A) We need to find the rate of change of the function first.
The rate of change or slope of the line is:
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}[/tex]Where x and y are the coordinates of a point in line.
In order to calculate the slope we can take the poinst:
x1 = -6, y1 = 4
x2 = -2, y2= 1
Using the formula of above we find that the slope is:
[tex]m=\frac{1-4}{-2-(-6)}=-\frac{3}{4}[/tex]Now, in order to find the value of y-intercept of the line we can use formula:
[tex]y=m\cdot x+b[/tex]Which is the function of the line. From the formula of above we don't know the value of b (the y-intercept).
But we know that the formula must be valid for a point in the line. We can find the value of b replacing the coordinates of a point in the line, let's choose: x = -6 and y = 4, so:
[tex]4=\text{ m}\cdot(-6)+b[/tex]Now we use the value of m of above:
[tex]4=(-\frac{3}{4})\cdot(-6)+b[/tex]And from the last equation we can see that:
[tex]b=4-\frac{3}{4}\cdot6=4-\frac{9}{2}=\frac{8}{2}-\frac{9}{2}=-\frac{1}{2}[/tex]So, the equation of the line is:
[tex]y\text{ = -}\frac{\text{3}}{4}\cdot x-\frac{1}{2}[/tex]And the y-intercept is obtain replacing x = 0, so the y-intercept is: y = -1/2
b) From the stepts of above we already know an equation that represents the function! It is:
[tex]y\text{ = -}\frac{\text{3}}{4}\cdot x-\frac{1}{2}[/tex]c) Now, we need to use the last equation to find y = n in the table. We know from the table that the value x for that value of y is x = 3, so we replace that value in the equation of the line:
[tex]y\text{ = -}\frac{\text{3}}{4}\cdot3-\frac{1}{2}=-\frac{9}{4}-\frac{1}{2}=-\frac{9}{4}-\frac{2}{4}=-\frac{11}{4}[/tex]So the value of n is:
[tex]n\text{ = -}\frac{\text{11}}{4}[/tex]Which is a way to model 9485 with base ten blocks
The most appropriate way to model 9485 with the base ten blocks is
9 - thousand, 4 - hundred, 8- ten, and 5 - once.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Base ten block implies the number of blocks according to the digit representation,
For the given question,
The number represents there are 9485 cubes, which can be represented as 9 - thousand, 4 - hundred, 8- ten, and 5 - once.
Thus, the most appropriate way to model 9485 with the base ten blocks is 9 - thousand, 4 - hundred, 8- ten, and 5 - once.
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Evaluate when n=5 4n
We are given an expression "4n"
The question says to evaluate this expression when n = 5
Here, evaluation simply means, finding the value of "4n" when n = 5. This is a simple problem of substitution. By substitution I mean replacing every occurence of n in the given expression by 5. This would be done as follows:
Given expression = 4n
Note that here 4 is being multiplied to n.
Replacing n by 5, we get the result as:
[tex]4\text{ }\times\text{ 5 = 20 }[/tex]From here, we can conclude that the value of expression "4n" for n = 5 will be 20.
helpppppp plssssssssssssssssssss
Answer:
No.
Step-by-step explanation:
Pre-SolvingWe are given the following inequality:
[tex]76 < 5-\frac{136}{s}[/tex]
And we want to know if s=2 is a solution, meaning if s is 2, will the inequality still be true?
SolvingWe can substitute 2 for s in the inequality to test it.
Replace s with 2.
[tex]76 < 5-\frac{136}{2}[/tex]
First, let's divide 136 by 2.
136/2 = 68
The inequality is now:
76 < 5 - 68
Subtract 68 from 5.
76 < -63
The inequality reads "76 is less than -63", which is a false statement (76 is positive, -63 is negative, and positive numbers are greater than negative numbers).
Ergo, s = 2 is not a solution to the inequality.
need help with this as soon as possible, answer quick
Answer:
Given points are,
A'(2,3) and A(3,-4), under the translation.
we get the graph as,
where B is A(3,-4) and A is A'(2,3).
A translation by 1 unit left and 7 units up.
Answer is:
A translation by 1 unit left and 7 units up.
Assuming a fixed hourly pay rate, how much would an employee earn for working 4 hours based on this wage table? Hourly Pay Table Hours Worked 2 Money Earned $12.00 $24.00 $36.00 ? A. $36.00 B. $45.00 C. $64.00 D. $48.00
We have the following table
hour pay
1 12
2 24
3 36
4 ?
It seems that for each hour we work, we end up earning $12. Then, we know that if we work 3 hours we earn 36. So, if we work one more hour (4) we should add 12 to what we earn for working 3 hours. That is
[tex]12+36\text{ = 48 }[/tex]So we aren 48 for working 4 hours.
A building worth $829,000 is depreciated for tax purposes by its owner using the straight-line depreciation method.
The value of the building, y, after x months of use, is given by y=829,000-2700x dollars. After how many years will
the value of the building be $699,400?
The value of the building would be $699,400 in 4 years.
What will be the value of the building?Depreciation is the when the value of an asset reduces as a result of wear and tear. Straight line depreciation is a method used in depreciating the value of an asset linearly with the passage of time.
The equation that can be used to determine the value of the building with a straight line depreciation is:
Value of the asset = initial value of the asset - (number of months x deprecation rate)
y = 829,000 - 2700x
The first step is to determine the number of months it would take for the building to have a value of $699,400.
$699,400 = 829,000 - 2700x
829,000 - 699,400 = 2,700x
129,600 = 2,700x
x = 129,600 / 2,700
x = 48 months
Now convert, months to years
1 year = 12 months
48 / 12 = 4 years
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As Mars revolves around the sun, it travels at a rate of approximately 15 miles per second. Convert this rate to miles per minute. At this rate, how many miles will Mars travel in 3 minutes? Do not round your answers. Rate:mi/minDistance traveled in 3 minutes:mi
We have:
1 minute = 60 seconds
Then, 15 miles per second to miles per minute is:
[tex]15\frac{miles}{second}\times\frac{60\text{ seconds}}{1\text{ minute}}=15\times60=900\frac{miles}{minute}[/tex]Next, Distance traveled in 3 minutes is given by:
[tex]distance=900\times3=2700\text{ miles}[/tex]Answer:
rate = 900 mi/min
distance = 2700 miles
3t^2-2t+5; find the company revenues last month if t=-1
Given revenue function is:
[tex]R=3t^2-2t+5[/tex]Now revenue at t=(-1)
[tex]\begin{gathered} R=3(-1)^2-2(-1)+5 \\ R=3+2+5 \\ R=10 \end{gathered}[/tex]So the revenue at t=-1 is 10.
These figures are similar. Thearea of one is given. Find thearea of the other.area=32 in?9 in12 in[ ? Jina
To find the area of similar figures whe you know the area of one of the figures and the length of corresponding sides:
1. Find the scale factor: in this case as you have the area of the largest figure find the scale factor for a reduction:
[tex]SF=\frac{small}{\text{big}}=\frac{9}{12}=\frac{3}{4}[/tex]2. Find the missing area: the area in similar figures is equal to the scale factor squared multiplied by the given area.
[tex]\begin{gathered} A=(\frac{3}{4})^2\cdot32in^2 \\ \\ A=(\frac{9}{16})\cdot32in^2 \\ \\ A=\frac{288}{16}in^2 \\ \\ A=18in^2 \end{gathered}[/tex]Then, the missing area is 18 square inchesOn Friday, you and your friends took a 140 mile road trip to go to a concert.On Sunday you returned home and calculated that the round trip was 7 hours.What was your average speed?Your answer
20 miles per hour
1) Gathering the data from the question:
S=140 miles
Time spent =7 hours
Average speed=?
2) The average speed is calculated using a ratio:
[tex]A\text{ =}\frac{140}{7}=\text{ 20}[/tex]Since the units are in a standard usual way, we don't need to do any conversion so, the answer is
20 miles per hour
kenny has red marbles, 3 blue marbles,and 4 black marbes. Which ration compares a part to the whole? Please help me
A ratio comparing a part to the whole must then have 9 as the second number.
In this question, we have been given Kenny has red marbles, 3 blue marbles, and 4 black marbles.
We need to find the ratio that compares a part to the whole.
Here, the total number of marbles are:
2 red + 3 blue + 4 black = 9 marbles.
Let x be either number of marbles (either red marbles or blue marbles or black marbles)
Then the ratio that compares a part to the whole would be,
x : 9
Therefore, a ratio comparing a part to the whole must then have 9 as the second number.
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Graph the inequality. Then write the solution set in interval notation.
Representing intervals as we are doing for your question means we will represent all the possible values of x. To do that we will colour in blue all possible values of x but there is a detail we must to consider. The limits of the interval. for that we have two symbols, [ that means "closed on the value" and ( that means "opened on the value". So if there is a [ on a number it means that number makes part of the interval, but if there is a ( it means that number is not in the interval.
Now, for our inequality we have
Once x can be equal or superior to 2 it means 2 is part of the interval because x can be this value, but x is inferior to 8 but it can not be 8 so 8 is not on the interval. Once we know that, know we can represent our interval as follows:
And that is our final answer.
For an interval notation we can write [2,8).
The cost of 5 gallons of ice cream has a varianceof 36 with a mean of 36 dollars during the summer.What is the probability that the samplean would differ from the true mean by more than 0.6 dollars if a sample of 107 5-gallon pails is randomly selected? Roundyour answer to four decimal places.
Given:
[tex]\begin{gathered} Variance=36 \\ mean=36 \end{gathered}[/tex]To Determine: The samplean would differ from the true mean by more than 0.6 dollars
Solution
Please note that standard deviation is the square root of variance
[tex]\begin{gathered} SD=\sqrt{Variance} \\ SD=Standard-deviation \\ SD=\sqrt{36}=6 \end{gathered}[/tex][tex]\begin{gathered} S.E=\frac{SD}{\sqrt{n}} \\ S.E=Standard-Error \\ n=107 \\ S.E=\frac{6}{\sqrt{107}}=0.5800 \end{gathered}[/tex]Please note that Z is the number of SE(standard error away from the mean. Therefore
[tex]\begin{gathered} Z=\frac{0.6}{0.5800} \\ Z=1.0345 \end{gathered}[/tex][tex]P(|Z|<1.0345)[/tex][tex]P(|Z|<1.0345)=1-P(Z<-1.0345)=1-0.1515=0.8485[/tex]Hence the probability is 0.8485
4(y – 4) = 8 O A. -2 O B. 2 0 C. 4 D. 6
To find the value of y
4(y – 4) = 8
Divide both-side of the equation by 4
y - 4 = 2
Add 4 to both-side of the equation
y = 2 + 4
y = 6
D is the correct option
which is the new equation written in the slope-intercept form
he slope-intercept form is
y = mx + c
here, m = slope of the line and C is intercept on y axis.
An electrician charges $25 per hour plus a one-time service fee of $50. Write an equation to
represent the cost, y, he charges for x hours of service. How much would he charge for 3 hours of
service.
The equation that represents the cost and the charges for the service is y = $25x + $50. And the he charges $125 for 3 hours of service.
Equation:
An equation state that the value of two mathematical expressions is equal.
For example,
2x + 5 = 7
is an equation.
Given,
An electrician charges $25 per hour plus a one-time service fee of $50.
Here we need to find the equation for the given situation and we have also find the charge for the 3 hour of service.
Let us consider the equation of the line y = mx + c, where m represents the constant change and c represents the fixed constant.
While we apply these equation to the given situation we can get the value of
m = $25
And the value of
c = $50.
Therefore, the equation of the situation is
y = $25x + $50.
We have already now that the y represents the cost and the x represents the hour of service.
Now we have to find the service charge for 3 hours,
So we have to apply the value of x as 3 then we get,
=> y = $25 (3) + $50
=> y = $75 + $50
=> y = $125
Therefore, the cost for 3 hours is $125.
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Consider the polynomial function q ( x ) = − 2 x 8 + 5 x 6 − 3 x 5 + 50
The function has an end behaviour of x → ∞, q(x) → -∞ and x → -∞, q(x) → -∞
How to determine the end behaviour of the function?The equation of the polynomial function is given as
q(x) = -2x⁸ + 5x⁶ - 3x⁵ + 50
To determine the end behaviour of the function, we calculate
q(∞) and q(-∞)
So, we have
q(∞) = -2(∞)⁸ + 5(∞)⁶ - 3(∞)⁵ + 50
Evaluate the exponents
q(∞) = -2(∞) + 5(∞) - 3(∞) + 50
This gives
q(∞) = -∞ + ∞ - ∞ + 50
q(∞) = -∞
Also, we have
q(-∞) = -2(-∞)⁸ + 5(-∞)⁶ - 3(-∞)⁵ + 50
Evaluate the exponents
q(-∞) = -2(∞) + 5(∞) - 3(-∞) + 50
This gives
q(-∞) = -∞ + ∞ + ∞ + 50
q(-∞) = -∞
Hence, the end behaviour of the graph is x → ∞, q(x) → -∞ and x → -∞, q(x) → -∞
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Complete question
Consider the polynomial function q(x) = -2x⁸ + 5x⁶ - 3x⁵ + 50
Calculate the end behaviour
Is the number -3.7 a natural number, a whole number, an integer, a rational number, an irrational number or a real number?
ANSWER
Rational number and Real number
EXPLANATION
We want to identify what type of number -3.7 is.
A natural number is a number that is a positive integer, used in counting things. Examples are 4, 7 and 55.
A whole number is a number that is used in counting, including 0 i.e. natural numbers including 0.
An integer is a whole number but the difference is that an integer can be positive, negative or zero.
A rational number is a number that can be expressed as a fraction of two integers i.e. a/b while an irrational number is one that cannot be expressed as a fraction of two integers.
A real number is any number that can be found as a distance between two points on the number line.
From the definitions above, we see that we can classify -3.7 as a rational number and a real number.
It is not a natural number, whole number, irrational number or an integer.
Benny is flying a kite directly over his friend Frank, who is 125 meters away.When he holds the kite string down to the ground, the string makes a 39° anglewith the level ground. How high is Benny's kite?Draw a sketch depicting the situation above.b.)Use trigonometry to determine the height of Benny's kite.
Solution
Let us draw a diagram to illustrate the information
Using SOHCAHTOA
[tex]\begin{gathered} tan\theta=\frac{opposite}{adjacent} \\ \\ tan39=\frac{h}{125} \\ cross\text{ multiply} \\ h=125\times tan39 \\ \\ h=101.2230041 \\ \\ h=101.22m\text{ \lparen to two decimal places\rparen} \end{gathered}[/tex]
Use any strategy to determine a combination of apples
and pineapples that will balance the scale.
Explain how you know it will balance.
1 Pine- apple equal to 9 Apples.
What is Ratio proportion?The divisional comparison of two quantities yields a ratio, and the equality of two ratios yields a proportion.
A ratio is commonly written as "x: y," though it can also be read as "x is to y" or "x/y."
In terms of comparison, a proportional equation says that two ratios are equal.
When x: y: z: w is used to represent a ratio, it is understood to mean that x is to y as z is to w.
In this case, w and Y are not equal to 0, therefore x/y Equals z/w.
6 Apples = 4 Pomegranates
6 Pomegranates = 1 Pine- apple
1 Pine- apple = 9 Apples.
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Sarah Meeham blends coffee for Tasti-Delight. She needs to prepare 190 pounds of blended coffee beans selling for
$4.55 per pound. She plans to do this by blending together a high-quality bean costing $5.50 per pound and a cheaper
bean at $3.50 per pound. To the nearest pound, find how much high-quality coffee bean and how much cheaper coffee
bean she should blend.
She should blend lbs of high quality beans.
(Round to the nearest pound as needed.)
By solving an equation we can say that Sarah needs to blend a total of 96 pounds of coffee beans.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, the total pounds Sarah needs to blend:
Let the number of pounds by 'x'.Now form an equation as:
5.50x + 3.50x = 190 × 4.55Then, solve equation for 'x' as follows:
5.50x + 3.50x = 190 × 4.559x = 864.5x = 864.5/9x = 96 pounds
Therefore, by solving an equation we can say that Sarah needs to blend a total of 96 pounds of coffee beans.
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43/1/2 divided by 1/1/4
When 43/1/2 is divided by 1/1/4 , the value will be 34 4/5.
What is a fraction?A fraction simply means a numbers that's represented as a/b where a = numerator and b = denominator
In this case, the division of the fraction will be:
43 1/2 ÷ 1 1/4
= 87/2 ÷ 5/4
= 87/2 × 4/5
= 174 / 5
= 34 4/5
This shows the. concept of fractions.
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Finding a time to reach the limit in a word problem on exponential growth or decay
We are told that each year the value of the laptop is 75% of the value of the value of the previous year. This means that every year the current value of the laptop is multiplied by 0.75. Then if v is the original value of the laptop its value after t years is given by:
[tex]V(t)=v0.75^t[/tex]We need to find after which year V(t) is equal to 500 or less then we have V(t)≤500 and since the original value of the laptop was 4200 we have v=4200:
[tex]4200*0.75^t\leq500[/tex]We divide both sides by 4200:
[tex]\begin{gathered} \frac{4200\times0.75^t}{4200}\leqslant\frac{500}{4200} \\ 0.75^t\leq\frac{5}{42} \end{gathered}[/tex]Then we apply the logarithm to both sides:
[tex]\log_{10}(0.75^t)\leqslant\log_{10}(\frac{5}{42})[/tex]Then we use the property of logarithm regarding exponents:
[tex]\begin{gathered} \operatorname{\log}_{10}(0.75^{t})\leqslant\operatorname{\log}_{10}(\frac{5}{42}) \\ t\log_{10}(0.75)\leq\operatorname{\log}_{10}(\frac{5}{42}) \end{gathered}[/tex]And we divide both sides by the logarithm of 0.75 (we change the inequality symbol because log(0.75) is negative):
[tex]\begin{gathered} \frac{t\operatorname{\log}_{10}(0.75)}{\operatorname{\log}_{10}(0.75)}\ge\frac{\log_{10}(\frac{5}{42})}{\operatorname{\log}_{10}(0.75)} \\ t\ge\frac{\log_{10}(\frac{5}{42})}{\operatorname{\log}_{10}(0.75)} \end{gathered}[/tex]Then we get:
[tex]t\ge7.398[/tex]So the laptop's value is less than $500 after 7.398 years.
AnswerSince we are requested to write a whole number as the answer and the smallest whole number that is bigger than 7.398 is 8 we have that the answer is 8 years.
Suzanne is designing a garden for the Gateway Botanical Center. She used a scale of 1 : 600 to make the drawing below. 5 cm 15 cm What is the actual area of the garden, in square meters? (1m = 100 cm)
The given scale is 1:600.
The dimensions of the drawing are 5 by 15.
We just have to multiply each dimension by 600.
[tex]\begin{gathered} 5\times600=3000 \\ 15\times600=9000 \end{gathered}[/tex]So, the dimensions of the actual area are 3,000 cm and 9,000 cm. But, we know that 1 meter equals 100 centimeters, let's transform.
[tex]\begin{gathered} 3000cm\cdot\frac{1m}{100\operatorname{cm}}=30m \\ 9000\operatorname{cm}\cdot\frac{1m}{100\operatorname{cm}}=90m \end{gathered}[/tex]Then, we multiply the dimensions to find the area.
[tex]A=30m\times90m=2700m^2[/tex]Hence, the actual area is 2,700 square meters.Michael wants to save $55,000.00 for a down payment on a home. How much will he need to invest in anaccount with 8.5% APR, compounding daily, in order to reach his goal in 3 years?
Step 1. The information that we have is:
The final amount that Michael wants to save is:
[tex]A=55,000[/tex]We will call that amount A.
The annual percentage rate of the investment, which we will label as r, is:
[tex]r=8.5[/tex]We will need this annual percentage rate represented as a decimal number, therefore, we divide it by 100:
[tex]\begin{gathered} r=8.5/100 \\ r=0.085 \end{gathered}[/tex]The time of the investment, t, is 3 years:
[tex]t=3[/tex]And it is compounded daily, let n be the number of times of compounding in a year:
[tex]n=365[/tex]Step 2. We need to find the initial amount of the investment, which will be called P or principal.
The formula we will use to find it is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Step 3. Substituting the known values:
[tex]55,000=P(1+\frac{0.085}{365})^{(365)(3)}[/tex]From this equation, we need to solve the operations and solve for P, the principal amount of the investment.
Step 4. Simplifying the equation:
[tex]55,000=P(1+0.0002328767)^{1095}[/tex]Continue simplifying:
[tex]\begin{gathered} 55,000=P(1.0002328767)^{1,095} \\ 55,000=P(1.2904233) \end{gathered}[/tex]Then, we solve for P:
[tex]\begin{gathered} \frac{55,000}{1.2904233}=P \\ 42,621.6726=P \end{gathered}[/tex]Rounding to the nearest cent (2 decimal places) The amount that he needs to invest is $42,621.67
Answer: $42,621.67
helpppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:f(x) = 1/4x
Step-by-step explanation:
Assuming this is a linear equation, we simply use the two points given to find the slope (or gradient depending on where you’re from), to find the equation. So just do rise over run:
Edited: I divided backwards, apologies!
-3 - (-2)/-8 - (-12) = -5/-20 = 1/4x.
Instructions:Prepare a written response to the prompt below using a word processor. Please save your file in .doc or .docx format. Yourresponse should be in complete sentences.*To view the grading rubric for this assignment, click on the name of the assignment and click "View Rubric"Assignment Prompt:1. Explain, using the numeric expression below, how to use Order of Operations to compute a numeric value of anexpression.70-2052 - 22)3 +5.(-2)2. Why is it important to have an agreed upon set of rules to determine the order of how we add, subtract, multiply.divide, etc.?3. Please submit your document by clicking on the name of this assignment (above) and attaching your file on the nextscreen.4. If you have any questions, please ask your professor.
We need to solve the following expression:
[tex]70-2(5^2-22)^3+5(-2)[/tex]The order of operations is a rule that tells the correct sequence of steps for evaluationf a math expression. We can remember the order using PEMDAS: Parenthesis, Exponents, Multiplication and Division (from left to right).
Then, in our expression, we must solve parenthesis first. It yields
[tex]\begin{gathered} 70-2(25-22)^3-10 \\ 70-2\times3^3-10 \end{gathered}[/tex]The next step is to raise exponents,
[tex]70-2\times27-10[/tex]and now, the multiplication step
[tex]70-54-10[/tex]then, we get 70-64 and the solution is 6.
Jake and Joshua go to different theme parks during the day. Jake must pay a fee of $30 for a ticket and additional 4$ for every food/beverage. Joshua has to pay 50$ for a ticket and additional 6$ for the food and drinks. How many beverages and food would it take for Joshua to have the same amount of pay as Jake? Graph the item.Write a system of equations, graph them, and type the solution.
To answer this question, we will set a system of equations, and we will solve the system by the graphical method.
Let x be the number of times Jake buys drinks and food, then the total amount he will pay is determined by the following equation:
[tex]T=30+4x\text{.}[/tex]Its graph is:
Now, let x be the number of times Joshua buys drinks and food, then the total amount he will pay is determined by the following equation:
[tex]T=50+6x\text{.}[/tex]Graphing both equations we get:
The intersection of the graphs is the point,
what is 3 to the negative 8th power divided by 3 to the negative 4th power
Answer
Answer = 3⁻⁴ = (1/3⁴) = (1/81)
The answer is 3 raised to the power of negative 4 or 3 to the negative 4th power.
Explanation
The law of indices is usually applied when questions that involve same numbers with (different or the same) powers are considered.
When a number carrying a particular power is divided by the same number also carrying another power, the result is that same number raised to the power of the difference between the power of the numerator and the power of the denominator.
It'll be clearer in practice now.
[tex]\frac{3^{-8}}{3^{-4}}=3^{-8\text{ - (-4)}}=3^{-8+4}=3^{-4}[/tex]Hence, the answer is 3 raised to the power of negative 4 or 3 to the negative 4th power.
Hope this Helps!!!
5. A baker makes 275 wheat rolls.
He fills 9 boxes with 24 rolls in
each box. How many rolls are
not in boxes?
Answer:
59 rolls are not in boxes
Step-by-step explanation:
9×24=216-275=59