if f(x) = 2x - 4 find f(a^2)

The angle that is same side exterior angle to ∠ABC is ∠EFH.

When parallel line are cut by a transversal line, angle relationships are formed such as corresponding angles, vertically opposite angles, alternate angles, same interior angles, etc.

AD and EG are parallel to each other.

CH is a transversal line to the parallel lines.

Therefore, let's find the angle that has the same relationship as same side exterior angles as angle ABC.

Two angles that are exterior to the parallel lines and on the same side of the transversal line are called same-side exterior angles.

Same side exterior angles are supplementary.

Therefore,

∠ABC and ∠EFH are same side exterior angles.

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5. Based on arc and central angle relationship, m∠BCD is: B. 108°.

6. The length of arc PQ is: H. 3.14 m

7. Length of CF is: A. 6 cm.

To find the length of an arc, the formula to use is:

Arc length = ∅/360 × 2πr

5. Measure of arc AB = 72°

Measure of arc BD = 180 - measure of arc AB

Measure of arc BD = 180 - 72

Measure of arc BD = 108°

Measure of angle BCD = measure of arc BD [central angle theorem]

Measure of angle BCD = 108°

The answer is: B. 108°

6. ∅ = 60°

r = 3 m

Arc length = 60/360 × 2 × π × 3

Arc length = 3.14 m

The answer is: H. 3.14 m

7. Since the distance between the two chords, AB and CD are equal, therefore, AB = CD.

AB = CD = 12 cm

CF = 1/2(CD)

CF = 1/2(12)

CF = 6 cm.

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Answer:

(- 8, 0 )

Step-by-step explanation:

under a reflection in the line y = x

a point (x, y ) → (y, x ) , then

(0, - 8 ) → (- 8, 0 )

The solution to the inequality 6 + t ≤ 13 is given as follows:

t ≤ 7.

An inequality is solved similarly to an equality, isolating the variable of which the solution we want to find.

The difference, of the inequality compared to an equality, is that the solution contains an infinity number of values, instead of a finite number of values. This is because the solution of an inequality is composed by a range of values in one of the infinity number sets.

For this problem, the inequality is given as follows:

6 + t ≤ 13

Hence the solution for variable t is found isolating it as follows:

t ≤ 13 - 6 (moving every term that is not the variable to the opposite side)

t ≤ 7.

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The mean and standard deviation of this sampling distribution is 1 cm and 0.033 cm, respectively.

The sample mean is the arithmetic mean of all the samples of processor chips. The mean of the sample group is known as the sample mean.

Let X denote the multiple random samples of 35 processor chips and each of which represents the size of the processor chips.

Let 'x' be the sample mean of all the random samples X which represents the size of the processor chips.

The mean of the size of processor chips= μ =1 cm

The mean of the sampling distribution x of sample means is equal to the mean of the sizes of the processor chips μ

Mean of sampling distribution x  = mean of the size of the processor chips μ

⇒ x = μ

   x = 1 cm

The mean of this sampling distribution is 1 cm.

The standard deviation is the amount of variation among the set of values. It is the measure of the dispersion of values in the data set.

The size of the processor chips has a standard deviation of 0.2 cm so σ = 0.2 cm

Let 'x' be the standard deviation of random samples X of the size of processor chips.

Number of random multiple samples of processor chips, n =35

The standard deviation of this sampling distribution can be calculated by using the below formula;

x = σ/[tex]\sqrt{n}[/tex]

Substituting the value of \sigma as "0.2" cm and the value of "n" as 35 in the above formula, we get;

x = 0.2/√35

x = 0.033 cm

The standard deviation of this sampling distribution is 0.033 cm.

The mean of this sampling distribution is 1cm and the standard deviation of this sampling distribution is 0.033 cm.

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The probability of the next flip result in a trail is 0.5.

Given that,

If you flip a coin 100 times and receive 80 heads and 20 tails.

We have to find what is the probability that the upcoming flip will result in a tail based on these findings.

Probability refers to potential. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.

Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty.

One is the probability of every event in a sample space.

Next flip result is independent of the past results.

P(Next flip result is tail) = 1/2 = 0.5

Therefore, The probability of the next flip result in a trail is 0.5.

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The subtraction between the functions f(x) = 4 · x - 8 and g(x) = - 3 · x + 1 is equal to (f - g) (x) = 7 · x - 9.

Herein we find f(x) and g(x) defined as linear functions and we are asked to find the subtraction between two functions, which is defined below:

(f - g)(x) = f(x) - g(x)

If we know that f(x) = 4 · x - 8 and g(x) = - 3 · x + 1, then the result of the subtraction of the two functions is:

(f - g) (x) = f(x) - g(x)

(f - g) (x) = (4 · x - 8) - (- 3 · x + 1)

(f - g) (x) = 7 · x - 9

The subtraction between the two functions is (f - g) (x) = 7 · x - 9.

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If one leg is of length 5 inches then the lengths of the hypotenuse can be 2.113 inches or 4.5315 inches.

According to the question,

We have the following information:

A right triangle contains a 25° angle and length of one leg is 5 inches.

Now, the leg for which length is given can be opposite to given angle or adjacent to given angle. So, there are two possible for the length of hypotenuse (H).

Now, when it is opposite to the given angle:

Sin 25 = 5/H

H = Sin 25*5

H = 0.4226*5

H = 2.113 inches

Now, when it is adjacent to the given angle:

Cos 25 = 5/H

H = Cos 25*5

H = 0.9063*5

H = 4.5315 inches

Hence, if one leg is of length 5 inches then the lengths of the hypotenuse can be 2.113 inches or 4.5315 inches.

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Answer:

-7

Step-by-step explanation:

6/2=3

3+1= 4

2-5= -3

-3-4= -7

6/2+1= 4

2-5-4= -7

*Do what is in the parenthesis first!!*

Answer: [tex]g(2n)=4n^2 -8n[/tex]

Step-by-step explanation:

Substituting [tex]2n[/tex] for [tex]x[/tex],

[tex]g(2n)=(2n)^2 -4(2n)\\\\g(2n)=4n^2 -8n[/tex]

The equation of the line is y=3x+1 when the line is on the graph of the given picture.

Given that,

In the picture we have a graph.

We have to find the equation of the line.

We know that,

From the graph we can see the points,

(1,4) and (0,1)

We know that the equation of the line is y=mx +b

The y and x value are from the points and the m is the slope that is rise by run and b is the y intercept.

m is rise/run

m= 1-4/0-1

m=-3/-1

m=3

b is 4=3(1)+b

4=3+b

b=4-3

b=1

The equation of the line is y=3x+1

Therefore, The equation of the line is y=3x+1 when the line is on the graph of the given picture.

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The distance from the Sun to Mars is 3. 9 times farther

Ratio can be described as a mathematical comparison between two or more numbers or elements in relation to each other on the basis of their sizes or magnitudes.

It is however known to show how many times one number or elements contains another.

Based on the information given, we have;

To determine the ratio of their distances from the Sun, we have;

Distance from the Sun to Mars /Distance from the Sun to Mercury

Substitute the values

2.28×10^8/5.79×10^7

Divide through

3. 9 times

Hence, the distance is 3. 9 times farther.

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The coordinates of point N are (8.66, 21)

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The coordinates of a point dividing a straight line joining two coordinates in the ratio m : n is given by -

x =  [tex]$\frac{mx_2+nx_1}{m+n}[/tex]

y = [tex]$\frac{my_2+ny_1}{m+n}[/tex]

We have LMN as a straight line such that the coordinates of L are (-3,1) , coordinates of M are (4,9) and LM : MN is 2 : 3.

Assume the coordinates of point N are (a, b).

We can write -

9 =  (2b + 3)/5

4 = (-6 + 3a)/5

2b + 3 = 45

b = 21

3a - 6 = 20

3a = 26

a = 8.66

Therefore, the coordinates of point N are (8.66, 21)

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The blanks are -2 and 0.5 respectively, by solving the expression (8 - 2x) *(-0.25x)

What does the term Algebraic Expression means?

In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.

Solution:

Given the expression, we need to solve it by using the properties of basic multiplication.

= (8 - 2x)*(-0.25x)

= (8*(-0.25x)) + (-2x * (-0.25x))

= -2x + 0.5[tex]x^{2}[/tex]

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The factors of the number 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100. If you add them up, you will get the total of 217

The solution for k in the equation given as 20+ 7k = 8k+ 16 is 4

From the question, the algebraic expression is given as

20+ 7k = 8k+ 16

There is no constant to multiply or divide in the expression

So, the equation remains the same

20+ 7k = 8k+ 16

Collect the like term in the above equation

This gives

8k - 7k = 20 - 16

Evaluate the like term in the above equation

So, we have the following representation

k = 4

The above equation cannot be solved further

Hence, the solution is k = 4

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Answer:

Step-by-step explanation:

Isabella,  do you know how to do the "elementary row operations"?

Also, when did they begin teaching  linear algebra in H.S.  :DDD  nice work getting there.

Gauss Jordan, just mean get your matrix in RREF  (Reduced Row Echelon Form)

I suggest using Matlab to do this.  it's got the  "RREF(x)  function to do this exact thing.  

Your teacher probably wants you to do this by hand.  thou, huh.  :/  

here is my Matlab code and the answer

clc

close all

clear

format compact

A=[3 -4 2;0 -1 7]

mymatx=rref(A)

A =

    3    -4     2

    0    -1     7

mymatx =

   1.0000         0   -8.6667

        0    1.0000   -7.0000

Yes, maybe it's totally cheating, but it seems fair nowadays to use technology that is commonly available.    :)

So answer A) looks right

Step-by-step explanation:

In a candy box, there are 3 times as many candies with nuts as candies without nuts. There are 12 candies in the box. How many candies with nuts are in the box?

let:

without nuts = x

with nuts = 3x

so:

x + 3x = 12

4x = 12

x = 3, so there are 3 candies without nuts.

Because there are three times more candies with nuts than without:

3 * 3 = 9 candies with nuts

Answer:

9 candies with nuts

Step-by-step explanation:

Suppose the number of candies is x

there three times as many candies with nuts as candies without nuts, so 3x

there are 12 candies in total

3x+x=12

4x=12

x=3

3x=9

Answer:

-30  I don't see -30 as an answer option.  Please check the problem.

Step-by-step explanation:

c²a + 2a÷b

c²a + 2a/b   Enter values for a, b and c for a = -3, b= 2 and c = 3.

(3)²(-3) + 2(-3)/(2)

(9)*(-3) + (-6)/(2)

-27 + (-3)

-27 - 3 = - 30

Answer:

Step-by-step explanation:

3p. = 2m - 5q

-2m. = -3p - 5q

Divide through by -2

m. = (3p + 5q) \2

The equation can be rearranged and expressed in terms of p and q is m = (3p+5q)/2.

Given equation 3p = 2m - 5q

3p + 5q = 2m

(3p + 5q) / 2 =m

Hence, m = (3p+5q) / 2  

To express the equation in terms of p and q we need to put all the p and q terms to one side of the equation and m terms to another side of the equation. It can be easily seen that 3p is already on one side and we just need to bring a q term to this side which can be done by shifting 5q from the right-hand side to left-hand side. The equation is now 3p+5q. Now to get the equation in terms of m we need to divide the whole equation by 2 which will give m = (3p+5q) / 2.

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Answer:

No

Step-by-step explanation:

The sum of the squares of the lengths of the two shorter sides is [tex]10^2+12^2=244[/tex].

The square of the length of the largest side is [tex]14^2=196[/tex].

Because these two values are not equal, the side lengths do not satisfy the Pythagorean theorem. Therefore, the triangle is not a right triangle.

Answer: 0.0099

Step-by-step explanation:

Answer: 27/31 is the answer

Step-by-step explanation:

31/27 x 27/31 = 1 because 27/31 is the recprical

Answer:x = 31/27 = 1.148 

Step-by-step explanation:

Based on the solution set S:{4}, the false equation is 3m + 7 = 14, because the solution of the equation is not 4

The first equation is

3t = 12

t = 12/3

t = 4

The solution is {4}

The second equation is

3m + 7 = 14

3m = 14 - 7

3m = 7

m = 7/3

The solution is not {4}

The third equation is

4(4c + 1) = 68

4c + 1 = 68/4

4c + 1 = 17

4c = 17-1

4c = 16

c = 16/4

c = 4

The solution is {4}

The fourth equation is

9 = 5p - 11

5p = 9 + 11

5p = 20

p = 20/5

p = 4

The solution is {4}

Hence, Based on the solution set S:{4}, the false equation is 3m + 7 = 14, because the solution of the equation is not 4

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Answer:

23 and 24

Step-by-step explanation:

let the 2 consecutive numbers be n and n + 1 , then

n² + (n + 1)² = 1105

n² + n² + 2n + 1 = 1105 ( subtract 1105 from both sides )

2n² + 2n - 1104 = 0 ( divide through by 2 )

n² + n - 552 = 0 ← in standard form

(n + 24)(n - 23) = 0 ← in factored form

equate each factor to zero and solve for n

n + 24 = 0 ⇒ n = - 24

n - 23 = 0 ⇒ n = 23

However, n > 0 , then n = 23 and n+ 1 = 23 + 1 = 24

the numbers are 23 and 24

The length of the road in the simplest radial form is 10[tex]\sqrt{29}[/tex].

Here a rectangle of dimensions is 20m by 50m. So the length of 50m and the breadth is 20m

As the road is diagonal of the rectangle.

So we have to find the length of the diagonal of the rectangle.

Formula to find the diagonal of rectangle:

Diagonal = [tex]\sqrt{l^{2} + b^{2} }[/tex]

length (l) = 50m

Breadth(b) = 20m

Diagonal = [tex]\sqrt{50^{2} + 20^{2} }[/tex]

               = [tex]\sqrt{2500 + 400}[/tex]

               = √2900

              = 10√29

Therefore the length of the road is 10√29.

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Both the pairs of the points are linear.

Here i made the plot for the points and both the pairs of the points shows that the it follows a straight path which means it will be linear i nature.

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