Which of the following equations has only one solution?
x2 + 4x + 4 = 0
x2 + x = 0
ox²-1=0

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Explanation:

I'll use x in place of n

Let y = x^2 - 4x + 5

If we complete the square, then,

y = x^2 - 4x + 5

y = (x^2 - 4x) + 5

y = (x^2 - 4x + 4 - 4) + 5

y = (x^2 - 4x + 4) - 4 + 5

y = (x-2)^2 + 1

The quantity (x-2)^2 is never negative as squaring any real number value is never a negative result. Adding on 1 makes the result positive. So y > 0 regardless of whatever x is. Replace x with n, and this shows how n^2 - 4n + 5 is always positive for any integer n.

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You could also use the quadratic formula to find that x^2 - 4x + 5 = 0 has no real solutions, so there are no x intercepts. Either the graph is entirely above the x axis or it is entirely below the x axis.

Plug in any x value you want, say x = 0, and the result is positive. Meaning that whatever x value you plug in will be positive (as the graph can't cross the x axis to go into negative territory)

Answer:

The discount allowed per bag is kshs 4

while the discount allowed on all the 300 bags is kshs 1,200

Step-by-step explanation:

Here, we are interested in calculating the discount allowed on the sales of the bag of maize.

From the question, we are told that the sales man allowed a discount of 0.2% on the maize sold.

Now, to find the amount of this, we proceed as follows;

What we simply need to do is to find 0.2% of the each of the price of the maize bags, and then we can proceed to find the total discount given on all maize bags sold.

The discount on each bag of maize would be;

0.2% of kshs 2000

That would be;

0.2/100 * 2,000 = 400/100 = kshs 4

Since there are 300 bags, the total amount of discount allowed is 300 * kshs 4 = kshs 1,200

Answer:

please mark my answer brainliest

Step-by-step explanation:

- 2a -12

Answer:

  y = 5x

Step-by-step explanation:

The revenue (y) is 5 dollars for each car washed. The number of cars washed is x, so the revenue equation is ...

  y = 5x

_____

Additional comment

At the end of the exercise of writing revenue and cost and profit equations, you will find that the break-even number of cars is the ratio of fixed cost (start-up cost in this case) to the profit contribution of each car (per-car charge in this case). That is, it will take 75/5 = 15 cars to break even. Each additional car will contribute a positive profit.

Answer:

Equation INCLUDING the setup cost:   y = 5x - 75

Equation EXCLUDING the setup cost:   y = 5x

Step-by-step explanation:

It spent a total of $75 to set up the car wash.

It is charging $5 per car.

y = amount collected in $

x = number of cars washed

=> We can make an equation INCLUDING the setup cost and EXCLUDING the setup cost.

=> INCLUDING the setup cost.

=> y = 5x - 75

=> I subtracted 75 from 5x because they spent a total of $75 to set up the car wash.

=> I wrote 5x because they get $5 for each car so if they wash 10 cars they get 5 * 10 = $50.

An EXAMPLE  from the above equation:

y = 5x -75

=> y = 5*14 - 75

=> y = 70 - 75

=> y = -5

=> This means that if they wash 14 cars, they still have a debt of 5 dollars.

An equation EXCLUDING the setup cost will look like:

=> y = 5x

I wrote this because, they didn't spend any money so they will get 5 dollars per car. How many cars they wash, the answer will be 'number of cars x 5'.

An EXAMPLE from the above equation is:

=> y = 5x

=> y = 5 * 14

=> y = $70

=> This means that if they wash 14 cars, they get $70.

Answer:

option 2 with radius of 1.4 in, and height of 1.2 in.

Step-by-step explanation:

If two cylinders are similar, the ratio of one cylinder's radius to its height must be the same as that of the other.

To know which cylinder is similar to the given cylinder with radius 2.8 in and height of 2.4 in, find the ratio, and compare with the ratio of the options provided. The option with the same ratio, is the cylinder that is similar.

This,

The given cylinder => radius : height = [tex] \frac{2.8}{2.4} = \frac{0.7}{0.6} = \frac{7}{6} [/tex]

First option:

Radius : height = [tex] \frac{1.8}{1.4} = \frac{0.9}{0.7} = \frac{9}{7} [/tex]

Second option:

Radius : height = [tex] \frac{1.4}{1.2} = \frac{0.7}{0.6} = \frac{7}{6} [/tex]

Third option:

Radius : height = [tex]\frac{5.6}{4.2} = \frac{0.8}{0.6} = \frac{0.4}{0.3} = \frac{4}{3}[/tex]

Fourth option:

Radius : height = [tex] \frac{2.4}{2.8} = \frac{0.6}{0.7} = \frac{6}{7} [/tex]

The correct option with the cylinder that is similar with the given cylinder is option 2 with radius of 1.4 in, and height of 1.2 in.

Answer:

  all reals

Step-by-step explanation:

Simplified, you have ...

  20 -3n = 20 -3n

The equation is a tautology, true for all values of n.

The solution set is "all reals."

Answer:

Value of x is 8

Step-by-step explanation:

Given:

[tex]\sqrt{\frac{896z^{15}}{225z^6} }=\frac{xz^4}{15} \sqrt{14z}\\\\Computation: \\\\From\ squaring\ both\ side\\\\ {\frac{896z^{15}}{225z^6} }=\frac{x^2z^8}{225} ({14z})\\\\896z^9=14x^2z^9\\\\896=14x^2\\\\64=x^2\\\\x = 8[/tex]

So, Value of x is 8

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Hi my lil bunny!

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Let's solve your equation step-by-step.

[tex]2x-3x+5=18[/tex]

Step 1: Simplify both sides of the equation.

[tex]2x-3x+5=18\\2x + -3x + 5 = 18[/tex]

[tex]( 2x + -3x ) + ( 5) = 18[/tex] (Combine Like Terms)

[tex]-x + 5 = 18\\-x + 5 = 18[/tex]

Step 2: Subtract 5 from both sides.

[tex]-x + 5 - 5 = 18 - 5 \\-x = 13[/tex]

Step 3: Divide both sides by -1.

[tex]\frac{-x}{-1} = \frac{13}{-1} \\x = -13[/tex]

Answer : [tex]\boxed {x = -13}[/tex]

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Have a great day/night!

❀*May*❀

Answer:

Step-by-step explanation:

[tex] \mathsf{2x - 3x + 5 = 18}[/tex]

Collect like terms

[tex] \mathsf{ - x + 5 = 18}[/tex]

Move constant to R.H.S and change it's sign

[tex] \mathsf{ - x = 18 - 5} [/tex]

Calculate the difference

[tex] - x = 13[/tex]

Change the signs on both sides of the equation

[tex] \mathsf{x = - 13}[/tex]

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

[tex] \blue{ \mathsf{verification}}[/tex]

[tex] \mathsf{LHS \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: RHS}[/tex]

[tex] \mathsf{2x - 3x + 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 18}[/tex]

[tex] \mathsf{ = 2 \times ( - 13) - 3 \times ( - 13) + 5}[/tex]

[tex] \mathsf{ - 26 + 39 + 5}[/tex]

[tex] \mathsf{ = 13 + 5}[/tex]

[tex] = 18[/tex]

Thus, LHS = RHS

hope I helped!

Best regards!

Do you mean 32/192 or 192/32 because 32/192= 0.1666 where 192/32= 6

Answer:

1/6.

Step-by-step explanation:

32/192       Divide top and bottom by 8:

= 4 / 24       Now by 4:

= 1/6.

Answer: 7:55

Step-by-step explanation: in total the journey is 105mins so if she has to reach by 9:30. Then she has to leave her house 105mins before 9:30

[tex]8(9)+18[/tex]

$=8\cdot9+2\cdot9$

$=(8+2)\cdot9$

Answer:

x = -2

Step-by-step explanation:

To solve for x always get x on one side

First add 4 on each side, 4 + 7x - 4 = -18 + 4

Next subtract 18 from 4, making it -14    7x = -14

Now divide 7 on each side, x = -2

Answer:

y =( -1/2 )x + 2

Step-by-step explanation:

first step is to determine the slope of the line ( which is the rise over the run) or symbolically slope is defined as m= ∆x / ∆y, so plugging those values we get...

m= ∆x / ∆y = (-1 - 0) / (4 - 2) = -1 / 2

so next is to find the zero( y-intercept) of the function by ....

y = mx + b

y = ( -1/2)x + b (since m is equal to -1/2)

2 = ( -1/2)0 + b

2= b

Answer/Step-by-step explanation:

1. <B is an inscribed angle intercepting arc CA.

Therefore, m<B = ½*128 (inscribed angle theorem)

m<B = 64°

x = 180 - (m<B + m<A) (sum of angles in a triangle)

x = 180 - (64 + 43)

x = 180 - 107 = 73°

2. [tex] KH*HI = JH*HG [/tex] (intersecting chords theorem)

[tex] 10*x = 14*5 [/tex]

Solve for x

[tex] 10x = 70 [/tex]

[tex] \frac{10x}{10} = \frac{70}{10} [/tex]

[tex] x = 7 [/tex]

Answer:

Exact form:

25/9

Decimal form:

2.(7)

Mixed fraction form:

2 7/9

Step-by-step explanation:

Hope you found this helpful

Answer:

(-5/3)² = 25/9

Step-by-step explanation:

(a/b)ⁿ = aⁿ / bⁿ

(-5/3)² = -5² / 3² = 25 / 9

Answer:

The probability that a randomly selected person gets incorrect result is 2.2 × 10⁻⁴

Step-by-step explanation:

The parameters given are;

The accuracy of the test for a person who has the respiratory synctial virus = 97%

The accuracy of the test for a person who does not have the respiratory synctial virus = 99%

We have;

a = TP =

b = FP

c = FN

d = TN

a/(a + c) = 0.97

d/(d + b) = 0.99

a/(a + b) = 0.97*0.0055/(0.97*0.0055 + (1 - 0.99)*(1-0.0055))

PPV = 0.349 = 34.9%

Therefore, we have;

a/(a + c) = 0.97 and

a/(a + b)  =  0.349

0.97(a + c) =0.349(a + b)

(0.97 - 0.349)a = 0.349·b - 0.97·c

a = (0.349·b - 0.97·c)0.621

b × (1 - 0.0055) = (1 - 0.97)×(1 - 0.0055)

b = 1 - 0.97 = 0.03

Similarly,

c = 1 - 0.99 = 0.01

The proportion of the population that have false positive and false negative = 0.03 + 0.01 = 0.04 = 4%

The probability that a randomly selected person gets incorrect result = 0.04×0.0055 = 0.00022.

Answer:

0.01011

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

5+14a=9a-5

+5      +5

10+14a=9a

-9a      -9a

10+5a=0

-5a   -5a

10= -5a

÷5   ÷5

2= -a

*-1  *-1

-2=a

Answer:

B

Step-by-step explanation:

The greatest prime factor between 1 and 30 is 29. Remember that a prime number is a number whose only 2 factors is 1 and the number itself. To find out which number is a multiple of 29, all we have to do is divide it by 29, and if the quotient is a whole number then we have found our answer.

A: 1593 / 29 ≈ 54.93

B: 1247 / 29 = 43

We don't need to check C and D because we know that B is the answer.

1247 has the greatest prime factor between 1 and 30

The factor of a number that divides another number perfectly without leaving any remainder.  

For example, the factors of 12 are 1,2,3,4,6 and 12

A prime factor is a number that a prime number

A prime number is a number that can be divided only by 1 and that number

Prime numbers between 1 and 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29

The greatest prime factor between 1 and 30 is 29

To determine which number has the greatest prime factor, divide each of the numbers in the options by 29.

1593 / 29 = 54.9 (29 is not a prime factor of 1593)

1247/29 = 43 (29 is a prime factor of 1247)

1311 / 29 = 45.2  (29 is not a prime factor of 1311)

943 / 29 = 32.5  (29 is not a prime factor of 943)

To learn more about prime factors, please check: https://brainly.com/question/10371102?referrer=searchResults

Answer:

The corresponding point is (-8, -6).

Step-by-step explanation:

Given that

(-6,-6) lies on the graph of [tex]f(x)[/tex]

A function is represented in the form:

[tex]y = f(x)[/tex]

i.e. (-6,-6) means value of x = -6 is put and value y came out as -6.

[tex]f(-6) = -6[/tex]

Now, we have to find the corresponding point on [tex]f(\frac{3}{4}x)[/tex].

We know the value of [tex]f(-6)[/tex]

Let us find the value of x where [tex]\frac{3}{4}x[/tex] becomes equal to -6

[tex]\dfrac{3}{4}x=-6\\\Rightarrow 3x=-24\\ \Rightarrow x =-8[/tex]

So, let us put value of [tex]x = -8[/tex] in [tex]f(\frac{3}{4}x)[/tex]:

[tex]f(\frac{3}{4}\times (-8))\\\Rightarrow f(3\times (-2))\\\Rightarrow f(-6) = -6[/tex](as per given statement)

So, the corresponding point is (-8, -6).

Answer:

D

Step-by-step explanation:

Both are exponential decay.

Answer:

Step-by-step explanation:

f(0) = 24,  f(1) = 6 and f(2) = 0 means f(x) > 0 in (0,2)

and f(0) > f(1) > f(2) means f is decreasing in (0,2)

g(0) = 15 and g(2) = 0 means g(x) > 0 in (0,2)

and g(0) > g(2) means g is decreasing in (0,2)

Answer:

[tex]C=(x-32)\times\frac{5}{9}[/tex]

Step-by-step explanation:

The formula to convert the temperature in Fahrenheit to degrees Celsius is:

[tex]C=(F-32)\times\frac{5}{9}[/tex]

Here,

C = temperature in degrees Celsius

F = temperature in Fahrenheit

Suppose the boiling point for silver is x Fahrenheit, then then the temperature in degrees Celsius will be:

[tex]C=(x-32)\times\frac{5}{9}[/tex]

Answer:

P = 0,88          or       P  =  88 %

Step-by-step explanation:

The probability of having a married couple in nonadjacent desks is the total number of probabilities minus the probabilities of having them in adjacent places divide by total number of outcomes

The total possibilities (outcomes) of 9 elements in a row is:

P(₉) = 9!

P(₉) = 9*8*7*6*5*4*3*2*1

P(₉) = 362880

And the outcomes in which they are adjacent to each other is:

We consider them as one unit them we in this situation have 8 elements

P(₈) = 8!

P(₈) = 8*7*6*5*4*3*2*1

P(₈) = 40320

Then the probability that the married couple will have nonadjacent desks is:

P = P(₉)  -  P(₈) / P(₉)

P =  362880 - 40320 / 362880

P = 322560/ 362880

P = 0,88          or       P  =  88 %

Answer:

none of above .

Step-by-step explanation:

because the unit of area is always in square forms.

Answer:

m∠C = 102°

Step-by-step explanation:

This is a quadrilateral inscribed in a circle

The sum of opposite angles in a cyclic quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

We know what m∠B

We have external angles outside the circle.

m∠CDA is opposite m∠B

m∠CDA = 2 × m∠B

m∠CDA = 2 × 100°

m∠CDA = 200°

m∠CDA is the sum of m∠CD and m∠DA

m∠CDA = m∠CD + m∠DA

m∠DA = m∠CDA - m∠CD

m∠DA = 200° - 116°

m∠DA = 84°

m∠DAB is an exterior angle also, hence,

m∠DAB is the sum of m∠DA and m∠AB

m∠DAB = m∠DA + m∠AB

m∠DAB = 84° + 120°

m∠DAB = 204°

Finally we can solve for m∠C

m∠DAB is Opposite m∠C

So, m∠C = 1/2 × m∠DAB

m∠C = 1/2 × 204

m∠C = 102°

Answer:

The rectangular prism is 30 times larger than the cube.

Step-by-step explanation:

The Cube has a length of 2, a width of 2, and a height of 2.

Volume = length times width times height     or V=lwh

2 x 2 x 2= 8

The Rectangular prism has a length of 10, a width of 6, and a height of 4.

10 x 6 x 4= 240

240 divided by eight is 30.

Answer:

30 times larger than the cube.

Step-by-step explanation:

Answer:

three terms

Step-by-step explanation:

3x + 2y + 8z

Since we cannot simplify

There are three terms

3x, 2y, 8z

Answer:

m= 0 /(−3np+v2 )

Step-by-step explanation:

Answer:

fifth option

Step-by-step explanation:

Given

- 2(x - 5) ≤ 6x + 18 ← distribute left side

- 2x + 10 ≤ 6x + 18 ( subtract 6x from both sides )

- 8x + 10 ≤ 18 ( subtract 10 from both sides )

- 8x ≤ 8

Divide both sides by - 8, reversing the sign as a result of dividing by a negative quantity, thus

x ≥ - 1

A cube has sides that are all equal lengths .

Volume of a cube is S^3, where S is the length of the side.

Volume = 3^3 = 3 x 3 x 3 = 27 cubic inches.

The volume of box will be 27 inch³.

A square notepaper is stored in a cube shape box with an inside edge length of 3 inches.

We have to calculate the volume of the box.

What is the volume of a cube ?

The volume of a cube is the multiplication of the edge length (a) for three times i.e., a × a × a = a³ .

As per the question ,

Inside edge length of cube = 3 inches

So ,

the volume of box will be ;

= a × a × a

= 3 × 3 × 3

= 27 inch³

Thus , the volume of box will be 27 inch³.

To learn more about volume of cube click here ;

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Answer:

[tex]\frac{\pi }{10}[/tex] radians

Step-by-step explanation:

To convert degrees into radians, multiply the degrees with [tex]\frac{\pi}{180}[/tex].

If you have 18 degrees:

[tex]18*\frac{\pi}{180} = \frac{\pi }{10}[/tex]