2. State the domain and range of the relation shown. Is the relation a function?
Y=3x+1

Answer:

[tex]\boxed{\boxed{\bf x = 7}}[/tex]

Step-by-step explanation:

[tex] \sf \cfrac{4x - 4}{20} = \cfrac{30}{25} [/tex]

[tex]\sf 4x - 4 = \cfrac{(20)(30)}{25} [/tex]

[tex]\sf 4x - 4 = \cfrac{600}{25} [/tex]

[tex]\sf 4x - 4 = 24[/tex]

[tex]\sf 4x = 24 + 4[/tex]

[tex]\sf \cfrac{4x}{4} = \cfrac{28}{4} [/tex]

[tex]\sf x = 7[/tex]

The answer to the question is,

12 sin(∠B) = 2,           12 sin(∠C) = √3+√35

Sin rule is,

sin(A)/BC = sin(B)/AC = sin(C)/AB

sin(B) = (sin(A)×AC)/BC

sin(C) =(sin(B)×AB)/AC

To solve this question we apply sin rule,

Now we take

12 sin(∠B) =12 (sin(∠A)×AC)/BC

12 sin(∠B) =12 (sin(π/6)×(x/3x))          where ∠A =π/6 and AC=x, BC =3x

12 sin(∠B) =12 ((1/2)×(1/3))

12 sin(∠B) =12/6 = 2

12 sin(∠B) = 2

now we find the value of 12 sin(∠C)

12 sin(∠C) = 12(sin B)×(AB/BC)

now put the value of 12 sin(∠B) = 2

12 sin(∠C) = 2×(AB/BC)

12 sin(∠C) = (2/AC)×[AC×(cos(π/6))+BC×(cos B)]

12 sin(∠C) = 2×[cos(π/6)+(BC/AC)×(cos B)]

cos (π/6) = √3/2 and BC/AC =3

then

12 sin(∠C) = 2×[(√3/2)+3×(cos B)]

cos B= √1-sin²B

12 sin(∠C) = 2×[(√3/2)+3×√(1-sin²B)]

12 sin(∠B) = 2

sin B = 1/6

12 sin(∠C) = 2×[(√3/2)+3×√(1-(1/6)²]

12 sin(∠C) = 2×[(√3/2)+3×√1-(1/36)]

12 sin(∠C) = 2×[(√3/2)+3×√(36-1)/36]

12 sin(∠C) = 2×[(√3/2)+3×√(35/36)]

12 sin(∠C) = 2×[(√3/2)+(3/6)×√35]

12 sin(∠C) = 2×[(√3/2)+(1/2)×√35]

12 sin(∠C) = 2×[(1/2)(√3+√35)]

12 sin(∠C) = √3+√35

Hence the answer is,

12 sin(∠B) = 2,         12 sin(∠C) = √3+√35

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The inequality of the bridge's legal limit 100000x + 34000y ≤ 700000

The given parameters are:

Represent the 6-axle trucks with x and the y-axle trucks with y.

So, we have the following inequality

100000x + 34000y ≤ 700000

The number of 6-axle trucks at one time

Here, we assume that y = 0.

So, we have:

100000x ≤ 700000

Divide by 100000

x ≤ 7

Hence, the number of 6-axle trucks at one time is 7

The number of 2-axle trucks at one time

Here, we assume that x = 0.

So, we have:

34000x ≤ 700000

Divide by 34000

x ≤ 20.58

Round down

x ≤ 20

Hence, the number of 2-axle trucks at one time is 20

See attachment for the inequality of 100000x + 34000y ≤ 700000

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The length of x will be 4 cm if is the angle bisector of A.

A straight line that splits an angle in a triangle into two congruent angles is known as the angle bisector.

Given sides;

AB=12

AE=8

BD=6

DE=x

From the triangle angle bisector theorem;

[tex]\rm \frac{BD}{DE} = \frac{AB}{AE} \\\\ \frac{6}{x} =\frac{12}{8} \\\\ x=4[/tex]

Hence the length of x will be 4 cm.

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Hope this helped!

This is just what I drew. I believe the answer for B could be somewhat different than what I drew.

Have a nice day!

The inequality negative 3 and one-half greater-than negative 4.5 or -3.5 > -4.5 is true.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have inequalities given:

[tex]1.5 > 2\dfrac{1}{2}[/tex]

or

1.5 > 2.5  (false)

1/2 > 0.5

0.5 > 0.5 (false)

-2.5 > -1.5 (false)

[tex]-3 \dfrac{1}{2} > -4.5[/tex]

-3.5 > -4.5  (true)

Thus, the inequality negative 3 and one-half greater-than negative 4.5 or -3.5 > -4.5 is true.

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73 is a 46% increase of 50.

What is percentage ?

A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given amount.

Percentage is defined as a specific part or amount out of a hundred. It is a fraction with the denominator 100 and is denoted by the symbol "percent."

The percent increase formula is as follows:

Percent increase = [(new value - original value)/original value] * 100.

Number of car parking (original value)=50

Number of car parking(new value)=73

The Percentage increase =[(73-50)/50]*100

                                          = [(23)/50]*100  

                                          =.46*100

                                         =46%

73 is a 46% increase of 50.

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The exponential function is [tex]f(x) = 18(12)^{-x-4} + 2[/tex]

An exponential function is represented as:

y = b^x

Where b represents the base.

The base is given as:

b = 12

So, we have:

y = (12)^x

It is vertically compressed by a factor of 1/8.

So, we have:

y = 18(12)^x

When reflected across the y-axis, we have:

[tex]y = 18(12)^{-x}[/tex]

The horizontal asymptote is y = 2.

So, we have:

[tex]y = 18(12)^{-x} + 2[/tex]

It passes through the point (-3, 4).

So, we shift the function to the right by 4 units

[tex]y = 18(12)^{-x-4} + 2[/tex]

Express as a function

[tex]f(x) = 18(12)^{-x-4} + 2[/tex]

Hence, the exponential function is [tex]f(x) = 18(12)^{-x-4} + 2[/tex]

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Answer:

y = 3x + a (a > 0) - above the original line

y = 3x + b (b < 0) - below the original line

Step-by-step explanation:

Pick any number you want for a or b, as long as the number meets the condition I wrote down.

Answer:

y=3x+1 and y=3x-1

Step-by-step explanation:

y=3x+1 is above because it has a positive slope (3) while y=3x-1 is below because it has a negative slope (-3).

Since there are only two (2) sellers in the town with many buyers, the competitive situation which Jameson's Grocery is experiencing is an oligopoly.

An oligopoly can be defined as a market structure which comprises a small number of business firms (sellers) that are offering identical (similar) products to many buyers, wherein none of the sellers can limit the significant influence of others.

In this scenario, we can infer and logically deduce that the competitive situation which Jameson's Grocery is experiencing is an oligopoly because there are only two (2) sellers in the town with many buyers (1,000 students).

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Knowing which x-values would result in division by zero can help you avoid using certain x-values. Finding the domains of rational functions is therefore likely to be your initial step.

A function that measures two polynomials in comparison. Because one is divided by the other, just like a ratio, it is a "rational function."

All real numbers x, except those for which the denominator is 0, are included in the domain of a rational function. Equilibrate the denominator to zero and then solve for x to determine which x values are excluded from the scope of a rational function.

For instance, the set of all real numbers other than x=0 is the domain of the parent function f(x)=1/x.

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Answer: 4x^2 + 1

Step-by-step explanation:

I am assuming g(x) = x^2

4(x^2) + 1

4x^2 + 1

Answer:

[tex](fog)(x)=4x^2+1[/tex]

Step-by-step explanation:

Assume [tex]g(x)=x^2[/tex]

[tex](fog)(x)[/tex] is a composition of two functions such that [tex](fog)(x)=f(g(x))[/tex].

Consider the function:

[tex]f(x)=4x+1[/tex]

Replace [tex]x[/tex] with [tex]g(x)[/tex] into the equation:

[tex]f(g(x))=4\cdot g(x)+1[/tex]

Substitute [tex]g(x)=x^2[/tex] on the right side of the equation:

[tex]f(g(x))=4\cdot x^2+1[/tex]

Therefore, the expression for [tex](fog)(x)[/tex] is [tex]4x^2+1[/tex].

AMSWER :

Just remove the given angle from 180°

since , a straight line makes a angle of 180°

hence,

ROQ + ROP = 180°

144° + ROP = 180°

ROP = 180° - 144° = 36°

.

.

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The following requires the submission of the details of the parabola related to the equations.

A parabola, simply defined, is a plane curve that is created by a point that is moving such that it's distance from a fixed locus is equal to it's distance from a line that is fixed.

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Answer:

3/2

Step-by-step explanation:

We can use the slope formula to find the slope of the line

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

Using the points (0,-4) and (2,-1)

m = ( -1 - -4)/( 2 - 0)

   = (-1+4)/ (2 -0)

   = 3/2

"Draw a ray with one endpoint" demonstrates the correct first step in copying an angle. This is further explained below.

In general, the distance (which is sometimes stated as a degree) that occurs between two crossing lines or surfaces at or near the point where they meet. This distance might be positive or negative.

The formation of an angle is caused by the conjunction of two rays at a single point in space. The split or 'opening' that can be seen between these two rays is referred to as a 'angle,' and the symbol denotes this particular angle. The degree is the standard unit of measurement for angles, and its values include things like 60 degrees and 90 degrees, amongst other possible combinations.

In conclusion, "Draw a ray with one terminal" illustrates the correct first step in duplicating an angle. This step shows how to replicate an angle.

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Answer:

y≤-x+1

Step-by-step explanation:

Since the line is slanted down and crossing through a point every one unit the slope is negative one. The line is also crossing 1 on the y-axis. This is the y-intercept. The last thing we need to know is which sign to use, less than, greater than, less than or equal to, greater than or equal to. We can immediately cross out less than and greater than because it is a solid line. The sign used on the graph is less than or equal to because it is a solid line shaded to the left. Now, we can use the formula with the information we have found to create the linear inequality.

Formula: y≤x+b

I put the less than or equal to sign there instead of the equal sign because the line graphed is less than or equal to. Plug in the information we have.

y≤-x+1

Using function notation.

f(x)≤-x+1

I have also attached a picture for you to see it is correct.

Hope this helps!

If not, I am sorry.

Answer:

Step-by-step explanation:

So if you look at the first photo I sent you'll see I marked three points. So the first point is going to be the two lines meet and the other two are going to be at 0 degrees and 48 degrees. After that you're going to draw a line to connect 2 of the dots to the middle one or the one connecting the two. After this you're going to put the protractor back on the triangle and line it up and then draw a point at 24 degrees (half of 48 degrees) and then draw a line to it. And this will be the bisector. And then after that label all the points. Also for the congruency thing just do the same thing except without an angle bisector through it.

Answer:

3,-3

Step-by-step explanation:

g(3)= (3)³+6(3)²-9(3)-54

= 27+54-27-54

=81-81

= 0

g(-3) = (-3)³+6(-3)²-9(-3)-54

= -27+54+27-54

= 27-27

= 0

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We know that if [tex]m\angle ABD=2(m\angle DBC)[/tex], then [tex]m\angle ABD=\frac{2n}{3}[/tex] and [tex]m\angle DBC=\frac{n}{3}[/tex].

Since BE bisects [tex]\angle DBC[/tex], we know that [tex]\angle DBE \cong \angle EBC[/tex], and thus [tex]\angle EBC=\boxed{\frac{n}{6}}[/tex]

The number 2007 is in the 63rd row

The pattern is given as

1

2  3

4  5  6

The sum of n natural numbers is:

Sum = 0.5n(n + 1)

Assume n = 62

Sum = 0.5 * 62 * (62 + 1)

Sum = 1953

Assume = 63

Sum = 0.5 * 63 * (63 + 1)

Sum = 2016

2007 is between 1953 and 2016

Since 2016 is greater than 1953, we can conclude that 2007 is in row 63

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The The square root of R² (the coefficient of determination) is not r, the correlation coefficient. Therefore, it's false.

It should be noted that the correlation coefficient is used to measure how string the relationship between two variables are.

The correlation formula tells us the linear relationship between the variables. R² is the square of the correlation coefficient.

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The volume of the spherical solid resulting of the drill is of 11,226 units³.

The volume of a sphere of radius r is given as follows:

[tex]V = \frac{4\pi r^3}{3}[/tex]

In this problem, we have two spherical balls, one of radius 14 and other of radius 4, hence their volumes are given as follows:

[tex]V_1 = \frac{4\pi 14^3}{3} = 11494[/tex]

[tex]V_2 = \frac{4\pi 4^3}{3} = 268[/tex]

The volume of the resulting solid is the difference of the volumes, hence:

V = 11494 - 268 = 11,226 units³.

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The full set is;

(x + 7) (3x + 1) = 3x² + 22x + 7

This question introduces the concept of polynomial long division.

This is what we are

Given: (3x² + 22x + 7) ÷ (x + 7) = 3x + 1

Now, from the concept of polynomial long division, we can see that:

if, f (x) ÷ g (x) = h (x),

This means that we can write:

f (x) = g (x) × h (x)

Applying the same concept to the question, we can also say:

(3x² + 22x + 7) ÷ (x + 7) = 3x + 1,

Next; (x + 7) (3x + 1) = 3x² + 22x + 7

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Answer: Function 1 has the larger maximum at (4,1).

Step-by-step explanation:

The vertex of f(x) is at [tex]x=-\frac{2}{2(-1)}=1[/tex], and [tex]f(1)=-2[/tex].

For the graph, the maximum is obviously at (4,1).

So, Function 1 has the larger maximum at (4,1).

Answer:

  (a)  F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)

Step-by-step explanation:

Wherever the function crosses the x-axis, its sign changes. This lets us make a map of the signs of the function, and identify intervals where it is positive and negative.

The x-intercepts are said to be at x ∈ {-0.7, 0.76, 2.5}.  These three crossing points divide the graph into four (4) intervals. The sign of the function is given as positive at x=0 and negative at x = 1.9. So, our sign map is ...

  < -0.7 . . . . . negative

  -0.7 to 0.76 . . . . . positive (2 at x=0, for example)

  0.76 to 2.5 . . . . . negative (-5.7 at 1.9, for example)

  > 2.5 . . . . . positive

Choosing from the descriptions, the one that matches is ...

  F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)

Answer:

They used coordinates P(a,0), A(d,c), and R(b,c) instead of the given coordinates.