Liner systems of equations

Answer:

So the values of x for which the function is positive are x ≥ -3 and x ≤ -9.

Step-by-step explanation:

We are given a function and we have to find the intervals in which the function has positive value.

y = [tex]x^{2} +12x+27[/tex]

y =(x + 3)(x + 9)

For the function to be positive , y ≥ 0

(x + 3)(x +  9) ≥ 0

Here there are two cases , either both should be positive or both should be negative.

If both are positive,

(x + 3)≥0 and (x + 9)≥0

So, x ≥ -3

If both are negative,

(x + 3)≤0 and (x + 9)≤0

So, x ≤ -9

So the values of x for which the function is positive are x ≥ -3 and x ≤ -9.

The intervals on which the function y = x² + 12x + 27 is positive are

x > -3 and x > -9

For the function given to be positive, it has to be greater than zero.

Since the expression is greater then zero, hence;

x² + 12x + 27 > 0

Factorize the resulting expression

x² + 3x + 9x + 27 > 0

x(x+3) + 9(x+3) > 0

(x+3) (x+9) > 0

x+3 > 0 and x + 9 > 0

x > -3 and x > -9

Hence the intervals on which the function y = x² + 12x + 27 is positive are

x > -3 and x > -9

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Answer:

1.8

Step-by-step explanation:

Do the long division.

Answer:

The point lie outside the circle

Step-by-step explanation:

step 1

Find the distance between the center of the circle and the given point

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

(0,0) and (-3,-7)

substitute the values

[tex]d=\sqrt{(-7-0)^{2}+(-3-0)^{2}}[/tex]

[tex]d=\sqrt{58}\ units[/tex]

step 2

Compare the distance with the radius

If d=r ----> the point lie on the circle

If d > r -----> the point lie outside the circle

If d < r -----> the point lie inside the circle

we have

[tex]d=\sqrt{58}\ units[/tex]

[tex]r=\sqrt{53}\ units[/tex]

so

[tex]\sqrt{58}\ units > \sqrt{53}\ units[/tex]

[tex]d > r[/tex]

therefore

The point lie outside the circle

Answer:

C outside the circle

Step-by-step explanation:

khan

Answer:

The conversion of 2000 ft per min into miles per hour is 2.268 miles per hour .

Step-by-step explanation:

Given as :

The speed = s = 2000 ft per min

Now, ∵ 5280 feet = 1 miles

so, 1 feet = [tex]\dfrac{1}{5280}[/tex] miles

∴ 2000 feet =  [tex]\dfrac{1}{5280}[/tex] × 2000 miles

i.e 2000 feet = 0.378 miles

Again

∵ 1 minute = [tex]\dfrac{1}{60}[/tex] hour

So, The speed in miles per hour

s = [tex]\dfrac{distance}{time}[/tex]

∴ s = [tex]\frac{0.378}{\frac{1}{60}}[/tex]

i.e s = 2.268 miles per hour

Hence, The conversion of 2000 ft per min into miles per hour is 2.268 miles per hour . answer

To convert 2000 ft./min. to miles per hour, multiply by appropriate conversion factors, and round the result, yielding 22.7 miles per hour.

To convert 2000 ft./min. to miles per hour, follow these steps:

Convert feet to miles: 2000 ft/min x (1 mile/5280 ft) = 0.3788 miles/min

Convert minutes to hours: 0.3788 miles/min x 60 min/hr = 22.73 miles/hr

Rounded to the nearest tenth, 2000 ft/min is 22.7 miles per hour.

Answer:

The reflection will be on the point (3, 5).

Step-by-step explanation:

For a given point (x, y) reflection along the line x = k, the co-ordinates will be:

[tex]$ R_{x = k} (x, y) = (2k - x, y) $[/tex].

Here, we have (x, y) = (-1, 5)

Reflection across the line x = 1, we have:

[tex]$ R_{x = 1} (-1, 5) = (2(1) - (-1), 5) $[/tex]

                                  = (3, 5)

Hence, the reflection of the point (-1, 5) would be the point (3, 5).

Answer:

The possible values of v are 6 and -6

Step-by-step explanation:

The opposite operation of an absolute value is to add a ± to the other side, so when we solve for v we get

|v|=6

v=±6

Which is the same as

v=-6 and 6

Answer:

C

Step-by-step explanation:

|6| and |-6| have the same meaning. Both are equal to 6

The answer is C

Answer:

(i) 5

(ii) - 1

(iii) - 1

(iv) 0

(v) 1

(vi) 1

Step-by-step explanation:

See the graph attached to this question.

The blue graph shows y = f(x) and the red graph shows y = g(x).

(i) (f + g)(- 3) = f(-3) + g(-3) = 4 + 1 = 5

(ii) (g - f)(- 2) = g(- 2) - f(- 2) = 2 - 3 = - 1

(iii) (fg)(2) = f(2) × g(2) = (- 1) × (1) = - 1

(iv) [tex](\frac{g}{f})(3) = \frac{g(3)}{f(3)} = \frac{0}{- 3} = 0[/tex]

(v) (fog)(1) = f[g(1)] = f(1) = 1

(vi) (gog)(- 1) = g[g(-1)] = g(2) = 1  (Answer)

After using the graph with the values of f and g we find the values as follows:

(i) (f+g)(-3) = 5

(ii) (g-f)(-2) = -1

(iii) (fg) (2) = -1

(iv) (g/f) (3) = 0

(v) (f o g) (1) = 1

(vi) (g o g)(-1) = 1

i) ( f +g ) (-3)

= ( f (-3) + g(-3) )

Values we got from the graph are:

f(-3) = 4

g(-3) = 1

After substituting these values in the given equation we get

( f + g) (-3) = 5

ii) ( g - f ) (-2)

= ( g(-2) - f(-2) )

Values we got from the graph are:

g(-2) = 2

f(-2) = 3

After substituting these values in the given equation we get

( g - f ) (-2) = - 1

iii) ( fg) (2)

= ( f(2) g(2))

Values we got from the graph are:

f(2) = -1

g(2) = 1

After substituting these values in the given equation we get

( fg)(2) = -1

iv) (g/f) (3)

( g(3) / f(3) )

Values we got from the graph are:

g(3) = 0

f(3) = - 3

After substituting these values in the given equation we get

( g / f ) (3) = 0

v) ( f o g ) (1)

= ( f(1) o g(1) )

Values we got from the graph are:

g(1) = 1

f(1) = 1

After substituting these values in the given equation we get

( f o g ) (1) = 1

vi) ( g o g ) (-1)

= ( g(-1) o g(-1) )

Values we got from the graph are:

g(-1) = 2

g(2) = 1

After substituting these values in the given equation we get

( g o g ) (-1) = 1

Brian should purchase Choice C of fabric

Solution:

Given that Brian wants to purchase a piece of fabric  that is between 49 and 53 inches long

So piece of fabric should be between: 49 and 53 inches

Let us convert feet to inches

[tex]4\frac{3}{4} feet = \frac{4 \times 4 + 3}{4} = \frac{19}{4} feet[/tex]

Now convert to inches

We know that,

1 feet = 12 inches

[tex]\frac{19}{4} feet = \frac{19}{4} \times 12 = 57 inches[/tex]

But this choice is greater than given condition that piece of fabric should be between: 49 and 53 inches

So this is not correct

[tex]4\frac{1}{2} feet = \frac{2 \times 4 + 1}{2} = \frac{9}{2} feet[/tex]

Now convert to inches

[tex]\frac{9}{2} feet = \frac{9}{2} \times 12 inches = 54 inches[/tex]

But this choice is greater than given condition that piece of fabric should be between: 49 and 53 inches

So this is not correct

[tex]4\frac{1}{3} feet = \frac{3 \times 4 + 1}{3} = \frac{13}{3} feet[/tex]

Now convert to inches

[tex]\frac{13}{3} feet = \frac{13}{3} \times 12 inches = 52 inches[/tex]

So this 52 inches lies between 49 and 53 inches

So Brian should purchase Choice C of fabric

Answer:

4 workers

Step-by-step explanation:

A group of 9 workers was assigned to paint the walls in a house, which could be completed in 48 hours. Then 1 worker will complete the whole job in [tex]48\times 9=432[/tex] hours.

If 1 worker completes the whole work in 432 hours, then he completes [tex]\dfrac{1}{432}[/tex] of the work per hour.

9 workers complete [tex]9\times\dfrac{1}{432}=\dfrac{1}{48}[/tex] of work per hour and complete [tex]\dfrac{1}{48}\times 8=\dfrac{1}{6}[/tex] of work in 8 hours.

[tex]1-\dfrac{1}{6}=\dfrac{5}{6}[/tex] of work left.

This could be completed by n workers in 72 hours, so

[tex]\dfrac{n}{432} \times 72=\dfrac{5}{6}\\ \\\dfrac{n}{6}=\dfrac{5}{6}\\ \\n=5[/tex]

9 - 5 = 4 workers left the team.

Answer:

y=3x+6

Step-by-step explanation:

Perpendicular means negative reciprocal of the slope.

y-y1=m(x-x1)

y-0=3(x-(-2))

y-0=3(x+2)

y=3x+6+0

y=3x+6

Question:

Ten subtracted from the quotient of a number and 5 is 18. What is the number?

Answer:

140 is the number.

Step-by-step explanation:

Let consider the number as ‘X’

Quotient of a number and 5 can be written as

                         [tex]X \div 5[/tex]

Ten subtracted from the quotient of a number and 5 can be written as

                        [tex](X \div 5) - 10[/tex]

Ten subtracted from the quotient of a number and 5 is 18 can be written as

                        [tex](X \div 5) - 10 = 18[/tex]

By solving the above equation, find ‘X’

                        [tex](X \div 5) = 18 + 10[/tex]

                        [tex]\frac{X}{5} = 28[/tex]

                        [tex]X = 28 \times 5 = 140[/tex]

Answer:

100

Step-by-step explanation:

It will help in the future to memorize your time tables

10*10 is basically 10 plus 10, 10 times but in a easier form

10+10+10+10+10+10+10+10+10+10=100

10+10=20

20+10=30

30+10=40

40+10=50

50+10=60

60+10=70

70+10=80

80+10=90

90+10=100

Answer:

The graph in the attached figure

Step-by-step explanation:

we have the equation of the line in point slope form

[tex]y-5=\frac{1}{5}(x-5)[/tex]

where

the point is (5,5)

the slope is m=1/5

Remember that

The formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)

so

To graph the line

1. Plot the point (5,5).

2. From that point, count right 5 units and up 1 unit and plot a second point.

3. Draw a line through the two points

so

The new point is (5+5,5+1) ----> (10,6)

Plot the points (5,5) and (10,6) and draw a line through the two points

The graph in the attached figure

Answer:

The answer is 28 meters.

Step-by-Step Explanation:

Because the shape is a square, something times itself equals the area.

7 times 7 equals 49. Using this multiplication fact, and also using the fact that the shape is a square, 7+7+7+7=28.

And there you have it, a square with an area of 49 square meters has a perimeter of 28 meters.

The perimeter of the square with an area of 49 sq meters is 28 meters.

A square is a 2D figure of which all the sides are of equal length.

We know that area of a square is side multiplied by side.

Given the area of a square is 49 sq meters, So two same numbers that are multiplied by 49 are 7 and 7.

∴ The length of each side of the square is 7 meters.

We also know that the perimeter of a square is 4 times the length of the side.

∴ The perimeter of the given square is (4×7) = 28 meters.

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Answer:

365.35

Step-by-step explanation:

USE A CALCULATOR!!!!

Money earned after working for 15 hours and making 8 deliveries is $ 534

Solution:

Given that pizza delivery person earns 30 per hour plus 10.50 for each delivery made

The expression used to find the earnings for him is given as:

30h + 10.50d

Where "h" is the number of hours and "d" is the number of deliveries

We have to find the money earned by him after working for 15 hours and making 8 deliveries

Therefore we get, h = 15 and d = 8

Substitute h = 15 and d = 8 in given expression

Money earned = 30(15) + 10.50(8)

Money earned = 450 + 84 = 534

Thus money earned after working for 15 hours and making 8 deliveries is $ 534

Answer:

well it would kinda depend on their age,and size,but the average height of an ADULT male is : 5.6 ft

ADULT female:5.2ft

(remember it would depend on their age,but some people might even have medical reasons to be shorter or taller than their original height too. At a age children don't HAVE to be that exact height,but atleast close enough to that height.)

(changes may occur depending on medical reasons,or age too!)

Answer:

y <= -8

Step-by-step explanation:

This algebraic expression would read as:

Y is Less than or equal to -8

Answer:

No more than means less than or equal to

y <= -8

Answer:

X^2+6X-7=0

Step-by-step explanation:

To identify the quadratic equation use the following method

(X-a)(X-b)=0

Where

a=-7

b=1

(X+7)(X-1)=0

X^2+7X-X-7=0

X^2+6X-7=0

The valid conclusion based on the provided data is that 15% of students in the sample are below grade level in math, but this does not necessarily indicate the same for all students in grade 6 at HACS.

The question pertains to drawing a valid conclusion from given statistical data about the math proficiency level of students in a specific school.

When it states that 15% of students are below grade level in math, the conclusion can only pertain to the group specified in the data set.

Therefore, the most valid conclusion from the given choices is that 15% of students in the sample are below grade level in math, and we cannot infer the same for the entire grade 6 at High Achievers Charter School (HACS) without further context.

In light of the provided information, one cannot come to any conclusions regarding the math proficiency of students in other grades, nor can one generalize to all students in grade 6 at HACS from a mere sample unless the sample is clearly stated to be the entirety of the grade.

The correct conclusion is B. 15% of all students in grade 6 at HACS are below grade level in math.

To understand why this conclusion is valid, let's analyze the given information and the options provided:

- The school board determined that 15% of the students who took the test were below grade level in math. Since the test was administered to all grade 6 students at HACS, this percentage applies to the entire population of grade 6 students at the school, not just a sample.

Now, let's evaluate the conclusions:

A) 15% of students in the sample are below grade level in math, but we cannot conclude anything about the students in grade 6 at HACS.

- This conclusion is incorrect because the sample includes all grade 6 students at HACS. Therefore, we can generalize the results to the entire population of grade 6 students at the school.

B) 15% of all students in grade 6 at HACS are below grade level in math.

- This conclusion is correct because the test was given to all students in grade 6 at HACS, making the sample representative of the entire population of grade 6 students. Thus, the 15% figure accurately reflects the proportion of grade 6 students at HACS who are below grade level in math.

C) 15% of all students at HACS are below grade level in math.

- This conclusion is incorrect because the test was only administered to grade 6 students. We do not have data on students in other grades at HACS, so we cannot extend the 15% figure to the entire student body of the school.

Answer:

i think C

Step-by-step explanation:

Answer:

rate of interest=R=5.5%

Step-by-step explanation:

given principle=P=$1200

simple interest=S.I=$396

time=T=6 years

simple interest=[tex]\frac{P\times R\times T}{100}[/tex]

$396=[tex]\frac{1200\times R\times 6}{100}[/tex]

$396=[tex]72\times R[/tex]

R=[tex]396\div 72[/tex]

R=5.5%

rate of interest=R=5.5% answer

a) The equation for the amount of money (m) Scott has after a number of hours babysitting (h) is m = 15 + 6 h

b) Scott will babysitting for 6 hours to have $51.00

Step-by-step explanation:

The given is:

Write an equation for the amount of money (m) Scott has after a number of hours babysitting (h) and find the number of hours of babysitting if Scott have $51.00

a)

∵ Scott has $15.00

∵ He earns $6.00 an hour babysitting

∵ h is the number of hours of babysitting

∵ m is the amount of money that Scott has after h hours

- Equate m by the sum of 15.00 and the product of 6.00 and h

∴ m = 15 + 6 (h)

∴ The equation is m = 15 + 6 h

The equation for the amount of money (m) Scott has after a number of hours babysitting (h) is m = 15 + 6 h

b)

∵ Scott has $51.00

∴ m = 51

- Substitute the value of m in the equation to find h

∵ 51 = 15 + 6 h

- Subtract 15.00 from both sides

∴ 36 = 6 h

- Divide both sides by 6

∴ 6 = h

∴ h = 6 hours

Scott will babysitting for 6 hours to have $51.00

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Work is provided in the image attached.

Answer:

A) 8, 15, 17.

Step-by-step explanation:

Right triangle obey the Pythagorean theorem. Thus, we choose the two smaller numbers (being the cathetus) and if after applying the P. Theorem we get the biggest of each option  (the hypotenuse) that means that those numbers could be the sides of a right triangle.

The Pythagorean theorem states that: [tex]a^2+b^2=c^2[/tex]

Thus:

[tex]\sqrt{a^2+b^2}=c[/tex]

Option A:

[tex]\sqrt{8^2+15^2}=17[/tex] → 17 = 17 OK!

Option B:

[tex]\sqrt{6^2+8^2}  = 10[/tex] → 10 ≠ 12 NO

Option C:

[tex]\sqrt{9^2+11^2} = [tex]\sqrt{202}[/tex][/tex] → [tex]\sqrt{202}[/tex] ≠ 21 NO

Option D:

[tex]\sqrt{4^2+13^2} = \sqrt{185}[/tex] → [tex]\sqrt{185}[/tex] ≠ 16 NO

Answer:

x=-19/5

Step-by-step explanation:

-3x=2x+19

-3x-2x=19

-5x=19

x=19/-5

Answer:

get x to one side by subtracting 2x from 2x+19

new equation:

-3x-2x=19

-5x=19

divide both sides by -5

x=-19/5

or x=-3 4/5

Answer:

The solution of the system is x=-1, y=-2

Step-by-step explanation:

we have

[tex]y=-2[/tex] ----> equation A

[tex]y=3x+1[/tex] ----> equation B

Solve the system by graphing

Remember that the solution of the system is the intersection point both lines

using a graphing tool

The intersection point is (-1,-2)

see the attached figure

therefore

The solution of the system is x=-1, y=-2

Answer:

?

Step-by-step explanation:

It could be

Answer:

Yes

Step-by-step explanation:

Yes because it is a one-to-one relation. Every x-value maps to a unique value of y.

Answer:

The last system is that one with exactly one solution:

–2x + 7y = –5  

2x + 7y = –9

Step-by-step explanation:

We can easily check the number of solutions that each system has in this problem, since the equations contain most of them combinations of terms in y and in x that can be easily cancelled out via simple term by term addition.

Going through them system by system, and adding term by term the equations which are in standard form we get:

(1) –5x – 10y = 24  

      5x + 10y = 16  

---------------------------

     0x  +  0y   = 40  which sates a mathematical absurd: "0 = 40", and therefore there are no x and y solution values that could verify such. This also means that the lines represented by the system do NOT intersect (they are parallel lines)

(2)  3x + 4y = –7  

   –3x – 4y = 7  

   --------------------

    0x   + 0y  = 0 which gives that zero equals zero, which any pair (x, y) belonging to any of the two equations can verify, so an infinite number of solutions (the lines in the system overlap)

(3) –12x + 8y = 16  

      12x – 8y = 16  

      -------------------

       0x  +  0y   = 32 which sates a mathematical absurd: "0 = 2", and therefore there are no x and y solution values that could verify such. This also means that the lines represented by the system do NOT intersect (they are parallel lines)

(4)  –2x + 7y = –5  

        2x + 7y = –9

      ---------------------

        0x + 14y = -14

This is the only system that shows solution. It allows us first to solve for "y" in the resultant equation: 14 y = -14 giving us the value y = -14/14 = -1

and then using it the unique value for x can be determined:

        2x + 7y = –9

        2x + 7 (-1) = -9

        2x -7 = -9

        2x = -9 + 7

        2x = -2

          x = -2/2 = -1

Therefore, the pair (-1, -1) is the unique solution to the system

Answer:

Step-by-step explanation:

Trust me guys. The guy above me has a full explanation, but if you are just looking for a simple answer, then I gotchu

Answer:

Step-by-step explanation:

I think it means every data value should be equal to the "mean" to make the standard variation of this set to be zero. Or all data value of the set are equal.