solve the equations and verify the answer ​

Mina must have planned to read 8 pages everyday.

To accomodate reading in her everyday life, without spending extra time and not disturbing other activities, Mina should read particular number of pages everyday. These pages should be enough to be completed in 7 days.

So, relating the number of pages and days -

Number of pages to be read each day = total number of pages ÷ number of days

Keep the values in relation -

Number of pages to be read each day = 56 ÷ 7

Performing division

Number of pages to be read each day = 8

Thus, to return the book on time Mina should have planned to read 8 pages everyday.

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If we start with the parent function f(x) = cot(x), the transformation needed to go from this function to cot(x + π/6) is expressed as:

That is, we need to make a shift of π/6 units to the left, beginning with the cot(x) graph. The graph of cot(x + π/6) is:

The degree of the power function represented in the table f(x) is 2.

In order to find the degree of the power function represented in the given table, you must find the difference of the y-values.

The second difference is illustrated as:

2 - 6 = -4.

-2 - 2 = -4

-6 - (-2) = -4

This illustrates that the second differences are constant.

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What is the degree of the power function represented in the table?

1

2

3

4

x h(x)

−2 −8

−1 −2

0 0

1 −2

2 −8

From the table of the absolute value function the vertex and the range of the function is Vertex (2, 0), Range: {y | 0 ≤ y < ∞}

the vertex represents the point where the graph crosses the axis of symmetry. This point usually occurs mid way the graph.

Examining the table shows that the coordinates of the vertex is

Therefore vertex ( 2, 0)

The range is the point covered by the y coordinate. Since the ertex has the y coordinate as zero, this means that o is part of the values of the y making the third option the best choice

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Answer: Option 1

Step-by-step explanation:

just took the test

given: 100 cm = 1 meters

We need to convert 4 m to cm

so,

From the frequency bar graph, we can read the following information.

15 students got an A

6 students got a B

5 students got a C

10 students got a D

14 students got an F

a) As described above, 5 students got a C

b) Adding up the frequencies of the students who got C or higher:

5 + 6 + 15 = 26

26 students passed the course

c) Assuming the students who did not pass got any credits, then we add up the students with D and F: 10 + 14 = 24

24 students received no credit for the course

d) Total students in the course: 15 + 6 + 5 + 10 + 14 = 50

e) The mode is the letter grade that got the highest frequency:

Mode = A

A got 15

Answer:

9.7

Step-by-step explanation:

97/10= 9.7

formula for rectangle= length x width

area divided by width= 97/10

97/10=9.7

length=9.7

9.7x10=97

The ratio of surface to area to volume of the given rectangle is 5 : 4 : 8

Length of the rectangle , l = 8 cm

Breadth of the rectangle , b = 2 cm

Height of the rectangle , h = 2 cm

Perimeter of the rectangle is

            P = 2 (l +b)

               = 2(8 + 2)

               = 2 (10)

               = 20 cm

Therefore , the perimeter of the rectangle is 20 cm

Area of the rectangle is

           A = l x b

           A = 8 x 2

           A = 16 cm²

Therefore , area of the rectangle is 16 cm²

Volume of the rectangle is

         V = l x b x h

         V = 8 x 2 x 2

         V = 8 x 4

         V = 32 cm³

Therefore, volume of the rectangle is 32 cm³

Ratio of surface to area to volume = 20 : 16 : 32

                                                         = 5 : 4 : 8    

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1)

From the function given, the cost of 5 apples is $4.50

5 apples cost $4.50

Given:

a.) After 2 minutes, the tank contains 400 gallons.

b.) After 5 minutes, the tank is full.

For us to be able to determine how many gallons of water does the full tank hold, let's first determine the discharge rate of the water filling in the tank.

We get,

Since the tank is after 5 minutes of pumping water at a constant rate, we will just multiply the rate of discharge by the time it took for the tank to be full.

We get,

Therefore the volume of the tank is 1000 Gallons

The amount compounded monthly is 1092.63.

The expression for calculating the amount compounded monthly is given by the formula

CI = P[tex](1 + (\frac{r}{12} ) )^{12t}[/tex] - P

where P is the principal amount, r is the interest rate in decimal form, and t is the time.

The Data and information which are provided in the question are,

The principle amount, P = 750

The rate of interest, R = 3%, so 3÷100 = 0.03

The period, t = 30.

By substituting the data in the equation, the equation becomes

CI = 750×[tex](\frac{1+0.03}{12}) ^{360}[/tex] - 750.

By solving the above equation, the result is obtained as CI = 1092.63

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Answer: y = -3/2x - 1

Step-by-step explanation:

y = mx + b

1. m is the slope so substitute -3/2 for m. ( y = -3/2x + b)

2. b is the y intercept so substitute -1 in for b. ( y = -3/2x - 1)

The value of b is equal to  0 in slope-intercept form equation .

What is slope-intercept form?

The data points are:

(1,4), (2, 3), (3,5), (4,4), (5,5)

The equation of best fit line in the form of  and then find the value of b.

The general form of best fit line is  

  y = mx + c    ...(i)

Where, m is the slope of best fit line and b is the y-intercept of the line.

Using the graphing calculator, we get the equation for the best fit line and the equation is        

         y = x             ...(ii)

On comparing (i) and (ii), we get

                  c = 0

Therefore, the value of m is equal to  0

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Answer: y = -2x + 5

Step-by-step explanation:

y = _x + 5

(5,0) (3,4)

(y2 - y1) / (x2 - x1)

(4 - 0 ) / (3 -5)

4 / -2

-2

y = -2x + 5

The level of water decreases would be 21 inches in 6 weeks if the water level of a lake decreases by 3 inches every week.

The addition, subtraction, division, and multiplication of built-in functions can also be used to specify arithmetic operations. The term "arithmetic operator" refers to the operator that executes the calculation.

We have been given that a lake's water level decreases 3 inches every week when there is a drought.

We have to determine the lake's water level looks like after a seven-week drought.

As per the given condition,

Level of water decreases a week = 3 inches.

Level of water decreases in 6 weeks = 7 × 3 = 21 inches

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The mass of 21,000 molecules of oxygen in scientific notation is expressed as 1.1151 x [tex]10^{-28}[/tex] grams in the proper significant digits.

The number that is provided as digits is tried and established using significant figures. A meaningful representation of numbers is carried by these digits.

The crucial or important digits that can accurately represent the exact meaning of a certain number are known as the significant figures of that number.

Frequently, significant digits are employed in place of figures. By counting out each of the values beginning with the first non-zero digit on the left, we can use it to determine the number of significant digits.

The molecular mass of Oxygen is seen as 32 grams.

So, 6.023 x [tex]10^{23}[/tex] molecules of oxygen have mass as 32 grams

So, one molecule of oxygen has mass = [tex]\frac{32}{6.023 * 10^{23}}[/tex] grams

= 5.31 x [tex]10^{-23}\\[/tex] grams

So, 21,000 molecules will have mass = 21,000 x 5.31 x [tex]10^{-23}\\[/tex] grams

= 111510 x [tex]10^{-23}\\[/tex] grams

= 1.1151 x [tex]10^{-28}[/tex] grams

Thus 21000 molecules of oxygen have a mass of 1.1151 x [tex]10^{-28}[/tex] grams.

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We will write an equation to find the original cost as follows:

And the general equation will be:

Here y is the price after discount and x the price without discount.

****

Since we have that the price is a third of the original, then the discounted price is found by multiplying the original value of the shoe times 1/3. After this operation takes place, the value we will obtain is the discounted prices [1/3 their original value].

Let's call the distance to the appointment 'd', and the time of the first travel (going to the appointment) 't'.

Now, we need to use the formula for the distance:

For the first part of the trip, we have the distance 'd', the average speed is 40 mph and the time is 't':

Then, for the second part of the trip (return trip), the distance is also 'd', the average speed is 30 mph, and the time is 't + 1/3', because she took 1/3 hour longer than the first trip.

So we have that:

Now, we just need to equate both 'd':

So the time 't' is 1 hour. Now we can use that to find the distance 'd':

So the distance to the appointment is 40 miles.

The area of the given figure ABCDEFG is 28 units².

So, the area of the given figure:

Now, calculate areas separately and as as follows:

Area of square ECBD:

The area of square ECBD is 16 units².

Area of triangle ACB:

The area of triangle ACB is 6 units².

Area of triangle CEG:

The area of triangle CEG is 4 units².

Area of triangle BDF:

The area of triangle BDF is 2 units².

Area of the given figure: 16 + 6 + 4 + 2 = 28 units²

Therefore, the area of the given figure ABCDEFG is 28 units².

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Answer

The function is one-to-one.

Check Explanation.

Explanation

Like the name suggests, one-to-one functions have each input variable having exactly one unique output. That is, multiple inputs never give the same output.

Also noting that the data in the function are written as

(x, y) OR (Input, Output)

For this question, we see that all of the input variables are different and all have unique output variables.

Hence, this function is a one-to-one function.

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Given -

Money deposited in an account = $3,100

Interest rate = 2.5% compounded quarterly

Time = 5 years

To Find -

The final amount of money =?

Step-by-Step Explanation -

As we know there are 4 quarters in a year.

So,

In five years, there are 20 quarters.

On applying the formula:

Final Amount =

Final Answer -

The final amount of money = $3511.4

Every line through the center of a circle forms a line of reflection symmetry, and every angle has rotational symmetry around the center. The areas are 123.83 [tex]m^{2}[/tex] and[tex]209.07m^{2}[/tex]

The form having the greatest surface area for a given perimeter is a circle.

Every line through the center of a circle forms a line of reflection symmetry, and every angle has rotational symmetry around the center. The orthogonal group O is the symmetry group of it (2,R). Circle group T is the collection of rotations alone.

A distinct circle can be found through any three locations that are not all on the same line. It is feasible to express explicitly equations for the coordinates of the circle's center and radius in terms of the coordinates of the three specified points in Cartesian coordinates.

Circumference= [tex]2\pi r[/tex]= 220 and 286

[tex]2\pi r[/tex]= 220

2*3.14*r=220

r= 220/35.03= 6.28

area=[tex]\pi r^{2}[/tex]

     = 3.14*6.28*6.28

     = 123.83[tex]m^{2}[/tex]

[tex]2\pi r[/tex]= 286

2*3.14*r= 286

r= 286/35.03 = 8.16

area= [tex]\pi r^{2}[/tex]

      = 209.07[tex]m^{2}[/tex]

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According to the sum property, we have:

Solution

- To divide by a fraction, you simply invert the fraction and instead multiply by the inverted fraction.

- Thus, we have:

The best method for solving a system of linear equations is the substitution method.

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.

We have been given the system of the equations as;

y = -2x + 2

y = 4x + -4

Thus, y = -2 x + 2 ........ equation number 1

y = 4 x - 4.............. equation number 2

Then substitute equation number 2 in equation number 1

4 x - 4 = -2 x + 2

4 x + 2 x = 2 +4

6 x = 6

so, x = 1

Now substitute x= 1 in equation number 2;

Therefore y =( 4 × 1) - 4

             y = 4 - 4 = 0

For x = 1 and y = 0

Hence, the best method for solving a system of linear equations is the substitution method.

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The complete question is;

which best describes your ability to determine the best method for solving a system of linear equations. Then solve the system.

y = -2x + 2

y = 4x + -4

The factor by which the current changes if the resistance increases 10% is; 90.9% reduction

Ohm's law states that the electrical current (I) flowing in a circuit is directly proportional to the voltage (V) and inversely proportional to the resistance(R). Therefore, if the voltage is increased, the current will increase provided the resistance of the circuit does not change. Thus;

I = V/R

Now, we are told that the resistance increases by 10%.

Thus, New value of resistance = 1.1R

Thus, new current/old current = 1/1.1 = 0.909 = 90.9%

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There are two shiftments, 1 to the side along the x-axis and 1 vertical along the y-axis

Horizontal shifts:

Vertical shifts

Since the x is substracted 4 units, it means that the graph is translated 4 units to the right.

Since the function is completely added 1 unit its means that all the graph is shifted 1 unit up.

Select all expressions that are equivalent to (2n + 6)(n + 3)

we have

(2n + 6)(n + 3)

apply distributive property

2n^2+6n+6n+18

2n^2+12n+18

Verify each option

option A

2(n^2 + 6n +9)=2n^2+12n+18 -------> is ok

option B

is not correct

option C

is correct

option D

is not correct

option E

2(n + 3)(n + 3)= (2n + 6)(n + 3) ------> is correct

option F

2(n + 3)^2=2(n^2+6n+9)=2n^2+12n+18 -----> is ok

therefore

Given the graph, we cam find f(-3)+g(-2) below.

Explanation

Answer: -2