Evaluate the expression 1^4+3(10-2)^2show your work

Therefore , the solution of the given problem of expression comes out to be 4x² +1 cannot equal 0 and thus (4x²≥0+1) has no Real factors.

Verifying an algebraic expression requires substituting a number for each variable and performing arithmetic operations. Given that 6 + 6 equals 12, the answer variable in the example above is equivalent to 6. If we are aware of the values of the variables, we can substitute those values for the original ones, which will allow us to evaluate the expression.

Here,

It is important to note that now the ratio of a coefficient of the terms 

The coefficient ratio of the words

8x³ and 2x is 8:2 = 4:1, and the coefficient ratio of the phrases 12x² and 3 is 12:3 = 4:1.

This suggests that we should categorize the original statement as follows: 

This suggests that we should combine the original expression, which is written as

=> (8x³+2x)(12x²+3)=2x(4x²+1))3(4x²+1),

before determining the common component (4x2+1)=(2x³)(4x2+1).

The fact that 4x²≥0 for x ∈ R means that

4x² +1 cannot equal 0 and thus (4x²≥0+1) has no Real factors.

Therefore , the solution of the given problem of expression comes out to be 4x² +1 cannot equal 0 and thus (4x²≥0+1) has no Real factors.

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In the graphic below, assuming the lines are parallel, the value of x is 15.

Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance. Parallel lines in geometry are two lines in the same plane that are at equal distance from each other but never intersect. They can be both horizontal and vertical in orientation. Parallel lines can be found in everyday life, such as zebra crossings, notepad lines, and railway tracks.

Here,

6x+3=7x-12

x=15

The value of x in the figure below assuming that the lines are parallel is 15.

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a) To evaluate loga 15, we can use the property of logarithms that states logab = loga + logb. Since 15 = 3 * 5, we can use this property to find that loga 15 = loga 3 + loga 5. Since loga 3 = 0.56 and loga 5 = 0.83, we can add these values to find that loga 15 = 0.56 + 0.83 = 1.39.

The power to which a number must be increased in order to obtain additional values is referred to as a logarithm. The easiest approach to express enormous numbers is this manner.

Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms may also be represented as multiplication and division of logarithms.

b) To evaluate loga(2/5), we can use the property of logarithms that states log(a/b) = loga - logb. Since 2/5 = 2*(1/5) we can use this property to find that loga(2/5) = loga2 - loga(1/5). Since loga2 = 0.36 and loga(1/5) = -loga5, we can subtract these values to find that loga(2/5) = 0.36 - 0.83 = -0.47

c) To evaluate loga (8a^4), we can use the property of logarithms that states log (a^n) = nloga. We get, loga (8a^4)=loga 8 + log (a^4)

=> loga 8 + loga (a^4)

=>3loga 2 + 4 loga a

=>3loga 2 + 4

=>3 * 0.36 + 4

=5.08

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Answer:1111

Step-by-step explanation:1111

Reason:

Point C is located at (3,3)

Triple each coordinate since the scale factor is 3. That's how we go from (3,3) to (9,9)

If the scale factor was 5 for instance, then we'd go from (3,3) to (15,15)

This trick works only if the center of dilation is the origin.

Answer:

C' = (-3, 4)

Step-by-step explanation:

When a shape is dilated by a factor of 3, the size of the shape is multiplied by 3 in both the x and y directions. To find the new coordinates of point C' after a dilation by a factor of 3, we can multiply the original coordinates of point C by 3.

The original coordinates of point C are (-2, -10). When we multiply these coordinates by 3, we get (-6, -30) for the new coordinates of C' after the dilation. So the answer is (-6, -30)

Joe made a mistake in his calculations by multiplying 28 quarts by 4.

To know the mistake that Joe made and the possible correction, we shall convert 28 quart to gallon.

Recall that 4 quart = 1 gallon

Therefore, 28 quart will be:

= 28 quart × 1 gallon / 4 quart

28 quart = 7 gallon

Therefore, 28 quarts is equivalent to 7 gallons.

Hence, Joe made a mistake in his calculations by multiplying 28 quarts by 4 instead of dividing 28 quart by 4.

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The measure of angle L is 66 degrees, which is found using the sum of the internal angle of a triangle. The length is 3.56 units.

A polygon's interior angle is the angle created between its two adjacent sides. Alternately, we may state that the internal angle of a polygon refers to the angle measured at the interior portion of a polygon.

Given that the measure of angle M is 24 degrees and angle K is 90 degrees.

The sum of internal angles of a triangle is 180 degrees, thus:

[tex]\angle M + \angle K + \angle L = 180\\\\24 + 90 + \angle L = 180 \\\\\angle L = 66[/tex]

The length of side LK can be found as follows:

tan 24 = LK / MK

tan 24 = LK / 8

0.44 * 8 = LK

LK = 3.56 units.

The length of LM can be found by applying the Pythagorean theorem.

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Answer:

a)  See below.

b)  Geometric sequence

[tex]\textsf{c)} \quad a_n=7.5(0.5)^{n-1}[/tex]

Step-by-step explanation:

From inspection of the given table, t(n) halves each time n increases by 1.

Therefore:

[tex]\implies a_4=1.875 \div 2 = 0.9375[/tex]

[tex]\implies a_5=0.9375 \div 2 =0.46875[/tex]

Completed table:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&t(n) \\\cline{1-2} \vphantom{\dfrac12} 1& 7.5\\\cline{1-2} \vphantom{\dfrac12} 2& 3.75\\\cline{1-2} \vphantom{\dfrac12} 3&1.875 \\\cline{1-2} \vphantom{\dfrac12} 4& 0.9375\\\cline{1-2} \vphantom{\dfrac12} 5& 0.46875\\\cline{1-2} \end{array}[/tex]

As the given sequence has a constant ratio of 0.5, it is a geometric sequence.

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

The first term of the sequence is 7.5.  Therefore,:

The common ratio is 0.5. Therefore:

Therefore, to write an equation for the given geometric sequence, substitute the found values of a and r into the formula:

Luis genera $13680 al mess, sir se incremental un 14% ell valor de sub seldom actual.

De actedron con las condictiones dadas, planter=12000*(14% + 1)

Calculary loss dos primero's terminus =12000*1.14

Calculary loss dos primero's terminus =13680

get the result=13680

Explication paso a paso:

multiplicate ell 14% de 12.000= 1.680

le sulfas ese 1.680 a 12.000 y tee da ell resulted de 13.680

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Answer:

See below

Step-by-step explanation:

You could say "2 times the difference between n and 7 is equal to -14"

The best estimate willl 20

Step-by-step explanation:I

Brooke's yard is a square with a side length of 22 meters.

Perimeter is the total distance around the outside edge of a two-dimensional shape. Perimeter is a measure of the length of the boundary of a shape and is typically expressed in units of length, such as feet or meters. Calculating the perimeter of a shape can help you measure the size of a yard, garden, or other outdoor area.

Since the perimeter of the part covered in gravel is 22 meters, we can use the formula for the perimeter of a square (4s) to find the length of one side of the square. Therefore, the side length of the part covered in grass is 4s = 22, or s = 5.5 meters.

Using the formula for the area of a square (A = s²), we can calculate the area of the grass section of Brooke's yard. The area of the grass section of Brooke's yard is A = s²= 5.5²= 30.25 square meters.

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Answer:

she had here eyes open for 12.4 more hours than she had them closed

Step-by-step explanation:

1/10 eyes closed = 9/10 eyes open

9/10 is 90% is 0.9

1/10 is 10% is 0.1

15 1/2 is 15.5

15.5 x 0.9 = 13.95

15.5 x 0.1 = 1.55

13.95-1.55 = 12.4

The the average age of the remaining 4 students is 9.5 years.

The average may be calculated by dividing the total number of values by the sum of all the numbers. An average of the values in a sample of data may be used to determine a mean. In other words, the arithmetic mean is another name for an average. A mean is a term used to describe the average.

The average age of 5 students is 10 years.

∴  Sum of age of 6 students =5 × 10 = 66

⇒  When two more students of age 5 and 1 added to 4 students then, total students will become 8

⇒  Sum of age of 6 students =66 + 6 + 4 = 76

∴  Required average =

76 / 8  = 9.5

=9.5 years

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Answer:

5%

Step-by-step explanation:

105=100

110=x

*cross multiply*

=100x110/105

=104.76

=100-105

=5%

subtract the answer gotten with the 100 %

In linear equation, 16 is represent The speed at which Serena is cycling from the dance class to her home

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

6x + y = 16

6x = 16 - y

x = 8/3 - y/6

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Answer:

x intercepts (-2,0) and (-4,0)

y intercept: (0,8)

Vertex: (-3,-1)

Axis of symmetry x = -3

Step-by-step explanation:

Answer:

159

Step-by-step explanation:

Median = When ordered least to greatest, the number in the middle

140, 141, 146, 148, 151, 156, 159, 159, 160, 167, 170, 173, 174

Answer:

True

Step-by-step explanation:

True

The value of X is 7.625 while the two sides are 38.125 and 27.875.

Perimeter = 2(L+B)

112 = 2(5x + 3x + 5)

112 = 2(8x + 5)

Dividing both sides by 2

56 = 8x + 5

56 + 5 = 8x

61 = 8x

x = 61/8

x = 7.625

The sides are;

5x = 5(7.625)

5x = 38.125

3x + 5 = 3(7.625) + 5

3x + 5 = 22.875 + 5

3x + 5 = 27.875

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The possibility that someone randomly guesses the correct combination in five attempts is 1/200

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

Given;

There are three wheels

Each numbered from 0 to 9

For the first wheel, you have 10 possible digits.

For the second wheel, you have 10 possible digits.

For the third wheel, you have 10 possible digits.

10 x 10 x 10 = 1000

For 5 attempts= 5/1000

=1/200

Therefore, the probability will be 1/200

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The value of dy when x changes from -1 to -1.1 for equation y = 4x² is 0.84.

Here we are given an equation y = 4x²

In an equation, dy/dx, implies the change in y due to a change in x.

Now here we already have given that x changes from -1 to -1.1.

Hence, here we need to find the values of y when x = -1 and when x = -1.1

Then we need to subtract the value of y when x = -1.1 and when x = -1

We are given y = 4x²

Hence when x = -1,

y = 4 X 1

= 4

When x = -1.1

y = 4 X 1.21

= 4.84

Hence dy = 4.84 - 4

= 0.84

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Therefore , the solution of the given problem of graph comes out to be

x = 0 , y =22 and  x= 1 , y=23.

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

Here,

Given :

=> h(x) = g(x+3) - 6

g(x) = x+ 25

So,

=> g(x+3) = x +3 + 25 = x+28

and

=> h(x) = x + 28 -6

=>y= h(x) = x+ 22

Thus,

y= x+22

the points which can be graph area:

=> x = 0 , y =22

=> x= 1 , y=23

Therefore , the solution of the given problem of graph comes out to be

x = 0 , y =22 and  x= 1 , y=23.

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The polynomial's zeros must be located using a method of your choice, and the linear expressions that produce those zeros must then be combined in order to describe the polynomial as a product of linear factors.

The term "triple zero" or "zero with multiplicity 3" is used to describe this. The power p governs the behaviour close to the x-intercept if a polynomial has a factor of the type (xh)p. A zero of multiplicity p is defined as x=h. The x-axis will be touched at zeros with even multiplicities on a polynomial function's graph.

A real number is multiplied by an imaginary unit, I whose feature i2 = 1 defines it as an imaginary number. Bi is an imaginary number, while b2 is its square. For instance, the square of the fictitious integer 5i is 25. Zero is regarded as both real and fictitious by definition.

You must first determine the polynomial's zeros using the method of your choice, and then combine the linear equations that result in those zeros. If you factor, you will arrive at the third degree polynomial, which must then be sorted through.

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Answer: 25

Step-by-step explanation:

simple math

Answer:

25 cookies

Step-by-step explanation:

After she gives away 5 of her 10 cookies she is left with 5 cookies. Then she bakes 20 more. So you add 5 cookies to 20 cookies, and you get 25 cookies.

Or in total with all of the cookies she had before she gave away 5 of the 10, and the newly baked 20 cookies she has 30 cookies.

-Hope this helped

The truth of z scores that fall below the mean is - they are negative. Option(b) is the correct answer.

A z-score called a standard score gives an idea of how far from the mean a data point is. But technically it is a calculation of how many standard deviations below or above the population mean a raw score is.

A z-score can place on a normal distribution curve. Z-score ranges from -3 standard deviations up to +3 standard deviations.

A z-score is equal to 0 means that it is on the mean. A positive z-score shows the score is higher than the mean average.

A negative z-score reveals the score is below the mean average.

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Answer:

  a)  93 cm²

  b)  98 cm²

Step-by-step explanation:

You want the areas of the squares shown in each of the figures.

The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the other two sides of a right triangle.

The square of the hypotenuse is 17² = 289.

The sum of the squares of the other two sides is ...

  shaded square + (14)² = 17²

  shaded square + 196 = 289

  shaded square = 289 -196 = 93 . . . . cm²

Sabcd = 93 cm².

The square of the diagonal is the sum of the squares of the sides. Each of those squares is the area of interest:

  14² = (shaded square) + (shaded square)

  196 = 2(shaded square)

  98 = shaded square

Sabcd = 98 cm².

__

Additional comment

Perhaps you have seen the attached figure. It is intended to show the squares on each of the legs of the right triangle, and to illustrate that the sum of the areas of the green and purple squares is the area of the red square. This figure compares to the one for part (a) of the problem.

  a² +b² = c²   ⇒   a² = c² -b²