Which new angle is created by extending one side of a triangle?

a remote interior angle
an adjacent interior angle
an exterior angle
a complementary angle

Answer: 1) m=12/7   2) y=(12/7)x

Step-by-step explanation:

C(0,0)   D(7,12)

[tex]\displaystyle\\1)\ Slope=m=\frac{rise}{run} =\frac{y_D-y_C}{x_D-x_C} \\\\m=\frac{12-0}{7-0} \\\\m=\frac{12}{7}[/tex]

[tex]\displaystyle\\2)\ y=mx+b\ \ \ \ m=\frac{12}{7} \ \ \ \ C(0,0)\\0=\frac{12}{7} *0+b\\\\0=0+b\\\\0=b\\\\Hence,\\\\y=\frac{12}{7} x+0\\\\y=\frac{12}{7}x[/tex]

Answer:

No. They include 2 different elements that are unrelated, being x and y, making them unlike terms.

Answer:no

Step-by-step explanation:in order for them to be like terms they would have to have the same variables

The expression in scientific notation is given as follows:

3.5 x 10³.

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

For this problem, the expression is given by:

[tex]\frac{5 \times 10^2 \times 4.2 \times 10^4}{6 \times 10^3}[/tex]

When two factors of a multiplication have the same base and different exponent, we keep the base and add the exponents, hence:

[tex]10^2 \times 10^4 = 10^6[/tex]

5 x 4.2 = 21, hence the expression is:

[tex]\frac{5 \times 10^2 \times 4.2 \times 10^4}{6 \times 10^3} = \frac{21 \times 10^6}{6 \times 10^3}[/tex]

When we divide two terms with the same base and different exponents, we keep the base and subtract the exponents, hence:

[tex]\frac{21 \times 10^6}{6 \times 10^3} = 3.5 \times 10^3[/tex]

Which is the simplified expression.

More can be learned about scientific notation at https://brainly.com/question/16394306

#SPJ1

Answer:

1400x

Step-by-step explanation:

10^3 in scientific notation means to move the decimal 3 places to the right.

Answer:212

Step-by-step explanation: 36 plus 36 40 plus 40 29 plus 29 19 plus ten then add the sums then u get 212

The value of the underlined digit 2.439 , 1.987 ,  6.175 , and 0.618 is equal to tenth, thousandth, Ones and tenth.

As given in the question,

Given number = 2.439 , 1.987 ,  6.175 , and 0.618

Value of underlined digit :

2.439 = Tenth or 4 / 10

1.987 = Thousandth or 7/1000

6.175 = Ones or 6

0.618 = Hundredth or 1/100

Therefore, the value of the underlined digit 2.439 , 1.987 ,  6.175 , and 0.618 is equal to tenth, thousandth, Ones and tenth.

The complete question is :

How do i write the value of this underlined digit 2.439 , 1.987 ,  6.175 , and 0.618 ?

Learn more about digit here

brainly.com/question/10913044

#SPJ4

We need to know about cube-root function and reflection to solve this problem. The function is f(x)=[tex]-\sqrt[3]{x-4}[/tex]

A cube-root function is the inverse of a cubic function, a cubic function can be given by f(x)=[tex]x^{3}[/tex], the inverse of this is a cube-root function which can be given by f(x)=[tex]\sqrt[3]{x}[/tex] with vertex at (0,0). The general formula for a cube root function is given be

f(x)=a[tex]\sqrt[3]{x-h} +k[/tex] where a is the measure of how horizontally compressed the graph is and (h,k) is the vertex of the graph. In the question we have to find a cube root function which has been reflected about the y-axis, which means our a will be negative. The vertex of the graph is at (4,0) so (h,k) is (4,0). Thus the cube root function we need is

f(x)=-[tex]\sqrt[3]{x-4}[/tex]

Therefore we found the cube root function that has been reflected about y-axis and the vertex at (4,0) to be  f(x)=[tex]-\sqrt[3]{x-4}[/tex]

Learn more about cube root function here:

https://brainly.com/question/15818396

#SPJ9

Answer:

The function is odd.

Step-by-step explanation:

A function is always odd when f(−x) = −f(x). In this case, that rule applies.

[tex]-f(x)=-(x^3+5/x)\\-f(x)=-x^3-5/x\\-x^3-5/x=-x^3-5/x = odd[/tex]

Answer:Yes,these are pythagorean triplets because you can divide all three by the same number which is 4.

Step-by-step explanation:12 divided by 4 is 3. 16 divided by 4 is 4. And 20 divided by 4 is 5.

Answer:

Yes

Step-by-step explanation:

They all have a scale factor of 4 and 3,4,5 are also Pythagorean triplets

Answer:

C= [tex]\frac{AD}{B}[/tex]

Step-by-step explanation:

the answer is c because I said it c and the way you get the answer is by dividing the equality of the fraction

1. A. 2/3 of the volume of the rectangular prism crate = 5.7 ft³

B. Amount of space the dog will occupy is: 2.55 ft³. Josiah should buy the medium crate.

2. 21.05 ft²

The volume of a rectangular prism = (length)(width)(height).

1. Part A:

Length of the rectangular prism crate = 2.5 ft

Width = 1.7 ft

Height = 2 ft

Volume of the rectangular prism crate = (2.5)(1.7)(2)

Volume of the rectangular prism crate = 8.5 ft³

2/3 of the volume of the rectangular prism crate = 2/3(8.5) = 5.7 ft³

Part B:

Amount of space the dog will occupy = volume = (length)(width)(height).

Length = 2 ft

Height = 1 2/3 = 1.7 ft

Width = 3/4 = 0.75 ft

Amount of space the dog will occupy = volume = (2)(0.75)(1.7)

Amount of space the dog will occupy = volume = 2.55 ft³

The space the dog will occupy is less than 2/3 of the space of the crate, therefore, Josiah should buy the medium crate.

2. Amount of fabric needed to cover the crate = surface area of rectangular prism - (lw) = 2·(1.7·2.5+2·2.5+2·1.7) - (2.5)(1.7)

= 25.3 - 4.25

= 21.05 ft²

Learn more about rectangular prism on:

https://brainly.com/question/1015291

#SPJ1

Answer:

Let x = the cost of a movie

Let y = the cost of a game

Using these variables, we can set up equations.

3x + 5y = 42 eq1

9x + 7y = 72 eq2

We have here a system of equations, where we have two or more equations with two or more different variables. We use the elimination method to solve for the variables.

Multiply eq1 by 3. Keep eq2.

9x + 15y = 126 eq1

9x + 7y = 72 eq2

Subtract eq2 from eq1 to eliminate the x terms.

8y = 54

y = 6.75

This rental cost of one video game is $6.7

Substitute the value of y into eq1 to solve for x. This will give you the rental cost of one movie.

Step-by-step explanation:

pa brainly po

The cost of movie is $4.5 and cost of video game is $5.75.

Two or more expressions with an Equal sign is called as Equation.

Let x be the cost of movie and y be the cost of video game

Calvin rents 3 movies and 2 video games and spends a total of $25.

3x+2y=25...(1)

Samantha rents 2 movies and 1 video game and spends a total of $14.75.

2x+y=14.75

y=14.75-2x..(2)

Substitute (2) in equation (1)

3x+2(14.75-2x)=25

3x+29.5 -4x=25

-x+29.5 = 25

Subtract 29.5 from both sides

-x=25-29.5

x=4.5

Now let us plug in x value in equation (2)

y=14.75-2(4.5)

y=5.75

Hence, the cost of movie is $4.5 and cost of video game is $5.75.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ2

The system of inequalities is y ≤ 12 - x and y ≥ 8 - (3/5)x and the point (2 , 8) satisfies both inequalities.

A mathematical statement known as an inequality contrasts two algebraic expressions using the greater-than (>), less-than (<), and other inequality symbols. A compound inequality is a pair of inequality related by and or or or. The properties of inequalities will be used in this course to solve linear and compound inequalities in one variable. Absolute-value equations and inequalities continue to be studied.

While there are many similarities between solving equations and solving inequalities, we must also take the direction of the inequality into consideration.

Now let us form the two inequalities:

If x is the number of hours she worked babysitting and y is the number of hours she spent lifeguarding then

x + y ≤ 12

or, y ≤ 12 - x

Now if she makes 12 dollars babysitting and 20 dollars lifeguarding then

12 x + 20 y ≥ 160

or , 20y ≥ 160 - 12x

or , y ≥ 8 - 3/5x

Let us solve the inequalities graphically.

From the graph we can see that

the point (2 , 8) satisfies both inequalities.

So if Naomi works 2 hours babysitting and 8 hours lifeguarding she can satisfy both conditions.

To learn more about inequality visit:

https://brainly.com/question/20383699

#SPJ1

The solution for the system of equations 3x + 6y = 6 and 2x + 2y = 6 is

B) There is one unique solution, (4, -1).

The solutions for a system of equation is the intersecting points between them

We know that system of equations has an infinite number of solutions when they coincide with each other as every point of a line falls into another line.

Systems of equations have a unique solution when they intersect each other and that intersecting point is the solution.

The system of equations has no solution when they are parallel to each other.

So, now we'll graph this system of equations and observe where they lie in XY coordinate.

Observing the graphs of both of these equations we can conclude that they have a unique solution (4,-1).

We can also solve these equations by multiplying equation(ii) by 3 and subtracting it from equation(i) and obtaining the values of (x,y).

learn more about the system of equations here :

https://brainly.com/question/24065247

#SPJ1

Answer:i have same question

Step-by-step explanation:

Percent of residents have at least one traffic violation with 80% held a valid driver’s license,10% has at least one traffic violation and 30% does not have valid license is 14%.

As given,

A=Person has a driver license

A'=Person does not have a driver license

P(A)=0.80

P(A')=0.20

For A, 10% has at least one traffic violation

For A', 30% had at least one traffic violation.

Probability with at least one traffic violation

=Probability of( A and one traffic violation +A' and one traffic violation)

=0.80(0.10)+0.20(0.30)

=0.08+0.06

=0.14

=14%

Therefore, percent of the residents with at least one traffic violation is 14%.

Learn more about percent here

brainly.com/question/14699403

#SPJ1

When a coin will be flipped three times, and the number of heads recorded. The reason that, this is a binomial experiment is "there are a set number of trials, n. The coin would be flipped three times, a fixed number of times."

A binomial experiment is one that has a fixed number of independent trials only with two outcomes. For instance, the outcome could be a yes or no response. When you toss a coin, you might wonder, "Will I get heads?" The response is either yes or even no.

That is the basic idea, but in order to label an experiment a binomial experiment, the following rules must be followed.

To know more about the binomial experiment, here

https://brainly.com/question/15557838

#SPJ4

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

First Question:

  [tex]\text{Copy the equation}\\\hookrightarrow \frac{xy^4}{x^3y^2} \\\\\text{Exponents with common bases when dividing from each other}\\\hookrightarrow \text{the power of the denominator can be subtracted from the power of the numerator}\\ \text{ --- } \dfrac{xy^4}{x^3y^2} =\dfrac{x}{x^3}*\dfrac{y^4}{y^2}=x^{1-3}*y^{4-2}=x^{-2}*y^{2} =\dfrac{y^2}{x^2}[/tex]

Second Question:

[tex]\hookrightarrow\text{simply start from the most inner calculation before going out}[/tex]

  [tex]\text{---}-(-x)^3= -1 *(-1 * x)^3=-1*(-1)^3*x^3=-1*-1*x^3=x^3[/tex]

Answer:

Hope that helps!

#LearnwithBrainly

Three answers all equivalent:

5.476190...

115/21

5 10/21

pick whichever is applicable, they are all the same

Answer:

Answer:9

Step-by-step explanation:

9

Answer:

x = -7

Step-by-step explanation:

2(x-4) = -22

2*x + 2*-4 = -22

2x - 8 = -22

2x = -22 + 8

2x = -14

x = -14/2

x = -7

Check:

2(-7-4) = -22

2*-11 = -22

Answer:

The last option

y = ⅓x-3

Step-by-step explanation:

Slope-intercept form :

y=mx+c

[tex]x - 3y = 9 \\ - 3y = - x + 9 \\ \frac{ - 3y}{ - 3} = \frac{ - x}{ - 3} + \frac{9}{ - 3} [/tex]

[tex]y = \frac{1}{3} x - 3[/tex]

Answer:

Hello,

Step-by-step explanation:

[tex]u_2=u_1*r\\u_3=u_1*r^2\\u_4=u_1*r^3\\\\\dfrac{u_4}{u_3} =r=\dfrac{-56}{28} =\boxed{-2}\\\\u_1=\dfrac{u_3}{r^2} =\dfrac{28}{(-2)^2} =\dfrac{28}{4}=\boxed {7}\\\\\\\displaystyle\ s=\sum_{i=1}^6\ u_i\\\\=u_1*\sum_{i=1}^6\ r^{i-1}\\\\=7*\dfrac{(-2)^6-1}{-2-1} \\\\=-7*\dfrac{65}{3} \\\\\\\boxed{s=-\dfrac{455}{3} }\\[/tex]

Answer:

x = 3

Step-by-step explanation:

Separate | 2 + x | = | x - 8 | into 2 possibilities

2 + x = x - 8

2 + x = -x + 8 (right side's signs are swapped)

Solve the equations:

Top equation results in no solution as the x's cancel out.

2 + x = -x + 8

2x = 6

x = 3

| 2 + 3 | = | 3 - 8 |

| 5 | = | -5 |

5 = 5

This is the correct solution.

Let's solve the problem,

→ |2 + x| = |x - 8|

→ 2 + x = -(x - 8)

→ 2 + x = -x + 8

→ x + x = 8 - 2

→ x = 6/2 = 3

Hence, the value is 3.

Answer:

Step-by-step explanation:

Answer:

M = n(y/x)

Step-by-step explanation:

M/n = y/x

Multiply both sides by N to cancel it out.

M = n(y/x)

The table which represents the function g(x) is: answer option A.

x                g(x)

1                  -3

2                  3

3                  9

In Mathematics, a function can be defined as a mathematical expression which can be used to define and show the relationship that exist between two or more variables in a data set.

This ultimately implies that, a function typically shows the relationship between input values and output values of a data set, as well as showing how the elements in a table are paired (mapped).

When x = 1, the function f(x) is given by:

f(x) = 2x − 3

f(1) = 2(1) − 3

f(1) = 2 - 3

f(1) = -1.

Therefore, the function g(x) = f(3x) = 3 × -1 = -3.

When x = 2, the function f(x) is given by:

f(x) = 2x − 3

f(2) = 2(2) − 3

f(2) = 4 - 3

f(2) = 1.

Therefore, the function g(x) = f(3x) = 3 × 1 = 3.

When x = 3, the function f(x) is given by:

f(x) = 2x − 3

f(3) = 2(3) − 3

f(3) = 6 - 3

f(3) = 3.

Therefore, the function g(x) = f(3x) = 3 × 3 = 9.

In conclusion, the table which represents the function g(x) is as follows:

x                g(x)

1                  -3

2                  3

3                  9

Read more on function here: https://brainly.com/question/12789432

#SPJ1

Answer: A

Step-by-step explanation:

rxl ontop

The graph of the combined inequality, 1 < y + 7x ≤ 12, is shown below. The correct graph is graph b.

From the question, we are to graph the given inequality

The given inequality is

1 < y + 7x ≤ 12

First, we will separate the inequality

1 < y + 7x and y + 7x ≤ 12

1 < y + 7x

We will determine two points on the line

1 = y + 7x

When x = 0

1 = y + 7(0)

1 = y

y = 1

(0, 1)

When y = 8

1 = y + 7x

1 = 8 + 7x

1 -8 = 7x

-7 = 7x

x = -7/7

x = -1

(-1, 8)

We can use these two points to plot the line of 1 < y + 7x

Also,

We will determine two points on line y + 7x ≤ 12

y + 7x = 12

When x = 0

y + 7(0) = 12

y + 0 = 12

y = 12

(0, 12)

When y = 5

5 + 7x = 12

7x = 12 - 5

7x = 7

x = 7/7

x = 1

(1, 5)

We can use these two points to plot the line of y + 7x ≤ 12

The graph of the combined inequality, 1 < y + 7x ≤ 12, is shown below. The correct graph is graph b.

Learn more on Graphs of Inequality here: https://brainly.com/question/17136458

#SPJ1

Answer: 401

Step-by-step explanation:

-177 + 578 = 401

Answer:

see explanation

Step-by-step explanation:

the 3 consecutive even integers are x , x + 2 and x + 4 , then their sum is

x + x + 2 + x + 4 = 72 , that is

3x + 6 = 72 ( subtract 6 from both sides )

3x = 66 ( divide both sides by 3 )

x = 22

x + 2 = 22 + 2 = 24

x + 4 = 22 + 4 = 26

the 3 consecutive even integers are 22, 24 , 26