Which equation represents a line which is parallel to the y-axis?
A.x=−4y
B.x=−8
C.y=x−3
D.y=−7

The smallest positive integer n will be 10 .

To find : the smallest positive integer n such that the rightmost digits of  n ! and ( n + 1 ) ! are same .

Since ,

putting n = 10 gives

n ! = 10 ! = 3628800

and ( n + 1 ) ! = 39916800

Last three digits ( rightmost digits ) ie. 800 are same .

Hence , n = 10 is the required answer ,

Therefore , the smallest positive integer is n = 10 such that the rightmost digits of  n ! and ( n + 1 ) ! are same .

To learn more on integers follow link :

https://brainly.com/question/14453211

#SPJ4

Answer:

the correct she answer should be 5

Step-by-step explanation:

The solution set for the given inequality is  {.......-4, -3, -2, -1, 0, 1, 2, 3}, so the for x=5 the inequality is false. Therefore, the correct answer is option B.

The given inequality is 5x+6≤2x+15.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Here, the inequality can be solved as follows

5x+6≤2x+15

Subtract 6 on both the sides of the inequality, we get

5x+6-6≤2x+15-6

5x≤2x+9

Subtract 2x on both the sides of the inequality, we get

5x-2x≤2x+9-2x

3x≤9

Divide 3 on both the sides of the inequality, we get

x≤3

Here, solution set is {.......-4, -3, -2, -1, 0, 1, 2, 3}

So, the for x=5 the inequality is false.

Therefore, the correct answer is option B.

To learn more about the inequalities visit:

https://brainly.com/question/20383699.

#SPJ6

The required probability for three numbers rolled on the dice are the sides of a triangle is 31/36.

The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability.

Here,

When three dice are rolled, there are 63=216 possible outcomes, or triplets (x, y, z).

Once more, in a triangle, any two sides added together are larger than the third side, or (x+y)>z.

As a result, 186 outcomes or triplets are possible and satisfy this property.

Hence, the required probability is 186/216=31/36.

The required probability is 31/36 for three dice rolls to produce triangle sides.

To know more about probability,

https://brainly.com/question/11234923?referrer=searchResults

#SPJ4

Answer:

144 cm²

Step-by-step explanation:

1.) Find the area of all of the faces

10*4=40 (Top Face)

4*8=32 (Bottom Face)

6*8*0.5=24 (One Triangle)

6*8*.5=24 (Other Triangle)

6*4=24 (Back Face)

2.) Add them all together to get the surface area

40+32+24+24+24= 144

***Don't forget the cm². Some teachers are really annoying about this

The possible number of license plates is 6084000 .

We have to make a 6 word license plate in which first two are letters and remaining four are digits.

conditions are :

1. letters and digits can repeat themselves

2. 1st digit can't be 0.

taking into account these conditions

we know total letters are 26 and total digits are 10 ( 0,1,2,3,4,5,6,7,8,9)

Now if we divide number plate in 6 columns where first two are filler by letters and rest four by digits so

1st column can be filled in ways = 26

2nd column can be filled in ways = 26

3rd column can be filled in ways = 9 ( as zero is not allowed )

4th column can be filled in ways = 10

5th column can be filled in ways = 10

6th column can be filled in ways = 10

therefore, total number of ways = 26x26x9x10x10x10

                                                      = 6084000 ways

The possible number of license plates is 6084000 .              

learn more about permutation here :

https://brainly.com/question/16937255

#SPJ4

The total volume of both cubed boxes, combined, is of:

612 cubic inches.

The volume of a cube of side length s is given by the side length s cubed, as shown by the formula presented as follows:

V = s³.

In this problem, the boxes are given as follows:

The volume of the box with side length 8 inches is given as follows:

V = 8³ = 512 cubic inches.

(measure is in inches, hence the cubed measure is in cubic inches).

The total volume is given by the sum of the volumes of the two boxes, hence:

Total volume = 512 cubic inches + 100 cubic inches = 612 cubic inches.

The image showing the cubes is given at the end of the answer.

More can be learned about the volume of a cube at https://brainly.com/question/1972490

#SPJ1

Answer:

(C.) 5/13

Step-by-step explanation:

The sine proportion is opposite / hypotenuse

Given the reference angle, the side measuring 5 units is the opposite side and the side measuring 13 units (and opposite of the right angle) is the hypotenuse

Thus, sine is 5/13

Michael drinks 33.5 fl oz more fluid ounces than Lydia.

Given in question,

30 ml = 1 fl oz

  1 ml = 1/30 fl oz

1 bottle = 335 milliliters

No. of bottles of water Michael drank = 6

                                                              = 6 * 335 milliliters

                                                              = 2010 milliliters

                                                              = 2010/30 fl oz

                                                              = 67 fl oz

No. of bottles of water Lydia drank = 3

                                                           = 3 * 335 milliliters

                                                           = 1005 milliliters

                                                           = 1005/30 fl oz

                                                           = 33.5 fl oz

Therefore, 67 - 33.5 = 33.5

Hence, Michael drinks 33.5 fl oz more fluid ounces than Lydia.

To learn more about fluid ounces here:

https://brainly.com/question/8500307

#SPJ1

The equation of the straight line, in point-slope form, is  

          [tex]y +3 = \frac{1}{4} ( x + 4)[/tex]

we have , the required line is perpendicular to the given line.

Also let us take any two coordinates of the given line , like  (-1 , 1 ) and  

( 0 , -3) . So the slope (m₁) of given line = [tex]\frac{y2 -y1}{x2 - x1 }[/tex]

                                      m₁ = -4

as the required line is perpendicular to the given line so , we know

for two perpendicular lines

                                   m₁  m₂ =  -1

therefore ,                 m₂ = 1/4

Now the required line passes through (-4,-3)

and the equation of straight line in point slope form is given by

                                               [tex](y_{} - y_{1}) = m (x - x_{1} )[/tex]

here m = 1/4

y₁ = -3

x₁  = -4

therefore the required equation  in point-slope form is

         y + 3 = 1/4 ( x +4 )

learn more about straight line here :

https://brainly.com/question/28951560

#SPJ4

answer:

100 text messages.

$50-$40 = $10

$10/$0.1 = 100

100 text messages

Given function:

y = |x − 3| + 1

Table:

x     y  

1     3

2    2

3    1

4    2

5    3

Here the vertex is (3,1).

Graph is in the image uploaded.

Learn more about the graph and function here:

https://brainly.com/question/9834848

#SPJ1

Answer: [tex]f^{-1}(x)=\frac{\sqrt{x}-1}{2}[/tex]

Step-by-step explanation:

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

[tex]x=(2y+1)^2\\\\\pm \sqrt{x}=2y+1\\\\-1 \pm \sqrt{x}=2y\\\\y=-\frac{1}{2} \pm \frac{\sqrt{x}}{2}[/tex]

Since the domain of the original function is the same as the range of the inverse, the rate of [tex]f^{-1}(x)[/tex] is [tex]f^{-1}(x) \geq -1/2[/tex]. This means we consider the positive case.

[tex]\therefore f^{-1}(x)=\frac{\sqrt{x}-1}{2}[/tex]

Marcus is accurate. Jeremy is wrong because he overlooked the negative sign in the equation's initial addend. Since -25 has a greater absolute value than 3, it is obvious that the sum should be negative.

Marcus is correct; the solution is -22.

The simplified expression is given as:

= -(5²)+ 3

= -(25) + 3

= - 22

The right response is this. Marcus saw the bracket or parentheses symbol when he condensed his sentence. This has major significance.

Jeremy scored 28. He squared -5 without noting that it was in a bracket or parenthesis, therefore his response is incorrect.

Consequently, Jeremy calculated this.

= -(5²) + 3

= 25 + 3

= 28

Jeremy gave a false response. He made a computation but failed to see the bracket.

To know more about Mathematical expressions, refer to this link:

https://brainly.com/question/14462529

#SPJ4

Complete Question

Marcus and Jeremy both evaluated the expression −(5²) + 3. Marcus said the answer was −22. Jeremy said the answer was 28. Who is correct? Explain the error in the other student’s work.

[tex]{\sf{ \frac{10}{50} = \frac{y}{125} \\ →50y = 10 \times 125 \\→ y = 25}}[/tex]

Please mark the brainliest if you like.

The value of x which makes the given expression 1/2(3x+4) = 1/2x true is -2

We have to simplify the given expression to find the value of x

1/2(3x + 4) = 1/2x

Cancel 1/2 from both sides

⇒ 3x + 4 = x

⇒ 2x = -4

⇒ x = -2

Hence, the value of x is -2 which makes the given expression true.

Learn more about value here

https://brainly.com/question/4806080

#SPJ1

When equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.

So, the equations are graphs are:

Now, graph both equations as follows:

Therefore, when equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.

Know more about graph equations here:

https://brainly.com/question/24696306

#SPJ13

The solution for g(7) in the piecewise function g(x) = (x + 1)(x - 5) is 16

From the question, we have the equation that can be used in our computation to be a piecewise function

This piecewise function is represented as g(x)

Also from the question, we have the following function that we are to compute

g(7)

This means that the value of x is 7, and we calculate g(x) when x = 7

To do this, we make use of an equation in the piecewise function, where the domain occupies x = 7

This domain is x c (2, oo)

And the function is

g(x) = (x + 1)(x - 5)

Substitute the known values in the above equation, so, we have the following representation

g(7) = (x + 1)(x - 5)

So, we have the following equation

g(7) = (7 + 1)(7 - 5)

There is no constant to add or subtract to both sides of the equation

Also, there is no factor to multiply or divide from both sides of the equation

So, we have the following representation

g(7) = (7 + 1)(7 - 5)

Solving further, we have

g(7) = 16

Hence, the solution is 16

Read more about piecewise function at

https://brainly.com/question/3628123

#SPJ1

Answer:

X=30

Step-by-step explanation:

[tex](4x + 30) + (2x - 30) = 180 \\ 4x + 2x + 30 - 30 = 180 \\ 6x = 180 \\ x = 30[/tex]

Answer:

x = 30

Step-by-step explanation:

We are told that:

• m∠A =  (4x + 30)°

• m∠B = (2x - 30)°,

and that these two angles are supplementary to each other.

When two angles are supplementary to each other, it means that they add up to 180°.

Therefore:

∠A + ∠B = 180°

⇒ (4x + 30)°  +  (2x - 30)° = 180°

⇒ 4x + 30 + 2x - 30 = 180

⇒ 4x + 2x + 30 - 30 = 180      [Combining like terms]

⇒ 6x = 180

⇒ [tex]\frac{6}{6}x = \frac{180}{6}[/tex]     [Dividing both sides of the equation by 6]

⇒ x = 30

Answer:

A=-3,b=1,C=19

Step-by-step explanation:

y-7=3(x+4)

we will just simplify the bracket like this

y-7=3x+12

y=3x+12+7

y=3x+19

y-3x=19

A=-3,b=1,C=19

if u find the answer correct mark as brainliest

The total interest that Magdalena's parents would have to pay to repay the loan is  $864.50

The interest that Magdalena's parents will pay per year is:

= Value of loan x Simple interest rate per year

= 2, 600 x 7%

= $182

To find the total interest paid, this amount should then be multiplied by the number of years it would take Magdalena's parents to repay the loan. 4 years and 9 months in years is:

= 4 + 9/12 months in a year

= 4 + 3 / 4

= 4 + 0.75

= 4.75 years

The total interest is:

= 4.75 x 182

= $864.50

Find out more on simple interest at https://brainly.com/question/20690803

#SPJ1

Considering the figure the required angle is solved using the vertical angle theorem. The values are

The problem is solved considering this theorems

vertical angle theorem

According to this theorem, when two straight lines cross, they create two sets of linear pairs and the vertical opposite angles are equal.

solution for the missing angle

x + 70 + 60 = 180 sum of angles of a triangle

x = 50

Using vertical angle theorem

? + 88 + 50  = 180 sum of angles of a triangle

? = 180 - 88 - 50

? =  42

solution for the missing angle

x + 75 + 30 = 180 sum of angles of a triangle

x = 75

Using vertical angle theorem

? + 88 + 75  = 180 sum of angles of a triangle

? = 180 - 85 - 75

? =  20

Learn more on angles here:

https://brainly.com/question/29322749

#SPJ1

The size if the angle NOM is 54.

What is angle?

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

What is tangent of circle?

A Tangent of a Circle is a line that touches the circle’s boundary at exactly one point. The tangential point is the place where the line and the circle meet.

Given,

M and N are points on a circle.

QMT is the tangent

O is the center.

angle NOM = 2 angle NLM

NOM = 2(27)

= 54.

To know more about angle and tangent of circle, visit:

https://brainly.com/question/11067500

#SPJ1

choose any 2 points on the graph

To calculate the slope use the formula:

slope = y (point 2)-y (point 1)/x (point 2)-x (point1)

substitute the choses points in

calculate your awnser

It will take 25 minutes for the two containers to have the same amount of water .

In the question ,

it is given that ,

water present in container A = 200L

water present in container B = 500L

rate at which the water is filling in container A= 6 liter/minute

rate at which the water is draining in container B = 6 liter/minute

let the time taken = m minutes ,

So , According to the question ,

the equation representing the situation is  

200 + 6m = 500 - 6m

Simplifying further , we get

6m + 6m = 500 - 200

12m = 300

m = 300/12

m = 25

Therefore , It will take 25 minutes for the two containers to have the same amount of water .

Learn more about Equations here

https://brainly.com/question/13304287

#SPJ1

Answer: the square root of twenty-four would be plotted (A) between 4 and 5, but closer to 5 on a number line.

Step-by-step explanation:

Answer:

y = [tex]\frac{7}{2}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{7}{2}[/tex] x + 6 ← is in slope- intercept form

with slope m = [tex]\frac{7}{2}[/tex]

• Parallel lines have equal slopes , then

y = [tex]\frac{7}{2}[/tex] x + c ← is the partial equation of line h

to find c substitute (- 2, - 3 ) into the partial equation

- 3 = - 7 + c ⇒ c = - 3 + 7 = 4

y = [tex]\frac{7}{2}[/tex] x + 4 ← equation of line h

Answer: 2176 cm^2 i think

Step-by-step explanation:

Answer:

60 cm

Step-by-step explanation:

we can use the Pythagorean theorem:

a^2 = b^2 + c^2 where a is the hypothenuse

so 68^2 = 32^2 + c^2

rearrange: 68^2 - 32^2 = c^2

so 4624 - 1024 = c^2

= 3600

square root of 3600 = 60

missing side = 60 cm

now, the assumption in this implicit differentiation is that "y" is really a function in x-terms, whilst "x" is just a simple variable

[tex]x^2y-3x=y^3-3\implies \stackrel{product~rule}{\left( 2xy + x^2\cdot \cfrac{dy}{dx} \right)}-3=\stackrel{chain~rule}{3y^2\cdot \cfrac{dy}{dx}} \\\\\\ 2xy-3=3y^2\cdot \cfrac{dy}{dx}-x^2\cdot \cfrac{dy}{dx}\implies 2xy-3=\cfrac{dy}{dx}(3y^2-x^2) \\\\\\ \left. \cfrac{2xy-3}{3y^2-x^2}=\cfrac{dy}{dx} \right|_{(-1,2)}\implies \cfrac{2(-1)(2)-3}{3(2)^2-(-1)^2}\implies -\cfrac{7}{11}[/tex]

The equation of the graph in the figure is f(x) = |x - 3| + 5

Given that the graph is an absolute value graph

We start by calculating the vertex of the graph

In this case, the graph has it minimum point located at the coordinate (3, 5)

This coordinate can then be interpreted as

(h, k) = (3, 5)

As a general rule, the general representation of the equation of an absolute value function is f(x) = |x - h| + k

Substitute the known values in the above equation

So, we have the following equation

f(x) = |x - 3| + 5

Hence, the equation of the graph is f(x) = |x - 3| + 5

Read more about absolute value functions at

brainly.com/question/3381225

#SPJ1