Therefore, when w = 1/2, the expression w + 1/2w + 2 evaluates to 17/4.
What structure should a math evaluation follow?You must replace each variable with a number and carry out the arithmetic procedures to evaluate an algebraic expression. Variable x in the preceding example is equivalent to 6, as 6 + 6 = 12. We can substitute our variables with their values before evaluating the expression if we are aware of their values.
To evaluate the expression for w = 1/2, we substitute w = 1/2 into the expression:
w + 1/2w + 2
= 1/2 + 1/2(1/2) + 2 (substitute w = 1/2)
= 1/2 + 1/4 + 2 (simplify multiplication)
= 9/4 + 2 (convert 1/2 to 2/4 and add fractions)
= 17/4 (add fractions)
Therefore, when w = 1/2, the expression w + 1/2w + 2 evaluates to 17/4.
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List the factors of the following numbers. 14, 22, 30, 25,
Step-by-step explanation:
factors of 14: 1, 14, 2, 7
factors of 22: 1, 22, 2, 11
factors of 30: 1, 30, 2, 15, 3, 10, 5, 6
factors of 25: 1, 25, 5, 5
Answer:
Factors 14 : 1, 14, 2, 7
Factors 22 : 1, 22, 2, 11
Factors 30 : 1, 30, 2, 15, 3, 10, 5, 6
Factors 25 : 1, 25, 5
The question is present in the problem
Write an equation or proportion. Define the
variable/s. Solve and label the answer/s. The
measure of the smallest angle in a triangle is 40
degrees less than the measure of the largest angle
and 20 degrees less than the measure of the next
smallest angle. What is the measure of each
angle?
Answer:
Step-by-step explanation:
40-20 =20 then times 3 which is 60.
A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is a/4, this angle is decreasing at a rate of 1/3 rad/min. How fast is the
plane traveling at that time?
Answer:
-csc^2 θ = dθ/dt = 1/5 (dx/dt)
or
3.49 km/min
Step-by-step explanation:
dx/dt
- 5cosec^2 θ * (rate of change of angle of elevation)
- 5 cosec^2 (π/3) * (-π/6)
(5π/6) * (4/3)
= 10π/9 km/min. = 3.49 km/min
increase 1352 by the sum of 897.23 and 39.89
Answer:
2289.12
Step-by-step explanation:
Answer:
2289.12
Step-by-step explanation:
the sum of 897.23 and 39.89 is 937.12
937.12+1352=2289.12
NO LINKS!!!! URGENT HELP PLEASE!!!!
If f(x) is an exponential function where f(-1) = 30 and f(4) = 85, then find the value of f(3), to the nearest hundredth.
========================================================
Work Shown:
The notation f(-1) = 30 tells us that (x,y) = (-1,30) is a point on the exponential curve.
Plug in x = -1 and y = 30 and solve for 'a'
y = a*b^x
30 = a*b^(-1)
30 = a*(1/b^1)
30 = a/b
a = 30b
--------------------------------------------------
Now plug that into the equation to get
y = a*b^x
y = 30b*b^x
y = 30b^1*b^x
y = 30b^(1+x)
Afterward, plug in x = 4 and y = 85 to solve for b.
85 = 30b^(1+4)
85 = 30b^5
b^5 = 85/30
b = (85/30)^(1/5)
b = 1.23157122757057
We can then determine the value of 'a'
a = 30b
a = 30*1.23157122757057
a = 36.947136827117
--------------------------------------------------
To summarize,
a = 36.947136827117b = 1.23157122757057both of which are approximate.
Since we want f(3) to the nearest hundredth, we don't really need to go too overboard with precision. Let's round 'a' and b to 4 decimal places.
We then get
a = 36.9471b = 1.2316This means
y = a*b^x
turns into
y = 36.9471*(1.2316)^x
As a check, plug in x = -1 to get y = 29.999269; we'll have rounding error since we rounded those 'a' and b values earlier. But when rounding 29.999269 to the nearest hundredth, we get y = 30.
Also, plug x = 4 into the equation to get y = 85.00785875 which rounds to 85.
--------------------------------------------------
The last step is to plug x = 3 into the equation
y = 36.9471*(1.2316)^x
y = 36.9471*(1.2316)^3
y = 69.0222951885528
y = 69.02 which is the final answer
--------------------------------------------------
If you were to use those more accurate values of 'a' and b, then x = 3 would lead to y = 69.0175266335801; that rounds to 69.02 when rounding to the nearest hundredth (aka 2 decimal places). So this shows we can stick with the less accurate 'a' and b values while still getting the correct final answer.
GeoGebra and Desmos are great tools to help quickly verify the answer.
Answer:
f(3) = 69.02 (nearest hundredth)
Step-by-step explanation:
Exponential FunctionAn exponential function is used to calculate the exponential growth or decay of a given set of data. In an exponential function, the variable is the exponent.
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Given:
f(-1) = 30f(4) = 85Substitute these values into the general form of an exponential function to create two equations in terms of a and b:
[tex]\begin{aligned}\implies f(-1)&=30\\ab^{-1}&=30\end{aligned}[/tex]
[tex]\begin{aligned}\implies f(4)&=85\\ab^{4}&=85\end{aligned}[/tex]
Divide the second equation by the first equation to eliminate a:
[tex]\begin{aligned}\implies \dfrac{ab^4}{ab^{-1}}&=\dfrac{85}{30}\\\\\dfrac{b^4}{b^{-1}}&=\dfrac{85}{30}\\\\\end{aligned}[/tex]
Solve for b:
[tex]\begin{aligned}\implies \dfrac{b^4}{b^{-1}}&=\dfrac{85}{30}\\\\b^{4-(-1)}&=\dfrac{17}{6}\\\\b^{5}&=\dfrac{17}{6}\\\\b&=\sqrt[5]{\dfrac{17}{6}}\end{aligned}[/tex]
Substitute the found value of b into ab⁴ = 85:
[tex]\implies a\left(\sqrt[5]{\dfrac{17}{6}}\right)^4=85[/tex]
Solve for a:
[tex]\implies a=\dfrac{85}{\left(\sqrt[5]{\dfrac{17}{6}}\right)^4}[/tex]
[tex]\implies a=\dfrac{85}{\sqrt[5]{\dfrac{17^4}{6^4}}}[/tex]
[tex]\implies a=\dfrac{85}{\sqrt[5]{\dfrac{83521}{1296}}}[/tex]
Substitute the found values of a and b into the exponential function formula to create an exponential equation for the given parameters:
[tex]f(x)=\left(\dfrac{85}{\sqrt[5]{\dfrac{83521}{1296}}}\right)\cdot \left(\sqrt[5]{\dfrac{17}{6}}\right)^x[/tex]
To find the value of f(3), substitute x = 3 into the equation:
[tex]\begin{aligned}\implies f(3)&=\left(\dfrac{85}{\sqrt[5]{\dfrac{83521}{1296}}}\right)\cdot \left(\sqrt[5]{\dfrac{17}{6}}\right)^3\\\\&=69.0175266...\\\\&=69.02\; \;\sf (nearest\;hundredth)\end{aligned}[/tex]
Therefore, the value of f(3) to the nearest hundredth is 69.02.
I NEED HELPPPPPPP 10 POINTS FOR WHOEVER GETS IT CORRECT
Answer:
72; Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Gwen has $800 in a savings account that earns 10% annually. The interest is not compounded .How much interest will she earn in 1 year?
Write an equation in slope-intercept form for the line with y-intercept -7 and slope 1/4
Answer:
Step-by-step explanation:
So your slope intercept is on the y line to you will go to your y line and find the -7
Once you find your -7 you rise 1 and run 4 which mean go up by 1 and right by 4
Hope this helps!!
Question
Joe has 20 hot dogs. He is purchasing more hot dogs. He can purchase up to 8 boxes of hot dogs. Each box contains 48 hot dogs. Joe cannot purchase partial boxes. The function that models the number of hot dogs Joe has is f(b)=48b+20, where b is the number of boxes of hot dogs he purchases.
What is the practical domain of the function?
A) {68, 116, 164, 212, 260, 308, 356, 404}
B) all integers from 1 to 8 inclusive
C) all real numbers from 1 to 8 inclusive
D) all real numbers
Answer:
The practical domain of the function is the set of integers from 0 to 8, inclusive, which is option B.
Step-by-step explanation:
The practical domain of the function is limited by the given constraints: Joe can purchase up to 8 boxes of hot dogs, and he cannot purchase partial boxes. Therefore, the number of boxes he can purchase is a whole number between 0 and 8, inclusive.
Substituting the values from 0 to 8 into the function, we get:
f(0) = 48(0) + 20 = 20
f(1) = 48(1) + 20 = 68
f(2) = 48(2) + 20 = 116
f(3) = 48(3) + 20 = 164
f(4) = 48(4) + 20 = 212
f(5) = 48(5) + 20 = 260
f(6) = 48(6) + 20 = 308
f(7) = 48(7) + 20 = 356
f(8) = 48(8) + 20 = 404
Therefore, the practical domain of the function is the set of integers from 0 to 8, inclusive, which is option B.
What would the missing length be?
Answer:
B
Step-by-step explanation:
step by step you will learn
Which equations represent a proportional relationship?
A) y = 5 + x
B) y = 4x
C) y = 7x²
D) y = 2 - x
The equation which represents a proportional relationship from the given set of equations is y = 4x.
What is meant by a proportional relationship?
Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. y= k x, where k is the proportionality constant, is the equation that depicts a directly proportional relationship, or a line. y = k(1/x) or xy = k, where k is the proportionality constant, is the equation that depicts an indirectly proportional relationship, or a line. One can argue that two variables are in a proportional relationship if one variable is always equal to a constant multiplied by the other variable.
So according to the above explanation, we can say that the equation y = 4x is an example of a proportional relationship.
This is because the ratio y/x is always a constant 4.
Therefore the equation which represents a proportional relationship is y = 4x.
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The nth term of a sequence is 3n + 1.
Work out the 5th term of this sequence.
Answer:
[tex]3[/tex]×[tex]5[/tex][tex]=15[/tex]
[tex]15+1=16[/tex]
Write a quadratic function in standard form to represent the data in the table.
X=2,4,6,8,10
Y=3,1,3,9,18
The quadratic functiοn in standard fοrm that wοuld represent the data in the table is y = 2x² + x - 9.
What is quadratic functiοn?A quadratic functiοn is a type οf pοlynοmial functiοn that can be written in the fοrm οf f(x) = ax² + bx + c, where a, b, and c are cοnstants, and x is an unknοwn variable. The graph οf a quadratic functiοn is a parabοla, and the rοοts οf the equatiοn (the x-intercepts) are the pοints where the parabοla crοsses the x-axis. Quadratic functiοns are used tο mοdel a variety οf natural phenοmena, such as the trajectοry οf a prοjectile οr the grοwth οf a pοpulatiοn οver time.
This can be determined by putting the given values intο the standard fοrm equatiοn: y = ax² + bx + c and sοlving fοr a, b and c.
When x = 2, y = 3. Therefοre, 3 = 2a + b - 9, which gives b = 11.
When x = 4, y = 1. Therefοre, 1 = 8a + 11 - 9, which gives a = -1/4.
When x = 6, y = 3. Therefοre, 3 = 18a - 1/4 + 11 - 9, which gives c = -5/4.
The quadratic equatiοn in standard fοrm, y = 2x² + x - 9, can then be written using the values οf a, b and c fοund.
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Find the exact value of tan G in simplest radical form.
2
F
√58
√54
E
Answer:
[tex] \tan G = \dfrac{3\sqrt{6}}{2} [/tex]
Step-by-step explanation:
tan G = opp/adj
[tex] \tan G = \dfrac{\sqrt{54}}{2} [/tex]
[tex] \tan G = \dfrac{\sqrt{9 \times 6}}{2} [/tex]
[tex] \tan G = \dfrac{3\sqrt{6}}{2} [/tex]
Using the grouping method use this equation to put it in factored form
A beetle is 1/5 inch wide and 2/5 inch long.How much greater is the beetle’s length than it’s width?
Answer: To find how much greater the beetle's length is than its width, we need to subtract the width from the length:
Length - Width
Substituting the given values, we get:
2/5 inch - 1/5 inch
Simplifying the expression by finding the common denominator of 5, we get:
(2/5 - 1/5) inch
= 1/5 inch
Therefore, the beetle's length is 1/5 inch greater than its width.
Step-by-step explanation:
Can someone answer this just read the picture? Right answers only please!
The linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.
What is temperature?Temperature is a unit of hotness and coldness that can be described in terms of any number of arbitrary scales. It also represents the direction wherein heat energy will naturally flow, from either a hotter (i.e., higher temperature) body to a colder body.
Temperature is not the same as the energy of such a thermodynamic system; for instance, an iceberg has a significantly larger total heat energy than a match, despite the fact that a match is burning at a significantly higher temperature. The linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.
Therefore, the linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.
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Melissa has a savings account. She deposited $1,000 into the account the first year. For each year after the first, she plans to deposit an amount that is 2 percent greater than the amount deposited the preceding year. If she makes no other deposits, the total amount of the deposited money in years is the sum Sn
of a geometric series of n terms.
The formula for Sn
can be expressed as (1000(1−rn)1−r)
.
Melissa will have deposited approximately how much by year 30?
Responses
A.$30,000
B.$35,729
C.$40,568
D.$87,453
Answer:
Step-by-step explanation:
The formula for Sn of a geometric series with first term a and common ratio r is:
Sn = a((1-r^n)/(1-r))
In this case, the first term a is $1,000, the common ratio r is 1.02 (since she's depositing 2% more each year), and n is 30 (since we're looking for the amount deposited after 30 years).
Plugging in these values, we get:
Sn = 1000((1-1.02^30)/(1-1.02))
Sn ≈ $87,453
Therefore, the answer is D. $87,453.
In △STU , t = 1.3 inches, u = 3.5 inches and ∠S=159° . Find the length of s, to the nearest tenth of an inch. Responses 2.7
A ball is thrown upward with an initial velocity of 75 feet per second and an initial height of 4 feet. Given h(t) = −16t2 + v0t + h0, complete function h to model the vertical motion of the ball. Then find the ball’s maximum height, to the nearest foot.
Therefore , the solution of the given problem of function comes out to be the ball can reach a height of 74 feet, to the closest foot.
What is meant by the word function?The study of mathematics includes topics such as numbers, symbols, and their component components, as well as anatomy, building, and that both true and fictitious geographic locations. A function describes the relationships between different components that all lead to the same result. A function is made up of several variable distinct components that, when placed together, produce specific outputs for every input.
Here,
The starting height (h0) is 4 feet, and the initial speed (v0) is 75 feet per second.
The ball's vertical movement is modelled by the formula h(t) = 16t2 + v0t + h0.
When we change the numbers, we obtain:
h(t) = −16t2 + 75t + 4
The vertex of the parabolic function marks the height of the spheroid at its greatest height.
The vertex's t-value is determined by:
t = −v0/2a
where a represents the t2 component in the h-function (t).
When we change the numbers, we obtain:
t = −75/(2(−16)) = 2.34375
2.34375 seconds pass after the ball is thrown before it hits its highest point.
Given is the utmost height:
h(2.34375) = −16(2.34375) (2.34375)
2 + 75(2.34375) + 4 = 74 feet
The ball can therefore reach a height of 74 feet, to the closest foot.
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Use the Simple Interest formula to find the simple interest. (l=prt)
The Simple Interest is $10
What is Simple Interest?Simple Interest is the method of calculating the interest amount for some principal amount of money. It is also finding the product of the principal amount borrowed or lent, the rate of interest and the term or repayment period of the loan.
Where the Principal is the borrowed money which is given for a specific period.
Simple Interest = P * R * T/100
Where P = Principal = $1000
R = Rate = 2%
T = Time = 6 months
When 6 months converted to year = 6/12 = 1/2 = 0.5 year
SI = 1000 * 2 * 0.5/100
SI = 1000/100
SI = $10
Therefore, the Simple Interest is $10
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Answer:
Step-by-step explanation:
Simple Interest formula = P * R * T/100
p = $1000
r = 2%
t = 6 months (0.5 year)
so, SI = 1000 * 2 * 0.5/100
SI = $10
hope this helps :))
What is the expression for 20 and 6
Answer:
2 ( 10 + 3 )
Step-by-step explanation:
What the tape diagram and how to find the equation true.
Answer:
20=2g
g=10
20/2=10
g=10
Which graph shows a system of equations with one unique solution at (0, 5)?
Answer:
The 2nd graph
Step-by-step explanation:
We know
The solution is (0,5)
Looking at the options, we only see graph 2 has two lines intersecting at the solution point (0,5). So, the answer is graph 2.
Help! Factoring Bottoms up method:
1. 2x²-9x-18=0
2. 8x²+2x-3=0
3. 5x²-11x+2=0
In response to the query, we have that Hence, the following are the answers to this equation: 5x - 2 = 0 or x - 1 = 0 Thus, x = 2/5 or x = 1.
What is quadratic equation?A quadratic equation in a single variable is x ax2+bx+c=0, a form of quadratic equation. a 0. The fact that this polynomial is of second sample guarantees that it comprises at least one solution according to the Basic Theorem of Algebra. Solutions might be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least single word in it has to be rounded. The formula "ax2 + bx + c = 0" constitutes one of the widely used solutions for complex numbers. where the undefined variable "X" is represented by the numerical values or constants a, b, and c.
2x² - 9x - 18 = 0
Secondly, we must identify two integers whose total is -9 and whose product is 2(-18)=-36. These are the numbers -12 and +3. Hence, we may say:
2x² - 9x - 18 = (2x + 3)(x - 6) = 0
Hence, the following are the answers to this equation:
2x + 3 = 0 or x - 6 = 0
Thus, x = -3/2 or 6.
8x² + 2x - 3 = 0
8x² + 2x - 3 = (4x - 3) (4x - 3)
(2x + 1) = 0
Hence, the following are the answers to this equation:
4x - 3 = 0 or 2x + 1 = 0
Thus, either x = 3/4 or x = -1/2.
5x² - 11x + 2 = 0
5x² - 11x + 2 = (5x - 2)(x - 1) = 0
Hence, the following are the answers to this equation:
5x - 2 = 0 or x - 1 = 0
Thus, x = 2/5 or x = 1.
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Which inequality represents "One more than 2 times n is greater than 21?
A. 2n< 21
B. n +3> 21
C. 2n +1 <1
D. 2n +1> 21
g(n)=−50−15n. complete the recursive formula of g(n).
Answer: To complete the recursive formula for g(n) = -50 - 15n, we need to find an expression for g(n) in terms of previous terms of the sequence.
One way to do this is to notice that g(n) can be obtained by subtracting 15 from the previous term, g(n-1):
g(n) = -50 - 15n
= -50 - 15(n-1) - 15 (adding and subtracting 15)
= g(n-1) - 15
Therefore, the recursive formula for g(n) is:
g(0) = -50 (base case)
g(n) = g(n-1) - 15 (recursive step)
This means that to find g(n), we need to first find g(n-1) and then subtract 15 from it. We can use this recursive formula to generate any term in the sequence of g(n).
Step-by-step explanation:
A. x > 19
B. x _> 19
C. x < 19
D. x_< 19
Answer:
C) x < 19
Step-by-step explanation:
It is an open circle pointing in the negative direction starting at 19.
Which part of a prism gives a prism its characteristic name?
Answer:
Bases
Step-by-step explanation: