Answers
Answer:
The edge length of the storage cube is 30 centimeters.
Step-by-step explanation:
All sides/edges of a cube has equal length.
Let's take the length of a edge as [tex]a[/tex] centimeters.
The volume a the cube = Height * Width * Length
All height, width and length are equal([tex]a[/tex] centimeters).
Now we can write the equation again as,
The volume a the cube = [tex]a*a*a[/tex]
Volume of the cube is given as 27,000 cubic centimeters.
Therefore,
[tex]a*a*a=27,000[/tex]
[tex]a=\sqrt[3]{27,000}[/tex]
[tex]a=30[/tex]
Therefore, the edge length of the storage cube is 30 centimeters.
Related Questions
Convert the density of the textbook to slug/in^3. (1 slug =14.59kg)(1in =2.54 cm)
Answers
To convert the density of the textbook to slug/in³, we first convert the density from g/cm³ to kg/m³ and then use the given conversion factors to convert it to slug/in³.
Explanation:To convert the density of the textbook to slug/in³, we need to use the given conversion factors: 1 slug = 14.59 kg and 1 in = 2.54 cm. First, we need to convert the density from g/cm³ to kg/m³ by dividing by 1000. Then, we can convert from kg/m³ to slug/in³ using the given conversion factors. Let's calculate:
Given density = 3 g/cm³
Step 1: Convert g/cm³ to kg/m³
Density in kg/m³ = 3 g/cm³ / 1000 = 0.003 kg/m³
Step 2: Convert kg/m³ to slug/in³
Density in slug/in³ = 0.003 kg/m³ × (1 slug / 14.59 kg) × (1 in³ / (2.54 cm)³)
Performing the calculations gives us the density of the textbook in slug/in³.
Learn more about Converting density units here:https://brainly.com/question/33833616
#SPJ2
HELP FAST PLS!! Drag each function to correct location on the image. Identify exponential functions.
Answers
Answer:
See the attached
Step-by-step explanation:
An exponential function has the variable in the exponent.
Answer:
Exponential functions: [tex]f(x)=8e^x[/tex],[tex]f(x)=e^{-3x}[/tex] and [tex]f(x)=20^{\frac{x}{3}}[/tex]
Non-exponential functions: [tex]f(x)=5x^{\frac{3}{7}}[/tex], [tex]f(x)=4x^3-6x[/tex] and [tex]f(x)=\sqrt{x}+3x[/tex]
Step-by-step explanation:
The general form of an exponential function is
[tex]f(x)=ab^x[/tex]
where, a is initial value and b is growth factor.
It means the variable term i.e., x must be the exponent . In other words we can say that the variable term must be in the power of constant terms.
We need to check whether the given function is an exponential function or not.
The given function is
[tex]f(x)=8e^x[/tex]
It is an exponential function with initial value 8 and growth factor e≈2.718.
Similarly,
[tex]f(x)=e^{-3x}[/tex] and [tex]f(x)=20^{\frac{x}{3}}[/tex] are exponential functions.
[tex]f(x)=5x^{\frac{3}{7}}[/tex], [tex]f(x)=4x^3-6x[/tex] and [tex]f(x)=\sqrt{x}+3x[/tex] are non-exponential functions.
If you ever swam in a pool and your eyes began to sting and turn red, you felt the effects of an incorrect pH level. pH measures the concentration of hydronium ions and can be modeled by the function p(t) = −log10t. The variable t represents the amount of hydronium ions; p(t) gives the resulting pH level.
Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3.
Create a graph of the pH function either by hand or using technology. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph.
The pool maintenance man forgot to bring his logarithmic charts, and he needs to raise the amount of hydronium ions, t, in the pool to 0.50. To do this, he can use the graph you created. Use your graph to find the pH level if the amount of hydronium ions is raised to 0.50. Then, convert the logarithmic function into an exponential function using y for the pH.
Recall from 07.02 how to convert a log to an exponential function. The equation y equals b to the power of x is written on the left. The equation x equals log base b of y is written on the right. A double-ended arrow points to both equations. The word exponent is written above the equations with arrows pointing to the x on the left and the x on the right. The word base is written below the equations with arrows pointing to the b on the left and the b on the right.
The pool company developed new chemicals that transform the pH scale. Using the pH function p(t) = −log10t as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Use complete sentences and show all translations on your graph.
p(t) + 1
p(t + 1)
−1 • p(t)
Answers
Hello,
Please, see the attached files.
Thanks.
Answer:
hey i think the answer is 7
Step-by-step explanation:
Simplify -52 + 8|-1| + (-3).
A. 30
B. 14
C.-20
D. -36
Please help!
Answers
Answer:
C. -20
Step by step explanation:
It appears you want the value of the expression -5² +8|-1| +(-3).
Order of operationsThe order of operations tells us that the first step is to evaluate expressions in parentheses. Here, the absolute value symbols effectively serve as parentheses, so we start there.
|-1| signifies the absolute value of -1, its magnitude, or positive value. That simplifies to 1. So, your expression is ...
-5² +8·1 -3
The next step is to evaluate the term with an exponent: -5² = -(5·5) = -25.
= -25 +8·1 -3
Now, we perform the multiplication:
= -25 +8 -3
And finally, the addition/subtraction
= -17 -3
= -20
__
Additional comment
The expression you show in the problem statement looks like the first term is negative fifty-two. That is very different from negative five squared. An exponent is indicated using a caret (^), as -5^2, or using a superscript font, as -5². Please be careful to use appropriate math symbols where exponents are involved.
63 less than four times a number is equal to the number. what is the number?
Answers
4x - 63 = x
-63 = -3x
-63/-3 = x
x = 21
Beth and Mark would like to put some savings in the bank. They most likely will not need this money for 4 years, so Beth wants to put it in a four-year CD. Mark wants to put the money in a passbook savings account. What is the advantage of a CD
Answers
Quite often, the CD will earn more interest—even if you have to pay a penalty for early withdrawal.
_____
For example, my local credit union offers 0.10% interest on passbook savings and 1.46% interest on a 4-year CD. One of my local banks offers 0.01% interest on passbook savings, and 0.60% on a 4-year CD.
A CD (Certificate of Deposit) generally offers a higher interest rate than a passbook savings account, which may lead to a greater return on investment. But it has a drawback where money cannot be withdrawn without penalty until a set time period ends.
Explanation:The primary advantage of a CD (Certificate of Deposit) over a passbook savings account is typically a higher interest rate. A CD is a type of timed deposit, meaning that the money is typically put in the bank for a fixed amount of time. During this time, the interest rate is usually higher than that of a typical savings account, allowing for a greater return on the initial investment. Unlike a passbook savings account, however, you cannot withdraw money from a CD without penalty until the time period ends, which in this case is four years. This is an important consideration for Beth and Mark.
Learn more about Investment here:https://brainly.com/question/34489138
#SPJ2
Solve for x. y=c(x+b)
Answers
x = [tex]\frac{y}{c}[/tex] - b
divide both sides by c
x + b = [tex]\frac{y}{c}[/tex] ( subtract b from both sides )
x = [tex]\frac{y}{c}[/tex] - b
The equation solved for x is x = y/c - b.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
The given equation is y = c(x + b).
y = c(x + b)
y/c = x + b
y/c - b = x
Or, x = y/c - b
Hence, the equation solved for x is x = y/c - b.
To learn more about equations, click here:
brainly.com/question/10413253
#SPJ2
ain ABC, AB=x, because=y, and CA=2x. A similarity transformation with a scale factor of 0.5 Maps ABC to MNO, such that vertices M,N and O correspond to A,B,C respectively. If OM=5, what is AB?
Answers
We are given: Triangle ABC sides, AB = x, BC = y and CA = 2x.
Another triangle MNO whose vertices M,N and O correspond to A,B,C respectively.
Therefore, AB corresponding to sides MN , BC corresponding to sides NO and CA corresponding to sides OM.
Also, we are given " A similarity transformation with a scale factor of 0.5 Maps ABC to MNO".
That means triangle ABC is dilated by a factor of 0.5.
Each side of the triangle MNO is 0.5 times(half) of Triangle ABC.
We could also say that each side of Triangle ABC is two times of sides of triangle MNO.
We are given side OM = 5 units.
CA = Times of OM = 2 * 5 = 10 units.
CA = 2x = 10 units or 2x=10.
Dividing both sides by 2, we get
[tex]\frac{2x}{2}=\frac{10}{2}[/tex]
x=5.
AB = x.
Therefore, AB = 5 units.
Answer:
Step-by-step explanation:
The English Alphabet has 20 letters more than one-fourth the number of letters in the Greek Alphabet. The English Alphabet has 26 letters. Which of the following equations would you use to find the number of letters, g, in the Greek Alphabet?
A) g + 20/4 = 24
B) 4g − 20 = 26
C) 1/4g + 20 = 26
D) 4g − 26 = 20
Answers
we are given that the English Aplhabet has 26 letters. we let g represent the number of letters in the Greek alphabet. From the statement given, English alphabet which is 26 = 20 + 1/4 *g. The expression which is similar to this is in option A. 1/4g + 20 = 26.
U is between C and D.
True Or false
Answers
Q # 14 please . .Write the slope-intercept of the equation for the line
Answers
You can see that this line passe through the points (-4,-2) and (4,3).
The slope of the line passing through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is
[tex]\dfrac{y_2-y_1}{x_2-x_1}.[/tex]
Thus, the slope is
[tex]\dfrac{3-(-2)}{4-(-4)}=\dfrac{5}{8}.[/tex]
Then the equation of the line is
[tex]y-3=\dfrac{5}{8}(x-4),\\\\y=\dfrac{5}{8}x+\dfrac{1}{2}.[/tex]
Answer: correct choice is C.
The population of a town is 6500 and is increasing at a rate of 4% each year. Create a function for this scenario. At this rate, approximately what will the town's population be in 4 years?
Answers
Answer:
[tex]P_4 = 7604.08[/tex]
Step-by-step explanation:
If the population increases at a rate of 4% per annum, then:
In year 1:
[tex]P_1 = P_0 + 0.04P_0[/tex]
Where [tex]P_0[/tex] is the initial population and [tex]P_n[/tex] is the population in year n
In year 2
[tex]P_2 = P_1 + 0.04P_1[/tex]
It can also be written as:
[tex]P_2 = P_0 + 0.04P_0 + 0.04 (P_0 + 0.04P_0)[/tex]
Taking out common factor [tex]P_0[/tex]
[tex]P_2 = (1 + 0.04) (P_0) + 0.04P_0 (1 + 0.04)[/tex]
Taking out common factor (1 + 0.04)
[tex]P_2 = (1 + 0.04) (P_0 + 0.04P_0)[/tex]
Taking out again common factor [tex]P_0[/tex]
[tex]P_2 = (1 + 0.04) (1 + 0.04) P_0[/tex]
Simplifying
[tex]P_2 = P_0 (1 + 0.04) ^ 2[/tex]
So
[tex]P_n = P_0 (1 + 0.04) ^ n[/tex]
This is the equation that represents the population for year n
Then, in 4 years, the population will be:
[tex]P_4 = P_0 (1 + 0.04) ^ 4\\P_4 = 6500(1 + 0.04) ^ 4\\P_4 = 7604.08[/tex]
3. A town's population has been decreasing at a constant rate, In 2010, the population was 5,900 By 2012 the population jad dropped to 4,700 Assume the tren contiues
a. Predict te population in 2016
b. Identify the year in which the population will reach 0
4. A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for five year
a. Find the linear function that models the town's population P as a function of the year, t where t is the number of years since the model began
b. Graph y==p(t) Interpret the meaning of the Intercepts.
c. When does the model expect the population to reach 100,000?
5. The weight of a newborn baby is 7.5 pounds. The baby gained one-half pound a month in its first year.
a. Find the linear function that models the baby's weight W as a function of the age of the baby t, in months
b. Fine a reasonable domain and range for the function W
Answers
The population of the first town decreases at a rate of 600 people per year, and is predicted to be 2,100 in 2016. The town with an initial population of 75,000 grows at a linear rate, represented by the function P(t) = 75000 + 2500t, with the population expected to reach 100,000 after 10 years.
Explanation:For the first part of your question regarding the town's decreasing population, we need to establish a rate of decrease. The town's population went from 5,900 in 2010 to 4,700 in 2012—this is a decrease of 1,200 over two years, or 600 people per year. Therefore, we can predict that the population will continue to decrease by 600 people per year. In 2016, this suggests the population would be 4,700 (population in 2012) - 600*4 (4 years from 2012 to 2016), which equals 2,100. For identifying the year when the population will reach 0, we use the same rate and find it by using the formula (current population / rate of decrease) + current year. As for the part about the town with an initial population of 75,000 growing at a constant rate, we can model this as a linear function such as P(t) = 75000 + 2500t. This equation states that the population at any given year is the initial population plus the annual growth times the number of years since the model began. In terms of the graph of this function, the y-intercept represents the initial population, while the slope is the constant rate of growth. The model expects the population to reach 100,000 after (100,000 - 75,000) / 2,500 = 10 years.
Learn more about Population Change here:https://brainly.com/question/17155082
#SPJ3
Judy took $30 with her to spend on popcorn and drinks for herself and her friends at the movie theater. The price for each bag of popcorn was $5. The price of each drink was $3. (a) Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of bags of popcorn and the other axis to represent the number of drinks. (b) Explain your graph.
Answers
I need help on this one please
Answers
8: 16,24,32,40,48,56
the smallest dollar amount would be 24, so the both sold $24 worth of cookies
Ahmad sold 3 boxes of cookies
tammy sold 4 boxes of cookies
The multiples for 6 : 6, 12, 18, 24, 30,36, 42, 48
The multiples for 8 : 8, 16, 24, 32, 40, 48, 56, 64
Hope this helps
helpppppp meeeee PLEASE DUE TOMORROW
Answers
Answer: 40,000,000
Population: 400,000,000
40X1010
Step-by-step explanation:
Jordan and Sharla are saving money to go on a study abroad trip. They must provide a down payment of $650 to sign up for the trip, and they can pay the remaining balance later. Jordan raises money by mowing lawns in his neighborhood and charges $25 per lawn. Sharla raises money by selling handmade necklaces for $15 each. Sharla raises less money than Jordan does because Sharla 3. only has enough materials to make 40 necklaces. (A) write two constraints to model the problem. Let x respresent the number of lawns Jordan mows and y represent the number of necklaces Sharla sells. (B) can sharla afford the down payment with the money she earns selling her necklaces? Explain your answer . PLEASE HELP its due NOW! I’ll make you brainliest
Answers
How would the fraction 1/3+square root of 2 be rewritten if its denominator is rationalized using difference of squares? A. 3-square root of 2 B. 3-square root of 2/5 C. 3-square root of 2/7 D. - 3+square root of 2/7
Answers
C
given 1 /( 3 + √2 )
then rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator
the conjugate of 3 + √2 is 3 - √2
1 / (3 + √2 ) × (3 - √2 ) / (3 - √2 )
= (3 - √2 ) /( 9 - 2 ) = (3 - √2 ) / 7
The fraction [tex]\frac{1}{3+\sqrt{2}}[/tex] can be written as [tex]\frac{3-\sqrt 2}{7}[/tex]. Option C is correct.
What is a fraction simplification?Fraction simplification is a method of fraction reduction that entails making a fraction as simple as possible.
This is accomplished by dividing the numerator and denominator by the biggest integer that divides both integers exactly.
Given fraction;
[tex]\frac{1}{3+\sqrt{2}}[/tex]
Multiplying the numerator and denominator by the conjugate of the denominator will rationalize the denominator;
The conjugate of the denominator (3 + √2) is 3 - √2;
Apply the rationalization of fraction;
[tex]\frac{1}{3+\sqrt{2}} \\\ \frac{1}{3+\sqrt{2}} \times \frac{3-\sqrt2}{3-\sqrt 2} \\\\ \frac{3-\sqrt 2}{9-2} \\\\\ \frac{3-\sqrt 2}{7}[/tex]
Hence option C is correct.
To learn more about fraction simplification, refer to https://brainly.com/question/11479469.
#SPJ2
Point C is the center of the circle. angle ACB measures 49. What is the of arc ADB
Answers
If arc ADB is that portion of the circle that is not arc AB, then its measure is ...
... 360° -49° = 311°
_____
The sum of the measures of the arcs of a circle is 360°.
Which expressions are polynomials? Select each correct answer. 30y^2 30y^2+x 30y2x 30y2+x12
Answers
To know which of the following expressions are polynomials, let us look at the definition of a polynomial:
Polynomial is derived from poly- (which means "many") and -nomial (meaning "term"), so it says "many terms".
For an instance: [tex]2x^2y+2y^2[/tex] is a polynomial, but [tex]4xy^2[/tex] is not a polynomial because it contains single term only.
We must keep in mind that in polynomial it can have variables, constants, and exponents but it can never have division by a variable.
Now lets, look at the
[tex]30y^2[/tex] since it has got one term it can not be a polynomial.
[tex]30y^2+x[/tex]: it has got more than one term therefore, it is a polynomial.
[tex]30y^2x[/tex]: again it has got just one term so it is not a polynomial.
[tex]30y^2+x^{12}[/tex]: Since it has got more than one term, so again it is a polynomial.
The correct polynomial expressions are 30y²+x and 30y². Option A and D is the correct answer.
Polynomials are expressions that consist of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and exponentiation.
30y²+x: This expression is a polynomial because it consists of a constant term (30), a variable term (y²) raised to a non-negative integer exponent, and an additional variable term (x).
30y²: This expression is a polynomial because it consists of a constant term (30) and a variable term (y²) raised to a non-negative integer exponent.
These expressions are considered polynomials because they consist of variables, constants, and non-negative integer exponents, and they involve the appropriate mathematical operations of addition and multiplication.
Learn more about Polynomial here:
https://brainly.com/question/1496352
#SPJ6
The complete question is, "Which expressions are polynomials? Select each correct answer.
a. 30y²+x
b. 30y²+x (¹/²)
c. (30y²) ÷ x
d. 30y²"
Please show work: This is for my daughter in 7th. Grade; Needed some insight 15 Points, and Brainliest to whom show work with correct answers!
1a - A boat travel 468 kilometers on 117 liters of gasoline. How much gasoline will it need to go 168 kilometers
1B: A car travels 138 miles in 4 hours (With constant speed) How far can it travel in 10 hours (With the same speed)
2A: A boat travels 261 miles in 15 hours (With a constant speed) How much time will it take traveling 180 miles?
2B: A car travels 452 Km. in 5 hours (with a constant speed) How far can it travel in 4 hours?
5A: 50 LBS. of tomatoes cost $200. How much would 2 LBS cost?
5B: A boat travels 381 km. in 6 hours (with a constant speed) How far can it travel in 7 hours (with the same speed)?
5C: A boat travels 427 km. in 43 hours (with constant speed) How much time will it take traveling 459 kilometers?
5D: 11 Kg. of bananas cost $88 how much would 20 kg cost?
Thanks -P-
Answers
Answer:
1a. 42 liters
1b. 345 miles
2a. 10 h 20 min 41.4 sec
2b. 361.6 km
5a. $8
5b. 444.5 km
5c. 46 h 13 min 20.9 sec
5d. $160
Step-by-step explanation:
Each of these problems expresses a proportion and asks you to find a missing value. You are given, for example, value 1 and related value 1. You are asked to find value 2 that corresponds to related value 2.
Solving the Proportion
Expressed as a proportion, this looks like ...
... (value 1)/(related value 1) = (value 2)/(related value 2)
If you multiply both sides of this equation by related value 2, you can find value 2.
... (related value 2)/(related value 1)×(value 1) = value 2
Another way to think about it
I like to think of the related values as making a fraction. If the related value 2 is larger than related value 1, the fraction is greater than 1 and the value 2 will be larger than value 1. (This realization can serve as a check on your answer.)
1a. related value 2 = 168 km. This is the value for which you want to find value 2, the number of liters of gasoline. related value 1 has the same units as related value 2 (km), and value 1 has the same units as value 2 (liters).
Then the fraction of interest is (168 km)/(468 km), and it multiplies 117 L. The result is ...
... (168/468)×(117 L) = 42 L
1b. (10 h)/(4 h)×(138 mi) = 345 mi
2a. (180 mi)/(261 mi)×(15 h) ≈ 10.3448 h
2b. (4 h)/(5 h)×(452 km) = 362.6 km
You may have noticed that I keep the units with the numbers. When the same units are in the numerator and denominator, they cancel—the way any common factors cancel. The remaining units will be the units of the answer. This practice of keeping units with numbers can help ensure you're using the right numbers for the right purpose. If the units don't work out, your math has an error.
5a. (2 lb)/(50 lb)×$200 = $8
5b. (7 h)/(6 h)×381 km = 444.5 km
5c. (459 km)/(427 km)×(43 h) ≈ 46.2225 h
5d. (20 kg)/(11 kg)×$88 = $160
What is the value of f(x) at x=8? F(8)=
Answers
Whenever variables are together without a sign you multiply. Answer is 64.
The value of F(8) is 64.
Given that,
the value of f(x) at x=8.Based on the above information, the calculation is as follows:
[tex]F(8) = 8 \times 8[/tex]
= 64
learn more: https://brainly.com/question/13496810?referrer=searchResults
What is the product of -2x^3 + x - 5 and x^3 - 3x - 4? Are the products equal to those of x^3 - 3x - 4 and -2x^3 + x - 5? Explain
I am soooo lost on working this out.
Answers
Answer:
Step-by-step explanation:
( -2x³ + x - 5) × ( x3 - 3x - 4)
= ( -2x³)×( x3 - 3x - 4) +(x)×( x3 - 3x - 4) - (5)( x3 - 3x - 4)
= - 2x^6 +6x^4 +8x³ + x^4 - 3x² -4x - 5x³ +15x + 20
= - 2x^6 +7x^4 +3x³-3x²+11x +20
Write the rational number as a decimal. Show your work. 5/9 -3/8 -3/11.
Answers
I have memorized facts about fractions like these, so can tell you ...
[tex]\dfrac{5}{9}=0.5\overline{5}\\\\-\dfrac{3}{8}=-3\times 0.125=-0.375\\\\-\dfrac{3}{11}=-0.27\overline{27}[/tex]
_____
A fraction with 9 as a denominator is a repeating 1-digit decimal with the decimal digit being the numerator of the fraction.
A fraction with 11 as a denominator is a repeating 2-digit decimal with the two digits being 9 times the numerator of the fraction.
1/8 = 0.125, so any multiple of 1/8 is that multiple of 0.125.
To convert 5/9 - 3/8 - 3/11 into a decimal, you find a common denominator (792), subtract the numerators, resulting in -73/792, and then divide the numerator by the denominator to find the decimal, which is -0.0922.
Explanation:The problem is asking us to write the rational number 5/9 - 3/8 - 3/11 as a decimal. To do this, we need to first subtract these fractions and then convert the result into a decimal.
First, find a common denominator for all three fractions, which is 792. Convert the fractions to have this denominator, to get 440/792 - 297/792 - 216/792. Then, you subtract these three fractions by subtracting the numerators: 440 - 297 - 216 = -73. So, our fraction is -73/792. And finally, divide the numerator by the denominator to convert the fraction into a decimal: -73 ÷ 792 = -0.0922 to four decimal places. Learn more about Converting Fractions to Decimals here:
https://brainly.com/question/35123994
#SPJ3
I need a little help with the second part of b and part c! + can y'all check my explanations please
a. (my answer for context) The system for this word problem is x+y=14; 11.99x+24.99y=245.86 (x is shirts and y is pants)
b. 1. Explain, without solving, which method is most efficient in solving this system: substitution, elimination, graphing, or making a table?
(my answer is substitution, because the solutions to x and y can easily be substituted into the first equation).
b. 2. Explain why the other methods are not as sufficient.
(I need a little help but I'm thinking it's because for this system solving method you basically only have to solve the second equation and then just substitute)
c. How could you simplify the numbers used in this system to simplify the system? Does this new system change your answer to part b? Explain. (What does this mean? How can I answer it?)
Answers
Answer:
b. Your answer is appropriate.
c. The decimals can be eliminated by multiplying by 100. (You can also add 0.14 to the problem, adding .01 to each individual price and 0.14 to the total. This will make the second equation be 12x +25y = 246, which makes the numbers slightly easier to work with.) Unfortunately, there don't seem to be any common factors that would reduce the size of the numbers.
Step-by-step explanation:
a. We assume you're finding quantities of shirts and pants for a purchase of 14 total items costing $245.86. If so, your equations are appropriate.
b. The solution for one variable or the other can be found in 6 arithmetic operations using your suggested method. Any other method takes as many or more. (Multiplying the first equation by -11.99 and adding to the second gets you the equivalent of substituting for x in as many operations.)
Graphing can be quick and easy with the right tool. Since you know the solutions are integers, just about any graphing tool will get you close enough.
Another method (using only 5 arithmetic operations) is to calculate the average price of an item as 245.86/14, then figuring the ratio of the difference from the lower price to the total difference in price. Multiplying this ratio by the number of items gives the number of the higher-priced item (pants). (245.86/14 -11.99)/(24.99 -11.99)·14 = 6 This method treats the problem as a "mixture" problem, finding the numbers of each consitutuent that make the average come out what it is.
c. See above for how to simplify the numbers. Done properly, the answer is not changed. (Some people don't work well with decimals or fractions, so like to see those eliminated from the problem. Some folks work better with small integers than with large ones, so like to see the numbers be made as small as possible.)
Rewrite in terms of sin(x) and cos(x).
sin(x+[7pi/4])
Answers
The term sin(x+[7pi/4]) can be rewritten in terms of sin(x) and cos(x) using the formula for sine of the sum of two angles. Given A = x and B = 7pi/4, the equation can be simplified to sin(x + [7pi/4]) = sin(x)(√2/2) - cos(x)(√2/2).
Explanation:To rewrite the term sin(x+[7pi/4]) in terms of sin(x) and cos(x), we can use the formula for sine of the sum of two angles. The formula is given by:
sin(A + B) = sinAcosB + cosAsinB
Substituting our given values into this formula, where A = x and B = 7pi/4, we get:
sin(x + [7pi/4]) = sin(x)cos(7pi/4) + cos(x)sin(7pi/4)
Note that cos(7pi/4) = √2/2 and sin(7pi/4) = -√2/2. Therefore:
sin(x + [7pi/4]) = sin(x)(√2/2) - cos(x)(√2/2)
Learn more about Sine of Sum of Angles here:https://brainly.com/question/37065283
#SPJ3
Choose the expressions that are perfect cubes.
–3
125a^6
8m^20
100w^24x^3
–64q^12
–c^30d^9f^18g^3
Answers
Answer:125a6
-64q12
-c^30d^9f^18g^3
Step-by-step explanation:
Got it right on edgy
Find 5x − 3y − z if x = −2, y = 2, and z = −3
Answers
So the equation would be
5(-2)-3(2)-(-3)
Solve
5(-2)-3(2)-(-3)
-10-6+3
-16+3
-13
The answer is -13
ILL GIVE MEDAL AND BRAINLIST AWNSER TO whoEVER IN THE FIRST!!!!Roland's heart beats 495 times in 6 minutes. At that rate, how many times would it beat in 20 minutes?
A.
9900
B.
2970
C.
1650
D.
615
Answers
Answer,
C. 1650
Explanation,
495/6 = 82.5
82.5 x 20 = 1650
Hope this helps :-)
maria is bringing her sick dog pedro in for a series of appointments at the veterinary clinic. Her total over the course of treatment with be $150 for tests and medidine plus $30 per appointment,a. the clinic offers Maria a 15% discount off her total cost. Write an equation to show her updated cost.
Answers
After the 15% discount, Maria pays 85% of the cost. That cost is the sum of the fixed cost and the variable (per visit) cost.
... (updated cost) = 0.85×($150 +$30×a)
... (updated cost) = 127.50 +25.50a . . . . in dollars