The product of some negative number and 10 less than three times that number is 8

Answers

Answer 1

Answer: So,

"The product of some negative number"
n *

"and 10 less than three times that number"
-10 + 3n or 3n - 10

"is 8"
= 8
n * (3n - 10) = 8
n(3n - 10) = 8

Distribute.
$3n^2 - 10n = 8$

Subtract 8 from both sides.
$3n^2 - 10n - 8 = 0$

Factor.
$(3n + 2)(n - 4) = 0$

Set each factor to zero.
3n + 2 = 0
n - 4 = 0

There are two apparent solutions, but we must remember that the problem says that the number is negative. We must therefore discard the second equation as extraneous.

3n + 2 = 0

Subtract 2 from both sides.
3n = -2

Divide both sides by 3.
$n = (-2)/(3)$

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Evaluate the expression: -6 - |3 - 7| × 4 ÷ 8 - (-2) =

Answers

The required simplified solution of the given expression is -4.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
= -6 - |3 - 7| × 4 ÷ 8 - (-2)

Simplifying the above expression using the PEMDAS rule,
= -6 -|-4|×4÷8+ 4
= -6 - 16÷18 + 4 [∵ |-4| = 4]
= -6 - 2 + 4
= -4

Thus, the required simplified solution of the given expression is -4.

Learn more about simplification here:

brainly.com/question/12501526

#SPJ2

-6-/3-7/*4/8-(-2)
-6-4*4/8-(-2)
-6- 16 /8-(-2)
-6 -2 - (-2)
-8 - (-2)
-6
Hope this helped

Find the area of the given circle. Round to the nearest tenth.11.0 ft^2
38.5 ft^2
42.8 ft^2
113.0 ft^2

Answers

$diameter=12\ ft\n\ndiameter=2\ radius\n\n2r=12\ ft.\ \ \ /:2\nr=6\ ft.\n\nA=\pi r^2\n\nA=\pi\cdot6^2=36\pi\ (ft^2)\approx36\cdot3.14=113.04\ (ft^2)\approx113.0\ (ft^2)$

si hay seis puntos no colineales marcados en un papel ¿ cual es el numero de triangulos que se puede trazar?

Answers

(If there are six non-collinear points marked on a paper, what is the number of triangles that can be drawn?)
1.dos

The value of the expression StartFraction 2 x squared Over x EndFraction plus x (100 minus 15 x) when x = 5 is

Answers

Answer:119

Step-by-step explanation:

Answer:

119

Step-by-step explanation:

A car leaves a town traveling at 60 miles per hour. Two hours later, a second car leaves the town traveling the same route and overtakes the first car in 6 hours and 40 minutes. How fast was the second car traveling?

Answers

After two hours, the first car has traveled (2 x 60) = 120 miles.
That's the gap that the second car has to close.

The second car closes the gap of 120 miles in 6-2/3 hours.
He must have exceeded the first car's speed by (120/6-2/3) mph.

6-2/3 = 20/3

120 divided by 20/3 = 120 x 3/20 = 360/20 = 18 mph

The second car exceeded the first car's speed by 18 mph,
so he had to be traveling (60 + 18) = 78 mph to catch up.

Check:

In 6-2/3 hours . . .

The first car covers (60 x 20/3) = 400 miles.

The second car covers (78 x 20/3) = 520 miles.
This is the same distance as the first car PLUS the 120
that he was behind when he started out.
yay !

78 mph
The second car travels 520 miles in 400 minutes. 520/400=1.3. 1.3*60=78.

Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late and y represents the total fee?Answers:
(–3, –0.90)
(–2.5, –0.75)
(4.5, 1.35)
(8, 2.40)

Answers

Let's say the number of days library book is late is X, and the total fee is Y.

Liability charges $0.30 dollars as a fee for being 1 day late,

For being 1 day late, fee charge is: 1* $0.30
So, for X days the charge would be: X*$0.30.

Total charge for being X days late is Y, Which means: Y= 0.30 * X.

Now We would have to check all the viable solutions in the answer to see if they satisfy the equation Y= 0.30 * X

Optionone(-3, -0.9) and two (-2.5, -0.75) Would not be a viable solutionbecause the value of number of days can not be negative and in optionone and two, value of days -3 and -2.5 is negative.

Optionthree(4.5, 1.35) can not be correct because library charges fee for afull day so the number for days would be a whole number. Library wouldnot charge for 4.5 days, they would either charge of 4 days or 5 daysbecause 4.5 is not an whole number.

Option four(8, 2.40) is the correct answer because it satisfies our equation;

Y= 0.30 * X

2.40= 0.30 * 8

2.40 = 2.40.

Fourth option (8, 2.40) is the only viable solution to this question.

(–3, –0.90)

(–2.5, –0.75)

(4.5, 1.35)

(8, 2.40)

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