the logarithm of a product of two numbers is the same as the sum of the logarithms of these numbers. so log4(16 · 64) = log4(16) .

Check the picture below.

\(\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=4 \end{cases}\implies S=180(4-2)\implies S=360 \\\\[-0.35em] ~\dotfill\\\\ (40)+(2x)+( ~~ 360-(x+100) ~~ )+(x)~~ = ~~360 \\\\\\ (40)+(2x)+( ~~ 360-x-100 ~~ )+(x)~~ = ~~360\implies 2x+300=360 \\\\\\ 2x=60\implies x=\cfrac{60}{2}\implies \boxed{x=30}\)

The linearized equation for the non-linear equation z = x² + 4xy + 6xy² in the region defined by 8 ≤ x ≤ 10, 2 ≤ y ≤ 4 is given by :

z ≈ 244 + 20(x - 8) + 128(y - 2).

When using the linearized equation to calculate the value of z at x = 8, y = 2, the error is 0.

1.1. To linearize the equation in the given region, we need to find the partial derivatives of z with respect to x and y:

∂z/∂x = 2x + 4y

∂z/∂y = 4x + 6xy

At the point (x₀, y₀) = (8, 2), we substitute these values:

∂z/∂x = 2(8) + 4(2) = 16 + 8 = 24

∂z/∂y = 4(8) + 6(8)(2) = 32 + 96 = 128

The linearized equation is given by:

z ≈ z₀ + ∂z/∂x * (x - x₀) + ∂z/∂y * (y - y₀)

Substituting the values, we get:

z ≈ z₀ + 24 * (x - 8) + 128 * (y - 2)

1.2. To find the error when using the linearized equation to calculate the value of z at x = 8, y = 2, we substitute these values:

z ≈ z₀ + 24 * (8 - 8) + 128 * (2 - 2)

= z₀

Therefore, the linearized equation gives the exact value of z at x = 8, y = 2, and the error is 0.

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The rule of obtuse angle is that one angle measures more than 90° and total sum og angle should be 180°.

Acute, obtuse, right, straight, reflex, and complete rotation are some of the terms used to describe fundamental angles. Two rays are joined at their termini to form the geometric shape known as an angle. The most common way to express an angle is in degrees.

A measure of an angle or the amount of turning required to bring one line or plane into coincidence with or parallel to another angled is represented by two lines extending from the same point.

A triangle is said to have an obtuse angle if one of the inner angles is greater than 90 degrees. If one of the angles of an obtuse triangle is greater than 90°, then the total of the other two angles is also less than 90°.

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In the given equation x = 9 is the value that satisfies the equation.

The square root of a number is a value that, when multiplied by itself, equals the original number. For example, the square root of 9 is 3, because \(3*3 = 9\). The symbol for square root is "√" and it can also be represented as "sqrt".

In the given equation \(x = 9\) is the value that satisfies the equation.

To find the value of x in the equation \(3 \sqrt{x} = 9\), we first need to square both sides of the equation to eliminate the square root.

\(3 \sqrt{x} = 9\)

Squaring both sides:

\((3 \sqrt{x} )^2 = 9^2\)

\(x = 9^2 / 3^2 = 9^2 / 9 = 9\)

Therefore, x = 9 is the value that satisfies the equation.

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x = 6 can be represented on the number line and hence it is real

Step-by-step explanation:

by simply plugging in 6 for x thus

x=6 becomes 6=6 which is true

Answer:

For 1 cup of  pineapple 1 .5  cups of strawberries are used.

Step-by-step explanation:

This question can be solved by using ratios

Strawberry       :      Pineapple

1     cup              :          2/3 cup

x cup                  ;            1 cup

Using the cross product rule

2/3 * x= 1*1

x= 1*1 ÷ 2/3

x= 1*3/2= 1 1/2= 1.5

For 2 cups of pineapple 3 cups of strawberries are used.

For 1 cup of  pineapple 1 .5  cups of strawberries are used.

For 3 cups of pineapple 4.5 cups of strawberries are used.

The diseases that affect the xylem and phloem of trees are called vascular diseases. It is important to monitor the health of trees and identify and treat any vascular diseases early on to prevent further spread and damage to the tree and surrounding environment.

Vascular diseases are caused by different types of pathogens, such as fungi, bacteria, viruses, and nematodes. These pathogens can infect the xylem and phloem, leading to the disruption of water and nutrient transport within the tree. Vascular diseases can cause severe damage to the tree, including wilting, yellowing or browning of leaves, stem and root rot, and ultimately, death.

There are several types of vascular diseases that affect trees, including Dutch elm disease, oak wilt, Verticillium wilt, and citrus greening disease, to name a few. Dutch elm disease is caused by a fungus that invades the xylem, leading to blockage and eventual death of the tree. Oak wilt is another fungal disease that affects the xylem and causes rapid wilting and death of the tree. Verticillium wilt, caused by a soil-borne fungus, affects the xylem and phloem, leading to yellowing and wilting of leaves and branches. Citrus greening disease, caused by a bacterium, affects the phloem and disrupts nutrient transport, leading to stunted growth and eventual death of the tree.

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The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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Answer:

yup. looks right to me

Step-by-step explanation:

Answer:

No the answer is square root {2}

Step-by-step explanation:

1/2+1/square root 2+ Square root 3/2 1\square root 2

The probability of a selected sample is 0.0001.

What is a normal distribution?

It is also known as Gaussian distribution. It shows the data near the more. This appears as bell curve in graphical form. It is a bell shaped frequency distribution curve of a continuous random variable.

Given that,

μ= 10 pounds

σ=2 pounds

n=16

Sampling distribution of mean is

μₓ⁻ =μ=10

Standard error of mean is

σₓ⁻ =σ/√n

=2/√16

=0.5

p(μₓ⁻ >12.5)

=1-p((x⁻-μₓ⁻/σₓ⁻ )≤ ((12.5-10)/0.5)

=1-p(z≤5)

using standard normal table,

=1-0.9999

=0.0001

The probability of a selected sample is 0.0001.

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Answer:

\(\sqrt{20\\}\)

Step-by-step explanation:

a^2 +b^2=c^2

c is the hypotenuse

assuming that 2 is a and 4 is b, then it would be:

2^2 + 4^2= c^2

4+16=c^2

20=c^2

take the square root of both sides

\(\sqrt{20}=\sqrt{c^{2} }\)

c=\(\sqrt{20}\)

hope this helped!! <333

Problem N 9

we have that

UW=UV+VW -----> by addition segment postulate

substitute given values

(2x-8)=(x-8)+(12)

solve for x

2x-8=x+4

2x-x=4+8

therefore

The answer is

PART A) Janet needs only three cups of sugar to make three batches of chocolate chip cookies.

PART B) One cup of sugar will be left over after making three batches of cookies.

What is the unit price?

A unit price is the cost of a single object or unit of measurement, such as a pound, a kilogram, or a pint, and it is used to compare the prices of similar products offered in various weights and quantities. Selling more than one unit of the same product at a discount from its unit price is known as multiple pricing.

Given that Janet needs One cup of sugar to make one batch of chocolate chip cookies.

Part A:

Let The number of cups of sugar Janet needs to make three batches of cookies be 'x'.

Now,

1 batch/ 1 cup = 3 batch/ x cups

x= 3

Therefore, Janet needs only three cups of sugar to make three batches of chocolate chip cookies.

Part B:

Given that Janet has four cups of sugar.

From part A, we found that she only need three cups of sugar.

Available - Needed = Excess

4-3=1

So, one cup of sugar will be left over after making three batches of cookies.

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Answer:

$24.32

Step-by-step explanation:

I'm assuming that this is combining percentages, so we just need to multiply twice.

38*4/5=30.40

30.40*4/5=24.32

$24.32

(1) Sequence: an = cos (πn/4n+1).  To determine if the sequence converges or diverges, we need to find the limit as n approaches infinity. Let's calculate the limit:

lim n→∞ cos (πn/4n+1)

As n approaches infinity, the argument of the cosine function becomes 0/∞, which is an indeterminate form. We can apply l'Hôpital's Rule to find the limit:

lim n→∞ (d/dn (πn/4n+1)) / (d/dn (1))

Taking the derivatives, we have:

lim n→∞ (π(4n+1) - πn(4)) / 0

Simplifying further:

lim n→∞ π(4n + 1 - 4n) / 0

lim n→∞ π / 0

Since the denominator is 0, this limit is undefined. Therefore, the sequence diverges.

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Answer:

We have,

side= a

= 8 cm

We know that the area of the regular hexagon

\( = \frac{3 \sqrt{3} }{2} {a}^{3} \)

\( = \frac{3 \sqrt{3} }{2} {8}^{2} \)

\( = \frac{3 \sqrt{3} }{2} \times 64\)

\( = 96 \sqrt{3} \: \: {cm}^{2} \)

Step-by-step explanation:

Hope it is helpful...

Answer:

40

Step-by-step explanation:

The 3 part of the ratio 3 : 4 represents 30 black socks, thus

30 ÷ 3 = 10 ← value of 1 part of the ratio , thus

4 parts = 4 × 10 = 40 ← number of white socks

The Spectrochemical Series is a concept in inorganic chemistry that ranks ligands (molecules or ions) based on their ability to split or shift the d-orbital energy levels of a central metal ion in a coordination complex.

It helps in understanding the bonding and properties of transition metal complexes. The Spectrochemical Series arranges ligands in order of increasing strength of their field, known as the ligand field strength. Ligands at the weaker end of the series induce a smaller splitting of the d-orbitals, while ligands at the stronger end cause a larger splitting.

The ligand field strength affects various properties of transition metal complexes, such as color, magnetic properties, and reactivity. Ligands that produce a larger splitting result in more intense color and higher paramagnetic behavior. On the other hand, ligands that cause a smaller splitting lead to less intense color and lower paramagnetic behavior.

The Spectrochemical Series is typically arranged as follows, from weakest to strongest ligand field:

I- < Br- < Cl- < F- < OH- < H2O < NH3 < en < NO2- < CN- < CO

Here, I- (iodide) is the weakest ligand, and CO (carbon monoxide) is the strongest ligand in terms of their ability to split the d-orbitals.

It's important to note that the Spectrochemical Series is a general guide, and the actual ligand field strength can depend on various factors, such as the nature of the metal ion, its oxidation state, and the coordination geometry of the complex.

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Answer:

9/10 NINE OVER 10

Step-by-step explanation:

To add two fractions they must be over a common denominator, which for this problem is  10. To put each fraction over a common denominator we must multiply each fraction by the appropriate form of  1. 2/5 + 1/2 ( 2/2 X 2/5 ) +  (5/5 X 1/2 ) --> 4/10 + 5/10

We can now add the numerators of the two fractions over the common denominator: 4/10 + 5/10 ---> 4+5/10 ---> 9/10.

Hope this helps! I know what does though, marking me brainliest.

Answer:

n= -4

Step-by-step explanation:

Divide by -5 on both sides, regularly, 20/5 is equal to 4 so basically all youre doing is making it -4. Hope this helps :)

-5n=20

-4

I belive........

3 number of can soup and 4 number of frozen dinners was purchased at the grocery store.

Let y represent the number of dinners purchased and x the number of can soups.

Hence:

x + y = 7   (1)

Also:

400x + 600y = 3600  (2)

Plotting both equations on the graph, the solution is the point of intersection which is at (3, 4)

3 number of can soup and 4 number of frozen dinners was purchased at the grocery store.

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We can form a total of 42 stacks of 8 cans each from the 7 boxes of cat food received by the pet store.

Now, We can use a bar model to represent the total number of cans and the number of stacks that can be formed.

First, let's find the total number of cans:

7 boxes x 48 cans/box = 336 cans

Now, let's use a bar model to represent this total:

| 336 cans of food  |

Next, we want to find how many stacks of 8 cans we can form. We can use a separate bar model to represent the size of each stack:

| 42 stacks of 8 cans each |

Hence, The number of stacks that can be formed, we need to divide the total number of cans by the number of cans in each stack:

336 cans ÷ 8 cans/stack = 42 stacks

So the final bar model looks like this:

| 336 cans of food  | = | 42 stacks of 8 cans each |

Therefore, we can form a total of 42 stacks of 8 cans each from the 7 boxes of cat food received by the pet store.

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A scatter plot or a line graph could be used to represent the relationship between the two variables.

A scatter plot is a graph in which each data point is represented by a dot on the graph. In this case, the data points would represent the amount of money spent on groceries and the percentage of that money spent on fruits and vegetables. Each data point would be plotted based on its corresponding values for the two variables, with the horizontal axis representing the amount of money spent on groceries and the vertical axis representing the percentage of that money spent on fruits and vegetables. The scatter plot would allow us to see if there is any relationship between the two variables, such as whether people who spend more on groceries tend to spend a higher percentage of that money on fruits and vegetables.

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The solution to the inequality is: 2 > x > 25/18 or, in interval notation: (25/18, 2)

What is Inequality?

An inequality in math is a statement that two values or expressions are not equal, usually with a comparison symbol such as < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to).

The given inequality is:

(5/6)x - 1/3 > 4/3

To solve for x, we can begin by adding 1/3 to both sides:

(5/6)x > 4/3 + 1/3

(5/6)x > 5/3

Next, we can multiply both sides by the reciprocal of 5/6, which is 6/5. We must flip the inequality because we are multiplying by a negative number:

x < (5/3) × (6/5)

x < 2

Therefore, the solution to the inequality is:

2 > x > 25/18

or, in interval notation:

(25/18, 2)

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Answer:

Step-by-step explanation: yes

Answer:

x = -6

Step-by-step explanation:

5x² + 60x + 180 = 0

5 x 180 = 900

you need 2 numbers that multiplies into 900 and adds into 60. these numbers are 30 and 30. now we can rewrite it

5x² + 30x + 30x + 180 = 0.

split it in half and factorise

5x(x + 6) + 30(x + 6) = 0

this means the brackets are:

(5x + 30)(x + 6) = 0

5x + 30 = 0

5x = -30

x = -6

x + 6 = 0

x = -6

therefore, x = -6.

The value of K is 2.

Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.

We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.

Using the formula for the surface area, we have:

Initial surface area * (scale factor)^2 = Final surface area

50 * K^2 = 200

Dividing both sides of the equation by 50:

K^2 = 200/50

K^2 = 4

Taking the square root of both sides:

K = √4

K = 2

Therefore, the value of K is 2.

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