4x − 1 < 11 solve for x

Answer:

(3x+4)(2x-5)

Step-by-step explanation:

Factor by grouping.

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

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.

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

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:

-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:

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:

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:

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:

[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]

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:

  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:

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

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:

m= 0 /(−3np+v2 )

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:

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:

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 ;

https://brainly.com/question/25248189

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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:

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

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:

The population of Namibia in the years 1940, 1997, and 2005 was 371.2 , 1671.64 and 2064.74 respectively.

Step-by-step explanation:

Refer the attached figure

We will use equation calculator to find the equation of given plot

[tex]y = 483.36 \times e^0.0264x[/tex]

We are supposed to find the population of Namibia in the years 1940, 1997, and 2005.

x values are years

y values are population

For 1940, [tex]x = -10, y = y = 483.36 \times e^{0.0264(-10)} = 371.2[/tex]

For 1997, [tex]x = 47, y = y = 483.36 \times e^{0.0264 \times 47} = 1671.64[/tex]

For 2005,[tex]x = 55, y = y = 483.36 \times e^{0.0264 \times 55} = 2064.74[/tex]

Hence The population of Namibia in the years 1940, 1997, and 2005 was 371.2 , 1671.64 and 2064.74 respectively.

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:

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:

9 for part b 40 for part a

Step-by-step explanation:

if u do 5 times the numbers it gives u the product so 45 is 9 times 5 and 40 os 8 times 5

Answer:

Part A: 9 orange beads

Part B: 40 blue beads

Step-by-step explanation:

Notice that you need to have the proportion of blue beads always 5 times larger than the number of orange beads. therefore you need to complete the table following such pattern:

Part A:  for 45 blue beads, she needs to use : 45/5 = 9 orange beads

Part B: for 8 orange beads, she needs to use 8 * 5 = 40 blue beads

Answer:

6:30 pm

Step-by-step explanation:

Given the following :

Four machines give out a signal at intervals of 24 seconds, 27 seconds, 30 seconds and 50 seconds respectively.

Time when all four machines gave out signal simultaneously = 5:00 pm

To find the time all four will give out the next simultaneous signal :

Take the lowest common factor of the four intervals :

L. C. M of 24, 27, 30, 50

Using the Lowest Common Multiple calculator :

L. C. M. = 5400

5400 seconds.

Adding 5400 seconds to the last time a simultaneous signal was produced :

5:00 pm + 5400 seconds

5400 seconds = (5400/60) = 90 minutes = 1hour 30 minutes

5:00 pm + (1 hour 30 minutes)

= 6:30 pm

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

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:

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:

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

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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!

Answer:

Equations:

a + b = 19

a = b + 2

a = Money that spent Laura

b = Money that spent Laureen

then:

(b+2) + b = 19

2b + 2 = 19

2b = 19-2

2b = 17

b = 17/2

b = 8.5

a = b + 2

a = 8.5 + 2

a = 10.5

Check:

10.5 + 8.5 = 19