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1 year ago

Solve x2 14x = −24 by completing the square. what is the solution set of the equation?

2 answers:

5 0

First, rearrange the equation so that only zero will be on the right side:

x^2 + 14x +24 = 0

Let the coefficients be:

a = 1
b = 14
c = 24

To complete the square, add (b/2)^2 to both sides of the equation:

(b/2)^2 = 49

x^2 + 14x + 49 + 24 = 49
x^2 + 14x + 49 = 25
(x+7)^2 = 25

Therefore, the solution set of the equation is {-12, -2}

Mashcka [7]1 year ago

3 0

Answer:

the answer on ed is A

Step-by-step explanation:

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a shark can swim 24 meters in 36 seconds. at this rate, how far, in meters, will the shark swim in 2 minutes?

blagie [28]

Answer:80 meters

Step-by-step explanation: 24 meters = 36 secs

2 mins = 120 secs

Cross multiply

24×120/36

= 80 meters

Hope I helped you!!

8 0

2 years ago

Read 2 more answers

Sophia was selling tickets at the high school dance. At the end of the evening, she picked up the cash box and noticed a $5 bill

borishaifa [10]

The first thing we will do in this case is to define variables:
x = number of individual tickets.
y = number of tickets per couple.
We have then that the system of equations that represents the problem is:
10x + 15y = 590
x + 2y = 68
Solving the system we have:
x = 32
y = 18
Substituting we have:
10 (32) + 15 (18) = 590
320 + 270 = 590
590 = 590
Equality is met, therefore the $ 5 bill belongs to the box.
Answer:
the $ 5 bill belong inside the cash box

4 0

2 years ago

Triangle N T M is shown. Angle N T M is a right angle. An altitude is drawn from point T to point U on side N M to form a right

stich3 [128]

Answer:

The value of y is 6 $\sqrt{3}$ units ⇒ 2nd answer

Step-by-step explanation:

In the attached figure

∵ ∠MTN is a right angle

∵ TU is the altitude of the triangle

- There are some rules in this triangle let us revise them

(NT)² = NU . NM
(MT)² = MU . MN
(TU)² = MU . NU
TM . TN = TU . MN

∵ NU = 9 units

∵ UM = 3 units

∵ MN = UM + NU

∴ MN = 3 + 9 = 12 units

- By using the 1st rule above

∴ (NT)² = 9 × 12

∴ (NT)² = 108

- Take a square root to both sides

∴ NT = $\sqrt{108}$

- Simplify the root

∴ NT = 6 $\sqrt{3}$ units

∵ NT is y

∴ y = 6 $\sqrt{3}$ units

The value of y is 6 $\sqrt{3}$ units

8 0

1 year ago

Read 2 more answers

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. −2y2 + 6y = −2

andrezito [222]

-2y^2 + 6y + 2 = 0
a = -2, b = 6, c = 2
x = (- b + - sqrt(b^2-4ac))/(2a)
x=(-6+-sqrt(36-4*-2*2))/-4
x=(-6+-sqrt(36+16))/-4
x=(-6+-sqrt(52))/-4
x = (-6 +- 2sqrt13)/-4
x = (3 + - sqrt13)/2

8 0

2 years ago

Read 2 more answers

There are 527 pencils 646 erasers 748 sharpeners there are to be put in seperate packets containing the same number of items fin

blsea [12.9K]

Step 1

<u>Find the Greatest Common Factor (GCF)</u>

the prime factorization of each number is equal to

$527=17*31\\ 646=2*17*19\\ 748=2^{2} *11*17$

The GCF is 17

That means that the maximum number of packets is 17 and the maximum number of the items possible in each packet is

Number of pencils=527/17=31 pencils in each packet

Number of erasers=646/17=38 erasers in each packet

Number of sharpeners=748/17=44 sharpeners in each packet

7 0

2 years ago