The length of a rectangle is 3 centimeters less than five times its width. Its area is 14 square centimeters. Find the dimensions of the rectangle.
Find the Width and the Length
W=
L=​

Answer:

[tex]x = 9.4[/tex]

[tex]y = 17.7[/tex]

Step-by-step explanation:

Given: The figure

Required: Find x and y

The relationship between length x, length 15 and angle 32 is as follows:

[tex]tan \theta = \frac{opp}{adj}[/tex]

So, we have:

[tex]tan\ 32= \frac{x}{15}[/tex]

Cross multiply:

[tex]x =15*tan\ 32[/tex]

[tex]x = 15 * 0.6248693519[/tex]

[tex]x = 9.3730402785[/tex]

[tex]x = 9.4[/tex] --- approximated

Similarly:

The relationship between length y, length 15 and angle 32 is as follows:

[tex]cos \theta = \frac{adj}{hyp}[/tex]

So, we have:

[tex]cos\ 32= \frac{15}{y}[/tex]

Cross Multiply:

[tex]y * cos\ 32= 15[/tex]

Solve for y

[tex]y = \frac{15}{cos\ 32}[/tex]

[tex]y = \frac{15}{0.84804809615}[/tex]

[tex]y = 17.6876760506[/tex]

[tex]y = 17.7[/tex] --- approximated

Answer:

the b is 20

Step-by-step explanation:

The computation of the b is shown below

Given that

y = mx + b

where

m = -2

x = 3

y = 14

Now placing these values to the above formula to determine the value of b

14 = -2(3) + b

14 = -6 + b

b = 14 + 6

= 20

Hence, the b is 20

We simply applied the above formula so that the correct value could come

And, the same is to be considered

Answer:

D. 18.0

Step-by-step explanation:

edge

The value of |q-r| will be 18 for the given two vectors q and r.

A quantity or phenomenon with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation.

Given, |q| = 5 at an angle of 45° and |r| = 16 at an angle of 300°.

Let OA =|q|

OB = |r|

BA = |q|-|r|

Hence ∠AOB = 45°+(360°-300)

∠AOB = 45°+60°

∠AOB = 105°

Given  |q| = 5,  |r| = 16

The Cosine Rule can be used in any triangle to relate all three sides to one angle.

Now using the cosine rule

|q-r| = √(16)²+(5)²-2×16×5×cos105°

|q-r| = 18

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Answer:

it depends on the rest of the equation

Step-by-step explanation:

sss is used for using 3 sides to determine if the triangles are congruent, asa uses an angle then a side then an angle, sas uses a side then an angle then a side, ssa uses a side, then another side, then an angle

Answer:

the slope is -2/3 hope that helps

Answer:

B

Step-by-step explanation:

false

Answer:

the answer is someone else can

Answer:

S = P (r)(t)

Step-by-step explanation:

S = Simple interest

P = Principle

r = rate

t = time

S = (10000 x 2%)x2

Work brackets first 10000 x 2% = 200

then 200 x 2 = 400

S = 400

Answer: c

Step-by-step explanation:

Answer:

7x+4846

Step-by-step explanation:

Answer:

The cost of one balloon is 4 dollars

the cost of one cake is 6 dollars

Step-by-step explanation:

The way I did it was by substituting different numbers and seeing if they equaled forty or 26.

my thought process:

1 balloon= 5

1 cake= 10

that doesnt work for 2 balloons and 3 cakes

1 balloon=5

1 cake=5

that works for 4 balloons and 4 cakes but not 2 balloons and 3 cakes

1 balloon=4

1 cake=7

I'm sorry I'm way too tired to finish this 0-0 anyways yeah that's the correct answer :)

Answer:

Not sure what number sense is, but 3 is the answer.

Step-by-step explanation:

Answer:

the answer would be 3.

Step-by-step explanation:

5 times 3 is 15 plus 40 is 55. Hope this helps!!! Please let me know if i'm right!!!

Answer:

The account interest rate is 0.80%

Step-by-step explanation:

A=P(1+r/100)^10

1462=1350(1+r/100)^10{divide both sides by 1350}

1462/1350=(1+r/100)^10{find the 10th root of both sides}

1.00800=1+r/100{multiply through by 100}

100.800=100+r

r=100.800-100

r=0.80%

Answer: statistically significant

Step-by-step explanation:

The p-value of a statistical test tell us the conclusion to our hypothesis. When the result of the p-value lies between 0.27 it means there is a 27% chance of it occurring, when it is at 0.02 it means there is a 2% chance of it occurring. When it lies between 0.0027 it means there is 0.27 chance of it occurring this becomes statistically significant as this won’t have much changes or effects on the hypothesis. So what this means is there is chance it won’t occur.

Answer:

The total value of the discount is $14

Step-by-step explanation:

40 x 0.35 = 14

Answer: 361

Step-by-step explanation: 4(the change) times 93 (the term u want) minus 11 (your starting number/term)

Answer:

0.05

Step-by-step explanation:

The Effect size  = (Difference in Means) / (Standard deviation)

= (20 - 19) / 20

= 1/20

= 0.05

Answer:

-1

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

(1--2)/(2-5)

3/-3

-1

Answer:

3

Step-by-step explanation:

Remember that when we are dividing two exponents with the same base (here, it's 13), we can subtract the values of the powers:

[tex]\frac{a^m}{a^n} =a^{m-n}[/tex]

So, here, we have [tex]\frac{13^{10}}{13^7}[/tex] , so we subtract 7 from 10:

[tex]\frac{13^{10}}{13^7}=13^{10-7}=13^3[/tex]

Thus, 3 should go in the box.

Answer:

12/18

Step-by-step explanation:

Answer:

15) The ratio of hours to miles is 1 hour to 75 miles; 1/75

16) They will have traveled 900 miles.

17) It will take them around 9 hours.

Step-by-step explanation:

15) Finding the unit rate of the trend (which in this case I considered to be line) can be done by finding the slope and simplifying it. There is a constant linear slope in this graph so it was evident that as the x-values increased by 1, the y-values increased by 75. All you had to do was convert the values into ratio form which would be 1/75. The 1 should remain "numerator" and the 75 as denominator because it is the hour-to-mile ratio (the units were listed in thw instructions in the chronological order in which they were to be answered in ratio form; 1 hour to 75 miles).

16) You can set up an equivalent-ratios equation. Because we know that the unit ratio is 1 hour to 75 miles, and we were given the value of 12 hours, we can set up the equation like this: 1/75=12/x. I would then multiply the 75 miles by 12 so that the ratios will be proportionate. This gives me 900 miles. Now I know, based on the ratio 12 hours to 900 miles (12/900), that if the family travels for 12 hours, they will have traveled 900 miles.

17) We can do the same thing as we did in number 16. We just have to switch the value we use in the second ratio. This means that the equivalent-ratios equation will look like 1/75=x/700, because 700 miles is our given value as opposed to a value with a unit of hours, and miles are the denominators in these ratios. Now we have to see how many times 75 goes into 700 to figure out what to multiply the 1 by to get our proportionate ratios. We have to divide 700 by 75 which is roughly 9 (rounded down from 9.3). The ratio now reads: 1/75=9/700. This means that it will take the family around 9 hours to drive 700 miles (9 hours to 700 miles was the ratio).

angle1 + angle2 = 180

[tex]4x + 20 + x + 20 = 180[/tex]

[tex]5x + 40 = 180[/tex]

[tex]5x = 180 - 40[/tex]

[tex]5x = 140[/tex]

[tex]x = \frac{140}{5} [/tex]

[tex]x = 28[/tex]

Answer:

D

Step-by-step explanation:

25% of 16 is 1/4x16=4, which leaves D as as your answer

Answer:

d

Step-by-step explanation:

instead of taking away 4 add it until you have 100%

The equivalent algebraic expression to [tex]\sqrt[3]{200k^{15}}[/tex] is [tex]2~k^5~\sqrt[3]{25}[/tex]

The correct answer is an option (B)

"It is a mathematical statement which consists of numbers variables and some algebraic operations."

"It refers to the number of times a number is multiplied by itself."

For given question,

We have been given an algebraic expression [tex]\sqrt[3]{200k^{15}}[/tex]

We need to find an equivalent algebraic expression to given expression.

We know that the properties of exponents,

for positive integers a, b, n

[tex]\sqrt[n]{a}=a^{(\frac{1}{n} )}\\\\\sqrt[n]{ab}=a^{(\frac{1}{n} )}b^{(\frac{1}{n} )}[/tex]

We can write algebraic expression [tex]\sqrt[3]{200k^{15}}[/tex] as,

[tex]\sqrt[3]{200k^{15}}\\\\=\sqrt[3]{25\times 8\times k^{15}}\\\\=(25)^{\frac{1}{3} }\times (8)^{\frac{1}{3} }\times (k^{15})^{\frac{1}{3} }\\\\=\sqrt[3]{25}\times 2\times (k)^{\frac{15}{3} }\\\\ =2\sqrt[3]{25} \times k^5\\\\=2~k^5~\sqrt[3]{25}[/tex]

Therefore, the equivalent algebraic expression to [tex]\sqrt[3]{200k^{15}}[/tex] is [tex]2~k^5~\sqrt[3]{25}[/tex]

The correct answer is an option (B)

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Answer:

vertex: (-3,2) because the vertex would be the center point of the parabola

axis of symmetry: x=-3, the axis of symmetry is the the center/split in the parabola.

y-intercept: y= -1, because this is the point where the parabola crosses through the y-axis

Answer:

76

Step-by-step explanation:

Answer: 76

Step-by-step explanation: may be dead