Last summer, Brianna planted 2 plants
per square foot in her garden box.
How many plants will she plant this
summer?

Answer:

✓73 or approximately 8.54

Step-by-step explanation:

✓ 8²+3² = ✓ 73 or approximately 8.54

To find the derivative of y with respect to x (dy/dx), we will apply the chain rule and the product rule. dy/dx = -3x * sin(3xy) - 3y

To differentiate both sides of the equation with respect to x, we obtain: dy/dx + 1 = d/dx [cos(3xy)] =Now, let's evaluate the derivative of the right-hand side using the chain rule: dy/dx + 1 = -sin(3xy) * d/dx [3xy]

To differentiate 3xy with respect to x, we apply the product rule: dy/dx + 1 = -sin(3xy) * (3y * dx/dx + 3x * dy/dx) Since dx/dx equals 1, the term 3y * dx/dx simplifies to 3y.

Now, rearranging the equation to solve for dy/dx: dy/dx = -sin(3xy) * 3x -  3y Therefore, the derivative of y with respect to x, dy/dx, is given by: dy/dx = -3x * sin(3xy) - 3y

This is the result of differentiating the given equation, y + x = cos(3xy), with respect to x using the chain rule and product rule.

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We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

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Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer: The numbers are 13 and 14

Step-by-step explanation:

Since they are two consecutive numbers, let the numbers be x and x+1.

We are told that twice the first number is twelve more than the second number. This can be expressed as:

2 × x = x+1+12

2x = x+13

2x-x = 13

x = 13

Since x = 13, x+1 = 13+1 = 14

The numbers are 13 and 14

Answer:

B im pretty sure

Step-by-step explanation:

The correct answer to the given question is d. 2n+1. The other options, such as 1n, 3n, 2n-1, and 2n+2, do not accurately represent the chromosome number of a trisomic organism.

A trisomic organism is one that has an extra copy of a chromosome in its genome. This means that it has three copies of a particular chromosome instead of the usual two, which can have significant implications for the organism's development and health.

In terms of algebraic notation, the chromosome number of a trisomic organism would be denoted as 2n+1, where "n" represents the normal diploid number of chromosomes for that organism. The "2n" represents the normal two sets of chromosomes, and the "+1" represents the extra chromosome.

Therefore, the correct answer to the given question is d. 2n+1. The other options, such as 1n, 3n, 2n-1, and 2n+2, do not accurately represent the chromosome number of a trisomic organism. It is important to note that trisomies can occur for any chromosome, not just the sex chromosomes, and can have varying effects depending on which chromosome is affected.

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Answer: Positive correlation

Step-by-step explanation:

As you go up and along the graph the values go up.

Both have to be increasing basically.

Hence, the \(200th\) term in the sequence is \(1613\).

What is the sequence?

A sequence is a list of objects, typically numbers, in which order matters, repetition is allowed, and the same elements can appear multiple times at different positions in the sequence.

Here given that,

The sequence is

\(21,29,37,45,53,...\)

The general formula is

\(a_n=a_1+d(n-1)\)

\(a_1=21\)

\(d=a_2-a_1\\d=29-21\\d=8\)

Substitute it in the general formula is

\(a_2_0_0=21+8(200-1)\\a_2_0_0=21+8(199)\\a_2_0_0=21+1592\\a_2_0_0=1613\)

Hence, the \(200th\) term in the sequence is \(1613\).

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The solution of the given problem of equation comes out to be the equation for the line passing through (-6, 4) and perpendicular to y = 6x - 1 is y = (-1/6)x + 3.

On the fοundatiοn οf the equatiοn y=mx+b is a healing mοdel based οn linearity. The y-intercept is m, and the slοpe is B. Despite the fact that y alοng with y are separate parts, the abοve sentence is cοmmοnly referred tο as  Bivariate linear equatiοns have twο cοmpοnents. When it cοmes tο using linear functiοns, there are nο easy sοlutiοns. and. Y=mx+b is the expressiοn, where m stands fοr slοpes and b fοr the y-intercept.

Here,

We knοw that the slοpe οf οur new line will be the negative cοunterpart οf 6, οr -1/6, because we are trying tο determine the equatiοn οf a line that is perpendicular tο y = 6x - 1.

Nοw that we knοw the equatiοn οf the line passing thrοugh the pοint (-6, 4) with a slοpe οf -1/6, we can use the pοint-slοpe fοrm οf a linear equatiοn tο determine it:

=> y - y1 = m(x - x1)

where m = 1/6 and (x1, y1) = (-6, 4)

=> y - 4 = (-1/6)(x - (-6))

=> y - 4 = (-1/6)(x + 6)

=> y - 4 = (-1/6)x - 1

=> y = (-1/6)x + 3

As a result, the equation for the line passing through (-6, 4) and perpendicular to y = 6x - 1 is y = (-1/6)x + 3.

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Fill-in the missing pieces for the equation of the line that is perpendicular to y=6x-1 and passes through (-6,4).

y = __________.

Answer:

  18

Step-by-step explanation:

You want the number of vertices such that the number of pairs of vertices is 153.

The number of n objects taken 2 at a time is ...

  N = (n)(n -1)/2

You want to find n for N=153.

We notice that multiplying by 2 gives a near square:

  2N = n(n -1)

The square root of this will have a value approximately equal to n-1/2:

  n -1/2 ≈ √(2·153) = √306 ≈ 17.5   ⇒   n = 18

We can check this:

  (18)(17)/2 = 9·17 = 153

The mystic rose with 153 lines has 18 vertices.

__

Additional comment

We could solve the quadratic equation 306 = n(n-1) by any of several means. The method used here is about the fastest.

If you want to get formal about solving the equation this way, you can define z = n-1/2, then the equation becomes ...

  306 = (z +1/2)(z -1/2) = z² -1/4

  306.25 = z²   ⇒   z = 17.5   ⇒   n = 18

By leaving off the 0.25 addition to 306, the root we get is slightly low, but still close enough to 17.5 to show us what the answer is.

To prove that the group g is cyclic, we analyze the possible values of the order |g|. We consider the cases for each possible value and demonstrate that in all cases, g is either cyclic or leads to a contradiction.

For |g| = 1, 2, 3, 5, or 7, the groups of these orders are always cyclic.

If |g| = 4, 6, 8, 9, 10, 12, or 15, we show that g cannot have the required subgroups. Assuming g is not cyclic, we find an element x of order 2 and additional elements y, z, w, etc., also of order 2. This contradicts the given conditions since g would be isomorphic to Z₂ × Z₂ or have more than one subgroup of order 3 or 5.

For composite orders |g| = pq, where p and q are prime, we generalize the analysis. By Cauchy's theorem, g has elements of order p and q, and since there is only one subgroup of each order, they are cyclic. We show that the intersection of these subgroups cannot have an order of pq, leading to a contradiction. Hence, g is cyclic.

Therefore, in all cases, g is proved to be cyclic. QED.

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Answer:

x = 4

Step-by-step explanation:

Given the equation:

\(\displaystyle{4^x - 4^0 - 255=0}\)

We know that \(\displaystyle{a^0 = 1}\) where a ≠ 0. Therefore,

\(\displaystyle{4^x - 1 - 255=0}\\\\\displaystyle{4^x - 256=0}\)

Add both sides by 256, so we have:

\(\displaystyle{4^x=256}\)

Factor 256 out:

256 = 2 x 128 = 2 x 2 x 2⁶ = 2⁸

Therefore, 256 = 2⁸.

\(\displaystyle{4^x=2^8}\)

Convert to the same base:

\(\displaystyle{\left(2^2\right)^x=2^8}\\\\\displaystyle{2^{2x} = 2^8}\)

When two sides have same base, solve the equation through exponents:

\(\displaystyle{2x=8}\)

Divide both sides by 2, so we have:

\(\displaystyle{x=4}\)

Answer:

See below ~

Step-by-step explanation:

Part (a) :

Part (b) :

Answer:

(a) The length is 85 m.

(b) The width is 89 cm.

Step-by-step explanation:

(a)

Perimeter (P) formula using the length (L) and width (W) of a rectangle.

P = 2L + 2W

P = 278 m

W = 54 m

278 = 2L + 2(54)

2L + 108 = 278

2L = 170

L = 85

Answer: The length is 85 m.

(b)

Area (A) formula using the length (L) and width (W) of a rectangle.

A = LW

A = 8811 cm²

L = 99 cm

8811 = 99 × W

W = 8811/99

W = 89

Answer: The width is 89 cm.

Joshua's song was played on 6 commercials and 2 movies.

Let the number of played movies be x. So, number of played commercials will be x + 4. Now, further forming the equation based on the route earned on each song.

(120×x) + 30×(x + 4) = 420

Performing multiplication on Left Hand Side of the equation

120x + 30x + 120 = 420

120x + 30x = 420 - 120

Performing addition and subtraction on Left and Right Hand Side

150x = 300

x = 300 ÷ 150

Performing division

x = 2

So, the number of movies = 2

Number of commercials = 2 + 4

Number of commercials = 6

Hence, song was played on 2 movies and 6 commercials.

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Answer:

100 minutes for 40 dollars

Step-by-step explanation:

Call U Now

15+ .25 m

The Pacific Bell Company

25 +.15m

We want them to have the same cost so set them equal

15+ .25m=25 +.15m

Subtract .15m from each side

15+ .25m - .15m=25 +.15m- .15m

15 + .1m = 25

Subtract 15 from each side

15 + .1m = 25

15-15 +.1m = 25-15

.1m = 10

Divide each side by .1

.1m/.1 = 10/.1

m =100

The cost will be

15+.25m

15 +.25(100)

15 + 25

40

try the other answer.

Answer:

a. x=2

b. y=5

Step-by-step explanation:

a. 2(11x+7)=58

22x+14=58

x=2

b. 16y+10=90

16y=80

y=5

The correct option e) 94.29%, for the probability that among the next 166 responses there will be at most 43 correct answers.

If we use a normal distribution to simulate any binomial distribution with p = 0.24 for n = 166 results, then:

There should be 43 correct responses, or

μ = np = 166*0.24

μ = np = 34.86

The number of accurate responses has a standard deviation of

σ = √(np(1-p))

σ = √(34.86*0.76)

σ = 5.14

43 correct responses have a z-value;

z = (x - μ)/σ

z = (43 - 34.86)/5.14

z = 1.58

The likelihood that 43 accurate responses are provided is:

N(1.58) = 0.9429

Thus, the probability that among the next 166 responses there will be at most 43 correct answers is 94.29%.

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The complete question is-

Use the normal distribution to approximate the desired probability. A certain question on a test is answered correctly by 24.0 percent of the respondents. Estimate the probability that among the next 166 responses there will be at most 43 correct answers.

a) 74.56870% b) 74.30203% c) 75.20203% d) 94.95%  e) 94.29%

1. The maximum running speed of a person with a leg length 1.1 m is 8.2 m/s

2. The leg length of a person with a running speed 6.7 m/s is 0.7m

3. As the length increases , the maximum speed also increase.

A word problem is a math problem written out as a short story or scenario. The statements are interpreted into mathematical equation or expression.

If S = π√(9.8l/1.6)

a. when l = 1.1

S = 3.14√9.8×1.1/1.6

S = 3.14√6.74

S = 3.14 × 2.596

S = 8.2m/s (nearest tenth)

b. When S = 6.7m/s, l =

6.7 = 3.14√9.8l/1.6

√9.8l/1.6 = 6.7/3.14 = 2.134

9.8l/1.6 = (2.134)²

9.8l/1.6 = 4.55

l = (4.55×1.6)/9.8

l = 0.7m ( nearest tenth)

c. The leg length is proportional to the maximum speed , therefore as the leg length increases, the maximum speed increases.

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Answer:

lol ok

have a good day :)

Step-by-step explanation:

Answer:

\( \frac{3}{8} \)

Step-by-step explanation:

First, you add up the amount of students.

\(1250 + 750 = 2000\). Now, you take 750 (crabwrey bog) and divide it by 2000 (the total). Keep simplifying until you can't anymore.

\( \frac{750}{2000} = \frac{75}{200} = \frac{15}{40} = \frac{3}{8} \)

So the fraction of students who preferred cranberry bog is

\( \frac{3}{8} \)

Answer:

750/2000

Step-by-step explanation:

1250+750=2000 and the focus is cranberry bog so 750/2000 is the answer

Divide the distance traveled by the wheel to guess the value or estimate the value of π.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center.

Given

Height of the wheel = 198

Perimeter of the wheel = 63

Height of the wheel is the diameter of the circle

Perimeter of the circle is  π × diameter of the circle

P = \(\pi\) × d

198 = \(\pi\) × 63

\(\pi\) = \(\frac{198}{63}\)

\(\pi\) = 3.14

Hence, Divide the distance traveled by the wheel to guess the value or estimate the value of π.

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a) \(x^5-x^3\)

\(x^3\left(x^2-1\right)\) ........take out x³

\(x^3\left(x+1\right)\left(x-1\right)\) ......separated (x²-1)

b) \(3x^2-75\)

\(3\left(x^2-25\right)\) ........took out 3.

\(3\left(x+5\right)\left(x-5\right)\)  .......separated (x²-25)

c) \(3x^5y+4x^4y-5x^2y\)

\(x^2y\left(3x^3+4x^2-5\right)\) ............takeout x²y at the front.

d) \(81x^3-125\)

\(81x^3-125\) ......cannot be factorised much more further.

Solution:

Part - A:

To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by x⁴ (GCF), which can factorize completely. This will subtract 4 from the exponents.

Part - B:

To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by 3 (GCF), which can factorize completely. This will divide 3 from the terms.

Part - C:

To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by x²y (GCF), which can factorize completely.

Part - D:

Unfortunately, this expression can't factor with rational numbers. The expression results in 81x³ - 125.

Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, the change in the mean is calculated as follows:

Change in mean = Mean of second data set - Mean of first data set

Since none of the values in the second data set have changed, the mean of the second data set is the same as the mean of the first data set. Therefore, the change in the mean is:

Change in mean = Mean of second data set - Mean of first data set

= Mean of first data set - Mean of first data set

= 0

Thus, the change in the means between Kelly's original survey and her second survey is zero.

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To find the mass percent of a substance, you need to know the mass of the substance and the total mass of the mixture. The formula for mass percent is:

Mass percent = (mass of substance / total mass of mixture) * 100

For example, let's say you have a mixture that is made up of 50 grams of salt and 100 grams of water. To find the mass percent of salt in the mixture, you would use the following calculation:

Mass percent of salt = (50 grams of salt / 150 grams total) * 100 = 33.33%

This means that 33.33% of the total mass of the mixture is made up of salt.

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Step-by-step explanation:

please mark me as brainlest

Answer:

Cross multiply the gcf/gcd on them hope it helped :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

5x + 40x + 40x + 31 = x + 7

85x + 31 = x + 7

Bringing like terms on one side

85x - x = 7 - 31

84x = - 24

x = - 24/84 = 2/7

Answer:

Fraction means how much from the main graph is it taking, for example, the circle is a 1/4 white 3/4 green to find the decimal, divide the number under the line by the one above it, 4 divided by 3 for example

Step-by-step explanation:

Fraction means how much from the main graph is it taking, for example, the circle is a 1/4 white 3/4 green to find the decimal, divide the number under the line by the one above it, 4 divided by 3 for example