Math problem please help

Step-by-step explanation:

Two interior opposite angles of a triangle are equal to the exterior angel

[tex]60 + 60 = 2x - 80 \\ 120 = 2x - 80 \\ 2x = 120 + 80 \\ 2x = 200 \\ x = \frac{200}{2} \\ x = 100[/tex]

So, the correct simplification for the expression (3x^3 y^4 z^4) (2x^3 y^4 z^2) is option d: 6x^6 y^8 z^6.

What is simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

The given equation is -

(3x^3 y^4 z^4) (2x^3 y^4 z^2)

On simplification -

=[3·2(x^3+3)(y^4+4)(z^4+2)]

=6x^6y^8z^6

Therefore, the value obtained is 6x^6y^8z^6.

To learn more about simplification from the given link

https://brainly.com/question/28780542

#SPJ1

Infinite series, the total of an infinite number of numbers connected in a specific method and listed in a specific order.

We get,

a)  [tex]$\sum_{n=0}^{\infty}$[/tex]

Infinity

b)  [tex]$\sum_{n=1}^{\infty}\left(\frac{4}{2^n}\right)$[/tex]

[tex]\sum_{n=1}^{\infty} \frac{4}{2^n}[/tex]

[tex]& =4 \cdot \sum_{n=1}^{\infty} \frac{1}{2^n} \\[/tex]

[tex]& \sum_{n=k}^{\infty}\left(a_n\right)=\sum_{n=0}^{\infty}\left(a_n\right)-a_0-a_1- \\[/tex]

[tex]& =4\left(\sum_{n=0}^{\infty} \frac{1}{2^n}-\frac{1}{2^0}\right)[/tex]

[tex]& \sum_{n=0}^{\infty} \frac{1}{2^n}=2 \\[/tex]

[tex]& =4\left(2-\frac{1}{2^0}\right)[/tex]

Then we get,

=4

c) [tex]$\sum_{n=1}^{\infty}\left(\frac{7}{10^n}\right)$[/tex]

[tex]$\sum_{n=1}^{\infty} \frac{7}{10^n}[/tex]

[tex]& =7 \cdot \sum_{n=1}^{\infty} \frac{1}{10^n} \\[/tex]

[tex]& \sum_{n=k}^{\infty}\left(a_n\right)=\sum_{n=0}^{\infty}\left(a_n\right)-a_0-a_1- \\[/tex]

[tex]& =7\left(\sum_{n=0}^{\infty} \frac{1}{10^n}-\frac{1}{10^0}\right)[/tex]

[tex]& \sum_{n=0}^{\infty} \frac{1}{10^n}=\frac{10}{9} \\[/tex]

[tex]& =7\left(\frac{10}{9}-\frac{1}{10^0}\right)[/tex]

Simplify

[tex]$7\left(\frac{10}{9}-\frac{1}{10^0}\right): \quad \frac{7}{9}$[/tex]

= 7/9

Therefore,

a) infinity, b) =4, and c) = 7/9

To learn more about infinite series, refer to:

https://brainly.com/question/17082455

#SPJ1

The amount that Victoria will have in one year if she invests $20 at 7.2% simple interest is $21.44.

The simple interest system does not compound the interest.

This statement implies that interest is not computed on the accumulated interest.  Periodically, the interest is computed on the principal, using the following simple interest formula:

Simple interest = Principal x Rate x Time

Simple interest rate = 7.2% per year

Investment = $20

Investment period = 1 year

Amount in account after 1 year = P + (P x R x T)

= $20 + ($20 x 7.2% x 1)

= $20 + $1.44

= $21.44

Learn more about the simple interest system at https://brainly.com/question/25793394

#SPJ1

Answer:If you make ₱ 58,000 you will be taxed ₱ 4,711. That means that your net pay will be ₱ 53,289 per year, or ₱ 4,441 per month.

The solution of the given equation 3x²+ 5x +2= 0 is given by :

option c. x = -2 / 3 or x = -1.

As given in the question,

Given equation is equal to :

3x²+ 5x +2= 0

Solve the given equation by splitting the middle term of the quadratic equation we have,

3x²+ 5x +2= 0

⇒ 3x²+ 3x + 2x + 2 = 0

⇒ 3x ( x + 1 ) + 2 ( x + 1 ) = 0

⇒ ( 3x + 2 ) ( x + 1 ) = 0

⇒ ( 3x + 2 ) = 0 or ( x + 1 ) = 0

⇒ x = -2 / 3 or x = -1

From the given options :

option c. x = -2 / 3 or x = -1 is the solution.

Therefore, the solution of the given equation 3x²+ 5x +2= 0 is equal to :

option c. x = -2 / 3 or x = -1 .

The above question is incomplete, the complete question is:

Which of the following is a solution of the equation 3x²+ 5x +2= 0?

a. x = 2/3 or x = 1

b. x = -2/3 or x = 1

c. x = -2/3 or x = -1

d. x = 2/3 or x = -1

Learn more about equation here

brainly.com/question/29538993

#SPJ4

The equation and diameter CD of the parabola are x=1/10 y^2and 2√110

In this question we have four case of parabolas with vertical axes of reference, whose standard formula is:

a(x – h)2 + k

Where:(h, k) - The vertex of the parabola.

a - Least distance between the vertex and the focus of the parabola.

Please notice that p < 0 when the directrix is above the focus, otherwise p < 0. The vertex is the midpoint of line segment between the directrix and the focus.

Given;

Vertex is at origins (0,0) and latus rectum = 10 and the graph open right so a is positive and the equation is:

x=a (y-k)^2+h.

To write the equation we need to find a using the latus rectum equation.

We substitute the values.Then inverse place of a with 10

Latus rectum=|1/a|                

10=|1/a|                              

a=1/10

The equation:

x=a (y-k)^2+h                      

x=1/10(y-0)^2+0

x=1/10 y^2

-Assume the distance between C and the center is EC. If E is (11,0) and C is (11, y).

-EC=y

-The equation of the parabola is x=1/10 y^2

Now, Substitute the value of C coordinate, which

x=1/10 y^2                          

Substitute the value of C coordinate, which is (11, y).

11×10=1/(10×10) y^2    

√(y^2 )=√110                

y=EC=√110

Because the distance of EC = ED

CD=EC×2                                  

CD=√110×2

CD=2√110

Therefore, the equation of parabola and CD will be x=1/10 y^2 and 2√110

To learn more on parabolas:

brainly.com/question/4074088

#SPJ1

Answer:

$37.50

Step-by-step explanation:

[tex]P+Prt=39.75 \\ \\ P+P(2)(0.03)=39.75 \\ \\ 1.06P=39.75 \\ \\ P=\$37.50[/tex]

The dimensions of the marble is thus 10∛18 cm when the volume is 18000 cm³.

An object's capacity is the amount of material it can hold inside, while an object's volume is the amount of space it takes up. Here, the cubic unit is used to measure either of the two.

Cubic units are used to measure volume. The quantity of cubes needed to completely fill any given figure, such as blocks in a box, is its volume.

As there is no  definite shape is given we can assume that the shape is cube.

Volume of cube = a³

given the volume 18000cm³

dimensions of the marble,

a × a × a = 18000

a³ = 18000

a = ∛18000

a = 10∛18

a = 26.21

Hence, the dimensions of the marble is thus 10∛18 cm when the volume is 18000 cm³.

Learn more about volume

https://brainly.com/question/28058531

#SPJ1

Answer: 1. Given

2. Combine like terms

3. Division

Answer: 343

Step-by-step explanation:

7 to the 3rd power

⇒7³

⇒7 × 7 × 7

⇒343 ... answer

hope that helps...

Answer:

Step-by-step explanation:

what 1\3 of a full rotation?

so

360° x 1/3 =

360° : 3 =

120°

Answer:

english

Step-by-step explanation:

because by guessing he could only get 1 right on english quiz

Joel should study for science, because the probability of getting all questions correct is 0.004 which is less than 0.016.

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

Given that Joe has to take two quizzes tomorrow.

He has only enough time to study for one of them, such that the science quiz has 7 true-or-false questions and

The English quiz has 4 multiple-choice questions.

We have to find the probability that he will get each question correct by guessing.

P(sciene)=0.5⁸

=0.0039

=0.004

P(English)= 0.25³

=0.0156

=0.016

As we know that 0.0156>0.0039

Hence, Joel should study for science, because the probability of getting all questions correct is 0.004 which is less than 0.016.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ5

It is not possible to construct a triangle with lengths of its sides 7cm, 10cm and 20cm because the sum of two sides of a triangle is greater than the third side.

Now, According to the question:

We know that:

What is triangle inequality rule?

The triangle inequality theorem states that for any given triangle, the sum of the two sides is always greater than the  third side. The Triangle is a polygon with three line segments as its boundaries.

Suppose A, B and C are three sides of a triangle, then by using triangle inequality rule, A + B > C then A, B and C make a triangle.

We have the sides:

7, 10 and 20

7 + 10 > 20

It is not possible to construct a triangle with lengths of its sides 7cm, 10cm and 20cm because the sum of two sides of a triangle is greater than the third side.

Learn more about Triangle at:

https://brainly.com/question/29083884

#SPJ4

Exterior angle of a regular n-sided polygon = 360°/n

Interior angle = 180° - 360°/n

So, with 360/n = (1/8)(180 - 360/n)

360/n = 180/8 - 360/(8n)

(360/n)*(9/8) = 180/8

2*9/n = 1

n = 18

Answer:5.3%

Step-by-step explanation:

we say 150/1 multiplied by 0.74/1=$111

then when we convert it back to pounds, we say 111/1 multiplied by 1.28/1 =142.08

150.00-142.08=7.92

7.92/150.00 multiplied by 100=5.28 to 1 decimal place is 5.3%

hope you understand

Answer:

100

Step-by-step explanation:

If we add 100 to 8000, get 8100 which is a perfect square: 90^2=8100

The percentage by which Ezra should multiply the dimension of the stage so that the dimensions of the image are 1/2 the size of the original blueprint is of:

50%.

The perimeter of the updated blueprint will be 50% of the perimeter of the original blueprint.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

For this problem, we want for the dimensions of the updated stage to be half the dimensions of the original stage, hence the scale factor of the dilation is given as follows:

k = 1/2.

The percentage equivalent to a fraction of 1/2 is of 50%, and the perimeter of the updated stage will be 1/2 the perimeter of the original stage, as both the perimeter and the side lengths have the same unit.

More can be learned about dilation at brainly.com/question/3457976

#SPJ1

Answer: A = P(1 + r/n)^(nt)

Where

A is the future value of the account

P is the initial principal amount, which is $9,100

r is the annual interest rate, which is 3%

n is the number of times the interest is compounded per year, which is 4 (quarters)

t is the number of years

So the function for the value of the account after t years is:

A = 9100(1 + 0.03/4)^(4t)

To determine the percentage of growth per year (APY), we can use the formula:

APY = ( (A/P)^(1/t) - 1) * n

In this case,

APY = ( (A/9100)^(1/t) - 1) * 4

APY represents the annual percentage yield, which is the interest rate taking compounding into account.

Please note that in the above expression the coefficient 0.03 is rounded to four decimal places as instructed.

Step-by-step explanation:

Answer: 3/4 is the simplest form

Step-by-step explanation:

your welcome <3

The interval over which f(x) = x² - x - 1 has an average rate of change of zero is (1/2, 1/2) as it is the only point at which the average rate of change is zero.

An average rate of change of zero means that the function is not increasing or decreasing over the interval in question. To find the interval over which f(x) has an average rate of change of zero, we need to find the critical points of the function. A critical point is a point at which the function's derivative is equal to zero or is undefined.

The derivative of f(x) = x² - x - 1 is:

f'(x) = 2x - 1

Setting f'(x) = 0, we get:

2x - 1 = 0

Solving for x, we get:

x = 1/2

Since this is the only critical point of the function, it is the point where the function has an average rate of change of zero. To determine the interval, we need to check the sign of the function's derivative on either side of the critical point.

f''(x) = 2 > 0

So x = 1/2 is the minima of the function

f'(x) = 2(1/2) - 1 = 0, at x = 1/2

so f'(x) > 0 for x < 1/2 and f'(x) < 0 for x > 1/2

Therefore the interval over which f(x) has an average rate of change of zero is (1/2, 1/2) or {1/2}.

To know more on average rate of change

https://brainly.com/question/18391206

#SPJ4

On solving the provided question, we can say that in this equation, we can solve by , 13/6=y/3 = > y = 39/6 = 6.5

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

in this equation,

we can solve by

13/6=y/3

y = 39/6 = 6.5

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer: 7.29

Step-by-step explanation: you divide the total cost which is 21.87 by 3 to get how much one pair of socks would be and that would be the unit price hope this helps

One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. Both sides of an equation will remain equal if we add the same amount to each side.

Addition:

Subtraction:

Multiplication:

Division:

To know more about the equations, here

https://brainly.com/question/2972832

#SPJ4

Answer:

1The degree and the leading coefficient of a polynomial function determine the end behavior of the graph. The leading coefficient is significant compared to the other coefficients in the function for the very large or very small numbers.

2An asymptote is a line that a graph approaches but never touches. That line can be vertical, horizontal, or even slanted, and graphs can have multiple types of asymptotes.

3constant of variation (k) is a ratio that represents the relationship between the independent variable (x) and the dependent variable (y). It can be found by dividing y by x, if both of those variables have known values.

Answer:

A'(2,1) => A(1,-2)

B'(-4,-2) => B(-2,4)

C'(-4,-6) => C(-6,4)

D'(-1,-3) => D(-3,1)

Step-by-step explanation:

:)

Answer:

2.83 cm

Step-by-step explanation:

The other leg is also 2cm

Pythagorean Theorem

  hypot ^2 = 2^2 + 2^2

  Hypot = sqrt 8 =~ 2.83 cm

Answer:

Step-by-step explanation:

an isosceles triangle where the two legs form a 90-degree angle is an isosceles right triangle. So, the hypotenuse of the triangle is 2√2

The shortest altitude is 60m when the base of the triangle is 169m.

Altitude, height, or depth are terms used to describe the distance between a point or object and a reference datum. This phrase is also occasionally used to describe depth.

Different reference points and definitions are employed depending on the context (e.g., aviation, geometry, geographical survey, sport, or atmospheric pressure). Altitude can also be used to describe a location's height above sea level, though elevation is more frequently preferred in geography.

Let,  a = 65cm , b = 156cm , and c = 169cm

The Area of a triangle = A = √s(s−a)(s−b)(s−c) s ( s − a ) ( s − b ) ( s − c )

s = (65cm + 156cm + 169cm)/2

s = 195cm

A = √195(195−65)(195−156)(195−169)

A = 5070 m²

Now we find the height of each case

[tex]$ \text h = 2\frac{\text A}{\text {base}}[/tex]

Substitute each base a, b and c

[tex]$ \text h = 2\frac{5070}{ 65}[/tex]

h = 156

height of triangle when base is 65m = 156m

[tex]$ \text h = 2\frac{5070}{ 156}[/tex]

h = 65

height of triangle when base is 156m = 65m

[tex]$ \text h = 2\frac{5070}{ 169}[/tex]

h = 60

height of triangle when base is 169m= 60m

Thus, the shortest altitude is 60m when the base of the triangle is 169m.

Learn more about altitude

https://brainly.com/question/28273457

#SPJ1

Answer:

Step-by-step explanation:

An absolute value inequality for 35 degrees C with the temperature able to vary as much as 1% is 34.65 ≤ x ≤ 35.35

The term inequality is defined as a relationship between two expressions or values that are not equal to each other

Here we have given that in your chemistry experiment, you are trying to keep the water temperature at 35°C.

And in the experiment to work properly, here the actual temperature can vary as much as 1%.

Here let us consider that x refers the actual temperature

Then it can be written as,

=> 1% of 35

When we simplify this one then we get,

=> 0.01(35) = 0.35

Here let us consider that the value is less that the simplified version, then it can be written as,

=> l x - 35 l ≤ 0.35    

Therefore, it can be rewritten as,

=> -0.35 ≤ x - 35 ≤ 0.35

When we simplify this by add the value 35, then we get the resulting inequality as,

=> 34.65 ≤ x ≤ 35.35

To know more about inequality here.

https://brainly.com/question/28823603

#SPJ4