(01.03 MC)
Which of the following is a step in simplifying the expression
(Xy^4/x^-5y^5)^3

Answer:

y=(6(x+6)(x-3))/((x-2)(x+3))

Step-by-step explanation:

The vertical asymptote should be in the denominator. The x-interceps should be in the numerator. Because we have horizontal asymptote y=6, then we have to put 6 in the numerator. the horizontal asymptote is the leading coefficient of the numerator ÷ the leading coefficient of the denominator, when the degree of the numerator and denominator are the same.

Given the horizontal asymptote, vertical asymptotes and x intercepts, the equation of the rational function is y = 6((x+6)(x-3))/((x-2)(x+3)). The vertical asymptotes are found by setting the function's denominator equal to zero, while the x-intercepts come from setting the numerator to zero.

In this question, we are asked to write the equation of a rational function based on given conditions. The function's vertical asymptotes are located at x = 2 and x = -3, and has x-intercepts at (-6,0) and (3,0), with a horizontal asymptote at y = 6.

The general form of a rational function is y = (ax+b)/(cx+d). Asymptotes help define the behavior and boundaries of the function. In this situation, we can set the denominator of our function equal to zero to find our vertical asymptotes, giving us (x-2)(x+3). To achieve our stated x-intercepts, we set the numerator equal to zero, providing (x+6)(x-3). Combining these, the function becomes y = ((x+6)(x-3))/((x-2)(x+3)). The output of the function approaches the horizontal asymptote as x approaches infinity. Thus to have y = 6 as our horizontal asymptote, we adjust our function to maintain this behaviour, settling on y = 6((x+6)(x-3))/((x-2)(x+3)).

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Answer:

9

Step-by-step explanation:

70% of 30 is 21, so to find the number of boys, take the original 30, and subtract 21, leaving you with 9, hope this helps and good luck bud :)

There are 9 boys in the class.

To determine the number of boys in a class where 70% are girls, multiply the total number of students by the percentage of boys in the class.

Given:

Answer: There are 9 boys in the class.

Answer:

x = -2, x = 0, and x = 3

Step-by-step explanation:

it was right lol

Answer:

[tex]y=x^{2}+3[/tex]

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

[tex]y=a(x-h)^{2}+k[/tex]

where

(h,k) is the vertex

In this problem we have the vertex at point (0,3)

substitute

[tex]y=a(x-0)^{2}+3[/tex]

[tex]y=ax^{2}+3[/tex]

therefore

The option [tex]y=x^{2}+3[/tex] is the answer

In this case the coefficient a is equal to 1

Answer:

Step-by-step explanation:

(X+5)(X+1) = x²+x+5x+5 = x² +6x+5

(X+5)(X+1)

Use the FOIL method to expand.

This means multiply each term in the first set of parenthesis by each term in the second set.

x *x = x^2

x*1 = x

5*x = 5x

5*1 = 5

Now you have x^2 + x + 5x + 5

Now simplify by combining like terms:

x^2 + 6x + 5

Answer:

Second option:

[tex]d = 15.6\ mm,\ C = 49.01\ mm[/tex]

Step-by-step explanation:

We can observe that the radius of the circle is given. This is:

[tex]r = 7.8\ mm[/tex]

And the missing measures are the diameter of the circle and the circumference.

Since the diameter of a circle is twice the radius, we get that this is:

[tex]d=2r\\\\d=2(7.8\ mm)\\\\d=15.6\ mm[/tex]

To find the circumference of the circle, we can use this formula:

[tex]C=2\pi r[/tex]

Where "r" is the radius of the circle.

Substituting the radius into the formula, we get:

[tex]C=2\pi r\\\\C=2\pi (7.8\ mm)\\\\C=49.01\ mm[/tex]

Answer:

D is correct option

Step-by-step explanation:

The correct option is D.

The standard quadratic equation is ax²+bx+c=0

Where a and b are coefficients and c is constant.

It means that constant are on the L.H.S and there is 0 on the right hand side.

Therefore to make it a quadratic equation first of all you have to add 11 at both sides so that the R.H.S becomes 0.

The given equation is:

2x2-x+ 2 = -11

If we add 11 on both sides the equation will be:

2x2-x+ 2 +11= -11+11

2x^2-x+13=0

Thus the correct option is D

You can further solve it by applying quadratic formula....

Final answer:

The most logical first step to solve the quadratic equation 2x² - x + 2 = -11 is to set up smaller equations using the zero product rule and then applthe quadratic formula. The correct option is c.

Explanation:

The most logical first step to solve the quadratic equation 2x² - x + 2 = -11 is to:

C. Set up smaller equations using the zero product rule.

Once the equation is rearranged, apply the quadratic formula to determine the values of x.

Using the quadratic formula yields the solutions by substituting the values of a, b, and c correctly.

Answer:

=800 km

Step-by-step explanation:

Let the distance traveled by train be y and by bus be x.

Bus -x

Train -y

y=x+150 (since they traveled by train for a distance of 150 km more than by bus.)

The sum of the two is equal to 1450

x+y=1450

y=x+150

These two form simultaneous equations.

y+x=1450..............i

y-x=150.................ii

Adding ii to i gives:

2y=1600

Divide both sides by two

y=800

Distance traveled by train =y=800 km

Answer:

800

Step-by-step explanation:

Answer:

JM ≈ 12.9 miles

Step-by-step explanation:

The length of the arc is calculated as

arc = circumference × fraction of circle

     = πd × [tex]\frac{90}{360}[/tex]

JM = π × 16.4  × [tex]\frac{1}{4}[/tex]

     = [tex]\frac{16.4\pi }{4}[/tex] ≈ 12.9

The length of the arc JM will be 12.88 miles.

Let r is the radius of the sector and θ be the angle subtends by the sector at the center. Then the arc length of the sector of the circle will be

Arc = (θ/360) 2πr

The diameter is 16.4 miles. Then the radius will be

r = d / 2

r = 16.4 / 2

r = 8.2 miles.

And angle (θ) will be 90 degrees.

Then the length of the arc JM will be

Arc = (90/360) 2π x 8.2

Arc = 12.88 miles

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Answer:

The correct option is 3.

Step-by-step explanation:

The given equation is

[tex]2x^2+12x-14=0[/tex]

It can be written as

[tex](2x^2+12x)-14=0[/tex]

Taking out the common factor form the parenthesis.

[tex]2(x^2+6x)-14=0[/tex]

If an expression is defined as [tex]x^2+bx[/tex] then we add [tex](\frac{b}{2})^2[/tex] to make it perfect square.

In the above equation b=6.

Add and subtract 3^2 in the parenthesis.

[tex]2(x^2+6x+3^2-3^2)-14=0[/tex]

[tex]2(x^2+6x+3^2)-2(3^2)-14=0[/tex]

[tex]2(x+3)^2-18-14=0[/tex]

[tex]2(x+3)^2-32=0[/tex]             .... (1)

Add 32 on both sides.

[tex]2(x+3)^2=32[/tex]

The vertex from of a parabola is

[tex]p(x)=a(x-h)^2+k[/tex]        .... (2)

If a>0, then k is minimum value at x=h.

From (1) and (2) in is clear that a=2, h=-3 and k=-32. It means the minimum value is -32 at x=-3.

The equation [tex]2(x+3)^2=32[/tex] reveals the minimum value for the given equation.

Therefore the correct option is 3.

The correct answer is option 3. [tex]2(x + 3)^2 = 32[/tex].

To find the minimum value of the quadratic equation [tex]2x^2 + 12x - 14[/tex] = 0, we can rewrite it in vertex form, which reveals the minimum or maximum value of a quadratic function.

The given options are attempts at rewriting the quadratic equation in vertex form. Let’s rewrite the equation:

First, complete the square:

1. Start with the equation: [tex]2x^2 + 12x - 14[/tex]

2. Factor out the coefficient of x² from the first two terms: [tex]2(x^2 + 6x) - 14[/tex]

3. Complete the square inside the parentheses:
- Take [tex](\frac{6}{2})^2 =9[/tex] - Add and subtract 9 inside the parentheses: [tex]2(x^2 + 6x + 9 - 9) - 14[/tex]
- Simplify inside the square: [tex]2((x + 3)^2 - 9) - 14[/tex]

4. Distribute and simplify: [tex]2(x + 3)^2 - 18 - 14 = 2(x + 3)^2 - 32[/tex]

Comparing this with the options, we have [tex]2(x + 3)^2 = 32[/tex].

The correct answer is: [tex]2(x + 3)^2 = 32[/tex].

Answer:

4:3

Step-by-step explanation:

Given that P divides segment MN into 4/7, let MN to be x units in length then

MP = 4/7 x =4x/7 --------(i)

But MN =MP+PN so;

x=4x/7 +PN

x- 4X/7 =PN

3x/7 =PN ----------(ii)

To get the ratio of MP:PN

MP: PN

4x/7:3x/7

MP/PN = 4x/7 / 3x/7

MP/PN =4/3

MP:PN = 4:3

Answer: 4:3

Step-by-step explanation:

Given : A point P is 4/7 of the distance from M to N.

∴ Let the distance between M to N be d.

[tex]\Rightarrow\ MP=\dfrac{4}{7}\times d=\dfrac{4d}{7}[/tex]

Also,  the point P partition the directed line segment from M to N .

Thus , MN = MP+PN

[tex]\Rightarrow\ d=\dfrac{4d}{7}+PN\\\\\Rightarrow\ PN= d-\dfrac{4d}{7}=\dfrac{7d-4d}{7}\\\\\Rightarrow\ PN=\dfrac{3}{7}d[/tex]

Now, the ration of MP to PN will be :-

[tex]\dfrac{MP}{PN}=\dfrac{\dfrac{4d}{7}}{\dfrac{3d}{7}}=\dfrac{4}{3}[/tex]

∴ Point P partitioned the line segment MN into 4:3.

Answer:

73°

Step-by-step explanation:

Since WX = WZ then ΔWXZ is isosceles and WY is perpendicular to XZ

Hence ∠XYW = 90°

YW bisects XWZ, hence ⇒ ∠ YWX = ∠YWZ = 17°

The sum of the 3 angles in ΔWXY = 180°, hence

∠WXY = 180° - (90 + 17)° = 180° - 107° = 73°

Answer:

17/25

Step-by-step explanation:

First, convert the decimal into a fraction. To do so, move the decimal point to the right two place values and place over 100.

0.68 = 68/100

Next, simplify. Divide common factors. Remember, what you do to one side, you do to the other. Divide 4 from both sides:

(68/100)/4 = (17/25)

17/25 is your answer.

~

0.68 can be expressed as the fraction 17/25 in the lowest terms.

Step 1: Let x be the decimal representation of the fraction.

x = 0.68

Step 2: Since there are two digits after the decimal point, we can multiply both sides of the equation by 100 to eliminate the decimal.

100x = 68

Step 3: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which in this case is 4.

100 ÷ 4 = 25

68 ÷ 4 = 17

The simplified fraction is:

0.68 = 17/25

Therefore, 0.68 can be expressed as the fraction 17/25 in the lowest terms.

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Answer:

-3,3.1, 3 2/10

Step-by-step explanation:

When you are putting different numbers from least to greatest, you need to put them in the same form...

First things first we should put -3 wayy up front. negative numbers are worth less than positive numbers.

Then we need to turn 3 2/10 into a decimal.

3 2/10 -------> 3.2

3.2 is more than 3.1

Thus, the order is

-3,3.1, 3 2/10

Hope this helps and have a nice day.

Answer:

-3, 3.1, 3 2/10

Step-by-step explanation:

3 2/10, 3.1, -3

Negative numbers are smaller than positive numbers

-3

Then we need to compare fractions and decimals.

Lets change the fraction to a decimal

2/10 = .2

3.2 and 3.1

3.1 < 3.2

So in order from least to greatest

-3, 3.1, 3 2/10

Answer:

I believe the answer is C.

The trigonometric function gives the ratio of different sides of a right-angle triangle. The correct option is C.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

To find the measure of angle A, we need to use the tangent trigonometric function this is because except for the hypotenuse of the triangle the other two sides of the equation are known.

Therefore, the equation of the tangent function of trigonometry for angle A can be written as,

tan(A) = Perpendicular /Base

tan(A) = 9.4 / 6.7

Hence, the equations below that can be used to find the measure of ∠A is tanA=9.4/6.7.

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Answer:

g(3)=11 I think

Step-by-step explanation:

Since x is 3, you substitute it in for the x. So it would be 3 squared +2.

I'm not sure if this is right but I tried helping.

Answer:

g(3) =11

Step-by-step explanation:

g(x) = x^2 +2

Let x =3

g(3) = 3^2 +2

      = 9+2

      = 11

Answer:

Answer is Circle

Step-by-step explanation:

Check the picture below.

notice, all points are equidistant from the center of it, wherever the center happens to be.

Answer:

x =96 degree.

Step-by-step explanation:

Given : Triangle .

To find : The value of x is

Solution : We have given triangle

Exterior Angle sum property of triangle : Sum of all exterior angle of triangle is 360.

130 + 134 + x = 360 .

264 + x = 360.

On subtracting both sides by 264 .

x = 360 - 264 .

x = 96.

Therefore, x =96 degree.

Using Exterior Angle sum property of the triangle, The value of x will be 96 degree.

Exterior Angle sum property of the triangle states that the Sum of all exterior angles of the triangle is 360.

Given: Two exterior angles measure of 130 and 134 degrees.

To find: The value of x is

So,

130 + 134 + x = 360 .

264 + x = 360.

x = 360 - 264 .

x = 96.

Using Exterior Angle sum property of the triangle, The value of x will be 96 degrees.

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Answer:

27/20

Step-by-step explanation:

7+1=8

5*4=20

5*1=5

8/20+5/20+14/20

Add numbers from left to right to find the answer.

8+5=13+14=27

27/20 is the correct answer.

Answer:

$65720

Step-by-step explanation:

The job pays a starting salary of $62000, and raises $3720 per year. In one year, Carlos will be earning $62000 + $3720 =  $65720

Final answer:

Carlos's salary in one year will be $65720, which is the sum of his starting salary, $62000, and the promised annual raise of $3720.

Explanation:

After graduating from college, Carlos has received two different job offers, both offering a starting salary of $62000, and one includes a promise of a $3720 raise per year. To calculate his salary in one year, we need to add this annual raise to his starting salary.

Starting salary: $62000

Raise after one year: $3720

Carlos's salary in one year: $62000 + $3720 = $65720

This computation shows that with the promised annual raise, Carlos's salary for the next year would be $65720.

[tex]\huge{\boxed{f(4)=\bf{-3}}}[/tex]

In this case, you are replacing all instances of [tex]x[/tex] with [tex]4[/tex]. [tex]f(4)=3(4)-15[/tex]

Multiply. [tex]f(4)=12-15[/tex]

Subtract. [tex]f(4)=-3[/tex]

Answer:

125

Step-by-step explanation:

500 ÷ 4 = 125

I think this is the right answer. sorry if I'm wrong.

Answer:

x=5 assuming that x is the radius.

x is the radius?

Step-by-step explanation:

[tex]V=\frac{4}{3} \pi r^3[/tex] is the volume of a sphere.

We are given [tex]V=\frac{500}{3} \pi[/tex] cubic units.

We are asked to find the value of x.  If x is not the radius, please correct me:

[tex]V=\frac{4}{3}\pi r^3[/tex] with  [tex]V=\frac{500}{3} \pi[/tex]  and the assumption that x is r.

[tex]\frac{500}{3}\pi=\frac{4}{3}\pi x^3[/tex]

If you multiply both sides by 3, then you would have:

[tex]500 \pi=4 \pi x^3[/tex]

If you divide both sides by [tex]\pi[/tex] you will have:

[tex]500=4x^3[/tex]

If you divide both sides by 4, you will have:

[tex]125=x^3[/tex]

The last step would be to take the cube root of both sides:

[tex]\sqrt[3]{125}=x[/tex]

[tex]5=x[/tex]

[tex]x=5[/tex]

Answer:

11. r^2 + 12r + 27 = (r+3)(r+9)

12. g^2-9 = (g+3)(g-3)

13. 2p^3 + 6p^2 + 3p + 9 = (2p^2+3)(p+3)

Step-by-step explanation:

[tex]11.\ r^2 + 12r + 27\\Factorizing\\= r^2+9r+3r+27\\=r(r+9)+3(r+9)\\=(r+3)(r+9)\\\\12. g^2-9\\The\ expression\ will\ be\ factorized\ using\ the\ formula\\(a+b)(a-b)=a^2-b^2\\So,\\g^2-9\\=(g)^2-(3)^2\\=(g+3)(g-3)\\\\13. 2p^3 + 6p^2 + 3p + 9\\=2p^2(p+3)+3(p+3)\\=(2p^2+3)(p+3)[/tex] ..

To find the probability of drawing certain colour of balls, we first need to find the total number of balls:

5 + 7 +5 = 17

For the number of red balls that need to be added

The original probability of drawing a red ball:

red ball/ total number of balls

= 5/17

To find the number of balls required, we can set an equation.

Let the number of red balls that need to be added be x.

5+x / 17+x = 5/6

(5+x) x 6 = (17+ x) x5

30 +  6x = 85 + 5x

6x - 5x = 85 - 30

x = 55

Therefore, 55 red balls need to be added.

For the number of black balls that need to be added

The original probability of drawing a white ball:

white ball/ total number of balls

=5/17

To find the probability required, we can set an equation.

Let the number of black balls that need to be added be y.

5/ 17 + y = 1/6

5 x 6 = 17 + y

30 = 17 + y

30 - 17 = y

y = 13

Therefore, 13 black balls need to be added.

Hope it helps!

Answer:

sum of angles of triamgle is 180 degree

the half base× hight ue1/2×b×h

use the formula for all qusetions

For the first row, where x is equal to 7, to find y plug 7 in for x like so...

y = 7 - 3

y = 4

For the second row, where y is equal to 1, to find x plug 1 in for y like so...

1 = x - 3

To solve for x add 3 to both sides. This will cancel 3 from the right side:

1 + 3 = x - 3 + 3

4 = x + 0

x = 4

For the third row, where y is equal to 7, to find x plug 7 in for y like so...

7 = x - 3

To solve for x add 3 to both sides. This will cancel 3 from the right side:

7 + 3 = x - 3 + 3

10 = x + 0

x = 10

First row: y is 4

Second row: x is 4

Third row: x is 10

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

2 is your slope

Step-by-step explanation:

Find the slope. Use the slope-formula:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Let:

(x₁ , y₁) = (-1 , 1)

(x₂ , y₂) = (2 , 7)

Plug in the corresponding numbers to the corresponding variables:

m = (7 - 1)/(2 - (-1))

Simplify:

m = (6)/(2 + 1)

m = 6/3

m = 2

2 is your slope (or rise 2, run 1).

~

Answer:

slope = 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (2, 7)

m = [tex]\frac{7-1}{2+1}[/tex] = [tex]\frac{6}{3}[/tex] = 2

Answer:

y=2x-3

Step-by-step explanation:

The slope-intercept form of a linear equation is y=mx+b where m is the slope and b is the y-intercept.

The y-intercept is where it crosses the y-axis.  It cross the y-axis in your picture at -3 so b=-3.

Now the slope=rise/run.  So starting at (0,-3) we need to find another point that crosses nicely on the cross-hairs and count the rise to and then the run to it.  So I see (1,-1) laying nicely.  So the rise is 2 and the run is 1.

If you don't like counting.  You could just use the slope formula since we already identified the two points as (-1,1) and (0,-3).

The way I like to use the formula is line up the points and subtract vertically then put 2nd difference over 1st difference.

(0,-3)

-(1,-1)

----------

-1     -2

So the slope is -2/-1 or just 2.

We have that m is 2 and b is -3.

Plug them into y=mx+b and you are done.

y=2x-3.

Slope intercept equation of the line is y = 2x - 3.

Slope intercept form gives the graph of a straight line and is represented in the form of y=mx + c.

By checking the graph by drawing manually.

From that we get the equation

y = 2x - 3

Comparing above equation with the standard slope-intercept form y = mx +c, we get

Slope : m = 2

Now, given equation can be re-written as :

2x - y = 3

Divide by 3 on both sides

[tex]\frac{2x}{3} -\frac{y}{3} =\frac{3}{3}[/tex]

[tex]\frac{x}{\frac{3}{2} } -\frac{y}{3} =1[/tex]

Comparing above equation with intercept form:

[tex]\frac{x}{a}+\frac{y}{b}=1[/tex], we get

x-intercept : [tex]a=\frac{3}{2}[/tex]

y-intercept : [tex]b=-3[/tex]

Now the given straight line intersects the coordinate axes at [tex](\frac{3}{2} ,0)[/tex] and [tex](0,-3)[/tex]. Specify these plots on XY-plane & join by a straight line to get a plot.

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Answer:

The cost of each candy bar is $3....

Step-by-step explanation:

Let:

x= $4 (soft drink)

z= price of each candy bar

y=5z(Total price of 5 candy bars)

C= $19(spent money)

The equation is:

C= x+y

$19=$4+5z

Subtract 4 from both sides:

$15=5z

Divide both sides by 5

z=$3

Hence the cost of each candy bar is $3....

Answer:

280

Step-by-step explanation:

If a square has sides of length 70 meters, the perimeter is 280.

Formula: P=4a

P = 4a = 4·70 = 280