1. Add: 85 + (-96)


i need help

The rate of change of the demand is -16.538 per month.

Given that:

A price p (in dollars) and demand x for a product are related by:

2x² + 3xp + 50p² = 28000

Substitute p = 20.

2x² + 60x + 50(20²) = 28000

2x² + 60x - 8000 = 0

2(x² + 30x - 4000) = 0

x² + 30x - 4000 = 0

This can be factorized as:

(x + 80)(x - 50) = 0

So, x = -80 or x = 50

Negative demand is not possible.

So, x = 50.

Consider :

2x² + 3xp + 50p² = 28000

Differentiate this with respect to time.

4x (dx/dt) + 3x(dp/dt) + 3p(dx/dt) + 100p(dp/dt) = 0

(dp/dt)(3x + 100p) + (dx/dt)(4x + 3p) = 0

Substitute p = 20, x = 50, and dp/dt = 2.

2(150 + 2000) + (dx/dt)(200 + 60) = 0

260 (dx/dt) = -4300

dx/dt = -16.538

Hence the demand is decreasing at a rate of -16.538 per month.

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The value of the expression (8 1/5 + 4 1/5) - (6 6/8 - 6 2/4) is 243/20.

Let's simplify the addition within the parentheses:

8 1/5 + 4 1/5 = (8 + 4) + (1/5 + 1/5) = 12 + 2/5 = 12 2/5

Next, let's simplify the subtraction within the parentheses:

6 6/8 - 6 2/4 = (6 - 6) + (6/8 - 2/4) = 0 + (3/4 - 1/2) = 0 + 1/4 = 1/4

Now, we can substitute the simplified terms back into the original expression:

(8 1/5 + 4 1/5) - (6 6/8 - 6 2/4) = 12 2/5 - 1/4

To subtract mixed numbers, we need to find a common denominator. The common denominator for 5 and 4 is 20. Converting both terms:

12 2/5 = 12 * 5/5 + 2/5 = 60/5 + 2/5 = 62/5

1/4 = 1 * 5/5 * 5/20 = 5/20

Now we can subtract:

62/5 - 5/20 = (62 * 4)/(5 * 4) - 5/20 = 248/20 - 5/20 = (248 - 5)/20 = 243/20

Therefore, the value of the expression (8 1/5 + 4 1/5) - (6 6/8 - 6 2/4) is 243/20.

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Answer:

x¹=-6 x²=0

Step-by-step explanation:

Substitute y =0

Swap sides

Factor expression

Split into possible cases

Solve equation

Step-by-step explanation:

3^x eventually gets larger......it has exponential growth....the other is only linear growth

Answer:

Vincent’s plane is cruising at an altitude of 3.2 × 10^4 feet.

Convert the number to standard notation.

3.2 × 10^4 feet  

=

3.2 • 10,000 feet

=

32,000 feet

Step-by-step explanation:

This is the sample answer from Edmentum.

Answer:

Question 1 part a =

Vincent’s plane is cruising at an altitude of 3.2 × 104 feet.

Convert the number to standard notation.

3.2 × 104 feet  

= 3.2 • 10,000 feet

= 32,000 feet

Part b =

Felix’s skydiving altitude is 1.28 × 105 feet.

Convert the number to standard notation.

1.28 × 105 feet  

= 1.28 • 100,000

= 128,000 feet

Part c =

Subtract the two altitudes to find the difference.

128,000 feet − 32,000 feet = 96,000 feet

The difference of their altitudes is 96,000 feet.

Part d =

The difference of the altitudes is 96,000 feet.

Covert 96,000 to scientific notation:

96,000 feet = 9.6 × 104 feet

Question 2 part a  =

Vincent’s plane’s altitude is 3.2 x 10^4 feet.

Felix’s skydiving altitude is 1.28 x 10^5 feet.

Transform 3.2 x 10^4  so its exponent matches the power of 10 in 1.28 x 10^5.

To do so, multiply and divide the number by 10.

3.2 x 10^4 = 10/10 x 3.2 x 10^4

                 = 3.2/10 x 10^4 x 10

                 = 0.32 x 10^5

Part b =

Calculate the difference of the two altitudes:

1.28 × 105 – 0.32 × 105

=  (1.28 – 0.32) • 105

= 0.96 • 105

The difference of their altitudes is 0.96 •105 feet.

Part c =

The difference of Vincent’s and Felix’s altitudes is 0.96 x 10^5 feet.

To convert the answer to scientific notation, multiply and divide the number by 10.

0.96 x 10^5 = 10/10 x 0.96 x 10^5

                   = (0.96 x 10) x (10^5 x 10^-1)

                   = 9.6 x 10^4 feet

In scientific notation, the difference of Vincent’s and Felix’s altitudes is 9.6 x 10^4 feet.

Question 3 =

The altitudes are the same. That means you can subtract numbers given in scientific notation using either of two methods: convert them to standard notation and then perform the subtraction, or subtract the numbers in scientific notation without converting them to standard notation.

Step-by-step explanation:

Your answer is in bold. All edmentum answers :)

Hope this helps someone!

Answer:

-1.5 is the gradient (m), correct equation: y= -1.5x-7

Step-by-step explanation:

m=y2-y1/x2-x1

for getting the correct equation, input y, x and m in the equation y=mx+c to find c

Answer:

See below ~

Step-by-step explanation:

Sin A : opposing side of ∠A / hypotenuse

Sin C : opposing side of ∠C / hypotenuse

Cos A : adjacent side of ∠A / hypotenuse

Cos C : adjacent side of ∠C / hypotenuse

Answer:

subtract 2y

Step-by-step explanation:

x= 5-2y or x= -2y+5

The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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The ACT Math section tests a wide range of mathematical concepts and skills, so there are many formulas and concepts that you should be familiar with.

Here are some of the most important ACT math formulas that you should know:

1. Basic operations: addition, subtraction, multiplication, and division.

2. Exponents and roots: \(a^n\) means a multiplied by itself n times; the nth root of a is the number that, when raised to the nth power, gives a.

3. Order of operations: parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).

4. Fractions: converting between fractions, decimals, and percents; adding, subtracting, multiplying, and dividing fractions.

5. Algebra: solving equations and inequalities; simplifying algebraic expressions; factoring quadratics; understanding linear and quadratic functions.

6. Geometry: properties of lines, angles, and polygons; Pythagorean theorem; trigonometric functions; volume and surface area of 3D shapes.

7. Probability and statistics: calculating probabilities; mean, median, and mode; standard deviation.

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a) The area of Helen's circular garden is 314 m².

b) The estimation for the number of boxes of grass seed Helen needs, is 5 boxes.

c) B. The estimation we did in (b) is an underestimation.

The area of a circle is calculated by the formula,

A = πr² sq. units; r - radius

When we have the diameter, we can find the radius by

r = d/2 units

Given that Helen has a garden in the shape of a circle of diameter 20 m.

She is going to cover the garden with grass seed to make a lawn.

Grass seed is sold in boxes. Each box of grass seed will cover 58 m² of the garden.

a) The area of the circular garden is

A =  πr² = 3.14 × (d/2)²

⇒ A = 3.14 × (20/2)²

⇒ A = 3.14 × 100

∴ A = 314 m²

Thus, the area of Helen's garden is 314 m².

b) The number of boxes of grass seed to cover the area of 314 m² is

= area of the garden/area covered by each box of seeds

= 314 m²/58 m²

= 5.4179

So, on an estimation, there are 5 boxes of grass seed that Helen needs.

c) Here, in the above estimation, we rounded the decimal number 5.4179 to 5. Since the number is rounded to the nearest value (smallest value), the estimation is an underestimate.

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Answer:

it's 650 and 350

Step-by-step explanation:

3x+3y=3000

7x+6y=6650

7x+6y-2(3x+3y)=x=650

plug x in the first equation and then divide u find the 350

Answer:

x=-6, y=1

Step-by-step explanation:

Let's solve your system by substitution.

y=x+7;−2x−11=y

Step: Solve y=x+7 for y:

y=x+7

Step: Substitute x+7 for y in −2x−11=y:

−2x−11=y

−2x−11=x+7

−2x−11+−x=x+7+−x(Add -x to both sides)

−3x−11=7

−3x−11+11=7+11(Add 11 to both sides)

−3x=18

−3x/ −3 = 18/ −3  (Divide both sides by -3)

x=−6

Step: Substitute−6 for x in y=x+7:

y=x+7

y=−6+7

y=1  (Simplify both sides of the equation)

Answer:

x=−6 and y=1

Answer:

Step-by-step explanation:

144,72

Answer:

If you cut the rectangle in half, you have two squares of area 144 ft², or side length 12 ft.

The length of the rectangle is 24 ft; its width is 12 ft.

When a password consists of 2 letters followed by 2 digits. Then, number ,of different passwords can be formed using this combination is 67,600.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of a selection is irrelevant. You can choose the components of combos in any order.

The formula for calculating how many arrangements are feasible when only a few items are chosen from a set of items that are unique is as follows:

ⁿCₓ = n! / {(n-x)!×x!}

n = total elements given in the set.

x = total number of selected elements.

! = factorial

Calculation for the different password combination,

The total alphabets in English is 26 (A-Z)

The single digit number is 10 (0-9)

The combination for selecting first letter is;

²⁶C₁ = 26! / {25!×1!} = 26

Similarly, the combination for selecting second letter is;

²⁶C₁ = 26! / {25!×1!} = 26

The combination for selecting 3rd digit is;

¹⁰C₁ = 10! / {9!×1!} = 10

and, the combination for selecting 4th digit is;

¹⁰C₁ = 10! / {9!×1!} = 10

Thus, the total combination becomes;

= 26×26×10×10

= 67,600

Therefore, the number of total combination formed using 2 letters followed by 2 digits are 67,600.

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Answer:

x (x^2+4)

Step-by-step explanation:

See the steps below:)

Answer:

3x-2

Step-by-step explanation:

(-7x+6)-(-10x+8)

open the parenthesis

-7x+6+10x-8

combine like terms

3x-2

The counterexample that disproves the inequality n³ ≤ 3n² is n = 4.

To disprove the statement n³ ≤ 3n², we need to find a counterexample, which is a value of n for which the inequality is false.

Let's evaluate the inequality for the given options:

a. n = 0:

0³ ≤ 3(0)²

0 ≤ 0

The inequality holds for n = 0.

b. n = -1:

(-1)³ ≤ 3(-1)²

-1 ≤ 3

The inequality holds for n = -1.

c. n = 0.5:

(0.5)³ ≤ 3(0.5)²

0.125 ≤ 0.75

The inequality holds for n = 0.5.

d. n = 4:

4³ ≤ 3(4)²

64 ≤ 48

The inequality does not hold for n = 4.

Therefore, the counterexample that disproves the inequality n³ ≤ 3n² is n = 4.

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Answer:

30

Step-by-step explanation:

3 equals 10% of what? ​

10% = 0.1

3 = 0.1x

divide both sides by 0.1

3/0.1 = 0.1x/0.1

x = 30

Answer:

x =10

Step-by-step explanation:

10/100 = 3/x

cross multiply and you get 300 = 10x

divide by 10 on both sides 10x/10 get canceled out you want to get the varaible on one side of the equation then divide 300/10 and you get 30 so your final answer is x=30  hope this helped you sorry if incorrect

We know 3x16=48

Since there is a minus sign, the answer is -48.

:)

Answer:

x-intercept = (18/5,0)

y-intercept = (0,-2)

Step-by-step explanation:

I graphed it and found the intercepts

brainliest would be great

The formula nCr = n! / (n-r)!r! represents the number of combinations of r items that can be selected from a set of n distinct items without regard to order.

The formula nCr = n! / (n-r)!r!, where n is the total number of items and r is the number of items selected without replacement, represents the number of combinations of r items that can be selected from a set of n distinct items.

This  formula is known as the combination formula or the binomial coefficient formula.

The  symbol "nCr" is read as "n choose r", indicating the number of ways to choose r items from a set of n items without regard to order. The exclamation mark symbol (!) represents the factorial function, which is the product of all positive integers up to and including the given integer.

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Answer:

I think the answer is D

Answer:

y=-10x+34

Point-slope form: y + 6= -10(x - 4)

Slope-intercept form: y = -10x + 34

Answer:

y = -10x + 34

Step-by-step explanation:

Note the slope-intercept form:

y = mx + b

In which:

y = (x , y)

m = slope

x = (x , y)

b = y-intercept

-

Also, remember to follow PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponent (& Root)

Multiplication

Division

Addition

Subtraction

-

Note also the equal sign, what you do to one side of the equation, you will do to the other:

y + 6 = -10(x - 4)

First, distribute -10 to all terms within the parenthesis. Multiply -10 to x and -4. Note that:

1) When you multiply a negative and a positive term together, the answer will be negative.

2) When you multiply two negative terms together, the answer will be positive.

y + 6 = -10(x - 4)

y + 6 = (-10 * x) + (-10 * -4)

y + 6 = -10x + 40

Next, isolate the variable, y. Do so by subtracting 6 from both sides of the equation:

y + 6 (-6) = -10x + 40 (-6)

y = -10x + (40 - 6)

y = -10x + 34

y = -10x + 34 is your answer.

~

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The median of the given data set as required to be determined in the task content is; 4.

It follows from the task content that the value which represents the median of the data set is to be determined.

By observation, the number of data values in the data set is; 15. On this note, the median value would be the eighth term in an orderly arrange of the values.

Consequently, the median of the data set as required is; 4.

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285 yards of wire purchased in October will cost $3705.

We will use unitary method for calculation.

The cost of one yard of wire = total cost ÷ length of wire × unit length

Cost of one yard of wire = 1235 ÷ 95 × 1

Performing division on Right Hand Side of the equation

Cost of one yard of wire = $13

Now calculating the cost for purchase of 285 yards of wire in October.

Cost of wire in October = 285 × 13

Performing multiplication on Right Hand Side of the equation

Cost of wire in October = $3705

Thus, the cost of purchase in October is $3705.

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According to the information the proposed weights of the criteria are as follows: Cost: 0.7333333, Dimension: 1, Durability: 0.92857143, Ease of use: 0.625. Additionallt, The AHP scores for the alternatives are as follows: A1: 0.7333333, A2: 0.75, A3: 1. Finally, based on the criteria weights and AHP scores, the recommendation is to select alternative A3 due to its highest AHP score of 1, indicating that it is the most suitable choice considering the given criteria.

(a) The normalized weights provided in the table represent the proposed weights of the criteria. These weights are derived from the pairwise comparison matrix. Each weight corresponds to a criterion and indicates its relative importance compared to other criteria. In this case, the proposed weights are as follows:

The AHP scores represent the overall scores for each alternative based on the criteria weights. These scores are obtained by multiplying the normalized weights of the criteria by the corresponding entries in the pairwise comparison matrix and summing the results. In this case, the AHP scores for the alternatives are as follows:

(c) Considering the AHP scores, the alternative with the highest score is A3, which indicates that it is the most suitable choice according to the given criteria.

So, the recommendation is to select alternative A3. However, since the consistency of the weights was not calculated, it is important to note that this recommendation assumes the weights to be consistent.

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

Attached image

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Three consecutive integer, such that the sum of the 1st and the 2nd equal 5 time the 3rd are -3, -2, -1.

Consecutive numbers are those that come after one another in a predictable pattern or counting sequence. They are written in a sequential order with defined difference between the numerals and no gaps in between.

Let the three consecutive integer be (x-1), x, (x+1)

We have condition as,

the sum of the 1st and the 2nd equal 5 time the 3rd so,

(x-1) + x = 5(x+1)

2x -1 = 5x + 5

5x - 2x = -1 -5

3x = -6

x = -6/3

x = -2

Therefore, the three consecutive integers are -3, -2, -1.

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Answer:

8 of 10 free throws

Step-by-step explanation:

10/15 is .6666667 or about 67%

But 8/10 is .8 or 80%

80% > 60%