[tex]21 + 21 \leqslant - 4z \\ - 4z \geqslant 42 \\ \frac{ - 4z}{ - 4} \geqslant \frac{42}{ - 4} \\ z \leqslant - 10.5[/tex]
ATTACHED IS THE SOLUTION
BE AWARE THE SIGNS <> ONLY CHANGE SIGN WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.
A relationship between two expressions or values that are not equal to each other is called 'inequality. Z≤ -10.5 is the solution for inequality 21 ≤ −4z − 21.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is twenty one lesser or equal to minus four z minus twenty one.
21 ≤ −4z − 21.
We need to solve for z
Let us add twenty one on both sides
21+21≤ −4z − 21+21
42≤ −4z
Divide both sides by 4
10.5≤ -Z
-10.5≥Z
Z≤ -10.5
Hence Z≤ -10.5 is the solution for inequality 21 ≤ −4z − 21.
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Find the perimeter of the rectangle. Then, Find area of the rectangle. Round your answer to the nearest tenth
Answer:
To find the perimeter of the rectangle, simply add all sides of the rectangle together to get the answer. For finding the area, you have to multiply the length and width together.
Step-by-step explanation:
math.
Given g(x) = -2√x², find g(8 + x).
Answer:
g(8 + x) = - 2(8 + x)
Step-by-step explanation:
substitute x = 8 + x into g(x)
g(8 + x) = - 2[tex]\sqrt{(8+x)^2}[/tex] = - 2(8 + x)
A water tank initially contained 56 liters of water. It is being drained at a constant rate of 2.5 liters per minute. How many liters of water are in the tank after 9 minutes?
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3≤x≤6
STEP - BY - STEP EXPLANATION
What to find?
Rate of change of the given function.
Given:
Step 1
State the formula for rate of change.
[tex]Rate\text{ of change=}\frac{f(b)-f(a)}{b-a}[/tex]Step 2
Choose any two point within the given interval.
(3, 59) and (6, 44)
⇒a=3 f(a) =59
b= 6 f(b)=44
Step 3
Substitute the values into the formula and simplify.
[tex]Rate\text{ of change=}\frac{44-59}{6-3}[/tex][tex]=\frac{-15}{3}[/tex][tex]=-5[/tex]ANSWER
Rate of change = -5
NO LINKS!! Describe the domain and range (in BOTH interval and inequality notation) for each function shown.
Answers:
Domain as an inequality: [tex]\boldsymbol{-\infty < \text{x} < \infty}[/tex]
Domain in interval notation: [tex]\boldsymbol{(-\infty , \infty)}[/tex]
Range as an inequality: [tex]\boldsymbol{-3 \le \text{y} \le 3}[/tex]
Range in interval notation: [-3, 3]
=================================================
Explanation:
The domain is the set of allowed x inputs. This graph goes on forever in both directions, so we can plug in any real number for x. There are no restrictions to worry about.
As an inequality, we write [tex]-\infty < \text{x} < \infty[/tex] to basically say "x is between negative infinity and infinity". In other words, x is anything on the real number line.
That inequality condenses into the interval notation of [tex](-\infty , \infty)[/tex]
Always use curved parenthesis for either infinity, because we can't ever reach infinity. It's not a number on the number line but rather a concept.
----------------------
Now onto the range.
Recall the range is the set of possible y outputs. We look at the lowest and highest points (aka min and max) to determine the boundaries for the range.
In this case, the smallest y can get is y = -3
The largest it can get is y = 3
The range is any value of y such that [tex]-3 \le \text{y} \le 3[/tex] which in word form is "any value between -3 and 3, inclusive of both endpoints".
That inequality condenses to the interval notation [-3, 3]
We use square brackets to include the endpoints as part of the range.
Answer:
[tex]\textsf{Domain}: \quad (-\infty, \infty) \quad -\infty < x < \infty[/tex]
[tex]\textsf{Range}: \quad [-3,3] \quad -3\leq y\leq 3[/tex]
Step-by-step explanation:
The domain of a function is the set of all possible input values (x-values).
The range of a function is the set of all possible output values (y-values).
Interval notation
( or ) : Use parentheses to indicate that the endpoint is excluded.[ or ] : Use square brackets to indicate that the endpoint is included.Inequality notation
< means "less than".> means "more than".≤ means "less than or equal to".≥ means "more than or equal to".From inspection of the given graph, the function is continuous and so the domain is not restricted.
Therefore, the domain of the function is:
Interval notation: (-∞, ∞)Inequality notation: -∞ < x < ∞From inspection of the given graph, the minimum value of y is -3 and the maximum value of y is 3. Both values are included in the range.
Therefore, the range of the function is:
Interval notation: [-3, 3]Inequality notation: -3 ≤ y ≤ 3Simplify the expression √112x10y13. Show your work. pls help
Answer: [tex]4x^{5} y^{6} \sqrt{7y}[/tex]
Step-by-step explanation:
1) Separate the radicals
sqrt(112x^10y^13) = sqrt(112)*sqrt(x^10)*sqrt(y^13)
2) For sqrt(112), rewrite it as the product of a perfect square and some other number.
sqrt(112) = sqrt(16) * sqrt(7)
= 4*sqrt(7)
3) For sqrt(x^10), rewrite it in terms of it being raised to a fraction
[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex]
n = 2, so x^(10/2), and when simplified you have x^5
4) For sqrt(y^13), do the same thing.
y^(13/2) = sqrt(y)*(y^6)
5)Combine everything
4x^5y^6sqrt(7y)
i want to ask a question
We got to use the Secant-Tangent Theorem, here. It says that AC² is equal to the distance BC times the distance from C to the circumference. Let's denote the point in OC where it intercepts the circumference by D, so:
[tex]\begin{gathered} AC^2=CD\cdot BC \\ 20^2=CD\cdot BC \end{gathered}[/tex]Beucase the radius is equal in all points of the circumference, OA=OB=OD, so BC = OA + OC, and CD = OC - OA. So,
[tex]\begin{gathered} 20^2=CD\cdot BC=(OC-OA)\cdot(OA+OC)=OC^2-OA^2=OC^2-8^2 \\ 20^2=OC^2-8^2 \\ OC^2=20^2+8^2=464 \\ OC=\sqrt[]{464}=21.54\approx22\operatorname{cm} \end{gathered}[/tex]Suppose you have a monthly entertainment budget that you use to rent movies and purchase cds. You currently use your income to rent 5 movies per month at a cost of 5.00 per movie and to purchase 5 cds per month at a cost of 10 per cd. Your marginal utility from the fifth movie is 30 and your marginal utility from the fifth cd is 70
Total utility of movies and cds will be $160
What is Budget?
A spending plan based on income and costs is called a budget. In other words, it's a projection of your income and expenses for a specific time frame, like a month or a year. (Or, if you're keeping track of the money coming in and going out of your home as a whole, that's a family budget.)
The cost of 1 movie = $5
The cost of 1 CDS = $10
The marginal utility from fifth movie = 30
The marginal utility from fifth CDS = 70
Total cost spent in month for movies = 5+5+5+5+30
= $50
Total cost spent in month for CDS = 10+10+10+10+70
= $110
The total monthly entertainment budget will be
= 50 + 110
= $160
Hence, The total monthly entertainment budget is $160
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At store A, 3 pounds of apples cost $12. At store B, the cost is given by y = 2x where y is the cost in dollars and x is the number of pounds of apples. The cost of apples at store C is shown in the graph. Answer the questions to find out which store's apples are the least expensive. 1. What is the unit price of apples at store A? Explain how you found this unit price. (2 points) 2. What is the unit price of apples at store B? How did you use the equation to find the unit price? (2 points) 3. What is the unit price of apples at store C? How did you use the graph to find the unit price? (3 points) 4. Which store has the lowest unit price for apples? (3 points)
1. Store A's unit price = $4 per pound
2. Store B's unit price = $2 per pound.
3. Store C's unit price = $3 per pound.
4. Store B's unit price is the lowest.
How to Find the Unit Rate of a Relationship?The unit rate of the relationship between variables x and y, is given as:
Unit rate, m = y/x.
In a given equation, y = mx, the value of m represents the unit rate of the relationship.
In the scenario given, y represents cost in dollars while x represents the number of pounds of apples.
1. The unit rate = unit price of apples. For store A, we are given 3 pounds of apples will cost $12, therefore:
Unit price = y/x = 12/3
Unit price = $4 per pound
2. For store B, the "2" in the equation, y = 2x, represents the unit price.
Unit price for store B = $2 per pound.
3. Using one point on the graph for Store C, say, (2, 6):
Unit price = y/x = 6/2
Unit price = $3 per pound.
4. The lowest unit price is $2 per pound, therefore, Store B has the lowest unit price for apples.
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Derive the formular to find the area of the moon and state the assumption taken clearly, physically and mathematically, without defying Keplars laws
Answer:
Area = 4πr²
Step-by-step explanation:
- We know that a moon revolves around its orbit as per Keplar. The moon is not a perfect sphere, so we shall take an assumption;
Assume the moon is a perfect and regular sphere
[tex]{ \tt{volume \: of \: moon = \frac{4}{3} \pi {r}^{3} }} \\ \\ { \boxed{ \tt{ \: v = \frac{4}{3} \pi {r}^{3} }}}[/tex]
- From engineering mathematics (rates of change), we know that volume is first order integral of area and area is the first order derivative of volume;
[tex]{ \tt{area = \frac{d(volume)}{dr} }} \\ \\ { \tt{volume = \int area \: dr}}[/tex]
- So, from our formular;
[tex]{ \tt{area = \frac{dv}{dr} = \frac{4}{3}\pi ( \frac{d ({r}^{3} )}{dr} ) }} \\ \\ { \tt{area = \frac{4}{3}\pi(3 {r}^{2}) }} \\ \\ { \boxed{ \rm{area = 4\pi {r}^{2} }}}[/tex]
r is radius of the moon[tex]{ \boxed{ \mathfrak{DC}}}{ \underline{ \mathfrak{ \: delta \: \delta \: creed}}} \\ [/tex]
Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis,each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a/maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 persale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weeklysalary is $900.This task build on important concepts you've learned in this unit and allows you to apply those concepts to a variety ofsituations. Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis,each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with amaximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 persale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weeklysalary is $900. Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis,each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with amaximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 persale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weeklysalary is $900.
Given:
Salesman A earn = 65 per sale.
Salesman B earn = 40 per sales and 300weekly salary.
Salesman C earn = 900 weekly salary
Let "x" represent the number of sales each man
Salesman A earn is:
[tex]y=65x[/tex]Salesman B earn is:
[tex]y=40x+300[/tex][tex]\begin{gathered} 65x=40x+300 \\ 65x-40x=300 \\ 25x=300 \\ x=\frac{300}{25} \\ x=12 \end{gathered}[/tex]So total sales is 12 then.
S=0 For Zero week
[tex]\begin{gathered} \text{Salesman A} \\ y=65x \\ y=0 \end{gathered}[/tex][tex]\begin{gathered} \text{Salesman B} \\ y=40x+300 \\ y=40(0)+300 \\ y=300 \end{gathered}[/tex][tex]\begin{gathered} \text{ Salesman C} \\ y=900 \end{gathered}[/tex]For S=1
[tex]\begin{gathered} \text{Salesman A:} \\ y=65x \\ y=65(1) \\ y=65 \\ \text{Salesman B}\colon \\ y=40x+300 \\ y=40(1)+300 \\ y=340 \\ \text{Salesman C:} \\ y=900 \end{gathered}[/tex]For s=10
[tex]\begin{gathered} \text{Salesman A:} \\ y=65x \\ y=65(10) \\ y=650 \\ \text{Salesman B:} \\ y=40x+300 \\ y=40(10)+300 \\ y=700 \\ \text{Salesman c:} \\ y=900 \end{gathered}[/tex]A random number generator is used to select an integer from 1 to 50 (inclusively). What is the probability of selecting the integer 361?
The probability of selecting the integer 361 from the random generator is 0.
What is probability?It should be noted that probability simply has to do with the likelihood that a particular thing will take place.
In this case, a random number generator is used to select an integer from 1 to 50 .
The probability of selecting the integer 361 from the random generator will be 0. This is because the numbers given are from 1 to 50.
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3.50 : 1.50 ratio as a fraction
Answer:
7/3
Step-by-step explanation:
You want the ratio 3.50 : 1.50 written as a fraction.
RatioA ratio can be written 3 ways. Any of them can be reduced to a ratio of mutually prime integers:
3.50 : 1.50 = 3.50/1.50 = 3.50 to 1.50
Here, the fraction can be made to be a ratio of integers by multiplying both numerator and denominator by 2:
3.50/1.50 = (2·3.50)/(2·1.50) = 7/3
The ratio 3.50:1.50 is equivalent to the fraction 7/3.
I-intercept: C y-intercept y 7+ 5+ 3+ 2+ ... Leveled up to Familiar!
The x intercept is (-7.5,0).
The y intercept is (0,5.5).
A solution must be 14% Insecticide. To make 5 gallons of this solution how much insecticide must you use? A) 0.028 gallon B) .36 gallon C) .7 gallon D) 2.8 gallons
Insecticides = 14/100 x 5 = 0.7
i need help asap!!! im bad at graphing
Answer:
Step-by-step explanation:
eq. of any line with slope -1/2 and through (-1,-5) is
y+5=-1/2(x+1)
2y+10=-x-1
2y=-x-11
x+2y=-11
y=0
x=-11
point is (-11,0)
draw a line through (-11,0) and (-1,-5)
Given the diagram, classify the bolded line as a perpendicular bisector, angle bisector, median or alritude. I chose angle bisector. Am I right?
we have that
the answer is the option First
perpendicular bisector
because, is perpendicular to the segment at its midpoint
4. Solve the equation 3x + 2 = 17 using the bar diagram.17ххХ2
Given that 3x+2=17
3x=17-2
3x=15
x=15/3
x=5
so,the numbers we end up using are 17,3,15,5,2
Overnight the price of gasoline increased by 15% to settle at a price of $4.90 per gallon. What was the price before the 15% increase?
The price of gasoline before the 15% increase is $4.75/gallon.
What is gasoline?
Petroleum-derived clear flammable liquid known as gasoline or petrol is the primary fuel for the majority of spark-ignited internal combustion engines (also known as petrol engines). It mostly comprises of organic compounds made from petroleum fractional distillation that have been improved with various additions. In the United States, refineries typically create 19 to 20 gallons of gasoline, 11 to 13 gallons of distillate fuel, the majority of which is sold as diesel fuel, and 3 to 4 gallons of jet fuel from a barrel of crude oil. The crude oil test and oil refinery processing determine the product ratio. 42 US gallons, or around 159 litres or 35 imperial gallons, is the standard measurement for the volume of an oil barrel.
How can we calculate the price before the 15% increase?
Overnight the price of gasoline increased by 15% to settle at a price of $4.90 per gallon.
15÷100+x = $4.90/gallon
0.15+x = $4.90/gallon
Therefore, x = $4.90/ gallon - 15÷100
x = $4.90/gallon - 0.15
x = $4.75/gallon.
Hence , the price of gasoline before the 15% increase is $4.75/gallon.
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thirty-thousandths in decimal
Thirty thousandths in decimal is written as ;
[tex]0.3000[/tex]Note that numbers after the decimal point begin from tenths, hundredths, thousandths, tens of thousandths, and so on.
Thirty-thousandths therefore is four digits after the decimal point, starting from the digit 3.
At a dinner party, every 3 guests were served a dish of rice to share, every 4 guests were served a dish of greenbeans and every 2 guests were served a dish of meat. There were 17 dishes in all. How many guests were in attendance?"
The number of guests that were at the party is 16.
How many guests were at the party?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 1/2. 1 is the numerator and 2 is the denominator.
The equation that would be formed from the available information in this question is:
[tex]\frac{x}{3} + \frac{x}{4} + \frac{x}{2} = 17[/tex]
Where x represents the number of guests that are in the party.
[tex]\frac{x}{3} + \frac{x}{4} + \frac{x}{2} = 17[/tex]
Add the fractions:
[tex]\frac{3x + 4x + 6x}{12}[/tex] = 17
[tex]\frac{13x}{12}[/tex] = 17
Multiply both sides of the equation by 12
13x = 12 x 17
13x = 204
Divide both sides of the equation by 13
x = 204 / 13
x = 15.7 ≈ 16
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What two numbers are located 5/8 of a unit from 1/6 on a number line?Show your work.
ANSWER
[tex]\frac{19}{24}\text{ and }\frac{-11}{24}[/tex]EXPLANATION
To find the two numbers that are located 5/8 of a unit from 1/6 on the number line, we have to first understand that for a number on a number line, there are numbers both ahead and behind the number.
So, the numbers that are 5/8 from 1/6 on the number line will be:
=> one number that is +5/8 from 1/6
=> one number that is -5/8 from 1/6
Therefore, the two numbers are:
[tex]\begin{gathered} \frac{1}{6}\text{ + }\frac{5}{8}\text{ and }\frac{1}{6}\text{ - }\frac{5}{8} \\ \Rightarrow\text{ }\frac{19}{24}\text{ and }\frac{-11}{24} \end{gathered}[/tex]Those are the two numbers.
evaluate the expression 2(8-4)^2-10÷2
option 1 11
option 2 27
option 3 56
option 4 59
please help quick
I have a time limit
[tex] = 2(4)^{2} - (10 \div 2) \\ = 2(16) - 5 \\ = 32 - 5 \\ = 27[/tex]
THE ANSWER IS OPTION 2. 27
HOPE THIS HELPS
Answer:
Answer is 27
♬
⚫
Use the appropriate form of the percentages formula. What percent of 10 is 2?
To determine a percentage we can use the following formula:
[tex]\frac{part}{whole}\cdot100\%[/tex]In this case the part is equal to two, the whole is equal to 10, then we have:
[tex]\frac{2}{10}*100\%=20\%[/tex]Therefore, 2 is 20% of 10
22. After an article is discounted at 25%, it sells for $112.50. The original price of the article was:
A. $28.12
B. $84.37
C. $150.00
D. $152.00
Answer:
the answer is C
Step-by-step explanation:
25% of 150 is 37.5 so 150-37.5 is 112.5
C Dorothy drew a rectangle with length of 14.3 centimeters and width of 13.9 centimeters. Find its area (nearest tenth).
Area of rectangle = Length x Width
. = 14.3 x 13.9
. = (13.9+ 0.4) x 13.9
. = 13.9^2 + 5.56
. = 13•14 +( 1.4)•8 + 5.56
. =198.77 cm2
Aldo will take the 11:49 train to San Diego. The train is estimated to arrive in 4 hours and 32 minutes. What is the estimated arrival time?
Kevonta, this is the solution:
Time of departure : 11:49
Time of travel : 4:32
In consequence, the estimated arrival time if the train departs in the morning is:
11 + 4 = 15 hours
49 + 32 = 81 minutes
81 minutes = 1 hour + 21 minutes
4:21 pm
If the train departs at night, the estimated time of arrival is:
4:21 am
Sara wants to borrow money from her mother, and she is offered a five-year, simple interest loan of $7,000, with a 3% annual interest rate. What is Sara’s total repayment amount?
a.
1050
Answer: 1050 is the answer trust me i took the quiz and it was correct pls give me brainliest and friend request me ur welcome :)
Step-by-step explanation:
Eva counts up. by 3s, while Jin counts up by 5s. What is the least
number that they both say?
Explanation:
This is the LCM (lowest common multiple) of 3 and 5
3*5 = 15
Eva: 3, 6, 9, 12, 15, 18, 21, ...
Jin: 5, 10, 15, 20, 25, ...
The graph of F(x), shown below, has the same shape as the graph ofG(x) = x - x? Which of the following is the equation of F(x)?F(x) = ?
The graph of G(x) is symmetric with respect to the y-axis. It also passes through the origin.
Since the graph of F(x) moved 4 units upward, we must add 4 to the right of the equation. Thus, the equation of F(x) is as follows.
[tex]F(x)=x^4-x^2+4[/tex]