the common diiference of an ap is 4 . the last term is 72 and the sum of all terms is 600. find the first term and the number of terms​

3rd answer i believe

Answer:

the exact value is x =1/2 or x=0.5

your welcome!

The exact value is x = 1/2.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given an expression as;

[tex]27^{-1/3} = \frac{9^{1/4} }{3^{r + 1}}[/tex]

Now we can see that

27 = 3³

9 = 3²

Then the power are 3(-1/3) = -1

3(1/4) = 3/4

So we have;

[tex]3^{-1} = \frac{3^{2/4} }{3^{r + 1}}\\\\3^{-1} =3^{1/2 -r - 1} \\\\3^{-1} =3^{1 -2r - 2 /2}\\\\3^{-1} =3^{-2r - 1/2}[/tex]

So,

-2 = -2r - 1

-2r = -1

r = 1/2

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Answer:

HJ = 8  JE = 4

Step-by-step explanation:

it is given that H is the midpoint of GE and J is the midpoint of FE. According to the midpoint theorem the line segment connecting the midpoint of two sides is parallel to the three side and its length is half of the third side. since JH is connecting the midpoints.

HJ= 1/2 (GF)

x + 3 = 1/2 (4x - 4)

x + 3 = 2x - 2

x = 5

^ Thus meaning the value of x is 5.

Now you just fill into your equations:

HJ = x + 3 = (5)  + 3 = 8

JE = x - 1 = (5) - 1 = 4

Therefore, HJ = 8; JE = 4.

Answer:

HJ = 8

JE = 4

Step-by-step explanation:

Your welcome.

Answer:

[tex](16 \times 13 \times 0.5) \times 4 + 13 \times 13[/tex]

Answer:

I’m guessing 108 or 165

Step-by-step explanation:

because if 45/500 if you double that it would be 90/1000. after 200 is about half of 500 so 45 divided by 2 is 22.5. yeah i’m like no help sorry

The approximate solutions of the equations are

A, x = 1 and x = 4.2

To find the solution of a system of equations using a graph, you can Identify the point of intersection

Look for the point(s) where the graphs of the equations intersect. This point represents the solution(s) to the system of equations.

then read the coordinates of the point

From the graph, the x coordinates that gives the point of intersection can be traced to be x = 1 and x = 4.2

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Answer:

The answer is false.

Step-by-step explanation:

THE reason why it is false is because if so that wouldnt make any sense.

Answer:

1) $52,000

2) $43,200

3) P = 325 × x + 180 × y

4) x + y ≤ 240

2·x + y ≤ 320

325 × x + 180 × y ≤ 52,000

5) Please find a similar graph created with MS Excel

6) Corn will have 80 acres

Soybean will have 160 acres

7) $54,800

Step-by-step explanation:

The acres of cropland at the Waterbrook Farm, A = 240 acres

The profit per acre in corn production, p₁ = $325

The profit per acre in soybean production, p₂ = $180

The hours of labor required by each acre of corn = 2 hours

The hours of labor required by each acre of soybeans = 1 hours

The number of acres planted with corn = x

The number of acres planted with soybeans = y

1) The farm's profit, 'P', if they planted only corn is P = p₁ × A

∴ P = $325/acre × 320 hours/(2 hours/acre) = $52,000

The farm's profit if they planted only corn, P = $52,000

2) The farm's profit, 'P', if they planted only corn is P = p₂ × A

The required labor for cultivating the 240 acres at 1 hour/acre = 240 hours of labor

Therefore, the labor is sufficient for the entire farmland, we get;

The profit, P = $180/acre × 240 acres  = $43,200

∴ The farm's profit if they planted only soybeans, P = $43,200

3) The equation for the Waterbrook Farm's profit, 'P' can be found, depending on the area of the farm used for the corn and the soybeans as follows;

P = 325 × x + 180 × y

4) The system of inequalities includes;

x + y ≤ 240

2·x + y ≤ 320

325 × x + 180 × y ≤ 52,000

5) Using DESMOS, we have;

The graph of the systems of inequalities is plotted and a graph similar to the attached graph created with MS Excel is found

6) The maximum profit point found using DESMOS is (80, 160)

Therefore, for maximum profit, 80 acres should be used for corn while 160 acres should be used for soybeans

7) The maximum profit of planting both corn and soybeans is found from the profit obtained from the land divided between corn and soybeans in order to yield maximum profit as follows;

P = 325 × 80 + 180 × 160 = 54,800

The maximum profit of planting both corn and soybeans, P = $54,800.

Answer: $6.75

Step-by-step explanation:

25 hours times $9= $225/week

3% increase from $9.00= $0.27

$9.27 times 25 hours= $231.75

$231.75-$225= $6.75 more per week

Answer: The third option

Step-by-step explanation:

(6) (5) is the area of the quadrilateral, therefore you subtract that value by the area of the semi-circle.

to find the area of a semi circle the formula is: (1/2) π ( [tex]r^{2}[/tex])

The radius is 2.5 because the diameter is 5, and the radius is half the diameter.

Answer: b

Step-by-step explanation:

Answer:

$1.66 per pound of potatoes.

Step-by-step explanation:

7/4.20 = 1.66$ per Pound

Mark as brainllest

$1.66 per pound of potatoes.

Answer:

94 days

Step-by-step explanation:

That's a cheap rent-a-car place :)

Btw I took the test.

Answer:

-1 ; -1 ; the two lines are parallel

Step-by-step explanation:

To find the slope of the two lines, we can proceed in two different ways:

1) the faster is do the division: -a/b where a is the number the multiplies x and b is the number that multiplies y

line 1: m = 3/-3 = -1   line 2: -4/4 = -1

2) the second is to rewrite the two equation in the slope intercept form and find what term multiplies the x

line 1

-3y = 3x+6

-y = x + 2

y = -x -2

m = -1

line 2

x+y = 2

y = -x +2

m = -1

the two lines have the same slope, so they are parallel

Answer:

3/10. 0.3

Step-by-step explanation:

when you divide mixed numbers you should reciprocate them I mean take the reciprocal and that was 2 and over every number there is one so I took 1/2 hope you understand why I kept 1/2 I took its reciprocal hope you understand if I'm wrong tell me right away I'll try it out good luck.

Answer:

15, 18, 21

Step-by-step explanation:

Answer:

Women: 448  Men: 560  Children: 1232

Step-by-step explanation:

5+4+11 = 20/2240 = 112

Women = 4 x 112 = 448

Men = 5 x 112 = 560

Children = 11 x 112 = 1232

Total = 1232 + 560 +448 = 2240

Answer:

True

Step-by-step explanation:

Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay.

Answer:

Easy way is completing a square:

Correct choice is J

Answer:

D

Step-by-step explanation:

The required focus of the parabola (x - 1)^2 = 12(y + 2) is (1, 1). Option D is correct.

Given that, equation of the parabola,

A parabola is cross-section cut out of the cone and represented by an equation [tex]y = 4ax^2[/tex]. Where a is focus.

Here,
[tex](x - 1)^2 = 12(y + 2)[/tex]
Simplify the above parabola equation to stand equation
[tex]y = \frac{1}{4(f-k)} (x-h)^2 + k[/tex]
[tex]y =\frac{1}{4(1-(-2))} (x - 1)^2 - 2[/tex]
Now comparing above the equation,
vertex of a parabola,
h = 1 and k = -2

And focus
So the coordinate of the focus of the parabola = (h, f)
= (1, 1)      

Thus, the required focus of the parabola (x - 1)^2 = 12(y + 2) is (1, 1). Option D is correct.

Learn more about parabola here:

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Answer:

Step-by-step explanation:

4/5 x 10/1= 40/5

40 divided by 5 equals 8

The answer is 8

Answer:

AB = 48

AD = 7√2

Step-by-step explanation:

since AD - 26, DB = 26 and DC = 26

AE² = 26² - 10² = 676 - 100 - 576

AE = √576 = 24

AB = 2 x 24 = 48

If arc BC is 45°, then ∠BDC = 45°

AD² = 7² + 7² = 49 + 49 = 98

AD = √98 = 7√2

Answer:

i believe it is 70

Step-by-step explanation:

6×12=72

6-4=2

72-2=70

Answer:

A

Step-by-step explanation:

hope this helps and is right :)

Answer:

the polygon on the right side is doubled the size of the one on the left, therefore x=11

Answer:

-1952

Step-by-step explanation:

Answer:

1952

Step-by-step explanation:

12 x 76-8(456-98)

912-8 x 358

912-2864

1952

Answer:

c 62.8

Step-by-step explanation:

pi=3.14

3.14(2^2)5

3.14(4)5

3.14(20)

62.8 in