Multiply the rational expressions 2x^2 - 4x - 6 x^2 - 4 ——————- • ——————— x + 2 2x^2 + 2x

Answer:

1/4

Step-by-step explanation:

Let's call the aces for hearts, diamonds, clubs, and spades. So,  are red and [tex] c, s[/tex] is black.

Since the first card is replaced, the two picks are identical. This means that the sample space is given by all the possible couple

There are 16 such couples (we have four choices for the first card, and the same four choices for the second card). Now let's compute the odds in our favor to deduce the probability of winning:

If we want a player to draw two cards of the same color, the following couples are good:

so 8 possible couples over 16. This means that a player's probability of drawing two cards of the same color is 8/16 = 1/2.

Similarly, the probability of drawing a red ace first and then a black ace is represented by the following couples:

which are 4 over the same 16 as above, thus leading to a probability of 4/16 = 1/4.

Answer:

Num. 2: A = 25, Num. 3 = 63, Num. 4 = 80

Step-by-step explanation:

I'll help with as many as I can, so a few of them I won't be able too answer. You should re-post those later. Good luck, hope this helps.

For number 2:

First, turn the triangle into a rectangle by cutting it in half and attaching it to the other half so it forms a rectangle.

Since you cut the triangle in half, you also have to split 5 in half, so the bottom length is now 2.5.

Now, simply multiply 2.5 by 10, and you have the area for number 2.

The area for number 2 is 25.

For number 3:

This one is much easier. Just think of the shape as a normal square that has been tipped to the side. That means that you would solve for area the same way: 9 x 7, which means that the area for number 3 is 63.

For number 4:

This one is also easy. Simply cut, and paste. Now the right side is 10, and the top side is 8. Multiply, and the area will be 80 m.

Please re-post 1 and 5, as I am not able to solve them. Sorry this answer took so long!

Answer:

-$12

Step-by-step explanation:

Working backwards from the $63, you need to add back what was withdrawn and subtract what was deposited.

63+75+9+41+85-285= -$12

Answer:

x = 145

Step-by-step explanation:

The angles are same side exterior angle and same side exterior angles are supplementary

x +35 =180

Subtract 35 from each side

x = 180-35

x =145

Answer:

x=145

Step-by-step explanation:

180 -35 = 145

angle in a straight line add up to 180

x=145

F angle /corresponding angle are the same

Answer:

Option d) 2.1 + 2x = 7.5

Step-by-step explanation:

An isosceles triangle is a triangle with two equal sides.

Perimeter of a triangle is some of all the 3 sides.

Let the equal sides be x

Let the third side be y

Therefore,

              Perimeter = x + x + y

                         7.5 = 2x + y    

                          7.5 = 2x + 2.1                    [ given shortest side, y = 2.1m ]

Answer:

4th answer

Step-by-step explanation:

g(h(x)) means to put the formula for h(x) into the formula for g(  ).

[tex]g(h(x))=g(2x-2)=-3(2x-2)^3-2(2x-2)^2\\=-3(8x^3-24x^2+24x-8)-2(4x^2-8x+4)\\=-24x^3+72x^2-72x+24-8x^2+16x-8\\=-24x^3+64x^2-56x+16[/tex]

Cubing the binomial 2x - 2 can take some time!

Answer:

D.

Step-by-step explanation:

Standard Form (Quadratic): [tex]y=ax^2+bx+c[/tex]

Vertex Form (Quadratic): [tex]y=a(x-h)^2+k[/tex]

Intercept Form (Quadratic): [tex]y=a(x-p)(x-q)[/tex]

      p,q are x-intercepts

x-intercepts given in graph: -2,4

[tex]y=a[x-(-2)](x-4)[/tex]

eqn 1: [tex]y=a(x+2)(x-4)[/tex]

Plug in the given point to find 'a' : (3,-5)

[tex]-5=a(3+2)(3-4)[/tex]

[tex]-5=a(5)(-1)[/tex]

[tex]1=a[/tex]

Substitute 'a' in to eqn 1.

[tex]y=1(x+2)(x-4)[/tex]

eqn 2: [tex]y=(x+2)(x-4)[/tex]

Expand eqn 2. (can use FOIL)

[tex]y=x^2-2x-8[/tex]

Answer and Step-by-step explanation:

The last answer choice is correct.

Set the product of 7 and 24 equal to the product of 8 and x, and then solve for x

The process being used in the last answer choice is called Cross multiplication, and is used to find the unknown value in fractions.

[tex]\frac{7}{8}[/tex] × [tex]\frac{x}{24}[/tex]

7 × 24 = 8x

168 = 8x

21 = x

#teamtrees #PAW (Plant And Water)

Answer:

a

Step-by-step explanation:

follow the proportions

Answer:

A

Step-by-step explanation:

Answer:

XY=6

Step-by-step explanation:

13-7=6

Answer:

XY = 6

Step-by-step explanation:

We know that the whole line (XZ) is equal to 13, and we know that YZ + XY is equal to XZ.

XZ = XY + YZ

13 = XY + 7

6 = XY

Hope this helped :)

Answer:

6 sqrt(3) = x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hyp

sin 60 = x/12

12 sin 60 =x

12 ( sqrt(3)/2) =x

6 sqrt(3) = x

Answer:

x=6[tex]\sqrt{3}[/tex]

Step-by-step explanation:

take 60 degree as reference angle

using sin rule

sin 60=opposite/hypotenuse

[tex]\sqrt{3[/tex]/2=x/12

do cross multiplication

2*x=12*[tex]\sqrt{3}[/tex]

x=12[tex]\sqrt{3}[/tex] /2

x=6[tex]\sqrt{3}[/tex]

Answer:

∅ ≈ 34º

Step-by-step explanation:

sin = opp/hyp

∅ = arcsin opp/hyp

∅ = arcsin 14/25

Use calculator

∅ = 34.055797742567906

∅ ≈ 34º

Answer:

is 55

Step-by-step explanation:

×[tex]\frac{x}{1}*\frac{14}{25}[/tex]⇒0.56

cos0.56

55

Answer:

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

12-7=5

7-12=-5

If this helps please mark as brainliest

Arithmetic

7-12

Meaning, 12 less than 7.

7-12=-5

Answer:

x = 121°

Step-by-step explanation:

∠ 1 + 115° = 180°

∠ 1 = 180 - 115

∠ 1 = 65°

∠ 2 + 304° = 360°

∠2 = 360 - 304

∠ 2 = 56°

∠ 1 + ∠ 2 + ∠ 3 = 180°

65° + 56 ° + ∠ 3 = 180°

∠3 = 180 - 65 - 56

∠ 3 = 59°

∠3 + x = 180°

59° + x = 180°

x = 180 - 59

x =  121 °

Answer:

Aseem’s : 8.3, Stana’s : 11.6

Step-by-step explanation:

Aseem: x

Stana: 2x-5

X+2x-5=20

3x=25

X = 8.3

Answer:

y-8x+7=0

Step-by-step explanation:

slope(m)=8

using slope intercept form of equation of staright line we get

y=mx+b

y=8*x+b

y-8x=b ................  eq(i)

since the line include the point (2,9) it satisfies the euation,

here x=2 and y=9

equation: y-8x=b

9-8*2=b

9-16=-b

-7=b

substituting the value of b in eq(i) we get

y-8x=-7

y-8x+7=0   is a required equation of the line.

Answer:

-1 and 3

Step-by-step explanation:

The real roots of a function are located where the function passes through the x-axis. In this case, the function passes through x=-1 and x=3, making them the real roots of the function.

Answer:

B. [tex]^{5} P_{5}[/tex] × [tex]^{20} P_{15}[/tex]

Step-by-step explanation:

No. of students from first grade = 15

No. of students from second grade = 5

There are 5 rows of seats

Each row contains 5 seats

Total seats = 25

No. of ways for second-grade students to occupy the first row (i.e first 5 seats) = [tex]^{5} P_{5}[/tex]

Remaining seats = 20

So, now we are left with 15 first grade students  

So, No. of ways for first-grade students occupy remaining seats = [tex]^{20} P_{15}[/tex]

Using the counting rule principle,

No. of ways for the students can be seated if all of the second-grade students occupy the first row = [tex]^{5} P_{5}[/tex] × [tex]^{20} P_{15}[/tex]

So, Option B is the correct answer

Hence, no. of ways for the students can be seated if all of the second-grade students occupy the first row is ×

There are ¹⁵P₁₅ x ¹⁰P₅ possible way to seat, if all of the second-grade students occupy the first row.

A permutation in math is the number of ways in which a set of data or objects can be ordered or arranged, where the order matters.

Given that, a school bus has 25 seats, with 5 rows of 5 seats. 15 students from the first grade and 5 students from the second-grade travel in the bus.

Since you have to place all first-grade students in the first three rows,

Therefore,

For the 15 first-graders of the first three rows (15 seats), we have ¹⁵P₁₅ since all 15 places have to be occupied by all 15 first-graders.

Then we have 10 remaining seats left to be assigned to the 5 second-graders = ¹⁰P₅

We then multiply the permutation numbers of those two arrangements to get the total ways:

¹⁵P₁₅ x ¹⁰P₅

Hence there are ¹⁵P₁₅ x ¹⁰P₅ possible way to seat, if all of the second-grade students occupy the first row.

Learn more about permutation click;

https://brainly.com/question/30649574

#SPJ7

Refer to the attachment for complete calculation.

3²× 11^-9

Answer:

2m+8

Step-by-step explanation:

Answer:

y = 6·sin(3·(x - 1)) + c

Step-by-step explanation:

The general form of an equation for a sinusoidal function is presented ad follows;

y = a·sin(b·(x - h) + c

Where;

a = The amplitude of the equation

T = The period = 2·π/b

h = The phase shift

c = The vertical shift

From the question, we have;

a = 6,

2·π/3 = 2·π/b

∴ b = 3

h = 1

We get;

y = 6·sin(3·(x - 1)) + c.

Given:

Darcy harvests [tex]8\dfrac{3}{4}[/tex] acres of corn every [tex]\dfrac{5}{6}[/tex] of an hour.

Darcy harvests corn at a constant rate.

To find:

How many acres does she harvest per hour?

Solution:

We have,

Acres harvest in [tex]\dfrac{5}{6}[/tex] of an hours = [tex]8\dfrac{3}{4}[/tex]

Acres harvest in 1 hour = [tex]8\dfrac{3}{4}\times \dfrac{6}{5}[/tex]

                                      = [tex]\dfrac{32+3}{4}\times \dfrac{6}{5}[/tex]

                                      = [tex]\dfrac{35}{4}\times \dfrac{6}{5}[/tex]

Cancel out the common factors, we get

Acres harvest in 1 hour = [tex]\dfrac{7}{2}\times \dfrac{3}{1}[/tex]

                                      = [tex]\dfrac{21}{2}[/tex]

                                      = [tex]10\dfrac{1}{2}[/tex]

Therefore, she can harvest [tex]10\dfrac{1}{2}[/tex] acres of corn per hour.

The Answer is:

C.) (x+2)(x+3)

Answer:

(x-2)(x+3)

Step-by-step explanation:

1. Start by setting up the synthetic division. The numbers 1, -4, -11, and 30 go on the inside on the division. To get the number on the outside, set x-5 equal to 0. solve and get 5.

2. bring the one down. multiply the one and the five and place the number you get underneath the -4 in the next column. From there, add the two numbers in the column.

3. After adding those two numbers, put the number you get (which should be 1) directly below the 5. Now multiply that number and the 5 again.

4. Repeat these steps until you fill the spaces under the next two columns. If you do it correctly, the number at the bottom of the very last column should be 0. This zero is known as the remainder. The remainder is not needed to complete this problem.

 Now that you have finished synthetic division, it is time to set up the new equation you got.

5. The 1 on the bottom left will be your [tex]x^{2}[/tex] value, the next 1 will be your x value, and the -6 will be your c. You should get the equation [tex]x^{2} + x -6[/tex]

6. From here, factor the polynomial. The factors must add up to the middle value (1) and multiple to c (-6). The factors -2 and 3 add up to 1 and multiply to -6

Therefore, your answer will be (x-2)(x+3)

Complete Question

David bought a chain of fast food restaurants that operated 200 stores in 2009. The number of restaurants has grown at a rate of 12% annually.how many stores does the restaurant operate in 2020?

Answer:

[tex]N_{11} \approx 749[/tex]

Step-by-step explanation:

From the question we are told that:

Number of Fast Food Restaurants [tex]P=200[/tex]

Number of years [tex]t=11yrs[/tex]

Rate [tex]r=12%[/tex]

Generally the equation for the Number of restaurant in operation in 2020 is mathematically given by

 [tex]N(t)=Pe^{rt}[/tex]

Therefore

For t=11

 [tex]N_{11}=200*e^{0.12*11}[/tex]

 [tex]N_{11}=748.7[/tex]

 [tex]N_{11} \approx 749[/tex]