4log3 X + log7 help
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The quadratic equatiοn is x² + 2x + 3 and value οf c = 3.

it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm. A nοn-zerο term (a 0) fοr the cοefficient οf x² is a prerequisite fοr an equatiοn tο be a quadratic equatiοn.

The x² term is written first, then the x term, and finally, the cοnstant term is written when cοnstructing a quadratic equatiοn in standard fοrm.

In mοst cases, the numerical values οf letters a, b, and c are expressed as integral values rather than fractiοns οr decimals.

x² +2x +c = 0 (x+√c)² = 0

Nοw we can set the cοefficients οf x²and x equal tο each οther, and the cοnstant terms equal tο each οther:a = 12a = 2a + 2 = c

Frοm the secοnd equatiοn, we can sοlve fοr a:2a = 2a = 1

Substituting a = 1 intο the third equatiοn, we get:

c = a + 2c = 1 + 2c = 3

Therefοre, the quadratic equatiοn is x² + 2x + 3.

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Answer:

590,088

Step-by-step explanation:

So you divide 156,200 by 4.5 then once you have that times it bye the 17 years I think

Answer:

The correct statement is: ΔJDC ≅ ΔYAM.

This is because the given statement ΔJCD ΣΔMAY tells us that ΔJCD is congruent to ΔMAY by the SAS (side-angle-side) postulate.

We can use this information to conclude that ΔJDC is congruent to ΔYAM by the CPCTC (corresponding parts of congruent triangles are congruent) theorem. Specifically, the corresponding parts that are congruent are:

Therefore, the correct congruency statement is ΔJDC ≅ ΔYAM. The other statements are not correct.

Therefore , the solution of the given problem of unitary method comes out to be Daisy cream and Kremlin cream both have less cream per bulk 1 gallon and 4.5 gallons, respectively than Marble cream.

The objective can be accomplished by utilising what has already been discovered, taking advantage of this worldwide access, and including all essential components from earlier changeable study who employed a certain technique. If the anticipated claim outcome actually occurs, it will either be possible to contact the variable again or both important processes will undoubtedly miss the statement.

Here,

We must convert cups to gallons because daisy cream is sold in bulks of cups. Since a gallon of Daisy cream comprises 16 cups, one quantity of Daisy cream contains:

=> 16 cups per bulk = 1 gallon 16 cups per bulk = 1 gallon

Moscow cream is offered in bulk quantities of 4 1/2 gallons, which is one gallon.

Thus, we must convert pints to gallons. A gallon of Marble cream comprises eight pints, hence one quantity of Marble cream contains:

=> 40 pints in a bulk equal 1 gallon, 8 pints, or 5 gallons.

As a result, we can see that Marble cream, with 5 gallons per bulk, has the most cream.

Daisy cream and Kremlin cream both have less cream per bulk (1 gallon and 4.5 gallons, respectively) than Marble cream.

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The value of z in the equation 1/3(6z + 7.2) = 0.5(8z + 2) - 0.4 is z=0.9

How to solve the equation?

1/3(6z + 7.2) = 0.5(8z +2) -0.4

(6/3)z + 7.2/3 = (8/2)z + 2/2 - 0.4

2z + 2.4 = 4z + 1 - 0.4

2z - 4z = 0.6 - 2.4

-2z = -1.8

z= 0.9

Hence, the value of z in the equation 1/3(6z + 7.2) = 0.5(8z + 2) - 0.4 is z=0.9

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Answer:

Since A and B are not overlapping, their union will simply be the set of all their elements combined. Therefore, a + b will be the sum of the lengths of the two intervals that make up A and B respectively, which is:

a + b = (1-0) + (3-2) + (2-1) + (4-3) = 4

So, a+b=4.

Step-by-step explanation:

The notation A = ]0,1[ ∪ ]2,3[ means that A is the set of all real numbers that are strictly greater than 0 and strictly less than 1, or that are strictly greater than 2 and strictly less than 3. In other words, A consists of two separate intervals, ]0,1[ and ]2,3[, that do not overlap.

Similarly, the notation B = ]1,2[ ∪ ]3,4] means that B is the set of all real numbers that are strictly greater than 1 and strictly less than 2, or that are greater than 3 and less than or equal to 4. Like A, B consists of two separate intervals that do not overlap.

The union of two sets is the set of all elements that belong to either set. In this case, since A and B do not overlap, their union is simply the set of all real numbers that belong to either A or B. This set can be expressed as the union of the two intervals that make up A and B, which is:

A ∪ B = ]0,1[ ∪ ]2,3[ ∪ ]1,2[ ∪ ]3,4]

To find a + b, we need to add up the lengths of the two intervals that make up A and B respectively. The length of an interval is simply the difference between its upper and lower bounds. So, the length of the interval ]0,1[ is 1 - 0 = 1, the length of the interval ]2,3[ is 3 - 2 = 1, the length of the interval ]1,2[ is 2 - 1 = 1, and the length of the interval ]3,4] is 4 - 3 = 1. Therefore, the sum of the lengths of the two intervals that make up A and B respectively is:

a + b = (1-0) + (3-2) + (2-1) + (4-3) = 4

Hence, a + b = 4.

a. The missing values of the logarithm expression is log₃(40).

b. The missing values of the logarithm expression is log₅(8).

c. The missing values of the logarithm expression is  log₂(1/25).

The missing values of the logarithm expression is calculated as follows;

(a). log₃5 + log₃8, the expression is simplified as follows;

log₃5 + log₃8 = log₃(5 x 8) = log₃(40)

(b). The log expression is simplified as;

log₅3 - log₅X = log₅3/8

log₅X = log₅8

X = 8

(c).  The log expression is simplified as;

-2log₂5 = log₂Y

log₂5⁻² = log₂Y

5⁻² = Y

1/25 = Y

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Answer:

g(x) = -f(x) +5

Step-by-step explanation:

The sign on the 'x' changes, this implies a reflection.

g(x) = -f(x) = -(x+1) = -x -1

Now apply a vertical translation 'up 5' to f(x)

g(x) = -f(x) + 5 = (-x-1) +5 = -x +4

The false statement from the stem-and-leaf plot is given as follows:

b. The data for Paul’s group has two modes.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

The mode of a data-set is the data-set that appears the most times in a data-set.

Hence, for Paul's group, the mode is given as follows:

44.

As it is the only observation that appears the times, hence the data has one mode, and option b gives the false statement.

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Answer: E

Step-by-step explanation:

In general, there were more people per table on Tuesday with 8 number of people per table.

In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

By critically observing the given dot plots which is used to illustrate the numbers of people per table at a bingo hall on two nights, we can reasonably infer and logically deduce that there were more people per table on Tuesday than on Wednesday.

In conclusion, there were 8 number of people per table on Tuesday while there were 5 number of people per table on Wednesday.

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The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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This is due to the fact that the anticipated value is determined by multiplying the likelihood of each potential occurrence by its value, then adding the results.

Probability is a metric for determining the possibility of an event happening in mathematics and statistics. It is a number between 0 and 1, where 0 denotes that the action is impossible and 1 denotes that it is guaranteed to occur. Usually, the likelihood of a particular occurrence is calculated through dividing the number of possible outcomes by the number of alternative ways the event could happen. As an illustration, the likelihood of rolling a six on a regular die is 1/6 since there is just one method for scoring a six and a total of six options. Many practical applications of probability can be found in the fields of insurance, banking, and gaming. Also, it aids in risk management and assessment throughout scientific research and decision-making processes.

given

The assertion "I discovered that there should be 2.5 more boys in a household of five than was anticipated. A family of 2.5 boys cannot exist, thus I must have made a mistake "contradicts itself.

A family cannot have 2.5 males just because the number of boys in a household of five is supposed to be 2.5. Instead, it suggests that a family with five children may typically anticipate to have 2.5 boys.

This is due to the fact that the anticipated value is determined by multiplying the likelihood of each potential occurrence by its value, then adding the results.

It is indeed impossible to have 2.5 males in a family of five.

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The values of x for which f(x) = 7 are x = 61 and x = 21.

To find the values of x for which f(x) = 7, we can set up the equation and solve for x.

The given function is f(x) = 0.5|x - 41| - 3.

Setting f(x) equal to 7, we have:

0.5|x - 41| - 3 = 7.

First, let's isolate the absolute value term:

0.5|x - 41| = 7 + 3.

0.5|x - 41| = 10.

To remove the absolute value, we can consider two cases:

Case: (x - 41) is positive or zero:

0.5(x - 41) = 10.

Multiplying both sides by 2 to get rid of the fraction:

x - 41 = 20.

Adding 41 to both sides:

x = 61.

So x = 61 is a solution for this case.

Case: (x - 41) is negative:

0.5(-x + 41) = 10.

Multiplying both sides by 2:

-x + 41 = 20.

Subtracting 41 from both sides:

-x = -21.

Multiplying both sides by -1 to solve for x:

x = 21.

So x = 21 is a solution for this case.

Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.

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Hello there. To solve this question, we have to remember some properties about roots of polynomials.

Given the following function:

We want to determine its roots.

For this, we want to determine the values of x such that

Then we have that

We know that a product of two values is equal to zero if and only if one of them is equal to zero.

So we have that

Subtract 6 on both sides of the first equation, we get

Divide both sides of the equation by a factor of 2

Now for the second equation, add 4 on both sides of the equation

Hence we say that the roots of this function are

This is the answer contained in the last option.

The demonstration of magnitude of power given by 80 kg monkey by climbing a 15 meter tree in half a minute is equal to option b.  392 J/S.

Weight 'm' of the monkey is equal to 80kilogram

Height 'h' of the tree is equal to 15 meter

Time 't' taken by monkey to climb a tree = half a minute

                                                                    = 30 minutes

g = 9.8 m/s²

Magnitude of power = ( m × g × h )/ t

⇒ Magnitude of power = ( 80 × 9.8 × 15 )/ 30

⇒ Magnitude of power = 784 / 2

⇒ Magnitude of power = 392 J/S

Therefore, the magnitude of the power for the given weight , displacement and time is equal to option b. 392 J/S.

The above question is incomplete, the complete question is:

A 80 Kg monkey climbs a 15 meter tree in half a minute. What is the magnitude of power the monkey demonstrated?

a. 13.1 J/S

b. 392 J/S

c. 784 J/s

d. 11760 J/s​

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Step-by-step explanation: Well to begin, you take 15$ and multiply it by 4, since he wants to buy 4 of those tickets, which is 60$. Then, take the 10$ and multiply it by 2 since he wants 2 of those tickets, which is 20$, you then apply 10% to 60 and 20 by taking 10 percent of 60, then adding  it to 60 once have that, which is 66, you take the 3% and find 3% of 66, then add the answer of that to 66, which is 67.98$, you then do the same thing to the 20$.

Sorry if this didnt help, im sure it didnt because im a very bad explainer, but i tried..

Answer:

5=x

Step-by-step explanation:

Q=2(2x-5)=3x+x-2x

SOLUTION:

4x-10=4x-2x

-10=2x-4x

-10= -2x

(-+-=+ so 10 and 2 are positive now)

10/2=x

5=x

Answer:

5 and -5 (±5)

Step-by-step explanation:

x²-8=17

x²=25

√x²=√25

x=±5

Therefore, Kallie will need to use a total of 6 teaspoons of water conditioner for all the water in 12 fish tanks.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign, with the expression on the left being equal to the expression on the right. Equations are used to represent various relationships and situations in mathematics and other fields, and are solved to find the values of variables that make the equation true.

Here,

First, we need to determine the total amount of water in all 12 fish tanks. Since each fish tank is filled with 20 quarts of water, the total amount of water in all 12 fish tanks is:

12 fish tanks * 20 quarts per fish tank = 240 quarts of water

To convert quarts to gallons, we divide by 4 (since there are 4 quarts in a gallon):

240 quarts / 4 quarts per gallon = 60 gallons of water

Now, we can use the given conversion factor to determine how many teaspoons of water conditioner are needed for 60 gallons of water. Since for every 10 gallons of water, Kallie uses 1 teaspoon of water conditioner, for 60 gallons of water, she will use:

60 gallons / 10 gallons per teaspoon = 6 teaspoons of water conditioner

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Player B is the more consistent player, determined by the variability.

Range measures the difference between the highest and lowest numbers, whereas the IQR measures the difference between the first and third quartiles.

Range and IQR are both measures of variability that measure how spread out the data is.

Player B has a lower range and IQR than Player A, which indicates that Player B was more consistent.

Since Player B had a lower range and IQR than Player A, this indicates that Player B is the more consistent player.

This shows that Player B is more consistent because the data points are closer together.

This is because Player B had fewer outliers, which made the data points more consistent.

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Answer:

10.  Left 5

11.   Horizontal stretch by a factor of 5

12.  Horizontal reflection

Step-by-step explanation:

Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.

Transformations

For a > 0

\(f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}\)

\(f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}\)

\(f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}\)

\(f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}\)

\(y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a\)

\(y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}\)

\(y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}\)

\(y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}\)

Identify the transformations that take the parent function to the given function.

Question 10

\(\textsf{Parent function}: \quad f(x)=x^3\)

\(\textsf{Given function}: \quad f(x)=(x+5)^3\)

Comparing the parent function with the given function, we can see that 5 has been added to the x-value of the parent function.

Therefore, the transformation is:

\(f(x+5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units left}\)

Question 11

\(\textsf{Parent function}: \quad f(x)=x^3\)

\(\textsf{Given function}: \quad f(x)=\left(\dfrac{1}{5}x\right)^3\)

Comparing the parent function with the given function, we can see that the x-value of the parent function has been multiplied by ¹/₅.

Therefore, the transformation is:

\(y=f\left(\dfrac{1}{5}x\right) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{\frac{1}{5}}\)\(\textsf{As }\dfrac{1}{\frac{1}{5}}=5 \implies \textsf{horizontal stretch by a factor of 5}\)

Question 12

\(\textsf{Parent function}: \quad f(x)=x^3\)

\(\textsf{Given function}: \quad f(x)=(-x)^3\)

Comparing the parent function with the given function, we can see that the x-value of the parent function has been multiplied by -1.

Therefore, the transformation is:

\(y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}\)

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Answer:

The answer would be (0,3/2) or letter A.

Step-by-step explanation:

In conclusion the answer is letter A (0,3/2)

You welcome.

The co-ordinate of the focus of the given equation of the parabola x^2=6y is (0,3/2).

We have given the equation is

\(x^2 = 6y\)

We know that the general equation of the parabola is,

\(x^2=4ay\)

A line that passes through the focus and divides the parabola into two halves is known as the axis of symmetry.

The coordinates of the focus \(f(0, a)\)

We have to determine the value of

\(a4a=6a \implies 6/4a=3/2\)

Therefore the coordinate of the focus is\((0,3/2)\).

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There are 2518 sets of five marbles that include either the lavender one or exactly one yellow one, but not both.

To solve this problem, we need to find the number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both colors. Here's one way to approach the problem:

Number of sets of five marbles that include the lavender one: There is only one lavender marble, so we can choose any 4 other marbles to go with it.

There are a total of 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.

This gives us a total of 7 x 6 x 5 x 4 = 840 possible sets of five marbles that include the lavender one.

Number of sets of five marbles that include exactly one yellow one: There are two yellow marbles,

So there are 2 possible choices for the yellow marble. For each choice, we can choose any 4 other marbles to go with it.

As before, there are 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.

This gives us a total of 2 x (7 x 6 x 5 x 4) = 1680 possible sets of five marbles that include exactly one yellow one.

Number of sets of five marbles that include both the lavender one and exactly one yellow one:

We need to subtract these sets from the total number of sets that include either the lavender one or exactly one yellow one.

We have already found that there are 840 sets of five marbles that include the lavender one, and 1680 that include exactly one yellow one.

To find the number of sets that include both, we can choose any one yellow marble and the lavender one.

There are 2 choices for the yellow marble and 1 choice for the lavender one,

So there are 2 x 1 = 2 possible sets of five marbles that include both the lavender one and exactly one yellow one.

Number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both:

Finally, we need to subtract the number of sets that include both the lavender one and exactly one yellow one from the total number of sets that include either the lavender one or exactly one yellow one.

The total number of sets that include either the lavender one or exactly one yellow one is 840 + 1680 = 2520. The number of sets that include both is 2,

So the number of sets that include either the lavender one or exactly one yellow one, but not both, is 2520 - 2 = 2518.

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Answer: sin(0) = 40.804/41

Step-by-step explanation:

Answer:

Step-by-step explanation:

m = n + 1 + x/p

First, we can start by subtracting (n+1) from both sides:

m - (n+1) = x/p

Then, we can multiply both sides by p to isolate x:

p(m - (n+1)) = x

So the final answer is:

x = p(m - (n+1))

The graph of both the Functions will be Parallel

What are Functions?

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

Solution:

Please refer to the Graph attached

The graph of both the Functions will be Parallel

because, The Slope of both the functions is 2

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The length of side AB in right angled triangle ABC  will be 48 cm.

Every triangle with one 90° angle is said to have a right angle. The triangle with a right angle is known as a right triangle because a right angle is 90 degrees.The longest side of a right angle is known as the hypotenuse, and it is opposite the right angle.

Given,

∠B= 90°, AC = 96 cm, ∠C = 30°

Now, we know, Trignometric ratio sin θ in triangle can be given by-:

sin θ = \(\frac{perpendicular}{hypotenuse}\)

From given figure,

Perpendicular= AB= ?

and Hypotenuse= AC = 96

and θ= 30°

Hence,

sin 30° =\(\frac{perpendicular}{hypotenuse}\)= \(\frac{AB}{96}\)

\(\frac{1}{2} = \frac{AB}{96}\)                                      (∵ sin 30°= 1/2)

\(AB=\frac{96}{2}\)

\(AB= 48 cm\)

Thus, AB= 48 cm

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Correct Question:ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. Find AB = ?

The function d(x) = - |x - 3| + 5 is the result of using an horizontal translation, reflection about the x-axis and vertical translation on the function f(x) = |x|.

In this question we have the definition of a function (f(x)) and its image (d(x)), the latter is the result of three rigid transformations:

Horizontal translation

f'(x) = f(x - 3)

Reflection about the x-axis

f''(x) = - f'(x)

Vertical translation

d(x) = f''(x) + 5

If we know that f(x) = |x|, then the series of rigid transformations is shown below:

Horizontal translation

f'(x) = |x - 3|

Reflection about the x-axis

f''(x) = - |x - 3|

Vertical translation

d(x) = - |x - 3| + 5

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