43
Explanation
Step 1
let x represents the first number
first number=X
as the number are consecutives, the second number would be
[tex]\begin{gathered} \text{second number= first number +1} \\ \text{second number=x}+1 \end{gathered}[/tex]and the third number would be
[tex]\begin{gathered} \text{third number= second number +1} \\ \text{third number=(x}+1)+1 \\ \text{third number=x}+2 \end{gathered}[/tex]Now, we are told the sum of the three consecutive numbers is 126,so
[tex]\text{first number+second number+thir number=126}[/tex]replace
[tex]x+(x+1)+(x+2)=126\rightarrow equation\text{ (1)}[/tex]Step 2
solve the equation
[tex]\begin{gathered} x+(x+1)+(x+2)=126\rightarrow equation\text{ (1)} \\ x+x+1+x+2=126\rightarrow equation\text{ (1)} \\ \text{add like terms} \\ 3x+3=126 \\ \text{subtract 3 in both sides} \\ 3x+3-3=126-3 \\ 3x=123 \\ \text{divide both sides by 3} \\ \frac{3x}{3}=\frac{123}{3} \\ x=41 \end{gathered}[/tex]Step 3
finally, replace the x value to find the numbers
[tex]\begin{gathered} \text{first number= x} \\ \text{first number=}41 \\ \text{second number = x+1}=41+1 \\ \text{second number = }42 \\ \text{third number=x+2=41+2} \\ \text{third number=}43 \end{gathered}[/tex]theferore, the greatest number is 43
I hope this helps you
Which of the following mathematical patterns is evident in the piece below?
Consider that, of all the given options, the right side of the picture seems identical to the left side of the picture.
But it cannot be identical, since the letter on the right side "FIDES" cannot be seen on the right side of the picture.
Rest of all the designs seem symmetrical about the middle vertical line.
Since it is not perfectly identical, not perfectly symmetric, it can be referred as SIMILAR.
So similar patterns are evident in the given piece.
Therefore, option C is the most suitable choice.
Write the sum of 5x^2+2x-10 and 2x^3+6 as a polynomial in standard form
Given polynomials:
[tex]\begin{gathered} 5x^2\text{ + 2x - 10} \\ 2x^2\text{ + 6 } \end{gathered}[/tex]The sum of the polynomials is:
[tex]=\text{ 5x}^2\text{ + 2x - 10 + \lparen2x}^2\text{ + 6\rparen}[/tex]Simplifying the sum:
[tex]\begin{gathered} =\text{ 5x}^2\text{ + 2x - 10 + 2x}^2\text{ + 6} \\ Collect\text{ like terms} \\ \text{ = 5x}^2\text{ + 2x}^2\text{ + 2x - 10 + 6} \\ =\text{ 7x}^2\text{ + 2x - 4} \end{gathered}[/tex]Hence,the sum of the polynomials in standard form is:
[tex]=\text{ 7x}^2\text{ + 2x - 4}[/tex]Given that events A and B are independent with P(A)=0.9P(A)=0.9 and P(B)=0.71P(B)=0.71, determine the value of P(A\cap B)P(A∩B), rounding to the nearest thousandth, if necessary.
Remember that
If A and B are independent events, then
P(A∩B)=P(A)*P(B)
substitute given values
P(A∩B)=(0.9)*(0.71)=0.639
therefore
The answer is 0.639in the figure below , DGH was dilated and then rotated 180° about point G to create the other triangle .
We can eliminate some of these choices , knowing that if we dilate a triangle they are the same shape but not necessarily the same size. Thus , they are not congruent. Therefore, the last two choices are false since it denotes congruency.
It is also stated from the problem that the triangle is rotated by 180 degrees therefore the congurent pair of angle can be found on the opposite side in the figure. Therefore , we can eliminate the first choice since it states that the congruency among angles are at the same side.
Thus, CHOICE 2 is true.
5. The length of a rectangle is triple the width. If the perimeter is 104 cmn, find the length of therectangle.Equation:
We have that the length of the triangle is three times its width
We'll call "x" the unknown measurement
The statement tells us that the perimeter is 104 cm, that is the sum of all its sides is equal to 104 cm
Let's remember that a rectangle has 2 pairs of equal sides, in this case, 2 sides measure 3x and two sides measure x
Therefore the sum of the 4 sides must be equal to 104 cm, we can pose the following equation
[tex]\begin{gathered} 3x+3x+x+x=104 \\ \end{gathered}[/tex]Now we clear
[tex]\begin{gathered} 8x=104 \\ x=\frac{104}{8} \\ x=13 \end{gathered}[/tex]if we are being asked the length of the rectangle and we know that the length is 3x we solve it like this
[tex]\begin{gathered} L=3x \\ L=3\cdot13 \\ L=39 \end{gathered}[/tex]The answer is that length of the rectangle is 39 cm
Using the following image, solve for UW. 7 2x + 3 U V 2x+3 W X + 10 UW
Answer
UW = 10
Explanation
From the image attached, we can see that
UV + VW = UW
But
UV = 2x + 3
VW = 7
UW = x + 10
UV + VW = UW
(2x + 3) + 7 = x + 10
2x + 3 + 7 = x + 10
2x + 10 = x + 10
2x - x = 10 - 10
x = 0
UW = UV + VW
UW = 2x + 3 + 7
UW = 2 (0) + 10
UW = 0 + 10
UW = 10
Hope this Helps!!!
(a) rewrite as an exponential equation(b) rewrite as a logarithmic equation
Given:
a)
[tex]\log _3\frac{1}{81}=-4[/tex]For logarithmic equation,
[tex]\begin{gathered} \log _b(x)=y \\ \text{The exponential form is } \\ b^y=x \\ \text{Here, b=3,x=}\frac{1}{81}\text{ and y=-4} \\ 3^{-4}=\frac{1}{81}\text{ is the exponential equation for the given logarithmic equation.} \end{gathered}[/tex]b)
[tex]\begin{gathered} 8^1=8 \\ \text{For the equation a}^x=b\text{ is written in the logarithmic equation as,} \\ \log _a(b)=x \\ Here,a=8,b=8,x=1 \\ \log _88=1 \end{gathered}[/tex]Answer:
[tex]\begin{gathered} a)\text{ }3^{-4}=\frac{1}{81}\text{ } \\ b)\text{ }\log _8(8)=1 \end{gathered}[/tex]Complete the end behavior statement for the function shown above. Asx→−∞, f(x)→
Given
The function
[tex]f(x)=\frac{12x^5}{3x^5}[/tex]To find the end behavior of the function.
Explanation:
It is given that,
[tex]f(x)=\frac{12x^5}{3x^5}[/tex]That implies,
[tex]\begin{gathered} \lim_{x\to-\infty}f(x)=\lim_{x\to-\infty}(\frac{12x^5}{3x^5}) \\ =\lim_{x\to-\infty}(\frac{12}{3}) \\ =\lim_{x\to-\infty}(4) \\ =4 \end{gathered}[/tex]Hence,
[tex]As\text{ }x\rightarrow-\infty,f(x)\rightarrow4[/tex]A regular 9 sided building is 814 ft along one side what is the distance from a Vertex to the center of the building
A regular 9 sided building is 814 ft along one side what is the distance from a Vertex to the center of the building
we know that
A regular 9 sided polygon, can be divided into 9 isosceles triangle
The equal distances of the isosceles triangle is equal to the radius or the distance from a Vertex to the center of the building
the base of the isosceles triangle is given and is equal to 814 ft
The measure of the interior angle of the vertex is equal to
360/9=40 degrees
that means
we have
Applying the law of sines
814/sin(40)=r/sin(70)
solve for r
r=(814/sin(40))*sin(70)
r=1,190 ft
therefore
the distance is 1,190 fta story is making their pricces up 145% what fraction best represents 145%
the percentage is expressed as a division between the value and 100
on this case
[tex]\frac{145}{100}[/tex]and we can simplify
[tex]undefined[/tex]solve the equation for x. do not include x= in your answer.-2x+ : 3x-2=6
22
Explanation
[tex]-2+\sqrt[]{3x-2}=6[/tex]Step 1
a)add 2 in both sides
[tex]\begin{gathered} -2+\sqrt[]{3x-2}=6 \\ -2+\sqrt[]{3x-2}+2=6+2 \\ \sqrt[]{3x-2}=8 \end{gathered}[/tex]b) both sides to the 2 power
[tex]\begin{gathered} \sqrt[]{3x-2}=8 \\ (\sqrt[]{3x-2}^2=8^2 \\ 3x-2=64 \end{gathered}[/tex]c) again, add 2 in both sides.
[tex]\begin{gathered} 3x-2=64 \\ 3x-2+2=64+2 \\ 3x=66 \end{gathered}[/tex]d) finally, divide both sides by 3
[tex]\begin{gathered} 3x=66 \\ \frac{3x}{3}=\frac{66}{3} \\ x=22 \end{gathered}[/tex]I hope this helps you
Find the area of the sector. Round to the nearest tenth.459 m254.616.9O 31.8O 7.1
The area of the sector is 31.8m^2 ( nearest tenth)
Benadryl is a medicine used to treat runny noses, itching, and other cold and allergy symptoms. Ittakes an average of two to three days for the active ingredient of Benadryl, diphenhydramine, to leave the body. The formula below represents the amount, A, of diphenhydramine left in the body,measured in mg, t hours after taking 50 mg of the medicine.A = 50 (0.9217)^tA) How long does it take for the body to eliminate half of the initial amount of Benadryl? Solve thisalgebraically. Round decimal to two places.
We have to replace A= 25 mg in the equation and solve for t. Doing so, we have:
[tex]\begin{gathered} 25=50(0.9217)^t\text{ } \\ 0.5=(0.9217)^t\text{ (Dividing by 50 on both sides of the equation)} \end{gathered}[/tex][tex]\begin{gathered} \log _5(0.5)=\log _5(0.9217)^t(\text{ Taking the logarithm base 5 of both sides of the equation)} \\ \log _5(0.5)=t\cdot\log _5(0.9217)\text{ (Using the power rule of logarithms)} \\ -0.431=t\cdot(-0.0507)\text{ (Finding the logarithms for each case)} \\ 8.50=t\text{ (Dividing by }-0.0507\text{ on both sides of the equation)} \end{gathered}[/tex]The answer is 8.50 hours (Rounding to two decimal places)
I was a little confused on what to do or where to start, could you help?
Our approach is to determine the equation of the function and when we do, we can substitute as appropriate.
[tex]\begin{gathered} \text{ At x = 4, y = 12} \\ \frac{y}{x}=\frac{12}{4}=3 \\ y=3x \end{gathered}[/tex]Now we have established a relationship between x and y.
[tex]\begin{gathered} \text{ When y = 6,} \\ 6=3x \\ \text{ Divide both sides by 3 to get:} \\ x=2 \end{gathered}[/tex][tex]\begin{gathered} \text{ When x = 6,} \\ y=3(6)=18 \\ y=18 \end{gathered}[/tex]We can confirm these values by tracing downwards to 2 when y = 6
In the same way, we can trace leftward to 18 when x = 6
Jon had to put together a menu for his Science Club picnic bag lunch. The menu groups the items into sandwiches, drinks, and fruit. Jon had to put one food item from each group in a bag for the members.
ANSWER
[tex]\frac{1}{30}[/tex]EXPLANATION
We want to find the probability that Jon will get a peanut butter sandwich, a chocolate milk and a banana.
This can be obtained by finding the product of the probability of picking each item from their respective groups.
That means that we will find the probability of picking each item and multiply them together.
There are 2 sandwich options, which means that the probability of getting a peanut butter sandwich is:
[tex]P(PB)=\frac{1}{2}[/tex]There are 5 drink options, which means that the probability of getting a chocolate milk drink is:
[tex]P(CM)=\frac{1}{5}[/tex]There are 3 fruit options, which means that the probability of getting a banana is:
[tex]P(B)=\frac{1}{3}[/tex]Therefore, the probability that Jon will get a peanut butter sandwich, a chocolate milk and a banana is:
[tex]\begin{gathered} P(PB\&CM\&B)=\frac{1}{2}\cdot\frac{1}{5}\cdot\frac{1}{3} \\ P(PB\&CM\&B)=\frac{1}{30} \end{gathered}[/tex]Last year during the July 4th holiday, Americans ate about 150,000,000 hot dogs. Over the entire year, Americans ate a total of about 2 x 10^10. Compute how many times greater the total number of hot dogs eaten by Americans last year was than the number of hot dogs eaten during the 4th of July holiday. Round your answer to the nearest one. times greater than the number of The total number of hot dogs eaten by Americans last year was blank hot dogs eaten during the July 4th holiday.
July 4th quantity: 150,000,000 = 1.5 x 10^9
Entire year quantity: 2 x 10^10 = 2,000,000,000
2,000,000,000 - 150,000,000 = 2 thousand millions - 150 millions =
one thousand, eith hundred fifty millions
2,000,000,000 - 150,000,000 = 1,850,000,000
1,850,000,000 = 1.85x10^10
Americans eated 1,850,000,000 = 1.85x10^10 more hotdogs over the entire year than they eated on the 4th of July
2,000,000,000/150,000,000 = 13.33
Americans eated 13.33 times more hotdogs over the entire year than in the 4th of July
Find the supplementary of an angle that measures 110°. Question 18 options: 67° 70° 73° 85°
The angle that measures supplementary to 110° is b) 70°
It is given to us the angle 110°. The supplementary angle to 110° is to be found. Supplementary angles refer to pair of angles, whose sum measures add up to 180°. However, the supplementary angles need not be together always. It is mathematically given by,
180° = x° + y°..............(1)
To find the supplementary angle of 110°, the above equation(1) could be used.
180° = 110° + y°
180° - 110° = y°
y° = 70°
Therefore the supplementary angle pair of 110° is 70°. Hence, option b) is the correct answer.
To learn more about angles, click below:
https://brainly.com/question/25716982
2 3 Year months A 7 months B 3 months © 8 months D 9 months
In order to fill the blank space, consider that 1 year = 12 months
Then, you have:
(2/3) · 12 months = 24/3 months = 8 months
C) 8 months
What is the end behavior of f(x) in the function f(x) = log(x - 2) as x approaches 2?
Step 1
Given; What is the end behavior of f(x) in the function f(x) = log(x - 2) as x approaches 2?
Step 2
Graph the function
[tex]\begin{gathered} \lim _{x\to \:2}\left(\ln \left(x-2\right)\right) \\ \mathrm{If\:}\lim _{x\to a-}f\left(x\right)\ne \lim _{x\to a+}f\left(x\right)\mathrm{\:then\:the\:limit\:does\:not\:exist} \\ \end{gathered}[/tex]Thus;
[tex]\lim _{x\to \:2}\left(\ln \left(x-2\right)\right)=\mathrm{Does\:not\:exist}[/tex]Therefore the answer is;
[tex]f(x)\rightarrow-\infty[/tex]Shamara has been tracking her credit score. In October, her credit score was 702 but by April of the following year, it was 679. What is the absolute and relative change in Shamara's credit score from October to April?
Step 1
Given; Shamara has been tracking her credit score. In October, her credit score was 702 but by April of the following year, it was 679. What is the absolute and relative change in Shamara's credit score from October to April?
Step 2
[tex]Absolute\text{ change= 679-902=-23}[/tex][tex]Relative\text{ change=-}\frac{23}{702}\times100=-\frac{1150}{351}\%[/tex]Answer;
[tex]\begin{gathered} Absolute\text{ change=-23} \\ Relative\text{ change=-3.28\%} \end{gathered}[/tex]In the graph below, f(x) is a linear function, and g(x) is an exponential function. Which statement best explains the behavior of the graphs of the functions as x increases?
Given:
The graphs of f(x) and g(x)
Let us describe the behavior of f(x) and g(x) individually
Behavior of f(x)
f(x) is a straight-line graph. The rate of change of f(x) is constant
Behavior of g(x)
g(x) is the graph of an exponential function. The value of g(x) rises exponentially as x increases.
Combining the behavior of f(x) and g(x)
Since g(x) rises exponentially as x increases, it would eventually exceed f(x)
Answer:
g(x) eventually exceeds f(x) because the rate of change of g(x) increases as x increases, whereas the rate of change of f(x) is constant. (Option B)
XYZ is a dilation of ABC by a scale factor of 5. Which of the followingproportions verifies that ABC and XYZ are similar?eAсNA.ABXZАС些 --АВXYCABAC=X2D.ACYZBCX2
If the triangles are similar, then the 3 pairs of corresponding sides should have the same proportion.
In this case, the corresponding sides are:
- AB and XY
- BC and YZ (the largest sides)
- AC and XZ (the shortes sides)
Then, if they are similar we have:
[tex]\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}[/tex]From the options, the only option that match with our previous equality of proportions is:
[tex]\frac{AB}{XY}=\frac{AC}{XZ}[/tex]Answer: AB/XY = AC/XZ [Option B]
Sally can paint the office by herself in 10 hours. Dave can do the same job in 7 hours. How long will it take if they do it working together? Answer in fraction.
The answer is 70/17 hours.
Given:
The time required by Sally to paint is, S = 10 hours.
The time required byDave to paint is, D = 7 hours.
The objective is to find the number of hours it will take if they do it working together.
Work done by Sally in 1 hour can be calculated as,
[tex]\begin{gathered} 10\text{ hours = 1 work} \\ 1\text{ hour=}\frac{1}{10}work \end{gathered}[/tex]Work done by Dave in 1 hour can be calculated as,
[tex]\begin{gathered} 7\text{ hours=1 work} \\ 1\text{ hour=}\frac{1}{7}work \end{gathered}[/tex]The work completed by both together in 1 hour can be calculated as,
[tex]\begin{gathered} W(1)=\frac{1}{10}+\frac{1}{7} \\ =\frac{7+10}{7\cdot10} \\ =\frac{17}{70} \end{gathered}[/tex]Now, the time required to complete the work together can be calculated as,
[tex]\begin{gathered} T=\frac{1}{W(1)} \\ =\frac{1}{\frac{17}{70}} \\ =\frac{70}{17} \end{gathered}[/tex]Hence, the time required to complete the work together is 70/17 hours.
Julie asked 50 students in her school whether they do volunteer work. This table shows the results.The graph is in the pictureHow many more seventh graders than eighth graders did Julie survey?
Solution:
Given the table below:
From the table,
[tex]\begin{gathered} Number\text{ of seventh graders = 27} \\ Number\text{ of eighth graders = 23} \end{gathered}[/tex]Since there are more seventh-graders than eighth-graders, we can evaluate the number of more seventh-graders by subtracting the number of eighth-graders from the number of seventh-graders.
Thus, we have
[tex]\begin{gathered} 27-23 \\ =4 \end{gathered}[/tex]Hence, Julie surveyed 4 more seventh-graders than eighth-graders.
Figure B is a scaled copy of Figure A.44.446Figure A11.111.5Figure B
In order to determine the scale factor, calculate the quotient between the area of the two trapezoids.
Consider that the area of the trapezoid is given by the sum of the area of a rectangle ans a triangle.
For the bigger trapezoid you have:
A1 = (4)(4) + (6-4)(4)/2
A1 = 16 + (2)(4)/2
A1 = 16 + 4
A1 = 20
For the smaller trapezoid:
A2 = (1)(1) + (1.6 - 1)(1)/2
A2 = 1 + 0.3
A2 = 1.3
Finally, the scale factor is:
A1/A2 = 20/1.3 = 15.38
where is the point (-2,-3) located on the coordinate plane?
Any point on the 1st quadrant has coordinates (x, y)
Any point on the 2nd quadrant has coordinates (-x, y)
Any point on the 3rd quadrant has coordinates (-x, -y)
Any point on the 4th quadrant has coordinates (x, -y)
Since the given point is (-2, -3), then look at the 3rd case
It will be on the 3rd quadrant III
Commission Melanie receives a 3% commission on every house she sells. If she received a commission of $8571, what was the value of the house she sold?
Given:
The percentage rate of commission, R=3%.
The commission recieved by Melanie, C=$8571.
The expression for commission amount is,
[tex]C=\frac{R}{100}\times SP[/tex]Here, SP is the sale price of the house.
Put R=3% and C=$8571 in the above equation to find sale price.
[tex]\begin{gathered} 8571=\frac{3}{100}\times SP \\ SP=\frac{8571\times100}{3} \\ SP=285700 \end{gathered}[/tex]Therefore, the sale price is $285700.
Mr.Palacios delivers newspapers. He can deliver 60 papers in 3/4 of an hour. At this rate how may newspaper will Mr.Palacios deliver in 2 1/4 hours?
Given Data:
Total number of newspapers delivered is 3/4 hour is: 60
Let Mr.Palacios delivers 'x' number of newspaper in 2 1/4 hours.
The expression to calculate the total number of the newspaper delivered in 2 1/4 hour is,
[tex]\begin{gathered} \frac{x}{2\frac{1}{4}}=\frac{60}{\frac{3}{4}} \\ x=(2\frac{1}{4})\times(\frac{60}{3}\times4) \\ x=(\frac{2\times4+1}{4})\times(20\times4) \\ x=(\frac{9}{4})\times80 \\ x=2.25\times80 \\ x=180 \end{gathered}[/tex]Thus, Mr.Palocios delivers 180 newspapers in 2 1/4 hours.
5 6 3 4 13. Jose is 35 years old, and makes $40,000 per year. If he dies, how much would the beneficiaries of his life insurance policy receive if they can get by on 75% of his income? Muilples-of-Salary Chart PEET Շնոաս: Օրհi# ԵՆՔրցե 5.5 5.5 6.5 6.5 40 3.0 3.0 810 6.0 4.5 70 BD 85 6.5 75 5.5 2350 GO 5.0 1.5 70 00010 RO ED 70 7.5 60 65 5.5 75 50
We are told that jose is 35 years old and makes 40.000 per year. Also, we are told that they can get by 75% of his income. So, in the table, we look for the age column for 35 years and in the gross earnings we look for the 40000 row.
Inside the 35 years column, we take a look at the inner column that says 75%. Crossing all this information, we get that the table shows a multiplier of 8.0
This means that their beneficiaries would earn 8 times the salary of jose. That is
[tex]8\cdot40000=320000[/tex]Determine weather each question is an example of statistical question. Drag each question to the correct classification in the table.What is Steve favorite sport?How many books are on the shelf in our math class?What is the height of each player on the basketball team ?what temperature outside the school at 6 o'clock this morning? What is the number of tickets sold at the movie theater each day this month