The direct variation equation is a linear equation in two variables and is given by y = kx where k is the constant proportionality. The direct variation graph in a coordinate plane is a straight line. The ratio of two quantities in a direct variation is a constant.
Now, According to the question:
What is Direct Variation?
Direct variation exists between any two variables when one quantity is directly dependent on the other i.e. if one quantity increases with respect to the other quantity and vice versa. It is the relationship between two variables where one of the variables is a constant multiple of the other. Since the two variables are directly related to each other it is also termed as directly proportional.
Hence, The direct variation equation is a linear equation in two variables and is given by y = kx where k is the constant proportionality. The direct variation graph in a coordinate plane is a straight line. The ratio of two quantities in a direct variation is a constant.
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identify the angles as complementary or supplementary
Answer:
either of two angles whose sum is 90°.either of two angles whose sum is 180°.
Step-by-step explanation:
solve the system of equations using substitution
2x+2y=38
y=x+7
Answer:
x = 6 and y = 13
Step-by-step explanation:
2x + 2y = 38 ⇒ eq 1
y = x + 7 ⇒ eq 2
Substituting the value of y from eq 2 in 1:
2x + 2(x + 7) = 38
2x + 2x + 14 = 38
4x = 24
x = 24/4
x = 6
Now substituting the value of x in eq 2:
y = ( 6 ) + 7
y = 13
solve the system of equations using substitution
2x+2y=38
y=x+7
Answer:
x= 6, y= 13
An iceberg weighs 450,000 pounds. If it loses 0. 2% of its weight in a day, what is its new weight at the end of the day?
The new weight at the end of the day will be = 450000-9000 = 441000 Pounds.
The current weight of the Iceberg = 450,000 pounds
Percentage decrease in weight every day = 0.2%
So, for determining the value of the percentage decrease in the weight, we need to first find the value of 2% of 450000
For converting the value given in percentage to the fraction value we will divide the given number by 100.
So, the value 2% can be written as (2/100)
Now calculate the value of 2% of 450000
We will get it as:
(2/100)*450000 = (2*4500) = 9000 Pounds.
After a day, the weight of the iceberg decreases by 9000 Pounds
So, for determining the value of weight at the end of the day, we will subtract the value decreased during the day from the value of weight at the start of the day.
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write 3 √78 using exponents
Using exponents, 3√78 can be written as (3^(1/3))(78^(1/3))^3.
What is an ExponentAn exponent is a mathematical notation that represents the number of times a number, called the base, is multiplied by itself. For example, in the expression "2^3", the base is 2 and the exponent is 3. The exponent tells us that we need to multiply the base 2 by itself 3 times, resulting in 222 = 8. So, 2^3 = 8. The exponent is usually written as a small number above and to the right of the base, called the "power" or "index" of the base. Exponents can also be written using the notation "a^n" where a is the base and n is the exponent.
3 √78 can be written as (3^(1/3))*(78^(1/3)) using exponents.
3^(1/3) is the cube root of 3, and 78^(1/3) is the cube root of 78.
So, 3 √78 can be written as (3^(1/3))(78^(1/3)) or (3^(1/3))(78^(1/3))^3.
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A bank account of 45000 loses 3.5% of its value each month. What is the value of the account after 1 year?
If a bank account of 45000 loses 3.5% of its value each month, based on the exponential function, its value after 1 year is $29,345.40.
What is an exponential function?An exponential function is described as a mathematical function in the form of f(x) = aˣ.
In this function, x is a variable and a is a constant called the base.
Exponential functions may represent exponential growth or exponential decay.
In this situation, we have an exponential decay function as follows:
Initial value of the bank account = $45,000
Decay rate per month = 3.5%
Number of periods = 12
Decayed value after 1 year = Initial value x (1 - 0.035)^12
= $45,000 x 0.965^12
= $45,000 x 0.65212
= $29,345.40
Thus, the bank account will be valued at $29,345.40 after 1 year.
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help quick
A student has 4 fifths gallons of popcorn to give away. He wants to split it evenly between his 7 friends. How much popcorn does each friend receive?
1 over 3 gallons
4 over 35 gallons
11 over 5 gallons
28 over 5 gallons
Answer:
2nd option
Step-by-step explanation:
4/5 / 7 = 4/35 or 4 over 35 gallons
What is the quotient of x 3 3x 2 4x 12 )+( x 2 5x 6?
The quotient of (x^3 + 3x^2 - 4x - 12)/(x^2 + 5x + 6) is (x - 2).
To find the quotient of (x^3+3x^2-4x-12)/(x^2+5x+6) we can use polynomial long division method.
First, divide x^3 by x^2 and write down the quotient (x)
To find the remainder :
(x^3 + 3x^2 - 4x - 12) - x(x^2 + 5x + 6)
= x^3 + 3x^2 - 4x - 12 - x^3 - 5x^2 - 6x
= -2x^2 - 10x - 12
Now divide -2x^2 by x^2 and get the quotient (-2)
Then the remainder is :
(-2x^2 - 10x - 12) - (-2)(x^2 + 5x + 6)
= -2x^2 - 10x - 12 + 2x^2 + 10x + 12
= 0
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6. On the axes provided below, sketch a possible graph for a function f with the
specified properties.
i. the domain is -1,1]
ii. f(-1) = f(0) = f(1) = 0
iii. lim f(x) = lim f(x) = lim f(x) = 1
211-
4
Answer: The domain of the function f is [-1,1], meaning that the input values (x) can be any value between -1 and 1, inclusive of -1 and 1.
The function f(-1) = f(0) = f(1) = 0, meaning that the output value (y) is 0 when the input value (x) is -1, 0 or 1.
The limit of f(x) as x approaches -1,0 and 1 is 1. This means that as x gets closer and closer to -1, 0 and 1, the output value (y) approaches 1.
A possible graph of a function with these properties is a function that has a horizontal asymptote at y=1, and intersects the x-axis at -1, 0, and 1. It means that the function approaches y =1 as x gets closer to -1, 0, and 1 but never reach the point. Also, the function is zero at -1, 0, and 1.
This function is called the absolute value function, and it can be represented by f(x) = |x|.
However, the graph you provided in the question is not correct. The function is not a parabola, it's a step function. The graph is not smooth and it has vertical lines at -1, 0, 1.
Step-by-step explanation:
What is meant by associative property, commutative property and distributive property?
The commutative, associative, and distributive properties are the properties of addition and multiplication.
The associative and commutative characteristics in mathematics are constant rules that apply to addition and multiplication.
The commutative property states that moving numbers about will still result in the same answer, while the associative property states that rearranging the numbers will provide the same result.
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.
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Answer:
The distributive property tells us how to solve equations in the form of a(b + c). The distributive property is sometimes called the distributive law of multiplication and division. Normally when we see an equation like this … 4(8+3) distributive property format 4(8+3) -> 4(11) -> 44 we just evaluate what’s in the parentheses first, then solve it: 4(8+3)=4x8 + 4x3=44 These are the 2 methods
Step-by-step explanation:
How do you solve algebraic expressions in simplest form?
Answer:
Step-by-step explanation:
To solve an algebraic expression in simplest form, you can follow these steps:
1. Use the order of operations (PEMDAS) to simplify any arithmetic in the expression (parentheses, exponents, multiplication and division, addition and subtraction).
2. Combine like terms by adding or subtracting any coefficients in front of similar variables.
3. Divide or multiply both sides of the equation by the same non-zero number to solve for the variable.
4. If possible, factor the expression to make it simpler.
5. If the expression is a fraction, check for a common denominator and then simplify by canceling any common factors in the numerator and denominator.
6. If the expression is a radical, check for a perfect square and simplify by taking the square root of the number inside the radical.
7. Use the properties of exponents and logarithms to simplify the expression.
8. Evaluate the expression by plugging in the values of any known variables.
It's important to keep in mind that there may be multiple ways to simplify an algebraic expression and the solution that is in simplest form may not always be obvious.
(complete solution) can someone help me here please thank you everyone! lovelots
Hope it helps.
If you have any query, feel free to ask.
help please . ☠️☠️☠️just give me an answer tbh
This is a is a rectilinear shape, so the value of x is 4.
What is a rectilinear shape?A planar figure or form with all of its sides meeting at right angles is known as a rectilinear figure in geometry. A rectilinear has an internal angle at each of its vertices that is either 90 degrees (90°) or 270 degrees (270°).Simply multiply the lengths of the longer and shorter sides to determine the area of a rectangle. The units must be in cm2 because we are working with area (centimetres squared). Let's now examine how we might apply this information to determine the area of rectilinear forms.This is a is a rectilinear shape. so the value of x is 4.To learn more about rectilinear shape refer to:
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Given that a = 16 cm and b = 17 cm, work out the height of the triangle.
if a = 16 cm and b = 17 cm then the height of triangle is 15 cm
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given that a = 16 cm and b = 17 cm
We have to find the height of the triangle.
The height of the triangle is perpendicular to a.
It forms a right angle triangle.
The base is a/2=8 cm and b is 17 cm. we have to find h.
By pythagoras theorem,
8² + h² = 17²
64+h² =289
h² =225
Square root on both sides
h=15
Hence, if a = 16 cm and b = 17 cm then the height of triangle is 15 cm.
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The area of a rectangular ink pad is 32 square centimeters. The perimeter is 24 centimeters. What are the dimensions of the ink pad?
Answer:
ur mom
Step-by-step explanation:
Based on the results shown in the table, what is the experimental probability of rolling a 5?
Answer:
C
Step-by-step explanation:
26 divided by 200 = 13%
26 is the number of times 5 was the outcome of 200 rolls
Zachary invested $700 in an account paying an interest rate of 4. 9% compounded
continuously. Assuming no deposits or withdrawals are made, how long would it
take, to the nearest year, for the value of the account to reach $1,360?
The value of an account can be calculated using the formula for continuously compounded exponential growth given by A = P[tex]e^{rt}[/tex], where A is the final amount, P is the initial amount, r is the interest rate and t is the time.
What is an interest rate?A proportion of a sum of money is charged as interest for using it. Usually, it is stated as an annual percentage rate (APR). Interest rates can vary based on the kind of loan, the lender, and the borrower's creditworthiness. They are commonly charged on loans, credit cards, and savings accounts.
In the given question, the value of the account can be calculated using the formula for continuously compounded exponential growth given by A = Pe^rt, where A is the final amount, P is the initial amount, r is the interest rate, and t is the time.
Substituting the given values, we get:
$1,360 = $700[tex]e^{(0.049t)}[/tex]
To solve for t, we can take the natural logarithm of both sides:
ln(1360) = ln(700) + 0.049t
Rearranging and solving for t, we get:
t = (ln(1360) - ln(700))/0.049
t = 9.68 years
Rounding to the nearest year, it would take 10 years for the value of the account to reach $1,360.
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An art gallery has reserved 10 display locations for a show the artist has 10 paintings but is uncertain on how to display them she insists on trying every possible arrangement before making her decision. If she takes one minute to set up and view each arrangement and works 10 hours a day 6 days a week how many years will it take her to decide
It will take her approximately 2.76 years to decide.
The artist has 10 paintings, and there are 10 display locations. So, the total number of possible arrangements is 10! (10 factorial) which is equal to 3,628,800.
If she takes 1 minute to set up and view each arrangement, and she works 10 hours a day 6 days a week, she can work for 60*10=600 minutes in a day.
In a week, she can work for 600*6 = 3600 minutes.
Therefore, in a week, she can view 3600/1 = 3600 arrangements.
So, it will take her to view all possible arrangements is: 3,628,800/3600 = 1008 days
That's approximately 2.76 years.
So, it will take her approximately 2.76 years to decide.
Therefore, It will take her approximately 2.76 years to decide.
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Simplify √-45 please i need this for math to pass
Answer:3√5
Step-by-step explanation:
√ 45 = 3√5. Therefore, the square root of 45 in radical form is 3√5. Square Root of 45 in Radical Form: 3√5.
Answer:
The answer is 3√5
5x-y=64 and 6y=x solve using substitution method, type the answer as an ordered pair
The ordered pair for the equation is (384/29, 64/29).
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
5x-y=64..............(1)
6y=x........................(2)
Now, substitute the value of x from equation 2 into equation (1)
5(6y) - y= 64
30y - y= 64
29y= 64
y= 64/29
and, x= 6y
x = 6 (64/29)
x = 384/ 29
Hence, the ordered pair (384/29, 64/29).
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suppose that the area of a square were to triple in size. by how much did the length of the square change? give your answer to two digits.
The length of the square change by a factor of √3.
Let x be the initial side length of the square. The area of a square is equal to the length of one of its sides squared.
A = x²
If the area of a square were to triple in size, it means that the new area of the square has increased by a factor of 3.
initial Area x 3 = new Area
3x² = new Area
Let X be the side length of the new square. Hence, the area of the new square is X squared.
new Area = X² = 3x²
X = √3x²
X = x(√3)
Therefore, the length of the square increased by a factor of √3.
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There are kilograms 5/6 of salt in the kitchen. Mrs. Jackson used 1/10 of the salt when she was preparing dinner. How much salt did she use
Answer:
she used 6/60 or 1/10 of the salt
Step-by-step explanation:
5/6=50/60
1/10=6/60
Subtract (4 5/9y-7)-(y-7)
Answer: 4y
Step-by-step explanation:
6.6 oz for $2.50 or 30 oz for $11.29. Which one is better?
Answer:
30 oz for $11.29
Step-by-step explanation:
We can find the unit cost for each and compare.
We need both in dollars per ounce, so we divide the number of dollars by the number of ounces for each case.
6.6 oz for $2.50
Unit cost = $2.50 / 6 oz = 0.41666... $/oz
30 oz for $11.29
Unit cost = $11.29 / 30 oz = 0.376333... $/oz
At $0.38/oz, 30 oz for $11.29 is a better buy than 6.6 oz for $2.50 which is $0.42/oz.
Answer: 30 oz for $11.29
Game designers are testing two versions of the same video game. In the first version, the on-screen character begins in the center of the screen and moves −3 pixels lower each time players hit the down button. In the second version, the character's vertical position, v, is shown by the equation v = −5x + 1,136, where x is the number of times the player has pressed the down button. The number 1,136 shows that the character starts at the top of the screen, which is 1,136 pixels high. In which version of the game does hitting the down button have a greater effect? Complete the explanation.
the answer is v= -5x + 1136
Each bow required 34 3 4 foot of ribbon. She used the following steps to find the number of bows she could make with the ribbon. Step 1: 1012÷34 10 1 2 ÷ 3 4 Step 2: 212÷34 21 2 ÷ 3 4 Step 3: ? Step 4: 846 84 6 Step 5: 14 14 Which expression best represents the expression Marie should have used in Step 3?
An expression which best represents the expression Marie should have used in Step 3 include the following: C. 21/2 × 4/3.
How to determine the missing step?Since Marie had 10 1/2 of ribbon to make bows and each bow required 3/4 of ribbon, the number of bows she could make with the ribbon can be determined by dividing the total number of ribbons by the length required by each bow.
This ultimately implies that, all of the steps that best represents the expression Marie should have used are as follows;
Step 1: 10 1/2 ÷ 3/4
By converting the mixed fraction into an improper fraction, we have the following:
Step 2: 21/2 ÷ 3/4
Rewriting the expression as a function of multiplication, we have the following:
Step 3: 21/2 × 4/3
Step 4: 84/6
Step 5: 14 bows.
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Fawaz when shopping for a new phone sales tax where he lives 9% the price of the phone is $33 find the total price including tax round to the nearest cent
The total price of the phone including the tax is $35.97.
What is a percentage?The percentage is calculated by dividing the required value by the total
value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Price of the phone = $33
Tax = 9%
The total price of the phone.
= 33 + 9% of 33
= 33 + 9/100 x 33
= 33 + 2.97
= $35.97
Thus,
The total price of the phone is $35.97.
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A business is operating with a monthly debt for its account balance. In January, the account had a balance of $-\$1,350$ . In February, the account had a balance of $-\$725$ .
Part A
Write two different expressions that correctly represent the change in the account balance, in dollars, from January to February.
Answer:
Step-by-step explanation:
Step 1: Current Balance = $4700 debit
Step 2: Balance should equal = $900 debit
Step 3:
ADJUSTING ENTRY
Insurance Expense.....$3800 debit
...Prepaid Insurance.....$3800 credit
-----
Prepaid Insurance
$4700 debit
$3800 credit
Bal. $900
Definition
1 / 17
Prepaid Insurance
The Prepaid Insurance account has a $47000 debit balance to start the year. A review of insurance policies and payments shows that $900 of unexpired insurance remains at year-end.
Step 1: Determine what the account balance equals.
Step 2: Determine what the account balance should equal.
Step 3: Record the December 31, adjusting entry to get from 1 to 2.
Answer:
Step 1: Current Balance = $4700 debit
Step 2: Balance should equal = $900 debit
Step-by-step explanation:
What expression is equivalent to -5 - (-4)
Answer: The expression -5 - (-4) is equivalent to -5 + 4 = -1.
Step-by-step explanation:
What do I do for this because I don’t think my Equation
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{12})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{16}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{16}-\stackrel{y1}{12}}}{\underset{\textit{\large run}} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{4}{-4 +6} \implies \cfrac{ 4 }{ 2 } \implies 2[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{12}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-6)}) \implies y -12 = 2 ( x +6) \\\\\\ y-12=2x+12\implies {\Large \begin{array}{llll} y=2x+24 \end{array}}[/tex]
whether or not to continue a mardi gras parade through the downtown area of a certain town is a hotly debated topic. the parade is popular with students and many residents, but some celebrations have led to complaints and a call to eliminate the parade. the local newspaper conducted online and telephone surveys of its readers and was surprised by the results. the online survey site received more than 300 responses, with more than 60% favoring continuing the parade, while the telephone response line received more than 130 calls, with more than 90% favoring banning the parade. what factors may have contributed to these very different results? (select all that apply.)
Survey results may be impacted by response bias, sampling bias, question bias, mode of administration, and data collection method.
What is factor ?
A factor is a quantity or element that contributes to a particular result or outcome.
There are several factors that may have contributed to the different results of the two surveys:
Response Bias: The online survey may have attracted participants who are more tech-savvy and have a different perspective than those who are less comfortable with technology. On the other hand, the telephone survey may have attracted participants who are older or less mobile, and have a different perspective than those who prefer online communication.
Sampling Bias: The online survey may not have been representative of the entire population, as it was conducted on a specific website and only attracted those who use that website. Similarly, the telephone survey may have only reached those who answered the phone and were willing to participate.
Question Bias: The questions asked in the online survey may have been different from those asked in the telephone survey, leading to different results. The questions may have been worded in a way that biased the responses, either consciously or unconsciously.
Mode of Administration: The mode of administration, or the method of conducting the survey, may have influenced the responses. Online surveys allow participants to respond at their own pace and in their own environment, while telephone surveys may put pressure on participants to respond quickly and may not allow them to think through their responses.
Data Collection Method: The data collection method, such as self-reported data, may have influenced the results. Self-reported data may not always be accurate, as participants may not remember details accurately or may be unwilling to report certain information.
Survey results may be impacted by response bias, sampling bias, question bias, mode of administration, and data collection method.
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Survey results may be impacted by response bias, sampling bias, question bias, mode of administration, and data collection method.
A factor is a quantity or element that contributes to a particular result or outcome.
There are several factors that may have contributed to the different results of the two surveys:
Response Bias: The online survey may have attracted participants who are more tech-savvy and have a different perspective than those who are less comfortable with technology. On the other hand, the telephone survey may have attracted participants who are older or less mobile, and have a different perspective than those who prefer online communication.
Sampling Bias: The online survey may not have been representative of the entire population, as it was conducted on a specific website and only attracted those who use that website. Similarly, the telephone survey may have only reached those who answered the phone and were willing to participate.
Question Bias: The questions asked in the online survey may have been different from those asked in the telephone survey, leading to different results. The questions may have been worded in a way that biased the responses, either consciously or unconsciously.
Mode of Administration: The mode of administration, or the method of conducting the survey, may have influenced the responses. Online surveys allow participants to respond at their own pace and in their own environment, while telephone surveys may put pressure on participants to respond quickly and may not allow them to think through their responses.
Data Collection Method: The data collection method, such as self-reported data, may have influenced the results. Self-reported data may not always be accurate, as participants may not remember details accurately or may be unwilling to report certain information.
Survey results may be impacted by response bias, sampling bias, question bias, mode of administration, and data collection method.
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