99 POINTS!!! Find the least common denominator for these two rational expressions b/b^2+2b+1 -6/b^2+7b+6

Answer:

5/16

Step-by-step explanation:

It's a little easier when you write the problem like this:

 3      5

----- · -----

8       6

Now reduce that 3/6 to 1/2:

 1      5

----- · -----  =  5/16

8       2

Hello There!

We are given the fraction 3/8 multiplied by 5/6.

Step 1. First, we multiply across so we multiply 3*5 which is 15 and then we multiply 8*6 which equals 48.

Step 2. Both of these can be divided by 3 so we can put the fraction that we already have in simplest form. Dividing 15 by 3 equals 5 and dividing 48 by 3 equals 16.

Final step. We now have our simplified fraction which is 5/16.

Have a great day!

Be safe!

TheBlueFox

ANSWER

[tex]g(2) = 3[/tex]

[tex]g( - 2) = - 4[/tex]

[tex]g(5) = 5[/tex]

EXPLANATION

The given step function have constant y-values on certain interval.

To find g(2), we plug x=2 into

g(x) =3, because 2 belongs to the interval

2≤x<4

This implies that

[tex]g(2) = 3[/tex]

To find g(-2), we substitute x=-2 into g(x)=-4, because x=-4 belongs to

-3≤x<-1

This implies that,

[tex]g( - 2) = - 4[/tex]

Similarly,

[tex]g(5) = 5[/tex]

because x=5 belongs to the interval,x≥4

Answer:

g(2)=3,

g(-2)=-4,

g(5)=5

Step-by-step explanation:

g(2) means find the value of function g(x) when x=2

from given restriction we see that x=2 lies withing [tex]2 \leq x <4[/tex]

corresponding function value is 3

Hence g(2)=3

-------

g(-2) means find the value of function g(x) when x=-2

from given restriction we see that x=-2 lies withing [tex]-3 \leq x <-1[/tex]

corresponding function value is -4

Hence g(-2)=-4

-------

g(5) means find the value of function g(x) when x=5

from given restriction we see that x=5 lies withing [tex]x \geq 4[/tex]

corresponding function value is 5

Hence g(5)=5

The answer would be 14-12i. Hope this helps! Please mark brainliest! Thanks v much! :)

Answer:

Correct option is:

B. 5

Step-by-step explanation:

The triangle is a right angled triangle.

Let a be a angle adjacent to 90°

then, tana=Side opposite to angle a/Side adjacent to angle a which is not the hypotenuse

Here, Let a=60°

[tex]tan60\°=\dfrac{5\sqrt{3}}{Length\ of\ short\ leg}[/tex]

[tex]\sqrt{3}=\dfrac{5\sqrt{3}}{Length\ of\ short\ leg}[/tex]

⇒ Length of short leg=5

Hence, Correct option is:

B. 5

Answer:

C. [tex]N(t)=150\cdot 3^t[/tex]

Step-by-step explanation:

You are given the exponential function [tex]n(t)=ab^t.[/tex]

From the table, [tex]N(t)=150[/tex] at [tex]t=0,[/tex] thus

[tex]N(0)=a\cdot b^0\\ \\150=a\cdot 1\ [\text{ because }b^0=1][/tex]

Also [tex]N(t)=450[/tex] at [tex]t=1,[/tex] thus

[tex]N(1)=a\cdot b^1=a\cdot b.[/tex]

Since  [tex]a=150,[/tex] substitute it into the second equation

[tex]450=150\cdot b\\ \\b=\dfrac{450}{150}\\ \\b=3[/tex]

and the expression for the exponential function is

[tex]N(t)=150\cdot 3^t[/tex]

Answer:

Step-by-step explanation:

[tex]\text{4250 cm} \dfrac{1 m}{100 cm}=42.50m[/tex]

the answer is 42.5 meters

Answer:

Use Desmos, it is an online graphing calculator. You just input the function and you can play around with the graph.

This screenshot is from that :

A function assigns the values. The graph of the function can be made as shown in the image below.

A function assigns the value of each element of one set to the other specific element of another set.

For the given function, the graph can be made as shown below. The graph of the function is a parabola with the vertex at (0.215, 3.287).

Also, the parabola opens upwards, this is because the leading coefficient of the function is positive.

Further, the graph never touches the x-axis of the graph because the roots of the parabola are imaginary, which can be known by calculating the discriminant.

Hence, the graph of the function can be made as shown in the image below.

Learn more about Function here:

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Answer:

The answer would be d

Step-by-step explanation:

The value of given factorial 4! in the given problem is A. 24.

In mathematics, the factorial of a non-negative integer, denoted by the symbol "!", is the product of all positive integers less than or equal to that number. It is a fundamental mathematical operation used in combinatorics, probability theory, and other areas of mathematics.

Factorials have various applications, such as counting the number of permutations and combinations, calculating probabilities, solving equations, and representing coefficients in mathematical series. They are also used in formulae for binomial coefficients, as well as in calculus and other areas of mathematics.

4! = 4 [tex]\times[/tex] 3 [tex]\times[/tex] 2 [tex]\times[/tex] 1

   = 24

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Answer: g(x)=(3)-x

to reflect across the y-axis is to change the x coordinate values to opposite of what it is originally. ie;

f(x)=(3)x Now for a reflection across y-axis

g(x)=(3)-x

Answer:

[tex]g(x)= 3^{-x}[/tex]

Step-by-step explanation:

Given parent function is  [tex]f(x)= 3^x[/tex]

we need to find a function that is a reflection across y axis

For f(x) , reflection across y axis

f(x)  becomes f(-x)

For reflection across x axis, we multiply negative sign with x

f(x)  becomes f(-x)

[tex]f(x)= 3^x[/tex] becomes  [tex]f(x)= 3^{-x}[/tex]

Replace f(x) with g(x)

[tex]g(x)= 3^{-x}[/tex]

To change the mixed expression into a fraction, rewrite the mixed number as an improper fraction. Find the common denominator and combine the fractions by subtracting the second fraction from the first fraction.

To change the mixed expression into a fraction, we need to first rewrite the mixed number as an improper fraction.

The mixed number y-1 can be written as (y-1)/1.

Then, we can rewrite the expression as ((y-1)/1) - (5/(y+3)).

To combine these fractions, we need to find a common denominator.

The common denominator is (y+3), so we need to multiply the first fraction by (y+3)/(y+3) and the second fraction by 1/1.

This gives us ((y-1)(y+3))/((y+3)(1)) - (5/(y+3)).

Now, we can combine the fractions by subtracting the second fraction from the first fraction.

This gives us (((y-1)(y+3))-5)/(y+3).

Final answer:

To change the mixed expression into a fraction, find a common denominator and simplify the expression.

Explanation:

To change the mixed expression into a fraction, we need to find a common denominator.

The common denominator for the given expression y-1 and 5/y+3 is (y+3). To convert y-1 to have the common denominator, we multiply the numerator and denominator by (y+3), resulting in (y+3)(y-1)/(y+3). Next, we can simplify the expression by multiplying out the numerator and combining like terms. The final fraction is (y² + 2y - 3)/(y+3).

The answer is:

The second option:

The vector will change  direction and decrease in magnitude.

Multiplying a vector by a scalar will modify the magnitude of the vector, depending if the scalar is less or greater than "1" also, when a scalar has a negative sign, the direction of the new vector will be the opposite that the original vector.

Solving

We are given that the scalar value is equal to:

[tex]-\frac{\pi }{4}=-0.79[/tex]

Let's use as original vector, the following vector:

[tex]A=(2,2)[/tex]

Calculating its magnitude, we have:

[tex]|A|=\sqrt{2^{2} +2^{2} }=2.83[/tex]

Then, multiplying the vector by the given scalar, we have:

[tex](-0.79A)=((-0.79)*2,-(0.79)*2)=(-1.58,-1.58)[/tex]

As we can see, the vector changed its direction, since both components are negative.

Calculating the magnitude of the new vector, we have:

[tex]|A'|=\sqrt{(-1.58)^{2} +(-1.58)^{2} }=2.23[/tex]

We can see that the given scalar is less than "1", so the magnitude will decrease, also, the direction is the opposite of the original vector direction since both components have changed its sign.

Hence, we have that the magnitude of the new vector is less than the magnitude of the original vector, also, we can see that the direction of the new vector is the opposite of the original vector direction, so, the answer is the second option, the vector will change direction and decrease in magnitude.

Have a nice day!

The answer is negative one

Answer:

x = -3

-3+2 = -1

-1 = f(x)

The volume of a sphere with a diameter of 9 inches, using 3.14 for pi, is calculated using the formula V = (4/3)πr³. The radius is 4.5 inches, leading to a volume of 381.675 cubic inches, which rounded to the nearest tenth is 381.7 cubic inches.

The question is asking for the volume of a sphere with a diameter of 9 inches, using 3.14 for pi. To find the volume, we first need to calculate the sphere's radius. Since the diameter is 9 inches, the radius (which is half the diameter) is 4.5 inches. The formula for the volume of a sphere is V = (4/3)πr³. Substituting the radius into the formula, we get:

V = (4/3)(3.14)(4.5³) = (4/3)(3.14)(91.125) = 381.675 cubic inches. When rounded to the nearest tenth, the volume is 381.7 cubic inches.

The fourth option is the answer. When graphed, Min is 2, Q1 is 3, Median is 7, Q3 is 11, and Max is 24. The fourth option is the one that follow all of those!

Answer:

(D)

Step-by-step explanation:

The given data set is:

10, 12, 2, 4, 24, 2, 7, 7, 9

Firstly arrange the given data set in ascending order, we get

2, 2, 4, 7, 7, 9, 10, 12, 24

Now, the median of the above given data set is:

[tex]Median=7[/tex]

The upper quartile is:

9, 10, 12, 24

thus, [tex]LQ=\frac{10+12}{2}=\frac{22}{2}=11[/tex]

The lower quartile is:

2, 2, 4, 7

thus, [tex]LQ=\frac{2+4}{2}=3[/tex]

The highest value of the given data set is 24 and the lowest value is 2.

Therefore, option D is correct.

Step-by-step explanation:

It's easy. Just line up the denominators, and then say what's 16 divided by 2, 8, and then do the same thing for the numerators. Which is 2 divided by 2 and that equals 1. 1 is your answer.

It is 4.325 • 10^6 (thats ten to the sixth power :))

Hence 4325000 in scientific notation is [tex]4.325 \times 10^6[/tex]

The standard form of scientific notation is expressed as:

[tex]A \times 10^n[/tex] where:

Given the value 4325000

[tex]4325000 = 4 .324\times 10^6[/tex]

Note that the decimal point was shifted to the left 6 times to have [tex]4.325 \times 10^6[/tex]

Hence 325000 in scientific notation is [tex]4.325 \times 10^6[/tex]

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Answer:

10.8 cm

Step-by-step explanation:

we know that

The perimeter of the triangular face is equal to the sum of its sides

P=a+b+c

we have

a=28 mm=28/10=2.8 cm

b=4 cm

c=4 cm

substitute the values

P=2.8+4+4=10.8 cm

Answer:

10.8 cm

Step-by-step explanation:

[tex]

x^3-1=x^3-1^3 \\

(x-1)(x^2+2x+1)=\boxed{(x-1)(x+1)(x+1)}

[/tex]

Hope this helps.

r3t40

not really sure what the question is but if your question is but if ur question is asking what the possiblity is, the answer should be a possiblity of 8/15 for picking a black marble. If Amy picks a black marble in the fourth attempt, the probability of the fifth attempt she will pick a red or a black marble is 5/7

Answer:

The bottom-left graph.

Step-by-step explanation:

g(1) = 0+1 = 1 => g(1) = 1

=> (1,1) ∈ Gf

The graph of the square root function is the bottom left graph.

We want to see which graph represents the function:

g(x) = √(x - 1) + 1

The first thing we can notice is that the domain of the function is:

x ≥ 1

We can see that when x  = 1 the function becomes:

g(1) = √(1 - 1) + 1

g(1) = 1

So the first point of this function is (1, 1), like in the graph in the bottom left, so that is the correct option.

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Answer:

5 ≥ 4

Step-by-step explanation:

Answer:

No. A y-intercept equation forms a straight line. The points given in the graph do not form a straight line. So the answer is no.

Answer: y = mx + b, i think yes

Step-by-step explanation:

Answer:

Ratios and Proportions - Proportions - In Depth. A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a:b = c:d. The following proportion is read as "twenty is to twenty-five as four is to five."

Step-by-step explanation:

The probability of calling three girls consecutively in a mixed class will be 1/22.

There are 12 students in total.

The probability of the first student being a girl is 6 / 12 = 1/2.

After one girl has been chosen, there are now 5 girls left and a total of 11 students.

So, the probability of the second student being a girl is 5 / 11.

With one more girl removed, there would be 4 girls left and 10 students in total.

The probability of the third student being a girl then is 4 / 10 = 2/5.

To find the overall probability of all three events happening in sequence, we multiply the probabilities of each event:

Probability = (1/2) x (5/11) x (2/5)

= 1/22

The theoretical probability that the first 3 students called are all girls is: [tex]\[\boxed{\frac{1}{11}}\][/tex].

Given a class of 12 students, consisting of 6 girls and 6 boys, we are to determine the probability that the first 3 students called are all girls.

First, we calculate the total number of ways to select any 3 students out of 12. This is given by the combination formula:

[tex]\[\binom{12}{3} = \frac{12!}{3!(12-3)!} = \frac{12 \times 11 \times 10}{3 \times 2 \times 1} = 220\][/tex]

Next, we calculate the number of ways to select 3 girls out of the 6 available girls:

[tex]\[\binom{6}{3} = \frac{6!}{3!(6-3)!} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20\][/tex]

The theoretical probability that the first 3 students called are all girls is the ratio of the number of ways to choose 3 girls to the total number of ways to choose any 3 students. Thus, the probability \(P\) is:

[tex]\[P = \frac{\binom{6}{3}}{\binom{12}{3}} = \frac{20}{220} = \frac{1}{11}\][/tex]

Answer:

2x−5y=12

y = 2/5x + −12/5

Answer is x = 5/2y + 6 because....

First,  Add 5y to both sides.

2x − 5y + 5y = 12 + 5y

Then, Divide both sides by 2.

[tex]\frac{2x}{2} = \frac{5y+12}{2}[/tex]

Therefor, your answer is going to be x = 5/2y + 6

* Hopefully this helps:) Mark me the brainliest:)!!!

Answer:

2/5

Step-by-step explanation:

We are given the following equation of a line and we are to tell the slope of the line:

[tex]2x-5y=12[/tex]

We know that the standard equation of a line is given by:

[tex] y = m x + c [/tex] where m is the slope of the line.

So re-writing the given equation in the standard form:

[tex]y=\frac{2}{5} x-\frac{12}{5}[/tex]

Therefore, 2/5 is the slope of the line.

Answer:

Step-by-step explanation:

Look at the picture.

Freya begins started with 200 yards.

Freya then increased her distance by adding five yards a day for two days.

x = 200 + (n - 1)5.

[x = The distance Freya sprints on day 21]

x = 200 + (21 - 1)5

x = 200 +  (20) 5 = 300 yards

Answer:

[tex] a _ n = 200 + ( n - 1 ) 5 [/tex]

Step-by-step explanation:

We are given that initially, Freya started with sprinting 200 yards and then gradually increased the distance by adding 5 yards a day for 21 days.

So our initial value for distance is [tex]a_1=200[/tex]

and since she keeps on adding 5 yards everyday to her distance so this will be our common difference.

Therefore, the explicit formula will be:

[tex]a_n=200+(n-1)5[/tex]

[tex]\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}[/tex]

[tex]\bf ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}[/tex]

[tex]\bf ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}[/tex]

now with that template in mind

[tex]\bf h(x)=\stackrel{A}{2}|\stackrel{B}{1}x+\stackrel{C}{3}|\stackrel{D}{-1}\qquad \qquad \stackrel{\textit{C=C-2 a translation to the right}}{h(x)=2|x\boxed{+3-2}|-1} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill h(x)=2|x+1|-1~\hfill[/tex]

Using shifting concepts, it is found that the equation after a translation of 2 units to the right is:

d. f(x)=2|x+1|−1

The parent function is:

[tex]h(x) = 2|x + 3| - 1[/tex]

Shifting a function 2 units to the right, the equivalent function is:

[tex]f(x) = h(x - 2)[/tex]

Then:

[tex]h(x - 2) = 2|x - 2 + 3| - 1[/tex]

[tex]f(x) = 2|x + 1| - 1[/tex]

Thus, the function is:

d. f(x)=2|x+1|−1

A similar problem is given at https://brainly.com/question/24465194

So, you would reflect it over the y-axis first. (x,y)->(-x,y) and get A’ (1,2) B’ (2,6) C’ (4,4). Then, you rotate 90 degrees clockwise (x,y)->(y,-x). So, A”(2,-1) B” (6,-2) C” (4,-4). Hope this helps.

Answer:

Step-by-step explanation:

A(-1, 2), B(-2, 6), C(-4, 4)

You got the reflection part correct.

A'(-1, -2), B'(-2, -6), C'(-4, -4)

To rotate 90° clockwise, apply the following transformation:

A(x, y) = A(y, -x)

A"(-2, 1), B"(-6, 2), C"(-4, 4)

Answer:

AB = (2+2√3)r

Step-by-step explanation:

All three sides of an equilateral triangle equals 60° each.

Given that the circles are equal and are inscribed in a triangle, the angle bisectors pass right through the center of the circle present in front of that angle.

For example a figure has been attached with the answer, where angle bisectors make a triangle with center of the circle and a perpendicular projection of the center on side AB.

Finding AB:

Let us divide the side AB into three parts. One is the line joining the center of the two circles which is = 2

Then we have two equal parts, each joining one vertices with the center of the circle.

Let us assume that there is a point P on the side AB which forms a line segment PO₁ ⊥ AB.

We have the right angled triangle APO₁. Angle A = 30°    PO₁ = r

let the base AP = x

We know that tan 30° = perp/base

1/√3 = r/x

=> x = √3  r

Hence Side AB = √3  r + 2r + √3  r

AB = (2+2√3)r