At a certain vineyard it is found that each grape vine produces about 10 lb of grapes in a season when about 800 vines are planted per acre. for each additional vine that is planted, the production of each vine decreases by about 1 percent. so the number of pounds of grapes produced per acre is modeled by
a(n) = (800 + n)(10 − 0.01n)
where n is the number of additional vines planted. find the number of vines that should be planted to maximize grape production.

Answer:

I think of having straight line

The cost of the apples is 2.9 dollars.

The cost of the bananas is 5.7 dollars.

The total cost is 6 dollars, each apple cost $1.50 each banana cost $.30 and there’s two more bananas then apples.

Therefore,

let

x = number of apples

y = 2x

where

Therefore, using equations,

1.5(x) + y(0.30) = 6

Hence,

where

y = 2x

1.5(x) + 2x(0.30) = 6

1.5x + 0.6x = 6

2.1x = 6

divide both sides by 2.1

x = 6 / 2.1

x = 2.9 dollars

y = 2(2.9) = 5.7 dollars

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Answer:

Step-by-step explanation:

5x - 6y=-17 -15x + 18y = 51 and 3x + 2y =1

Answer:

  all values of x make the equation true

Step-by-step explanation:

Kendra's working is correct. The equation is a tautology. It is true for all values of x.

\(\Huge\boxed{Hi~there!}\)

On a number line, -5 is to the left of 0.

Remember, on a number line, positive numbers (including fractions, decimals and surds) are to the right of 0:

----------------------------------------------------------------------->

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Negative numbers (including rational and irrational numbers) are to the left of 0:

<-----------------------------------------------------------------

      -8      -7        -6     -5         -4     -3   -2    -1 0

Hope it helps! Enjoy your day!

~Just a determined gal

\(\bf{erutaNtneliS\)

The expression 27a^3 + 54a^2b + 36ab^2 + 8b^3​ has a cube root of 3a + 2b

From the question, the expression is given as

27a^3 + 54a^2b + 36ab^2 + 8b^3​

The above expression is the cube of the sum of two numbers or expressions

Where the numbers are

27a^3 and 8b^3​

The cube roots of 27a^3 and 8b^3​ are represented as

∛27a^3 and ∛8b^3​

Evaluate the cube roots

3a and 2b

Express as sum

3a + 2b

Hence, the cube root of the expression is 3a + 2b

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Based on the information, we can infer that the whole number equivalent to this fraction is 285.

To clear the fraction and obtain an integer we must perform all the mathematical operations that are in the fraction, in this case it is a division and seven multiplications. Here we show you the result:

As evidenced in the procedure, the multiplications were cleared and later the fraction was divided. In this case the result would be the integer 285.

Note: This question is incomplete. Here is the complete information:

How to express this fraction in whole numbers?

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Answer:

(6,8)

Step-by-step explanation:

the midpoint of 10 and 2 is 6

the midpoint of 10 and 6 is 8

Answer:

6

Step-by-step explanation:

Answer:

18 metres

Step-by-step explanation:

4.5/6 = x/24

¾= x/24

x = 18 m

Answer: The length of each of the two equal sides is 19 km

Step-by-step explanation:. Subtract the giver lengths of the bases: 4+1= 5

43 - 5 = 38.

The trapezoid is iscosceles, so the remaining two sides are equal.

Divide. 38/2 = 19

I hope this helps you!

Solving a system of equations, we see that she can plant 20 tomatoes and 20 squashes.

Let's define the variables:

The space is enough for 40 plants, then:

t + s = 40

And we know that she has a total of $80 to spend (we assume that she spends it all)

t*$1 + s*$3 = $80

Then our system of equations:

t + s = 40

t*$1 + s*$3 = $80

To solve this, we can isolate one of the variables in the first equation, for e xample if we isolate t, we get:

t = 40  - s

Now we can replace that in the other equation:

(40 - s)*$1 + s*$3 = $80

Now we can solve that for s:

$40 - s*$1 + s*$3 = $80

s*$2 = $40

s = $40/$2 = 20

Then she will buy 20 units of squash, and the other 20 plants will be tomatoes.

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Answer:

14.07

Step-by-step explanation:

First we need to add 5 percent to the 67 dollar cost. Which makes the price 70 dollars and 35 cents. 20 percent of 70.35 is 14.07 so the discount is 14.07

Hope this helps

The sum of the series s = ∑n=4^∞ 1/(n(n−1)) is 1/4.

To write the series s = ∑n=4^∞ 1/(n(n−1)) as a telescoping series, we need to manipulate the terms to cancel each other out and simplify the expression.

We can rewrite the series as:

s = ∑n=4^∞ (1/n - 1/(n-1))

Expanding the summation:

s = (1/4 - 1/3) + (1/5 - 1/4) + (1/6 - 1/5) + ...

Notice that the term -1/(n-1) in each subsequent term cancels out with the 1/n term in the next term, except for the first term (1/4 - 1/3).

We can simplify the expression by canceling out the terms:

s = 1/4 - 1/3 + 1/5 - 1/4 + 1/6 - 1/5 + ...

The consecutive terms cancel out, leaving only the first term:

s = 1/4

Therefore, the sum of the series s = ∑n=4^∞ 1/(n(n−1)) is 1/4.

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Answer:

\(m\angle ABE=52^\circ\)

Step-by-step explanation:

Angles and Lines

The figure shows a kite ABCD where the following data is given:

\(m\BAE=28^\circ\)

\(m\BCE=58^\circ\)

We also know

\(BC\cong CD\)

\(AB\cong AD\)

Since triangle BCD is isosceles, it follows that:

\(m\angle CBE=m\angle CDE\)

And triangles BCD and DCE are congruent.

Thus:

\(m\angle BCE=m\angle DCE=58^\circ\)

And also:

\(m\angle BCE=58^\circ+58^\circ=116^\circ\)

Since the sum of internal angles of BCD is 180°

\(m\angle CDE=m\angle CBE= ( 180 - 116 ) / 2=32^\circ\)

The sum of angles of triangle CDE is 180°, thus

\(m\angle CED=180^\circ - 32^\circ - 58^\circ = 90^\circ\)

Angles CED and BEA are vertical (opposite), thus:

\(m\angle BCE=m\angle CED= 90^\circ\)

Finally, since the sum of the angles of triangle ABE is 180°

\(m\angle ABE= 180 - 90 - m\angle BAE\)

\(m\angle ABE= 180^\circ - 90^\circ - 28^\circ = 52^\circ\)

\(\mathbf{m\angle ABE=52^\circ}\)

Answer:

11.21

Step-by-step explanation:

Arc length formula equals pi times the diameter (2 radius) times the angle measure (connecting to the center point of the circle) divided by 360

Basically just plug in the numbers to the formula and solve: 12pi times 107 over 360, which would equal to the answer given above.

Hope this helps (:

Answer: -7

Step-by-step explanation:

Answer:

a = 0, b = 6, c = 4

Step-by-step explanation:

To obtain the values of a, b, c substitute the corresponding values of x into f(x) , that is

f(- 2) = - (- 2)² + (- 2) + 6 = - 4 - 2 + 6 = 0 ⇒ a = 0

f(0) = - 0² + 0 + 6 = 0 + 0 + 6 = 6 ⇒ b = 6

f(2) = - 2² + 2 + 6 = - 4 + 8 = 4 ⇒ c = 4

Answer:

4 ounces

Step-by-step explanation:

1/3 x 12 = 4

The probability is approximately 0.9167 or 91.67%.

To find the probability that the sum of two dice numbers does not exceed 10, we need to determine the favorable outcomes (sums less than or equal to 10) and the total possible outcomes when rolling two dice.

There are 36 possible outcomes when rolling two dice because each die has six faces (1, 2, 3, 4, 5, and 6), and the total number of outcomes is obtained by multiplying the number of outcomes for each die (6 * 6 = 36).

Now let's determine the favorable outcomes (sums less than or equal to 10):

When the sum is 2: There is only one combination (1 + 1).

When the sum is 3: There are two combinations (1 + 2 and 2 + 1).

When the sum is 4: There are three combinations (1 + 3, 2 + 2, and 3 + 1).

When the sum is 5: There are four combinations (1 + 4, 2 + 3, 3 + 2, and 4 + 1).

When the sum is 6: There are five combinations (1 + 5, 2 + 4, 3 + 3, 4 + 2, and 5 + 1).

When the sum is 7: There are six combinations (1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, and 6 + 1).

When the sum is 8: There are five combinations (2 + 6, 3 + 5, 4 + 4, 5 + 3, and 6 + 2).

When the sum is 9: There are four combinations (3 + 6, 4 + 5, 5 + 4, and 6 + 3).

When the sum is 10: There are three combinations (4 + 6, 5 + 5, and 6 + 4).

Adding up the favorable outcomes, we get: 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 = 33.

Therefore, the probability that the sum of the two dice numbers does not exceed 10 is given by:

Probability = Favorable outcomes / Total outcomes = 33 / 36 = 11/12 ≈ 0.9167.

So, the probability is approximately 0.9167 or 91.67%.

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since its an isosceles triangle, which is divided at the centre,

the remaining length of the given right angle triangle is 5

using pythagoras theorem to find x

x^2 = 8^2 - 5^2

x^2 = 64 - 25

x^2 = 39

x = square root of 39

x = 6.25

therfore the answer is:

A. 6.25

Step-by-step explanation:

Puzzle 1

(a + bi) (c + di)

ac + adi + bci + bdi²

(ac − bd) + (ad + bc)i

Matching coefficients:

30 < ac − bd < 80

ad + bc = 0

We need to pick four integers between -9 and 9 such that these two equations are satisfied.  One possible combination is:

a = 8, b = -4, c = 6, d = 3

The number would be:

ac − bd = (8)(6) − (-4)(3) = 60

Puzzle 2

Using the result from Puzzle 1:

ac − bd = 34

ad + bc = 8

Like before, it makes sense to assume b is negative.  With some trial and error, one possible answer is:

a = 5, b = -6, c = 2, d = 4

Letters x, y, and z are angle measures. The following equations would ensure that lines p and q are parallel: x = z ; x + y = 180°

A Equation is a numerical explanation that is comprised of two articulations associated by an equivalent sign. In its simplest form in algebra, an equation is a statement that demonstrates that two mathematical expressions are equal.

The image with the angles x, y, and z, as well as the lines p and q, can be found in the link at the answer's conclusion.

Using the image provided;

We can see that the two parallel lines p and q are divided by a transverse line. As a result,

We can say that because we can see that x and z are angles that correspond to one another; Second, we can see that y and z are supplementary angles due to the fact that they form a straight line and that the sum of straight angles is 180 degrees.

therefore; We can say that, using the negotiation property of equivalency, y + z = 180° because x = z.

x + y = 180°

Question:

Angle measures are represented by x, y, and z. Which conditions could ensure that lines p and q are equal? Select all relevant options.

x = z, x + y = 180°, x = y, and z = 180°

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Answer:

The 2nd option

Step-by-step explanation:

As x approaches postive and negative infinity, y approches negavite infinity

start by graphing the function

After having the graph we can see that the function is decreasiong over the interval

and increasing over the interval

Answer:

Below

Step-by-step explanation:

Similar triangles due to A - A - A

Set up ratios

QR is to RS   as  QP is to TS

(x+2) / (2x-5) = 3/5       Cross multiply to get

5x+10 = 6x-15               subtract 5x from both sides of the equation

10 = x - 15                     add 15 to both sides

25 = x

Answer:

Option D, 4

Step-by-step explanation:

2 pizzas x 6 slices per pizza = 12 slices of pizza

12 slices of pizza divided by 3 friends eating equal slices = 4 slices per friend

Option D, 4, is your answer

The value of y = -1/6 if we solve 3y+3 = 9y+4 for the value of y.

Given that, 3y+3 = 9y+4 and we have to solve this linear equation in variable for the variable y. Simply we have to find out the value of y from the given equation.

Let's procced to solve the equation 3y+3 = 9y+4 step by step.

3y+3 = 9y+4

⇒3y-9y = 4-3

⇒-6y = 1

⇒6y = -1

⇒y = -1/6

Hence, the value of y = -1/6 if we solve 3y+3 = 9y+4 systematically.

Therefore, y = -1/6 is the required answer.

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