The algebraic expression for given statement is: 10x + 25 or 3(x + 4) + (7x + 13)
Solution:
Given the statement:
Three sets of a sum of a number and four are added to the sum of seven times the same number and thirteen
Let us first understand the given statement,
Let the number be "x"
" sum of a number and four" means x + 4
"Three sets of a sum of a number and four" translated to 3(x + 4)
"sum of seven times the same number and thirteen" means 7x + 13
Thus the algebraic expression for given statement is:
[tex]3(x+4)+(7x + 13)[/tex]
Using distributive property in above expression
[tex]a(b+c) = ab + bc[/tex]
Therefore,
[tex]3(x+4)+(7x + 13) = 3x + 12 + 7x + 13[/tex]
Combine the like terms
[tex]3(x+4)+(7x + 13) = 10x+25[/tex]
Thus the required expression for given statement is: 10x + 25 or 3(x + 4) + (7x + 13)
A physicist discovers an element whose atom has a mass of 0.00000000000000112 grams. He makes an entry in his journal and writes the mass in scientific notation as
Answer:
1.12*10^(-15)
Step-by-step explanation:
Answer:
1.12e-15
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Which of the following statements best describes the intersection of the sets of outcomes of events A and B?
A. The intersection of the sets is a list of all possible outcomes for event A.
B. The intersection of the sets is the set of all outcomes in events A and B.
C. The intersection of the sets is the set of all outcomes in the sample space of event A or event B.
D. The intersection of the sets is the set of all outcomes in the sample space of events A and B.
The intersection of the sets of outcomes of events A and B is the set of all outcomes that are common in both events A and B. This is a concept from set theory in mathematics.
The correct answer to the given question is option B.
The correct statement that best describes the intersection of the sets of outcomes of events A and B is 'The intersection of the sets is the set of all outcomes in events A and B'.
In mathematical terms, the intersection of two sets, often denoted as A ∩ B, is the set of elements which are in both A and B.
Thus, the intersection of two sets of outcomes of events A and B, would consequently be the set of all outcomes that are common in both events A and B.
This is mainly a concept from set theory, a fundamental part of mathematics that deals with the study of sets, which are collections of objects.
For instance, if the set A = {1, 2, 3} and the set B = {2, 3, 4}, then A ∩ B = {2, 3}. In this example, 2 and 3 are the outcomes that are common in both events A and B.
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A rectangular garage is 6 meters long and 5 meters wide. What is its area?
Answer:
30 meters
Step-by-step explanation:
You MUST multiply 5 and 6 to get 30 to find area you have to multiply length times width
Answer: 30 Meters
Step-by-step explanation: You find area by multiplying length by width. 6 times 5 is 30.
Which of the following represents "The sum of the abscissa and the ordinate is six"
X + y = 6
xy = 6
6xy
NEXT QUESTION
ASK FOR HELP
Answer:
The correct option: x + y = 6
Step-by-step explanation:
In a Cartesian system or a coordinate system, the abscissa is the value of the horizontal (x) value and the ordinate is the value of the vertical (y) value.
So, The sum of the abscissa and the ordinate = x + y when written as an algebraic expression.
Since given that The sum of the abscissa and the ordinate is six
So, the correct equation is x + y = 6
What is the algebric expression for
Multiply x by 3
Add 6
Raise to the second power
Answer:
[tex] {(3x + 6)}^{2} [/tex]
. $30 for 100 flyers or $65 for 250 flyers which is the better value
The second option of $65 for 250 flyers is the better value as it offers a lower cost per flyer.
Explanation:To determine which option is a better value, we need to calculate the cost per flyer for each option. For the first option of $30 for 100 flyers, the cost per flyer would be $0.30. For the second option of $65 for 250 flyers, the cost per flyer would be $0.26. Therefore, the second option is the better value as it offers a lower cost per flyer.
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X^-x^4-5x^3+4x-4
Please I need help and please show the steps.
Answer:
1-5x^4x+3 +4x^4x+1 -4x^4x/ x^4x
Step-by-step explanation:
Find the steps in the app photomath it helps.
If a company buys an item at a wholesale price of $45, which of the following would make sense as a retail price to charge the customers? Choose ALL that apply! $80 $60 $20 $40
Answer:
Step-by-step explanation:
buys it for $ 45
well...you know the business is gonna want to make a profit...so they would have to sell it for more then they bought it for.
I would say $ 60 or $ 80
Final answer:
Given the wholesale price of $45, the sensible retail prices to charge customers would be $60 and $80, as they both allow for covering costs and earning a profit, unlike $20 and $40, which would incur losses.
Explanation:
The question involves understanding wholesale and retail prices, essential concepts in economics and business mathematics. When a company buys an item at a wholesale price, it usually marks up the price when selling it at retail to cover costs and generate profit. Given the wholesale price of $45, the retail prices that make sense to charge customers would be those higher than $45 because selling at a lower price would result in a loss.
$60$80Both $60 and $80 are above the wholesale price and would allow the company to cover additional costs and earn a profit. $20 and $40 would not make sense as they are below the wholesale price, leading to a loss per item sold.
The table below shows selected points from a function.
The rate of change for the interval shown in the table is__ , so the function is a ____ function.
Answer:
The rate of change for the interval shown in the table is 1 , so the function is a linear function.
Step-by-step explanation:
See the table attached.
The table shows selected points from a function.
Now, the given interval is x = 1 to x = 4.
For, x = 1, f(x) = 2 and for x = 4. the function f(x) = 5.
Therefore, the rate of change for the interval shown in the table i.e slope of the line is [tex]\frac{5 - 2}{4 - 1} = 1[/tex] and it is constant throughout the interval so the function is a linear function. (Answer)
The rate of change for the interval shown in the table is constant , so the function is a linear function.
Note the following important points:
1. Linear Function:
If the difference between y values remains constant for any pair of consecutive points ([tex]y_2-y_1 = y_3-y_2 = y_4-y_3,[/tex]and so on), the function exhibits a constant rate of change, indicating a linear function. In this case, the rate of change would be the difference between two y values divided by the difference between their corresponding x values (e.g., [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]).
2. Non-Linear Function:
If the difference between y values varies between consecutive points, the function would be non-linear. The specific type of non-linear function (e.g., quadratic, exponential) would require further analysis with more data points or additional information about the function's behavior.
In this case, as shown in the attached table, it is clear that
For [tex]x_1=1, y_1=f(x)=2[/tex].
For [tex]x_2=2, y_2=f(x)=3[/tex].
For[tex]x_3=, y_3=f(x)=4[/tex].
For [tex]x_4=, y_4=f(x)=5[/tex], and so on.
Thus the rate of change for the interval shown in the table or its slope is constant as evident from the following calculation.
[tex]\frac{(y_2-y_1)}{(x_2-x_1)}=\frac{3-2}{2-1}=1\\ \frac{(y_3-y_2)}{(x_3-x_2)}=\frac{4-3}{3-2}=1\\\frac{(y_4-y_3)}{(x_4-x_3)}=\frac{5-4}{4-3} =1[/tex].
So it is clear that, the rate of change for the interval shown in the table is constant , so the function is a linear function.
what is 8,375 ÷ 45 need it fast!!!!!!
Answer:
186.111111111
Step-by-step explanation:
Answer: the answer is 186.111111
a wrestler is weighing in for their match this evening. their normal weight is 168 pounds, but that weight can vary by as much as 3.2 pounds. write an equation that models this situation and find their minimum and maximum weight.
Introduction
Wrestling is a wonderful activity with many advantages for the student-athlete. It is a sport that is highly
competitive, exciting and satisfying. It is a sport that provides for individual and team competition. It is -
and should be - fun. Unfortunately, the practice of losing weight by not eating, restricting fluid intake and
over-exercising reduces the sport's fun. This information is presented to help clear up misconceptions
regarding wrestling and weight loss. I also hope to give some guidance to those who desire to manage
their weight properly in preparation for and during the wrestling season.
History and Stigma
For too long, the wrestling community has unthinkingly accepted the myth that to be a good wrestler, you
must cut weight. The generally accepted thinking is something like this: if your natural weight is 135
pounds, you may be a good wrestler at 135 pounds. But if you wrestle at 130 pounds, you'll be a better
wrestler. And if you can make it down to 125, you'll be a state champion. No facts support that widely held
view, yet wrestlers and parents subscribe to that faulty reasoning. Looking further back, many remember
the days that losing excessive weight was a specific practice and expectation among wrestlers. It was
supposed to teach sacrifice, commitment, and the idea of “No Pain, No Gain.”
Regardless of the current attitude of the majority of the wrestling community, the stigma that an unhealthy
loss of weight is a requirement of wrestling among outside observers sticks. The Virginia High School
League has followed national guidelines to establish rules that encourage healthy weight management
among wrestlers.
Current Regulations
Preseason weight certification is accomplished with three steps. The first is determining each wrestler’s
body fat percentage using skin fold calipers. Next, the wrestler completes a hydration test, to insure
against a dehydrated weight measurement, and the wrestler weighs in. The third step is the calculation of
the wrestler’s minimum wrestling weight based on 7% body fat for males and 12% for females. The
wrestler may not wrestle at a weight class below his minimum weight during the season. The wrestler is
also restricted from losing more then 1.5% body weight loss per week (official weigh-ins at certification,
matches, and tournaments are used for this calculation). A one-pound per month growth allowance is
provided to allow for the natural growth of this age group. The VHSL advises, and we have instituted,
daily weigh-ins before and after practice to monitor weight-loss and dehydration.
Additionally, the National Federation of State High School Associations has adopted several other rules to
guide coaches and wrestlers while managing their weight. Wrestlers are discouraged from wrestling at a
weight class more then one weight class above their certified weight.
The equation that models the situation of a wrestler's varying weight is w = x +/- 3.2, with x representing the normal weight. The minimum weight is 164.8 pounds and the maximum weight is 171.2 pounds.
Explanation:To write an equation that models the situation, we can use the variables x and w to represent the normal weight and the varying weight, respectively. The equation can be written as w = x +/- 3.2, where the +/- sign represents that the weight can vary by as much as 3.2 pounds. Given that the normal weight is 168 pounds, the minimum weight would be 168 - 3.2 = 164.8 pounds, and the maximum weight would be 168 + 3.2 = 171.2 pounds.
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Shereen drew a scale drawing of a house and its lot. The scale she used was 2 inches : 1 foot. The house's driveway is 64 inches in the drawing. How long is the actual driveway?
Jane has rolled a fair die 7 times and each time has gotten a 3. She says that the probability that she will get a 3 on the next roll is high (close to 1). Is she correct?
A.No, the probability of getting a 3 on a fair die does not change. It will always be
1 /6 no matter what she got on the previous roll
B.Yes, since she has gotten a 3 on the last 7 rolls, the probability of getting a 3 is higher on the next roll.
C.No, the probability of getting a 3 will be slightly higher than any other number but not close to 1
D.There is no way to tell until she rolls the die. You cannot accurately predict what she will get.
plzzzzzzzzzzzzzzzzz help marked brainlyest
Answer:
A.No, the probability of getting a 3 on a fair die does not change. It will always be
Step-by-step explanation:
Get a good grade!
Lulu is taking a road trip to visit family. Her car has a 20-gallon gas tank and the car uses 12 gallons to travel 216 miles.
Which linear equation represents the number of gallons of gas, G, left in the tank after driving m miles?
A. G = 360 - 18m
B. G = 20 - 18m
c. G=20 - 1gm
D. G=360 - 16"
Answer:
The answer is G = 20 - m/18, but none of the answers given is correct.
Step-by-step explanation:
1. Let's review the information given to us to help Lulu to answer the question correctly:
Capacity of the gas tank of Lulu's car = 20 gallons
Lulu can travel 216 miles using 12 gallons
2. Which linear equation represents the number of gallons of gas, G, left in the tank after driving m miles?
G = number of gallons left in Lulu's car
m = Miles driven by Lulu
miles per gallon = 216/12 = 18 miles per gallon
Now, we can write the linear equation, this way:
G = Capacity of the gas tank of Lulu's car - miles driven/miles per gallon
Replacing with the values we know:
G = 20 - m/18
Let's assume Lulu drives 180 miles, using our linear equation, we have:
G = 20 - 180/18
G = 20 - 10 = 10 gallons left
Let's assume Lulu drives 54 miles, using our linear equation, we have
G = 20 - 54/18
G = 20 - 3 = 17 gallons left
The product of two whole numbers is 378 and their sum is 41. What are the two numbers?
Answer:
Step-by-step explanation:
Let the number be x and y
xy = 378.......(1)
x + y = 41......(2)
Making y as subject in (2)
y = 41 - x......(3)
Substitute it in (1)
x(41 - x) = 378
41x - x² = 378
x² - 41x + 378 = 0
x² - 27x - 14x + 378 = 0
(x² - 27x) - (14x - 378) = 0
x(x - 27) - 14(x - 27) = 0
(x -14)(x - 27) = 0
x - 14 = 0 or x - 27 = 0
x = 14 or x = 27
And y = 41 - x
When x = 14
y = 41 - 14 = 27
y = 27
When x = 27
y = 41 - 27 = 14
y = 14
The two numbers are 14 and 27.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
Let the numbers are x and y.
Then,
the system of equations
xy = 378 {equation 1}
x + y = 41 {equation 2}
y = 41 - x
Then
x(41 - x) = 378
41x - x² = 378
x² - 41x + 378 = 0
x² - 27x - 14x + 378 = 0
(x² - 27x) - (14x - 378) = 0
x(x - 27) - 14(x - 27) = 0
(x -14)(x - 27) = 0
x - 14 = 0 or x - 27 = 0
x = 14 or x = 27
And y = 41 - x
When x = 14
y = 41 - 14 = 27
y = 27
When x = 27
y = 41 - 27 = 14
y = 14
Therefore, the 14 and 27 are the numbers.
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Beyonce went to the mall and saw a massage chair that she would have to take a loan out for $6500 to purchase. The bank said that she could get a simple interest rate of 8% for 5 years. What is the total amount that Beyonce will pay for the chair?
Answer:
The total amount that Beyonce will pay for the chair is $9100.
Step-by-step explanation:
The Principal amount of chair = $6500
Rate of interest = 8%
Time = 5 years
Now, SIMPLE INTEREST = [tex]\frac{P\times R \times T}{100}[/tex]
So, here calculating the interest on the chair, we get:
[tex]SI = \frac{6500 \times 5 \times 8}{100} = 2600[/tex]
So, the interest on the amount of chair for 5 years is $2600.
Total amount of chair = Original Amount of Chair + Interest Amount
= $6500 + $2600 = $9100
Hence, the total amount that Beyonce will pay for the chair is $9100.
To find the total amount, calculate the interest and add it to the principal amount.
Explanation:Simple interest is calculated using the formula: I = P * r * t, where I is the interest, P is the principal amount (loan), r is the annual interest rate, and t is the time in years. In this case, the principal amount (loan) is $6500, the annual interest rate is 8%, and the time is 5 years. So, the interest can be calculated as: I = 6500 * 0.08 * 5 = $2600.
To find the total amount that Beyonce will pay for the chair, we need to add the interest to the principal amount. The total amount is given by the formula: Total Amount = Principal + Interest. Therefore, Total Amount = 6500 + 2600 = $9100.
So, Beyonce will pay a total amount of $9100 for the chair, including the principal amount and interest.
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What type of number can be written as a fraction a over b where a and b are integers and b is not equal to zero ?
What type of number can be written as a fraction a over b where a and b are integers and b is not equal to zero ?
The answer is integers.
Examples of integers: 5, -8, 6/9, 100, -4/2
Happy to help!
Find the measure of angle x in the figure below:
60°
50°
110°
70°
Answer:
Step-by-step explanation:
Consider A=60°, B=50°, C=y°=???
So, according to the measurement of angles of a triangle.
A+B+C= 180°
60°+80°+C= 180°
140°+C=180°
C=180°-140°
C=y°=40°
So, x is also 40° since x and y are vertically opposite angles.
trying to solve a exponential function question. Evaluate the function when t=5.
h(t) = 175(1028)t
Answer:
Step-by-step explanation:
a=175
r=2.8
A number to the 7th power divided by the same number to the 3rd power equals 256. What is the number?
Answer:
4
Step-by-step explanation:
7-3=4
then i just messed around with putting numbers to the 4th and got 4
The question asks for a number which, when raised to the 7th power and divided by the same number raised to the 3rd power, results in 256. By understanding the rules of exponents, we find that the number is 4 because 4^4 equals 256.
Explanation:To solve this problem, it's important to know that when you divide two numbers with the same base and different exponents, you subtract the exponents. So, a number to the 7th power divided by the same number to the 3rd power equals that number to the (7-3)th = 4th power.
Therefore, the question is asking for a number which to the 4th power equals 256. The fourth root of 256 is 4 because 4^4 equals 256. So the answer is 4.
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Please I need help on this I need HELP NOW
huh cant see nun............
which expression has a value of 15 when n=7
Answer:
n + 8
Step-by-step explanation:
Next time add a picture please.
Answer:
19 - 28/n
Step-by-step explanation:
i did the test ;)
I need help please and thank you
Answer:
35
Step-by-step explanation:
An isosceles triangle always has two equal angles. As there cannot be another 110° (the triangle cannot have over 180° total), the other two angles must equal eachother. 180° - 110° = 70°. 70° represents the other two angles, so it needs to be divided in 2 to get the answer of 35°.
Find mDEC
A) 90
B) 95
C) 100
D) 120
Answer:
C) 100
Step-by-step explanation:
line AC intersects line DB,
hence ∠AEB and ∠DEC are opposite angles and thus
∠AEB = ∠DEC
5x-10 = 4x+12 (subtract 4x from both sides)
5x - 4x - 10 = 12
x - 10 = 12 (add 10 to both sides)
x = 12 + 10 = 22 degrees
∠DEC = 4x+12
= 4(22) + 12
= 88 + 12
= 100 degrees
1. What is the solution to the system of equations?
3x - 6y = -12
x - 2y = -8
(a) Use the substitution method to justify that the given system of equations has no solution.
(b) What do you know about the two lines in this system of equations?
Answer:
Step-by-step explanation:
(a)
3x - 6y = -12.,......(1)
x - 2y = -8.…......(2)
from equation (2),by adding 2y to both sides, x= -8 + 2y.....(3)
Let's substitute the value of x in equation (1)
3(-8 + 2y) - 6y = -12
-24 + 6y - 6y = -12
6y - 6y = 12..,..(4)
From equation (4) we can see that both equations (1) and (2) has no solutions for x and y
(b)They are two parallel lines of slope of 2 and intercepts on y at 2 and 4
(a) The given system has no solution.
(b) The lines are parallel and never intersect.
To determine the solution of the system of equations using the substitution method, follow these steps:
Substitution Method
Start with the given system of equations:Interpretation of Result
Because the system of equations has no solution, we deduce that the lines represented by these equations are parallel and never intersect. Thus, they do not share any common points.
Therefore, the system of equations has no solution, and the lines are parallel.
I need help on that, please and thank you.
Answer:
Step-by-step explanation:
X + 61° = 90° {right angle}
X = 90° - 61°
X = 29°
The length of a snake in a video game doubles every minute. The function f(x) = 10. (2)* represents
the length of the snake in centimeters (cm). The time x = 0 represents when the game started.
Answer:
Part a) see the explanation
Part b) The graph in the attached figure
Step-by-step explanation:
The complete question is
The length of a snake in a video game doubles every minute. the function f(x)=10*(2)^x represents the length of the snake in centimeters. the time x=0 represents when the game started.
a) label the correct axes with "length (cm)" and"time (minutes)"
b) graph f(x)=10*(2)^x
Part a) we know that
we have a exponential function of the form
[tex]f(x)=a(b^x)[/tex]
where
f(x) -----> the length of a snake in a video game in centimeters
x ----> the time in minutes
a is the initial value or y-intercept of the linear equation
b is the base of the exponential equation
In this problem
[tex]f(x)=10(2^x)[/tex]
so
[tex]a=10\ cm[/tex] ---> initial value, value of y when the value of x is equal to zero[tex]b=2[/tex] ----> factor growth
[tex]b=(1+r)\\r=b-1=2-1=1[/tex]
[tex]r=100\%[/tex] ----> percent rate of change
Is a exponential growth function
Part b) Graph the function
To graph the function we need different points
assume different values of x and find the values of f(x)
For x=0 ----> [tex]f(0)=10(2^0)=10[/tex] ----> point (0,10)
For x=1 ----> [tex]f(1)=10(2^1)=20[/tex] ----> point (1,20)
For x=2 ----> [tex]f(2)=10(2^2)=40[/tex] ----> point (2,40)
For x=3 ----> [tex]f(3)=10(2^3)=80[/tex] ----> point (3,80)
For x=4 ----> f(4)=10(2^4)=160 ----> point (4,160)
Plot the points, connect them and draw the graph
see the attached figure
If Johnny hits 51 baseballs that are thrown to him and he has 73 pitches thrown
to him, what is his efficiency?
Answer:
0.699 (=69.9%)
Step-by-step explanation:
Efficiency = total hits / total attempted
given total hits = 51 and total attempted = 73
Efficiency = 51/73 = 0.699 (=69.9%)
88.1 - 2.3f = 72.46
i know how to do it but at the same time i dont lol
Answer:
[tex]f=6.8[/tex]
Step-by-step explanation:
Given equation:
[tex]88.1-2.3f=72.46[/tex]
To solve for the unknown variable [tex]f[/tex].
Solution:
In order to solve for [tex]f[/tex], we will isolate [tex]f[/tex] alone on one side by carrying out math operations to both sides.
We have:
[tex]88.1-2.3f=72.46[/tex]
Subtracting both sides by 88.1
[tex]88.1-88.1-2.3f=72.46-88.1[/tex]
[tex]-2.3f=-15.64[/tex]
Dividing both sides by -2.3
[tex]\frac{-2.3f}{-2.3}=\frac{-15.64}{-2.3}[/tex]
∴ [tex]f=6.8[/tex] (Answer)
Each bagel sells for $1.50 and a muffin sells for $2.00. One morning the bakery sells 35 bagels and muffins for $58.50. How many bagels and muffins did they sell?
The bakery sold 23 bagels and 12 muffins.
Step-by-step explanation:
Given,
Cost of each bagel = $1.50
Cost of each muffin = $2.00
Total sold = 35
Revenue generated = $58.50
Let,
x be the number of bagels
y be the number of muffins
According to given statement;
x+y=35 Eqn 1
1.50x+2y=58.50 Eqn 2
Multiplying Eqn 1 by 2
[tex]2(x+y=35)\\2x+2y=70\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](2x+2y)-(1.50x-2y)=70-58.50\\2x+2y-1.50x-2y=11.50\\0.50x=11.50[/tex]
Dividing both sides by 0.50
[tex]\frac{0.50x}{0.50}=\frac{11.50}{0.50}\\x=23[/tex]
Putting x=23 in Eqn 1
[tex]23+y=35\\y=35-23\\y=12[/tex]
The bakery sold 23 bagels and 12 muffins.
Keywords: linear equation, elimination method
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