Is math in Grade 6 hard?

Answer:

16a^4

Step-by-step explanation:

Answer:

16a^4

Step-by-step explanation:

The expression (2a)^4 can be written in exponential form as 2^4 * a^4. Using the laws of exponents, we can simplify this to:

2^4 = 2 * 2 * 2 * 2 = 16

a^4 = a * a * a * a

So, (2a)^4 = 16a^4

log 30+ log 6 is not equivalent to log 36

Equivalent expressions are expressions that perform the same function not with standing their appearance. If two algebraic expressions are equivalent, they have the same value when the same value(s) for the variable are used (s).

The original phrase is as follows

Log 36

Following that, we write the alternatives (a) log 2+ log 18

Apply the logarithmic rule log 2+ log 18 log (218)

Log 2 plus log 18 log (36)

Remove the bracket

Log 2 plus log 18 log36

(a) Log 2+ Log 18 is the same as log 36.

(b) Log 30 plus log 6

Use the logarithms’ law. 30 logs or more 6 logs (30 x 6)

Log 30 plus log 6 Equals log (180)

Remove the bracket

Log 30-plus log 6-log180

Hence,

(c) Log 30+log 6 does not equal log 36.

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The equation a²-4=0, which corresponds to the factorization of a²-4= (a+ 2)(a-2)

Factorization refers to the process of breaking down a mathematical expression into simpler parts that can be multiplied together to give the original expression. For example, factorizing the expression x² + 4x - 12 would give (x - 3)(x + 4) as the factors.

In algebra, factorization is used to simplify expressions and to find the solutions of equations. For example, in the quadratic equation ax² + bx + c = 0, the first step in solving the equation is to factorize the quadratic expression ax² + bx + c. Once this is done, it becomes easier to find the solutions of the equation by setting each factor equal to zero and solving for x.

Factorization can also be used to simplify expressions in other branches of mathematics, such as number theory. For example, the prime factorization of a composite number is the representation of that number as a product of prime numbers.

Given:

The equation a²-4= (a+ 2)(a-2) is a factorization of a quadratic expression. It states that the expression a²-4 can be represented as the product of two binomials, (a+ 2) and (a-2).

This can be visualized as the graph of a parabola, where the x-intercepts of the parabola are -2 and 2. These are the solutions of the equation a²-4=0, which corresponds to the factorization of a²-4= (a+ 2)(a-2)

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Therefore , the solution of the given question of triangle  comes out to be the only true option is A.

Triangles, which have three sides and three angles, can be made by joining any three points in a plane. One of the first geometric shapes to be examined was them. They are especially crucial because any polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle.

Triangles, which have three sides and three angles, can be made by joining any three points in a plane. One of the first geometric shapes to be examined was them. They are especially crucial because any polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle.

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No, 10, 12, and 15 are not the lengths of the sides of a right triangle.

A right triangle is a triangle with one 90 degree angle. The other two angles must be acute angles (less than 90 degrees).

The Pythagorean Theorem is a formula used to determine if three given side lengths can form a right triangle. The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side, also known as the hypotenuse.

In this case, the side lengths of the triangle are 10, 12, and 15. Therefore, the Pythagorean Theorem can be written as:

10^2 + 12^2 = 15^2

100 + 144 = 225

244 ≠ 225

Therefore, 10, 12, and 15 are not the side lengths of a right triangle.

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She needs to purchase 240 packets of each kind in order to have an equal amount of pencils, notebooks, and red pens.

Least Common Multiple is referred to as LCM. The smallest number that is a multiple of both numbers is the least common multiple of the two. The first few multiples of each integer should be listed.

Look for duplicates that appear on both lists. Write out additional multiples for each number if the lists don't contain any common multiples. The least integer shared by both lists should be found. The LCM is this figure.

given

This entails determining the 16, 12, and 20 Least Common Multiples (LCM).

2⁴ = 16 = 2 * 2 * 2 * 2

2²*3 = 12 = 2 * 2 * 3

2²*3 = 12 = 2 * 2 * 3

2²*5 =  2 * 2 * 5

Keep in mind that LCM is the prime factorization of the involved integers multiplied by the highest power of each prime factor;

22 * 3 * 5 = 240.

She needs to purchase 240 packets of each kind in order to have an equal amount of pencils, notebooks, and red pens.

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Answer: The slope is the cost per hour (in this case $20 per hour).

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

Further Explanation:

Recall that,

[tex]\text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}[/tex]

The rise tells us how much to go up or down, depending if the rise is positive or negative. The run tells us how much to go to the right. Always move to the right.

In this problem, the change in y is the change in price. The change in x is the change in hours. Dividing the two items gives cost per hour, aka unit cost.

-----------------------

Example:

Let's pick two points from this line and use the slope formula. I'll pick (1,60) and (3,100) as they are the only two points with coordinate labels.

So,

[tex](x_1,y_1) = (1,60) \text{ and } (x_2,y_2) = (3,100)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{100 - 60}{3 - 1}\\\\m = \frac{40}{2}\\\\m = 20\\\\[/tex]

The slope is 20, or 20/1

It says that each time the number of hours x goes up by 1, the cost variable y goes up by 20.

Put simply: The hourly fee is $20 per hour.

This matches what it says in the instructions when your teacher wrote "A roofer charges $60 for the first hour and $20 per hour for each additional hour".

There is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.

At the null hypothesis, it is tested if there is no evidence of different performance, that is, the mean is of 8.5 hours, hence:

[tex]H_0: \mu = 8.5[/tex]

At the alternative hypothesis, it is tested if there is evidence of different performance, with a mean different of 8.5 hours, hence:

[tex]H_1: \mu \neq 8.5[/tex]

We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, hence the critical value is of:

|z| = 1.96.

(p-value of 1 - (0.05/2)).

Hence the decision rule is given as follows:

The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.

The equation is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 8.8, \mu = 8.5, \sigma = \sqrt{1.21} = 1.1, n = 21[/tex]

Hence the test statistic is of:

[tex]z = \frac{8.8 - 8.5}{\frac{1.1}{\sqrt{21}}[/tex]

z = 1.24.

|z| < 1.96, hence there is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.

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Answer:

They should sell the computer for $287.50

Step-by-step explanation:

Let's solve the 25% increase first

100% = $200

100% + 25% = 125% = 1.25

200 x 1.25 = $250

Then we find the 15% increase

100% = $250

100% + 15% = 115% = 1.15

250 x 1.15 = $287.50

So, they should sell the computer for $287.50

The number of hours that Julius can spend online this week is 1 1/3 hours.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Since Julius is allowed to surf the internet for only 3 hours a week. He has already been online for 1 2/3 hours this week.

This will be Illustrated as x.

x + 1 2/3 ≤ 3.

x ≤ 3 - 1 2/3

x ≤ 1 1/3.

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Place a dot at the origin, sometimes referred to as the center of the Cartesian coordinate axis, to begin. We may then plot a point on the graph after placing the necessary points there.

An x-y (or bivariate) plot is any graph or plot with two axes.

The "x-axis" is often the horizontal axis, whereas the "y-axis" is typically the vertical axis.

However, if you have a data set with two sets of related data, you may utilize any variable for either one.

There are a few procedures you may take when plotting data on a graph to make sure you don't neglect anything:

Make sure you are working with two variables (two columns of data).

Make a decision on which variable will be represented on the x-axis and which on the y-axis.

Your plot's axes should be identified, and the scale should be chosen (if the graph is not already labeled).

Plot the first two pairs of numbers first (the top row of numbers).

Plot pairs of points repeatedly until all the points have been plotted.

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The answer to the iterated integral after the evaluation is 2.

The iterated integral evaluates to the area of the region bounded by the curves x = 0, x = y, and y = π/2, which can be calculated by setting up a double integral. The outer integral is with respect to x, from 0 to π/2, and the inner integral is with respect to y, from 0 to x.

The integrand is xsin(y), meaning that the area of the region is the integral of xsin(y) with respect to y from 0 to x, and then with respect to x from 0 to π/2. The solution is found by evaluating the inner integral first, which yields -xcos(x), and then evaluating the outer integral. The result is 2, which is the area of the given region.

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According to the following graph, the reflection point of (-3,4) across the line y = 2 is (-3,0).

The term reflection point in math is defined as

Here we need to find the reflection point of (-3, 4) across the line y = 2.

Here first we have t plot the point on the graph, and then we have to plot the line equation y = 2 on the graph,

Here in order to find the reflection of a point along the x-axis, then we have to keep the abscissa constant and see the reflection of ordinate along the x-axis.

Based on these rule, the resulting graph is obtained as follows.

Through the graph we have identified that the resulting reflection point is (-3,0).

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On solving the provided question, we can say that by the help of unitary method total 28 + 40 = $ 68

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

One package of chicken costs  = $7

steaks cost  = $4 per pound.

cost of 4 chicken = 4 * 7 = $28

cost of 10 steaks = 4*10 = $40

total 28 + 40 = $ 68

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The unit rate of change of the proportional relationship is given as follows:

2.25.

The graph of the proportional relationship is given by the image presented at the end of the answer.

A proportional relationship is a linear function with an intercept of zero modeled as follows:

y = kx.

In which k is the constant of proportionality.

The input and output variables for this problem are given as follows:

The constant k, representing the unit rate, is obtained by the division of the output of the input from the table, hence:

k = 4.5/2 = 6.73/3 = 9/4 = 2.25.

Meaning that the function is defined as follows:

y = 2.25x.

The function is graphed for a domain of x ≥ 0, as the number of cups of sugar must be a countable, non-negative amount.

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The measure of angle is, 62°.

The sum of two or more angle is 90 degree then the angle is called the complementary angle.

We have to given that;

⇒ Supplement of an angle is 6 more than 4 times of its complement.

Now,

Let measure of an angle = x

So, By given condition, we can formulate;

The supplement of an angle = 180 - x

And, The complement an angle = 90 - x

Hence, We get;

⇒ (180 - x) = 6 + 4 (90 - x)

Solve for x as;

⇒ 180 - x = 6 + 360 - 4x

⇒ 4x - x = 366 - 180

⇒ 3x = 186

⇒ x = 62°

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Jane should land 1.5 mi down the shoreline and walk the remaining 4.5 mi to the village to minimize her travel time.

Let x = distance travelled along the shore over water.

Then, 6 − x = distance travelled along the shore over land.

Let T = the total time taken to reach the destination.

T = distance/velocity = √(4 + x²)/3 + (6-x)/5 on [0, 6].

Note that T must be non negative and that x = 6 means the destination

is reached solely by rowing and without the benefit of faster land

travel. In actual fact, T is valid over [0, ∞) but [0, 6] is reasonable here.

T' = x/3√(4 + x²) - 1/5 = 5x - 3√(4 + x²) = 0

⇒5x = 3√(4 + x²)

⇒25x² = 9(4 + x²)

⇒16x² = 36

⇒x = ±6/4 = ±1.5

The negative x value is discarded since it does not belong to [0,6].

T(0) = 28/15 = 1.8667

T(1.5) = 1.733

T(6) = 2.1082

Therefore, Jane should land 1.5 mi down the shoreline and walk the

remaining 4.5 mi to the village to minimize her travel time.

Her minimum travel time will be T(1.5) = 1.733 hrs. or 1hr 44 min.

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

"Jane is 2 mi, offshore in a boat and wishes to reach a coastal village 6 mi, down a straight shoreline from the point nearest the boat. She can row at 3mph and can walk at 5 mph. Where should she land her boat to reach the village in the least amount of time?"--

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Answer:

Function Domain and Range

g(x)=\sqrt{x} -5

what is the range and domain

To find the range of g(x), we can substitute a few values of x into the expression for g(x) to see what the output is. For example, when x = 0, g(x) = sqrt(0) - 5 = 0 - 5 = -5. When x = 1, g(x) = sqrt(1) - 5 = 1 - 5 = -4. When x = 2, g(x) = sqrt(2) - 5 = 1.4142 - 5 = -3.5858.

As we can see, the output of g(x) is always a negative number for any value of x in the domain. Therefore, the range of g(x) is the set of all negative real numbers, or (-infinity, 0).

So, the domain of g(x) is all real numbers x such that x >= 0, and the range of g(x) is all negative real numbers (-infinity, 0).

The remaining miles are 660 miles.

This month, Diaz drives 28 miles each day using the car allotted to him by his company.

But the company allows him to drive up to 1500 miles each month by his car.

To calculate the remaining miles that Diaz has not traveled this month, we have to use the formula m = 1500 - 28d, where d is the number of days in that particular month.

A month general consists of 30 days.

So, this month Diaz has traveled 28×30 miles = 840 miles ( using multiplication)

Therefore, the remaining miles(m) that Diaz has not traveled this month comes to 1500 - 840 = 660 miles.

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The complete question is:

Diaz has a company car that allows him to drive up to 1,500 miles each month. He averages 28 miles each day. The remaining miles for this month can be calculated using the formula m = 1500 - 28d where m is the remaining miles and d is the number of days driven this month. What are the remaining miles?

Answer:1000000

Step-by-step explanation:

Answer:

Step-by-step explanation:

original equation equivalent to 7x+5-3x-2 = 7x-3x+5-2=4x+3

the answer is 4x+3

Answer:

The answer is 4x+3

A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.

In a right triangle, the hypotenuse is the longest side, the "opposite" side is the one that faces a particular angle, and the "adjacent" side is the one that faces that angle.

Step 1: Simplify both sides of the equation.

[tex]$$4 g-6=8$$\\Step 2: Add 6 to both sides.$$\begin{aligned}& 4 g-6+6=8+6 \\& 4 g=14\end{aligned}$\\$Step 3: Divide both sides by 4 .$$\begin{aligned}& \frac{4 g}{4}=\frac{14}{4} \\& g=\frac{7}{2}\end{aligned}$$[/tex]

[tex]$g=3 \frac{1}{2}$[/tex]

Therefore, the correct answer is option a)[tex]$g=\frac{7}{2}$[/tex].

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Step-by-step explanation:

there are a few things from school everybody has to burn into their brains for life. one of them : Pythagoras for right-angled triangles :

c² = a² + b²

c is the Hypotenuse (the triangle side opposite of the 90° angle), a and b are the triangle legs.

now, it depends on what you teacher agreed with you regarding naming the sides of such a triangle.

sometimes "base" is the Hypotenuse (baseline), sometimes it is one of the legs, and then the height is the second leg (as the legs are standing at a 90° or right angle at each other).

we have to assume the second one, as for the first one we have not enough information to solve the question (because with just a given Hypotenuse and the height to the Hypotenuse we can draw infinitely many different triangles with different perimeters).

so, we have

Hypotenuse² = 24² + 7² = 576 + 49 = 625

Hypotenuse = sqrt(625) = 25 m

the perimeter of the triangle is then

25 + 24 + 7 = 56 m

Answer: In this exercise we have to calculate the values ​​of the people who voted to expand the parking lot, so we have to:

Yes: parents will be 150 and not parents 40

No; parents will be 40 and not parents 30

As it is about sets, we have to use the data that were:

   total: 250 adults

   180 of whom were parents a park should be expanded.

   40 of the adults who were not parents thought the park should be expanded.

then calculate that:

Step-by-step explanation:

The surveyed parents favor park extension, and two way table is a way or representation of data. and The two-way table is completed as,

                        yes      no

parents              150  |    30

                                 |

not parents        40   |      30

The two-way table shown in the table is attached below.

What is two way table?

Two-way table is a way of representing of data to better understand it.

Given information-

The total number of adults took the survey is 250.

Total number of parents took the survey is 180.

150 of the adults with children and 40 of those without thought the park should be expanded.

Suppose the number of adults who are not the parents and took the survey is .

As the total number of adults took the survey is 250 in which the number of parents took the survey is 180. Thus the number of adults who are not the parents and took the survey is,

Suppose the parents who does not thing that the park should be expanded is .

There is total 180 parents. As 150 of the adults with children thought the park should be expanded. Thus, the parents who does not thing that the park should be expanded is,

Form the 70 adults who are not parents things that park should be expanded is 40, hence the adults who are not parents does not thing the park should be expanded is (70-40) which is 30.

Hence the two way table is completed as,

                        yes      no

parents              150  |    30

                                 |

not parents        40   |      30

the two way

YES                    NO

                          30  

                          30

(parents 150

not parents_40

The sample space for the experiment, S= {Q, R, S, T}.

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.

Given:

From the Spinner we can see four portions as

Q(Orange)

R(Green)

S(Blue)

T(Purple)

So, if the spinner spined then it will point Q, R, S or T which is the Sample space for the Spinner.

Hence, the Sample space is {Q, R, S, T}.

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Answer: B: S = {Q, R, S, T}

Step-by-step explanation:

This is the only answer listed with the letters on the spinner.

The relationship between the input  and output  is that the perimeter of a square is always equal to four times the length of one of its sides.

The perimeter of a square is the total distance around the outside of the square. It is the sum of the lengths of all four sides. To find the perimeter of a square, you simply multiply the length of one side by four, since all sides of a square are equal in length. The formula is P=4S

1.The relationship established between (side length of the square) and output (perimeter of the square) represent that A square's perimeter is always equal to 4 times one of its sides.

2.Yes, the function can be represented with an equation. The equation would be:

Perimeter = 4 × Side Length.

Side Length (input) 1  2  3  4  5

Perimeter (output)  4 8 12 16 20

This equation states that the perimeter of a square is equal to four times the length of one of its sides.

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The given expression , 4x2 – 3xy is having two terms which are 4x2 and –3xy.

The term 4x2 is a product of 4 and x, whereas the other  term (–3xy) is a product of (–3), x and y.

When we will join these two terms using the addition operation we will get the result as  4x2 – 3xy .

The given equation is an example of an algebraic expression and they are made up of combination of constants and variables. They are joined to each other by various operations such as addition , multiplication , division and subtraction.

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On solving the provided question, we can say that - here in the equation, [tex]x^2- x = 4[/tex]

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

so, x = 2

therefore

[tex]x^2- x \\6-2\\4[/tex]

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