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Decide whether there is enough information to prove a || b. If so, explain your reasoning using if-then statements. Parts a - f.

By using some exponent properties, we can simplify the expression to get:

√(100)² = 100

Here we will be using two exponent properties, these are:

√a = a^(1/2)

And:

(a^n)^m = a^{n*m}

The given expression here is:

√(100)²

Using the first property, we can rewrite this as:

( 100¹/²)²

And using the second property, we can rewrite as:

( 100¹/²)² = 100²*⁽¹/²⁾ = 100¹ = 100

That is the simplified expression.

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Answer: x = 1, -13

Step-by-step explanation:

      We will solve this by completing the square, as asked in the instructions. If we do this correctly, we will end up with a perfect square that will allow us to solve more easily.

Given:

      x² + 12x = 13

Set the equation equal to 0 by subtracting both sides of the equation by 13:

      x² + 12x - 13 = 0

Group the first two terms:

      (x² + 12x) - 13 = 0

Add and subtract [tex]\frac{b}{2} ^2[/tex] to the grouped terms:

      (x² + 12x + 36 - 36) - 13 = 0

Regroup the terms, move the negative out and simplify:

      (x² + 12x + 36) - 49 = 0

Factor the grouped terms (6 is our perfect square here):

      (x + 6)(x + 6) - 49 = 0

Add 49 to both sides of the equation and simplify the factors:

      (x + 6)² = 49

Square root both sides of the equation:

      x + 6 = 7           x + 6 = -7

Subtract 6 from both sides of each equation:

    x = 1           x - 13

Answer: D - 124°

Step-by-step explanation: Since y and a are vertical angles, we can determine that angle a is equal to 34°

90° + 34° = 124°

180° - 124° = 56°

Now we know the last angle in the triangle. Since this angle is on the same line as angle b, subtracting it from 180 would give us angle b

180° - 56° = 124°

Answer:

If an engineer typically makes 50% more than a school teacher, then the engineer's income is 150% of the school teacher's income. Because 100% represents the school teacher's income, and 50% represents the engineer's additional income, the sum is 100%+50% = 150%.

The engineer's income is also 1.5 times as large as the school teacher's income. This can be found by dividing the engineer's income percentage (150%) by the school teacher's income percentage (100%), which gives 150% / 100% = 1.5.

So the engineer's income is 150% of the school teacher's income, and it is 1.5 times as large as the school teacher's income.

- C

The value of the rational expression is q⁴ / 14p⁴

A rational expression is the ratio of two polynomials. If f is a rational expression, then f can be written in the form p/q where p and q are polynomials.

Given are rational expressions,

5pq / 16p³ ÷ 35p²q² / 8q⁵

Using identity, a/b ÷ c/d = a/b × d/c

5pq / 16p³ × 8q⁵ / 35p²q²

= 40q⁴ / 560p⁴

= q⁴ / 14p⁴

Hence, the value of the expression is q⁴ / 14p⁴

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Answer: True

Step-by-step explanation: Impulse is a vector quantity Like momentum, impulse is not fully described unless a direction is associated with it.

The Angle Bisector Theorem states that in a triangle, if a line bisects one angle of a triangle and is also a median to the side opposite of that angle, then the ratio of the length of the median to the length of the side opposite the angle bisected is equal to the ratio of the length of the other two medians.

Therefore, if the angle bisector divides the opposite side into segments 6 cm and 9 cm long, the ratio of the length of the median to the length of the side opposite the angle bisected is 6/9.

Let x be the length of the third side of the triangle.

The Angle Bisector Theorem states: (x/22.5) = (6/9)

Solving for x, we get: x = (22.5 * 6/9) = 15

So the length of the third side of the triangle is 15 cm.

This is the only possible length for the third side of the triangle because the Angle Bisector Theorem only holds if the angle bisector is also a median to the side opposite of that angle.

The correct equation of quadratic equation is,

⇒ f (x) = (x + 4)² - 3

We have to given that;

The table of values represents a quadratic function f(x).

And, Values are,

x           f(x)

−8          13

−7           6

−6           1

−5         −2

−4         −3

−3         −2

−2           1

−1           6

0            13

Now, By given options;

f (x) = (x + 5)² - 2

Put x = - 8, f (x) = 13;

13 = (- 8 + 5)² - 2

13 = 9 - 2

13 ≠ 7

From (ii);

f (x) = (x + 4)² - 3

Put x = - 7, y = 6;

6 = (- 7 + 4)² - 3

6 = 9 - 3

6 = 6

Hence, The correct equation of quadratic equation is,

⇒ f (x) = (x + 4)² - 3

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The alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.

State Alternate angle theorem?

The angles which are formed inside the two parallel lines, when intersected by a transversal, are equal to its alternate pairs. These angles are called alternate interior angles.

When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equal.

Angles that are on opposite sides of the transversal are called alternate angles. All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent.

In the above-given figure, you can see, two parallel lines intersected by a transversal AB.

So according to the alternate angle theorem,

m∠3 = m∠6

Now moving on to the students' explanations, both logics are correct.

Hence we can say that according to the alternate angle theorem,

m∠3 = m∠6

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Answer:

5x=33y,4x=21y I hope this is helpful

Answer: This is evaluataion, To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.

Step-by-step explanation: In this situation you are going to divide the numerator and denominator by 2. For example 2/8 makes 1/4. 1/4 is equivalent to 2/8 but not fully simplified.

Another way to solve this is to reduce to lowest terms. For example, 5/15 is reduced by dividing the numerator and denominator by 5 to get 1/3.

Divide the numerator and denominator to get a decimal form of the fraction or divide 5+2 by 3+6

Answer:

x = 5

Step-by-step explanation:

5x - 1 = 24

=5x = 24 + 1

=5x = 25

=5x/5 = 25/5

x = 5

Hence the value for x is 5.

Answer:

Step-by-step explanation: 5x - 1 = 24

                                         => 5x = 24 + 1

                                         =>  x = 25/5

                                         =>  x = 5

Therefore , solving the provided vector question we can say that Figure B best describes the voltage and current in parallel LC circuit

In mathematics, a vector is a quantity with magnitude and direction but no location. Acceleration and velocity are two examples of such numbers. A thing with both magnitude and direction is called a vector. A vector can be conceptualised geometrically as a directed line segment, the length of which corresponds to the magnitude of the vector, and the direction of which is denoted by an arrow.

Given :

Vector as given :

Figure A, Figure B , Figure C and Figure D

Voltage and current

parallel LC circuit

=>Iₙ * Eₙ = Iₙ

Size and direction are two independent characteristics of a quantity or phenomena known as a vector.

The phrase also describes how these numbers are represented mathematically or geometrically. In nature, vectors may be found in electromagnetic fields, weight, momentum, force, and velocity.

Here,

From observation we can say that ,

Figure B best describes the voltage and current in parallel LC circuit

Figure B

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Step-by-step explanation:

A. Hawa Enterprise is a small retail business located in Changlun, Kedah. Follows are information on bank transactions of Hawa Enterprise as at 31 July 2022:

a. Cash on the book was RM34,635.

b. Cash as shown on the bank statement was RM35,296.

c. A deposit of RM3,500, representing cash receipts on 31 July, did not appear on the bank statement.

d. Outstanding cheque include cheques No 2031, No 2558, and No 2783 with the amount respectively RM530, RM1,551 and RM2,100.

e. The bank collected RM810 on a note receivable for Hawa Enterprise. The bank charged a collection fee of RM10 which was credited to Hawa Enterprise’s account.

f. An NSF cheque for RM950 from a customer, En Mansor, was returned with the bank statement.

g. The bank paid correctly an amount of RM3,680 for cheque No 2805 which was recorded in a book as RM3,860. h. Bank service charges for July 2022 amounted to RM50.

REQUIRED:

Prepare the bank reconciliation statement for Hawa Enterprise as at 31 July 2022.

B. Beginning July 2022, Hawa Enterprise has established a petty cash fund for its small expenditures. The following transactions took place during the month of July:

5/7 Established a RM300 petty cash fund with cash withdrawn from the company’s current account.

30/7 The petty cash fund has RM12 remaining and is replenished. Expenditures for July were RM75 for supplies, RM60 (meals), RM80 (postage), RM50 (amenities) and RM25 (freight-in).

REQUIRED:

Prepare the journal entries for the above transactions.

Answer: No

Step-by-step explanation:

to be proportional, both numbers have to increase by the same number

because if u multiply 6 by 2 you get 12, but when you multiply 10 by 2 you get 20, not 60 it would be proportional if you said 6 and 10 in to 12 and 20 in

Answer:

13.25

Step-by-step explanation:

1. you have to subract the cost of the drink:

94.25-1.50=92.75

2.you have to divide to get the individual cost of pizzas by doing

92.75÷7=13.25

so therefore your answer is 13.25 per pizza

Answer: 68y+106=36-y

the answer is letter d)

if u arrange it correctly it will be -x +2y=2

-½x+y=1

then multiply -½ by the first equation and multiply -1 by the second equation..

then change the signs of the second equation

then cancel x .. then y =1

then substitute y with 1

..it won't be correct

Serena added 10 grams of sugar to 20 grams of water to make a sugar syrup.

The total amount of sugar syrup made is the sum of the weight of sugar and the weight of water, so:

10 grams (sugar) + 20 grams (water) = 30 grams (sugar syrup)

To find the percentage of sugar in the syrup, we can divide the weight of the sugar by the total weight of the syrup and multiply by 100.

% sugar = (weight of sugar / total weight of syrup) * 100

% sugar = (10 / 30) * 100 = 33.333 %

So the sugar syrup made by Serena contains 33.333% sugar by weight.

It's important to note that the sugar syrup doesn't have only sugar, it also have water, the sugar is just the main ingredient and the percentage of sugar is just the proportion of sugar within the syrup.

The percent of the baked foods that are cakes will be 25.33%

It should be noted that a percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

The percentage then refers to a component per hundred. The word percentage simply means per 100 and it is represented by %. In this situation, the bakery produces 280 loaves of bread and 95 cakes daily.

The percent of the baked foods that are cakes will be:

= Number of cakes / Number produced daily × 100

= 95 / (280 + 95) × 100

= 95 / 375 × 100

= 25.33%

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Answer:

Step-by-step explanation:

You want a couple of interior angles and the value of x given the parallelogram in the figure.

The diagonals of a parallelogram bisect each other, and divide the figure into two pairs of congruent triangles. Here, the congruent triangles of interest are ...

  ∆NKJ≅∆NML

In these triangles, that means ...

  ∠J ≅ ∠L = 50° = ∠NJK

  ∠K ≅ ∠M = 42° = ∠NKJ

The halves of diagonal JL are congruent, so we have ...

  4x -3 = 13

  4x = 16 . . . . . . . . add 3

  x = 4 . . . . . . . . . divide by 4

Answer:

( - inf, 5) (9, inf )

Step-by-step explanation:

The arrow(s) at the end of the line indicate that the highlighted green line does not stop at a specific number, hence the use of infinity signs (inf). If the arrow is going to the left on a line, then the value would be negative infinity. If it is going to the right, then it would be positive.

As for the space in between the green arrows pointing separate ways, there are two points, one which is positioned at the number 5 and the other at the number 9. Because there are two separate points which are both solid green, the use of parentheses is needed. The final answer is, as mentioned, ( - inf, 5) (9, inf ).

Answer:

380m

Step-by-step explanation:

1km=100m

0.38km=

0.38×1000/1=

380m

Answer:

Step-by-step explanation:

the answer will be option 4

The output voltage, in millivolts (mV), for the circuit would be equal to 1,350 millivolts.

An amplifier is defined as the electronic device that can be used to increase the electrical signal of a power source.

The output voltage of an amplifier= input voltage × gains.

We have been given that input voltage = 45 mV

The gain = 30

Therefore, the output voltage= 45×30

= 1350millivolts.

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The smallest possible value of the number that is an integer is -21

From the question, we are to determine the smallest possible value of the number

From the given information, we have that

"Twenty less than a number is more than twice the same number"
Let the number be x

Then,

we can write that

x - 20 > 2x

Now, we will solve for x

x - 20 > 2x

-20 > 2x - x

-20 > x

Therefore,

x < -20

The possible integers are -21, -22, -23, -24, -25, -26, ...

Then,

The smallest integer is -21

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Answer:

No, Jasmine is not correct. The Lowest Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. Multiplying the two numbers together is not always the correct method to find the LCM.

For example, the LCM of 5 and 8 is 40, but the product of 5 × 8 = 40 is not the LCM.

A more accurate way of finding the LCM is by using the prime factorization of the numbers. By finding the prime factorization of the two numbers, you can take the highest exponent of each prime factor and multiply them together. The result of that multiplication is the LCM of the two numbers.

In this case, the prime factorization of 5 is 5 and 8 is 2^3. The LCM of 5 and 8 is 2^3*5 = 40. So Jasmine's claim that 5 x 8 = 40 and the LCM of 5 and 8 is 40 is not correct.

Answer:990

Step-by-step explanation:10%=0.1

X*0.1=99

99/0.1=990

x=990