What are the missing parts that correctly complete the proof?


Drag the answers into the boxes to correctly complete the proof.

(Please refer to the images provided for the answer options and equation image.)

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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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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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:

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

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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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]

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

Answer: X = 1

Step-by-step explanation:

25/50 = 4x/8

First, multiply both sides by 8, therefore, the 8 on the right side will be canceled out.

25*8/50 = 4x*8/8

25*8/50 = 4x

25*8 = 200

200 divided by 50 = 4

4 = 4x

After that, you just need to divide 4 on both sides, therefore, the 4 on the right side will cancel out.

4/4 = 4x/4

1 = x

X = 1

Hope I helped! :]

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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Answer:

1) -
2) +

3) -
4) +

Step-by-step explanation:

сумма внутренних углов треугольника не должна превышать 180 градусов

Answer: [tex]x=-\frac{5}{4}[/tex] and [tex]x=-2[/tex]

Step-by-step explanation:

To factor an equation in the form of [tex]ax^2+bx+c[/tex] you need to find the value of [tex]ac[/tex]. So first solve for that

[tex](4)(10) = 40[/tex]

Now we need to find two numbers that add up to b and multiply together to make ac. In this case those numbers are 5 and 8 since 5+8=13 and (5)(8)=40

Now split 13x into 5x+8x and solve by grouping

[tex]4x^2+5x+8x+10\\(4x^2+5x)+(8x+10)[/tex]

Factor out the GCF in each quantity

[tex](4x^2+5x)+(8x+10)\\x(4x+5)+2(4x+5)[/tex]

Now group x+2 together

[tex](x+2)(4x+5)[/tex]

Finally, set each factor equal to 0 and solve for x

[tex]x+2=0\\x+2-2=0-2\\x=-2\\\\\\4x+5=0\\4x+5-5=0-5\\4x=-5\\\frac{4x}{4} =\frac{-5}{4} \\x=-\frac{5}{4}[/tex]

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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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%

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)

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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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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Step-by-step explanation:

see photo for detailed analysis

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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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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The number of seconds it takes for the waste to hit the ground for the given function is: 5 seconds.

We are given the function of height to time as, h(t) = -16t² + initial height, and we have the following:

Plug in the values into the equation of the function

0 = -16t² + 400

Solve for t

0 - 400 = -16t²

-400 = -16t²

-400/-16 = t²

400/16 = t²

√(400/16) = t

20/4 = t

5 = t

t = 5

The number of seconds it takes is: 5 seconds.

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If she rides for 6 more days, what is the average number of miles she would have to ride each day to meet her goal is 4.7

We have given that,

Bilquis wants to ride her bicycle 47.6 miles this week. She has already ridden 8 miles.

We have to determine that If she rides for 6 more days, what is the average number of miles she would have to ride each day to meet her goal.

Based on the given conditions, formulate: 8+4x=26

Rearrange unknown terms to the left side of the equation:4x=26-8

Calculate the sum or difference:4x=18

Divide both sides of the equation by the coefficient of the variable:4x/4=18/4

Calculate the product or quotient:x=18/4

We get the result:4.7

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Answer: The answer is 6.6

Step-by-step explanation:

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:

X

Step-by-step explanation:

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.

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

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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