Find the value of x such that PQ = QRwhere P, Q and Rare the pints (2, 5), (x, -3) and (7, 9) respectively.

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.

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:

[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:

12.5

Step-by-step explanation:

first you do the one in the 40-15 then you add 50 the you divide by 6

Answer: [tex]54\frac{1}{6}[/tex]

Step-by-step explanation:

Order of Operations (PEMDAS) states that we need to do the parenthesis first then division and then addition.

                    50 + (40 - 15) ÷ 6

parenthesis: 50 +     25      ÷ 6

division:        50 +           [tex]4\frac{1}{6}[/tex]

addition:           [tex]54\frac{1}{6}[/tex]

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:

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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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

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

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:

The two angles are each 31 degrees.

Step-by-step explanation:

Find x

3x + 10

5x - 4

By setting 3x+10 equal to 5x-4, we find x=7. Substituting this value back into the expressions for both angles 1 and 2, we find that both angles measure 31 degrees, confirming that our solution is correct.

The question asks you to solve for the degree measure of both angles 1 and 2, which are represented by the expressions (3x+10)° and (5x-4)° respectively. Because these angles are vertical, we know that they are congruent, or equal in measure.

Therefore, we can form an equation by setting the two expressions equal to each other and then solving for x:

(3x+10) = (5x-4)

Subtracting 3x from both sides yields:

10 = 2x - 4

Then, adding 4 to both sides, we get 14 = 2x. Dividing both sides by 2, we find x = 7.

To check our work, we substitute x = 7 into the original equations for both angle 1 and angle 2:

Angle 1: 3(7) + 10 = 31°

Angle 2: 5(7) - 4 = 31°

As you can see, the degree measures are the same, which verifies that we solved for the variable correctly.

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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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Use photo math

Hope this helps

Answer:

the answer would be 6.5 pounds

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

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:

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

Final answer:

(m-p)(x) represents the subtraction of function p(x) from m(x). Assuming p(x) is -4x + 2, (m-p)(x) simplifies to 7x - 4.

Explanation:

To calculate (m-p)(x), we need to subtract the function p(x) from the function m(x).

Given m(x) = 3x - 2 and noting there seems to be an error in p(x), as it should likely be a function of x, let's assume the student meant p(x) = -4x + 2 based on the pattern of the provided information.

The subtraction of these two functions is performed as follows:

m(x) - p(x) = (3x - 2) - (-4x + 2)

Simplify by distributing the negative sign through the second polynomial:

(3x - 2) + 4x - 2 = 3x + 4x - 2 - 2

Combine like terms:

7x - 4

So, (m-p)(x) = 7x - 4.

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).

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

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:

52.94  miles per unit

Step-by-step explanation:

The unit rate is found by dividing miles per time

90 miles /1.7 unit

52.94117647  miles per unit

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.

Answer:

5/8=0.625

Step-by-step explanation:

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

Look at the picture.

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:

a(5) = 7

Step-by-step explanation:

Look at 5 on the n line, the horizontal line look up to the dot on that line.  Whats it value on the vertical line a(n)?  7 so a(5) = 7

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

Because AC lies opposite the angle of the smaller measure than the angle opposite FH. The sides at these angles have the same length.

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

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.

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