Simplify the given expression’s

( )

And

( )

Triangle classification will always help us to prove congruency in triangle. Each of the three angles in an acute triangle is acute. One right angle and two acute angles make up a right triangle. Additionally, an obtuse triangle has two acute angles and one obtuse angle.

The triangles are congruent when two sets of corresponding sides and the corresponding angles between them are in agreement. Two triangles that have a congruent angle in the middle and two congruent sides.

Instead of using the unit measure, it is based on the proportion of the side lengths to one another. As a result, triangles are categorized according to how many of their sides are the same length as one another or not at all equal.

Angles are another way to categorize triangles. Each of the three angles in an acute triangle is acute (less than 90 degrees). One right angle and two acute angles make up a right triangle. Additionally, an obtuse triangle has two acute angles and one obtuse angle (greater than 90 degrees).

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An infinite geometric series is the outcome of an unlimited geometric sequence. If the value of S = 12 and r = 1/6 then the value of a₁ = 10.

An infinite geometric series is the outcome of an unlimited geometric sequence. This series wouldn't have a finish. It is possible to calculate the sum of all finite geometric series. The terms in the sequence will grow steadily larger, but adding the larger numbers together will not provide a solution if the common ratio of an infinite geometric series is greater than one.

The sum of an infinite geometric series be S = a/1-r

S be the sum = 12

a₁ be the first term = ?

r -be the common ratio = 1/6

We know,

S = a₁/1-r

substitute the values in the above equation, we get

12 = a₁/1-(1/6)

simplifying the equation,

12 = 6a₁/5

a₁ = 60/6 = 10

If the value of S = 12 and r = 1/6 then the value of a₁ = 10.

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30m by 90m is the length and width of the sandy island beach snak shack.

What is a rectangle shape?

20 x 1 = 20

20 x .5 = 10

20 + 10 = 30

60 x 1 = 60

60 x .5 = 30

60 + 30 = 90..

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The complete question is -

Sandy Island Beach is building a new Snack Shack based on a scale drawing that is 20 centimeters by 60 centimeters and uses the scale 1 cm : 1.5 m.

According to the question, Let us assume the total number of students is [tex]100[/tex]. In which [tex]43[/tex] students own a CD player. And [tex]28[/tex] students own both CD player as well as MP3 Player.

Now, to calculate the probability that a student owns an MP3 player and also they own a CD player. It is clear from the given data, the percentage is higher than [tex]28[/tex] percent.

Using conditional probability rule:

[tex]P(MP3|CD) = \frac{P(MP3 and CD)}{P(CD)} = \frac{0.28}{0.43} = 0.65[/tex]

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

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The required value of x is 4 by using constant of proportion.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of y

When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion      —-- 1

Now, find k for given x = 2 and y = 6, we need to put these values in equation 1, i.e.

6 = k(2)

k = 6/2

k = 3

Further calculate x for given y = 12 and constant of variation = 3 i.e.

12 = (3)x

x = 4

Hence, the required value of x is 4.

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After calculating we have come to find that  [tex]\frac{1 + 2 \sqrt3 }{2}[/tex]  is the rationalized form of the expression 1/2 + √3

Rationalizing is the process of multiplying one surd by another similar surd to produce a rational number. The rationalizing factor is the surd used to multiply (RF).

We rationalize the denominator to make it easier to perform any calculation on the rational number. When we rationalize the denominator of a fraction, we remove any radical expressions from the denominator, such as square roots and cube roots.

We have been asked to rationalize 1/2 + √3

⇒ 1/2 + √3

=  [tex]\frac{1 + 2 \sqrt3 }{2}[/tex]

As the denominator is a rational number  1/2 + √3 has been rationalized

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The first five terms of the sequence are -3, -5, -7, -9, -11

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.

Given,

aₙ =-2 n-1

a1 = -2 - 1 = -3

a2 = -4 -1 = -5

a3 = -6 -1 = -7

a4 = -8 -1 = -9

a5 = -10 - 1 = -11

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Luis and Baca would be the same weight after 60 weeks of weightlifting.

A linear equation is one in which the highest power of the variable is consistently 1. A one-degree equation is another name for it. A linear equation with one variable has the formula Ax + B = 0, which is its standard form. x is a variable, A is a coefficient, and B is constant in this situation.

To create an equation that Luis and Baca can use to determine how long it will take for them to be the same weight:

Let the time taken by Luis and Baca to be of the same weight be x weeks,

Given:

Initial weight of Luis = 194 pounds

Initial weight of Baca = 218 pounds

Then,

Weight gained by Luis in x weeks = 0.6x pounds

Weight gained by Baca in x weeks = 0.2x  pounds

Total weight of Luis after x weeks = (194 + 0.6x ) pounds

Total weight of Baca after x weeks = (218 + 0.2x) pounds

For Luis and Baca to be of the same weight,

Total weight of Luis after x weeks = Total weight of Baca after x weeks

Therefore, we equate the total weight gained by Luis and Baca after x weeks to determine the value of x

⇒ 194 + 0.6x  = 218 + 0.2x

⇒ 0.6x - 0.2x =218 - 194

⇒ 0.4x = 24

⇒ x = 60

Hence, Luis and Baca would be the same weight after 60 weeks of weightlifting.

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Answer: coordinates would be 0,1 and 3,-3

Step-by-step explanation:

The correct option is (C) ∠ MJK ≅ ∠ MKJ by construction.

When two parallel lines have a transversal cutting those parallel lines, the alternate angle theorem holds true. According to the alternate angle theorem, all alternate angles are equal.

We have a similar circumstance here, where we are employing the alternate angle theorem approach to design and build two parallel lines. To prove that the two alternate angles are equal and the lines are parallel, we must first identify the two alternate angles.

The two alternate angles are:

∠ MLN and ∠ MJK

Therefore, for the lines, JK and LN to be parallel the two angles must be congruent.

Hence, ∠ MLN ≅ ∠ MJK

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The complete question is mentioned below:

In the straightedge and compass construction of the parallel line below, which of the following reasons can you use to prove that JK and LN are parallel?

A.  ∠ MLN ≅ ∠ MNL by construction.

B.  ∠ NLJ ≅ ∠ MJK by construction.

C.  ∠ MJK ≅ ∠ MKJ by construction.

D.  ∠ MLN ≅ ∠ MJK by construction.

ok:).

poop

.........

Answer:

x= -(2y+7)/(4)

Step-by-step explanation:

4x+2y=7

4x = -2y+7

x= -(2y+7)/(4)

Answer:

x = [tex]\frac{7-2y}{4}[/tex]

Step-by-step explanation:

4x + 2y = 7 ( subtract 2y from both sides )

4x = 7 - 2y ( divide both sides by 4 )

x = [tex]\frac{7-2y}{4}[/tex]

The relationship between the ∠4 and ∠6 is that both are alternate interior angle.

Given,

The angles = ∠4 and ∠6

Here,

The ∠4 and ∠6 lie on the opposite sides of the transversal and both are nonadjacent interior angles

So, ∠4 and ∠6 are alternate interior angle.

Hence, The relationship between the ∠4 and ∠6 is that both are alternate interior angle.

Complete question is:

Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

∠4 and ∠ 6

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Answer:

i think 10 is in between -8 and

Step-by-step explanation:

hope this

Place value is defined as the value of a digit in a number which depends on its position in the number. On the other hand, Total value is the product of a digit and its place value.

Rounding off entails changing a number into an approximation such that it has fewer significant numbers. To change the digit 5 in this question to 0, we will need to round off the given numbers to the most appropriate place value.

a. 478 578

We round off to the nearest thousands, this becomes 479 000

b. 353 897

We round off to the nearest tens of thousands, this becomes 400 000

c. 294 025

We round off to the nearest ones, this becomes 294 030

d. 500 000

The 5 in this value cannot be converted to 0 since 5 is the largest place value in the number.

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Answer:

B. will take 7.5 more days

Using technology, the weighted average ROR of the investment, rounded to the nearest tenth of a percent is 2.1%

What is the weighted average ROR?

The weighted average ROR means the rate of return of the four investments combined together to give a single return, which is computed as the sum of the RORs multiplied by the percentage of total portfolio invested in each security.

total investment=$2600+$3700+$575+$1225

total investment=$8100

% invested in each security=amount invested in each security/total investment

weighted average ROR=(1.7%*$2600/$8100)+(3.2%*$3700/$8100)+(12.9%*$575/$8100)+(-5.6%*$1225/$8100)

weighted average ROR=2.1%

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The dimensions of the sticker are 6 centimeters and 9 centimeters, respectively.

According to the statement, we find a rectangular sticker whose perimeter and area are known. By the perimeter and area formulas of the rectangle we have the following system of equations:

x · y = 54                      (1)

2 · (x + y) = 30              (2)

By (2):

2 · x + 2 · y = 30

2 · x = 30 - 2 · y

x = 15 - y

(2) in (1):

(15 - y) · y = 54

15 · y - y² = 54

y² - 15 · y + 54 = 0

(y - 9) · (y - 6) = 0

The solutions are y₁ = 9 and y₂ = 6, respectively.

By (2):

x₁ = 15 - y₁

x₁ = 15 - 9

x₁ = 6

x₂ = 15 - y₂

x₂ = 15 - 6

x₂ = 9

The solutions are x₁ = 6 and x₂ = 9, respectively.

The dimensions of the sticker are 6 centimeters and 9 centimeters, respectively.

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Answer:

The product of 6 and Gail’s height is 66

Use g to represent Gail’s height

Step-by-step explanation:

The equation of the line which is perpendicular to 2x - y = 4 and passing through (4, 1) will be y = (-1/2)x + 3

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given below.

2x - y = 4

Then the slope of the perpendicular line will be

y = 2x - 4

m = 2

Then the equation of line will be

y = -(1/2)x + d

Then the line is passing through (4, 1), then we have

1 = -(1/2)4 + d

3 = d

The equation of the line which is perpendicular to 2x - y = 4 and passing through (4, 1) will be y = (-1/2)x + 3

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Answer:

1)  y = 6

2) Paul has 20 quarters

Step-by-step explanation:

Answer:

6 inches

Step-by-step explanation:

it's just 36/6 which equals 6

Answer: C

Step-by-step explanation:

A says an odd number (neg) + (neg)+ (neg) = positive and that is not right

B. quotients are not always positive

C.  A even number of negatives (neg) + (neg) = a positive

D. is not true

ll and lll is the answer.      

never said anything about

Given the area, the equation that Noor should use to determine the width of pen is x² + 3x = 70.

The length and width of the rectangular pen are 10m and 7m respectively.

The area of a rectangle is expressed as;

A = l × w

Where l is length and w is width.

Given the data in the question;

Let the width of the rectangular pen be 'x'

To determine the equation that Noor will use to find the width of the pen, plug the values into the equation above.

A = l × w

70 = (x+3) × x

70 = x² + 3x

x² + 3x = 70

We can go further and solve for the width of the pen.

x² + 3x = 70

x² + 3x - 70 = 0

Factor sing AC method; find two integer whose addition gives 3 and multiplication gives -70.

-7 and 10

(x-7) (x+10) = 0

x - 7 = 0, x + 10 = 0

x = 7, x = -10

But the dimension of the width can not be negative.

Hence

x = 7

Width = x = 7m

Length x + 3 = 7 + 3 = 10m

Given the area, the equation that Noor should use to determine the width of pen is x² + 3x = 70.

The length and width of the rectangular pen are 10m and 7m respectively.

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Answer:

5

Step-by-step explanation:

it's because one shelf is 40 then the second shelf is 80 and then the third is 5.

The interpretation of the interval is that the solution set is all real numbers equal or greater to -4.

The standard interval notation of an interval of lower bound a and upper bound b is given by:

[a,b].

For the interval given in this problem, we have that:

Hence the interpretation of the interval is that the solution set is all real numbers equal or greater to -4.

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The runner completes a 10 miles race in 16 minutes.

According to the question we have been given that,

Runner takes 8 minutes to complete = 5 miles race

We need to find that if the runner is in the same pace then how many miles the runner completes in 16 minutes

This multi-step problem can be solved using the unitary method. That is,

              8 minutes = 5 miles

              1 minute = 5/8 miles          

             16 minutes = 5/8*16 miles

                                  = 5*2 miles

                                  = 10 miles

Hence runner completes a 10miles race in 16 minutes

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Each neighbourhood will receive 23.34 pands.

So, 39¼ + 17⅕ + 52½ + 7¾.

Now, solve the above mathematical operation as follows:

LCM of 4, 5, 2, and 4: 20

Now,

Now, divide 116.7 by 5:

Therefore, each neighbourhood will receive 23.34 pands.

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