In the first week students at RSM solved 25 percent of their monthly quota of problems. In the second week, they solved 110 percent of the number of problems solved in the first week. In the third week they solved 60 percent of the number of problems they had solved in the first two weeks and, in the fourth week, they solved the remaining 320 problems. How many problems did students solve in the four-week month?

Given : (3x² - 2y² + 5x) + (4x² + 12y² - 7x)

Rearranging like terms, we get :

⇒ (3x² + 4x²) + (12y² - 2y²) - 7x + 5x

⇒ 7x² + 10y² - 2x

But, Marcus got the Answer as : 7x² - 10y² - 2x

Marcus combined the terms -2y² and 12y² Incorrectly

Following are the solution to the given expression:

Given:

[tex]\bold{(3x^2-2y^2+5x)+(4x^2+12y^2-7x)=7x^2-10y^2-2x}[/tex]

To find:

Solve equation=?

Solution:

[tex]\to \bold{(3x^2-2y^2+5x)+(4x^2+12y^2-7x)=7x^2-10y^2-2x}[/tex]

Solving the L.H.S part:

[tex]\to \bold{(3x^2-2y^2+5x)+(4x^2+12y^2-7x)}\\\\\to \bold{(3x^2-2y^2+5x+4x^2+12y^2-7x)}\\\\\to \bold{(7x^2+10y^2-2x)}\\\\[/tex]

Solving the R.H.S part:

[tex]\bold{=7x^2-10y^2-2x}[/tex]

Since in this question the [tex]L.H.S \neq R.H.S[/tex] , and when we solve the equation so, except the third choice all were correct.

Therefore, the final answer is " He combined the terms [tex]\bold{-2y^2\ and\ 12y^2}[/tex]incorrectly."

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NOTES:

Degree: the largest exponent in the polynomial

End Behavior:

Multiplicity (M): the exponent of the zero. e.g. (x - 3)²  has a multiplicity of 2

Relative max/min: the y-value of the vertices.  

Rate of Change: slope between the two given points.

********************************************************************************************

1. f(x) = (x-1)²(x + 6)

a) Degree = 3

b) end behavior:

c) (x - 1)²(x + 6) = 0

   x - 1 = 0                     x + 6 = 0

       x = 1 (M=2)                   x = -6 (M=1)

d) The midpoint between 1 and -6 is -3.5, so axis of symmetry is at x = -3.5

y = (-3.5 - 1)²(-3.5 + 6)

  =  (-4.5)²(2.5)

  = 50.625

50.625 is the relative max

e) see attachment #1

f) The interval at which the graph increases is: (-∞, -3.5)U(1, ∞)

g) The interval at which the graph decreases is: (-3.5, 1)

h) f(-1) = (-1 - 1)²(-1 + 6)

          = (-2)²(5)

          = 20

    f(0) = (0 - 1)²(0 + 6)

          = (-1)²(6)

          = 6

Find the slope between (-1, 20) and (0, 6)

m = [tex]\frac{20-6}{-1-0}[/tex]

   = [tex]\frac{14}{-1}[/tex]

   = -14

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2.    y = x³+3x²-10x

         = x(x² + 3x - 10)      

         = x(x + 5)(x - 2)

a) Degree = 3

b) end behavior:

   Coefficient is positive so right side goes to positive infinity

   Degree is odd so left side goes to negative infinity

c) x(x + 5)(x - 2) = 0

   x = 0                     x + 5 = 0                     x - 2 = 0

   x = 0 (M=1)                   x = -5 (M=1)                x = 2 (M=1)

d) The midpoint between -5 and 0 is -2.5, so axis of symmetry is at x = -2.5

y = -2.5(-2.5 + 5)(-2.5 - 2)

  =  -2.5(2.5)(-4.5)

  = 28.125

28.125 is the relative max

The midpoint between 0 and 2 is 1, so axis of symmetry is at x = 1

y = 1(1 + 5)(1 - 2)

  =  1(6)(-1)

  = -6

-6 is the relative min

e) see attachment #2

f) The interval at which the graph increases is: (-∞, -2.5)U(1, ∞)

g) The interval at which the graph decreases is: (-2.5, 1)

h) f(-1) = -1(-1 + 5)(-1 - 2)

********************************************************************************************

3. y = -x(x + 2)(x - 7)(x - 3)

a) Degree = 4

b) end behavior:

   Coefficient is negative so right side goes to negative infinity

   Degree is even so left side goes to negative infinity

c)  -x(x + 2)(x - 7)(x - 3) = 0

  -x = 0                     x + 2 = 0                     x - 7 = 0             x - 3 = 0

   x = 0 (M=1)                 x = -2 (M=1)                x = 7 (M=1)          x = 3 (M=1)

d) The midpoint between -2 and 0 is -1, so axis of symmetry is at x = -1

y = -(-1)(-1 + 2)(-1 - 7)(-1 - 3)

  =  1(1)(-8)(-4)

  = 32

32 is a relative max

The midpoint between 0 and 3 is 1.5, so axis of symmetry is at x = 1.5

y = -(1.5)(1.5 + 2)(1.5 - 7)(1.5 - 3)

  =  -1.5(3.5)(-5.5)(-1.5)

  = -43.3125

-43.3125 is the relative min

The midpoint between 3 and 7 is 5, so axis of symmetry is at x = 5

y = -(5)(5 + 2)(5 - 7)(5 - 3)

  =  -5(7)(-2)(2)

  = 140

140 is the relative max

e) see attachment #3

f) The interval at which the graph increases is: (-∞, -1)U(1.5, 5)

g) The interval at which the graph decreases is: (-1, 1.5)U(5, ∞)

h) f(-1) = -(-1)(-1 + 2)(-1 - 7)(-1 - 3)

          = 1(1)(-8)(-4)

          = 32

    f(0) = -(0)(0 + 2)(0 - 7)(0 - 3)

          = 0

Find the slope between (-1, 32) and (0, 0)

m = [tex]\frac{32-0}{-1-0}[/tex]

   = [tex]\frac{32}{-1}[/tex]

   = -32

Answer: 14

Step-by-step explanation:

Step 1: Graph both equations to find the vertices (see attached):

Step 2: Input the coordinates of the vertices into the given function                  (c = 4x + 2y):

Step 3: Evaluate the value from Step 2 to find the maximum (largest).

11/20 + x = 9/10

x = 9/10 - 11/20

x = 18/20 - 11/20

x = 7/20

Answer:

x = 7/20

Step-by-step explanation:

11/20 +x= 9/10

Subtract 11/20 from each side

11/20-11/20 +x= 9/10-11/20

x = 9/10-11/20

We need a common denominator of 20

x = 9/10 *2/2 - 11/20

x =18/20 -11/20

x = 7/20

Answer:

336 dollars

Step-by-step explanation:

Set up a proportion. Because you know that three pairs of pants costs sixteen dollars, you can put three over sixteen because they are both the same part of the equation, the same part being that they are pairs of pants. Then you set up another proportion, sixty three over x, because you do not know how much sixteen pairs of pants costs. It should look like this. Then you cross multiply and divide.

3                          63

---            =          ----

16                          x

16 times 63 = 1008

1008/3 = 336

Answer:  $336

Answer:

10 seconds

Step-by-step explanation:

AS it is given in the question that

h(t) = -5t² + 30t + 200                     ...........................(i)

We have to find the time when it will touch the ground

so it will be touching the ground when its height from ground will be zero

i.e. h(t)=0

so equation (i) becomes

0 = -5t² + 30t + 200

Now we will solve this to get the value of t

Dividing whole equation with (-5) it will give us

t² - 6t - 40 = 0

Using the mid term breaking rule which will break the mid term and we will get the factors from the mid term

t² - 10t + 4t - 40 = 0

Now we will do the factorization of it

t(t-10)+4(t-10)=0

(t-10)(t+4)=0

so either

t-10 = 0              or   t+4=0

t=10                  or      t= - 4

as t is time so it can not be negative

so

t=10 seconds will be the time in which it will touch the earth

Answer: 10 seconds

Step-by-step explanation:

When the object hits the ground, the height (y-value) is 0.

h(t) = -5t² + 30t + 200

  0 = -5t² + 30t + 200   set height equal to zero

  0 = -5(t² - 6t - 40)      factored out -5

  0 = -5(t - 10)(t + 4)     factored the quadratic

0 = t - 10     0 = t + 4    applied the Zero Product Property

  t = 10         t = -4        solved for t

                        ↓

                    t = -4 is not valid (since time cannot be negative)

So, t = 10

Answer:

15

Step-by-step explanation:

25 percent of 20 is 5, and 20-5 equals 15.

In a group of 20 students, 15 do not wear glasses.

Use photo math

Hope this helps

Answer:

the answer would be 6.5 pounds

Step-by-step explanation: 19 1/2 divided by three

Answer:

3149/999 = 3  152/999

Step-by-step explanation:

I'll assume the bar is over 152 and there is a typo.

Use a step-by-step calculator (I recommend Symbolab) OR:

Let x equal 3.152...

1000x = 3152.152...

1000x-x = 3152.152... - 3.152...

999x =

3152.152...

-     3.152...

3149

Cancel out the .152...

999x = 3149

Divide by 999 on each side

x=3149/999 = 3 152/999

Answer:

The given number is 3.152.

Notice that this is a rational number without a repetition pattern, that means we just need to divide all digist without the decimal point by 1000, because the number of zeros always depends on the number of decimals, which are three in this case.

[tex]\frac{3152}{1000}[/tex]

Then, we simplfy

[tex]\frac{3152}{1000}=\frac{1576}{500}=\frac{788}{250}=\frac{394}{125}[/tex]

So, the improper fraction equal to 3.152 is 394/125.

The mixed number is [tex]\frac{394}{125}=3\frac{19}{125}[/tex]

Answer:

[tex]\frac{r}{2\pi r} =\frac{1}{2\pi }[/tex]

Step-by-step explanation:

A ratio is a comparison of two quantities and can be written in several forms including fractions. It is most commonly written in fraction form or a:b.

To write a ratio, we count the number of each quantity we are comparing or use the variable for that quantity. We write radius:circumference. Recall, the circumference of a circle can be found using [tex]\pi d[/tex] or [tex]2\pi r[/tex].

We write r: [tex]\pi d[/tex]  or r:[tex]2\pi r[/tex].

We can also write in fraction form:

[tex]\frac{r}{\pi d}[/tex] or [tex]\frac{r}{2\pi r} =\frac{1}{2\pi }[/tex]

You can use the fact that ratio of one quantity to other is fraction involving one quantity over another quantity.

The specified ratio is given as

[tex]r:2\\\\or\\\\\dfrac{r}{2}[/tex]

The ratio of a to b is  [tex]\dfrac{a}{b}[/tex]

It is sometimes written as [tex]a:b[/tex]

We can remove common factors of a and b to simplify them.

Thus, if

[tex]a = c \times x\\b = d \times x\\[/tex]
then

[tex]\dfrac{a}{b} = \dfrac{c \times x}{d \times x} = \dfrac{c}{d}[/tex]

The area of a circle with radius r units is

[tex]Area = \pi r^2[/tex]

The circumference of a circle with radius r units is

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

( Remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2 \times x = 2x[/tex] )

Their ratio is

[tex]\dfrac{Area_r}{Circumference_r} = \dfrac{\pi r^2}{2\pi r} = \dfrac{r}{2}[/tex]

Thus,

The specified ratio is given as

[tex]r:2\\\\or\\\\\dfrac{r}{2}[/tex]

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Answer:

39 yards

hope it helps

Step-by-step explanation:

52 ÷ 4 = 13 per quarter of an hour  

we are gonna divide by four because there are 4 quarters in a hour and in 3 quarters there is 45 minutes  

13 x 3 = 39

The seamstress can sew 39 yards of material in 45 minutes.

To find out how many yards the seamstress can sew in 45 minutes, we need to convert 45 minutes into hours. There are 60 minutes in an hour, so 45 minutes is equal to 45/60 = 0.75 hours.

Next, we can use the given information that the seamstress can sew 52 yards of material in one hour. Multiply the yards per hour by the fraction of an hour to find out how many yards can be sewn in 45 minutes:

Yards in 45 minutes = 52 yards/hour × 0.75 hours = 39 yards.

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Final answer:

To determine the number of pairs of female dolphins, the total number of dolphins is divided equally between males and females, resulting in 8 female dolphins. Then, dividing by 2 as they swim in pairs, we find there are 4 pairs of female dolphins.

Explanation:

The question involves dividing the total number of dolphins in the pod by two to find out how many male and female dolphins there are since the pod has an equal number of each gender. Since the females are swimming in pairs, we then divide the number of female dolphins by two to find out how many pairs there are.

There are 16 dolphins in total. Half of them are females, so there are 8 female dolphins. The females swim in pairs, so to find the number of pairs we divide the number of female dolphins by two:

8 females ÷ 2 = 4 pairs of female dolphins.

Wrongs guys  ok don’t pick it

Answer: It's A. 2/5

Step-by-step explanation:

1. It's asking for the probability of picking a vegetable

We can see in the model that 2 carrots and 2 broccoli are vegetables so 4

2. Add up the values

2+2+2+1+2+1= 10

3. 4/10---> 2/5

Answer: A+C = 180 (first answer choice)

This statement is only true if and only if we are dealing with a rectangle (where all four angles are 90 degrees). Otherwise, the statement is false.

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

side notes:

The second statement that AN = NC and DN = NB is true because a parallelogram has its diagonals bisect each other. In other words, the diagonals cut in each other in half.

The third statement that AD = BC and DC = AB is true because opposite sides of a parallelogram are parallel and congruent.

The fourth statement is true because opposite angles of a parallelogram are congruent. If A = C = 90, then A+C = 90+90 = 180 backing up the claim I made earlier, but it's possible that A and C are non-right angles making this parallelogram non-rectangular.

Answer:

m∠A + m∠C = 180

Step-by-step explanation:

Answer:

L = V / WH

Step-by-step explanation:

Solve for L: V = LWH

To solve, all you have to do is get L on its own on one side.

Because the only operation used in this equation is multiplication, only one operation is needed to solve it: division. Just divide both sides by WH to isolate L.

V / WH = LWH / WH

V / WH = L

[tex]LWH=V\qquad\text{divide both sides by}\ WH\neq0\\\\\boxed{L=\dfrac{V}{WH}}[/tex]

Answer:

f(-3) = 27

Step-by-step explanation:

f(x) = (-x)^3

We want the value when x =-3

Substitute this in

f(-3) = (--3)^3

f(-3) = 3^3

f(-3) = 27

If PA = PB ,then P is located on perpendicular bisector of AB.

Look at the picture.

Answer:

Relative Size, S, is 1584.89

Step-by-step explanation:

The equation is [tex]R=log_{10}(S)[/tex]

Where,

It is given that in Richter Scale, an earthquake measured 3.2, so [tex]R=3.2[/tex].

They want to know relative size, S, so we put given information in equation and solve for S:

[tex]R=log_{10}(S)\\3.2=log_{10}(S)[/tex]

Converting to exponential form, we have:

[tex]3.2=log_{10}(S)\\S=10^{3.2}\\S=1584.8932[/tex]

Rounding to nearest hundredth, we have:

[tex]S=1584.89[/tex]

Final answer:

To find the relative size of an earthquake measured at 3.2 on the Richter scale, calculate 10 to the power of 3.2. This results in a relative size of approximately 1584.89 when expressed to the nearest hundredth.

Explanation:

The relationship between the relative size of an earthquake, S, and the measure of the earthquake on the Richter scale, R, is given by the equation log S = R. If an earthquake measured 3.2 on the Richter scale, we can calculate its relative size by finding the antilogarithm (typically the base 10) of the Richter scale magnitude. This means finding 10 to the power of the magnitude.

To find the relative size for an earthquake that measured 3.2 on the Richter scale:

The relative size or seismic-wave amplitude of the earthquake is therefore approximately 1584.89 when expressed to the nearest hundredth.

The solution to the basic vector problems are given as,
1)  (5, -11), option C is correct.
2) . No, the two vectors have different initial points, option B is correct.

Vector is defined as the quantities that have both magnitude and direction is called a vector quantity and the nature of the quantity is called a vector.  

Here,
1)
initial point (5,3) and a terminal point (10,-8),
Vector = 10i -8j - 5i - 3j
Vector = 5i - 11j or [5, -11]

2)
Vector v with an initial point of (0,0) and a terminal point of (50, 120), is not equal to vector u with an initial point of (50, 120) and a terminal point of (0,0).

Thus, the solution to the basic vector problems are given as,
1)  (5, -11), option C is correct.
2) . No, the two vectors have different initial points, option B is correct.

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Final answer:

To find the component form for vector v, subtract the initial point from the terminal point. The answer is option C. The vectors in the second question have different initial points, so they are not equal.

Explanation:

To find the component form for vector v, we need to subtract the initial point from the terminal point. Subtracting the x-coordinates and y-coordinates separately, we get (10 - 5, -8 - 3), which simplifies to (5, -11). Therefore, the component form for vector v is option C, (5, -11).

For the second question, the vectors have the same initial points but different terminal points, so they cannot be equal. Therefore, the correct choice is option B, No, the two vectors have different initial points.

Answer:  1.4 f or [tex]1f +\frac{4f}{10}[/tex]

Step-by-step explanation:

Since, According to the question,

The snowfall in February in Delphine's house had = f cm

Again according to the question,

In March, Delphine's house had 40% more snowfall than in February.

Therefore, The snowfall in March in Delphine's house had = 140% of The snowfall in February in Delphine's house had

= 140 % of f

= [tex]\frac{f\times 140}{100}[/tex]

= 1.4 f cm

= 1 f + 0.4 f

= [tex]1 f + \frac{4f}{10}[/tex] cm

Answer:

It should be c & e

Answer:

[tex]y=39\degree[/tex]

Step-by-step explanation:

The given triangle is a right angle triangle .

The known sides of the triangle that is opposite to angle y is 8 units while the side adjacent is 10 units.

The value of y can be calculated using the tangent ratio.

[tex] \tan(y)=\frac{8}{10}[/tex]

We solve for y to get,

[tex]y=arctan(\frac{4}{5})[/tex]

We evaluate to obtain,

[tex]y=38.66[/tex]

[tex]y=39\degree[/tex] to the nearest degree

Answer:

x + y = 1

Step-by-step explanation:

If the two equations are the same, then it can be shown by this:

6x + 8 = -4x - 2

We need to isolate the x values, so we need to move the -4x over to the other side making it a +4x:

6x + 4x + 8 = -2

Next, move the +8 over to the other side making it a -8:

6x + 4x = -2 - 8

10x = -10

x = -1

So now we can plug this value into the first equation:

6(-1) + 8 = y

-6 + 8 = y

y = 2

x + y = -1 + 2 = 1

So x + y = 1

Answer:

x=32, y=17

Step-by-step explanation:

Difference between two numbers is 15:

x-y=15

Greater number (x) is two less than twice the lesser number:

x=2y-2

-----

x-y=15,

x=2y-2.

x-y-x=15-2y+2

-y=15-2y+2

y=15+2

y=17

-----

x-y=15

x-17=15

x=17+15

x=32

To solve the word problem, we transcribe the information into algebraic equations. We then isolate one variable to solve for it first, and then substitute that variable's value into the second equation. The solution we find is that the two numbers are 17 and 32.

To solve the problem, we must translate the word problem into algebraic equations. We're trying to find two numbers based on the information that's given to us: their difference is 15, and the larger number is two less than twice the smaller number.

First, let's define the numbers as follows: x = smaller number and y = larger number. Now we can set up our two equations based on the problem:

Now we can substitute equation (2) into equation (1) which gives us: 2x -2 - x = 15. Simplify the equation, we get x = 17 and substitute x = 17 into equation (2), we get y = 32.

So, the two numbers are 17 and 32.

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Solution:

As given , g(x)= f(x) + k --------(1)

As also given : f(x) = [tex]\frac{1}{3}[/tex](x+2)

g(x) =  [tex]\frac{1}{3}[/tex](x+5)

Putting the value of f(x) and g(x) in equation (1).

→ [tex]\frac{1}{3}[/tex](x+5) = [tex]\frac{1}{3}[/tex](x+2) + k

→ [tex]\frac{1}{3}[x+5-x-2][/tex]= k

→ k = [tex]\frac{1}{3} \times 3=1[/tex]

So , the value of k is 1.

Answer:

K=5

Step-by-step explanation:

there you go

Final answer:

To find how many cups of flour are needed for every dozen muffins made, set up a ratio using the given information, and solve for x.

Explanation:

To find how many cups of flour are needed for every dozen muffins made, we can set up a ratio using the information given in the question. We know that to make 1 1/2 dozen muffins, 3 1/2 cups of flour are needed. So we can set up the ratio:

1 1/2 dozen muffins : 3 1/2 cups of flour = 1 dozen muffins : x cups of flour

To solve for x, we can cross multiply, and divide:

(1 1/2) * x = (1) * (3 1/2)

x = (1 * 3 1/2) / (1 1/2) = 7/2 cups of flour

Therefore, for every dozen muffins made, 7/2 cups of flour are needed.

Answer:

Its more because 9.36 has a bigger beginning then 9.359.

Ur welcome plzzz mark this as brainlest and thank me

Answer:

No

Step-by-step explanation:

9.36= 9.360

9.360> 9.359

The hundredeth's place of 9.360 is greater than the hundredth's place of 9.359.

Answer:

Multiply each equation by the coefficient of y in the other one.  

Step-by-step explanation:

(1)  6x + 5y = 2

(2) 4x + 2y = 8

Multiply each equation by the coefficient of y in the other one.

Multiply (1) by 2 and (2) by 5.

(3)   12x + 10y =   4

(4) 20 x + 10y = 40     Subtract (3) from (2)

                8x = 36      Solve for x

                  x = 9/2

Answer:

Subtract 5 times the first equation from 2 times the second equation

Step-by-step explanation:

2(6x + 5y = 2)

5(4x + 2y = 8)

12x + 10y = 4

20x + 10y = 40

Subtracting the second equation from first gives:

−8x = −36

x =  

−36

−8

x =  

9

2

Answer:

the answer is $151.56

Step-by-step explanation:

our formula of interest is I = PxRxT

P (principal) = 421

R (rate) = 4%  (we have to turn it into a decimal which is 0.04)

T (time) = 9 years

so :

I = 421 x 0.04 x 9

I = 151.56

The total interest paid will be $151.56.

To find out how much interest you will pay on a loan of $421 over nine years at an annual interest rate of 4%, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Where the Principal amount is $421, the Rate is 4% (or 0.04 when converted to a decimal), and the Time is 9 years.