1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anna35 [415]
3 years ago
9

The length of a rectangle is 4 meters less than twice its width. The are of a rectangle is 70m^2. Find the dimensions of the rec

tangle.
Mathematics
1 answer:
igomit [66]3 years ago
8 0

Answer:

The length is 7 m

The width is 10 m

Step-by-step explanation:

length = x

width = 2x - 4

length * width = area

It is given that the area is 70 m^{2}

From there

x * (2x - 4) = 70

2x^{2} - 4x = 70

2x^{2} - 4x - 70 = 0

x^{2} - 2x - 35 = 0

Now we have a quadratic equation, which is  ax^{2} + bx + c = 0, where a \neq 0

In this equation a = 1, b = -2 and c = -35

Discriminant (D) formula is b² - 4ac

D = -2^{2}  - 4 * 1 * (-35) = 144 > 0

This discriminant is more than 0, so there are two possible x

Their formulas are  \frac{- b - \sqrt{D}  }{2a} and \frac{- b + \sqrt{D}  }{2a}

x_{1} =  \frac{- (-2) - \sqrt{144} }{2} = -5 < 0 (the length of the rectangle has to be more than 0, so we don't use this x)

x_{2} = \frac{- (-2) + \sqrt{144} }{2} = 7 > 0 (this one is right)

Calculating the dimensions

length = x = 7 (m)

width = 2x - 4 = 2 * 7 - 4 = 10 (m)

You might be interested in
Which statements about the factors of the terms in the expression 20 a + 15 a b + 24 b are true? Select three options.
ExtremeBDS [4]

Answer:

Following are the true statements

2. The factors common to 20a and 15ab are 1, 5, and a.

3. The factors common to 20a and 24b are 1, 2, and 4.

5. The GCF of the expression is 1

Step-by-step explanation:

Expression is  20a + 15ab + 24b

Now lets have a look at each of the options provided!

1. The factors common to 20a and 15ab are 1, 5, a, and b.

False

As you can see there is no b in 20a term only 1,5,a are common hence it is false.

2. The factors common to 20a and 15ab are 1, 5, and a.

True

The terms 20a and 15ab are divisible by 1,5,a hence it is true.

3. The factors common to 20a and 24b are 1, 2, and 4.

True

The terms 20a and 24b are divisible by 1,2,4 hence it is true

4. The GCF of the expression is ab.

False

20a + 15ab + 24b

As you can see ab is not common in all of the terms hence it cannot be greatest common factor

5. The GCF of the expression is 1

True

Factor of 20 are: 2,2,5,1

Factor of 15 are: 3,5,1

Factor of 24 are: 2,2,2,3,1

As you can see the only common factor among all the terms is 1 hence GCF is 1.

5 0
3 years ago
Approximate: log5 4/7
Evgesh-ka [11]
   Properties of Logs

logb(x/y) = log<span>bx</span> - log<span>by</span>.

therefore

log5 (4/7)= log5 (4)- log5 (7)

<span>Solve log 5 (4) and log 5 (7)  with the base change of the logarithm</span>

<span>log 5 4 = log 4 / log 5 </span>

 Use the calculator: 

<span> <span>log 5 4 =0.8613531161 </span></span>

 log 5 7 = log 7 / log 5 

<span>log 5 7 =1.2090619551</span>

<span>log5 (4/7)= log5 (4)- log5 (7)=-0.347708839</span>

6 0
3 years ago
Read 2 more answers
Some help with this
Anna71 [15]

Answer:

Growth

Step-by-step explanation:

7 0
3 years ago
Use inverse operation to solve the question <br><br> 2/3z = -4<br><br><br> Z= ?
sweet [91]

Answer:

z=(-6)

Step-by-step explanation:

(2/3)*z=(-4)

2*z=3*(-4) --> We move the 3 from the left to the right part of the equation. It was dividing, so we move it multiplying.

2*z=(-12)

z=(-12)/2 --> It's the inverse case of before. 2 was multiplying, so we move it to the right by dividing it.

z=(-6)

7 0
3 years ago
Hello, i was confused in this if anyone could help me with it
umka2103 [35]

Answer:

hmmmmmm Okay From what question?

8 0
3 years ago
Other questions:
  • What is 10 times as much as 130
    6·1 answer
  • Solve 2x + 4y = 11 for y​
    14·1 answer
  • A confidence interval (CI) is desired for the true average stray-load loss u (watts) for a certain type of induction motor when
    8·1 answer
  • Is a maximum increasing Or decreasing
    14·1 answer
  • What is the value of each expression in simplest form?<br><br> 5/6 + 2 1/6
    10·2 answers
  • Explain how to solve the compound dependent event question.
    14·1 answer
  • Chicken strips at a restaurant sell for the following prices: 4 pieces for $2.40 6 pieces for $3.00 How much do customers save p
    14·1 answer
  • Sam is a cashier at the local grocery store. He earns $8/hr and works there 10 hours per
    5·1 answer
  • Find cosX and cosZ. Write each answer as a fraction and as a decimal. Round to four decimals places, if necessary. Fractions to
    13·1 answer
  • What is this! I will mark u as branilyst
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!