100 POINTS !! WILL MARK BRANILEST !! PLS HURRY
What are the potential solutions of log4x+log4 (x+6)=2
x=-2 and x=-8
x=-2 and x=8
x=2 and x=-8
x=2 and x=8

The function f(x, y) = sqrt(xy) is differentiable at point (1, 4) and the linearization L(x, y) of the function at point (1, 4) is given by L(x, y) = 2 + (x - 1) + (y - 4)/4

The partial derivatives of f(x, y) are given by,fx(x, y) = y/(2 * √(xy))
fy(x, y) = x/(2 * √(xy))
Hence, the partial derivatives of the function are continuous in a neighborhood of the point (1, 4) and hence the function is differentiable at the point (1, 4). Now, let's find the linearization L(x, y) of the function at point (1, 4).
The general form of a linear function in two variables is given by,L(x, y) = f(a, b) + fx(a, b) (x - a) + fy(a, b) (y - b)
where (a, b) is the point at which we want to find the linearization.
Therefore, the linearization L(x, y) of f(x, y) at point (1, 4) is given by,L(x, y) = f(1, 4) + fx(1, 4) (x - 1) + fy(1, 4) (y - 4)
Here, f(1, 4) = √(1 * 4) = 2
fx(1, 4) = 4/(2 * √(4)) = 1
fy(1, 4) = 1/(2 * √(4)) = 1/4
Therefore, the linearization L(x, y) of the given function f(x, y) at point (1, 4) is given by,L(x, y) = 2 + (x - 1) + (y - 4)/4

Thus, the function f(x, y) = √(xy) is differentiable at point (1, 4) and the linearization L(x, y) of the function at point (1, 4) is given by L(x, y) = 2 + (x - 1) + (y - 4)/4.

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1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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The slope of the line in the graph is -3/4

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane. Calculating the slope of a line is similar to finding the slope between two different points. In general, to find the slope of a line, we need to have the values of any two different coordinates on the line.

Taking two points from the line;

The slope of a line is given as

m = y₂ - y₁ / x₂ - x₁

Substituting the values into the formula;

m = 0 - 3 / 4 - 0

Slope = -3/4

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Answer:

y = 2x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = A (1, 7 ) and (x₂, y₂ ) = B (- 3, - 1 )

m = \(\frac{-1-7}{-3-1}\) = \(\frac{-8}{-4}\) = 2 , then

y = 2x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (1, 7 )

7 = 2(1) + c = 2 + c ( subtract 2 from both sides )

5 = c

y = 2x + 5 ← equation of line

The value of DF = 20.

Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.

Given:

Using theorem

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

ΔSDF/Δ RTY = (SD/RT)= (DF/TY)=  (FS/ YR)

ar ΔSDF² / ar  ΔRTY² = 16/81

SD/ RT = 4/9

SD = 4x,  RT= 9x

SD= 8

4x = 8

x = 2

So,

RT=  9*2 = 18

SF = RT -2

SF = 16

(SD/RT)= (FS/ YR)

8 / 18 = 16/ YR

YR= 36

TY= 9 +RY = 45

(DF/TY)=  (FS/ YR)

DF / 45= 16/ 36

DF=20

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Answer: 76 degrees

Step-by-step explanation:

Because the measure of an inscribed angle is half the measure of the central angle (where both angles intercept the same arc), the measure of angle U is 38(2)=76 degrees.

Answer:

C

Step-by-step explanation:

They all have and addition and subtraction pattern in each cube, thank me later - PrObLeM OcCuReD

Answer:

A

Step-by-step explanation:

Answer:

The equation — E = mc2 — means "energy equals mass times the speed of light squared." It shows that energy (E) and mass (m) are interchangeable; they are different forms of the same thing. If mass is somehow totally converted into energy, it also shows how much energy would reside inside that mass: quite a lot.

Step-by-step explanation:

hope this helps..................

Answer: 135

Step-by-step explanation: We know that the forerunner is 1/5 the speed of the water skier as 20/100 is 1/5. Now if we "reverse" this we can multiply 27 by 5 to find the speed of the water skier, this is 135 which is the speed of the water skier. Hope this helped :)

Answer:

60 goldfish

Step-by-step explanation:

2 + 3 = 5

150/5 = 30

2 · 30 = 60

The number of goldfish in the pet store is equal to 60 fishes.

Given the following data:

To calculate the number of goldfish that the pet store have:

Ratio can be defined as an expression that is used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

Mathematically, the number of goldfish in the pet store is given by this expression:

\(G = \frac{2}{5} \times 150\\\\G=0.4 \times 150\)

G = 60 fishes.

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(a) The probability of a particular individual getting 12 heads in a row is 1/4096. (b) The probability of at least one person in the group of n people getting 12 heads in a row is 1 - (1 - 1/4096)ⁿ. (c) To find the smallest integer n that ensures the probability in part (b) is at least 0.40, solve the inequality 1 - (1 - 1/4096)ⁿ ≥ 0.40 for n.

(a) To calculate the probability that a particular individual gets 12 heads in a row, we need to determine the probability of getting a single head on each toss and then multiply those probabilities together.

Assuming the coin is fair and unbiased, the probability of getting a head on a single toss is 1/2. Since we want to get 12 heads in a row, we need to multiply this probability 12 times:

P(12 heads in a row) = (1/2)¹² = 1/4096 ≈ 0.00024414

So the probability that a particular individual gets 12 heads in a row is approximately 0.00024414.

(b) To calculate the probability that at least one person in the group of n people gets 12 heads in a row, we can use the concept of complementary probability. The complementary probability is the probability that the desired event does not occur.

The probability that no person in the group gets 12 heads in a row can be calculated as:

P(no one gets 12 heads in a row) = (1 - P(12 heads in a row))ⁿ

Since we know the probability of a particular individual getting 12 heads in a row is 1/4096, we can substitute that value into the formula:

P(no one gets 12 heads in a row) = (1 - 1/4096)ⁿ

To find the probability that at least one person gets 12 heads in a row, we subtract the complementary probability from 1:

P(at least one person gets 12 heads in a row) = 1 - P(no one gets 12 heads in a row)

                                            = 1 - (1 - 1/4096)ⁿ

(c) To determine the smallest integer n that ensures the probability in part (b) is at least 0.40, we can set up the following inequality:

1 - (1 - 1/4096)ⁿ≥ 0.40

Solving this inequality will give us the smallest integer value of n.

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Answer:

No, it doesn't indicate that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company

Step-by-step explanation:

Let's first state the hypotheses.

Null hypothesis; H0: p = 0.68

Alternative hypothesis; Ha: p > 0.68

A random sample of 53 claims showed that 41 were made by single people under the age of 25.

Thus; p^ = 41/53 = 0.7736

Let's find the test statistic from the formula;

z = (p^ - p_o)/√(p_o(1 - p_o)/n)

z = (0.7736 - 0.68)/√(0.68(1 - 0.68)/41)

z = 0.0936/0.07285

z = 1.28

From online p-value from z-score calculator, using z = 1.28, one tail hypothesis and significance level of 0.05,we have;

P(z > 1.28) = 0.100273

The p-value gotten is greater than the significance value and so we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim.

Answer:8 feet

Step-by-step explanation:

Answer:

X=1, y=6

Step-by-step explanation:

Let's solve your system by substitution.

−8x−2y=−20;x+2y=13

Rewrite equations:

x+2y=13;−8x−2y=−20

Step: Solvex+2y=13for x:

x+2y=13

x+2y+−2y=13+−2y(Add -2y to both sides)

x=−2y+13

Step: Substitute−2y+13forxin−8x−2y=−20:

−8x−2y=−20

−8(−2y+13)−2y=−20

14y−104=−20(Simplify both sides of the equation)

14y−104+104=−20+104(Add 104 to both sides)

14y=84

14y

14

=

84

14

(Divide both sides by 14)

y=6

Step: Substitute6foryinx=−2y+13:

x=−2y+13

x=(−2)(6)+13

x=1(Simplify both sides of the equation)

Answer:

x=1 and y=6

Hope this helped!

Answer:

1) I believe 6 (im wrong I know it)

Step-by-step explanation:

you do whatever like 13902-1 , im so smart

By looking at the degree, we conclude that we have 4 roots.

Here we want to see how many roots the function:

x⁴ - 2x³ - 6x² + 22x - 15 = 0

The numer of roots (repeated, complex, or real) is given by the degree of the g

In this case we can see that the maximum exponent is 4, so the degree is 4, which means that we have 4 roots

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The exponential equation that models the population of the bacteria is:

y = 5*(7)^x

The general exponential equation is of the form:

y = A*(b)^x

Where A is the initial value, b is the base, and x is the variable.

Initially, Zach counted 5 bacteria, then:

A = 5

And we know that after one hour, Zach saw 35 bacteria, then we can write the equation:

35 = 5*(b)^1

35 = 5*b

35/5  =b

7 = b

Then the exponential equation is:

y = 5*(7)^x

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Answer:

good for him

Step-by-step explanation:

Answer:

Im pretty sure its 5

Step-by-step explanation:

5:1 due to 20/4 would be 5. I can give you more of an explaination if needed.

Answer:

5 triangles to 4 circles.

The equation of parabola is f ( x ) = -2 ( x + 5 )² - 3 and the vertex of the parabola is ( -5 , -3 )

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

y = a ( x - h )² + k

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the equation of parabola be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = -2x² - 20x - 53   be equation (1)

On simplifying the equation , we get

A = -2x² - 20x - 50 - 3

Taking the common factor in the equation , we get

A = -2 ( x² + 10x + 25 ) - 3

On factorizing the equation , we get

A = -2 ( x + 5 )² - 3

So , the the equation of parabola is of the form y = a ( x - h )² + k

where ( h , k ) is the vertex and ( h , k + p ) is the focus

Therefore , the vertex of the parabola is ( -5 , -3 )

Hence , the equation of parabola is A = -2 ( x + 5 )² - 3

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Answer:

She should walk at a rate of 16 km/hr

Step-by-step explanation:

At a rate of 12 km/hr, she would have traveled 4 km in 20 minutes. This can be calculated by finding the ratio of 20 minutes to 1 hour which is 1/3. We then multiply this ratio by the rate to find the distance Shalu needs to walk to school.

We then need to find the necessary km/hr in order for Shalu to travel 4 km in 15 minutes. 15 minutes is a quarter of 1 hr. Therefore a rate of 4 km/15 minutes is equal to a rate of 16 km/hr. This means that the average speed Shalu would have to walk is 16 km/hr.

Points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.

True

If Leslie leaves $9,000 in a savings account for 3 years with an annual compound interest rate of 4 percent, the amount of money that will accumulate is approximately $10,174.88.

To calculate the future value of Leslie's investment, we can use the compound interest formula:

Future Value = Principal Amount * (1 + Interest Rate)^Time

Given that the principal amount is $9,000, the interest rate is 4 percent (or 0.04), and the time is 3 years, we can substitute these values into the formula:

Future Value = $9,000 * (1 + 0.04)^3

Future Value ≈ $9,000 * 1.124864

Future Value ≈ $10,174.88

Therefore, if Leslie leaves $9,000 in the savings account for 3 years at an annual compound interest rate of 4 percent, the amount that will accumulate is approximately $10,174.88.

This calculation demonstrates the relationship between interest rates, time, and future sums. As the interest rate increases, the future value of the investment also increases. Similarly, as the time period increases, the future value of the investment grows. This shows that higher interest rates and longer time periods have a compounding effect on the accumulation of funds. It emphasizes the importance of considering both the interest rate and the length of time when making financial decisions, as they significantly impact the growth of an investment.

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The sunflower had a height of 13 inches on day 0 and 13.91 inches on day 1.

Because sunflowers are big feeders and require a slightly alkaline soil (pH 6.0 to 7.5), make sure we put them in nutrient-rich soil. Before planting, we should also make sure the soil is weed-free. Since a sunflower is cultivated in a garden, its height grows by 7% every day. The sunflower is 15.7 inches tall 2.79 days after being planted. To get the sunflower's 1-day growth factor, apply the following calculation:

X x (1 + 0.07) ^ 2.79 = 15.7

X x 1.07 ^ 2.79 = 15.7

1.2077X = 15.7

X = 15.7 / 1.2077

X = 13

13 x 1.07 = 13.91

The sunflower therefore measured 13 inches on day 0 and 13.91 inches on day 1.

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Answer:

C.

Step-by-step explanation:

You'll find that both equal 3x+3. Have a great day!

Answer: C

Step-by-step explanation:

x + x + x + 1 + 1 + 1

Combine like terms

3x + 3

3 (x + 1)

Distribute

3x + 3

Sentence Set A: Argument with conclusion "Have you no common decency?" Sentence Set B: Not an argument. Sentence Set C: Argument with conclusion "Dr. Sullivan, how could you possibly suggest giving my husband a painful cancer treatment when he has only two weeks to live?" Sentence Set D: Not an argument.

Sentence Set A is an argument because it presents a series of statements aimed at persuading or challenging someone's behavior. The first two sentences express the speaker's emotional response to the way they are being spoken to and the potential hurt caused by it.

The final sentence, "Have you no common decency?" serves as the conclusion of the argument, implying that the person being addressed should consider their actions and exhibit basic manners.

Sentence Set B, on the other hand, does not form an argument.

While it discusses the speaker's frustration with outdated reference materials at the library and proposes an alternative solution of doing research online, it lacks a clear claim or conclusion that presents a logical appeal or challenge to persuade others.

In Sentence Set C, an argument is made against Dr. Sullivan's suggestion of a painful cancer treatment for the speaker's husband. The statements express concerns about the potential lack of success of the treatment and the additional suffering it may cause during the final two weeks of the husband's life.

The conclusion is formed by the initial question: "Dr. Sullivan, how could you possibly suggest giving my husband a painful cancer treatment when he has only two weeks to live?"

Sentence Set D does not constitute an argument as it involves an expression of surprise and disappointment regarding someone's math skills, but it lacks a clear claim or conclusion that presents a logical challenge or persuasive appeal.

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The complete question is:

Sentence Set A:

S1: Don't ever speak to me like that again.

S2: Don't you know how much it hurts my feelings when you talk to me like that?

S3: Have you no common decency?

Sentence Set B:

S1: I'm so tired of having to go to the library to do my research.

S2: Can you believe that half of the reference materials I found there last time were outdated?S3: Let's just tear down the library and do our research online from now on.

Sentence Set C:

S1: Dr. Sullivan, how could you possibly suggest giving my husband a painful cancer treatment when he has only two weeks to live?

S2: What if the treatment isn't successful?

S3: Would you want your spouse to suffer even more during her final two weeks?

Sentence Set D:

S1: How could you possibly have got x = 5 as your answer?

S2: Didn't you see that y = 47?

S3: I have never seen such sloppy math in my entire life.

Which of the sentence sets are arguments? If applicable, what is the conclusion of each argument?

Answer:  \(\frac{n-m}{n}\)

This is the same as writing (n-m)/n

Don't forget about the parenthesis if you go with the second option.

==================================================

Explanation:

The probability that she wins is m/n, where m,n are placeholders for positive whole numbers.

For instance, m = 2 and n = 5 leads to m/n = 2/5. This would mean that out of n = 5 chances, she wins m = 2 times.

The probability of her not winning is 1 - (m/n). We subtract the probability of winning from 1 to get the probability of losing.

We could leave the answer like this, but your teacher says that the answer must be "in the form of a combined single fraction".

Doing a bit of algebra would have these steps

\(1 - \frac{m}{n}\\\\\frac{n}{n} - \frac{m}{n}\\\\\frac{n-m}{n}\\\\\)

and now the expression is one single fraction.