Prove: 45= m/ZXY
Complete the proof. Number your reasons in the textbox below.

Step-by-step explanation:

see photo for detailed analysis

The real number of the given expression is a=-2.

Given that the expression is [tex]\frac{1}{a^3+7}-7=\frac{-a^3}{a^3+7}[/tex]

Real numbers is known as the union of both rational and irrational numbers. Real numbers can be both positive or negative and are denoted by the symbol “R”.

To compute the value of a.

In the given expression multiply both sides with (a³+7) as

[tex]\frac{(a^3+7)}{a^3+7}-7=\frac{-a^3(a^3+7)}{a^3+7}[/tex]

Simplify the expression as,

1-7(a³+7)=-a³

Expand out terms of the left hand side

1-7a³-49=-a³

-7a³-48=-a³

Taking out minus common from both sides and cancel them

-(7a³+48)=-(a³)

7a³+48=a³

Add -a³-48 on both sides

7a³+48-a³-48=a³-a³-48

6a³=-48

Divide both sides with 6

(6÷6)a³=(-48÷6)

a³=-8

write -8 in the expansion form which is (-2)×(-2)×(-2)=-8

a³=(-2)³

From above it says that

a=-2

Hence, real number that satisfy [tex]\frac{1}{a^3+7}-7=\frac{-a^3}{a^3+7}[/tex] is a=-2.

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Answer:

22.5 hours

Step-by-step explanation:

One cubic foot of water contains 7.48 gallons, so 40 cubic feet of water would equal 7.48 × 40, or 299.2 gallons. So the pumping rate is 299.2 gallons per minute. Multiplying 299.2 by 60, we have

299.2 × 60, or 17952 gallons per hour. Finally, divide 403,920 by 17,952 to find the number of hours to remove all the water: 403,920 ÷ 17,952 = 22.5 hours

Answer:

Each point (or pair) in a proportional relationship must share the same difference is the false statement.

The 24 walls must paint by each volunteer if the work is divided evenly and the club has 36 volunteers.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

As part of a community-service project, a local club has decided to paint 864 walls across town. The club has 36 volunteers.

Total number of volunteers = 36

Number of walls = 864

The number of walls each volunteer paint can be expressed as a fraction:

= 864/36

= 24

Thus, the 24 walls must paint by each volunteer if the work is divided evenly and the club has 36 volunteers.

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According to the commutative property of multiplication, changing the order of components has no effect on the product. The correct option is B.

According to the commutative property of multiplication, changing the order of components has no effect on the product.

For example: 4 × 8 = 8 × 4 = 32

The equation that correctly shows the Commutative Property of Multiplication is,

5 × 1 3 = 5 × 1 3

Hence, the correct option is B.

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Answer:

x=1/5

Step-by-step explanation:

You have to isolate x. First, add the one to the sider to give you 5x=1. In order to get the x by itself, you have to divide the 5 into both sides. In the end, this gives you x=1/5.

The probability that a participant successfully catches 3 rainbow trout, given that the participant was a woman is 0.0042.

P(woman) = 12/28

= 3/7

P(men) = 16/28

= 4/7

P(3 trouts) = P(3 trout | women)*P(woman) + P(3 trout | men)*P(man)

= P(3 trout | women)*(3/7) + (15C3 * (0.09^3)*(1-0.09)^(15*3))*(4/7)

= P(3 trout | women)*(3/7) + (0.00476)*(4/7)

P(woman | 3 trout) = P(3 trout | women)*P(woman) / P(3 trouts)

{P(3 trout | women) = p}

p*(3/7) / (p*(3/7) + (0.00476)*(4/7)) = 0.40

p*(3/7)/0.40 = (p*(3/7) + (0.00476)*(4/7))

p*((3/7)/0.40 - (3/7)) = (0.00476)*(4/7)

p = [(0.00476)*(4/7)] / [((3/7)/0.40 - (3/7))]

= 0.0042

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By finding the probability, we can expect that 2 out of the 30 students will win the prize.

First, we should get the probability of winning this game.

Here the students select two numbers out of 6, just to make the calculations let's say that these numbers are 1 and 2.

Now, we need to get these two numbers in two balls. The probability of getting the ball with the number 1 out of the 6 balls is:

p = 1/6

The probability of getting the ball with the number 2 out of the remaining 5 balls (because we already got one) is:

q = 1/5

The joint probability is then:

P = 2*(1/6)*(1/5) = 1/15.

Where the factor 2 comes to take in account the permutations, for the case where we first draw the number 2 and then the number 1.

Then the expected number of students that will win is equal to the probability times the total number of students:

(1/15)*30 = 2

So out of the 30 students, we can expect that 2 will win.

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The value of sin x in Q II is 0.86 .

This the field in Maths which deals with a right angled triangle and the other angles in the triangle.

It is given that cot = -0.59

cot x = cos x / sin x

Using online trigonometric calculator

sin x in Q II is 0.86 .

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A ratio shows how many times one number contains another.

Hence, the sand is in the ratio [tex]\frac{1}{6}[/tex] of the mixture is

[tex]\frac{1}{6}[/tex]×[tex]1800=300kg[/tex]

The Gravel is in the ratio [tex]\frac{2}{6}[/tex]×[tex]1800=600kg[/tex]

And the cement is in ratio [tex]\frac{3}{6}[/tex]×[tex]1800=900kg[/tex]

What is the ratio ?

A ratio is an ordered pair of numbers [tex]a[/tex] and [tex]b[/tex], written [tex]\frac{a}{b}[/tex] where [tex]b[/tex] does not equal [tex]0[/tex]. A proportion is an equation in which two ratios are set equal to each other.

Here the given ratio is [tex]1:2:3[/tex].

Here given that,

The dry concrete is   [tex]1800kg[/tex].

And the multiplication of the ratio is [tex]1[/tex]×[tex]2[/tex]×[tex]3=6[/tex]

Hence, the sand is in the ratio [tex]\frac{1}{6}[/tex] of the mixture is

[tex]\frac{1}{6}[/tex]×[tex]1800=300kg[/tex]

The Gravel is in the ratio [tex]\frac{2}{6}[/tex]×[tex]1800=600kg[/tex]

And the cement is in ratio [tex]\frac{3}{6}[/tex]×[tex]1800=900kg[/tex]

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Answer:34

Step-by-step explanation:

Giving away all that is not new or fav so 12 fav + 18 new + 4 which are new an favorite = 34

Answer:

22

Step-by-step explanation:

63 is the total

14 are new

8 are fav

14+8=22

Based on the amount of cash that Elias Rubio brings, we can calculate that his total cash deposit is $1,323

This can be found as:

= (75 x 1) + (78 x 5) + (83 x 10) + (80 x 0.25) + (32 x 0.10 or 10 cents) + (95 x 0.05 or 5 cents) + (5 x 0.01 or 1 cent)

Solving gives:

= 75 + 390 + 830 + 20 + 3.20 + 4.75 + 0.05

= $1,323

Remaining part of the question:

How much did he deposit in cash?

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Answer:

1) -
2) +

3) -
4) +

Step-by-step explanation:

сумма внутренних углов треугольника не должна превышать 180 градусов

If the subset y is the empty set, then the statement is false. That is the counterexample.

We know that for an invertible function, we always have that:

[tex]f(x) = y\\f^{-1}(y) = x[/tex]

Now, the range of f(x) is the set b. This means that the domain of the inverse is the set b. Such that:

f^{-1} is defined on b→a

Now we want to work on a subset y ⊆ b.

And here comes the problem.

The empty set {∅} is a subset of ay other set. So, if y is the empty set, there are no elements where we can evaluate the inverse function. From that counterexample, we conclude that the statement is false.

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Answer:

x = 10

Step-by-step explanation:

5(2x - 12) + 21 = 2x + 41 ← distribute parenthesis and simplify left side

10x - 60 + 21 = 2x + 41

10x - 39 = 2x + 41 ( subtract 2x from both sides )

8x - 39 = 41 ( add 39 to both sides )

8x = 80 ( divide both sides by 8 )

x = 10

Yes, they can be added and simplified further. 2√3 + 5√3 = 7√3 .

Take √3 as common factor:

2√3 + 5√3

(2 + 5)√3

7√3

The two irrational numbers sums to form another irrational number 7√3 . In decimals that is 12.12435...

[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Yes, The terms assigned above are alike so they can be added easily by simple algebric method where root number can be treated as a variable.

[tex]\qquad \sf  \dashrightarrow \: 2 \sqrt{3} + 5 \sqrt{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2 + 5) \sqrt{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 7 \sqrt{3} [/tex]

The table of values for the comparison of a function and its inverse function is shown in the image attached below.

An inverse function refers to a type of function that is obtained by reversing the operation of a given function (f(x)).

In Mathematics, a given function (f(x)) and its inverse function has the following property f⁻¹(f(x)) = x. By applying this property to the table (see attachment), we have:

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Answer:

C

Step-by-step explanation:

1.75n = 7 ( to isolate n divide both sides by 1.75 )

n = [tex]\frac{7}{1.75}[/tex] = 4

Answer:

c.)  Divide by 1.75

Step-by-step explanation:

Given equation:

⇒ 1.75n = 7

Here the coefficient of n which is 1.75 needs to be removed. There is only one way of doing that - by dividing both sides by 1.75.

When done so:

⇒ 1.75n/1.75 = 7/1.75

⇒ n = 4

The length and width of this rectangle are 15 cm respectively

The perimeter is given as:

Perimeter, P = 60

The greatest area is calculated as:

Greatest = (P/4)^2

Substitute 60 for P

Greatest = (60/4)^2

Evaluate the quotient

Greatest = 15^2

Evaluate the exponent

Greatest = 225 square centimeters

Hence, the greatest area is 225 square centimeters

We understand that the area is the greatest.

In such a scenario;

Length = Width

This means that:

Area =Length^2 =Width^2

So, we have:

Length^2 =Width^2 = 225

Take the square root

Length =Width = 15

Hence, the length and width of this rectangle are 15 cm respectively

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Answer:

Your classmate says that there is not enough information to determine whether the two triangles below are congruent. Is your classmate correct?

yes it is

The two triangles are congruent triangles by RHS theorem of congruent triangles

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the first triangle be represented as ΔMLJ

Let the second triangle be represented as ΔLJK

Now , the measure of ∠MLJ = 90°

The measure of ∠LJK = 90°

The measure of side MJ = measure of side LK

So , the two sides of the triangles are similar and they have a common hypotenuse

Therefore , the triangles are congruent by right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Hence , the triangles are congruent

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Answer: C. 7.5%

Solve as decimal

0.5*0.15=0.075

Move two decimal points over

0.075 -> 7.5

Change back to percent

7.5%

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:m\overbrace{DB}= 90 \degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \qquad \tt \rightarrow \: m \overbrace{DB} + m \overbrace{TB} = 180 \degree[/tex]

[ linear pair ]

[tex] \qquad \tt \rightarrow \: m \overbrace{DB} + 90 \degree = 180 \degree[/tex]

[tex] \qquad \tt \rightarrow \: m \overbrace{DB} = 180 \degree - 90 \degree[/tex]

[tex] \qquad \tt \rightarrow \: m \overbrace{DB} = 90 \degree[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The molar heat of fusion for substance X , given the data is 775.6 cal/mol

Mole = mass / molar mass

Mole = (326 / 58.45) moles

Q = n × ΔHf

4325.8 = (326 / 58.45) × ΔHf

4325.8 = (326 × ΔHf ) / 58.45

Cross multiply

326 × ΔHf = 4325.8 × 58.45

Divide both sides by 326

ΔHf = (4325.8 × 58.45) / 326

ΔHf = 775.6 cal/mol

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Answer:

X

Step-by-step explanation:

d) 5x ≥ 15

Let's solve your inequality step-by-step.

5x≥15

Step 1: Divide both sides by 5.

[tex]\frac{5x}{5} \geq \frac{15}{5}[/tex]

[tex]x\geq 3[/tex]

(Attachment #1)

e) 3(2x + 1) ≤ 15

Let's solve your inequality step-by-step.

3(2x+1)≤15

Step 1: Simplify both sides of the inequality.

6x+3≤15

Step 2: Subtract 3 from both sides.

6x+3−3≤15−3

6x≤12

Step 3: Divide both sides by 6.

[tex]\frac{6x}{6} \leq \frac{12}{6}[/tex]

[tex]x\leq 2[/tex]

(Attachment #2)

Answer:

2 sqrt(2)

Step-by-step explanation:

To simplify a square root

sqrt(8)

sqrt(4*2)

sqrt(4) sqrt(2)

2 sqrt(2)

Answer:

2√2

Step-by-step explanation:

√8 =[tex]\sqrt{4 \times 2}[/tex]

= 2√2 (√4 = 2)

Hence, 2√2 is the required answer.

The probability of selecting a jack, replacing the card, and then selecting a king is 1/169

In a standard deck of cards, we have:

Total = 52

Jack = 4

King = 4

The probability of each is:

P(Jack) = 4/52

P(King) = 4/52

So, we have:

P = 4/52 * 4/52

Simplify

P = 1/13 * 1/13

Evaluate

P = 1/169

Hence, the probability is 1/169

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