does anyone know this :/ ?

We can use the logarithmic identity log_a(b) + log_a(c) = log_a(bc) to simplify the left side of the equation:

log_2(x) + log_4(x+1) = log_2(x) + log_2((x+1)^(1/2))

Using the rule log_a(b^c) = c*log_a(b), we can simplify further:

log_2(x) + log_2((x+1)^(1/2)) = log_2(x(x+1)^(1/2))

Now we can rewrite the equation as:

log_2(x(x+1)^(1/2)) = 3

Using the rule log_a(b^c) = c*log_a(b), we can rewrite this as:

x(x+1)^(1/2) = 2^3

Squaring both sides, we get:

x^2 + x - 8 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 1, and c = -8. Plugging in these values, we get:

x = (-1 ± sqrt(1^2 - 4(1)(-8))) / 2(1)

x = (-1 ± sqrt(33)) / 2

x ≈ -2.54 or x ≈ 3.54

However, we must check our solutions to make sure they are valid. Plugging in x = -2.54 to the original equation results in an invalid logarithm, so this solution is extraneous. Plugging in x = 3.54 yields:

log_2(3.54) + log_4(4.54) = 3

0.847 + 0.847 = 3

So x = 3.54 is the valid solution to the equation.

The correct answer is D. The graph of k(x) is the graph of f(x) vertically compressed by a factor of 8.

To see this, let's compare the equations of the two functions:

f(x) = x²

k(x) = (1/8)x²

The function k(x) is obtained by multiplying the function f(x) by (1/8).

This multiplication affects the vertical scale of the graph.

The factor of 1/8 causes the graph of k(x) to be compressed vertically compared to the graph of f(x). This means that the values of k(x) will be smaller than the corresponding values of f(x) for the same x-values.

Therefore, the graph of k(x) is the graph of f(x) vertically compressed by a factor of 8.

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Answer:

Step-by-step explanation:

Given trapezoid ABCD, where:

Since AB and DC are parallel, the diagonal BD is transversal and:

Consider ΔABD

Since its two sides are equal, it is isosceles hence ABD and ADB are equal angles:

If p then q if not q, then not p.

The argument is invalid and,

Argument is Denying the antecedent,

Consider the following argument form:

If p then q if not q, then not p.

To check Is the argument valid?

Denying the antecedent, sometimes also called inverse error or fallacy of the inverse, is a formal fallacy of inferring the inverse from the original statement. It is committed by reasoning in the form: If P, then Q. Therefore, if not P, then not Q.

Any argument whose conclusion is not supported by its premises is invalid (i.e., faulty). That is, the conclusion could still be wrong even though all the premises are true.

Now, According to the statement, The argument is invalid.

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Answer:  134 miles

Step-by-step explanation:  

f(m) = 16.95 + 0.92m

140.23 = 16.95 + 0.92m

0.92m = 140.23 - 16.95

0.92m = 123.28

m = 123.28/0.92

m = 134 miles

Hence, the measure of angle 3 is 108 degrees.

Answer:

B: (4, 2)

D: (-4, -1)

E: (3, -3)

F: (0, 4)

Step-by-step explanation:

(x-coordinate, y-coordinate)

Answer:

B: (4, 2)

D: (-4, -1)

E: (3, -3)

F: (0, 4)

Step-by-step explanation:

(x-coordinate, y-coordinate)

Answer: no

Step-by-step explanation:

Answer:

we have

Cos (a+b)=Cos aCosb-SinaSinb

for

Cos (a+a)=Cos aCosa-SinaSina=Cos²a-Sin²a

is a required answer.

Answer:

m∠H < m∠GIH < m∠G

IK < JK < IJ

Step-by-step explanation:

Theorem: Alternate angles are equal

m∠H = m∠J = 57°

Theorem:  Sum of interior angles of a triangle is 180°

m∠G = 180 - m∠H - 60 = 180 - 57 - 60 = 63°

Theorem: Vertically opposite angles are equal

m∠GIH = m∠JIK = 60°

Therefore, m∠H < m∠GIH < m∠G

57 < 60 < 63

Theorem: The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle

∠K = 63°

∠JIK = 60°

∠J = 57°

Therefore, IK < JK < IJ

Answer:

392

Step-by-step explanation:

hope this helps dont 4get to like and star

-mercury

Answer:

D

Step-by-step explanation:

a quartic function is a polynomial of the 4th degree. that means that in the function expression the highest exponent of a term of x is 4.

y = ax⁴ + bx³ + cx² + dx + e

with a not 0.

the degree of a polynomial expression defines also how many zeroes (x values that create y = 0, that means points where the graph intersects the x-axis) there are.

a function has as many zeroes as the degree of the polynomial.

so, we are looking for potentially 4 zeroes.

the only graph that fulfills that is D.

the left "touch" of the graph on the x-axis counts for 2 (but equal) zeroes.

you can always test by virtually shifting the graph up or down and see, what are the max. x-axis intersections you can create.

if shifting D down a little bit you see, that this left "touch" turns into 2 intersections.

the same would apply for a "bend" or turn in the graph that does not even touch the x-axis.

if the original graph has not enough real x-axis intersections, it means that the remaining zeroes are then "imaginary" complex numbers (based on the sqrt(-1) = i).

a polynomial of the nth degree, must have n zeroes.

as a consequence it must have n-1 turns (even if the corresponding curve segments don't intersect with the x-axis in the real number space).

Answer:graph d

Step-by-step explanation:

just took the test

The cost per cookie, in dollars, for a sugar cookie is A; $0.54.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

WE know that Chocolate chip = $0.73

Double chocolate = $0.82

Oatmeal raisin = $0.70

Sugar = X

Butter pecan = $0.86

We need to find the  cost per cookie, in dollars, for a sugar cookie.

So, Mean = $0.73

Mean = 0.73 + 0.82 + 0.70+ X + 0.86 / 5

0.73 (5) =0.73 + 0.82 + 0.70+ X + 0.86

x = 0.54

Therefore, The cost per cookie, in dollars, for a sugar cookie is A; $0.54.

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Answer:

r=1/2πhA

Step-by-step explanation:

..................

Therefore, the formula of \(r\) is \(2A(\pi h)^{-1}\).

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given equation is

\(A=\frac{1}{2}\pi rh\)

So,

\(A=\frac{1}{2}\pi rh\\\\r=2A(\frac{1}{\pi h})\\\\r=2A(\pi h)^{-1}\)

Hence, the formula of \(r\) is \(2A(\pi h)^{-1}\).

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Answer:

mLJKL=48 degrees

Step-by-step explanation:

mLLKM=48 degrees because NK bisects LLKM; therefore, mLJKL is 48 degrees because LK bisects LJKM.

Hope this helped! :)

Total number of rose and holly bushes that I had initially = 20

Let the initial number of rose bushes be r

Let the initial number of holly bushes be h

I had 3 times as many rose bushes as holly bushes in my garden

r  =  3h......................(1)

After moving seven of my rose bushes to my grandfather’s garden, the remaining number of rose bushes = r - 7

After planting 11 new holly bushes in my garden, the new number of holly bushes = h + 11

Now my garden has half as many rose bushes as holly bushes

r - 7   =  0.5(h  +  11)

r  =  0.5h  +  5.5 + 7

r  =  0.5h  +  12.5...............(2)

Compare equations (1) and (2)

3h  =  0.5h  +  12.5

3h - 0.5h  =  12.5

2.5h  =  12.5

h   =  12.5/2.5

h  =   5

Substitute h = 5 into equation (1)

r  =  3h

r  = 3(5)

r  =  15

Total number of rose and holly bushes that I had initially = h + r

Total number of rose and holly bushes that I had initially = 5 + 15

Total number of rose and holly bushes that I had initially = 20

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Step-by-step explanation:

Team A time is    1 garden / ( 1 garden/ 2 hr + 1 garden/4 hr) = 1 1/3 hr

Team B =   1 / ( 1/3 + 1/3) =  1 1/2 hr

Team A wins !

The value of R(A) = 4, N(AT ) = 3, R(AT ) = 4, and N (A) = 3.

Given that

Dimension of matrix  = 7×5

Rank of matrix = 4

The range space of A,

Which is a subspace of R, is known as R(A).

It is made up of all conceivable linear combinations of A's columns.

The dimension of R(A) =  rank of A,

Which is 4 in this case.

The null space of the transpose of A,

Which is also a subspace of R, is designated as N(AT).

All potential answers to the equation ATx = 0,

Where x is a R column vector, are included in it.

N(AT) has a dimension = nullity of A,

which in this case is 3 in this example.

The range space of the transposition of A, is designated as R(AT).

The rows of A are arranged in all conceivable linear configurations.

The rank of A = 4

Thus it equal to dimension of R(AT).

N(A) is the null space of A.

Axe = 0, where x is a column vector in R, are included in it.

The nullity of AT, which is three, is likewise equivalent to the dimension of N(A).

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Answer: 17.7

44.25

times .4  pLease mark me brainliest lol

The percentages to complete the table for the steaming time are 40 min, 20 min and 100 min respectively

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given: Percentage: 100% of 40 min, 50% of 40 min and 250% of 40 min

100% of 40 min:

100% of 40 min = (100/100) × 40 min = 1 × 40 min = 40 min

50% of 40 min:

50% of 40 min = (50/100) × 40 min = 0.5 × 40 min = 20 min

250% of 40 min:

250% of 40 min = (250/100) × 40 min = 2.5 × 40 min = 100 min

Therefore, the value of the percentages to complete the table for the steaming time are 40 min, 20 min and 100 min for 100% of 40 min, 50% of 40 min and 250% of 40 min respectively.

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The area of the shaded region, with a frame of 3 units wide, is 264 square units. The inner rectangle is 6x4 units, and the outer rectangle is 18x16 units.

To solve the given problem, we have to find the area of the shaded region if the frame is 3 units wide. If the frame is 3 units wide, then the dimensions of the inner rectangle (the shaded region) will be (12 - 6) × (10 - 6) which simplifies to 6 × 4.

Therefore, we can say that the inner rectangle has a length of 6 units and a width of 4 units.The dimensions of the outer rectangle are (12 + 3 + 3) × (10 + 3 + 3) which simplifies to 18 × 16. Therefore, we can say that the outer rectangle has a length of 18 units and a width of 16 units.

The area of the shaded region can be obtained by subtracting the area of the inner rectangle from the area of the outer rectangle. Therefore, the Area of the outer rectangle = length × width= 18 × 16 = 288 square units

Area of the inner rectangle = length × width= 6 × 4 = 24 square units

Area of the shaded region = Area of the outer rectangle - Area of the inner rectangle = 288 - 24= 264 square units

Therefore, the area of the shaded region is 264 square units.

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The reciprocal of 2/43 of the difference between 3 2/15 and 2 5/12 is 30.

Here, we have to subtract 2 mixed fractions i.e

=> (3 2/15) - (2 5/12)

which when converted to a proper fraction is equal to,

=> (47/15) - (29/12)

= 43/60

∵ (3 2/15) - (2 5/12) = 43/60

now, 2/43 of the difference of 3 2/15 and 2 5/12,

=> (2/43) × (43/60) = 1/30............(i)

taking the reciprocal of the value obtained above,

∴ reciprocal of 1/30 = 30.

Thus, The reciprocal of 2/43 of the difference between 3 2/15 and 2 5/12 is 30.

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Answer: 53

Step-by-step explanation:

Answer:

3/11

Step-by-step explanation:

Divide both the numerator and denominator by 2.

\(\dfrac{6}{22}=\dfrac{2*3}{2*11}=\dfrac{3}{11}\)

Given the radical:

Let's reduce the radical.

Factor out 16 from 224

Rewrite 16 as 4²:

Thererfore, the simplified radical is:

Answer:

b

Step-by-step explanation:

b

Answer:

Area: 378.5

Perimeter: 71.4

Step-by-step explanation:

Area = 3 square + 2 semicircle

A = 3 x 10² + 2 x (3.14 x 5²)/2 = 300 + 78.5 = 378.5

perimeter = 2 square/2 + 2circle/2

P = 2 x(10 + 10) + 2 x (2 x 3.14 x 5) / 2 = 40 + 31.4 = 71.4

The correct statement is: g(x) is translated up 5 units compared to f(x).

The correct answer is A.

The correct answer is A.

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Let A be the event that a family chose at random indicated an intention to buy a new car and let B be the event that a family chose at random bought a new car within 3 months.

We are asked to find P(A'), which is the probability that a family chosen at random had not previously indicated an intention to buy a car.

We can use the given information to write the following conditional probabilities:

P(B | A) = 60%

P(B | A') = 10%

P(A) = 26%

We can use these probabilities to apply Bayes' theorem to find P(A' | B), which is:

P(A' | B) = P(B | A') * P(A') / P(B)

Substituting the values from the problem, we have:

P(A' | B) = (10%) * (100% - 26%) / (60% * 26% + 10% * (100% - 26%))

= (10%) * (74%) / (60% * 26% + 10% * 74%)

= (10%) * (74%) / (15.4% + 7.4%)

= (10%) * (74%) / (22.8%)

= 43.86%

Therefore, the probability that a family chosen at random had not previously indicated an intention to buy a car is 43.86%.

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