Exterior angle, theorem, and triangle sum theorem

The value of the expression given as (3x + 2.05) + (-x + 1.09) + (2x) + (x) is 5x  + 3.14

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

(3x + 2.05) + (-x + 1.09) + (2x) + (x)

Start by opening the brackets

(3x + 2.05) + (-x + 1.09) + (2x) + (x) = 3x + 2.05 - x + 1.09 + 2x + x

Next, we collect the like terms

(3x + 2.05) + (-x + 1.09) + (2x) + (x) = 3x - x + 2x + x  + 2.05 + 1.09

Next, we evaluate the like terms

(3x + 2.05) + (-x + 1.09) + (2x) + (x) = 5x  + 3.14

Hence, the value of the expression is 5x  + 3.14

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Possible question

What is (3x + 2.05) + (-x + 1.09) + (2x) + (x)

Answer:

slope(m) is -4

Step-by-step explanation:

[tex]m=\frac{-17-(-1)}{5-1} \\\\m=\frac{-16}{4} \\\\m=\frac{-4}{1} \\\\m=-4[/tex]

now substitute with one of the points

y=mx+b

-1=-4+b

+4  +4

3=b

now you have both m and b

y=-4x+3

Answer: X=-8

Step-by-step explanation:

(x+8)(x+8)= 0

x=-8

there is a jar containing 27 black and 33 gold jelly beans. you will get a chance to draw 10 jelly beans at random from the jar. on each draw, 0.5 is the probability of drawing a gold jelly bean

How can I find the probability?

The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.

there is a jar containing 27 black

and 33 gold jelly beans.

you will get a chance to draw 10 jellybeans at random from the jar.

on each draw, what is probability of drawing a gold jelly bean

Add up the total number of jellybeans, 27 + 33 = 60

Divide the number of gold jellybeans by the total: 33/60 and reduce the fraction to 11/20

=0.55

Hence, there is a jar containing 27 black and 33 gold jelly beans. you will get a chance to draw 10 jelly beans at random from the jar. on each draw, 0.5 is the probability of drawing a gold jelly bean

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Answer: -1.4

Step-by-step explanation: simply subtract negative 185 by 1.7

The average fraction of students in  Mr. Zanker's class and  Mr. Haynes  who went on the field trip is 11/8.

From the question, the fraction of the students in Mr. Zanker's class that attended the field trip is  3/4.

The  fraction of the students in  Mr. Haynes class that attended the field trip is 5/8 .

Then the we can calculate the average fraction of student in the class of the two teacher is

= (3/4 + 5/8) = 11/8.

Therefore, the average fraction of the number of the student can be calculated as 11/8.

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Answer:

44, 54, 82. Acute

Step-by-step explanation:

x + x + 10 + 2x - 6 = 180 (Triangle Sum Theorem)

4x + 4 = 180 (Combine Like Terms)

4x = 176 (Subtraction Property of Equality)

x = 44 (Division Property of Equality)

Now that we have found the value of x, we need to substitute it with the provided angles.

∡1 = x = 44°

∡2 = x + 10 = 54°

∡3 = 2x - 6 = 2(44) - 6 = 82°

So, the answer is an Acute triangle (Option 4).

The most appropriate choice for HCF and LCM will be given by

The other number is 120

What is HCF and LCM?

HCF of two numbers A and B is the highest common factor of A and B. HCF is the highest number which divides both A and B.

LCM of two numbers A and B is the lowest common multiple of A and B. LCM is the least number which is divided by both A and B.

Here,

Let the other number be [tex]x[/tex]

HCF of 90 and [tex]x[/tex] = 30

LCM of 90 and [tex]x[/tex] = 360

Product  of HCF and LCM = 30 [tex]\times[/tex] 360

Product of 90 and [tex]x[/tex] = 90 [tex]\times[/tex] [tex]x[/tex]

By the problem,

                         90 [tex]\times[/tex] [tex]x[/tex] = 30 [tex]\times[/tex] 360

                                  [tex]x = \frac{360 \times 30}{90}[/tex]

                                  [tex]x = 120[/tex]

The other number is 120

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The given exponential function represents the growth in function with a percentage increase as 57.3%.

Given we have the exponential function as :

y=8800(1.573)ˣ

it is in the form of: y=k.aˣ

therefore, if a>2 then the function represents growth.

and if a<1 then the function represents decay.

now, x=1.573

1.573 > 1

so, the function represents change in growth.

therefore, 1.573 - 1

= 0.573

= 57.3%

hence the change in growth of the function is increased by 57.3%.

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The probability of happening of the events either B or C is [tex]\frac{2}{3}[/tex]

The probability that event A or event B happens is equal to the

probability that A happens plus the probability that B happens minus the probability that both happen. If events A and B are mutually exclusive, then the probability that event A or B happens is simply the sum of the probabilities. Given that

A = rolling a number greater than four

B = rolling an even number

C = rolling a multiple of 3

So,

P(A) = [tex]\frac{2}{6} =\frac{1}{3}[/tex]

P(B)=[tex]\frac{3}{6} =\frac{1}{2}[/tex]

P(C) = [tex]\frac{2}{6} =\frac{1}{3}[/tex]

Now, We have to find the probability of occurence of either event B or C

So, We know that

P(B or C ) = P(B) + P(C) + P(B or C)

P(B or C )= [tex]\frac{3}{6} +\frac{2}{6} -\frac{1}{6} =\frac{4}{6}[/tex]

P(BorC)= [tex]\frac{2}{3}[/tex]

Therefore, the probability of occurence of either event B or C is [tex]\frac{2}{3}[/tex].

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Answer: i believe the answer is 113.1 square feet

Step-by-step explanation: pi times 30

The average rate of change on the interval [2, 4] is 56

Here we have the function:

f(x) = 2x^3 + 1

And we want to find the rate of change on the interval [2, 4].

Remember that for a function f(x) the rate of change on an interval [a, b] is.

R = ( f(b) - f(a))/(b - a)

Then in this case, the rate of change is:

R = [ f(4) - f(2)]/[4 - 2] = ( 2*4^3 + 1 - 2*2^3 - 1)/2 = (4^3 - 2^3) = 56

So the rate is 56.

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The horizontal asymptote of the function is y=36 and vertical asymptote is x = 6 and its end behavior is f(x)→6.

As the independent variable approaches a certain value, the function approaches asymptotes, but does not cross them. They could be angled, vertical, or horizontal.

ascending asymptotes

There will be a vertical asymptote at x=a if the denominator factor of a rational function, (x - a), is not matched by the same factor in the numerator.

horizontal asymptotes:

When x is large, the value of a rational function approaches the ratio of the highest-degree terms in the numerator and denominator.

Given the function is f(x) = 6x/x-36

limx→±∞ 6x/x-36

= limx→±∞ 6/1-36/x

= 6 ⇒ horizontal asymptote: y = 6

Consider denominator = 0 ↔ x-36 = 0 ↔ x=36

limx→₊₂₅ 6x/x-36

= 6×36/0⁺ = ∞ ⇒ vertical asymptote: x = 36

End behavior of f(x):

As x → -∞ or x → ∞, f(x) → 6.

Hence we get the asymptote and the end behavior of the function.

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Answer: b 67

Step-by-step explanation:

180-152 is 28

28+85=113

180-113=67

Answer:

B) 67°

Step-by-step explanation:

 The exterior angle of a triangle equals the sum of opposite interior angles.

      85 +  x = 152

Subtract 85 from both sides,

                x = 152 - 85

                x = 67°

Answer:

Flynn stays at the trampoline park for an additional 3 hours.

Step-by-step explanation:

30 - 12 = 18

18 / 6 = 3

As for the "Select the equation that represents the given situation" I don't know what this really means so I didn't do that. Sorry.

Answer: You will need 185 square feet of wallpaper. It will cost you $125.

Step-by-step explanation:

18.5 x 10= 185

185/44= 4.2

4.2 is a little over 4 so you would need 5. You will have extra.

$25 x 5 rolls= $125

Answer:

1. 1/2

2. 1/5

Step-by-step explanation:

I used a calculator!

Answer:

1.3/6 or 1/2

2.1/5

Step-by-step explanation:

Just write that out, thats all the steps there is, 3/6 simplifies to 1/2 because they're equivalent

The distance that's required to be kept geo either side will be 4.258 inches.

From the information, Foster is centering a photo that is 7 1/5 inches wide on a scrapbook page that is 16 inches wide.

It should be noted that 7 1/2 is the same as 7.5. Therefore,we can subtract and this will be:

= 16 - 7.5

= 8.5

Since we know that the scrapbook is 8.5 inches wider,we will divide the width by 2 to get the distance of either side and this will be:

= 8.5 / 2

= 4.25

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Foster is centering a photo that is 7 1/5 inches wide on a scrapbook page that is 16 inches wide. How far from each side go the page did he put the picture?

After James adds stamps , the ratio of number of stamps in James's collection to the number of stamps in Roy's collection is 2:3 , the correct option is (D) 2:3  .

In the question ,

it is given that

Number of stamps that James has = 6 stamps

Number of stamps Roy has = 12 stamps

also , James adds 2 stamp to his collection ,

So number of stamps in James collection become = 8 stamps

So the ratio of number of stamps in James's collection to the number of stamps in Roy's collection is given by

= (number of stamps in James's collection)/(umber of stamps in Roy's collection)

Substituting the values , we get

= 8/12

Simplifying , we get

=2/3

Therefore , After James adds stamps , the ratio of number of stamps in James's collection to the number of stamps in Roy's collection is 2:3 , the correct option is (D) 2:3  .

The given question is incomplete , the complete question is

James has 6 stamps in his stamp collection. Roy has 12 stamps in his stamp collection. James adds 2 stamps to his stamp collection. After James adds these stamps, what is the ratio of the number of stamps in James's collection to the number of stamps in Roy’s collection?

(A) 1 : 2

(B) 2 : 1

(C) 3 : 2

(D) 2 : 3

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Answer:

Step-by-step explanation:

[tex]\displaystyle\\8 > \frac{x}{4}(x+5)-3[/tex]

Part a

[tex]f(g(x))=6\left(x-\frac{5}{6})+5=6x-5+5=6x[/tex]

Part b

[tex]g(f(x))=g(6x+5)=(6x+5)-\frac{5}{6}=6x+\frac{25}{6}[/tex]

Therefore, the functions are not inverses of each other since [tex](f(g(x)) \neq x[/tex].

The number of vegetable bearing plants are : 0.45x, where x is the total number of plants.

A fraction in mathematics represents a portion or element of the whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator. The numerator indicates the number of equal parts that were actually taken, whereas the denominator shows the total number of equal parts in the whole.

Let x be the initial plant population.

Now that 1/10 of plants bear fruit, the quantity of fruit-bearing plants is equal to 0.1x.

Plants remaining then equal x - 0.1x = 0.9x.

Once more, because half of the remaining plants give flowers, the number of flower-bearing plants is equal to 0.5(0.9x) = 0.45x.

As a result, the number of plants left is equal to 0.9x - 0.45x = 0.45x.

Given that all remaining plants produce veggies, the number of plants that do so is equal to 0.45.

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By doing multiply of = [tex]\frac{2}{3}[/tex] with =[tex]\frac{-3}{2}[/tex] we get -1 .

Algebra is one of the areas of mathematics where mathematical expressions can be used to represent situations or problems. In order for a mathematical statement to make sense, it must have mathematical operations like addition, subtraction, multiplication, and division as well as variables like x, y, and z. Every branch of mathematics, including calculus, trigonometry, and coordinate geometry, uses algebra. The equation 2x + 4 = 8 is a simple algebraic formula.Mathematical branch known as algebra deals with symbols and arithmetic operations on them. These symbols are referred to be variables since they lack set values. We frequently observe specific values that change in our day-to-day situations. However, there is a continuing need to depict these shifting values. These values are frequently represented in algebra by symbols, which are known as variables, such as x, y, z, p, or q. In order to determine the values, additional arithmetic operations such as addition, subtraction, multiplication, and division are performed on these symbols.

Given that : = [tex]\frac{2}{3}[/tex]  x ___ = -1

[tex]\frac{2}{3}[/tex] ×[tex]\frac{-3}{2}[/tex]

=-1

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Six students measure the acceleration of an object in free fall. The students want to state that the absolute deviation for each measured value x from the mean is at most d is 0.86.

The average of absolute deviations from a central point makes up the average absolute deviation (AAD) of a data collection. It is a statistical summary of the statistical variability or dispersion. A mean, median, mode, or the result of any other central tendency measure or any reference value associated with the specified data set can all serve as the central point in the general form. The mean absolute deviation and the median absolute deviation are part of AAD (both abbreviated as MAD).

Find the mean of the data set first, then use that value to calculate the mean absolute deviation of the data. Divide the total number of data values by the sum of the individual data values. Assess the magnitude of the absolute difference between each data point and and the mean.

The measured data is

x = [10.56, 9.52, 9.73, 9.80, 9.78, 10.91]

There are 6 measurements.

Calculate the mean.

m = (10.56+9.52+9.73+9.80+9.78+10.91)/6 = 10.05

Calculate deviations from the mean.

y = |x - m|

  = [0.51, 0.53, 0.32, 0.25, 0.27, 0.86]

The greatest deviation from mean is d = 0.86.

Calculate the average absolute deviation.

(0.51+0.53+0.32+0.25+0.27+0.86)/6 = 0.4567

The answer is: d = 0.86

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The perpendicular distance ( height ) between the parallels sides of the trapezoid is 5cm.

A trapezoid is simply a quadrilateral with at least one pair of parallel sides.

The area of trapezoid is expressed as;

A = h × (a + b)/2

Where a is base a, b is base b and h is height.

Given the data in the question;

To determine the height of the trapezoid, plug the given values into the above formula and solve for h.

A = h × (a + b)/2

31.5cm² = h × ( 7.3cm + 5.3cm)/2

31.5cm² = h × ( 12.6cm )/2

31.5cm² = h × 6.3 cm

h = 31.5cm² / 6.3 cm

Height h = 5cm

Therefore, the height of the given trapezoid is 5 centimeters.

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Answer:

Angle EDC = 180 - 90 - 30 = 60° (sum of angles in triangle add up to 180°)

Angle ADC + angle DCB = 180° (interior angles, AB//CD)

59 + 60 + 30 + angle ECB = 180

Angle ECB = 180 - 59 - 60 - 30 = 31°

The relationship between operating cost per hour and the number of passenger seats is shown by the equation of the least squares regression line, where y=1136+14.673x is the expected operating cost per hour and x is the number of passenger seats.

a plane figure in geometry with four equal sides and four right angles of 90 degrees. A square is both an equilateral rectangle and a special kind of parallelogram (an equilateral and equiangular one).

In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides. The confronting or opposed sides and the opposing angles of a parallelogram are of equal length.

based on the available facts;

y=1136+14.673x

where

x= number of passenger seat

y=predicted operating cost per hour.

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Answer:

lol

Step-by-step explanation:

I dunno my brain isn't braining

By combining numerical or algebraic expressions that share a basis, distributing exponents among products and quotients, and simplifying powers of powers, one can exploit the properties of integer exponents to create similar expressions.

Based on the information, it's important to simply transfer the base and exponent to the other side of the fraction line, change the exponent to positive, and you have an analogous expression.

For example, the expression 2/3² can be illustrated to an equivalent expression as:

2/3² = 2 / (3 × 3)

= 2/9

This shows how the exponent has been used to form the new value.

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