Point Q is plotted on the coordinate grid. Point P is at (20, −30). Point R is vertically above point Q. It is at the same distance from point Q as point P is from point Q. Which of these shows the coordinates of point R and its distance from point Q?

On a coordinate grid from negative 50 to positive 50 in increments of 10, Point Q is plotted at the ordered pair negative 40, negative 30.

Point R is at (−40, 30), a distance of 60 units from point Q
Point R is at (−40, −10), a distance of 20 units from point Q
Point R is at (−40, −30), a distance of 60 units from point Q
Point R is at (−40, 10), a distance of 20 units from point Q

Given:

The objective function, [tex]C=2x+3y[/tex],

Constraints,

[tex]2x+3y\leq 24[/tex]

[tex]3x+y\leq 15[/tex]

[tex]x\geq 2[/tex]

[tex]y\geq 3[/tex]

To find:

The minimum value of the given objective function.

Solution:

We have,

Objective function, [tex]C=2x+3y[/tex]            ....(i)

The related equations of given constraints are

[tex]2x+3y=24[/tex]       ...(ii)

[tex]3x+y=15[/tex]              ...(iii)

[tex]x=2[/tex], it is a vertical line parallel to y-axis and 2 units left from y-axis.

[tex]y=3[/tex], it is a horizontal line parallel to x-axis and 4 units above from y-axis.

Table of value for (i),

x :   0     12

y :   8     0

Table of value for (ii),

x :   0      5

y :   15     0

Plot these points on a coordinate plane and draw these 4 related lines.

The sign of inequality of [tex]2x+3y\leq 24[/tex] and [tex]3x+y\leq 15[/tex] is ≤, it means the related lines are solid lines and the shaded region lie below the related line.

For [tex]x\geq 2[/tex], left side of the line [tex]x=2[/tex] is shaded.

For [tex]y\geq 3[/tex], shaded region is above the line [tex]y=3[/tex].

From the below graph it is clear that the vertices of the feasible (common shaded region) are (2,3), (4,3), (3,6) and (2,6.667).

Points                     [tex]C=2x+3y[/tex]    

(2,3)                        [tex]C=2(2)+3(3)=4+9=13[/tex]    (Minimum)

(4,3)                        [tex]C=2(4)+3(3)=8+9=17[/tex]    

(3,6)                        [tex]C=2(3)+3(6)=6+18=24[/tex]    

(2,6.667)                 [tex]C=2(2)+3(6.667)=4+20=24[/tex]

Therefore, the objective function is minimum at point (2,3).

Answer:

FH =KH if triangle FJH and KJH is congruent

Step-by-step explanation:

If two triangles FJH and KJH as shown n figure is congruent if,

FJ = KJ,

FH =KH and

JH =JH common

Triangle is congruent by SSS theorem

Therefore FH =KH

Answer:

FH=39

Step-by-step explanation:

FGH~KJH

GH=x+8

FH=4x-25

JH=32

KH=52

(these are the measurements I have)

x+8 / 32 = 4x-25 / 52

(cross multiply)

52(x+8) = 32(4x-25)

52x+416 = 128x-800

(subtract the 52x from the 128x)

416 = 76x-800

(add the 800 to the 416)

1216 = 76x

(divide the 76 over the 1216)

x = 16

(now plug x into FH)

FH = 4x-25

FH = 4(16)-25

FH = 39

(hope this helped)

Answer:

the thing is black for me.. pls retake

Step-by-step explanation:

Answer:

Its A

Step-by-step explanation:

Answer:

D. -3.86,3.86

Step-by-step explanation:

I calculated logically

Answer:

60 pounds

Step-by-step explanation:

5(5 times)*12(weight of lans dog)=60+12=72

Answer:

57.6

Step-by-step explanation:

72/5 = 14.4

72-14.4=57.6

I checked the answer by:

57.6+14.4=72

Answer:

what is the question? May you please show us

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

5/6 - 4/6 = 1/6

Answer:

the answer is 9

Step-by-step explanation:

Answer:

C. Yes, you can prove that x = 12

Step-by-step explanation:

My friend is correct because by the HL Congruence Theorem, ∆MNP is congruent to ∆MKL. The hypotenuse and leg of one right ∆ is congruent to the hypotenuse and corresponding leg of the other right ∆. So, enough information was given to prove that x = 12.

Answer:

6y + 6x

Step-by-step explanation:

the expanded form would be 6 multiplied to each item in the parenthesis

this gets you 6x + 6y

Answer:

Mean = 4.1

Step-by-step explanation:

Let the scores be denoted by x

Given the following data;

Scores (x) = 1, 2, 3, 4, 5, 6, 7

Frequency, F = 5, 9, 12, 17, 14, 10, 6

Total number, n = sum of frequency

[tex] Total \; number, n = 5 + 9 + 12 + 17 + 14 + 10 + 6 [/tex]

Total number, n = 73

[tex] F(x) = (1*5) + (2*9) + (3*12) + (4*17) + (5*14) + (6*10) + (7*6) [/tex]

[tex] F(x) = 5 + 18 + 36 + 68 + 70 + 60 + 42 [/tex]

F(x) = 299

[tex] Mean = \frac {F(x)}{n} [/tex]

[tex] Mean = \frac {299}{73} [/tex]

Mean = 4.1

Therefore, the mean of this frequency distribution is 4.1.

Answer:

how bad do u need this answer 1 through 10

Answer:

D. $845.00

Step-by-step explanation:

$13 per hour x 65 hrs total = $845 before taxes and deduction.

Answer:

The answer is $845

Step-by-step explanation:

Answer:

y = 542 years

Step-by-step explanation:

Given that,

The regression equation, y= 4.39x-6.77 is used to predict the age of a tree.

y is age of a tree and x is diameter

Put x = 125 cm

Put the value of x in above equation.

y = 4.39(125)-6.77

=548.75  - 6.77

= 541.98

or

y = 542

So, the tree is 542 years old.

Answer:

26

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

thats the answer im not sure if u want me to explain it. But if you do need it to be explained look it up. Give brainliest please.

Answer:

15

Step-by-step explanation:

Turn 3 1/3 to an Improper Fraction

to do that you have to multiply the Whole Number (3) by the Denominator(3)

3×3=9

Then add the numerator (1)

9+1=10

3 1/3 will turn into 10/3

then since you're divided you're going to have to KCF(Keep, Change, Flip)

2/9 will turn into 9/2

When you Flip, Divison will turn into Multiplcation

Look at the picture on how to solve it....

Answer:

the answer is A

Step-by-step explanation:

Hope this helps!

Answer:

It is B The quantity in Column B is greater.

Step-by-step explanation:

Just took the assessment

Answer:

a = 16

w = 125

x = 120

y = 55

Step-by-step explanation:

FINDING 'a'

31 = a + 46 / 2

62 = a + 46

16 = a

FINDING 'w'

* This section looks Non-Isosceles trapezoid so I will be following the rule according it

w + 55 = 180

w = 125

FINDING 'y'

y = 55

- Because of corresponding angles

FINDING 'x'

* In this case it looks like we are still dealing w/ an non-isosceles trapezoid.

x + 60 = 180

x = 120

Hope this helped ^^

(Please inform me of any mistakes or misunderstandings!)

Answer:

Step-by-step explanation:

13x+11y-3x+3y+9

10x+11y+3y+9

13x + 11y - 3x + 3y + 9

This problem consists of combining alike parts of the equation. This means 13x and - 3x go together, 11y and 3y go together, and 9 has no other alike parts.

This shows that the answer (when combining like terms) is:

10x + 14y + 9

Answer:

g=-1/2    can u you also mark me brainliest?

Step-by-step explanation:

Answer:

3,-2.

Step-by-step explanation:

hope this helps. :-)

Answer:

The probability that exactly 10 insects will die

                     P( X = 10 ) = 0.06385        

Step-by-step explanation:

Step(i):-

Given a certain insecticide kills 60% of all insects in laboratory experiments

Given proportion  p = 0.60

                           q = 1 - 0.60 = 0.40

Given sample size 'n' = 12

Step(ii):-

Let "X' be the random variable of binomial distribution

                              [tex]P(X=r) = n_{C_{r} } p^{r} q^{n-r}[/tex]

The probability that exactly 10 insects will die

                              [tex]P(X=10) = 12_{C_{10} } (0.60)^{10} (0.40)^{12-10}[/tex]

                          [tex]n_{C_{r} } = \frac{n!}{(n-r)!r!} = \frac{12!}{(12-10)!10!} = 66[/tex]

                          [tex]P(X=10) = 66 X (0.60)^{10} (0.40)^{2} = 0.06385[/tex]

Final answer:-

The probability that exactly 10 insects will die

                     P( X = 10 ) = 0.06385        

Hey there! I'm happy to help!

Here's José's equation.

J=2a+15

And here is Nancy's.

N=3a+5

We want to find the number of animals where they are the same amount, or where J=N. We can write these equations as equal and solve for a to find the answer!

2a+15=3a+5

Subtract 15 from both sides.

2a=3a-10

Subtract 3a from both sides.

-a=-10

Divide both sides by -1.

a=10

Therefore, José and Nancy charge the same amount for 10 animals.

Have a wonderful day! :D

Answer:

draw the same shape but multiply all the sizes to be bigger or smaller

Answer:

LxWxH= 920

Step-by-step explanation:

hope this helps!

Answer:

your answer would be C

Step-by-step explanation:

line segment JK,Modifying above upper L upper J with bar, Modifying above Upper L Upper K with bar

Answer:

24 / 2500

Step-by-step explanation:

Experimental probability = (number of successes / total number of trials)

For rolling :

Total number of trials = ( 10 + 4 + 8 + 11 + 8 + 9) = 50

Number of times 2 is rolled = 4

P(rolling a 2) = 4 /50

For spinning :

Total number of trials = (8 + 6 + 9 + 11 + 9 + 7) = 50

Number of times 2 is spunned = 6

P(rolling a 2) = 6 /50

Hence,

4 / 50 * 6/50 = 24 / 2500