

Answer:

the answer your looking for is (-3,-3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]100x^2-20x+1=0\\\\(10x)^2-2\cdot10x\cdot1+1^2=0\\\\(10x-1)^2=0\\\\10x-1=0\\\\10x=1\\\\x=0.1[/tex]

Answer:

The original width was 94.71 cm

Step-by-step explanation:

Given:

new smaller area = 1.2m^2

Decrease in length of the rectangular sheet = 34.5cm

Therefore:

1. the final width of the sheet is given as

2X^2 = 1.2 m^2

X^2 - 0.6 m^2

X^2 = 10000 * 0.6 cm

X = 77.46 cm (this is the width)

2. The length of the sheet

= 2 * 77.46

= 154.92 cm.

3. Initial length of the sheet

= 154.92 + 34.5

= 189.42 cm.

4. Initial width of the sheet ( original ).

= 189.42 / 2

= 94.71 cm.

5. Initial area of the sheet

= 94.71 * 189.92

= 17939.9 cm^2

New area of the sheet

= 79.46 * 154.92

= 12000.1 cm^2

Difference between the initial and new area

= 17939.9 - 12000.1

= 5939.86 cm^2

Percentage of area decrease

= 5939.86 ' 17939.9

= 33.1%

Answer: 120

Step-by-step explanation:

Given: A bag contains two red marbles, two green ones, one lavender one, five yellows, and six orange marbles.

The total number of marbles in the bag : 2+2+1+5+6=16

Now, the number of ways of selecting sets of four marbles include one of each color other than lavender is

[tex]\( C(2,1) \times C(2,1) \times C(5,1) \times C(6,1)=2 \times 2 \times 5 \times 6\)=120[/tex]  [[tex]\because\ C(n,1)=n[/tex]]

Hence, the number of sets of four marbles include one of each color other than lavender = 120

Answer:

Step-by-step explanation:

[tex]21\: square\:meters = 6 \:wizard \:cloak\\x\:square\:meters\:\:=4 \:wizard\:cloaks\\\\Cross\:Multiply\\6x = 84\\\frac{6x}{6} =\frac{84}{6} \\\\x = 14 \:square\:meters[/tex]

Answer:

14.0 square meters

Step-by-step explanation:

Answer:

125 degrees

Step-by-step explanation:

Using a theorem, you know that angle a is half of 110. Also, in all quadrilaterals   inscribed in a circle, the opposite angles are supplimentary. So then, knowing that angle a is 55 degrees, you can come to the conclusion that b is 125 degrees.

Hope this is helpful! :)

Answer:

[tex]\boxed{D = 15/8}[/tex]

Step-by-step explanation:

=> [tex]x^2-\frac{1}{2} x +\frac{1}{2} = 0[/tex]

Comparing it with the standard form of quadratic equation [tex]ax^2+bx+c = 0,[/tex] we get

a = 1, b = -1/2 and c = 1/2

Discriminant = [tex]b^2-4ac[/tex]

[tex]D = (-1/2)^3+4(1)(1/2)\\D = -1/8 + 2\\D = \frac{-1+16}{8} \\D = \frac{15}{8}[/tex]

Answer:

D. 4√2

Step-by-step explanation:

A triangle with 45°, 45°, and 90° is a special right triangle.

hypotenuse = √2 · leg

1. Set up the equation

8 = √2 · x

2. Divide by √2 and solve

x = [tex]\frac{8}{\sqrt{2} }[/tex] · [tex]\frac{\sqrt{2} }{\sqrt{2}}[/tex] = [tex]\frac{8\sqrt{2} }{2}[/tex] = 4√2

Answer:

Option (A)

Step-by-step explanation:

Every cube has 8 vertices and 6 faces.

Cube shown in the picture attached,

Diagonal through interior of the given cube will be the segments joining the vertices A-H, G-B, C-F and D-E.

Therefore, from the given options diagonal of the interior of the cube will be Side AH.

Option A will be the answer.

Answer:

the awnser is A

Step-by-step explanation:

i took a quiz

(i) Note that it is given to you that 3a + 2b = 9

You are trying to find the value of 9a + 6b. Find what is multiplied to both the variable a & b. Divide:

(9a + 6b)/(3a + 2b) = 3

Next, multiply 3 to the 9 on the other side of the equation:

3 x 9 = 27

27 is the value of 9a + 6b.

(ii) Note that it is given to you that 8x + 6y = 60

You are trying to find the value of 4x + 3y. Find what is multiplied to both the variable x & y. Divide:

(8x + 6y)/(4x + 3y) = 2

Next, divide 2 from the 60 on the other side of the equation:

60/2 = 30

30 is the value of 4x + 3y.

~

Answer:

(i) 27, (ii) 30

Step-by-step explanation:

i. since 9a + 6b is 3 times 3a + 2b then the and is 3 times 9 = 27

ii. since 4x + 3y is half of 8x + 6y then 60 /2 = 30

Answer: x=-10

Step-by-step explanation:

5*(12+x)=10

Distribute

60+5x=10

Subtract(60)

5x=-50

x=-10

Hope it helps <3

Answer:

Heeyyy hope it helps

Step-by-step explanation:

Ok, so the product is the answer to a multiplication problem.

The product of 5 and the sum of a number(X) and 3 is

5(X + 3) = 12

5X + 15 = 12

5X = 12 - 15

5X = -3

X = -3/5

Answer:

The equation, when graphed together with the line y=-3x +6, which will form a system of equations with no solution is y=-3(x +6), meaning the second option on the picture.

Step-by-step explanation:

hope this helps!

Answer: 2 or B

Step-by-step explanation:

Answer:

A. Undefined slope (no slope)

B. [tex]\frac{5}{4}[/tex]

Step-by-step explanation:

A slope is rise over run.

The points (6, 2) and (6, -3) are located on the same x coordinate, therefore they have an undefined slope.

However, the points (-4, -7) and (4, 3) do have a slope. The rise is 10 ( | -7+ 3 | ) and the run is 8 ( | -4 + 4 | ). 10/8 is equivalent to 5/4.

Hope this helped!

Answer:

[tex]\boxed{\sf 30 \ bean \ cans}[/tex]

Step-by-step explanation:

The ratio of bean cans to corn cans is 6 : 7

Given that Corn cans = 35

Let the bean can be x

So,

The proportion for it will be:

6 : 7 = x : 35

Product of Means = Product of Extremes

7 * x = 6 * 35

7x = 210

Dividing both sides by 7

x = 30

So, 30 bean cans have to be put on the table to hold the needed ratio

Answer:

Hey there!

We have the angle is equal to half the measure of the arc of 120 degrees. (Just another rule for circles)

7x-10=0.5(120)

7x-10=60

7x=70

x=10

Hope this helps :)

Answer:

x = 10

Step-by-step explanation:

Tangent Chord Angle = 1/2 Intercepted Arc

7x-10 = 1/2 ( 120)

7x -10 = 60

Add 10 to each side

7x -10+10 = 60+10

7x = 70

Divide by 7

7x/7 = 70/7

x = 10

Answer:

x = 2

Step-by-step explanation:

Add 5 to both sides to get the 5 to the right side since we are trying to isolate the variable x:

3x – 5 + 5 = 1 + 5

Simplify: 3x=6

Divide each side by 3 to isolate and solve for x:

3x/3=6/3

Simplify: x=2

Answer:

20

Step-by-step explanation:

use the cos or sin function to solve

Step-by-step explanation:

using 30°

we use cos

using 60

we use Sin

Answer:

to be honest I'm not sure how to do

it is transformed [tex]|x|[/tex] function. moved down by and right by 1 unit,

so $y=|x-1|-1$

Answer:

5.76

Step-by-step explanation:

Answer:

$105

Step-by-step explanation:

Each student buys one package of seeds and one container

s = Amount of students; p = price of seed package; c = price of container

s*(p+c)=30(1.00+2.50)=30(3.5)$105.

Hope This Helps!

Answer:

77

Step-by-step explanation:

slope equation

Answer:

The ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.

Step-by-step explanation:

The question is:

A company knows that if it produces "x" monthly units its utility "u" could be calculated with the expression: u (x) = - 0.04x ^ 2 + 44x-4000 where "u" is expressed in dollars. Determine the ratio of the average change in profit when the level of production changes from 600 to 620 units per month. Remember that the slope of the secant line to the graph of the function represents the average rate of change.

Solution:

The expression for the utility is:

[tex]u (x) = - 0.04x ^ {2} + 44x-4000[/tex]

It is provided that the slope of the secant line to the graph of the function represents the average rate of change.

Then the ratio of the average change in profit when the level of production changes is:

[tex]\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}[/tex]

Compute the values of u (x₁) and u (x₂) as follows:

x₁ = 600

[tex]u (x_{1}) = - 0.04x_{1} ^ {2} + 44x_{1}-4000[/tex]

         [tex]= - 0.04(600) ^ {2} + 44(600)-4000\\=-14400+26400-4000\\=8000[/tex]

x₂ = 620

[tex]u (x_{2}) = - 0.04x_{2} ^ {2} + 44x_{2}-4000[/tex]

         [tex]= - 0.04(620) ^ {2} + 44(620)-4000\\=-15376+27280-4000\\=7904[/tex]

Compute the average rate of change as follows:

[tex]\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}[/tex]

                                      [tex]=\frac{7904-800}{620-600}\\\\=\frac{-96}{20}\\\\=-\frac{24}{5}\\\\=-24:5[/tex]

Thus, the ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.

Answer:

[tex]\large \boxed{\sf \ \ 70\% \ \ }[/tex]

Step-by-step explanation:

Hello,

We assume that the year is 52 weeks, and we note r the interest rate we are looking for. The rate is expressed in percent and is annually, meaning that the investment is, after the first week :

   [tex]1000\cdot (1+\dfrac{r\%}{52})=1000\cdot (1+\dfrac{r}{5200})[/tex]

For the second week

   [tex]1000\cdot (1+\dfrac{r}{5200})^2[/tex]

After 52 weeks

   [tex]1000\cdot (1+\dfrac{r}{5200})^{52}[/tex]

and we want to be equal to 2000 so we need to solve:

[tex]1000\cdot (1+\dfrac{r}{5200})^{52}=2000\\\\\text{*** divide by 1000 both sides ***}\\\\(1+\dfrac{r}{5200})^{52}=\dfrac{2000}{1000}=2\\\\\text{*** take the ln **}\\\\52\cdot ln(1+\dfrac{r}{5200})=ln(2)\\\\\text{*** divide by 52 ***}\\\\ln(1+\dfrac{r}{5200})=\dfrac{ln(2)}{52}\\\\\text{*** take the exp ***}\\\\\displaystyle 1+\dfrac{r}{5200}=exp(\dfrac{ln(2)}{52})=2^{(\dfrac{1}{52})}=\sqrt[52]{2}\\\\r = 5200\cdot (\sqrt[52]{2}-1)=69.77875...[/tex]

Rounded to the nearest percent, the solution is 70%.

If you want to double your capital in one year with weekly compounding you need an interest rate of 70% !!

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

4%

Step-by-step explanation:

Answer: The length is 7/10 inches.

Step-by-step explanation:

So if is says that the string is  1/10 times 7 inches long, then it represents the length of the string.

So  L = [tex]\frac{1}{10}*7[/tex]  

     L = 7/10

Answer:

l=7/10

Step-by-step explanation:

Answer:

2x-11

Step-by-step explanation:

2 x X = 2x + 11

Answer:

D. ( 2w+6). (w)

i tried my best

hope this is the answer

stay at home stay safe

Answer:

C.I = (371.88  , 458.12)

Step-by-step explanation:

Given that:

sample size n = 100

sample mean [tex]\overline x =[/tex] 415

standard deviation = 220

The objective is to calculate the  95% confidence interval for the average increase in number of words students who can read in a minute without losing comprehension.

At 95% confidence interval; level of significance ∝ = 1 - 0.95

level of significance ∝ = 0.05

[tex]z_{\alpha/2} = 0.05/2[/tex]

[tex]z_{\alpha/2} = 0.025[/tex]

The critical value at [tex]z_{\alpha/2} = 0.025[/tex] is 1.96

C.I = [tex]\overline x \pm M.O,E[/tex]

C.I = [tex]\overline x \pm z_{\alpha/2} \dfrac{\sigma }{\sqrt{n}}[/tex]

C.I = [tex]415\pm 1.96 \dfrac{220 }{\sqrt{100}}[/tex]

C.I = [tex]415\pm 1.96 *\dfrac{220 }{10}[/tex]

C.I = [tex]415\pm 1.96 *22[/tex]

C.I = [tex]415\pm 43.12[/tex]

C.I = (371.88  , 458.12)

Answer:

Step-by-step explanation:

i^{11}+i^{16}+i^{21}+i^{26}+i^{31}

[tex]=(i^{2} )^5i+(i^{2} )^8 +(i^{2} )^{10} i+(i^{2} )^{13}+(i^{2} )^{15} i\\=(-1)^5 i+(-1)^8+(-1)^{10} i+(-1)^{13} +(-1)^{15} i\\=- i+1+i-1-i\\=0- i[/tex]