What is the value of x? x + 12 < 180

Answer:

a. 6km

b. 6.185 km

c. 18.37 km

Step-by-step explanation:

The question is on finding the distance of between two points

The general formulae is given by;

[tex]d= \sqrt{(X2-X1)^2+(Y2-Y1)^2}[/tex]

Where d is the distance

Given that;

1 unit on grid = 1.5 km

a. Finding distance between the library and Town A

A (-2,3)  and library (2,3)

[tex]d= \sqrt{(2- -2)^2  + (3-3)^2} \\\\= \sqrt{4^2} \\= 4[/tex]

Actual distance = 4 × 1.5 = 6 km

b. Distance between the library and Town B is

library (2,3)  and town B (1, -1)

[tex]d=\sqrt{(1-2)^2+ (-1-3)^2} \\\\\\d=\sqrt{-1^2 +-4^2}\\ \\\\d=\sqrt{1+16} \\\\\\d=\sqrt{17}  = 4.123[/tex]

Actual distance = 4.123×1.5 =6.185 km

c. First find the distance between Town B and Town C

Town B (1, -1) and Town C (-3,-2)

[tex]d=\sqrt{(-3-1)^2 + (-2--1)^2} \\\\d=\sqrt{-4^2 + -1^2} \\\\d=\sqrt{16+1} \\\\d=\sqrt{17} \\\\d=4.123[/tex]

Actual distance= 4.123×1.5 =6.185 km

Total distance traveled by Amelia = 6 +6.185 +6.185 =18.37 km

Answer:

- 56 - 7k

Step-by-step explanation:

Given

- 7(8 + k)

Each term in the parenthesis is multiplied by - 7

= (- 7 × 8) + (- 7 × k)

= - 56 + (- 7k)

= - 56 - 7k

To solve the expression -7(8 + k), the distributive property is used. Multiplying -7 to each of the terms within the parentheses yields -56 - 7k. This is an example of product multiplying monomials.

The given expression is -7(8 + k). To find the product, you should use the distributive property. This property states that the multipliers of a sum or difference, multiplied separately by each addend or minuend, sum to the product. So -7 * 8 gives -56 and -7 * k gives -7k. Hence, the expression becomes -56 - 7k. This process is a demonstration of product multiplying monomials.

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Answer:

n = - 3

Step-by-step explanation:

It's not cheating unless this question is from a quiz or test.

5+0.5(6n+14)=3                Subtract 5 from both sides.

5-5 + 0.5(6n+14) = 3 - 5   Combine

0.5(6n+14) = - 2                There are two ways to go. I prefer dividing by 0.5

0.5(6n+14)/0.5 = -2/0.5    Do the division

6n + 14 = - 4                      Subtract 14

6n+14-14= -4-14                 Combine

6n = - 18                             Divide both sides by 6

6n/6 = - 18/6                      Combine

n = - 3      

The solution to the equation 5+0.5(6n+14)=3 will be n = - 3      

WE are given the equation as;

5+0.5(6n+14)=3                

We need to find the value of n here;

Subtract 5 from both sides.

5-5 + 0.5(6n+14) = 3 - 5  

Combine

0.5(6n+14) = - 2                

0.5(6n+14)/0.5 = -2/0.5    

6n + 14 = - 4                      

6n+14-14= -4-14                

6n = - 18                            

Divide both sides by 6

6n/6 = - 18/6                      

n = - 3      

Therefore, the solution to the equation 5+0.5(6n+14)=3 is n = - 3      

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let's firstly convert the mixed fractions to improper fractions and then divide.

[tex]\bf \stackrel{mixed}{-4\frac{3}{5}}\implies \cfrac{-4\cdot 5+3}{5}\implies \stackrel{improper}{\cfrac{-23}{5}}~\hfill \stackrel{mixed}{1\frac{1}{5}}\implies \cfrac{1\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{6}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{-23}{5}\div \cfrac{6}{5}\implies \cfrac{-23}{\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\cdot \cfrac{\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{6}\implies \cfrac{-23}{6}\implies -3\frac{5}{6}[/tex]

Okay I'm assuming this is a mixed fraction -4 ⅗ ÷ 11/5

First step get rid of the mixed fraction.

4 multiplied by 5 is 20 then you add 3 and you get 23

Next step cross cancel

-23     times    11     equals   -23

 5                    5                     11

improper fraction so convert to mixed number

answer is -2 1/11    

if you're still confused lemme know

ANSWER

$28

EXPLANATION

The profit function is given as:

[tex]p(x) = - 2 {(x - 9)}^{2} + 100[/tex]

where x is the price of the T-shirt in dollars.

To find the profit on a T-shirt whose price is $15, we substitute x=15 into the function and simplify.

[tex]p(15) = - 2 {(15 - 9)}^{2} + 100[/tex]

We simplify to get:

[tex]p(15) = - 2 {(6)}^{2} + 100[/tex]

[tex]p(15) = -72+ 100[/tex]

[tex]p(15) = 28[/tex]

ANSWER

A. x-8

EXPLANATION

The given functions are:

[tex]f(x) = {x}^{2} - 11x + 24[/tex]

We factor this to get,

[tex]f(x) = (x - 8)(x - 3)[/tex]

and

[tex]g(x) = x - 3[/tex]

[tex]( \frac{f}{g} )(x) = \frac{f(x)}{g(x)} [/tex]

[tex]( \frac{f}{g} )(x) = \frac{ {x}^{2} - 11x + 24}{x - 3} \: for\: x \ne3[/tex]

[tex]( \frac{f}{g} )(x) = \frac{(x - 8)(x - 3)}{x - 3} [/tex]

Cancel the common factors to get,

[tex]( \frac{f}{g} )(x) = x - 8[/tex]

Answer: OPTION A

Step-by-step explanation:

You need to divide the function f(x) by the function g(x):

Then:

[tex](\frac{f}{g})(x)=\frac{x^2-11x+24}{x-3}[/tex]

Now, you need to simplify:

Factor the numerator. Find two numbers whose sum be -11 and whose product be 24. Theses numbers are -8 and -3. Then you get:

[tex](\frac{f}{g})(x)=\frac{(x-8)(x-3)}{x-3}[/tex]

Remember that:

[tex]\frac{a}{a}=1[/tex]

Then, you get that the expresson that is equal to  [tex](\frac{f}{g})(x)[/tex] is:

 [tex](\frac{f}{g})(x)=(x-8)[/tex]

In Bar Graphs;

- Bars have equal space

- One the y-axis, we have numbers & on the x-axis, we have data which can be anything.

In Histograms;

- Bars are fixed

- On the y-axis, we have numbers & and on the x-axis, we have data which in continuous & will always be number.

An easy way you can remember the difference is looking at the spaces of the bars.

A bar graph has gaps

A histogram has no gaps.

Answer:

Check attached graph

Step-by-step explanation:

Given equation is [tex]y=x-2[/tex].

Now we need to graph the given equation [tex]y=x-2[/tex].

To graph that we can find two points then join them by a straight line.

We are free to plug any number for x say x=0 and x=2

plug x=0

[tex]y=x-2=0-2=-2[/tex]

Hence first point is (0,-2).

plug x=2

[tex]y=x-2=2-2=0[/tex]

Hence first point is (2,0).

Now graph both points and joint them to get final graph as shown below.

If the parabola looks like an “n,” your vertex will be a maximum. If the parabola looks like a “u,” the vertex will be a minimum.

To determine if a vertex is a minimum or maximum, evaluate the behavior of the function at that point. If the function is increasing before the vertex and decreasing after, it is a minimum point. If the function is decreasing before the vertex and increasing after, it is a maximum point.

In mathematics, a vertex is a point where two or more lines, curves, or edges meet. When determining if a vertex is a minimum or maximum, we need to look at the behavior of the function or equation at that point.

If the function is increasing before the vertex and decreasing after the vertex, then the vertex is a minimum point. Conversely, if the function is decreasing before the vertex and increasing after the vertex, then the vertex is a maximum point.

For example, consider the parabola y = x^2. The vertex of this parabola is at (0, 0).

Since the parabola opens upwards and the function values increase on either side, the vertex is a minimum point.

Answer:

x = 3

Step-by-step explanation:

Only one of the choices matches the given points:

x = 3

Answer:

See below in bold.

Step-by-step explanation:

Arrange in order first:

1 1 2 3 4 6 8 9 15

Median ( middle number) = 4.

Mode ( the number which occurs most) = 1.

Mean =  (1+1+2+3+4+6+8+9+15) = 49/9 = 5.4.

Range = 15 - 1 = 14.

List the numbers in order from smallest to largest:

1, 1 , 2, 3, 4, 6, 8, 9, 15

Median is the Middle value of the set = 4

Mode is  the number that appears the most = 1

Mean is the average add the numbers together and divide by the quantity of numbers:

1 + 1 +2 + 3+ 4+ 6 +8 + 9+15 = 49 / 9 = 5.44

Range is the difference between the largest number and smallest number: 15 -1 = 14

Answer:

8) h = 30

r = 16

l= 34

Surface Area= 2514.28

Volume= 8045.71

9) r = 12

h = 2

l = 5/2

Surface Area= 908.08

Volume= 298.42

Step-by-step explanation:

8)

h = 30

r = 16

l=?

Since its is right angled triangle, using pythogras theorem we can find the length of cone

l^2 = h^2 + r^2

l^2 = (30)^2 + (16)^2

l^2  = 900 + 256

l^2 = 1156

Taking square root on both sides

√l^2 = √1156

l = 34

Surface Area = [tex] [tex]\pi r(r+\sqrt{h^2+r^2} )[/tex][/tex]

π = 22/7, r = 16, h=30

Surface Area = [tex]=\frac{22}{7}* 16(16+\sqrt{(30)^2+(16)^2})\\=\frac{22}{7}* 16(16+34)\\=\frac{22}{7}* 800\\=2514.28[/tex]

Volume = [tex]\pi r^2\frac{h}{3}[/tex]

π = 22/7, r = 16, h= 30

Volume = [tex]\frac{22}{7} * (16)^2 *\frac{30}{3}\\=\frac{22}{7} * 256 *10\\= 8045.71[/tex]

9)

r = ?

h = 2

l = 5/2

Since its is right angled triangle, using pythogras theorem we can find the radius of cone

l^2 = h^2 + r^2

(5/2)^2 = (30)^2 + (r)^2

25/4  = 900 + r^2

r^2 = 900 * 4/25

Taking square root on both sides

√r^2 = √144

r = 12

Surface Area = [tex] [tex]\pi r(r+\sqrt{h^2+r^2} )[/tex][/tex]

π = 3.14, r = 12, h=2

Surface Area = [tex]=3.14* 12(12+\sqrt{(12)^2+(2)^2})\\=3.14* 12(12+12.1)\\=3.14* 289.2\\=908.08[/tex]

Volume = [tex]\pi r^2\frac{h}{3}[/tex]

π = 22/7, r = 12, h= 2

Volume = [tex]3.14 * (12)^2 *\frac{2}{3}\\=3.14 * 144 *0.66\\= 298.42[/tex]

Answer:

8) h = 30

Step-by-step explanation:

ANSWER

1. No real roots

2. [tex] \frac{ 7\pm \: \sqrt{33} }{ - 4}[/tex]

3. The discriminant is negative.

EXPLANATION

1. The given equation is

[tex] - 2 {x}^{2} - 9x - 5 = 0[/tex]

We have a=-2,b=-9 and c=-5.

The discriminant is given by:

[tex]D= {b}^{2} - 4ac[/tex]

[tex]D= {( - 9)}^{2} - 4( - 2)( - 5)[/tex]

This simplifies to:

[tex]D= 36 - 40 = - 4[/tex]

Since the discriminant is less than zero, the quadratic equation has no real roots.

2. The given equation is:

[tex] - 2 {x}^{2} - 7x - 2= 0[/tex]

We have a =-2, b=-7 and c=-2.

The roots of this equation are given by;

[tex]x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

We plug in the values to get;

[tex]x = \frac{ - - 7\pm \: \sqrt{ {( - 7)}^{2} - 4( - 2)( - 2) } }{2( - 2)} [/tex]

[tex]x = \frac{ 7\pm \: \sqrt{33} }{ - 4} [/tex]

3. The given graph is hanging downwards. This means that it doesn't have x-intercepts.

Therefore the roots are complex or imaginary.

This implies that, the discriminant of the corresponding equation is negative.

The area of the rectangular field given the dimensions of the field is 5000m^2.

a + b = 150 equation 1

a = 2b equation 2

Where:

a = length

b = width

Subsiture for b in equation 1 using equation 2

2b + b = 150

3b = 150

b = 50m

a = 2 x 50

q = 100m

Area = length x width

100 x 50 = 5000 m^2

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The rectangular field is found to be 5000 square meters. Option (1) 5000 m² is the correct answer.

To find the area of a rectangular field given its perimeter and that the length is twice the width, follow these steps:

Lets do the math together.

3.5/2 to find the weight loss per week= 1.75.

We know that every week the friend will reduce her goal by 1.75.

15/1.75= 8.6.

This means that in 8.6 weeks the friend will lose 15 pounds.

I hope this Helps! :)

Hello there! It should take her 8.6 weeks.

Well, the question doesn't specify whether it wants how long it'll take her in weeks, months, or days, so let's go with weeks. To do this, find the unit rate by dividing the amount she lost by the number of weeks it took.

3.5 pounds ÷ 2 weeks = 1.75 pounds lost a week.

Now, divide the total she wants to loose (15 pounds) by the 1.75 pounds a week to see how many she looses in total.

15/1.75 = 8.57142... Which is a little over 8.5 weeks, so we can round up to 8.6 weeks.

To get the length of AC, you would add AB to BC

AB = 3x

BC = 2x +3

Add together:

3x + 2x +3 = 5x +3

The answer is A.

Answer:

x >  2

Step-by-step explanation:

Given

- 8x + 2x - 16 < - 5x + 7x ← simplify both sides

- 6x - 16 < 2x ( subtract 2x from both sides )

- 8x - 16 < 0 ( add 16 to both sides )

- 8x < - 16 ( divide both sides by - 8 )

Remembering to reverse the symbol as a consequence of dividing by a negative value.

x > 2

5 weeks

8×2.5=20

2×2.5=5

Answer: 1/16

Step-by-step explanation:

1/2 would become 8/16 so 9-8 equals 1 and then just add the denominator so 1/16

Answer:

a)

x≥3

b)

[tex]t<-\frac{7}{3}[/tex]

c)

y < 28

d)

x > 5/2

Step-by-step explanation:

a)

We have been given the following inequality;

4x-3≥9

add 3 to both sides of the equation,

4x-3+3≥9+3

4x≥12

divide both sides by 4,

x≥3

b)

We have been given the following inequality;

3(t+4)<5

we open the brackets on the left hand side,

3t + 12 <5

subtract 12 on both sides of the equation,

3t + 12 -12 <5-12

3t < -7

divide both sides by 3,

[tex]t<-\frac{7}{3}[/tex]

c)

We have been given the following inequality;

[tex]\frac{2y}{7}<8[/tex]

multiply both sides by 7,

2y < 56

divide both sides by 2,

y < 28

d)

5x + 4 > -3(x-8)

we open the brackets on the right hand side,

5x + 4 > -3x + 24

add 3x to both sides of the inequality,

5x + 4 + 3x > -3x + 24 + 3x

8x + 4 > 24

subtract 4 on both sides,

8x + 4 - 4 > 24 - 4

8x > 20

divide by 8 on both sides,

x > 5/2

Exponential form, would be the number of times X gets multiplied by itself.

(x)(x)(x)(x)  there are 4 x's, so the exponential form would be x^4

(x)(x)(x)(x) in exponential form can be written as

[tex]\rm \bold{x^4}}[/tex]

According to the properties of exponent with same base number the powers/exponents of the number are added

This can be simply expressed in the form as formulated in equation (1)

[tex]\rm a ^x \times a^y = a ^{x +y} ............(1)[/tex]

here a = base  number

x and y are the exponents of number  a  

According to the  given question same number "x" is multiplied 4 times

let  the given expression be represented by a variable "y"  

[tex]\rm y = x\times x \times x \times x ...........(2)[/tex]

Equation (2)  can be simply written as follows

[tex]\rm y = x^1 \times x^1 \times x ^1 \times x^1 \\y = x ^{(1+1+1+1)} \\\bold{y = x ^4}[/tex]

So we can conclude that (x)(x)(x)(x) in exponential form can be written as

[tex]\rm \bold{x^4}}[/tex]

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L=4 and s=5 I’m to lazy to type it out

Answer:

L= 4

S= 5

Step-by-step explanation:

Given in the question, L+s = 9

So

L= 9-s

Substituting the value of L in the following equation

1.5L + 0.9s = 10.5

1.5 (9-s) + 0.9s = 10.5

13.5 - 1.5s +0.9s = 10.5

13.5 - 10.5 = 1.5s - 0.9s

3= 0.6s

s= 5

Now substituting the value of s in the equation L+s=9, we get the following

L= 9-5

L=4

Check the picture below.

Answer:

See below.

Step-by-step explanation:

Either 3 packets of 6 pens  or

2 packets of 9 pens.

he could buy 3 packs of 6

or 2 packs of 9

Answer:

6x=90

Divide by 6 for 6x and 90

6x/6=90/6

x=15

Check answer by using substitution method

6x=90

6(15)=90

90=90

Answer is x=15

Answer:

Step-by-step explanation:

6x = 90                  Divide by 6

6x/6 = 90/6

x = 15

Answer:

$2

Step-by-step explanation:

Answer:$2.04

Step-by-step explanation:

Answer:

What's your question?

Answer:

Step-by-step explanation:

(6x - y)(2x - y + 2)=

= 12x^2 - 6xy + 12x - 2xy + y^2 - 2y

= 12x^2 - 8xy + 12x + y^2 - 2y

Answer:

B 12x2 – 8xy + 12x + y2 – 2y

Step-by-step explanation:

Answer:

A motor-powered bike has wheels that travel a linear distance of approximately 62.8 inches in one

revolution. What is the central angle the bike wheels turn through, in degrees, when the bike travels 2

inches?​

Step-by-step explanation:

PLEASE HELP!!

A motor-powered bike has wheels that travel a linear distance of approximately 62.8 inches in one

revolution. What is the central angle the bike wheels turn through, in degrees, when the bike travels 2

inches?​

The central angle the bike wheels turn through, in degrees when the bike travels 2 inches will be 11.46°.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

Area of the circle = πr² and the perimeter of the circle = 2πr where r is the radius of the circle.

The linear distance in one revolution = perimeter of a circle or wheel

Perimeter = 2πR

R = 62.8/(2π)

R = 9.99 = 10 inches.

When L = 2 inches the center angle will be as,

Ф = L/R

Ф = 2/10 = 0.2 radian

In degree → 0.2 × 180/π = 11.46°

Hence "The central angle the bike wheels turn through, in degrees when the bike travels 2 inches will be 11.46°".

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Answer: You should use dot plot.

Step-by-step explanation:

1. you should use a dot plot

(correct dot plot)

Its C

How many friends has three pencils?

3

20. dot plot, box plot, and histogram.