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
Paladinen [302]
2 years ago
14

The length of a rectangle is 5 cm more than twice a number. the width is 4cm less than the same number. if the area of the recta

ngle is 15cm2, find the number
​
Mathematics
1 answer:
lana [24]2 years ago
7 0
A = Lw (area of rectangle is length times width)
A = 15 (Area is 15)
L = 2x + 5 (length is 2 times a number plus another 5)
w = x - 4 (width is 4 less than that number

Plug in the values:
15 = (2x + 5)(x - 4)
FOIL
15 = 2x2 - 8x + 5x - 20
simplify:
15 = 2x2 - 3x - 20
Subtract 15
0 = 2x2 - 3x - 35
Factor out the quadratic. We know that one number has to be 7 and the other 5 so that they multiply together to make 35, and that one of them has to be negative so that it's actually -35.
That means we have m * n = -35
We also need it set up so that so that 2m + n = -3:
2 * -5 + 7 = -3
0 = (2x + 7)(x - 5)
So:
0 = 2x + 7, or 0 = x - 5
x = -7/2 or 5
We cannot have a negative length, so x = 5

Check:
15 = (2 * 5 + 5) (5 - 4)
15 = 15 * 1
15 = 15
You might be interested in
What are the intercepts for x and y ? thanks in advance
SpyIntel [72]

Answer:

see explanation

Step-by-step explanation:

The x- intercept is the value of x where the line crosses the x- axis.

The x- intercept is (0.3, 0)

The y- intercept is the value of y where the line crosses the y- axis

The y- intercept is (0, 0.4)

3 0
3 years ago
A line contains the point (4, 2) and has a slope of −3.
Naya [18.7K]

Answer: the equation is y = - 3x + 14

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

c represents the y intercept

m represents the slope of the straight line.

The slope of the given line is - 3 and it contains the point (4, 2)

To determine the y intercept, we would substitute m = - 3, x = 4 and

y = 2 into y = mx + c. It becomes

2 = - 3 × 4 + c

2 = - 12 + c

c = 12 + 2

c = 14

The equation becomes

y = - 3x + 14

8 0
3 years ago
What is 2x=8a+2b; solving for x
Eddi Din [679]

Answer:

Step-by-step explanation:

Flip the equation 1) 8a + 2b = 2x

Subtract 2b from both sides 2)8a + 2b(-2b) =<em> 2x + (-2b)</em>

Divide by 8 on both sides 3) 8a/8 =<em> -2b - 2x/8</em>

4) a = 1/-4b + 1/4x

7 0
3 years ago
SOLVE THE FOLLOWING BY SUBSTITUTION AND PLEASE SHOW STEPS:
Elza [17]
5x + 2y =9
X + y= -3

5x+2y=9
2x+2y=-6
__________
3x =15
X =5


5+y=-3
Y=-8

Answer is : (5,-8)
6 0
3 years ago
Read 2 more answers
Please show work . . .
Alenkasestr [34]

Answer:

19.64

the permieter is 5 so 5/2=2.5 2.5x2.5=6.25 6.25x3.14=19.64

8 0
3 years ago
Other questions:
  • Find the circumference of the circle. Leave answer in terms of pi (meaning there should be 3.14 in your answer).
    15·1 answer
  • A card is drawn at random from a standard pack of playing cards. Then a fair coin is flipped. What is the probability of selecti
    8·1 answer
  • Anyone know the answer to this one ?
    12·1 answer
  • Solve by factoring 25x^2+1=10
    15·2 answers
  • Find the missing side. Round your answer to the nearest tenth.
    7·1 answer
  • Which terms in the expression 9d2+15d3+11c2+7 have 14c2 as a like term?
    8·1 answer
  • NEED HELP ASAP! WILL CRY OR SOMETHING
    6·1 answer
  • Please helpp find the volume of each figure
    10·1 answer
  • Chuy wants to buy a new television. The television costs $1,350. Chuy decides to save the same amount of money each week, for 27
    5·1 answer
  • Need the answers and dont know it
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!