Which property justifies the following equation? 7[6+5+(-6)] = [6+(-6)+5] A.distributive B.commutative C.associative D.identity

Answer:  -1 < x < 3

Step-by-step explanation:

[tex]\dfrac{5}{(x+2)(4-x)}<1[/tex]

Step 1   The denominator cannot equal zero:

x + 2 ≠ 0    and     4 - x ≠ 0

     x ≠ -2                4 ≠ x

Place these restrictive values on the number line with an OPEN dot:

    <----------o-------------------o--------->

                -2                       4

Step 2   Find the zeros (subtract 1 from both sides and set equal to zero):

[tex]\dfrac{5}{(x+2)(4-x)}-1=0\\\\\\\dfrac{5}{(x+2)(4-x)}-\dfrac{(x+2)(4-x)}{(x+2)(4-x)}=0\\\\\\\dfrac{5-(-x^2+2x+8)}{(x+2)(4-x)}=0\\\\\\\dfrac{5+x^2-2x-8}{(x+2)(4-x)}=0\\\\\\\dfrac{x^2-2x-3}{(x+2)(4-x)}=0\\\\\\\text{Multiply both sides by (x+2)(4-x) to eliminate the denominator:}\\x^2-2x-3=0\\(x-3)(x+1)=0\\x-3=0\quad x+1=0\\x=3\quad x=-1[/tex]

Add the zeros to the number line with an OPEN dot (since it is <):

    <----------o-----o----------o----o--------->

                -2     -1            3      4

Step 3    Choose test points to the left, between, and to the right of the points plotted on the graph. Plug those values into (x - 3)(x + 1) to determine its sign (+ or -):

Left of -2: Test point x = -3: (-3 - 3)(-3 + 1) = Positive

Between -2 and -1: Test point x = -1.5: (-1.5 - 3)(-1.5 + 1) = Positive

Between -1 and 3: Test point x = 0: (0 - 3)(0 + 1) = Negative

Between 3 and 4: Test point x = 3.5: (3.5 - 3)(3.5 + 1) = Positive

Right of 4: Test point x = 5: (5 - 3)(5 + 1) = Positive

          +         +        -          +       +

    <----------o-----o----------o----o--------->

                -2     -1            3      4

Step 4  Determine the solution(s) based on the inequality symbol. Since the original inequality was LESS THAN, we want the solutions that are NEGATIVE.

Negative values only occur between -1 and 3

So the solution is:     -1 < x < 3

Answer and Step-by-step explanation:

A) Probability of taken two odd numbered token without replacement:

P(3) = 2/5 = 0.4

P(7) = 1/4 = 0.25

Construct a probability distribution:

 X          3          7

p(X)      0.4      0.25

B) Mean of the probability distribution:

E(X) = ∑xp

E(X) = 3*0.4 + 7*0.25

E(X) = 2.95

Variance of the probability distribution:

V(X) = [tex]\Sigma X^{2}p - [E(X)]^{2}[/tex]

V(X) = [tex]3^{2}*0.4+7^{2}*0.25 - (2.95)^{2}[/tex]

V(X) = 7.1475

Mean and variance of the probability distribution are 2.95 and 7.145, respectively.

Answer:  see graph

Step-by-step explanation:

Look at the Unit Circle to see the coordinates of the quadrangles.

Build a sine table for one period (0° - 360°).

    x        y = sin(x)          y² = (sin(x))²      (x, y²)    

    0°       sin(0°) = 0          (0)² = 0              (0°, 0)

   90°     sin(90°) = 1          (1)² = 1               (90°, 1)

  180°     sin(180°) = 0        (0)² = 0            (180°, 0)

  270°     sin(270°) = -1       (-1)² = 1             (270°, 1)

  360°     sin(360°) = 0       (0)² = 0            (360°, 0)

Now plot the (x, y²) coordinates on your graph.

Answer:

Value of F(2) = 12

Step-by-step explanation:

Given:

F(x) = 7x - 2

Find:

Value of F(2)

Computation:

F(x) = 7x - 2

putting x = 2

f(2) = 7(2) -2

f(2) = 14 - 2

f(2) = 12

So, Value of F(2) = 12

The question is not complete, so i have attached it.

Answer:

Option A - The data may not be reliable because there is an outlier.

Step-by-step explanation:

Looking at the question attached and the number of the gorrila vis - a - vis the time to interact, we can see that majority of the time to interact falls between 2.5 and 3.4.

However, we have a time of 8.3 days which is for gorrila 3.

This 8.3 is far higher than the range of the other values. Thus, we have an outlier because an outlier is a value is much more smaller or larger than most of the other values in a set of given data.

Thus, the data may not be reliable because there is an outlier.

Answer: "B. [tex]12p^6q^5[/tex]

Step-by-step explanation:

The given monomial : [tex]6a^2b^8c[/tex]

Degree of this monomial = Sum of powers of variables=2+8+1= 11

Let's check all the options

A   [tex]18t^8[/tex]

Degree = 8

B [tex]12p^6q^5[/tex]

Degree = 6+5 =11

C [tex]9a^5b^3c^2[/tex]

Degree = 5+3+2=10

D [tex]6w^4x^2y^3z^3[/tex]

Degree =4+2+3+3=12

We can see that only option B has degree 11.

So, the monomial has the same degree as [tex]6a^2b^8c[/tex] is "B. [tex]12p^6q^5[/tex] "

Answer:

number ten: x=5

number two: x=5³/5

Step-by-step explanation:

number ten:

4x + 3x - 9 = 26

4x + 3x = 26+9

7x = 35

x = 5

number two:

3x + 2x - 8 = 20

3x + 2x = 20+8

5x = 28

x = 5³/5

Answer:

17 quarters

Step-by-step explanation:

Let q = quarters

n = nickels

.25q + .05n = 5.90

we have 16 more nickels than quarters so add 16 quarters to make them equal

n = q+16

Substitute

.25q + .05( q+16) = 5.90

Distribute

.25q+.5q+.80=5.90

Combine like terms

.30q +.8 = 5.90

Subtract .8 from each side

.30q = 5.10

Divide each side by .3

.3q/.3 = 5.1/.3

q = 17

Answer:

Gisel have:

17

quarters

Step-by-step explanation:

1 nickel = 5 cents

1 quarter = 25 cents

1 dollar = 100 cents

5,90 dollars = 5,9*100 = 590 cents

then:

n = t + 16

5n + 25t = 590

n = quantity of nickels

t = quantity of quarters

5(t+16) + 25t = 590

5*t + 5*16 + 25t = 590

5t + 80 + 25t = 590

30 t = 590 - 80

30 t = 510

t = 510 / 30

t = 17

n = t + 16

n = 17 + 16

n = 33

Check:

5n + 25t = 590

5*33 + 25*17 = 590

165 + 425 = 590

Answer:

7y - 2y² - 4

Step-by-step explanation:

5y - 5y² - 5 + 2 + 2y + 3y² - 1

5y + 2y - 5y² + 3y² - 5 + 2 - 1   (combine like terms)

7y - 2y² - 4

Answer:

A. You can see which shape the bases are, how many bases there are, how many faces there are, and how many edges there are.

B. The bases are ABC and DEF, and I know because they are two congruent triangles on two opposite sides of the shape.

Answer:

4 cm

Step-by-step explanation:

Volume is given by area of cross section * height

_______________________________

For condition 1

height = 12 cm

base for area of cross section is 5*8

that is length 8 cm and width 5 cm

thus area of cross section = 5*8 = 40 cm square

volume of milk =  area of cross section* height of milk = 40*12 = 480 cm cube.

_______________________________________________

now milk is turned such that base of area of cross section will

15 by 8

that is length: 15 cm and width : 8 cm

thus area of cross section = 15*8 = 120 cm square

let the depth of milk be x

thus, volume of milk =  area of cross section* height of milk = 120*x

= 120x cm cube

Since milk is in the same container , its volume before and after the change of alignment of container will remain same

thus

120x cm cube = 480 cm

=> x = 480/120 = 4

Thus, depth under given situation will be 4 cm.

Answer:

c(1) = -15

c(n) = c(n - 1) + 4

Step-by-step explanation:

Given arithmetic sequence is,

-15, -11, -7, -3...........

Common difference between each successive and previous term is,

d = -11 - (-15)

  = -11 + 15

  = 4

Since recursive formula of the arithmetic sequence is represented by,

a₁ = First term of the sequence

a(n) = a(n - 1) + d

where a(n) is the nth term and a(n-1) is the previous term of the nth term.

Form the given sequence,

c₁ = -15

c(n) = c(n - 1) + 4

Answer:

D

Step-by-step explanation:

This would be using the SSS.

Which means knowing three sides.

The other options do not relate to any of the SSS, SAS, ASA, RHS

Hope that helped!!! k

Answer:

Option (3)

Step-by-step explanation:

This question is not complete; here is the complete question.

Triangle A″B″C″ is formed by a reflection over y = −3 and dilation by a scale factor of 2 from the origin. Which equation shows the correct relationship between ΔABC and ΔA″B″C″?

Coordinates of the vertices of the triangle ABC are,

A(-3, 3), B(1, -3) and C(-3, -3)

When triangle ABC is reflected over y = -3

Coordinates of the image triangle A'B'C' will be.

A(-3, 3) → A'(-3, -9)

B(1, -3) → B'(1, -3)

C(-3, -3) → C'(-3, -3)

Further ΔA'B'C' is dilated by a scale factor of 2 about the origin then the new vertices of image triangle A"B"C" will be,

Rule for the dilation will be,

(x, y) → (kx, ky) [where 'k' is the scale factor]

A'(-3, -9) → A"(-6, -18)

B'(1, -3) → B"(2, -6)

C'(-3, -3) → C"(-6, -6)

Length of AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

                      = [tex]\sqrt{(-3-1)^2+(3+3)^2}[/tex]

                      = [tex]\sqrt{52}[/tex]

                      = [tex]2\sqrt{13}[/tex]

Length of A"B" = [tex]\sqrt{(-6-2)^2+(-18+6)^2}[/tex]

                         = [tex]\sqrt{64+144}[/tex]

                         = [tex]\sqrt{208}[/tex]

                         = [tex]4\sqrt{13}[/tex]

Therefore, [tex]\frac{\text{AB}}{\text{A"B"}}=\frac{2\sqrt{13}}{4\sqrt{13}}[/tex]

[tex]\frac{\text{AB}}{\text{A"B"}}=\frac{\sqrt{13}}{2\sqrt{13}}[/tex]

[tex]AB(2\sqrt{13})=A"B"(\sqrt{13})[/tex]

Option (3) is the answer.

Answer:

330.00cm²

Step-by-step explanation:

find the area of both circles and subtract the smaller one from the bigger one.

area of a circle= πr²

π wasn't given so I will use 22/7

so area of the bigger circle = 22/7 × 11²

=22/7 × 121

=380.28cm²

area of the small circle=22/7 × 4²

= 22/7 × 16

= 50.28cm²

Area of the shaded portion = 380.28 - 50.28

= 330.00cm²

Step-by-step explanation:

Multiplying the vertex matrix with the matrix gives us a reflection matrix. The most common matrix reflections are seen as reflection in the x - axis as well as reflection in the y - axis.  

It can also be reflect by  90 degree or by 180 degree.

So, one way to remember the elements is by multiplying the given matrix by a unit matrix. And on the other hand you can remember the elements remembering by what degree we are reflecting the matrix. This way makes it easier to remember the elements.

The explanation regarding the elements of the reflection is explained below:

The following information should be considered:

Learn more: https://brainly.com/question/17961582?referrer=searchResults

Hey there! I'm happy to help!

The factors are the numbers you multiply to get 47. And they can't be fractions or numbers with fractions. They have to be integers (numbers without fractions).

So far, we see that we can multiply 1 and 47 to get 47. To see if there are any more, we see what numbers 1-10 we can divide by.

We cannot divide by 2 because 47 is odd.

We cannot divide by 3 because it gives us 15.6666...

We can't divide by 4 because 47 is odd.

We can't divide by 5 because 47 does not have a 5 or 0 in the ones place.

We can't divide by 6 because 47 is odd.

We can't divide by 7 because it gives us 6.714285....

We can't divide by 8 because 47 is odd.

We can't divide by 9 because it gives us 5.2222

And we obviously can't divide it by 10.

Therefore, the factors of 47 are 1 and 47. A number whose only factors are 1 and itself is called a prime number.

I hope that this helps! Have a wonderful day! :D

Answer: 47 is a prime number

The exponent of prime number 47 is 1 . Adding 1 to that exponent we get (1+1)=2

Factor of 47: 1, 47

Answer:

ok so

faf

Step-by-step explanation:

Factor 20x2 + 25x – 12x – 15 by grouping.

1. Group terms with common factors.

2. Factor the GCF from each group.

3. Write the polynomial as a product of binomials.

(20x2 – 12x) + (25x– 15)

4x(5x – 3) + 5(5x – 3)

(5x – 3)(

x +  

)

Answer:

32

Step-by-step explanation:

If y is 2 times as much as x, then 1 = 2

5 x 3 = 15 + 1 = 16

10 x 3 = 30 + 2 = 32, or 16 x 2 = 32

Please tell me if I'm wrong.

Answer:

29

Step-by-step explanation:

conjugate of a+ib=a-ib

conjugate of 2-5i=2+5i

(2+5i)(2-5i)=2²-(5i)²=4-25i²=4-25(-1)=4+25=29

Answer:

29

i had the same question and 29 was the right answer

Answer:

57 units^2

Step-by-step explanation:

First find the area of the triangle on the left

ABC

It has a base AC which is  9 units and a height of 3 units

A = 1/2 bh = 1/2 ( 9) *3 = 27/2 = 13.5

Then find the area of the triangle on the right

DE

It has a base AC which is  6 units and a height of 1 units

A = 1/2 bh = 1/2 ( 6) *1  = 3

Then find the area of the triangle on the top

It has a base AC which is  3 units and a height of 3 units

A = 1/2 bh = 1/2 ( 3) *3  = 9/2 = 4.5

Then find the area of the rectangular region

A = lw = 6*6 = 36

Add them together

13.5+3+4.5+36 =57 units^2

Answer:

Total Area = 57 sq. units

Step-by-step explanation:

will make it simple and short

Total Area = A1 + A2 + A3

A1 = (7 + 6) * 6/2 = 39 sq. units  (area of a trapezoid)

A2 = 1/2 (9 * 3) = 13.5 sq. units (area of a triangle)

A3 = 1/2 (3 * 3) = 4.5 sq. units  (area of a triangle)

Total Area = 39 + 13.5 + 4.5 = 57 sq. units

Answer:

1) The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle

2) The joint equations of diagonals are;

5·y = 56 - 6·x and 5·y = 6·x + 14.

Step-by-step explanation:

The equations are;

x² - 7·x + 6 = 0......................(1)

y² - 14·y + 40 = 0.................(2)

Factorizing equation (1) and equation (2) , we get

x² - 7·x + 6 = (x - 6)·(x - 1) = 0

Which are vertical lines at points x = 6 and x = 1

For equation (2) , we get

y² - 14·y + 40 = (y - 10)·(y - 4) = 0

Which are horizontal lines at point y = 4 and y = 10

The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle

2) The points of intersection of the equations are;

(1, 4), (1, 10), (6, 4), and (6, 10)

The end point of the diagonals are;

(1, 10), (6, 4) and  (1, 4), (6, 10)

The slope of the diagonals are;

(10 - 4)/(1 - 6) = -6/5 and (4 - 10)/(1 - 6) = 6/5

The equation of one of the diagonals are then, y - 10 = -6/5×(x - 1)

y = -6/5·x + 6/5 + 10 = -6/5·x + 56/5

5·y = 56 - 6·x

The other diagonal is therefore;

y - 4 = 6/5×(x - 1)

y = 6/5·x - 6/5 + 4 = 6/5·x + 14/5

5·y = 6·x + 14.

The joint equations of diagonals are therefore;

5·y = 56 - 6·x and 5·y = 6·x + 14.

Answer:

x-6/2=2x/7

7x-42=4x

7x-4x=42

3x= 42

X = 42/3

Hey there! I'm happy to help!

LENGTH OF CONVEYOR BELT

We are going to have to use some trigonometry. Let's think of this as a right triangle. The conveyor belt is the diagonal or the hypotenuse, while the ground is  and the height of the room make a right angle as the legs.

We have a sixty degree angle between the conveyor belt and the ground. This is means that the 21 foot height is the opposite side of our right triangle. So, we are dealing with the opposite and the hypotenuse, so we will use the sine. The sine of an angle is equal to the opposite length divided by the hypotenuse length.

We will set up the following equation and solve for the length of our conveyor belt (c).

[tex]sin60=\frac{21}{c}[/tex]

We multiply both sides by c.

[tex]c(sin60)=21[/tex]

We divide both sides by sin60.

[tex]c=\frac{21}{sin60}[/tex]

If we evaluate this with a calculator, we get that c is equal to 24.2487113..., or 24 when rounded to the nearest foot.

So, the supplies travel 24 feet from one end to the other.

DURATION OF TRAVEL

We want to find how long it takes the supplies to move across the conveyor belt. We see that every minute, it moves 75 feet. We want to see how many minutes it will take to move 24 feet, as that is the length of the conveyor belt as we previously solved. Let's set up a proportion.

[tex]\frac{feet}{minute} =\frac{75}{1} =\frac{24}{m}[/tex]

We cross multiply, giving us the following equation.

75m=24

We divide both sides by 75.

m=0.32

We want to round to the nearest tenth of a minute, so it will take 0.3 minutes for the supplies to move to the second floor.

Have a wonderful day! :D

Answer:

[tex]\displaystyle \boxed{y = -1\frac{1}{3}x + 22}[/tex]

Step-by-step explanation:

Parallel Equations have SIMILAR RATE OF CHANGES [SLOPES], so keep [tex]\displaystyle -\frac{4}{3}[/tex]as is and do this:

14 = −4⁄3[6] + b

14 = −8 + b

+ 8 + 8

_________

[tex]\displaystyle 22 = b \\ \\ y = -1\frac{1}{3}x + 22[/tex]

I am joyous to assist you at any time.

Answer:

The correct option is;

Formal

Step-by-step explanation:

The common levels of diction are formal, informal, and popular, with formal diction being the most selective of the word choices

Formal diction is used when when communicating in a situation that is formal

Formal diction uses languages that is devoid of slang and grammatically correct

Formal language is precise, grammatically correct language that does not use slang used in communication for legal, professional, business and academic purposes.

Answer:

225.78 grams

Step-by-step explanation:

To solve this question, we would be using the formula

P(t) = Po × 2^t/n

Where P(t) = Remaining amount after r hours

Po = Initial amount

t = Time

In the question,

Where P(t) = Remaining amount after r hours = unknown

Po = Initial amount = 537

t = Time = 10 days

P(t) = 537 × 2^(10/)

P(t) = 225.78 grams

Therefore, the amount of iodine-131 left after 10 days = 225.78 grams

Answer:

9, 13, 17, 21

Step-by-step explanation:

If x=2,

y=1+4(2)

y=9

This goes on, like a pattern. If x increases by 1, y inreases by 4. So, if y=3, x=13. If x=4, y=17, and so on.

Answer:

6 grams

Step-by-step explanation:

(3/2)*4 = 12/2 = 6

Answer:

[tex]\boxed{\sf 6 \ grams \ of \ food}[/tex]

Step-by-step explanation:

1 week = [tex]\frac{3}{2} g\ of \ the \ food[/tex]

Multiplying both sides by 4

4 weeks = [tex]\frac{3}{2} * 4[/tex]

4 weeks = 3 * 2 g of the food

4 weeks = 6 g of food

Answer:

AB = 72°

Step-by-step explanation:

The inscribed angle ADC is half the measure of its intercepted arc, thus

56° = [tex]\frac{1}{2}[/tex] ( m ABC ) ← multiply both sides by 2

112° = ABC

ABC = AB + BC = AB + 40, so

AB + 40 = 112 ( subtract 40 from both sides )

AB = 72°