Sven is trying to find the maximum amount of time he can spend practicing the five scales of piano music he is supposed to be working on. He has 70 minutes to practice piano and would like to spend at least 55 minutes playing songs instead of practicing scales. So, Sven sets up the following inequality, where t is the number of minutes he spends on each scale, and solves it.
70 − 5t ≤ 55
−5t ≤ −15
t ≥ 3
Sven has concluded that he should spend 3 minutes or more on each scale. Is this correct? If not, what mistake did he make? Then solve for the correct answer.
Answer:
He should spend 3 minutes or less on each scale
Sven made a mistake in the symbol of inequality, placing lesser or equal instead of greater or equal
Step-by-step explanation:
Let
t ------> is the number of minutes he spends on each scale
Remember that the phrase "at least" is equal to "greater than or equal"
so
The inequality that represent this scenario is
[tex]70-5t \geq 55[/tex]
solve for t
[tex]-5t \geq 55-70[/tex]
[tex]-5t \geq -15[/tex]
Multiply by -1 both sides
[tex]5t \leq 15[/tex]
Divide by 5 both sides
[tex]t \leq 3[/tex]
Sven is incorrect
He should spend 3 minutes or less on each scale
Sven made a mistake in the symbol of inequality, placing lesser or equal instead of greater or equal
Answer:
i dont think he made a mistake
Step-by-step explanation:
lmk if you need an explanation
Como resolver 2a(ab+b)-b (3x+a2) eliminando os parenteses
36 is 12% of what number?
A gardener is attempting to put a fence around a rectangular garden. The total length of the fence is 30 feet. The width of the garden is 3 ft longer than the length. What are the length and width of the garden?
Jillian is selling boxes of cookies to raise money for her basketball team. The 10 oz. box costs $3.50, while the 16 oz. box costs $5.00. At the end of one week, she collected $97.50, selling a total of 24 boxes. The system of equations that models her sales is below. x+ y= 24 3.50x + 5.00y = 97.50 Solve the system of equations. How many 10 oz. boxes were sold?
Answer:
There are 15 boxes of 10 oz boxes
Step-by-step explanation:
Let the number of boxes of 10 oz = x
and let the number of boxes of 16 oz = y
By the statement
"Total number of boxes sold is 24"
Equation for the statement will be
x + y =24 ---------------(1)
By the statement
"she collected $97.50 while rate of 10 oz box is $3.50 and rate of 16 oz box is $5.00."
Equation for the statement will be
1.5x + 5y = $97.50 ------------(2)
From equation (1) we put the value of y = 24 - x in equation (2)
1.5x + 5(24 - x) = 97.50
1.5x + 120 - 5x = 97.50
-3.5x = 97.50 - 120
3.5x = 22.50
x = [tex]\frac{22.5}{1.5}[/tex]
x = 15
Therefore, number of 10 oz boxes is 15.
Is |a+b|=|a|+|b| for all rational numbers a and b? Explain.
The equation |a+b|=|a|+|b| is not always true for all rational numbers a and b.
Given that, |a+b|=|a|+|b|.
We need to check whether |a+b|=|a|+|b| for all rational numbers a and b.
What is a rational number?Rational numbers are in the form of p/q, where p and q can be any integer and q ≠ 0. This means that rational numbers include natural numbers, whole numbers, integers, fractions of integers, and decimals (terminating decimals and recurring decimals).
Now,
Example 1:
a=-3 and b=5
|-3+5|=|-3|+|5|
⇒2≠8
Example 2:
Take a=2 and b=4
|2+4|=|2|+|4|
⇒6=6
Therefore, from the above examples, we understood that |a+b|=|a|+|b| are not always true.
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Answer: |a+b|=|a|+|b| is not always true
Step-by-step explanation:
The equation |a+b|=|a|+|b| is not always true for all rational numbers a and b.Given that, |a+b|=|a|+|b|.We need to check whether |a+b|=|a|+|b| for all rational numbers a and b.What is a rational number?Rational numbers are in the form of p/q, where p and q can be any integerand q ≠ 0. This means that rational numbers include natural numbers, whole numbers, integers, fractions of integers, and decimals (terminating decimals and recurring decimals).Now, Example 1:a=-3 and b=5|-3+5|=|-3|+|5|⇒2≠8Example 2:Take a=2 and b=4|2+4|=|2|+|4|⇒6=6Therefore, from the above examples, we understood that |a+b|=|a|+|b| are not always true.To learn more about the rational number visit:brainly.com/question/17450097.
How many solutions does an equation have when you isolate the variable and it equals a constant?
Final answer:
Isolating a variable to equal a constant typically results in one solution, but special cases may have no solution or infinitely many. The number of solutions depends on the form of the equation once the variable has been isolated.
Explanation:
When you isolate the variable in an equation and it equals a constant, the equation typically has exactly one solution. This is because each value of the variable corresponds to exactly one value of the constant, establishing a one-to-one relationship. For instance, if an equation is simplified to the form x = 5, then the solution set consists of the single number 5. However, if you have an equation like 0x = 0, you encounter a special case where any value of x satisfies the equation, resulting in infinitely many solutions. Alternatively, an equation like 0x = 5 has no solution, as there is no value of 'x' that can make this equation true. When equations are rearranged to isolate a natural logarithm, such as In A, ensuring consistency with assumptions, as in symmetric solutions and physical calculations, can help determine valid solutions.
Is every isosceles triangle equilateral? Is every equilateral triangle isosceles? Explain
turn 4b-2 into a word phrase
how do you put 4.110 in words
Which function represents a horizontal shift of f(x)=5^x by 4 units to the right?
Answer: [tex]g(x)=5^{x-4}[/tex]
Step-by-step explanation:
When a function f(x) is shifted horizontally by n units to the right , the new function will become :-
[tex]g(x)=f(x-n)[/tex]
The given function : [tex]f(x)=5^x[/tex]
Now, if the given function shifted 4 units to the right , then the new function will become :
[tex]g(x)=f(x-4)[/tex]
[tex]g(x)=5^{x-4}[/tex]
Hence, the function represents a horizontal shift of [tex]f(x)=5^x[/tex] by 4 units to the right will be :-
[tex]g(x)=5^{x-4}[/tex]
Jermey drew a polygon with four right angles and four sides with the same length . Name all the polygons that he could have drawn
Ashley has started a blog and is using the bar chart below to keep track of how many followers she has. How many followers will she have on day n
15 POINTS!!!
A third-degree polynomial has 4 intercepts. A third-degree function can have as many as 3 zeros only. Is there a way for both statements to be correct? Explain your answer.
Perform the indicated operation. 2/3 - 5/8
1. 5/12
2. 5/6
3. 1/24
Compare the expressions using <, >, or =. Show all your work. (18 – 3) ÷ (6 - 1) _____ 4 • (10 – 3) – 4 • 2
Following the order of operations, (18 – 3) ÷ (6 - 1) simplifies to 3 and 4 • (10 – 3) – 4 • 2 simplifies to 20. Therefore, comparing these two statements using the symbols '>', '<', or '=', we infer that 3 < 20.
Explanation:To solve this problem, we need to follow the order of operations (also commonly known as BODMAS or PEDMAS), which stands for Brackets, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
Let's first simplify the expressions on both sides of the comparison:
(18 – 3) ÷ (6 - 1) simplifies to 15 ÷ 5 = 3 4 • (10 – 3) – 4 • 2 simplifies to 4 • 7 - 8 = 28 - 8 = 20.
Now, we can compare these two numbers. Since 3 is less than 20, we use the symbol '<' to compare these two numbers. Therefore, (18 – 3) ÷ (6 - 1) < 4 • (10 – 3) – 4 • 2.
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if l=prt, which equation is equivalent to t ?
you would divide both sides by pr
so the equation would be t= I/pr
Which expression is equivalent to −1.3+(−4.9)+(−2.6) ?
A −(1.3−4.9)+(−2.6)
B −1.3−(4.9+2.6)
C −1.3+(4.9+2.6)
D (1.3+4.9+2.6)
Answer:
B −1.3−(4.9+2.6)
Please mark me as brainlyistAnswer:
-1.3-(4.9+2.6)
I
is 10/25 and 40/100 equal to 2/5
The ratio of height to width of a tv screen is 9 to 16 how high is a screen that is 30 inches wide
Final answer:
The height of a TV screen with a width of 30 inches and a ratio of height to width of 9 to 16 is approximately 16.875 inches.
Explanation:
To find out how high a TV screen is that is 30 inches wide with a ratio of height to width of 9 to 16, we can set up a proportion using the given ratio and solve for the height. The ratio can be written as:
Height : Width = 9 : 16
Let's call the actual height of the screen 'h'. Using the proportion we have:
9/16 = h/30
To solve for 'h', we cross-multiply:
9 * 30 = 16 * h
270 = 16 * h
Now, to find the height 'h', we divide both sides of the equation by 16:
h = 270/16
h = 16.875 inches
Therefore, the height of the screen that is 30 inches wide is approximately 16.875 inches.
Two cars on a roller coaster hold 14 riders combined. If 12 cars are linked together, how many riders can fit on the roller coaster at one time? Explain how to solve this problem.
Answer:
The rate of riders to cars is 14 divided by 2. So the unit rate is 7 riders per car. Multiply 7 riders by 12 cars to find that 84 riders can fit on the roller coaster at one time.
Wot it's the missing number x9=6x3
What do you add to 2 3/8 to make 6
The number must be added to [tex]2\frac{3}{8}[/tex] to make 6 is [tex]3\frac{5}{8}[/tex].
We need to find what we need to add to [tex]2\frac{3}{8}[/tex] to make 6.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
The fraction [tex]2\frac{3}{8}[/tex] can be written as 19/8
Let x be the number added to given fraction, that is
19/8 +x=6
⇒ x=6-19/8
⇒ x= (48-19)/8
⇒ x= 29/8
⇒ x= [tex]3\frac{5}{8}[/tex]
Hence, the number must be added to [tex]2\frac{3}{8}[/tex] to make 6 is [tex]3\frac{5}{8}[/tex].
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2⋅(3^6*3^−5)
1. 2/3
2. 3
3. 6
4. 18
The circle with center (1,5) and radius 4 has equation
1. Kim's age is twice that of her sister. When you add Kim's age to her sister's age, you get 36. How old is each sister? You must complete all sections of this questions to receive full credit.
(a) Write an equation that represents the situation. Explain any variable used.
(b) Solve the equation from Part (a). Show your work. State your solution as a complete sentence.
0.567 as a fraction
Only the 5 and 7 repeats
a typical marathon is 26.2 miles Aleexis averages 12 km per 1 hour when running in marathons. Use dimensional Analysis to determine how long it would take Aleexis to complete a marathon
Suzi starts her hike at an elevation below sea level .when she reached the end of the hike she is still below sea level at - 127feet. What was the change in elevation from the beginning of Suzi hike to the end of the hike?
Kenya has 2 hours to make a 104 mile trip. What rate must she average to make the trip in 2 hours? A) 50 mph B) 51 mph C) 52 mph D) 53 mph