Factor the difference of two perfect squares - 3m^2 - 243 =0

Median of the data 78 , 56 , 22 , 34 is 45.

The middle value of the observations in a data set , arranged in the order of size is known as the median.

It is calculated differently for odd and even number of observations.

1. For odd no. of observations, it is the middle value .

2. For even number of observations, it is calculated as the average of the middle two values.

In this problem , first we arrange the observations in the order of size i.e. 22 , 34, 56, 78.

Since, here the no. of observations is even , 4. So, the median is the average of middle two values.

The middle two values are 34 and 56 , and their mean is 45.

So, the median of the given data is 45.

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Answer:

$0.55/ounce

Step-by-step explanation:

The problem gives us the ratio of cost to ounce. We need to create a proportion (when you set two ratios equal to each other) to solve for one variable of the second ratio.

⭐ The first ratio is [tex]$4.95/9 ounces[/tex], which means that it costs $4.95 for 9 ounces.

⭐ The second ratio is [tex]x/1 ounce[/tex], where x is the cost for 1 ounce of frozen yogurt.

. . . . . . . "per ounce" means "for every 1 ounce"

⭐ We need to set these two ratios equal to each other and solve for x.

. . . . . . . In proportions, keep the units of the numerators and denominators the same. In this case, we'll keep the cost as the numerators and the ounces as the denominators.

. . . . . . . [tex]\frac{4.95}{9} = \frac{x}{1}[/tex]

. . . . . . . [tex]\frac{4.95}{9}(1) = x[/tex]

. . . . . . . ∴ x = $0.55/ounce

The 5 types of expression include:

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.

Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it. They include monomial, polynomial, binomial, trinomial, multinomial.

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The larger the base of a log function, the closer the graph approaches the asymptote of x = 0.

We know that for a exponential function b^x = y, b is the base, y is the exponent to which the base b is raised and x is the result obtained.

We can write this in logarithmic form as:

log_b(x) = y

A logarithm base is the subscript of the logarithm that carries or raises the exponent.

For example in case of log_(3) 9 = 2, the base here is 3.

The change of base formula is:

log_b(x) = log_c(x) / log_c(b)

Also as we know the bigger the logarithm base, the smaller the curve on the graph. This means, the larger the base of a log function, the closer the graph approaches the asymptote of x = 0.

The log function may increase at a slower rate if the base increases.

Therefore, if the base of a log function is large, the graph approaches the asymptote of x = 0.

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Answer:

Divide both sides by -3.

Step-by-step explanation:

This question is asking you how to get from step 1: [tex]-3(p-7) = -15[/tex] to step 2: [tex]p - 7 = 5[/tex].

We can see that the expression inside of the parentheses (p - 7) didn't go away from step 1 to step 2, and the term that was being multiplied by (p-7) had gone away. The only way you can "get rid" of a multiplied term is by doing the inverse of multiplication, which is division. Thus, you have to divide both sides by -3 to get to step 2.

The distance traveled by the arrow cannot be determined from the given information. The distance traveled by the arrow depends on the speed at which it is fired, which is determined by the amount of energy released when the bowstring is released.

Answer:

B)Write down a division that has an answer of 54.8.

Answer:

61

Step-by-step explanation:

Using the exterior angle theorem,

[tex]c-15+c-18=c+28 \\ \\ 2c-33=c+28 \\ \\ c-33=28 \\ \\ c=61[/tex]

Answer: The answer is 100 :)

Step-by-step explanation:

you multiply L x W and that would be 10 x 10 and if you do the math right you should get an answer of 100

Answer:

You are correct

This is my answer: -3x^a y^f+b z^g+c

Step-by-step explanation:

(3x^a y^b z^c) (-y^f z^g)

-3x^a  y^f+b z^g+c

Because both have the same base is y, so we add both f and b

Same with z, both have the same base is z, so we have z^g+c

My answer is different in order, but both are correct!

The required graph of the given function y = -5x + 3 which has been attached below.

A graph can be described as a visual representation or a diagram that represents data or values.

To graph the function y = -5x + 3, you can start by making a table of values.

Here's an example:

x y

-2 -11

-1 -6

0 3

1 -2

2 -7

To plot these points, start by graphing the point (0,3). This is the y-intercept, where the line crosses the y-axis.

Then, use the slope of the line (-5) to find the next point. For example, if you go one unit to the right on the x-axis (from 0 to 1), the y-value decreases by 5 (from 3 to -2).

Continue graphing points in this way until you have plotted enough points to see the shape of the line. You should see that the line has a negative slope, meaning it goes down from left to right.

The required graph of the given function y = -5x + 3 has been plotted.

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The graph of the given function is a straight line.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point and has no curve.

Equation of straight line ( slope-intercept form) is, y= mx+ c

Where, m= slope of the line  & c= y-intercept.

Here, given function is, y=-5x+3 , which is an equation of straight line.

So, here, m= -5 & c=3

That is the line will passes through the point (0,3)

Now, if we put, y=0 then, x= 3/5=0.6

i.e., the line will also passes through the point (0.6,0)

So, we get, the required graph of the function ,

Hence, the graph of the function is a straight line.

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The Coefficient of x² in the equation (3x²-5)(4+4x²) after simplification is -8 .

The Equation is given as : (3x²-5)(4+4x²)

To simplify , we first multiply the terms inside the bracket ;

So , given equation can be written as  (3x²-5)×(4+4x²)

⇒ 12x² + 12x⁴ - 20 - 20x²

Adding the like terms of the equation ,

we get ;

⇒ (12 - 20)x² + 12x⁴ - 20

Simplifying further , we get

⇒ 12x⁴ - 8x² - 20 .

In the equation above we see that the numerical term with the x² is (-8) .

Therefore , the required coefficient is -8 .

The given question is incomplete , the complete question is

What is the coefficient of x² in the equation after simplification ; (3x²-5)(4+4x²) ?

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Answer:

A gain of 3 points

Step-by-step explanation:

I'm not sure the options are correct. But normally, you add up the lost points on the both days. Then you compare it to the gained point on Wednesday.

Answer:

x>=-11/4

Step-by-step explanation:

f(x)=[tex]\sqrt{4x+9+2}[/tex]

The number which has a square root has to be greater than or equal to 0.

Hence, 4x+9+2>=0

Solve the inequality:

4x+9+2>=0

4x+11>=0

4x>=-11  ==> subtract 11 on both sides to isolate x

x>=-11/4 ==> divide both sides by 4

Arya needs to add 2 gallon of 70% antifreeze must be added to a  3-gallon mixture containing 20% antifreeze to obtain the mixture they need.

What is antifreeze?

Antifreeze is an additive that lowers a liquid's freezing point that is made of water. For cold environments, freezing-point depression is accomplished using an antifreeze mixture. Additionally, common antifreezes raise the liquid's boiling point, enabling higher coolant temperatures.

Let x be the amount of 70% antifreeze to be added, in gallons.

In terms of percentage of antifreeze, we write:

20% of 3 gallons + 70% of x gallons = 50% of (3 + x) gallons

0.2(3) + 0.7x = 0.5(3 + x)

0.6 + 0.7x = 1.5 + 0.5x

0.7x - 0.5x = 1.5 - 0.6

0.2x = 0.4

x = 2

Hence, Arya needs to add 2 gallon of 70% antifreeze must be added to a  3-gallon mixture containing 20% antifreeze to obtain the mixture they need.

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Bar graph is best for comparing change over time.

Using rectangular bars with heights or lengths proportionate to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

The visual display of data (often grouped) in the shape of vertical or horizontal rectangular bars, with the length of the bars corresponding to the measure of the data, is called a bar graph. Bar charts are another name for them. One tool used in statistics for processing data is the bar graph.

Bar graph components

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When comparing data between groups or monitoring changes over time, bar graphs are utilized.

Hence, When comparing data between groups or monitoring changes over time, bar graphs are utilized.

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Answer:

x = -10

Step-by-step explanation:

Solve means to get the x all by itself on one side of the equation.

40 = -3x + 10

Subtract 10 from both sides.

30 = -3x

Divide both sides by -3.

30/-3 = x

-10 = x

x = -10

You can check your answer by putting it back into the equation and seeing if you get a true statement.

40 = -3x + 10

x = -10

Substitute.

40 = -3(-10) + 10

Multiply.

40 = 30 + 10

Add.

40 = 40

True! This means

x = -10 is correct.

If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.

Volume of A /Volume of B =  ( a / b )^3

a is the radius of solid A and b is the radius of solid B.

solid figures

In Geometry, the shape or the figure that has three dimensions (length, breadth and height), are known as solids or three-dimensional shapes. Example:-Cube, Cuboid and Sphere. The major types of solid shapes are: cubes, cuboids, prisms, pyramids, platonic solids, torus, cone, cylinder, and sphere.

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Answer:

the inverse of f(x)=2x−7 f ( x ) = 2 x - 7 .

Step-by-step explanation:

check if f−1(f(x))=x f - 1 ( f ( x ) ) = x and f(f−1(x))=x f ( f - 1 ( x ) )

Answer:

f(x) = 1/4 x² - 7

Step-by-step explanation:

x + 7 ≥ 0

x ≥ -7

y/2 = 2 /2 √(x+7)

y/2 = √(x+7)

y ≥ 0

(y/2)² = √(x+7)²

y²/4 = x +7

x = y²/4 - 7

f(x) = x²/4 - 7

The sum of two or more numbers that results in a third number is called a factor.

The factor of [tex]$x^2+\frac{x}{6}-\frac{1}{6}$[/tex] exists 2x + 1.

The definition of a factor is a number that divides another number by itself with no remainder. In other words, if multiplying two whole numbers results in a product, the numbers we are multiplying are factors of the product since the product is divisible by them.

What can split a number exactly are factors. So there is no residual after division. Factors are the sums of two or more numbers that produce a third number. Consequently, a factor is a number that divides another.

The use of more variable factors—those whose values do fluctuate with output—occurs as production rises and falls. Workforce, energy, and directly used raw materials are examples of typical variable components.

Let the given equation be [tex]$& x^2+\frac{x}{6}-\frac{1}{6} \\[/tex]

[tex]$& =\frac{6 x^2+x-1}{6} \\[/tex]

simplifying the above equation, we get

[tex]$& =\frac{1}{6}\left(6 x^2+x-1\right)[/tex]

We will factorize the polynomial by splitting its middle term.

[tex]$& \frac{1}{6}\left(6 x^2+x-1\right) \\[/tex]

[tex]$& =\frac{1}{6}\left(6 x^2+3 x-2 x-1\right) \\[/tex]

simplifying the above equation, we get

[tex]$& =\frac{1}{6}(3 x(2 x+1)-1(2 x+1)) \\[/tex]

[tex]$& =\frac{1}{6}(3 x-1)(2 x+1)[/tex]

[tex]$\frac{1}{6^{}}(3 x-1)$[/tex] and (2x + 1) are factors of [tex]$x^2+\frac{x}{6}-\frac{1}{6}$[/tex]

Therefore, the correct answer is option B. 2x + 1

The complete question is:

Which among the following is a factor of [tex]$x^2+\frac{x}{6}-\frac{1}{6}$[/tex] ?

A. 3x + 1

B. 2x + 1

C. [tex]$x-\frac{1}{5}$[/tex]

D. [tex]$x-\frac{1}{2}$[/tex]

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Refer to the photos taken.

Answer:

2+3=5

Step-by-step explanation:

2+

3=

5

answer 2+3=5

The asymptotes in a given function is a line that the graph of a function approaches as either x or y go to positive or negative infinity.

An asymptote in a function is defined as the a line that the graph of a function approaches as either x or y go to positive or negative infinity.

There are various types of asymptote which include the following:

To determine the asymptote of a function in a graph is a descending curve that approaches but does not reach the horizontal axis is said to be asymptotic to that axis, which is the asymptote of the curve.

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Answer:

8.8 mins

Step-by-step explanation:

to find how long in mins it would take to fill the tank

at 180 degrees the speed of water is 15 liters/min at 123 degrees

so [tex]\frac{15}{180} *123[/tex] = 10.25 liters/min

the capacity of the tank is 90.2 liters

[tex]\frac{90.2}{10.25} \\[/tex] = 8.8 mins

Answer:

The boats cross paths at the points (1,8) and (4,11)

Step-by-step explanation:

First, we want to find the points of intersection between the two paths. We are given two equations, both in the form y=(equation). Since we want to find the intersection points, we set the two equations equal to each other (since both equal y we can plug one of the equations in for y into the other equation) to get

-x^2+6x+3=x+7

From here, we solve this like a normal quadratic equation, move all variables to one side first

-x^2+5x-4=0

This factors to -(x-1)(x-4)=0, giving us x=1 and x=4

Now we plug these back into one of the original equations (in this case the linear equation is much more simple) to give us the points (1,8) and (4,11)

One of the factor of the given polynomial 6x^4 - 21x^3 - 4x^2 + 24x - 35 is (2x-7).

According to Rational Root Theorem,

Leading coefficient = 6

Trailing constant = 35

Factors of leading coefficient = 1, 2, 3, 6

Factors of trailing constant = 1, 5, 7, 35

Check for the rational roots

Let P = 7, Q = 2, then

P/Q = 3.5

F(P/Q) = 0

Apply Factor theorem which means the given polynomial must be divisible by P/Q, that is (2x-7)

Divide the polynomial into two groups

Group 1  6x^4 - 21x^3

Take 3x^3 common, we get

3x^3(2x - 7)

Group 2  - 4x^2 + 24x - 35

When we divide it by (2x - 7) we get (-2x + 5)

⇒ - 4x^2 + 24x - 35 = (-2x + 5)(2x - 7)

⇒ 6x^4 - 21x^3 - 4x^2 + 24x - 35 = (2x - 7)(3x^3 - 2x + 5)

Hence the correct option is A.

-- The given question is incomplete, the complete question is

"Which is a factor of the polynomial f(x) = 6x^4 - 21x^3 - 4x^2 + 24x - 35? A) 2x - 7 B) 2x + 7 C) 3x - 7 D) 3x + 7" --

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Answer:

-9z + 72

Step-by-step explanation:

Answer:

m∠DFE = 69°

Step-by-step explanation:

The tangent of a circle is always perpendicular to the radius.

Therefore, as ABC is the tangent to the circle, and OB is the radius of the circle:

⇒ m∠CBO = 90°

Interior angles of a triangle sum to 180°.  Therefore:

⇒ m∠COB + m∠CBO + m∠BCO = 180°

⇒ m∠COB = 180° - m∠CBO - m∠BCO

⇒ m∠COB = 180° - 90° - 48°

⇒ m∠COB = 42°

Angles on a straight line sum to 180°.  Therefore:

⇒ m∠DOE + m∠COB = 180°

⇒ m∠DOE = 180° - m∠COB

⇒ m∠DOE = 180° - 42°

⇒ m∠DOE = 138°

The angle at the center is twice the angle at the circumference.

Therefore:

⇒ m∠DOE = 2 × m∠DFE

⇒ m∠DFE = m∠DOE ÷ 2

⇒ m∠DFE = 138° ÷ 2

⇒ m∠DFE = 69°

Answer:

linear inequation with 1 variable

The probability that the upward face shows a number that is a multiple of 3 is p = 1/3 .

Given :

When a dodecahedral die is rolled the possible outcomes are:

s = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }

The total numbers of possible outcomes is 12.

The numbers of outcomes whose upward face is multiple of 3 .

= { 3 , 6 , 9 , 12 }

so Number of favorable outcomes = 4

What is probability ?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Probability = number of favorable outcomes / number of possible outcomes

= 4 / 12

= 1 / 3

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