Rosen 15 how many solutions are there to the equation x1 x2 x3 x4 x5
Which properties of equality justify steps b and d?
1. Multiplication Property of Equality; Subtraction Property of Equality
2. Subtraction Property of Equality; Division Property of Equality
3. Subtraction Property of Equality; Multiplication Property of Equality
4. Subtraction Property of Equality; Subtraction Property of Equality
The properties that justify steps b and d, is 1. Multiplication Property of Equality; Subtraction Property of Equality.
Understanding these properties is crucial in solving equations properly.
Key Properties of Equality:
Multiplication Property of Equality: This property states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal.
Example: If [tex]a = b[/tex], then [tex]a \times c = b \times c[/tex].
Subtraction Property of Equality: This property indicates that if you subtract the same number from both sides of an equation, the two sides will also remain equal.
Example: If [tex]a = b[/tex], then (a - c = b - c.
Division Property of Equality: Similar to multiplication, this property states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal.
Example: If [tex]a = b[/tex] and [tex]c \neq 0[/tex], then [tex]\frac{a}{c} = \frac{b}{c}[/tex].
Justification Steps b and d:
Given the context, let's assume step b involves subtracting a term from both sides of an equation, and step d involves multiplying both sides by a number.
For step b (subtracting x):
This step is justified by the Subtraction Property of Equality because the same amount [tex]x[/tex] is subtracted from both sides, which keeps the equality balanced.
For step d (multiplying by a number):
This step is justified by the Multiplication Property of Equality as you are multiplying both sides of the equation by the same non-zero number, thus preserving the equality.
helppppppppppppppppppppppppppppppp
Select all of the potential solution(s) of the equation 2log5x=log54.
Given :[tex] 2log_{5} x^{2} =log_{5} 2^{2} [/tex]
To solve for x we use the logarithm rule for powers.
The log rule for powers states:
[tex] mlog_{a}n =log_{a} n^{m} [/tex]
We apply this rule to the left side of the equation.
[tex] log_{5} x^{2} =log_{5} 4
Both sides have log with same base so it can be eliminated.
Eliminating log from both sides we have:
[tex] x^{2} =4
To solve for x we take root of both sides
x=2,-2.
How do I solve #21???? Please don't just give me the answer.... tell me how u got it... thanks!
The volumes of two similar solids are 53cm³ and 1113cm³. Which is the ratio of the corresponding sides?
A. 7
B. 21
C. √21
D. ³√21
Each chef at "sushi emperor" prepares 151515 regular rolls and 202020 vegetarian rolls daily. on tuesday, each customer ate 222 regular rolls and 333 vegetarian rolls. by the end of the day, 444 regular rolls and 111 vegetarian roll remained uneaten. how many chefs and how many customers were in "sushi emperor" on tuesday?
Answer:
There were 2 chefs and 13 customers.
Step-by-step explanation:
Kana earns a $25,000 salary in the first year of her career. Each year, she gets a 4% raise. How much does Kana earn in the first 10 year of her career? (Round the final answer to the nearest dollar)
Please help !!! Need fast
Find the equation, f(x) = a(x-h)2 + k, for a parabola that passes through the point (2,4) and has the origin as its vertex. what is the standard form of the equation
What is the probability that a point chosen at random in the rectangle is also in the blue triangle
Answer:
The probability that a point chosen at random in the rectangle is also in the blue triangle is:
1/2
Step-by-step explanation:
We are given a figure
We have to find the probability that a point chosen at random in the rectangle is also in the blue triangle.
Area of rectangle= 4×5 sq. in.
= 20 sq. in.
The area of blue triangle=[tex]\dfrac{1}{2}\times 4\times 5[/tex]
= 10 sq. in.
P(that a point chosen at random in the rectangle is also in the blue triangle)
= area of blue triangle/whole area of the rectangle
= 10/20
= 1/2
Answer: the answer is 1/2
Step-by-step explanation:
This is embarrassing.. went to a Hobby Lobby job interview.. and flunked the math test.. ack! this involved percentages..how do you get 66% off of a total, and like tax % 7.5 we are not allowed to use a calculator
To get a percentage off of a total without a calculator, multiply the total by the percentage as a decimal. To calculate the total amount including tax, multiply the total by the tax percentage as a decimal and then add the result to the total.
Explanation:To calculate a percentage off a total without using a calculator, you can multiply the total by the percentage as a decimal. For example, to find 66% off of a total, multiply the total by 0.66. To calculate the total amount including tax, you can add the tax amount to the original total. For a 7.5% tax, multiply the total by 0.075 and then add the result to the total.
Learn more about Percentages here:https://brainly.com/question/32197511
#SPJ11
Polynomials are closed under the operation of subtraction.
Which statement best explains the meaning of closure of polynomials under the operation of subtraction?
A. When any two polynomials are subtracted, the coefficients of like terms are always subtracted.
B. When any two polynomials are subtracted, the result is always a polynomial with negative coefficients.
C. When any two polynomials are subtracted, the result is always a polynomial.
D. When any two polynomials are subtracted, the result is always a monomial or a binomial.
A polynomial is an expression consisting of variables and coefficients, that involves the operations of addition, subtraction, multiplication .
polynomials are closed under the operations of addition, subtraction, and multiplication.
Polynomials will be closed under an operation if the operation produces another polynomial.
The statement that best explains the meaning of closure of polynomials under the operation of subtraction is
option C. When any two polynomials are subtracted, the result is always a polynomial.
z varies jointly with x and y. when x=2 and y=3, z=60. what is the value of z when x=4 and y=9?
A. 360
B. 60
C. 90
D. 40,
.please help me thank you you will be given brainley
Soybean meal is 14% protein; cornmeal is 7% protein. How many pounds of each should be mixed together in order to get 280lb mixture that is 8% protein?
How many pounds of the cornmeal should be in mixture?
How many pounds of the soybean meal should be in mixture? 50 POINTS!!!!
The relationship between the monthly fee that the cable company charges for internet service and the fee for downloading over 32KB of information is modeled by the linear function f (x) = 1.25x + 45, where x is the number of KB over 32. If the total bill for a month is $170, how many KB was in excess of 32 KB that month?
I need help ASAP. I don't understand how to solve this
3. Your fixed expenses are $1,500.45/month. Your emergency fund has 4 month’s worth of coverage. You invest half in a savings account with an interest rate of 3.15% APR and the other half in a 45 day CD with an interest rate of 4.65% APR. How much is your total interest in 45 days?
4. If you had invested only 1 month’s worth of the emergency fund in the saving account at a 3.15% APR and the remainder in the 45 day CD at a 4.65% APR, what is the difference in the interest earned in 45 days when compared with question #3?
The total interest earned in 45 days when the emergency fund is evenly split between a savings account and a CD is approximately $29.17. If 1 month's worth of emergency funds were in the savings account and the rest in a CD, the total interest would be approximately $38.05. The difference between the two scenarios is approximately $8.88.
Calculating Interest for Emergency Funds in Savings and CDs
To answer the student's question about the interest earned in 45 days on the emergency fund invested half in a savings account and half in a 45-day CD, as well as the comparison with an alternative investment scenario, we need to perform several calculations using the given interest rates and time periods.
Answer to Question 3
Firstly, the student's fixed expenses are $1,500.45/month, so for a 4-month emergency fund coverage, the total amount saved would be $1,500.45 x 4 = $6,001.80.
Half of this amount goes into the savings account and the other half into the CD, so each gets $3,000.90.
The interest in the savings account with an APR of 3.15% for 45 days (1.5 months) would be calculated using the formula for simple interest: Interest = Principal x Rate x Time.
So the interest earned on the savings account would be: $3,000.90 x (3.15% per year / 12 months) x 1.5 months ≈ $11.85.
The interest in the 45-day CD with an APR of 4.65% would be calculated similarly: $3,000.90 x (4.65% per year / 12 months) x 1.5 months ≈ $17.32.
Therefore, the total interest earned in 45 days would be approximately $11.85 + $17.32 = $29.17.
Answer to Question 4
If only 1 month's worth of emergency fund ($1,500.45) was invested in the savings account and the remainder in the CD, the interest from the savings account would not change, but the interest from the CD would, as it would be calculated on a larger principal of $4,501.35.
The new interest for the CD investment would be $4,501.35 x (4.65% per year / 12 months) x 1.5 months ≈ $26.20.
So the new total interest would be $11.85 (from savings) + $26.20 (from CD) = $38.05.
The difference in interest between the two scenarios would be $38.05 - $29.17 = $8.88.
This is when one word has more than one definition and its 15 letters
Find the average rate of change of the function over the given interval. f(x) = 3x − 2; [0, 5]
The average rate of change of the function over the given interval is 3.
Explanation:To find the average rate of change of the function over the given interval, we need to calculate the change in the function values and divide it by the change in the input values.
Step 1: Calculate the function values for the two endpoints of the interval.
f(0) = 3(0) - 2 = -2
f(5) = 3(5) - 2 = 13
Step 2: Calculate the change in the function values.
Change in function values = f(5) - f(0) = 13 - (-2) = 15
Step 3: Calculate the change in the input values.
Change in input values = 5 - 0 = 5
Step 4: Divide the change in function values by the change in input values.
Average rate of change = (Change in function values) / (Change in input values) = 15 / 5 = 3
if 7(t-4)-2t=4(t-3), what is the value of t?
The table shows the percentage of students in each of three grade levels who list soccer as their favorite sport. Soccer Sophomores (35%) 50%
Juniors (33%) 45%
Seniors (32%) 30%
Total (100%) (0.5)(0.35) + (0.45)(0.33) + (0.32)(0.3) = 0.4195 or about 42%
Find the probability that the student is a junior, given that soccer is the favorite sport listed.
P(junior | soccer) = ???%
The probability that the student is a junior, given that soccer is the favorite sport listed is 0.354.
How to calculate the probability?The percentage of student on Junior level who like soccer will be:
= 33% × 45%
= 0.1485
The total percentage of students who like soccer is 42%. Therefore, probability that the student is a junior, given that soccer is the favorite sport listed will be:
= 0.1485/0.42
= 0.354
Learn more about probability on:
https://brainly.com/question/24756209
Please help and show all work. 20 points.
A spinner with
9
equally sized slices is shown below. The dial is spun and stops on a slice at random. What are the odds in favor of landing on a white slice?
note their are 7 white and 2 black
True or False. (0,0) is a solution to problem #1. This means that (0,0) is in the solution region.
The angle of depression from D to F measures 10°. If DE = 300 m, find DF. Round your answer to the nearest tenth.
304.6 m
1,910.2 m
1,727.6 m
1,701.4 m
Answer:
Option C) 1727.6 m
Step-by-step explanation:
Given that the angle of depression from D to F measures 10°.
Also given that DE =300 m.
Since 10 is angle of depression, we can visualize a right triangle with hypotenuse DF=300 m and EF, DE two legs.
In the right triangle DEF, the angle opposite 10 is the side DE[tex]\frac{DF}{DE} =\frac{hypotenuse}{opposite side}= cosec 10\\\\DF =300 cosec 10 = 1727.6 m[/tex]
by Using trignometric ratios
15p for an answer please
The diagram shows a line with intercepts 3 and 9 and one of many rectangles which can be inscribed under this line and within the first quadrant.
a. Write an equation for the line.
b. Determine if the rectangle can have x = 4 and y = 2 as its dimensions.
c. Find x and y if the rectangle is a square.
d. Write an expression for A, the area of the rectangle, using x as the only variable.
e. Find x if the area of the rectangle is 6.
f. Which x gives the rectangle its largest area?
The histogram shows the number of hours volunteers worked one week.
What percent of the volunteers worked 8 to 11 hours or 16 to 19 hours?
Enter your answer in the box.
%
Answer: 45%
Step-by-step explanation:
From the given histogram, The number of volunteers worked 8 to 11 hours = 5
The number of volunteers worked 16 to 19 hours = 4
The number of volunteers worked 8 to 11 hours or 16 to 19 hours =5+4=9
Total number of volunteers = 4+2+5+4+4+1=20
The percent of volunteers worked 8 to 11 hours or 16 to 19 hours is given by :-
[tex]\frac{9}{20}\times100=45\%[/tex]
Hence, the percent of the volunteers worked 8 to 11 hours or 16 to 19 hours =45%
Simone is buying 10 bracelets for her friends. Each bracelet costs $8. Simone is also buying a necklace for her mother for $18. She believes that her total will be $98. Which expression could be used to estimate the reasonableness of Simone’s total? 8 × $8 + $10 8 × $8 + $18 10 × $8 + $20 10 × $10 + $10