Solve the following system of equations . Plot the solution to the system on the provided graph

Answer:

x=12

Step-by-step explanation:

Solve for x:

(3 (x/6 + 16))/4 = (3 ((4 + 3/8) x - 21))/7

Put 4 + 3/8 over the common denominator 8. 4 + 3/8 = (8×4)/8 + 3/8:

(3 (x/6 + 16))/4 = (3 ((8×4)/8 + 3/8 x - 21))/7

8×4 = 32:

(3 (x/6 + 16))/4 = (3 ((32/8 + 3/8) x - 21))/7

32/8 + 3/8 = (32 + 3)/8:

(3 (x/6 + 16))/4 = (3 ((32 + 3)/8 x - 21))/7

32 + 3 = 35:

(3 (x/6 + 16))/4 = (3 ((35 x)/8 - 21))/7

Put each term in x/6 + 16 over the common denominator 6: x/6 + 16 = x/6 + 96/6:

3/4 x/6 + 96/6 = (3 ((35 x)/8 - 21))/7

x/6 + 96/6 = (x + 96)/6:

3/4 (x + 96)/6 = (3 ((35 x)/8 - 21))/7

3/6 = 3/(3×2) = 1/2:

(x + 96)/(2×4) = (3 ((35 x)/8 - 21))/7

Put each term in (35 x)/8 - 21 over the common denominator 8: (35 x)/8 - 21 = (35 x)/8 - 168/8:

(x + 96)/(2×4) = 3/7 (35 x)/8 - 168/8

(35 x)/8 - 168/8 = (35 x - 168)/8:

(x + 96)/(2×4) = 3/7 (35 x - 168)/8

2×4 = 8:

(x + 96)/8 = (3 (35 x - 168))/(8×7)

8×7 = 56:

(x + 96)/8 = (3 (35 x - 168))/56

Multiply both sides by 56:

(56 (x + 96))/8 = (56×3 (35 x - 168))/56

56/8 = (8×7)/8 = 7:

7 (x + 96) = (56×3 (35 x - 168))/56

(56×3 (35 x - 168))/56 = 56/56×3 (35 x - 168) = 3 (35 x - 168):

7 (x + 96) = 3 (35 x - 168)

Expand out terms of the left hand side:

7 x + 672 = 3 (35 x - 168)

Expand out terms of the right hand side:

7 x + 672 = 105 x - 504

Subtract 105 x from both sides:

(7 x - 105 x) + 672 = (105 x - 105 x) - 504

7 x - 105 x = -98 x:

-98 x + 672 = (105 x - 105 x) - 504

105 x - 105 x = 0:

672 - 98 x = -504

Subtract 672 from both sides:

(672 - 672) - 98 x = -672 - 504

672 - 672 = 0:

-98 x = -672 - 504

-672 - 504 = -1176:

-98 x = -1176

Divide both sides of -98 x = -1176 by -98:

(-98 x)/(-98) = (-1176)/(-98)

(-98)/(-98) = 1:

x = (-1176)/(-98)

The gcd of -1176 and -98 is -98, so (-1176)/(-98) = (-98×12)/(-98×1) = (-98)/(-98)×12 = 12:

Answer:  x = 12

Answer:

X=28

Step-by-step explanation:

3x-8=2x+20. So x=28

Answer:

The given sequence is neither arithmetic not geometric.

Step-by-step explanation:

A sequence is in arithmetic if it has a common difference.

i.e., a sequence a, b, c is in arithmetic if

b - a = c - b

Let's check if the given sequence is in arithmetic.

[tex]\frac{4}{3} -\frac{4}{9} =\frac{12}{9} -\frac{4}{9}[/tex]

[tex]= \frac{8}{9}[/tex]

[tex]4-\frac{4}{3} =\frac{12-4}{3}[/tex]

[tex]=\frac{8}{3}[/tex]

So, [tex]\frac{4}{3} -\frac{4}{9} \neq 4-\frac{4}{3}[/tex]

Hence, the given sequence is not arithmetic.

Let's check if the given sequence is in geometric.

A sequence is in geometric if it has a common ratio.

i.e., a sequence a, b, c is in geometric if

[tex]\frac{b}{a} =\frac{c}{b}[/tex]

[tex]\frac{4/3}{4/9} =\frac{4}{3} (\frac{9}{4} )[/tex]

= 3

[tex]\frac{4}{4/3} =4(\frac{3}{4} )[/tex]

= 3

Clearly, [tex]\frac{12}{4} =\frac{36}{12} =3[/tex]

But, [tex]\frac{0}{36} =0[/tex]

Therefore, the given sequence is not in geometric.

Hence, the given sequence is neither arithmetic not geometric.

Answer:

y-2 = 2/3(x-8)

Step-by-step explanation:

We have the line 6x-9y = -7

Let's rewrite it in the form y=mx+b

6x-9y = -7

Subtract 6x from each side

6x-6x-9y = -7 -6x

-9y = -6x-7

Divide by -9

-9y/-9 = -6x/-9 -7/-9

y = 2/3 x + 7/9

The slope is 2/3

If the line is parallel, the slope will be the same so the slope will be 2/3

We have the slope and a point (8,2) on the new line, so we can use the point slope form of a line

y-y1 = m(x-x1)

y-2 = 2/3(x-8)

use both points to find the slope

[tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{-13-3}{9-(-3)}[/tex]

[tex]\frac{-16}{12} =\frac{-4}{3} =slope[/tex]

Now, to find b, plug in one of the points in y=mx+b

3=[tex]\frac{-4}{3}[/tex](-3)+b

3=4+b

b= -1

therefore, your final equation should be,

y=[tex]\frac{-4}{3}[/tex]x-1

Answer:

x = 4

Step-by-step explanation:

4x+41=3x+45

Subtract 3x from both sides

x + 41 = 45

Subtract 41 from both sides

x = 4

Answer:

He paid $6,000 in taxes.

Step-by-step explanation:

His final amount after taxes is $24000.  In order to obtain this number we had to tax 20% of the total (Note that 100%-20%=80%).  In other words if he was taxed 20% he took home 80% of what he was paid.  Therefore mathematically we have:

[tex]0.8A_{pre-tax}=A_{taxed}[/tex]

Since we know he was left with $24000 after taxes then:

[tex]0.8A_{pre-tax}=24000\\\\\frac{0.8A_{pre-tax}}{0.8}=\frac{24000}{0.8}\\\\A_{pre-tax}=\frac{24000}{0.8}\\\\A_{pre-tax}=30000[/tex]

So originally he had $30,000.  So how much did he pay in taxes? We can calculate the difference of both pretax and after tax and we get:

$30,000 - $24,000= $6,000 taxed

Answer:

r= -5 , r= 17

Step-by-step explanation:

5|-6+r|=55

solve for 'r'

First we isolate absolute function

We divide both sides by 5

|-6+r| = 11

for absolute function we consider two cases, one with positive and one with negative. Now we make two equations

-6+r = 11   or -6+r = -11

Now solve both equations

-6 + r= 11

Add 6 on both sides

so , r= 17

-6 + r= -11

add 6 on both sides , so r= -5

Answer:

97/100

Step-by-step explanation:

9/10 = 90/100

90/100 + 7/100 = 97/100

Answer:

Step-by-step explanation:

lets say in the shown triangle x=165

so speed [tex]\frac{dx}{dt} =25[/tex]

and  [tex]\frac{dy}{dt} =35[/tex]

Also since distance = speed* time

time = pi minutes = pi/60 seconds

y = [tex]\frac{35\pi \pi }{60}[/tex]

y = [tex]\frac{7\pi }{12}[/tex]

Now using the pythagorean :

[tex]x^2+y^2=z^2\\so \\165^2+(\frac{7\pi }{12} )^2 =z^2[/tex]

derivate the equation so  we get :

[tex]x\frac{dx}{dt} +y\frac{dy}{dt} =z\frac{dz}{dt} \\[/tex][tex]165*25+35*\frac{7\pi }{12}=\sqrt{165^2+(\frac{7\pi }{12})^2} *\frac{dz}{dt}[/tex]

[tex]\frac{dz}{dt} =25.387[/tex] m/s

So Rate of change = 25.387 m/s

Answer:

0.707 to nearest thousandth

Step-by-step explanation:

People who go at least 2 times a month = 219 + 180 + 96

= 495

So the required probability = 495 / 700

= 0.707 14

The equation[tex]x^5 - y^5 = (x - y)(x^4 + x^3y + x^2y^2 + xy^3 + y^4)[/tex]  is a representation of the Difference of Powers formula in algebra. This formula can be proven accurate by expanding the expression on the right hand side and simplifying.

Your question essentially asks about the proof of a formula in algebra known as the Difference of Powers. This formula is applied when you have a difference of two terms, each raised to the same power.

Let us prove[tex]x^5 - y^5 = (x - y)(x^4 + x^3y + x^2y^2 + xy^3 + y^4):[/tex]

This demonstrates that the original formula you asked about is accurate.

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Answer:

y = [tex]\frac{1}{2}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

here m = [tex]\frac{1}{2}[/tex] and b = 4, hence

y = [tex]\frac{1}{2}[/tex] x + 4 ← equation of line

Answer:

where is the question?

Answer:

Step-by-step explanation:

35 x .08 = $2.80

35 + 2.80 = 37.80

Answer:

T = 0.08 × 35

Step-by-step explanation:

The cost of a jacket = $35

The tax rate on the jacket = 8% =  [tex]\frac{8}{100}[/tex]

                                           = 0.08

The expression to find the cost of the tax on the jacket would be

T = 0.08 × 35

Answer:

D

Step-by-step explanation: 1/3 x 3 = 1/9 same with 2/3

Answer:

B is the one here as well

Two lines perpendicular to a third line are parallel to each other because they both inherit the slope from their perpendicularity. The resulting lines only differ in their y-intercepts, indicating they run parallel.

The theorem you're referring to essentially relates to the slope of the lines. If two lines are each perpendicular to the same line, this means the slope of all three lines are related. This occurs because the slope of any line perpendicular to y=-1/3x is 3, the negative reciprocal of -1/3. For example, if we have two lines L1: y = 3x + b1 and L2: y = 3x + b2 which are both perpendicular to y= -1/3x (and thus parallel to each other), their formulas would only differ by their y-intercepts (b1 and b2). Since the coefficient of x (the slope) remains the same (3), we can conclude that these two lines are indeed parallel to each other which confirms the mentioned geometric theorem.

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Answer:

She gave away 24 cards

Step-by-step explanation:

(36)*([tex]\frac{2}{3}[/tex])=24

The distributive property: a(b + c) = ab + ac

Answer:

c) -3 · (6.48) = -3 · (6 + 0.4 + 0.08) = (-3 · 6) + (-3 · 0.4) + (-3 · 0.08)

Step-by-step explanation:

I would say B. The mean is a good measure of central tendency.

I hope this helps!

Answer:

2/25 chance for both.

Step-by-step explanation:

There is a total of 25 students = 25 as my denominator.

11 + 12 = 23.

25 -23 = 2

Therefore my numerator is 2.

----> 2/25

Answer:

40

Step-by-step explanation:

5+1 3/8n=60

Subtract 5

1 3/8n=55

11/8n=55

8/11(55/1)  

n=40

Answer:

D) x ≤ -2

Step-by-step explanation:

The dot is at -2 = -2

the dot is filled in = ≤ or ≥ because its means equal too

think of ≤ or ≥ like arrows = it points left.  

so its x ≤ -2

Note on using the  ≤ or ≥  like pointing arrows

this only works if its written:

variable <   constant form,

which is the way they are usually seen, like x < 5

but it could be 5 > x which means the > points the opposite way

Hello! :)

Answer:

D. x≤-2

*The answer must have a negative sign and less than or equal to.*

Step-by-step explanation:

Lesson: It's about the graphing inequalities

An inequality is a statement that compares mathematical expressions that are not equal. The expressions are separated by an inequality symbol (<,>, ≤, ≥, or ≠).

The arrow points to the left. The circle is closed.

Hope this helps!

Have a nice day! :)

:D

-Charlie

Thanks!

Answer: The answer is 12 days

Step-by-step explanation: miles total=miles per day times number of days

3000=250 times days

divide both sides by 250

12=days

30/2 =15. So 182 times 15 is 2730, or D.

Answer: -2,0,2,4,6

The solution of the inequality is x<1

Step-by-step explanation:

Answer:

x < 1

Step-by-step explanation:

2x < 2

Divide 2 on both sides

x < 1

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

Table: (I think)

-2 , 0 , 2 , 4 , 6

Answer:

B

Step-by-step explanation:

For a relationship to be a function

Each value of x in the domain can only have 1 unique value of y in the range. That is, one-to-one correspondence.

The only relation which meets this criteria is B

Answer:

The answer is option B: {(1,3);(-1,5);(2,7);(-2,7);(3,5);(-3,3)}

Step-by-step explanation:

Each element is composed of a first and second point, or by an 'x' and 'y' coordinates, respectively.  In this way, all x coordinate from the set of elements constitute the 'domain', and all y coordinates of the set of elements constitute the 'image'.

So, for a set of elements be a function, each point of the domain have to have one an only one image. In other words, two elements with the same image have to have a distinct x's coordinate.

If we take a look at the set of elements in the different options, we find different elements which repeat image:

1) The pairs (1,0) and (1,-1) in the set of point of option A

2) The pairs (-2,-1) and (-2,-2) in the set of point of option C

3) The pairs (1,3) and (1,3) in the set of point of option  

In the set of elements of B option, all the elements with the same y coordinate have different x's coordinates.

Answer:

The expression represents

[tex]a\geq\frac{1}{4}\times (10^{-2})[/tex] and solution is   [tex]a \geq 0.0025[/tex]  

Step-by-step explanation:

Given : Expression represents a number one fourth as great as [tex]10^{-2}[/tex]

To find : What is the expression?

Solution :

Let the number be 'a'.

According to question,

A number one fourth as great as [tex]10^{-2}[/tex]

i.e.  [tex]a\geq \frac{1}{4}\times (10^{-2})[/tex]

Now, we solve the expression

[tex]a \geq \frac{1}{4}\times\frac{1}{100}[/tex]

[tex]a \geq\frac{1}{400}[/tex]

[tex]a \geq 0.0025[/tex]

Therefore, The expression represents

[tex]a\geq\frac{1}{4}\times (10^{-2})[/tex] and solution is   [tex]a \geq 0.0025[/tex]

Answer:

x = .140741

Step-by-step explanation:

0.7(3x−0.2)=0.3(0.8−2x)

Distribute

.7 * 3x - .7*.2 = .3*.8 - .3 * 2x

2.1x - .14 = .24 - .6x

Add .6x to each side

2.1x +.6x -.14 = .24 -.6x+.6x

2.7x -.14 = .24

Add .14 to each side

2.7x -.14+.14 = .24+.14

2.7x = .38

Divide by 2.7 on each side

2.7x/2.7 = .38/2.7

x = .140741

Answer: The statement is false because 1.2 is calculating 120% of the cost of pizza. The expression should be .2p.

Step-by-step explanation:

The expression 1.2p correctly represents the total bill for a pizza including a 20% tip, with p representing the price of the pizza. To determine the total cost, you multiply the price by 1.20.

The expression 1.2p does indeed represent the total bill including a 20% tip for the delivery of a pizza where p is the cost of the pizza. When you give a tip of 20%, you are adding 20% of the cost of the pizza to the original price. This is calculated by multiplying the price by 1.20 (which is equivalent to 100% + 20%).

Example Calculation:

If the cost of the pizza is $10 (p = $10), then the total bill with a tip would be 1.2 × $10 = $12. The 20% tip on $10 is $2, so the total bill equals $10 + $2 = $12.