Find the 12th term of the geometric sequence 2,10,50

According to the linear equation, He takes 9 weeks will it take to reach his goal.

According to the statement

We have to find that the weeks will it take to reach his goal.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

The job pays $12 per hour with a $250 signing bonus. John hopes to make $2950 before the fall so he uses the following equation 12t+ 250 = 2950

Then

The given equation is:

12t+ 250 = 2950

12t = 2950 -250

12t = 2700

t = 2700/12

t = 225 hours.

And

If John works 25 hours a week

Then

Number of weeks he takes = 225 /25

Number of weeks he takes = 9

So, According to the linear equation, He takes 9 weeks will it take to reach his goal.

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The length of the KL by additive property is 5 units.

The additive property of equality in an equation asserts that the sides stay equal whether we add or subtract the same amount from both sides of the equation. For entire numbers as well, this property is valid.

An example of the additive property is :

If A=B then A+n=B+n where n∈R.

Now the given line segment is KM is x+10

And KL=5x and LM=6

Now using additive property we can say that

KL+LM=KM

Substituting the values in the equations we get:

5x+6=x+10

or, 4x=4

or, x=1

Now using this value of x we can find the length of KL.

Therefore KL=5x=5×1=5

Hence the length of the KL by additive property is 5 units.

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Answer:

a) 41 customers purchased only mysteries.

b) 19 customers purchased mysteries and science fiction, but not romance novels.

c) 19 customers purchased mysteries and science fiction.

d) 19 customers purchased mysteries and science fiction, but not romance novels.

e) 15 and 10 customer purchased mysteries

Answer:

x = 0, x = 5

Step-by-step explanation:

2x² = 10x ( subtract 10x from both sides )

2x² - 10x = 0 ← factor out 2x from each term on the left side

2x(x - 5) = 0

equate each factor to zero and solve for x

2x = 0 ⇒ x = 0

x - 5 = 0 ⇒ x = 5

Answer:

  x + 9

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

  x + 1

Step-by-step explanation:

2x + 4          -x + 5           x + 9

------------  +  ------------  =  -----------

  x + 1             x + 1           x + 1

I hope this helps!

Step-by-step explanation:

MAR ME AS A BRAINLIST

THANKS

Answer:

x = 14

Step-by-step explanation:

m<DBC = m<DBE + m<EBC

105 = 4x + 5x - 21

105 = 9x - 21

126 = 9x

9x = 126

x = 126/9

x = 14

Answer:

  (c)  39 mm²

Step-by-step explanation:

You want to know an estimate of the area of the irregular figure.

The areas of irregular figures are often easily computed by decomposing the figure into shapes whose areas have formulas. Here, we can draw a vertical line from the upper left vertex to divide the figure into a triangle on the left and a trapezoid on the right.

The triangle has a base of 3 squares and a height of 6 squares, so an area of ...

  A = 1/2bh = 1/2(3)(6) = 9 . . . . square mm

The trapezoid has vertical parallel bases of 6 and 7 squares, and a width of 5 squares. Its area is ...

  A = 1/2(b1 +b2)h = 1/2(6 +7)(5) = 65/2 = 32 1/2 . . . . square mm

Then the total area of the figure shown is ...

  area = triangle area + trapezoid area

  area = 9 mm² +32.5 mm² = 41.5 mm²

The closest estimate of those offered is 39 square mm.

The examples of error and trial method and quadratic system are shows below.

Number problems and try to solve either trial and error or a Quadratic System

Trial and error is a fundamental method of Problem solving. It is characterized by repeated, varied attempts which are continued until success, or until the agent stops trying. Until getting the right answer the problem is repeating through various steps. This type of problem solving is called trial and error method.

A linear quadratic system is a system containing one linear equation and one quadratic equation (which is generally one straight line and one parabola). A simple linear system contains two linear equations (which is two straight lines).

ERROR AND TRIAL METHOD

Question: 44 people live in eight houses (3 on each side of the Albert Square). Each house has a different number of people living in it. Each line of three houses has 15 people living in it. How many people live in each house?

Solution: Simplifying, we have to get 4 sets of numbers, each of which add up to 15. So start guessing.

The average number of people in a house is 44/8 is roughly 4.5. So what numbers should we take? 2, 3, 4, 5, 6, 7, 8, 9. Now, we should also have an average close to 5 for each set. Let's start:

Set 1: 3, 5, 7

Set 3: 2, 4, 9

Now, the other two sets will have an overlap. So let's guess the overlaps:

Set 2: Overlaps are 2 and 7. So the third number will be 6. Because we have not used 6 yet.

Set 4: Overlaps are 3 and 9. Then the third number ends up to 3 again. Wrong guess! So we need to try again. Overlaps are 3 and 4. In this case third number works out to be 8, which we have not used. So here is the answer

The first row: 2,6,7.

Second row: 4,8,3.

First column : 2,9,4.

Second column: 7,5,3.

QUADRATIC SYSTEM:

Find the points of intersection between the line y=2x+1  and the parabola y=x2−2.

Substitute 2x+1  for y in y=x2−2.

2x+1=x2−2

Write the quadratic equation in standard form.

2x+1−2x−1=x2−2−2x−10=x2−2x−3

Use the quadratic formula to find the roots of the quadratic equation.

Here, a=1,  b=−2,  and c=−3.

x=−(−2) ± (−2)2 − 4(1)(−3)√2(1)=2 ± 4 + 12√2=2 ± 42=3,  −1

Substitute the x-values in the linear equation to find the corresponding y-values.

x=3⇒y=2(3)+1

 =7x=−1⇒y=2(−1)+1      =−1

Therefore, the points of intersection are (3,7)  and (−1,−1).

Graph the parabola and the straight line on a coordinate plane.

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The equation of slope-intercept form of the line is y = 14/3x + 8.

What is in slope-intercept form?

Given,

        m = 14/3

the point = ( 0,8 )

A line with a slope of 14/3 passes through the point (0,8).

y - y₁ = m ( x- x₁)

y - 8 = 14/3 ( x - 0 )

3(y - 8 )  = 14x

3y - 24  = 14x

3y = 14x + 24

y = 14/3x + 8

Finally, the equation of the line is

y = 14/3x + 8

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Using proportions, it is found that:

a) 75% of the respondents believe the action is morally​ acceptable.

b) Supposing there are 217 million adults, 39.06 million believe that the action is morally​ wrong.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

In item a, 75 out of 7 + 18 + 75 = 100 adults believe that the action is morally acceptable, hence the percentage is:

75/100 x 100% = 75%

75% of the respondents believe the action is morally​ acceptable.

In item b, we suppose that there are 217 million adults, hence the amount that believe the action is morally wrong is:

0.18 x 217 = 39.06.

Supposing there are 217 million adults, 39.06 million believe that the action is morally​ wrong.

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Answer:

Rick will have in interest 646.00 for a total of 38646. Charles will have 2052.00 interest for a total of 40052. Charles has a total of 1406.00 more than Rick.

Answer: Depth d = 767 feet.

Step-by-step explanation:

In certain deep parts of oceans, the pressure of sea water, P, in pounds per square foot, at a depth of D feet below the surface, is given by the following equation:

                               P= 13+ 5d/13

If a scientific team uses special equipment to measures the pressure under water and finds it to be 308 pounds per square foot, at what depth is the team making their measurements?

Given data,

The relationship between the pressure, p of sea water in certain deep parts of oceans is and the distance, d below the surface is given by the following equation,

                                 P= 13+ 5d/13

Where,

p is in pounds per square foot.

d is in feet

The pressure of seawater is 308 pounds per square foot at a depth

                             308 = 13+ 5d/13           (eq-1)

                             308 - 13 = 5d/13

Cross multiplying, it becomes                            

                             295 = 5d/13

                             295 * 13 = 5d

                              3,835 = 5d

                               3,835/5 = d

                                d = 767 feet

At a depth of 308 feet below the surface of the water, the pressure of seawater is,

Substitute d value in equation 1,

So, we can write,

                              P= 13+ 5d/13

                              P = 13+ 5 (767) /13

                              P = 13 + 3835/13

                              P = 13 + 295

                              P = 308 pounds per square foot.

Therefore,

                        Depth d = 767 feet.

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Its between B and c but i reckon C

Answer

Estimate each product 13.92*2.7

37.584

Answer:

the answer is two because the absolute value delete the negative in result not in question

Answer:

(0, 3)

[tex]x=0\\y=3[/tex]

Step-by-step explanation:

You can rewrite the first equation as [tex]y=3-x[/tex]. Then, you can substitute into the second equation as follows:

[tex]x-3(3-x)=-9\\x-9+3x=-9\\4x=0\\x=0\\[/tex]

Now, we can substitute this value into the first equation.

[tex]x+y=3\\0+y=3\\y=3[/tex]

Writing this in the form of [tex](x, y)[/tex] will yield [tex](0, 3)[/tex].

Remember when setting this out, align your equal signs and give good mathematical reasoning as shown above.

Hope this helps you!

She must have a score greater than the average of 75 on her final exam.

Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.

Let the required score be x

Mean = 79 + 69 + 61 + 91 + x/5

⇒ 79 + 69 + 61 + 91 + x/5 > 75

⇒ 300 + x/5 > 75

⇒ 300 + x > 375

⇒ x > 375 - 300

⇒ x > 75

This implies that she needed a score on her final exams that were higher than the average of 75.

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Answer: $180

Step-by-step explanation:

a right triangle has three sides: the two smaller ones and the big one. the two smaller ones squared add up to the bigger one squared.

this is the pythagorean theorem, a^2 + b^2 = c^2.

in this case, it would be 9 squared + 12 squared = c squared.

81 + 144 = 225

225 is the square of 15, so the third side is 15.

now, solve for the perimeter.

the perimeter is the 3 sides added up, so 9+12+15 = 36 feet of perimeter.

each foot costs $5, so 36x5= 180.

$180 is the answer.

Answer:

im not to sure but i think its this

Step-by-step explanation:

The expected duration of participant participation

Yana opened her saved paper, wrote, took a break, deleted some of the words, and then began writing again. Then the correct option is A.

What is a function?

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

Yana is in the school computer lab writing a paper for history class. The graph represents the number of words Yana has written after a number of minutes.

The graph is given below.

From the graph, Yana opened her saved paper, wrote, took a break, deleted some of the words, and then began writing again.

Then the correct option is A.

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Answer:

24 is the answer to the Equation

a) the average velocity during each time period.

(b) 0.08 cm/s is the instantaneous velocity of the particle when t = 1.

Step-by-step explanation:

Given that

                s = 5 sin(t) + 5 cos(t),

To find

                (1)[1,2]? cm/s

                (2)[1,1.1]? cm/s

                (3)[1,.101]? cm/s

                (4)[1,1.001]? cm/s

So, according to the question

a) The average velocity during each time period.

                (1)[1,2]? cm/s

                (2)[1,1.1]? cm/s

                (3)[1,.101]? cm/s

                (4)[1,1.001]? cm/s

We have the displacement equation at time t :

                s = 5 sin(t) + 5 cos(t)

Now differentiate it by t to get velocity.

               v(t) =  ds/dt

                     [tex]= \frac{d}{dt} (5sint+5cost)\\= 5(\frac{d}{dt} sint+\frac{d}{dt}cost)\\\\[/tex]

              v(t)  [tex]= 5( cost - sint)[/tex]    

velocity at t = 1,

               v(1) = 5 { cos(1)- sin(1) }    = 5( 0.99-0.017) = 5 x 0.982 = 4.91 cm/s        

velocity at t = 2,

               v(2) = 5 { cos(2)- sin(2) }    = 5( 0.999 - 0.0348)  = 4.82 cm/s  

velocity at t = 1.1,

               v(1.1) = 5 { cos(1.1)- sin(1.1) }    = 5( 0.999 - 0.0191)  = 4.90 cm/s  

velocity at t = 0.101,

          v(0.101) = 5 { cos(0.101)- sin(0.101) } = 5( 0.999 - 0.0176)  = 4.99 cm/s

velocity at t = 1.001,

         v(1.001) = 5 { cos(1.001)- sin(1.001) } = 5( 0.999 - 0.0174)  = 4.911 cm/s    

Now,

The average velocity at [1,2]

          = (4.91+4.82)/2 = 4.87 cm/s

The average velocity at [1,1.1]

          = (4.91+4.90)/2 = 4.90 cm/s

The average velocity at [1,0.101]

          = (4.91+4.99)/2 = 4.95 cm/s

The average velocity at [1,1.001]

          = (4.91+4.911)/2 = 4.91 cm/s

b) instantaneous velocity at 1s.

        instantaneous velocity[tex]= \frac{instantaneous\; displacement }{instantaneous\; time}[/tex]

                                   v(1) = [tex]\frac{s(1)-s(0)}{1-0}[/tex]

  s(1) = 5 {sin(1) + cos(1)} = 5 (0.017 + 0.999) = 5.08 cm

  s(0) = 5 {sin(0) + cos(0)} = 5 (0 + 1) = 5.0 cm

Now, putting the all values

                v(1) = (5.08 - 5.0)/1 = 0.08 cm/s

Answer:

   a) the average velocity during each time period.

  (b) 0.08 cm/s is the instantaneous velocity of the particle when t = 1.

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The value of x is 81 since similar triangles have equal ratios of corresponding sides.

Given:

PQ ǁ MN

OQP=  N

QPO=  M

ΔOQP=ΔONM

OP/OM=OQ/ON  

45/X=40/72

X= (72×45)/40

X=81

If two figures have the same shape, they are said to be comparable. In more formal terms, two figures are said to be comparable if their respective angles are congruent and their corresponding side length ratios are identical. The scale factor is the name of this usual ratio.

Therefore, the value of X is calculated as 81.

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The inequalities could be used to determine the amount you have left to spend will be 60 - 15.

From the information, the person have a gift card for your favorite clothing store for the amount of $60 and found a shirt you want to buy that costs $15.

The inequalities could be used to determine the amount you have left to spend will be:

= Total amount - Shirt

= 60 - 15

Therefore, inequalities could be used to determine the amount you have left to spend will be 60 - 15.

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From the given coordinates, we can say that the Midpoint of AC = a/2, b/2 and the Midpoint of BD = a/2, b/2

Since the midpoints of the diagonals have the same coordinates, then we can conclude that AC and BD bisect each other.

From the given image, we see that the coordinates of parallelogram ABCD are;

A (0, 0)

B (a, 0)

C (a , b)

D (0, b)

Thus;

1) The coordinates of the midpoint of AC are;

Midpoint of AC = (0 + a)/2, (0 + b)/2

Midpoint of AC = a/2, b/2

2) The coordinates of the midpoint of BD are;

Midpoint of BD = (a + 0)/2, (0 + b)/2

Midpoint of BD = a/2, b/2

Since the midpoints of the diagonals have the same coordinates, then we can conclude that AC and BD bisect each other.

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Answer: 9/13 ==> A

Step-by-step explanation:

sin is between 0 and 1 if 0° < theta < 180° ==> sin is positive when y is positive

sin is between -1 and 0 is 180° < theta < 360° ==> sin is negative when y is negative

sin theta * csc theta = 1

sin theta * 13/9=1

sin theta * 13/9 * 9/13 = 1 * 9/13

sin theta = 9/13 ==> A

The rounded numbers are   1200 and 1100

The two numbers that we have been given are 1183 and 1145.

We have been asked to round of each number to the nearest hundred.

Note that when we are rounding of number to the nearest hundred then we have to check the tens place.

If it is greater than or equal to 5 then we will increase the hundred place number by 1

And if it is less than 5 then we will not change anything in the hundreds place.

And after the required changes in the hundred place number, the numbers after that will convert into zero.

Therefore,  

1183 is rounded of to = 1200 as 8 which is in the tens place is greater than 5, we will add 1 to 1 in the hundreds place

1145 is rounded of to = 1100 as 4 is less than 5, 1 will not change

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Answer: [tex]\pm3[/tex]

Step-by-step explanation:

[tex][(4(x^{2} -5)-7)/3]+6=9[/tex]

[tex]((4x^{2} -20)-7)/3=9-6[/tex]

[tex]4x^{2} -27=3*3[/tex]

[tex]4x^{2} =9+27[/tex]

[tex]x^{2}=36/4=9[/tex]

[tex]x=\sqrt{9} =\pm3[/tex]

[tex]x = 3[/tex]