Here is an equation that is true for all values of x: 6(x + 3) = 6x + 18. Londyn saw this equation and says she can tell 18( x + 3) + 32 = 3(6x + 18) + 32 is also true for any value of x. How can she tell? Explain your reasoning.

The answer of the given fraction after simplification is 2.11.

To simplify simply means to make anything easier. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common components from the numerator and the denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.

Given fraction is:

= 3 * 3/9 + 2 * 10/18

By simplifying the given fraction, we get

=  3 * 1/3 + 10/9

= 1 + 1.11

= 2.11

The answer of the given fraction after simplification is 2.11.

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Answer:

Step-by-step explanation:

0 0. 4 0

9 3 3 8. 0 0

 − 0      

   3 8    

 −   0    

   3 8 0  

 − 3 7 2  

       8 0

     −   0

       8 0

0.40

2.45 is the answer to 9.3 divided by 3.8

We are asked to find how many deciliters can be found in 1 mililiter.

To get the solution we have to find the conversion factor. All we need to do is divide the volume by 100.

Here is a formula

This implies,

ANSWER: 0.01

To earn exactly $252, madison needs to work for 21 hours.

Time         money

worked      earned

5                    60

8                    96

12                  144

15                  180

We need to find how many hours should madison work to earn exactly $252

For 5 hours she earns $60

So in 1 hour she earns $ 60/5 = 12

For $1 she needs to work for 1/12 hour

For 252 she need to work for (1/12) 252

For 252 she need to work for 21

Therefore, to earn exactly $252, madison needs to work for 21 hours.

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The resultant answer of the given quadratic equation is x₁,₂ = -1 ± √61/6.

So, solve  3x²+x-5=0 as follows:

Now, evaluate as follows:

Therefore, the resultant answer of the given quadratic equation is x₁,₂ = -1 ± √61/6.

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Given the graphed equation:

Let's determine the point that represents a negative solution for x.

The solutions are the points where both lines meet.

From the graph, the solution which has a negative solution for x is:

(-2, -3)

In this point of intersection, the value of the x-coordinate is -3 (which is a negative value).

Therefore, the point which represents a negative solution for x is:

(-2, -3)

ANSWER:

(-2, -3)

$145.60 ---> 74%

x -------------> 100%

answer: $196.76 is the orginal price

Answer:

y = -x - 2

Step-by-step explanation:

Write an equation in slope-intercept form for the line with a slope of -1 and a y-intercept of -2.

slope-intercept form: y = mx + b where m = slope and b = y-intercept

when:

slope of -1

y-intercept of -2

then:

y = -1x + (-2)

y = -x - 2

Answer:

y= -x-2

Step-by-step explanation:

y=mx+b

slope=m

y intercept=b

m= -1

b= -2

input values of m and b to get equation:

y=(-1)x+(-2)

y= -1x-2

y =  -x-2

y= -x-2

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Answer:

40q7572928254949262618394938282920420

Answer: 19/24

Explanation:

From the information given,

Number of green marbles = 15

Number of red marbles = 9

Total number of marbles = 15 + 9 = 24

Probability is expressed as

number of favorable outcomes/number of total outcomes

Probability f selecting a greeen marble = 15/24

Even numbers divide 2 without a remainder. The even numbered marbles are

red = 2, 4, 6, 8

green = 2, 4, , 68, 10, 12, 14

Total number of even numbered marbles = 11

Probability of selecing an oevennumber = 10124

The events are not mutually exclusive becuse they can occur together. For two ebvents, A and B that are not mutually exclusive,

P(A U B) = P(A) + P(B) - P(A and B)

Thus,

the probability that the marble is green or even numbered = Probability of selecting a green marble + Probability of selecting an even number - Probability of selecting a green and even numbered marble

Number of green even numbere marble s = 7

Probability of selecting a green and even numbered marble = 7/24

Thus,

the probability that the marble is green or even numbered = 15/24 + 11/24 - 7/24

the probability that the marble is green or even numbered = 19/24

Regression

A) We can see the graph and through the data that the most indicated form is to find the regression model since there is not much uniformity among the data to describe it as a purely linear model.

Plotting that scatterplot, and generating the equation we know that the equation is:

Daphne makes 5 bows for every 3 feet of ribbon, this means that for every 3 feet increase in length of ribbon the bows increases by five. So,

For 3 feet, bows are 5,

For 6 feet bows are 10,

For 9 feet bows are 15,

For 12 feet bows are 20

For 15 feet bows are 25,

for 18 feet bows are 30,

For 21 feet bows are 35,

For 24 feet bows are 40.

For 27 feet bows are 45

For 30 feet bows are 50.

Thus option C is correct.

Solution:

The volume of a cylinder is expressed as

Given the cylindrical water tank below:

where

By substitution, we have

Hence, the volume of the cylindrical water tank, to the nearest whole number, is

The sample space which is the total possibilities is 4

Answer:

D

Step-by-step explanation:

The total commission is the number of laptops times the commission per laptop. Thus, [tex]c=39.95l[/tex].

Setting [tex]l=15[/tex], [tex]c=39.95(15)=599.25[/tex].

Let the number of professors be x.

If there are 16 times as many students as professors, then the number of students will be:

If the number of students and professors is 42,500, then we have that:

Solving by dividing both sides by 17, we have:

Hence, we can calculate the number of students in the college to be:

Therefore, there are 40,000 students in the college.

Answer: I believe that the BP segment is equal to BP segment because of the reflexive property.

Step-by-step explanation:

The required reason is that segment BP is congruent to segment BP that  Segment BP is the common side among both triangles.

In congruent geometry, the shapes that are so identical. can be superimposed on themselves.

Here,
The necessary explanation is that segment BP and segment BP are congruent because segment BP is the common side of both triangles BPS and BPY, as shown in the figure.

Thus, the required reason is that segment BP is congruent to segment BP and that  Segment BP is the common side among both triangles.

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The relative extrema of the function  f(x) = x³ + 4x² - x - 4 is at

( [tex]-\frac{4+\sqrt{19}}{3} ,\frac{56+38\sqrt19}{27}[/tex] )and the graph of the function is attached below.

The given function is f(x) = x³ + 4x² - x - 4

For the relative extrema we will first have to find the first derivative of the function:

f'(x)  = 3x² + 8x - 1

Now for4 the function to have an extremum, f'(x) = 0

3x² + 8x - 1 = 0

Solving we get :

the values of x using the quadratic formula  are [tex](-\frac{4-\sqrt{19}}{3} , -\frac{4+\sqrt{19}}{3} )[/tex] .

Now we will substitute the values of x in the function f(x) to get the local extremum.

The maximum value of f(x) is [tex]\frac{56+38\sqrt19}{27}[/tex].

The minimum value of f(x) is [tex]\frac{56-38\sqrt19}{27}[/tex] .

Now we will use various points to find the values of f in the function.

At x = -3 , y = 8

At x = 0 , y = -4

At x =-1 , y = 0

Hence the relative extremum of the function is at [tex](-\frac{4+\sqrt{19}}{3} ,\frac{56+38\sqrt19}{27})[/tex] .

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Answer:

Step-by-step explanation:

equation of finding a midpoint is (x2+x1)/2 and (y1+y2)/2

7) (4+12)/2 = 8 and (9+-4)/2= 2.5

hence midpoint is (8,2.5)

8) we are told the midpoint so we can now find the co-ordinates of the other endpoint:

(5+x)/2= -3

rearrange to find x--> 5+x =-6, so x=-11

(-7+y)/2=2

rearrange to find y--> -7+y=4, so y=11

other endpoint: (-11,11)

5) the gradient of the new equation is parallel to y=3x+7 so it will stay the same

y=3x+c

we know that the points this line passes through is: (-4,-8) so we substitute this into our new equation to find c

-8= (3 x -4) +c

-8=-12 +c

so c= 4

Hence our new equation is y=3x+4

6) perpendicular gradient means that our existing gradient needs to be reciprocated (turned into negative and then flipped)

new gradient is -1/3

y=-1/3x+c

we know the value for x and y so we can substitute into our new equation to find c

9=(-1/3 x -6) +c

9=2 + c

c= 7

Hence our new equation is y=-1/3x+7

Hope this helps!

Using the compound interest formula, we have:

Answer:

See below

Step-by-step explanation:

Maximum height will be found at the t value = - b/2a  

  b = 192    a = -16  

      so max height will be at   t = - 192/(2 * -16) = 6 s

Max height will be   h = -16(6^2) + 192(6)   = 576 ft

Here, we want to evaluate the expression

We use the order of operations here PEDMAS ( parentheses, exponents (roots and powers) , division, multiplication, addition and subtraction)

We start out with the parentheses, then move on with the terms outside by multiplication

We have this as follows;

Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]

The perimeter of the sector is 2cm

The diagram shows a sector of a circle, center O.

The radius of the circle is 6cm.

The angle AOB is 120

We need to find the perimeter of the sector

s = r∅

Where ∅ is the angle subtended by the arc

r is the radius of the circle

s = 6 (120/360)

s = 6 (1/3)

s = 2

Therefore,  the perimeter of the sector is 2cm

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Answer:

A, B, F

Step-by-step explanation:

Well, to do this let's start by simplifying each of the ratios! If they can be simplified to 8:2 then they are a match

A: 16:4

Divide both sides by 2: 8:2 (This is an answer)

B: 40:10

Divide both sides by 5: 8:2 (This is also an answer)

C: 2:8

This one is not possible, because you would have to multiply the 2 by a whole number, and the 8 by a number less than one. Both have to be multiplied/divided by the same number.

D: 10:4

To get the 4 into a 2, we divide by 2. If we divide the 10 by 2 we get 5. Thus, this is not an answer.

E: 1:6

To get the 6 into a 2, we must divide it by 3. If we divide 1 by 3, we get a decimal, not 8.

F: 4:1

Multiply both sides by 2: 8:2 (This is our final answer)

Answer:

6(3a+7b+1)

Step-by-step explanation:

36a+42v-18a+6
18a+42b+6
GCF=6
6(3a+7b+1)

The factor of the given expression is 6(3a+7b+1).

A factor is a number that divides another number, leaving no remainder.

Given an expression, 36a + 42b - 18a + 6

On factoring, we get,

36a + 42b - 18a + 6

= 18a+42b+6

= 6(3a+7b+1)

Hence, The factor of the given expression is 6(3a+7b+1).

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Answer:

see explanation

Step-by-step explanation:

If the ratios of two pairs of corresponding sides of the 2 triangles are equal and the included angles are congruent then the triangles are similar by the

SAS postulate.

[tex]\frac{AC}{DF}[/tex] = [tex]\frac{5.1}{1.7}[/tex] = 3

[tex]\frac{BC}{EF}[/tex] = [tex]\frac{3.3}{1.1}[/tex] = 3

∠ C = 180° - (36 + 67)° = 180° - 103° = 77° , then the included angles

∠ C and ∠ F = 77° are congruent

Then

Δ ABC and Δ DEF are similar by the SAS postulate

£350 is divided in the ratio 3:11 is £75 and £275.

The given ratio is 3:11.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

We need to divide £350 in the given ratio

Now, 3+11=14

3/14 × 350

= £75

11/14 × 350

= £275

Hence, £350 is divided in the ratio 3:11 is £75 and £275.

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The equation of the regression line has the following shape:

Where m is calculated through the following equation:

And b is calculated through the following equation:

N is the number of samples. 8 for this case.

The values of all the sums present in the above equation are reported in the last row of the table:

Now, we can begin calculating m by replacing the values:

The slope of the equation is m = 25.333.

Now, we can calculate b:

Now that we know the parameters m and b for the linear regression, we can build the equation:

Where x represents the murders and y the robberies per 100,000 population.

Then, (a): the equation of the regression line is y = 25.333x - 13.153.

To predict the robberies per 100,000 population when x = 4.5 murders, we just need to replace that 4.5 in the equation that we just found:

Finally, (b): according to the linear regression, the number of robberies per 100,000 population when x = 4.5 murders is approximately 100,85.