Prime factorization of 64 + 144 as a product of the GCF and a sum of two numbers.

Answer:

C - Reflect over the x-axis

Step-by-step explanation:

This is a reflection over the x-axis.

To remember the difference between reflectinon over the x-axis and reflectino over the y-axis, memorize this.

If you reflect over the x-axis, the x value of the reflected point stays the same.  (only the y is multiplied by -1)

If you reflect over the y-axis, the y value of the reflected point stays the same. (only the x is multiplied by -1)

Roation about the origin involves multiplying both x and y by -1.  (x and y change)

The relation between curl vector and rotations is v = wdj

A vector field is a vector field's curl. The tendency of particles at point P to spin about the axis that faces the direction of the curl at P is measured by the curl of a vector field at P. If and only if its curl is zero, a vector field with a simply linked domain is considered conservative.

Let v represent the particle's velocity as a vector.

vector v=ui+vj+wk

curl v =

curl v  = [tex]\left[\begin{array}{ccc}i&j&k\\d/dx&d/dy&d/dz\\u&v&w\end{array}\right][/tex]

= (dw/dy - dv/dz )i - (dw/dx - du/dz)j +  (dv/dx - du/dy )k

Now by comparing with rotational matrix ,

We know that w = rotational matrix

[tex]w_{x}[/tex] = 1/2 (dw/dy - dv/dz )

[tex]w_{y}[/tex] = 1/2 (dw/dx - du/dz)

[tex]w_{z}[/tex] = 1/2  (dv/dx - du/dy )

w = [tex]w_{x} i +w_{y} j + w_{z} k[/tex]

w =  1/2[ (dw/dy - dv/dz )i + (dw/dx - du/dz)j + (dv/dx - du/dy )k]

w = 1/2 curl v , rotation = 1/2 curl v

let B be a rigid rotating about z axis

w = w.k

tangential speed =wk *di

v = wdj

curl of v=  [tex]\left[\begin{array}{ccc}i&j&k\\d/dx&d/dy&d/dz\\0&w_{x} &0\end{array}\right][/tex]

v = wdj ,

The relation between curl vector and rotations is v = wdj

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The congruent reason for the triangles is (b) HL theorem

From the question, we have the following parameters that can be used in our computation:

Triangles = FGH and JHK

The SSS similarity theorem implies that the corresponding sides of the two triangles in question are not just similar, but they are also congruent

From the question, we can see that the following corresponding sides on the triangles:

Sides GH and HK

Sides FH and JK

These parameters are given in reasons (2) and (3) and it implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following sides must also be congruent

GH must be congruent to HK

The above statement is true because point H is the midpoint of line GK

This is indicated in reason (2)

Hence, the congruent statement is SSS.

However, we can also make use of the HL theorem in (B)

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The perimeter of the triangle is 18 feet.

Polygon which has three sides and three vertices is called as triangle.

Sum of all the angles of the triangle is 180°.

Given the sides of the triangle are 4 feet , 6 feet and 8 feet.

And the perimeter of the triangle

= sum of all three side of the triangle.

The perimeter of the triangle = 4 + 6 + 8

perimeter of the triangle = 18 feet

Therefore, the perimeter of the triangle is 18 feet.

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Answer:

26.7%

Step-by-step explanation:

Percentages are values in terms of values divided by 100.

Eg.

[tex] \frac{34}{100} = 34percent [/tex]

To solve this question, we have to make sure the denominator is 100.

4 : 15

[tex] = \frac{4}{15} \\ = \frac{4 \\ \times 10}{15 \times 10} \\ = \frac{40 \div 1.5}{150 \div 1.5} \\ = \frac{26.667}{100} [/tex]

Therefore the percentage is 26.7%. (3 Significant Figures)

Answer:

D an even or odd sum from rolling two dice

what is uniform probability with three examples?

Uniform probability is a type of probability distribution in which all outcomes have the same probability of occurring. This means that all outcomes have an equal chance of being selected, and no one outcome is more likely to occur than any other. For example, if you were to roll a die, each of the six outcomes (1, 2, 3, 4, 5, 6) would have an equal probability of occurring. Here are three examples of uniform probability:

1. Tossing a coin: When a coin is tossed, the probability of it landing on either heads or tails is 50%. This is because both outcomes have an equal chance of occurring, making it a uniform probability.

2. Rolling a dice: When a dice is rolled, the probability of it landing on any of the six numbers (1, 2, 3, 4, 5, 6) is equal, at 16.67%. This is because all outcomes have an equal chance of occurring, making it a uniform probability.

3. Drawing a card from a deck: When a card is drawn from a deck, the probability of it being any of the 52 cards (13 of each suit) is equal, at 1.92%. This is because all outcomes have an equal chance of occurring, making it a uniform probability.

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Answer:

0.15

Step-by-step explanation:

10/x=67.50

10=x*67.5

10/67.5 = x

x=0.14814814814

At the 24th House, they will first meet.

List the multiples to determine the LCM.

List the initial range of each number's multiples.

Search for multiples that appear on both lists. Write out additional multiples for each number if there aren't any common multiples in the lists.

Find the least quantity that appears on both lists.

The LCM is this number.

According to the given information

Each sixth residence is visited by one group.

The second group visits every eighth house.

So

We need to find the house number where both the groups will meet

For that

We must determine the LCM of 6 and 8.

LCM(6) = LCM(8) = 3*2*4 = 24.

At the 24th House, they will first meet.

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Answer:

Step-by-step explanation:

45 out of 100

The equation of line for Pilar's rock climbing is given by y = -8x + 242 and the slope of the equation is m = -8

Connor's equation of line is y = -10x + 200 and slope m = -10

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the values of x be set x = { 1 , 2 , 3 }

Let the values of y be set y = { 234 , 226 , 218 }

Now , the equation of line for Connor's rock climbing is given by the formula y - y₁ = m ( x - x₁ )

And , the rate of change is given by the slope of the line

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 234 - 226 ) / ( 1 - 2 )

Slope m = -8

So , the rate of change is m = -8 feet per minute

Now , the equation of line for Pilar's rock climbing is

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 234 = -8 ( x - 1 )

y - 234 = -8x + 8

Adding 234 on both sides of the equation , we get

y = -8x + 242

So , the equation of line is y = -8x + 242

Now , when initial value , x = 0

y = -8 ( 0 ) + 242

y = 242 feet

Now , Connor's rock climbing is 10 feet per minute descending down

So , the slope Connor's equation is m = -10

And , the equation of line is y = -10x + 200

Hence ,

The equation of line for Pilar's rock climbing is given by y = -8x + 242

The equation of line for Connor's rock climbing is y = -10x + 200

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Answer:

End Balance: $5,160.00

Total Interest: $2,160.00

Step-by-step explanation:

Total Interest =$3000 × 2% × 3 × 12

=$2,160.00

End Balance =$3000 + $2,160.00

=$5,160.00

Answer:

can we get the options

Step-by-step explanation:

In the first problem, we calculated margin error =0.011, the 2nd problem we got population mean = 20.784 0r 19.216. the last problem true average age = 25.58 or 24.42

the margin of error indicates the differences between true result and estimated result.

The population means refers the average value of whole population where sample means indicate the average value of randomly selected samples only.

Given, size of population, n= 1936

random size of population, p = 121

probability 0.95 that means 95% confidence interval.

now margin error of sample mean is calculated by the following formula

Margin of error, ME= Z*×[√{p^(1-p^)/n}]

         where, p^ is proportion of population and p^= p/n

                            z* is the critical value of 95% confidence interval

                        p^ =p/n= 121/1936 =0.0625

                       z*= 1.96

      hence, ME= 0.011

In the next problem, size of random sample, n= 144

 sample mean, x⁻ = 20

population standard deviation, б = 4.8

confidence interval = 95.44% is equal to 95%

critical value z* =1.96

we need to estimate the population  mean,μ by the following formula

   μ = x⁻ ± z*(σ/√n)

        =20±1.96 (4.8/√144)

hence population mean is 20.784 or 19.216

in the last samples, true average ages can be calculated by the formula

 true average age = average age ±z*(σ/√n)

given, standard deviation σ = 2

  critical value for 98% confidence interval =2.33

  size of sample, n= 64

average age =25

  hence true average age = 25.58 or 24.42

hence, margin error is 0.011, population mean = 20. 784 or 19.216 and true average age = 25.58 or 24.42

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The simplification of the given expression is (a² + a + 1)/a².

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is a+1/2a + 3/a².

It can be evaluated as follows,

a+1/2a + 3/a²

Take the LCM of a and a² as a².

= (a(a + 1)+ 3)/a²

= (a² + a + 1)/a²

Hence, the given expression can be simplified to obtain (a² + a + 1)/a².

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Answer: Using proportions, it is found that of the remaining pins, 14 pins are green and 21 pins are yellow.

A proportion is a fraction of a total amount, and then operations such as multiplication are applied to find the equivalent amounts relative to the proportion.

In this problem, we have that:

3/7 of the x pins are green.

4/7 of the x pins are yellow.

With one less pin, 2/5 are green and 3/5 are yellow, hence:

3/7x - 1 = 2/5x.

Isolating for x and applying the least common multiple, we have that:

x = 35.

He has 35 pins remaining, hence:

2/5 x 35 = 14 pins are green.

3/5 x 35 = 21 pins are yellow.

What is the missing information?

The complete problem is:

Yaqub has a bag only containing green and yellow pins. 3/7 of the pins are green. He picks out a green pin from his bag and gives it to his sister.

2/5 of the remaining pins in his bag are green.

How many of the remaining pins in his bag are green and how many are yellow?

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Step-by-step explanation:

The algebraic expression known as a trinomial contains three terms then the trinomials exists 3y + 5y² + y and [tex]$$x^4[/tex] + x² + 1.

Three non-zero terms make up a trinomial, which is an algebraic expression. The algebraic expression known as a trinomial contains three terms. An mathematical equation called a trinomial has three terms with on-zero coefficients, each separated by a + or - sign. It is a trinomial if three monomials are divided by addition or subtraction.

When a polynomial has three terms, it is referred to as a trinomial. Its general expression is ax² + bx + c, where a and b are coefficients and c is a constant. In order to factor trinomials, you must follow these three easy steps: Calculate the values of b (middle term) and c. (last term).

A. 8x  

Not a trinomial because, it contains only one term.

B. 3y +5y² + y

A trinomial because, it contains three terms.

C. 6x²

Not a trinomial because, it contains only one term.

D. [tex]x^{4}[/tex] + x² +1

A trinomial because, it contains three terms.

E. x² + 3

Not a trinomial because, it contains two terms only.

F. x¹¹

Not a trinomial because, it contains only one term.

Therefore, the correct answer is

B. 3y + 5y² + y and D. [tex]$$x^4[/tex] + x² + 1

The complete question is:

Which of the following are trinomials?

A. 8x

B. 3y + 5y² + y

C. 6x²

D. [tex]$$x^4[/tex] + x² + 1

E. x² + 3

F. [tex]$$x^{11[/tex]

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Answer:

A0=3kg

t1/2=67y

λ=ln2/t1/2

λ=0.6931/67

λ=0.0103447761-> 0.0103

Final Amount=Aoe^-λ×t

Final Amount=A0e^-0.0103447761×t

You can put the time that you want to find how much of the material has been left after a certain amount of time

as an example

if t=143years

Final Amount=3×e^-0.0103447761×143

Final Amount=3×e^−1.479302982

Final Amount=0.6833892338

A0 is the amount of material that we have before it goes into radioactive decay

4

divide 16 by 4, which equals 4

Answer:

4 goes into 16 4 times

Step-by-step explanation:

4 x 4=16

Hope this helps!

 is that algebra?

If not it   is  [tex]2 < 2x < 6[/tex]

so 2 is smaller  Then then 2x with is most likely a decimal I could be a decimal are you working on decimals?

I can't give a great answer as i might mix thing up Also what grade are you in?

A. The meters that Gianna walk each hour is 5760 meters.

B. The kilometers that Gianna walk each hour is 5.760 kilometers.

The distance can be found by illustrating it as an expression. Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

There are 1000 meters in 1 kilometer

3600 seconds = 1 hour

Gianna's average walking rate is 1.6 meters per second. The distance in an hour will be:

= 1.6 × 3600

= 5760. meters.

The kilometers that Gianna walk each hour will be:

= 5760 meters / 1000

= 5.76 km

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Answer:

the solution of the system is x = 18/5 and y = 27/5.

Step-by-step explanation:

To solve a system of equations using elimination, we can add or subtract the equations to eliminate one of the variables. In this case, we can add the given equations to eliminate the x-variable:

(-3x - 4y) + (x + y) = -54 + 15

-2x - 3y = -39

Dividing both sides by -3, we get:

(2/3)x + (1/3)y = 13/3

This equation tells us that x is equal to 2/3 times the value of y. Substituting this expression for x in one of the original equations, we can solve for y:

-3(2/3)y - 4y = -54

This simplifies to:

(-6/3)y - 4y = -54

Combining like terms, we get:

(-10/3)y = -54

Dividing both sides by -10/3, we get:

y = 27/5

Substituting this value for y in the expression for x, we get:

x = (2/3)(27/5) = 18/5

Therefore, the solution of the system is x = 18/5 and y = 27/5.

Answer: x=6, y=9

(6,9)

Step-by-step explanation:

Multiply x+y=15 by 3 to eliminate x

3(x+y)=15(-3)

3x+3y=45

-3x-4y=-54

-1y=-9

y=9

sub in 9 to y to get x

x+9=15

x=6

The inequality that represents the possible depths d  reached by the vehicle is d < -725.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Depth record = less than -715 feet.

This means,

The depth must be -716 or less.

The vehicle breaks the depth record by more than 10 feet.

This means,

-715 - 10 = -725

The depth record must be less than -725

Thus,

The possible depths d reached by the vehicle is d < -725.

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The slope of the line that passes through (0, 5) and (8, 2) is -3/8

From the question, the points are given as

(0, 5) and (8, 2)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (0, 5) and (8, 2)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 5) and (8, 2)

Substitute the known values in the above equation

So, we have the following equation

Slope = (2 - 5)/(8 - 0)

Evaluate

Slope = -3/8

Hence, the slope of the line is -3/8

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Since the point negative 4.5 (-4.5) is labeled on this number line representing temperature change, the absolute value of the point labeled in the image means that: B. the temperature equals 4.5 degrees.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

In conclusion, the absolute value of a number is always positive and it can be used for describing the distance of a number from zero (0) on the number line, without taking its direction into consideration.

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Answer:

-2x² - 10xy + 2y²

Step-by-step explanation:

4x² - 9xy - 4y² - 6x² - xy + 6y² =

= 4x² - 6x² - 9xy - xy - 4y² + 6y²

= -2x² - 10xy + 2y²

[tex]P(x)=100_{e}({4}/{ln4} )x[/tex]

what is bacteria?

Microbes known as bacteria have simpler cell structures than many other types of creatures. One DNA loop serves as their command centre and houses all of their genetic data. Instead of a nucleus, some bacteria contain an additional ring of genetic material called a plasmid. Genes that offer the bacterium a competitive edge over other bacteria are frequently found on the plasmid.

There are a few options for doing this. A set of equations may be used.

Use the equation P = a*bx, where x is the number of hours and P represents the population of bacteria.

A and B are two unknowns.

We will enter form points to solve (x, P)

A point equals (2, 200). (after 2 hours, the population is 200)

Consequently, a formula is 200 = [tex]a*b^{2}[/tex]

Second, there is (6, 800).

A second equation is thus 800 = [tex]a*b^{6}[/tex]

We'll repeat the equations in writing:

800 = [tex]a*b^{6}[/tex]

200 = [tex]a*b^{2}[/tex]

These two equations can be divided.

When we divide the equations, we obtain 800/200 = 4 on the left.

When we split on the right side,the equations, we get [tex]a*b6 / (a*b2) = b4[/tex]

Therefore, [tex]4 = b^{4}[/tex]

Solve for b:

b = [tex]\sqrt[4]{4}[/tex]

Next, solve for a, by plugging in b into the second equation

[tex]200 = a * (\sqrt[4]{4})^{2} = a * \sqrt{4} = a * 2[/tex]

Therefore, dividing both sides by 2, gives us that a = 100

Lastly, write out the equation with the known values of a and b.

[tex]P(x)=100_{e}({4}/{ln4} )x[/tex]

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Answer:215.768

Step-by-step explanation:

Answer: about 216 liters

Step-by-step explanation:

Answer: The temperature was -21.75 after 5.5 hours passed.

Step-by-step explanation:

-2.5 starting degrees,

-3.5*5.5 = -19.25

-19.25 + the original -2.5 = -21.75