What is the value of x
in the equation, 5(x+2)+4x=6x+1
?

Responses

x=−3
, x is equal to negative 3

x=−1
, x is equal to negative 1

x=1
, x is equal to 1

x=3
, x is equal to 3

Reason:

[tex]\angle 1 = 62^{\circ}[/tex] because of the vertical angles theorem.

Then angle 1 and angle 2 add to 90 degrees (the angles are complementary).

[tex]\angle 1 + \angle 2 = 90\\\\62 + (2x-8) = 90\\\\2x + 54 = 90\\\\2x = 90 - 54\\\\2x = 36\\\\x = 36/2\\\\x = 18\\\\[/tex]

Step-by-step explanation:

Perimeter is the total of all three sides added together:

  2x^2 + x        +     3x^2 -3       + ?      =  3x^2 + 2      Simplify a bit on the L

     5x^2  + x  -3     + ?  = 3x^2 + 2           subtract 5x^2 from both sides

                  x-3   + ?    = - 2x^2 + 2           subtract x from both sides

                     -3  + ?   = - 2x^2 - x + 2       finally, add 3 to both sides

                            ?  = - 2x^2 -x + 5

4) Dane read an average of 400 minutes per week. 5)  Diane will have read 2000 minutes after 5 weeks.

4) The number "0200100300" represents the number of minutes Diane read each week for 3 weeks. To find out how many minutes she read after the first week, we simply look at the first digit, which is "0." This means that Diane did not read any minutes during the first week.

To find out how many minutes she read after the second week, we add the digits in the first two positions, which are "02." This gives us a total of 2 x 60 = 120 minutes.

To find out how many minutes she read after the third week, we add the digits in the first three positions, which are "020." This gives us a total of 20 x 60 = 1200 minutes.

To find out how many minutes she read each week, we simply divide the total number of minutes by the number of weeks, which is 3. So Diane read a total of 1200 minutes in 3 weeks, which means she read an average of 400 minutes per week.

5) If Diane reads the same number of minutes each week, then she will read that same number of minutes after 4 weeks and after 5 weeks. To find out how many minutes she reads after 4 weeks, we can skip count by the same number repeatedly: 400, 800, 1200, 1600. So Diane will have read 1600 minutes after 4 weeks.

Similarly, to find out how many minutes she reads after 5 weeks, we can skip count again by the same number repeatedly: 400, 800, 1200, 1600, 2000. So Diane will have read 2000 minutes after 5 weeks.

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The bunch of roses costs $12/$3 = 4 times as much as a single rose.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

The bunch of roses costs 4 times as much as a single rose.

To see why, we can divide the cost of the bunch of roses by the number of roses it contains. If a bunch of roses costs $12 and contains, say, 4 roses, then each rose in the bunch costs $3. On the other hand, a single rose costs $3 on its own.

Therefore, the bunch of roses costs $12/$3 = 4 times as much as a single rose.

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Answer:

8

Step-by-step explanation:

is it right?

Therefore, **x < 7** is the inequality that may be utilized to find x

A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).

For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".

Let x represent how many days the client paid for pet sitting.

$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.

We are aware that the customer's purchase was under $125. Consequently, we can write:

20 + 15x < 125

Putting this disparity simply:

15x < 105

x < 7

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On the basis of data reported by Carlita in form of fractions , on comparing the given fractions order of animals from least liked to most liked is option-D:Snakes, hamsters, cats, dogs.

What are fractions?

A fraction represents a portion of a total. This entire may refer to a place or a group of places. The Latin word "fractio," which meaning "to break," is the source of the English term "fraction." It is simpler to identify the greater or smaller fraction when comparing fractions with the same or similar denominators. We must change fractions with dislike or different denominators to fractions with like or the same denominators in order to compare them. To do this, we must determine the denominators' Least Common Multiple (LCM). We can compare fractions simply when the denominators are made the same or similar.

Given data collected by Carlita:

Fraction of students who like hamsters= [tex]\frac{3}{7}[/tex]  

Fraction of students who like dogs =  [tex]\frac{5}{6}[/tex]  

Fraction of students who like cats= [tex]\frac{1}{2}[/tex]  

Fraction of students who like hamsters= [tex]\frac{1}{9}[/tex]

To compare all four fractions  [tex]\frac{3}{7}[/tex]  ,   [tex]\frac{5}{6}[/tex]  ,  [tex]\frac{1}{2}[/tex]   &  [tex]\frac{1}{9}[/tex]

We find LCM of denominators 2,6,7 & 9

prime factors:

2=2

6=2 x 3

7=7

9= 3 x 3

LCM=2 x 3 x 3 x 7

       =126

Equivalent fractions with denominator 126:

 [tex]\frac{3}{7}[/tex]  =   [tex]\frac{3}{7}[/tex]  × [tex]\frac{18}{18}[/tex]  = [tex]\frac{54}{126}[/tex]

 [tex]\frac{5}{6}[/tex]  =   [tex]\frac{5}{6}[/tex]  × [tex]\frac{21}{21}[/tex]  = [tex]\frac{105}{126}[/tex]

 [tex]\frac{1}{2}[/tex]  =   [tex]\frac{1}{2}[/tex]  × [tex]\frac{63}{63}[/tex]  = [tex]\frac{63}{126}[/tex]

[tex]\frac{1}{9}[/tex]   =  [tex]\frac{1}{9}[/tex]   × [tex]\frac{14}{14}[/tex]  = [tex]\frac{14}{126}[/tex]

On arranging least to most  [tex]\frac{54}{126}[/tex],  [tex]\frac{105}{126}[/tex],  [tex]\frac{63}{126}[/tex] &  [tex]\frac{14}{126}[/tex] we get

 [tex]\frac{14}{126}[/tex] <   [tex]\frac{54}{126}[/tex] <   [tex]\frac{63}{126}[/tex] <   [tex]\frac{105}{126}[/tex]

snakes<hamsters<cats<dogs

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Refer to the attachment for the complete question.

Answer: C) -7.

Step-by-step explanation:

9 • (–1) – 20 ÷ (–10)

= -9 - (-2)

= -9 + 2

= -7

Therefore, the answer is C) -7.

To test whether the proportion of women in executive-level positions is significantly lower than the proportion of women in the company as a whole, we can perform a hypothesis test.

Null Hypothesis: The proportion of women in executive-level positions is equal to or greater than the proportion of women in the company as a whole.

Alternative Hypothesis: The proportion of women in executive-level positions is significantly lower than the proportion of women in the company as a whole.

Using a significance level of 0.05, we can perform a one-tailed z-test for the difference in proportions.

Assuming a total sample size of 43 executives and a proportion of women in the company as a whole of 0.4, we find that the expected number of women in executive-level positions would be 43*0.4 = 17.2.

Using a z-test, we find that the test statistic is z = (13-17.2)/sqrt(0.4*0.6/43) = -1.89.

Using a z-table, we find that the p-value for z = -1.89 is approximately 0.029.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the proportion of women in executive-level positions is significantly lower than the proportion of women in the company as a whole. The company's explanation is not sufficient to account for the observed discrepancy.

~~~Harsha~~~

For the given frequency table, (a) 5 (b) 137 (c) lower class boundary is 132.5, and the upper class boundary is 141.5.

What is a frequency table ?

A frequency table is a tabular summary of data showing the frequency (i.e., the number of occurrences) of each category or value in a data set. It usually consists of two columns: one listing the categories or values and the other listing the corresponding frequencies. Frequency tables are commonly used to summarize categorical data, but they can also be used to summarize numerical data by grouping it into intervals or classes.

Now,

(a) The class width is the difference between the upper class limit and the lower class limit. For this frequency distribution, we can see that the class width is the same for each class and is equal to 5.

(b) The class midpoints are found by taking the average of the lower and upper class limits. For the first class, the lower class limit is 135 and the upper class limit is 139. So, the class midpoint is (135 + 139) / 2 = 137.

(c) The class boundaries are found by adding and subtracting half of the class width to the lower and upper class limits. For the first class, the lower class limit is 135 and the upper class limit is 139. The class width is 5, so half of the class width is 2.5. The lower class boundary is 135 - 2.5 = 132.5, and the upper class boundary is 139 + 2.5 = 141.5.

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Answer:

  51.5

Step-by-step explanation:

You want the median of the data set {55, 44, 40, 55, 48, 44, 58, 67}.

There are an even number of elements in the set of data, so the median will be the average of the middle two.

Sorted into increasing order, the data set is ...

  {40, 44, 44, 48, 55, 55, 58, 67}

The middle two elements are (48, 55). Their average is ...

  median = (48 +55)/2 = 103/2 = 51.5

The median of the data is 51.5.

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Answer: 17999640

Step-by-step explanation:

The number of sides (100000) - 2. This gives you 99998 sides. Then you multiply it by 180. This equals 17999640

Answer: The sum of the exterior angles of a polygon is always 360 degrees. This is because when you travel around the exterior of a polygon, you make one complete revolution of 360 degrees.

To find the measure of each exterior angle of a regular n-gon (a polygon with n sides and angles of equal measure), you divide the total sum of the exterior angles (360 degrees) by the number of sides or angles in the polygon.

So for a regular 100000-gon, each exterior angle measures 360/100000 = 0.0036 degrees.

To find the sum of all the exterior angles in a 100000-gon, we multiply the measure of one exterior angle by the number of exterior angles (which is also equal to the number of sides/vertices in the polygon).

The number of exterior angles in a 100000-gon is also 100000, so:

Sum of exterior angles = 0.0036 degrees/angle × 100000 angles = 360 degrees

Therefore, the sum of the exterior angles of a 100000-gon is 360 degrees.

Step-by-step explanation:

The answer for the given trignomatric function is equal to tan(Q) = 1, where Q=45 degrees.

An angle is a shape created by two rays or lines that meet at the same terminal. The Latin word "angulus" (which means "corner") is where the term "angle" first appeared. The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean. The sign "∠" is used to denote angles. The Greek letter θ can be used to represent the angle between the two beams.

A line that only touches a circle or an ellipse at one point is said to be tangential in geometry. Assuming a line contacts the curve at P, "P" is referred to be the point of tangency. In other words, it is described as the line that, at that particular location, indicates the slope of a curve.

according to question,

we can say that sum of a triangle is 180 degrees

so, Q=45 degrees

Tan(45) = 1

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Answer:

7) x= 8[tex]\sqrt{3}[/tex]    y= 8

8) x= 10[tex]\sqrt{3}[/tex]  y= 15

9) x= 22      y= 11[tex]\sqrt{3}[/tex]

10) x= 4       y= 4[tex]\sqrt{3}[/tex]

11) x= 6[tex]\sqrt{3}[/tex]   y= 12[tex]\sqrt{3}[/tex]

12) x= 13      y= 26

Step-by-step explanation:

Just use your 30, 60, 90 triangle rules:

hypotenuse= 2x the shortest leg (the one opposite the angle measuring 30 degrees)

longer leg= the shortest leg times [tex]\sqrt{3}[/tex]

to find shortest leg, substitute the variables

Answer:

Step-by-step explanation:

Make a chart.

units                    hours

2                             5

4                             10

6                             15

1.) The probability of rolling two even numbers would be = 1/4

2.) The probability of rolling one even and one odd number = 1/2

3.) The probability of flipping tails on a coin and by rolling a factor of 6 on a six sided die would be = 1/3

To calculate the probability the formula that should be used is given as follows;

probability = possible outcome/sample space

For question 1.):

Sample space when two dice are thrown = 36

possible outcome = (2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)= 9

Probability = 9/36 = 1/4

For question 2.)

Sample space when two dice are thrown = 36

possible outcome = 18

probability = 18/36 = 1/2

for question 3.)

Sample space when two dice are thrown = 12

possible outcome = 4

probability = 4/12 = 1/3

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The area of the path is 80 square meters.

Given: A rectangular flower bed measures 10m by 6m. It has a path  2m wide around it.

To Find: The area of the path.

Solution: We need to subtract the area of the inner rectangle from the area of the outer rectangle.

So,

The outer rectangle has dimensions 14m by 10m (adding 2m to each side of the flower bed), so its area is:

A outer = 14m x 10m = 140 m²

Now,

The inner rectangle has dimensions 10m by 6m (the original dimensions of the flower bed), so its area is.

A inner = 10m x 6m = 60 m²

Now,

The area of the path.

A path = A outer - A inner

           = 140 m² - 60 m²

           = 80 m²

Thus, The area of the path is 80 square meters.

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Therefore, the value of x in the right triangle is 24 cm.

A triangle is a two-dimensional geometric shape that has three straight sides and three angles. It is formed by connecting three non-collinear points. The sum of the interior angles of a triangle is always 180 degrees, and the measure of each angle depends on the lengths of the sides and the type of triangle. There are different types of triangles based on their side and angle measures, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles have various properties and formulas that are used in geometry and other fields.

Here,

In a right triangle, the side opposite to the right angle is the longest side and is called the hypotenuse. Therefore, in this case, 25 cm is the hypotenuse of the triangle.

Using the Pythagorean Theorem, we can find the missing length x:

a² + b² = c²

where a and b are the lengths of the legs of the right triangle and c is the length of the hypotenuse.

In this case, a = 7 cm, b = x, and c = 25 cm.

Substituting these values into the Pythagorean Theorem, we get:

7² + x² = 25²

49 + x² = 625

x² = 625 - 49

x² = 576

x = √576

x = 24

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Answer:

x = -3 and x = 1 are the two zeroes of this function. Choose one of them for your answer.

Answer:

Hm

Step-by-step explanation:

The formula to find the circumference of a circle is:

Circumference = 2πr

Where "r" is the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14.

Substituting the given value of radius, we get:

Circumference = 2 x π x 6

Circumference = 12π

Circumference ≈ 37.7 cm (rounded to one decimal place)

Therefore, the circumference of a CD that has a radius of 6 centimeters is approximately 37.7 cm.

The value of cos(7π/6) = -√3/2

Explain values

Values are principles or beliefs that guide our behavior and decision-making. They are deeply ingrained in our personalities and are shaped by our upbringing, culture, and experiences. Values can be ethical, moral, social, or personal and influence how we prioritize our goals and interact with others. Understanding our own values can help us make better choices, build stronger relationships, and lead a more fulfilling life.

According to the given information

The cosine of π/6 is √3/2, so the cosine of 7π/6 is:

cos(7π/6) = -cos(π/6) = -√3/2

Therefore, cos(7π/6) = -√3/2.

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Answer:

-√3/2

Steps:

Rewrite the angle as a sum or difference with its reference angle:cos ([tex]\pi[/tex] + [tex]\frac{\pi }{6}[/tex])

Simplify the expression using the general reduction formula: -([tex]\frac{\pi }{6}[/tex])

Evaluate the expression: -√3/2

Answer: A

Step-by-step explanation: The bluebird Inn is more expensive per night because 475 is greater than 350.

21 is  the area, measured in square centimeters, of the green shape pictured below.

What is square?

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

the area of a parallelogram, we can split this shape up into a rectangle and two right triangles.

The rectangle:

The rectangle has dimensions of 4 by 3 centimeters therefore the area would be 4*3=12 cm squared

two right triangles:

The area of a triangle is 1/2 base * height, but since there are two triangles it would just be the base times the height. The base is 3 cm and the height is 3 so 3*3=9

Next, we add the two areas together: 12+9 = 21

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The correct answer is c: Two terms are even, then two terms are odd. This pattern follows the rule of adding 2, so each successive term is an even number followed by an odd number.

Number is a mathematical object used to count, measure and represent a quantity. It is used to symbolize a numerical quantity or value, and is used in various ways in mathematics, science, engineering, finance and other fields. Numbers are also used to represent relationships between objects, such as the number of sides in a triangle or the number of students in a classroom.

This alternating pattern of even and odd terms is a feature of the pattern, with two terms being even followed by two terms being odd. This pattern continues as the terms increase, with the even terms adding 2 and the odd terms adding 2 as well. This pattern is a good way to remember a sequence of numbers and can be used to help understand patterns in mathematics.

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Answer:

M ≈ $933.24

Step-by-step explanation:

To calculate Marcus's monthly payment for financing his car for 5 years at an annual interest rate of 8.5%, we can use the formula for the monthly payment on a loan:

M = P * (r/12) * (1 + r/12)^n / ((1 + r/12)^n - 1)

where:

M is the monthly payment

P is the principal (in this case, $45,000)

r is the annual interest rate (in this case, 8.5%)

n is the number of monthly payments (in this case, 5 years * 12 months/year = 60 monthly payments)

Substituting the given values, we get:

M = $45,000 * (0.085/12) * (1 + 0.085/12)^60 / ((1 + 0.085/12)^60 - 1)

Using a calculator, we get:

M ≈ $933.24

Therefore, Marcus's monthly payment for financing his car for 5 years at an annual interest rate of 8.5% is approximately $933.24.

The only equations n + 6 = 12 and 4 • n = 24 have n = 6 as a solution.

An equation is a collection of variables, constants, and mathematical operations like addition, subtraction, multiplication, or division that are balanced by the equal sign. The equation's right-hand side (RHS) is on the right, and its left-hand side (LHS) is on the left.

To check if a given equation has n = 6 as a solution, we simply substitute n = 6 into the equation and see if it is true.

2 + n = 6 : 2 + 6 = 8, not true for n = 6.

n + 6 = 12 : 6 + 6 = 12, true for n = 6.

4 • n = 24 : 4 • 6 = 24, true for n = 6.

n • 3 = 2 : 6 • 3 = 18, not true for n = 6.

Therefore, only the equations n + 6 = 12 and 4 • n = 24 have n = 6 as a solution.

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Answer:

Step-by-step explanation:

To determine the most you should pay for the annuity, you can use the present value formula for an annuity.

PV = C * [(1 - (1 + r)^(-n)) / r]

where PV is the present value, C is the annual cash flow, r is the interest rate, and n is the number of periods.

In this case, C is $1,000, r is 6%, and n is 5 years. Plugging these values into the formula, we get:

PV = $1,000 * [(1 - (1 + 0.06)^(-5)) / 0.06]

PV = $4,212.10

Therefore, the most you should pay for the annuity is $4,212.10. If you pay more than this amount, you would be better off investing your money elsewhere at a 6% interest rate.