Does the system shown always, sometimes, or never have a solution when a >b?
ax+y=8
bx + y = 5
always
sometimes
O
never

Answer:  B)-4

Step-by-step explanation:

The given equation: [tex]\dfrac{6}{x^2-9}-\dfrac{1}{x-3}=1[/tex]

Using identity: [tex]a^2-b^2=(a-b)(a+b)[/tex]

[tex]\dfrac{6}{(x-3)(x+3)}-\dfrac{1}{x-3}=1\\\\\Rightarrow\ \dfrac{6-(x+3)}{(x-3)(x+3)}=1\\\\\Rightarrow\ \dfrac{6-x-3}{(x-3)(x+3)}=1\\\\\Rightarrow\ 3-x=(x-3)(x+3)\\\\\Rightarrow\ (-1)(x-3)=(x-3)(x+3)\\\\\Rightarrow\ -1=x+3\\\\\Rightarrow\ x=-1-3=-4 \ \ \ [x\neq3][/tex]

Hence, the solution is : x=-4

The correct option is B.

Complete question is;

Two separate bacteria populations grow each month and are represented by the functions f(x) = 3^(x) and g(x) = 7x + 6. In what month is the f(x) population greater than the g(x) population?

A. Month 1

B. Month 2

C. Month 3.

D. Month 4

Answer:

Option D: Month 4

Step-by-step explanation:

We are given the functions;

f(x) = 3^(x)

And g(x) = 7x + 6

We want to find the month when f(x) > g(x)

Thus;

3^(x) > 7x + 6

For option A, month 1 means x = 1.thus;

LHS is 3¹ = 3

RHS = 7(1) + 6 = 13

Our LHS is not greater than RHS as the question demands, thus this option is not correct

For option B, month 2 means x = 2. thus;

LHS is 3² = 9

RHS = 7(2) + 6 = 20

Our LHS is not greater than RHS as the question demands, thus this option is not correct

For option C, month 3 means x = 3. thus;

LHS is 3³ = 27

RHS = 7(3) + 6 = 27

Our LHS IS equal to the RHS and not greater than RHS as the question demands, thus this option is not correct

For option D, month 4 means x = 4. thus;

LHS is 3⁴ = 81

RHS = 7(4) + 6 = 34

Our LHS is greater than RHS as the question demands, thus this option is correct

If Summer (starting from rest) runs from the 20 m mark to the 35 m mark with an acceleration of 5 m/s². then 12.25 m/s is the final velocity.

Velocity is the distance covered by an object in unit time.

Given that,

Summer (starting from rest) runs from the 20 m mark to the 35 m mark with an acceleration of 5 m/s²

a=0.5 m/s²

s is distance=35-20=15

We have a formula with velocity, acceleration and distance

Now v²=2as

Here v is velocity=2

a is acceleration=5

s is the distance.=15

v²=2×5×15

The multiplication value of 2×5×15 is 150.

v²=150

Take square root on both sides

v=√150

v=12.25 m/s

Therefore final velocity is 12.25m/s.

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Answer: x=9 and y=9

Step-by-step explanation: Y is in the same spot as x! Good luck! :D

Answer:

3 to 1

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original, that is

OA' : OA

= 27 : 9 ( divide both parts by 9 )

= 3 : 1

Answer:

x = 11, arc RB = 150°

Step-by-step explanation:

The secant- secant angle RDB is calculated as half the difference of its intercepted arcs, that is

∠ RDB = [tex]\frac{1}{2}[/tex] ( RB - EC ), that is

5x - 10 = [tex]\frac{1}{2}[/tex] ( 13x + 7 - 60 )

Multiply both sides by 2 to clear the fraction

10x - 20 = 13x - 53 ( subtract 13x from both sides )

- 3x - 20 = - 53 ( add 20 to both sides )

- 3x = - 33 ( divide both sides by - 3 )

x = 11

Thus

arc RB = 13x + 7 = 13(11) + 7 = 143 + 7 = 150°

Answer:

32 Divided by 34?

Step-by-step explanation:

That good?

Answer:

42 feet of string

Step-by-step explanation:

First, draw a diagram of the string, the height and the angle.

the length of the string is equal to the hypotenuse of the triangle

let length of the string=x

sin(θ)=opp/hyp

sin(72°)=40ft/x

x=40ft/sin(72°)

x=42.05848897ft≈42ft

Answer:

yes

Step-by-step explanation:

good job, it's correct.

Answer:

x = 16√3

y = 8√3

z = 24

Step-by-step explanation:

From the figure attached,

By applying cosine rule in ΔABD,

cos(45°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{1}{\sqrt{2} }=\frac{z}{24\sqrt{2} }[/tex]

z = 24

By applying sine rule in ΔABD,

sin (45°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{1}{\sqrt{2} }=\frac{AD}{24\sqrt{2} }[/tex]

AD = 24

By tangent rule in ΔADC,

tan(60)° = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

[tex]\sqrt{3}=\frac{AD}{DC}[/tex]

[tex]\sqrt{3}=\frac{24}{y}[/tex]

y = 8√3

Similarly, by sine rule in ΔADC,

sin(60°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{\sqrt{3} }{2}= \frac{AD}{AC}[/tex]

[tex]\frac{\sqrt{3} }{2}= \frac{24}{AC}[/tex]

AC = 16√3

x = 16√3

Answer:

$27.30

Step-by-step explanation:

$4.80×5=$24.00+$3.30=$27.30

Answer:

D.

Step-by-step explanation:

Compared to the others, it looks that steepest

Answer:

D by looking at it, it looks steeper

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Answer:

x ≈ - 5.32, x ≈ 1.32

Step-by-step explanation:

x² + 4x - 7 = 0 ( add 7 to both sides )

x² + 4x = 7

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(2)x + 4 = 7 + 4

(x + 2)² = 11 ( take the square root of both sides )

x + 2 = ± [tex]\sqrt{11}[/tex] ( subtract 2 from both sides )

x = - 2 ± [tex]\sqrt{11}[/tex]

Thus

x = - 2 - [tex]\sqrt{11}[/tex] ≈ - 5.32 ( to 2 dec. places )

x = - 2 + [tex]\sqrt{11}[/tex] ≈ 1.32 ( to 2 dec. places )

Answer:

x = -5.32, x = 1.32

Step-by-step explanation:

Ok. So to use the Complete the Square method, you divide the middle value by 2 and then square the number you get. This will give:

[tex](x^{2} + 4x + (\frac{4}{2}) ^2) - (\frac{4}{2}) ^2 -7 = 0[/tex]

[tex](x^{2} + 4x + 4) - 4 -7 = 0[/tex]

[tex](x^{2} + 4x + 4) - 11 = 0[/tex]

[tex](x^{2} + 4x + 4) = 11[/tex]      (now factor the left side)

[tex](x + 2)(x + 2) = 11[/tex]

[tex](x + 2)^{2} = 11[/tex]       (now square root both sides)

[tex]\sqrt{(x + 2)^{2}} = \sqrt{11}[/tex]

[tex]x + 2 = \sqrt{11}[/tex]

[tex]x = - 2 +/- \sqrt{11}[/tex]         (+/- = plus or minus)

x = -5.32, x = 1.32

Answer:21

Step-by-step explanation:1-63=90

Answer:

21

Hope this helps! :)

Answer:

93.99

Step-by-step explanation:

sin rule is:

sin A ÷ a = sin B ÷ b = sin C ÷ c

A B C are angles

a b c are the lengths opposite to each angle

to find angle opposite to x:

180- (90+57) = 33°

180: sum of angles in a traingle

90: since its a right angle traingle

to find x:

sin 57 ÷ 41 = sin 33 ÷ x

rearrange:

x= (sin 33 x 41) ÷ sin 57

x= 93.99 (2 d.p/2 decimal places)

Step-by-step explanation:

arccos(sin(5π/4))

= arccos(sin(-π/4))

= arccos(-√2/2)

= 3π/4.

The value of trigonometric function arccos(sin(5π/4)), π/4

Trigonometry is a branch of mathematics, which deals with the study of right angle triangles. Trigonometry is concerned with specified functions of angles and their applications to calculations.

There are 6 commonly used functions in trigonometry with their name and abbreviations-

sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), cosecant (cosec)

First, we can use the trigonometric identity sin(θ) = cos(π/2 - θ) to rewrite this expression:

sin(5π/4) = cos(π/2 - 5π/4)

Next, we can use the fact that cos(x) is an increasing function on the interval [0, π], so cos(x) is unique on this interval for each value of x.

This means that the inverse cosine function, arccos, is also unique on the interval [0, π].

Therefore, we can conclude that:

0 ≤ π/2 - 5π/4 ≤ π

arccos(sin(5π/4)) = π/2 - 5π/4 = π/4.

So the answer is π/4 in radians.

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this is the best thing i could find for you, good luck with your question,

5x is greater than or equal to -25

The product of 5 and a number is at least –25

we convert the given statement into inequality

product means multiplication

Let x be the unknown number

product of 5 and a number is 5x

5x is at least -25

For word at most we use <=

for word at least we use >=

So the expression becomes 5x <= -25

Answer:

7

Step-by-step explanation:

2-8÷-2-3-12÷-6×-2

2 - -4 - 3 - 2 x -2

2 + 4 + -3 - -4

6 + -3 + 4

3 + 4

7 :)

Answer:

88

Step-by-step explanation:

88 Degrees

Answer:

92

Step-by-step explanation:

Corresding angles

Answer:

Is a consistent independent system

Step-by-step explanation:

we know that

If a system has at least one solution, it is said to be consistent .

If a consistent system has exactly one solution, it is independent .

If a consistent system has an infinite number of solutions, it is dependent

If a system not have solution, it is said to be inconsistent

In this problem we have

----> equation A

----> equation B

Solve the system by graphing

The solution is the intersection point both graphs

The solution is the point (7.5,-20.5)

see the attached figure

therefore

Is a consistent independent system

Answer: Choice C  [tex]-3x+2y \ge 7[/tex]

===================================================

Explanation:

The boundary line is solid, so that means we'll be dealing with "or equal to" as part of the inequality sign. The answer is between choice A and choice C because of this.

Note how the point (0,0) is not in the shaded region. This must mean that plugging x = 0 and y = 0 into the answer will lead to a false statement.

If we plug x = 0 and y = 0 into choice A, then we get...

[tex]3x-2y \le 7\\\\3(0)-2(0) \le 7\\\\0 \le 7\\\\[/tex]

Which is a true statement, implying that (0,0) is in the shaded region. However, we're after a false statement, so we can rule out choice A.

The answer must be choice C

Let's plug (x,y) = (0,0) into choice C

[tex]-3x + 2y \ge 7\\\\-3(0) + 2(0) \ge 7\\\\0 \ge 7\\\\[/tex]

That is false because 0 is not equal to 7, nor is it larger than 7.

This helps confirm that choice C is the answer.

Answer:

C it c because i took the test

Step-by-step explanation:

Answer:

₹ 1920

Step-by-step explanation:

Since the room is cubical in nature, we will find the total surface area of the room

Total surface area of the cubical room = 6L²

L is the length of one side of the room

Given

L = 4m

Total surface area of the cubical room = 6(4)²

Total surface area of the cubical room = 6×16

Total surface area of the cubical room = 96m²

If the painting costs ₹ 20/m², this means;

₹ 20 = 1m²

For the total room:

x = 96m²

Divide both expressions

20/x = 1/96

x = 20×96

x = 1920

Hence the total cost of painting the room ₹ 1920

Answer:

The radius of the hole is 0.24 feet

Step-by-step explanation:

Firstly, we need to convert the miles to feet

Mathematically;

1 mile = 5,280 feet

4.3 miles is thus;

4.3 * 5,280 = 22,704 feet

Mathematically, the volume of a cylinder is;

V = pi * r^2 * h

here, we want to get r

4200 = 3.142 * r^2 * 22,704

r^2 = 4200/(3.142 * 22,704)

r = 0.24 feet

Answer:

The one on the graph

Step-by-step explanation:

Answer:

The prime factorization of 56 is 2 * 2 * 2 * 7. This can also be written with exponents as 2^3 * 7.

Step-by-step explanation:

Answer:  1. [tex]456\div2 =228[/tex] 2. [tex]538\div7=76.85[/tex]

Step-by-step explanation:

The given division problems :

[tex]1.\ 456\div2[/tex]

[tex]2.\ 538\div7[/tex]

By long division (see the attachment)

1. Divisor= 2

Dividend =456

Quotient = 228

Remainder =0

So, [tex]456\div2 =228[/tex]

2. Divisor= 7

Dividend = 538

Quotient =76.85

so, [tex]538\div7=76.85[/tex]