Solve the inequality and express your answer in interval notation.
x^2+ 12x+7<0

Answer:

Step-by-step explanation:

7(4x-5) - 4(6x+5) = -91

28x - 35 - 24x -20 = -91

28x - 24x = -91 + 35 + 20

4x = -36

x = -36 : 4

x = -9

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The factor (r + 3) is common. Then the greatest common factor will be (r + 3).

Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).

The expression is given below.

⇒ (5r - 6)(r + 3) - (2r - 1)(r + 3)

In both terms, the factor (r + 3) is common. Then the greatest common factor will be (r + 3). Then the expression will be

⇒ (5r - 6)(r + 3) - (2r - 1)(r + 3)

⇒ [(5r - 6) - (2r - 1)](r + 3)

⇒ (3r - 5)(r + 3)

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Answer:

120

Step-by-step explanation:

We note that 2, 4 is the least common multiple of 6,8 and 12

We have to find the smallest 3 -digit multiple of 24.

Also 24 × 4 = 96 and 24 ×5 = 120.

The smallest 3-digit number which is exactly divisible by 6,8 and 12 is 120.

Answer:

120

Step-by-step explanation:

When the subject is changed for x, the equation is x = 1 - 1/(1 - (1/(1 - y)^2)))

The equation is given as

x = 1 - 1/(1 - (1/(1 - y)^2)))

The question implies that we change the subject and make x the subject

However, in the equation;

The subject of the equation is x

This means that when the subject is changed for x, the equation is x = 1 - 1/(1 - (1/(1 - y)^2)))

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Answer:

y = 4x + 7

or y - 4x = 7

Step-by-step explanation:

x + 4y = 2

4y = -x + 2

y = -1/4x + 2

The slopes of two perpendicular lines are negative reciprocals of each other. So the slope of the perpendicular line should be negative reciprocal of -1/4, then it is 4

Given m = 4, y = 3, x = -1

y = mx + b

3 = 4(-1) + b

3 = -4 + b

b = 7

y = 4x + 7

There are two ways to say 1900 in word form.

1900 = nineteen hundred

1900 = one thousand, nine hundred

Both are equally valid.

Answer: one thousand nine hundred

Step-by-step explanation:

Answer: Tablet costs $225

Laptop costs $135

Step-by-step explanation:

Laptop is = x

Tablet = T

x + 3t = 810

x + t = 360

x = 360 - t

360 - t + 3t =810

2t = 450

t = 225

x + 225 = 360

x = 135

Answer:

Step-by-step explanation:

If a GP has a positive common ratio and negative first term, it means all its terms are negative since formed by a product of positive and negative numbers.

We can only see one sequence with all negative terms and common ratio of 5, this is REID's.

We get the speed of the object as 5365 miles / day after rounding off.

We are given that an object is moving at a speed of 360 kilometers per hour.

We know that:

1 km = 0.621 miles.

So, 360 km will be:

360 km = 223.56 miles.

Also, we know that:

we have 24 hours in 1 day.

1 day = 24 hours.

1 hour = 1 / 24 day.

Re-writing the speed of the object, we get that:

223.56 miles in 1 / 24 day

That is:

5365.44 miles / day.

Rounding off:

= 5365 miles / day.

Therefore, we get the speed of the object as 5365 miles / day after rounding off.

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Answer:

602,630

Step-by-step explanation:

Answer:

84 minutes

Step-by-step explanation:

360 per hour = 6 per min

140 per hour = 2 1/3 per min

Both together do 8 1/3 per min.

In 3 minutes, both machines together do 25 packages.

700/25 = 28.

In 3*28 minutes, which is 84 minutes, both machines together seal 700 packages.

Thanks!

a) The total distance covered is 56 feet

b) The total displacement is 14 feet

c) The average speed  in the first, second, and third parts of the car’s motion are; 5 feet/sec,  0 feet/sec and  4.2 feet/sec

d) The average speed of the car is 3.5 feet/sec

e) The average velocity of the car is 0.875 feet/sec

We must understand that the distance is the difference between two points but the displacement is the distance between two points in a definite direction. This implies that the distance is a scalar quantity while the distance is a vector quantity. Being a vector quantity means that when we are computing the displacement that we must take into account the direction of the motion and this also applies to the calculation of the velocity of the car.

Let us now carry pout the calculations;

a) Total distance = 35 feet +  21 feet = 56 feet

b) Total displacement =  35 feet -   21 feet = 14 feet

c) Average speed of the first, second, and third parts of the car’s motion;

i)  35 feet / 7 seconds = 5 feet/sec

ii) 0 feet/sec ( it sat still)

iii) 21 feet/5 seconds = 4.2 feet/sec

d) The cars average speed = 56 feet/16 seconds = 3.5 feet/sec

e) Average velocity = 14 feet/ 16 seconds = 0.875 feet/sec

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Answer:

128 feet

Step-by-step explanation:

8*16 is 128 feet

You require the score of 78 to do equally well in exam 2.

To compare both the scores, we need to compute the z scores of both exams and then compare the values. The formula for z-score is:

Z = (X - μ)/σ

Where X = score obtained

           μ = mean score

          σ = standard deviation

For Exam 1:

Z = (91 - 79)/8

  = 12/8

Z = 3/2

To perform similarly well on the second exam, let x equal z 3/2.

For Exam 2:

Z = (x - 60)/12

3/2 = (x - 60)/12

By cross multiplying we get

2(x - 60) = 12 * 3

x - 60 = 36 /2

x - 60 = 18

x = 18 + 60

x = 78

Therefore, Consequently, you must achieve a score of 78 to perform equally well in Exam 2.

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The amplitude of the function is 1/3

The function is given as:

y = negative one-third sine x

Rewrite properly as

y = -1/3sin(x)

A sine function is represented as:

y = Asin(x)

And the amplitude is

Amplitude = |A|

In y = -1/3sin(x), we have

A = -1/3

So, we have

Amplitude = |-1/3|

Evaluate

Amplitude = 1/3

Hence, the amplitude of the function is 1/3

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Answer:

equation : 3x + 5y + 2 = 0

Step-by-step explanation:

y - y1 = m (x - x1)

y - (-1) = -3/5 ( x - 1 )

5(y + 1) = -3(x - 1)

5y + 5 = -3x + 3

3x + 5y + 2 = 0

Answer:

x = 5.94

Step-by-step explanation:

They still loose 100 dollars

Answer:

The store lost $100....

Answer:

$235

Step-by-step explanation:

‎‎‎‎‎‎‎‎‎‎.....................

Let the equation of the line perpendicular to line 3x+2y=16 is:-

2x - 3y = C. ………………(1)

Line (1) passes through the point (9,-2), therefore

2×9 - 3×(-2)= C

or, C = 24.

Thus, the required equation is:-

2x - 3y = 24.

or, 3y = 2y - 24.

or, y = (2/3).x + (-8). Answer.

The translation of the phrase The sum of -15y and 16y is −4 is

-15y + 16y = -4 and the value of y is -4.

An algebraic equation is written in the form of variables and constants and we combine these variables and constants with arithmetic operations.

In the given question there is a statement The sum of -15y and 16y is −4 and we have to express it in form of numerical and solve for y or find the value of y.

∴ The sum of -15y and 16y is −4 can be expressed numerically as,

-15y + 16y = -4.

y = -4.

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Explanation:

"bisect" means to "divide in half"

So segment WY is split into two smaller equal pieces.

Segments WX and XY are the same length

WX = XY

6k+8 = 11k-12

6k-11k = -12-8

-5k = -20

k = -20/(-5)

k = 4

The answer for the given question is 59/90

A fraction is said to be in lowest terms when the greatest common factor (GCF) of the numerator and denominator is 1. Now that this is in mind, let's continue to solve.

Given, 5/9+1/10 and we have to convert or reduce it into the lowest terms.

So, let's proceed to solve this question

First add 5/9 and 1/10 i.e.,

= 5/9+1/10

Taken LCM of 9 and 10 which comes out to be 90.

Then, adding, we get

= 50+9/90

= 59/90

59/90 is already in its lowest form because the numerator and denominator have no common factor other than 1. So it's already at its most basic level.

Therefore, 59/90 is the required answer.

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The organization’s employees are a part of the finance team, if the size of the finance team makes up two-fifths of the remainder is 13%

What is the number of employees who are regarded as remainder?

The number of employees out of the total workforce left after having deducted the number of employees making up the sales team, the customer support team the software development and HR departments is computed as shown below:

remainder of workforce=80,000-16,000-24,000-14,000

remainder of workforce=26,000

finance team=2/5*26000

finance team=10,400

finance team as % of total workforce=10,400/80,000

finance team as % of total workforce=13.00%

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Answer: l=32/3 meters

w=16/3 meters

Step-by-step explanation:

P=perimeter, l=length, w=width

P=2l+2w

32=2(2w)+2w

32=4w+2w

6w=32

w=32/6

w=16/3 meters

32=2l+2(16/3)

32=2l+32/3

(32=2l+32/3)*3

96=6l+32

6l=64

l=64/6

l=32/3 meters

The range measures the difference between the minimum value and the maximum value in a dataset. The interquartile range measures the difference between the first quartile (25th percentile) and third quartile (75th percentile) in a dataset. This represents the spread of the middle 50% of values

Answer: 14 1/7

Step-by-step explanation:

Answer: 31 sides

Step-by-step explanation: 4 sides per quadrilateral so 16 sides and 5 sides per pentagon so 15 sides. 16 + 15 = 31.