Hi, so this isn't an equation but could somebody explain what domain and range are please? I'm not doing great with understanding it for whatever reason and it would be super helpful if you could dvmb it down a little bit please ​

Step-by-step explanation:

to "solve" this I need an equation.

this whole expression must be equal to something.

without that I can only try to simplify the expression.

remember that

a/b / c/d = ad / bc

so, here we have

3a/(((a²/x) - 1)(a/x - 1)) = 3a/(a³/x² - a²/x - a/x + 1) =

= 3a/(a³/x² - a²/x - a/x - a/a) =

= 3a/((a²/x² - a/x - 1/x - 1/a)×a) = 3/(a²/x² - a/x - 1/x - 1/a)

Let's take this problem step by step:

To find the ordered pair of the system:

⇒ must set both equations equal to each other

    ⇒ must solve for 'x'

Let's solve:

 [tex]x^2-2x+3=-2x+28\\x^2-2x+3+2x-28=0\\x^2-25=0\\(x-5)(x+5)=0[/tex]

Let's find the x-values:

 [tex](x-5)=0\\x=5\\\\(x+5)=0\\x=-5[/tex]

Let's find f(x)'s value for each of the 'x':

[tex]x=5\\f(5)=-2(5)+28=18\\\\x=-5\\f(-5)=-2(-5)+28=38[/tex]

Answer: (5, 18), (-5,38)

Hope that helps!

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Answer:

15

Step-by-step explanation:

divide the perimeter by two and minus 1

Answer: 15ft

Step-by-step explanation:

Start off by drawing a rectangle with the given information. Since it is a rectangle we know that the opposite side is also 1. So subtract 2 from 32 to get 30. Divide this by 2 and you will get your width of your rectangle. Hope this helps!

The distance that edgar runs in a 5-day week will be 4.45 miles.

Distance is defined as the length between the two points it can be represented in mm,cm, meters,km, and miles.

Given that:-

Edgar runs 8/9 of a mile each day. what is the total distance that Edgar runs in a 5-day week?

The total distance will be calculated as:-

D = [tex]\dfrac{8}{9}[/tex] x 5

D = 4.45 miles

Therefore the distance that edgar runs in a 5-day week will be 4.45 miles.

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Answer:

the answer is D

Step-by-step explanation:

I'm not good at explaining but, it is because the line is not touching more than 1 point on the graph. Basically making it pass the vertical line test, therefore making the answer D.

Good luck, hope this helps !!!

Answer:

(x - 9)(x^2 + 18x + 81).

Step-by-step explanation:

Use the difference of cubes factorization, which claims that a^3 - b^3 = (a - b)(a^2 + ab + b^2)

x^3 - 729 = (x - 9)(x^2 + 18x + 81)

Answer:[tex](x-9) (x^{2} +9x + 81)[/tex]

Step-by-step explanation:

Answer:

Vertex: (1, 5)

Focus: (0, 5)

Step-by-step explanation:

Given that the parabola's equation is y² - 10y + 4x + 21 = 0, solve for the vertex and the focus.

Vertex:

Step 1: Isolate x to the left side of the equation; we get x = - (y² / 4) + (5y / 2) - (21 / 4).

Step 2: Complete the square of the previous equation; here we get - (1 / 4) * (y - 5)² + 1. x is squal to this.

Step 3: Use the vertex form, x = a(y - k)² + 1. a is - 1 / 4, h is 1, and k is 5.

Step 4: Fill in (h, k). We get the answer (1, 5) as the vertex.

Focus:

Step 1: Find p, and distance from the vertex to the focus. We can find p by using 1 / (4a).

Step 2: Simplify. This gives us -1 as p.

Step 3: We plug in the values we just got earlier to get the vertex. The focus of a parabola can be found by using: (h + p, k).

Step 4: Substitude the values. We have (1 + -1, 5).

Step 5: Simplify. Therefore, the answer is (0, 5).

This uservabove me did it all for you. I don't have much to say...

Answer:

f(2) = 2

Step-by-step explanation:

Given function:

f(x) = 5x - 12

To Find:

f(2)

Solution:

Well,it is absolutely clear from the problem,that x = 2.So just substitute 2 in x's place on the function,then simplify using PEMDAS.

[tex]f(x) = 5x - 12[/tex]

[tex]f(2) = 5(2)- 12[/tex]

[tex]f(2) = 10 - 12[/tex]

[tex]\boxed{f(2) = - 2}[/tex]

Hence,f(2) is equal to -2.

Answer:

Part A -  2/5 of a dollar

Part B - It shows that 10 pounds of cabbage cost $4

Step-by-step explanation:

If 5 pounds cost $2 then 1 pound costs 2/5 of a dollar.

(10,4) - 10 is the x-axis which is pounds and 4 is the y-axis which is $. So 10 pounds cost $4.

Answer:

Given function:

[tex]q(x)=9x^2-24x+16[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex],  find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:

[tex]ac=9 \cdot 16=144[/tex]

Two numbers that multiply to 144 and sum to -24 are: -12 and -12

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies q(x)=9x^2-12x-12x+16[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies q(x)=3x(3x-4)-4(3x-4)[/tex]

Factor out the common term [tex](3x-4)[/tex]:

[tex]\implies q(x)=(3x-4)(3x-4)[/tex]

Therefore:

[tex]\implies q(x)=(3x-4)^2[/tex]

By the consideration of direct proportionality, the constant of proportionality for the height of the plant is equal to 3 inches per week.

Let x and y the number of weeks and the height of the plant, respectively. Given the consideration of direct proportionality, the height of the plant inasmuch as the number of weeks increases. Then, the constant of proportionality (in inches per week) is found by dividing the height of the plant by the number of the respective week:

k = 18 inches /6 weeks = 15 inches /5 weeks = 12 inches/4 weeks = 3 inches/week

By the consideration of direct proportionality, the constant of proportionality for the height of the plant is equal to 3 inches per week.

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Answer:

Step-by-step explanation:

You can use the Law of Cosines after you find y or θ. Using the given information, you can apply the Pythagorean theorem, the Law of Sines, or the definition of the cosine trig function.

The mnemonic SOH CAH TOA is intended to remind you of the relations between sides and angles in a right triangle. It tells you ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

The Pythagorean theorem relates the measures of the sides. It tells you ...

  y² +5² = 12²

  y = √(144 -25) = √119

The trig relations above tell you ...

  sin(α) = 5/12   ⇒   α = arcsin(5/12) ≈ 24.624°

 cos(θ) = 5/12   ⇒   θ = arccos(5/12) ≈ 65.376°

Of course, once you find one of the angles, you can find the other. The sum of the two acute angles in a right triangle is 90°.

Using the definitions above for the trig functions, you have ...

  sin(θ) = y/12 = (√119)/12

  cos(θ) = 5/12

  tan(θ) = y/5 = (√119)/5

Using trig identities, you have ...

  csc(θ) = 1/sin(θ) = 12/√119 = (12√119)/119

  sec(θ) = 1/cos(θ) = 12/5 = 2.4

  cot(θ) = 1/tan(θ) = 5/√119 = (5√119)/119

_____

Additional comment

The attached calculator screen shot shows you the angle θ on the first line, and the value of y on the second line. The csc, sec, and cot are shown on the third line. You will notice the angle mode (DEG) is seen in the lower left corner. If the calculator angle mode is set to radians, you will see the angles as relatively small radian values: θ ≈ 1.141, α ≈ 0.4298.

We have shown both exact values and decimal values you can round to the desired precision.

The weight of the smallest rectangular block is 1400 pounds.

The density refers to the heaviness of an object. It is the ratio of mass to volume.

Then we have

Density = Mass / Volume

A sculptor is planning to order a rectangular block of composite stone to sculpt a lion.

The sculptor anticipates that the lion will be 5 feet long, about 2 feet wide and at the tallest part of the lion's body, have a height of 3.5 feet.

The composite stone weighs 40 pounds per cubic foot.

To the nearest cubic foot, estimate the weight of the smallest rectangular block that the sculptor must purchase in order to create his statue.

Then the weight of the smallest rectangular block will be

Mass = density x volume

The volume will be

V = 5 x 2 x 3.5

V = 35 cubic feet

Then the weight will be

Mass = 40 x 35

Mass = 1400 pounds

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Answer:

k = 11, if I understand the question.

Step-by-step explanation:

Please rephrase the question if my interpretation is incorrect.  (BTW, isn't (k,9) a dog?)

======================

I'll assume that we want to find the value of k as given by the equation of a line that has a slope of (1/2).  

Let's determine if we can establish an equation with what we know:

1.  It goes through point (3,5), and

2.  It has a slope of (1/2)

We'll look for a line with the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).

From (2) we know y = (1/2)x + b.

We can find b by using the one known point that lies on the line (3,5).  Use y = (1/2)x + b, insert the point (3,5), and solve for b:

y = (1/2)x + b

5 = (1/2)(3) + b

5 = 1.5 + b

b = 3.5

The line is y = (1/2)x + 3.5.

Now use the point (k,9):

y = (1/2)x + 3.5

9 = (1/2)k + 3.5

(1/2)k = 5.5

k = 11

The point is (11,9) so k = 9

See the attached graph.

The least number of consecutive positive integer that is required to make the sum of the reciprocals greater than three is 7.

An integer is simply a number that is not  a  fraction.

The first four consecutive positive integers are:

1, 2, 3 , 4.

Their reciprocals are:

1/1, 1/2, 1/3, 1/4; and

The sum of them are greater than 2; that is

1/1 + 1/2 + 1/3 + 1/4 = 2.08333333333 > 2

to make the expression >3

We would require the following integers

1/1 + 1/2 + 1/3 + 1/4+ (1/5) + (1/6) + (1/7) + (1/8)+ (1/9) + (1/10) + (1/11) = 3.01987734488

Thus, the additional consecutive reciprocal integers that is required to make the sum of the reciprocal of the fist four greater than 3 is 7.

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Answer:

its e

Step-by-step explanation:

because e is is referring to savvy

From the power rules, the matching of  each expression with its equivalent expression is:

[tex]5^{-3}=\frac{1}{125}[/tex]

[tex]-5^{-3}=-\frac{1}{125}[/tex]

[tex](-5^{-3})^{-1}=-125[/tex]

[tex](-5^{-3})^{0}=1[/tex]

There are different power rules, see some them:

1. Negative exponent. For this rule when you have a negative exponent, you need to invert the number, i.e, the power base is converted to the denominator. After that, you should solve the power with a positive exponent.  See the  examples:

[tex]4^{-3}=\frac{1}{4^3} =\frac{1}{64} \\ \\ {\frac{4}{6} }^{-2}=( {\frac{6}{4} })^{2}=\frac{36}{16}[/tex]

2. Power. For this rule, you should repeat the base and multiply the exponents. See the  example, [tex](2^{2})^3=2^6=64[/tex].

3. Zero Exponent. When you have an exponent equals to zero, the result must be 1.  See the  example, [tex]2^0=1[/tex].

From this for your question, you have:

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Answer:

x=20

Step-by-step explanation:

The angles are 'Co-interior Angles', they make a C shape and add up to 180 degrees

so 4x +5x =9x

9x=180

x=20

4x=80

5x=100

The triangle is congruent by SSS congruency because the corresponding two sides of two triangles are of the same measurement Hence, Option D is correct.

If the corresponding two sides of two triangles are of the same measurement, then the considered pair of triangles are congruent.

We have given two triangles that are congruent to each other;

LMN is congruent to OPQ

Given;

LM = OP

MN = PQ

LN = OQ

Thus, the triangle is congruent by SSS congruency because the corresponding two sides of two triangles are of the same measurement

Hence, Option D is correct.

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Answer:

Step-by-step explanation:

When 2 lines are perpendicular, their slopes are negative reciprocals of one another.  Here, if the slope of A is -1/2, the slope of B is +2/1, or just 2.

Answer:

f(x) must be shifted 6 units down in order to produce the graph of g(x).

The length of AD is 5 units. so, option A is the correct answer.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

The length of DC is given as 13 units.

The length of AC is given as 12  units. We can see that angle D is a right angle, so the triangle will be a right-angle triangle.

by Pythagoras theorem;

[tex]DC ^2 = AD^2 + AC^2\\\\13^2 = AD^2 + 12^2\\\\AD^2 = 169 - 144\\\\AD^2 = 25\\\\AD = 5[/tex]

Hence, the length of AD is 5 units. so, option A is the correct answer.

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Answer: Option (2)

Step-by-step explanation:

Setting the equations equal to each other,

[tex]\frac{1}{3}x+2=\frac{4}{3}x-5\\\\7=x[/tex]

If x=7, then [tex]y=\frac{7}{3}+2=\frac{13}{3}[/tex]

Answer:

-3+15-75+375

=12-75+375

=-63+375

=302

n=8

302÷8 = 37

(f- g)(x) = 2x²-3x -8 , Option B is the correct answer.

A function is a mathematical statement that derives relation between two variables.

Two functions are given in the question

f(x) = 2x² - 5

g(x) = 3x + 3

(f- g)(x) = ?

(f- g)(x) = (2x² - 5 - (3x + 3))

(f- g)(x) = 2x²-3x -8

Therefore Option B is the correct answer.

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Step-by-step explanation:

please give this answer brainlist answer