Since the function describing the height is a quadratic function with negative leading coefficient this means that this is a parabola that opens down. This also means that the maximum height will be given as the y component of the vertex of the parabola, then if we want to find the maximum height, we need to write the function in vertex form so let's do that:
[tex]\begin{gathered} h(t)=-4.9t^2+19t+1.5 \\ =-4.9(t^2+\frac{19}{4.9}t)+1.5 \\ =-4.9(t^2+\frac{19}{4.9}t+(\frac{19}{9.8})^2)+1.5+4.9(\frac{19}{9.8})^2 \\ =-4.9(t+\frac{19}{9.8})^2+19.9 \end{gathered}[/tex]Hence the function can be written as:
[tex]h(t)=-4.9(t+1.9)^2+19.9[/tex]and its vertex is at (1.9,19.9) which means that the maximum height of the ball is 19.9 m
Set up the equation for the following word problem and solve the equation. Let x be the unknown number. -26 times a number minus 5 is equal to 56 less than the number. Step 2 of 2: Solve the equation for x. Express your answer as an integer, a reduced fraction, or a decimal number rounded to two pl Answer
Answer:
Step 1 of 2:
-26x - 5 = x - 56
Step 2 of 2:
17/9 or 1.89
Step-by-step explanation:
1. Putting word statement in algebraic form
Step 1:
Let x be the unknown number ==> x is the unknown variable to be used in the equation and to be solved for
Step 2:
-26 times a number minus 5 ==> -26x - 5
Step 3:
is equal to 56 less than the number ==> = x - 56
Putting it all together:
-26x - 5 = x - 56
2. Solving the equation
-26x - 5 = x - 56
1. Subtract x from both sides:
-26x - 5 - x = x - x -56
-26x -x - 5 = -56
-27x - 5 = -56
2. Add 5 to both sides
-27x - 5 + 5 = -56+ 5
-27x = -51
x = -51/-27 (dividing both sides by -27)
x = 51/27 (negative divide by negative results in positive)
Reduce 51/27 by dividing numerator and denominator by 3
x = (51 ÷ 3)/(27 ÷ 3) = 17/9
= 1.88888.... = 1.89 rounded to two decimal places
in this quadratic trinomial 20 is the _____. 3x^2 -7x-20
A trinomial has three terms. The first term contains the squared variable, the second term contains the variable with an exponent of 1, and the third term does not have any variable. That term is called the independent term.
In the polynomial:
[tex]3x^2-7x-20[/tex]The term -20 is the independent term because it does not depend on the value of the variable x.
can you please solve this for me I'll make sure to give the best review
-9 is an integer
the location of -9 is with 41
6.3 is a repeating decimal
the location is with 5.86666...
-4/5 is a fraction
the location is with 11/12
What happens to F(x) when x is negative but approaches zero for the functionF(x) = 1/x, whose graph is shown below?
Given: The graph of the function below
[tex]F(x)=\frac{1}{x}[/tex]To Determine: What happens to F(x) when x is negative but approaches zero
Solution:
It can be observed from the given graph that when x is negative but approaches zero, F(x) approaches negative infinity
This is as shown below
From the options provided, the best answer is F(x) is a negative number, OPTION C
set up a trigonometric ratio for angle H and solve for X
According to the picture, it is necessary to use cosine, which is the ratio between the side that is adjacent to a given angle and the hypotenuse.
In this case, the angle would be H, the adjacent side to it would be x and the hypotenuse 14. It means that cos H is the ratio between x and 14:
[tex]\cos H=\frac{x}{14}[/tex]Pls help me with this I will give brainless thank u <3
15.sum,neg
16.sum,neg
17.diff,neg
18.sum,neg
19.sum,pos
20.neg
21.pos
22.neg
23.pos
24.neg
13. Use the appropriate percent growth todetermine how much money Lyra will have incach ofthe following situations:(a) How much money will Lyra have after 10years if she invests $5,000 at 4% interestcom-poundcl annually?(1) Suppose that Lyra is saving for retirement,and has saved up $20,000. If her retirementaccount earns 3% interest each year, howmuch will she save in 25 years?(o) How much mowy will yra have after 20years if she $5,000 33.5% interestcompoundedannully?(d) How much money will yr hawwur 10 yearsit she is $6,000 AL 15% interestcompounded quarterly?(E) how much money will lyra have after 10years if she invests $5,000 at 0.8% interestcompounded continuously?(F) compare your answer to (a) and (c). Whichone made more money?
Given:
(a) P = $5000
t = 10 years
r = 4%
(b) P = $20,000
t = 25 years
r = 3%
(c) P = $5000
t = 20 years
r = 3.5%
(d) P = $5000
t = 10 years
r = 1.5%
(e) P = $5000
t = 10 years
r = 0.8%
(f) Compare the result of (a) and (c).
Required:
(a) Find the amount when interest is compound annually.
(b) To find the total amount after 25 years.
(c) Find the amount when interest is compound annually.
(d) Find the amount when interest is compound quarterly.
(e) Find the amount when interest is compound continuously.
Explanation:
The compound interest formula is given as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where p =principal amount
r = rate of interest
n = compound frequency
t = time period in years
(a)
[tex]undefined[/tex]Solve for u.u + 8 = 16
In this case the answer is very simple. .
We must apply algebraic rules to find the solution.
u + 8 = 16
u = 16 - 8
u = 8
The answer is:
u = 8
The drama club is selling tickets to their play to raise money foe the show's expenses. They are selling both adult tickets and student tickets. The auditorium can hold no more than 109 people. Write an inequality that could represent the possible values for the number of student tickets sold,s, and the number of adult tickets sold,a, that would satisfy the constraint
Adult (A)
student (S)
Total people= 109
the maximum number of tickets is 109, in this case is possible 109.
than means
A + S ≤ 109
or
109 ≥ A + S
Dejah is comparing two numbers shown in scientific notation on her calculator. The first number was displayed as 7.156E25 and the second number was displayed as 3.498E-10. How can Dejah compare the two numbers?
Answers
The first number is about
2 x 10¹⁵
2 x 10³⁵
2 x 10‐¹⁵
2 X 10‐³⁵
times bigger than the second number.
Answer:
2 x [tex]10^{35}[/tex]
Step-by-step explanation:
7 ÷ 3 is about 2
[tex]\frac{10^{25} }{10^{-10} }[/tex] = [tex]10^{35}[/tex] When you are dividing powers with the same bases, you subtract the exponents
25 - -10 = 25 + 10 = 35
|x|=-5 why is there no solution?
Absolute value is the distance a number is from zero.
Because distance cannot be negative, an absolute value can never be a negative.
Therefore,
|x| = -5 has no solutions
50 gramos de pechuga de un pollo contiene 10.4 g de proteínas, 0.5 g de carbohidratos y 1.6 g de grasas. Los valores medios de energía alimentaria de esas sustancias son de 4.0 kcal/g para las proteínas y los carbohidratos, y de 9.0 kcal/g para las grasas. a) Al jugar baloncesto, una persona representativa consume energía a una potencia de 420 kcal/h. ¿Cuánto tiempo debe jugar para “quemar” esa pechuga?
Tenemos lo siguiente:
Lo primero es calcular las kilocalorías para las proteínas y para los carbohidratos y grasas, de la siguiente día:
[tex]\begin{gathered} \text{Protenas} \\ 10.4\text{ g}\cdot4\frac{\text{ kcal}}{g}=41.6\text{kcal} \\ \text{Carbohidratos} \\ 0.5\text{ g}\cdot4\frac{\text{ kcal}}{g}=2\text{kcal} \\ \text{Grasas} \\ 1.6\text{ g}\cdot9\frac{\text{ kcal}}{g}=14.4\text{kcal} \end{gathered}[/tex]Ahora sumamos todas las kilocalorías y nos queda lo siguiente:
[tex]41.6+2+14.4=58[/tex]Es decir que en total en los 50 gramos de pechuga hay en total de 58 kilocalorías, ahora debemos calcular el tiempo dividiendo el numero de kilocalorías por la cantidad de consumo de kilocalorías al jugar baloncesto
[tex]\frac{58\text{ kcal}}{420\text{ kcal/h}}=0.138\text{ h}[/tex]Es decir que debe jugar 0.138 horas o un total de:
[tex]0.138\text{ h}\cdot\frac{60\text{ min}}{1\text{ h}}=8.28\text{ min}[/tex]Es decir que debe jugar 8.28 minutos
log(x) + log(x + 3) = 7
Answer:
[tex]x=3160.778016...[/tex]
Step-by-step explanation:
Given logarithmic equation:
[tex]\log(x)+\log(x+3)=7[/tex]
[tex]\textsf{Apply the product log law}: \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\implies \log(x(x+3))=7[/tex]
[tex]\implies \log(x^2+3x)=7[/tex]
[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies x^2+3x=10^7[/tex]
[tex]\implies x^2+3x-10000000=0[/tex]
Solve the quadratic equation by using the quadratic formula.
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]a=1, \quad b=3,\quad c=-10000000[/tex]
Substitute the values of a, b and c into the quadratic formula:
[tex]\implies x=\dfrac{-3 \pm \sqrt{3^2-4(1)(-10000000)}}{2(1)}[/tex]
[tex]\implies x=\dfrac{-3 \pm \sqrt{9+40000000}}{2}[/tex]
[tex]\implies x=\dfrac{-3 \pm \sqrt{40000009}}{2}[/tex]
[tex]\implies x=3160.778016..., \quad x=-3163.778016...[/tex]
As logs of negative numbers cannot be taken, the only valid solution is:
[tex]\boxed{x=3160.778016...}[/tex]
Send me Answers for Questions A, B, and C
Answer: A) 4 B) 30 C) 6
Step-by-step explanation:
For question A, you subtract the highest number and the lowest number (10-6)
For question B, you add all the frequency numbers together
For question C, you use your answer on B and divide it by 5
Determine the effect on the graph of the parent f(x)=x
To answer this question we first graph the parent function
Now we compare the two graphs. We notice that the graph shown is translated two units up.
To translate the graph of function we have to add the ammount we want to translate, then in this case
[tex]g(x)=f(x)+2[/tex]Therefore the answer is J.
Chen is opening a new account with a $1,200 deposit. She will be keeping money in the account, compounded monthly for no more than 3 years. the formula gives the value, V, of the account as a function of time, t. Which is a reasonable domain of this function?V(t)= 1,200(1 + 0.02)^t/12A) 0< or equal to t < or equal to 36B) 0C) 0 < or equal to t < or equal to 1,273.45D) 1,200 < or equal to t < or equal to 1,273.45
The Solution:
Given the function:
[tex]V(t)=1200(1+0.02)^{\frac{t}{12}}[/tex]We are required to find a reasonable domain for the given function.
The domain of the function V(t) is the range of values for t.
The question says Chen is will continue to keep money in the account for not more than 3 years, but the interest will be compound monthly.
Recall:
1 year = 12 months
So,
3 years will be
[tex]12\times3=36\text{ months}[/tex]This means that the range of values for t is:
[tex]0\leq t\leq36[/tex]Therefore, the correct answer is [option A]
a loaf of sandwich bread contains 24 slices. which of these tables correctly shows the ratios of different of loaves of bread to the number of total slices they contain
We have that a loaf of sandwich bread contains 24 slices, then we have that the ratio must be constant between the loaves and the slices. If we have 1 loaf: 24 slices, this ratio must be equal in the table.
Therefore, we have that the only table that follows this is the table that has:
If we have:
2/48 = 1/24
3/72 = 1/24
4/96 = 1/24
The ratio of loaves to slices is the same, that is, 1 / 24.
Given ABC below, with m B=25°, a = 9, and c = 16, find the area of the triangle.
It is given that the sides of the triangle are a =9 and c=16 . The angle is given mB=25 degree.
The area of triangle is determined as
[tex]A=\frac{1}{2}a\times c\times\sin B[/tex][tex]A=\frac{1}{2}\times9\times16\times\sin 25=72\sin 25^{\circ}[/tex][tex]A=30.428sq\mathrm{}\text{unit}[/tex]Thus the area of triangle is 30.428 sq.unit.
Referring to the figure, find the value of x in circle C.
The tangent-secant theorem states that given the segments of a secant segment and a tangent segment that share an endpoint outside of the circle, the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment.
Graphically,
[tex]PA\cdot PB=(PD)^2[/tex]In this case, we have:
[tex]3x\cdot5=10^2[/tex]Now, we can solve the equation for x:
[tex]\begin{gathered} 3x\cdot5=10^2 \\ 15x=100 \\ \text{ Divide by 15 from both sides of the equation} \\ \frac{15x}{15}=\frac{100}{15} \\ \text{Simplify} \\ x=\frac{20\cdot5}{3\cdot5} \\ x=\frac{20}{3} \\ \text{ or} \\ x\approx6.67 \end{gathered}[/tex]Therefore, the value of x is 20/3 or approximately 6.67.
The following triangles are not similar. Determine the ratio between AMCD and AOLN. Howcould you change the measurement(s) to make them similar?
The ratio between MD and DC IS
[tex]\frac{MD}{DC}=\frac{14}{6}=\frac{7}{3}[/tex]The ratio of ON to LN
[tex]\frac{ON}{LN}=\frac{49}{21}=\frac{7}{3}[/tex]The ratio CM to CD
[tex]\frac{CM}{CD}=\frac{12}{6}=\frac{2}{1}[/tex]The ratio of OL to LN
[tex]\frac{OL}{LN}=\frac{40}{21}[/tex]To make the
Jo started a business selling fishing supplies. He spent $5200 to obtain his initial supplies, and it costs him $350 per week for general expenses. He earns $750 per week in sales.
Create the linear function, in slope-intercept form, that represents the scenario.
The linear function is given by 5200+350x = 750x
What is linear function?
A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.
Amount spent to obtain merchandise = $5,200
Cost of general expenses = $350
Earnings from sales per week = $750
Now,
Let 'x' be the number of weeks taken to make profit
thus,
Total cost involved = $5,200 + ( $350 × x )
Total profit from sales = $750 × x
Now, the number of weeks after that the cost and earning will be equal, will be given by
5200+350x = 750x
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Find the volume of each prism. Round your answers to the nearest tenth, if necessary. Do not include units (i.e. ft, in, cm, etc.). (FR)
EXPLANATION:
Given;
We are given the picture of an isosceles trapezoidal prism.
The dimensions are as follows;
[tex]\begin{gathered} Top\text{ }base=4 \\ Bottom\text{ }base=9 \\ Vertical\text{ }height=4.3 \\ Height\text{ }between\text{ }bases=6 \end{gathered}[/tex]Required;
We are required to find the volume of this trapezoidal prism.
Step-by-step solution;
The area of the base of a trapezium is given as;
[tex]Area=\frac{1}{2}(a+b)\times h[/tex]For the trapezium given and the values provided, we now have;
[tex]\begin{gathered} a=top\text{ }base \\ b=bottom\text{ }base \\ h=height \\ Therefore: \\ Area=\frac{1}{2}(4+9)\times4.3 \\ Area=\frac{1}{2}(13)\times4.3 \\ Area=6.5\times4.3 \\ Area=27.95 \end{gathered}[/tex]The volume is now given as the base area multiplied by the length between both bases and we now have;
[tex]\begin{gathered} Volume=Area\times height\text{ }between\text{ }trapezoid\text{ }ends \\ Volume=27.95\times6 \\ Volume=167.7 \end{gathered}[/tex]ANSWER:
The volume of the prism is 167.7
You have a piggy bank containing a total of 66 coins in dimes and quarters. If the piggy bank contains $10.20, how many dimes are there in the piggy bank?
I have 42 dimes in my piggy bank according to the given condition of 66 coins and amount $10.20 and used the system of equation as well as substitution method.
What is system of equation?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system. A group of two or more equations that share the same variables is known as a system of equations. A set of values for a variable that simultaneously satisfy each equation is the solution to a system of equations.
What is substitution method?Finding the value of any variable from one equation in terms of another variable is the first step in the substitution method. For instance, if there are two equations, x+y=7 and x-y=8, we can deduce that x=7-y from the first equation. Applying the substitution method begins with this.
Here,
x+y=66 ......(1)
1 dime values 10 cents.
1 quarter values 25 cents.
10x+25y=1020 ........(2)
x=66-y
10(66-y)+25y=1020
660-10y+25y=1020
15y=360
y=360/15
y=24
x=66-24
x=42
I used the system of equations and the substitution method to determine that I have 42 dime coins in my piggy bank in accordance with the requirement of 66 coins totaling $10.20.
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Assume the hold time of callers to a cable company is normally distributed with a mean of 4.0 minutes and a standard deviation of 0.4 minute. Determine the percent of callers who are on hold between 3.4 minutes and 4.5 minutes. % (Round to two decimal places as needed.)
According to the problem, we have
[tex]\begin{gathered} \mu=4.0\min \\ \sigma=0.4\min \end{gathered}[/tex]We have to find the percent of callers who are on hold between 3.4 minutes and 4.5 minutes.
First, we find the z-score
[tex]z=\frac{x-\mu}{\sigma}[/tex]For x = 3.4
[tex]z=\frac{3.4-4.0}{0.4}=\frac{-0.6}{0.4}=-1.5[/tex]For x = 4.5
[tex]z=\frac{4.5-4.0}{0.4}=\frac{0.5}{0.4}=1.25[/tex]The probability we have to find is
[tex]P=(3.4Using a z-table, we have[tex]\begin{gathered} P(3.4Then, we multiply by 100 to express it in percetange.[tex]0.2351\cdot100=23.51[/tex]Hence, the probability is 23.51%.A company has 10 software engineers and 6 civil engineers. In how many ways can they be seated around a round table so that no two of the civil engineers will sit together? [ 9! × 10!/4!)]
The software engineers can be seated on a round table with no two civil engineers sitting together is 9!×10!/4!
Given, a company has 10 software engineers and 6 civil engineers.
we need to determine in how many ways can they be seated around a round table so that no two civil engineers will sit together.
10 software engineers can be arranged around a round table in :
=(10-1)!
= 9! ways .... eq(A)
Now, we must arrange the civil engineers so that no two can sit next to one another. In other words, we can place 6 civil engineers in any of the 10 *-designated roles listed below.
This can be done in ¹⁰P₆ ways ...(B)
From A and B,
required number of ways = 9!×¹⁰P₆
= 9! × 10!/4!
Hence the number of ways the engineers can be seated is 9! × 10!/4!.
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Which of the following statements must be true based on the diagram below!(Diagram is not to scale)O JL is a segment bisector.JL is a perpendicular bisector.OJT is an angle bisectora Lis the vertex of a right angle,Jis the midpoint of a segment in the diagramNone of the above.
From the diagram, we notice that the line JL bisects the angle J into two equal angles. Hence, we can conclude that the correct statement is this:
JL is an angle bisector
An angle bisector are
Convert 255 to base 2
We can count the number of zeros and ones to see how many bits are used to represent 255 in binary i.e. 11111111. Therefore, we have used 8 bits to represent 255 in binary.
Convert 255 to base 2?
255 = 8 bits
255 in Binary: 255₁₀ = 11111111₂
Binary is a system used in mathematics and computer science where values and numbers are stated as 0 or 1.Binary is base-2, which means that there are just two digits or bits used.For computers, 1 denotes truth or "on," while 0 denotes falsehood or "off." Computers communicate and represent information using binary code.Everything you see on a computer, including letters, numbers, and pictures—basically everything—is made up of multiple 0s and 1s combinations. One of the four different kinds of number systems is the binary number system.When used in computer programs, binary numbers are solely represented by the digits 0 (zero) and 1. (one).Here, the base-2 numeral system is used to represent the binary numbers.One binary number is (101)2, for instance. The modern binary number system was first suggested and refined by Gottfried Leibniz in the 17th century in his article Explication de l'Arithmétique Binaire [1].The system was created by Leibniz about 1679, although it wasn't published until 1703.He had already used 0 and 1.To learn more about binary refer
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The area of Bryce is 71.5 sq units.what is the area of abcd?
Solution
Step 1:
Area of BXYC = 71.5 square units
Step 2:
The area of ABCD is twice the area of BXYC
Step 3:
[tex]\begin{gathered} \text{Area of ABCD = 2 }\times\text{ Area of BXYC} \\ Area\text{ of ABCD = 2 }\times\text{ 71.5} \\ Area\text{ of ABCD = 143 square units} \end{gathered}[/tex]Deter mine the intervals for which the function shown below is increasing
Answer:
The interval at which the function is increasing is from x = -2 to x = 0. In interval notation, it is (-2, 0).
Explanation:
See the graph below for the pattern of the function.
As you can see above, from x = -∞ until x = -2, the value of the function decreases from y = +∞ to y = -7.
Then, starting at x = -2 to x = 0, the value of the function increases from y = -7 to y = -3.
Lastly, starting at x = 0 to +∞, the value of the function decreases again from y = -3 to -∞.
Hence, the interval at which the function is increasing is at (-2, 0).
a1. The amount of milk in a one-gallon milk container has a normal distribution with a meanof 1.07 gallons and a standard deviation of 0.12 gallons.Calculate and interpret the z-score for exactly one gallon of milk.
The z-score formula is given to be:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where
[tex]\begin{gathered} x=score \\ \mu=mean \\ \sigma=standard\text{ }deviation \end{gathered}[/tex]From the question given, the mean and standard deviations are provided as:
[tex]\begin{gathered} \mu=1.07 \\ \sigma=0.12 \end{gathered}[/tex]Therefore, the z-score of exactly 1 gallon is calculated to be:
[tex]\begin{gathered} x=1 \\ \therefore \\ z=\frac{1-1.07}{0.12}=\frac{-0.07}{0.12} \\ z=-0.583 \end{gathered}[/tex]Therefore, the z-score is -0.583.
This tells us that a container with exactly one gallon of milk lies 0.583 standard deviations below the mean.
