A small toy rocket is launched from a 12-foot pad. The height (h, in feet) of the rocket t seconds after taking off is given by the formulah=−2tcubed2−2+12How long will it take the rocket to hit the ground?t= (Separate answers by a comma if applicable. Write answers as integers or reduced fractions.)
Answers
Solution
Gievn:
[tex]h=-2t^2-2t+12[/tex]When the rocket hits the ground. The distance is zero
Set h = 0 and solve for t
[tex]\begin{gathered} -2t^2-2t+12=0 \\ 2t^2+2t-12=0 \\ 2t^2+6t-4t-12=0 \\ 2t(t+3)-4(t+3)=0 \\ (t+3)(2t-4)=0 \end{gathered}[/tex][tex]\begin{gathered} t+3=0\text{ or 2t-4=0} \\ t=-3\text{ or 2t=4} \\ t=-3\text{ or t=}\frac{4}{2}=2 \end{gathered}[/tex]But, time can not be in negative, hence the answer t = 2
Related Questions
You are interested in purchasing a $144,000 home. You plan to make a 25% downpayment and obtain an 8% mortgage for 20 years for the remaining amountthrough City Savings and Loan. Complete the form below to determine the totalclosing cost.
Answers
Cost of the house = $144,000
25% down payment = 25 / 100 * $144,000 = $36,000
Amount of mortgage = $144,000 - $36,000 = $108,000.
The closing costs are detailed in the form, and two rows need to be filled in and get the total closing costs row.
The first missing row is the Loan origination fee that corresponds to 2% of the mortgage:
2% of $108,000 = 2 / 100 * $108,000 = $2,160
The last row corresponds to 3/16 of the total interest on the mortgage.
Calculate the final value of the mortgage:
[tex]\begin{gathered} FV=\$108,000\cdot(1+0.08)^{20} \\ FV=\$503,383.37 \end{gathered}[/tex]The total interest is:
I = $503,383.37 - $108,000
I = $395,383.37
3/16 * $395,383.37 = $74,134.38
The area of the parallelogram is 273in squared what’s the height ?
Answers
The formula for determining the area of a parallelogram is expressed as
Area = base x height
Given that
base = 39
area = 273
Then,
273 = 39 x height
height = 273/39
height = 7 ft
Jim borrows $300 at 7% per annum compounded quarterly for 7 years. Determine the interest due on the loan.
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Answer:
[tex]I=\text{ \$187.62}[/tex]Step-by-step explanation:
Compounded interest is represented as;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{where,} \\ P=\text{ principal } \\ r=\text{ interest rate} \\ n=\text{ times compounded per unit time} \\ t=\text{ time in years} \end{gathered}[/tex]Therefore, for a principal of $300 at 7% per annum compounded quarterly;
[tex]\begin{gathered} A=300\cdot(1+\frac{0.07}{4})^{4\cdot7} \\ A=487.62 \\ \text{Then, the interest due would be the subtraction of A-P} \\ I=487.62-300 \\ I=\text{ \$187.62} \end{gathered}[/tex]How many solutions exist for the equation cos 2θ − sin θ = 0 on the interval [0, 360°)?
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We are given the following equation
[tex]\cos 2\theta-\sin \theta=0[/tex]Let us solve the above trigonometric equation.
Using the double angle identity,
[tex]\cos 2\theta=1-2\sin ^2\theta[/tex]So, the equation becomes
[tex]\begin{gathered} \cos 2\theta-\sin \theta=0 \\ 1-2\sin ^2\theta-\sin \theta=0 \end{gathered}[/tex]Now, let us solve the equation by substitution
Let sinθ = u
[tex]\begin{gathered} 1-2\sin ^2\theta-\sin \theta=0 \\ 1-2u^2-u=0 \\ -2u^2-u+1=0 \end{gathered}[/tex]Let us solve the above equation using the quadratic formula
[tex]u=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]The coefficients are
a = -2
b = -1
c = 1
[tex]\begin{gathered} u=\frac{-(-1)\pm\sqrt[]{(-1)^2-4(-2)(1)}}{2(-2)} \\ u=\frac{1\pm\sqrt[]{1+8}}{-4} \\ u=\frac{1\pm\sqrt[]{9}}{-4} \\ u=\frac{1\pm3}{-4} \\ u=\frac{1-3}{-4},\; \; u=\frac{1+3}{-4} \\ u=\frac{-2}{-4},\; \; u=\frac{4}{-4} \\ u=\frac{1}{2},\; \; u=-1 \end{gathered}[/tex]So, the two possible values are u = 1/2 and u = -1
Substitute them back into sinθ = u
[tex]\begin{gathered} \sin \theta=\frac{1}{2},\; \; \sin \theta=-1 \\ \theta=\sin ^{-1}(\frac{1}{2}),\; \; \theta=\sin ^{-1}(-1) \\ \theta=\frac{\pi}{6}\; and\; \frac{5\pi}{6},\; \; \theta=\frac{3\pi}{2}\; \\ \theta=30\degree\; and\; \; 150\degree,\; \; \theta=270\degree \end{gathered}[/tex]Therefore, the two solutions of the given equation are θ = 30°, θ = 150°, θ = 270° on the interval [0, 360°)
Answer:
I got it correct, by graphing on desmos
Step-by-step explanation:
Look at picture
$3.40 for a box of 20 trash bags. Find unit cost
Answers
Answer:
$0.17
Explanation:
To find the unit cost, we need to divide the total cost by the number of units, so
$3.40 divided by 20 is
$3.40/20 = $0.17
Therefore, the unit cost is $0.17
If this represents the sides of a triangle, classify it by it being an acute triangle, obtuse triangle, right triangle, or not being a triangle.
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1. Determine if it is a rtiangle by using the triangle inequality: the sum of any two sides of a triangle is greater than or equal to the third side.
[tex]\begin{gathered} 13+14\ge16 \\ 27\ge16 \\ \\ 14+16\ge13 \\ 30\ge13 \\ \\ 13+16\ge14 \\ 29\ge14 \end{gathered}[/tex]It is a triangle
2. To classify a triangle knowing its sides you use the next: In a triangle ABC with longest side c
Acute:
[tex]c^2Right:[tex]c^2=a^2+b^2[/tex]Obtuse:
[tex]c^2>a^2+b^2[/tex]For the given triangle;
- Find the square of the longest side:
[tex]16^2=256[/tex]-Find the sum of the squares of the other sides:
[tex]13^2+14^2=169+196=365[/tex]As the sum of the squares of the to smallest sides (365) is greater than the square of the longest side (256) it is an acute triangle.Answer: Acute triangleA scatter plot showed a positive correlation for 11 bowlers. As the number of strikes, s, a bowler made in a game increased, the number of points, p, the bowler scores also increased. The equation for the line of best fit for the data is p = 25s + 40. Estimate the number of strikes made by a bowler with 140 points. A) 4B) 6C) 25D) 40
Answers
The model variables the relationship between the strikes (s) and the number of points scored (p)
[tex]p=25s+40[/tex]To determine the number of strikes made, so that 140 points where scored, you have to replace the model with p=140 and solve for s
[tex]140=25s+40[/tex]The first step is to pass "40" to the others side of the equal sing, by performing the inverse operation "-40" to both sides of the expression
[tex]\begin{gathered} 140-40=25s+40-40 \\ 100=25s \end{gathered}[/tex]Then you have to divide both sides of the expression by 25 to determine the value of s
[tex]\begin{gathered} \frac{100}{25}=\frac{25s}{25} \\ 4=s \end{gathered}[/tex]The bowler made s=4 strikes, the correct choice is A.
why aren't 38 and 40 relatively prime
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No they aren't relatively because they don't come from the same prime number
Determine whether the given ordered pair is a solution of the system.
y = 6
2x - 5y = 24
Is (2,-4) a solution of the system?
Answers
Answer:
[tex](2, -4)[/tex] is not a solution.
Step-by-step explanation:
The ordered pair [tex](2, -4)[/tex] cannot be a solution of the system since, given the first equation of [tex]y=6[/tex], the only possible value for [tex]y[/tex] is 6. In other words, the only possible value that makes [tex]y=6[/tex] true is 6.
Therefore, to figure [tex]x[/tex], we substitute 6 for [tex]y[/tex] in the second equation and solve:
[tex]2x-5y=24[/tex]
[tex]2x-5(6)=24[/tex]
[tex]2x-30=24[/tex]
[tex]2x=54[/tex]
[tex]x=27[/tex]
The ordered pair, then, that solves the system is [tex](27,6)[/tex].
Write √32 in simplest radical form4√22√42√168√2
Answers
Answer:
4√2
Explanation:
To write √32 in its simplest radical form:
Express it as a product of two factors where one is a perfect square.
[tex]\sqrt[]{32}=\sqrt[]{16\times2}[/tex]Next, we can separate the product of radicals as follows:
[tex]\begin{gathered} =\sqrt[]{16}\times\sqrt[]{2} \\ =4\times\sqrt[]{2} \\ =4\sqrt[]{2} \end{gathered}[/tex]The simplest radical form is 4√2.
Evaluate each of the following. Illustrate with a point on the graph g(-2)=g(3)=g(0)=g(7)=
Answers
Solution
From the graph given we have this:
g(-2)= -3
g(3)= 4
g(0)= -3
g(7)= 0
0 2 4 6 8 10 12 14 16 What is the interquartile range of plot A
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The given Data set can be arranged in the ascending order as,
0,2,4,6,8,10,12,14,16.
Point D is in the interior of
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The given problem can be exemplified in the following diagram:
The conditions are:
[tex]\begin{gathered} m\angle ABD=6x+5 \\ m\angle ABC=10x+7 \\ m\angle DBC=36 \end{gathered}[/tex]We also have the following relationship:
[tex]m\angle ABD+m\angle DBC=m\angle ABC[/tex]Substituting the values we get:
[tex]6x+5+36=10x+7[/tex]Solving the operations:
[tex]6x+41=10x+7[/tex]Now we solve for "x", first by subtracting 10x on both sides:
[tex]\begin{gathered} 6x-10x+41=10x-10x+7 \\ -4x+41=7 \end{gathered}[/tex]Now we subtract 41 on both sides:
[tex]\begin{gathered} -4x+41-41=7-41 \\ -4x=-34 \end{gathered}[/tex]Now we divide both sides by -4
[tex]x=-\frac{34}{-4}=\frac{17}{2}[/tex]Now we replace the value of "x" in the expression for angle ABD:
[tex]\angle ABD=6x+5[/tex]Replacing the value of "x":
[tex]\angle ABD=6(\frac{17}{2})+5[/tex]Solving the operations:
[tex]\angle ABD=3(17)+5=56[/tex]Therefore angle ABD is 56 degrees.
PLS ANSWER, will mark brainliest
The total cost after tax to repair Deborah’s computer is represented by 0.08(50h)+50h, where h represents the number of hours it takes to repair Deborah’s computer. What part of the expression represents the amount of tax Deborah has to pay? Explain.
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Answer:
The expression of the total cost after tax, 0.08(50h) + 50h, has a tax part and a cost part.The tax part is 0.08(50h).The cost part is 50h.What is tax?Tax is the amount paid by the consumer to the government for the use of goods and services produced in/by the country.It is charged over the total cost for the particular good or service, at a pre-determined rate called the rate of tax.How to solve the question?In the question, we are informed that the total cost after tax to repair Deborah's computer is represented by 0.08 (50h) +50h, where h represents the number of hours it takes to repair Deborah's computer.We are asked what part of the expression represents the amount of tax Deborah has to pay.We know that the total cost = Tax + Fixed Cost,where tax = tax rate * fixed cost.Therefore, we write the total cost function like this:Total cost = Tax Rate(Fixed cost) + Fixed Cost.Comparing the given expression of the total cost, 0.08(50h) + 50h, with this expression, we can say that 0.08(50h) represents the tax part, where 0.08 is the tax rate and 50h is the fixed cost.Learn more about taxes atbrainly.com/question/5022774#SPJ2
Step-by-step explanation:
I need to know the sum of the two terms
Answers
Answer: 194 degrees
From the given figure, we can see a transversal forming between the pairs of parallel lines.
Let us focus on the lines n, a, and e. Here, we can see a pair of parallel lines a and e, cut by a transversal n.
We are given a measurement for angle 4, which is 97. Then we are asked to find the sum of angle 2 and angle 4.
One theorem with respect to transversals that we must be familiar with is the Alternate Interior Angles Theorem which states that:
When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
With this, we can see from the figure that angle 2 and angle 4 are actually alternate interior angles.
Since they are alternate interior angles, and they are congruent, this would mean that angle 2 also measures 97.
[tex]m\angle4=97;m\angle2=97[/tex]With this, we can now add the two measurements, and that would give us:
[tex]97+97=194[/tex]The sum of angle 2 and angle 4 is 194 degrees.
What is the slope of the line that passes through the points (9, 5) and (21,-5)?
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The equation of the line that passes through points (9, 5) and (21,-5) isy = (-5/6)x - 25/2.
How does the slope intercept form made?The slope-intercept form of an a line is a method of writing the equation of a line so that the slope as well as y-intercept are easily identifiable.The the line's slope represents its steepness, and also the y-intercept is the point at which the line intersects a y-axis.For the given question;
The line passes through points are-
(x1, y1) =(9, 5) and
(x2, y2) = (21,-5)
Slope = m = (y2 - y1)/(x2 - x1)
m = (-5 - 5)/(21 - 9)
m = -10/12
m = -5/6
Equation of the line is found using slope intercept form.
y - y1 = m (x - x1)
y - 5 = (-5/6)(x - 9)
y = (-5/6)x - 25/2
Thus, the equation of the line that passes through points (9, 5) and (21,-5) isy = (-5/6)x - 25/2.
To know more about the slope intercept form, here
brainly.com/question/1884491
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Out of 50 students, 17 want pepperoni pizza, 19 want sausage pizza and the rest want a supreme pizza. What percent of the students want a supreme pizza?
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First, lets find how many students want the supreme pizza. Let 'x' be the number of those students. Then, given the information, we have:
[tex]x+17+19=50[/tex]solving for 'x', we get:
[tex]\begin{gathered} x+17+19=50 \\ \Rightarrow x+36=50 \\ \Rightarrow x=50-36=14 \\ x=14 \end{gathered}[/tex]we have that x = 14 students want a supreme pizza.
Now, if we suppose that the 50 students are the 100%, then, using a rule of three, we get:
[tex]\begin{gathered} 50\rightarrow100\% \\ 14\rightarrow y\% \\ \Rightarrow y=\frac{14\cdot100}{50}=\frac{1400}{50}=28 \\ y=28\% \end{gathered}[/tex]therefore, 28% of the students want a supreme pizza
Write the equation of the line on the graph.
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Answer:
The correct equation is
[tex]y = - \frac{7}{5} x + 4[/tex]
3|x + 1| - 9 = 0? Solution set?
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x = (2, -4)
Explanation:Given:
[tex]\begin{gathered} 3|x+1|-9=0 \\ \\ 3|x+1|=9 \\ \\ |x+1|=3 \\ \\ x+1=3 \\ \Rightarrow x=2 \\ \\ OR \\ -(x+1)=3 \\ \\ -x-1=3 \\ \\ -x=3+1 \\ \\ -x=4 \\ \\ x=-4 \end{gathered}[/tex]x = (2, -4)
If △STU is similar to △XYZ, the sides of △STU must be congruent to thecorresponding sides of △XYZ.A. TrueB. False
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Similar triangles are triangles that have the same interior angles and the corresponding sides are proportional, that is, for triangles STU and XYZ we have the proportion:
[tex]\frac{ST}{XY}=\frac{TU}{YZ}=\frac{SU}{XZ}[/tex]The corresponding sides are congruent only if the proportion rate is 1, but that is not always true and it's not necessary.
Therefore the correct option is B: False
If the corresponding sides are congruent, the triangles are congruent.
If you will conduct a research about the poor study habits of Grade 7 students, how will you present your research problem using mathematical function?
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I would define what a poor study habit is, using a parameter like study time in hours or days.
Let a study time of at least 2 hours per day be good, and less than 2 hours per day be poor.
Let f(x) be the study habit of a particular grade, so we write:
Good study time as:
[tex]f(x)\ge2[/tex]Bad study time as:
[tex]f(x)<2[/tex]The last one can represent the study habits of Grade 7 students.
Which point has the coordinates (-2.5, 5.5)? A.point EB.point FC.point GD.point H
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After paying $7 for a movie ticket Grace still had $3.75 how much money did Grace have before buying the ticket A. $3.25B. $10.25C. $4.52D. $10.75
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D. $10.75
To solve this we have to write an equation:
Movie ticket price: $7
Money left : $3.75
Original amount: x
The original amount (x) minus the price of the ticket(7) must be equal to the money left after the purchase (3.75)
x-7 =3.75
Solving for x:
x = 3.75+7
x = 10.75
Write equation below matches the following statement?Five more than two times a number,n, is sixteen.
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"Five more than two times n" indicates that you have to multiply n by 2 and add 5, the result of this operation is 16, so the expression is:
[tex]2n+5=16[/tex]Choose all of the expressions that are equivalent to 2 1/2 divided by 1 2/6A 5/2 times 6/8B 2/5 times 6/8C 1 2/6 divided by 2 1/2D 5/2 divided by 8/6
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A fruit bowl contains 4 green apples, 7 red apples, and 5 yellow apples. What is the probability that a randomly selected apple will NOT be red?
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Problem
A fruit bowl contains 4 green apples, 7 red apples, and 5 yellow apples. What is the probability that a randomly selected apple will NOT be red?
Solution
For this case we can find the total number of apples like this:
4+7+5= 16 apples
And the number of apples not red are:
4 + 5= 9 apples
Then the probability of being not red would be:
p = 9/16
writing exponential functions (4, 112/81), (-1, 21/2)
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The given points are (4, 112/81) and (-1, 21/2).
To find an exponential function from the given points, we have to use the forms.
[tex]\begin{gathered} y_1=ab^{x_1} \\ y_2=ab^{x_2} \end{gathered}[/tex]Now, we replace each point in each equation.
[tex]\begin{gathered} \frac{112}{81}=ab^4 \\ \frac{21}{8}=ab^{-1} \end{gathered}[/tex]We solve this system of equations.
Let's isolate a in the second equation.
[tex]\begin{gathered} \frac{21}{8}=\frac{a}{b} \\ \frac{21b}{8}=a \end{gathered}[/tex]Then, we replace it in the first equation
[tex]\frac{112}{81}=(\frac{21b}{8})\cdot b^4[/tex]We solve for b.
[tex]\begin{gathered} \frac{112\cdot8}{81\cdot21}=b\cdot b^4 \\ \frac{896}{1701}=b^5 \\ b=\sqrt[5]{\frac{896}{1701}}=\frac{2\sqrt[5]{4}}{3} \\ b\approx0.88 \end{gathered}[/tex]Once we have the base of the exponential function, we look for the coefficient a.
[tex]a=\frac{21b}{8}=\frac{21}{8}(\frac{2\sqrt[5]{4}}{3})=\frac{7\sqrt[5]{4}}{4}[/tex]Therefore, the exponential function is[tex]y=\frac{7\sqrt[5]{4}}{4}\cdot(\frac{2\sqrt[5]{4}}{3})^x[/tex]The image below shows the graph of this function.
Many water bottles contain 16 fluid ounces, or 1 pint, of water. Drink labels often show the number of fluid ounces and the number of milliliters in a container. How many milliliters are in a 16-fluid-ounce drink?29.6 milliliters = 1 fluid ouncesPart A-D
Answers
Answer:
473.6 milliliters
Explanation:
A. One rate is the conversion factor
First, we know that 29.6 milliliters are equivalent to 1 fluid ounce, so the first rate of the conversion factor is:
[tex]\frac{29.6mL}{1\text{ fl oz}}[/tex]B. The other rate relates the known amount to the unknown converted amount
Then, we want to know how many milliliters are in 16 fluid ounces, so the other rate is:
[tex]\frac{x\text{ mL}}{16\text{ fl oz}}[/tex]C. Set the rates equal to one another.
[tex]\frac{29.6\text{ mL}}{1\text{ fl oz}}=\frac{x\text{ mL}}{16\text{ fl oz}}[/tex]D. multiply both parts of the left rate by a number that will make the number of fluid ounces in the two rates the same.
The number that will make the fluid ounces in the two rates the same is 16, so we need to multiply by 16
[tex]\frac{29.6\text{ mL x 16}}{1\text{ fl oz x 16}}=\frac{473.6\text{ mL}}{16\text{ fl oz}}[/tex]Therefore, there are about 473.6 milliliters in 16 fluid ounces.
You phone a plumber for a quote on fixing your leaky pipes. You are quoted $190 for the service call and $90 per hour for the work. You are on a budget and can afford no more then $460 . Write an inequality to find the number of hours of work h you can afford. ( assume h greater than or equal 0) then solve the inequality
Answers
We want to find h which represents the number of hours of work that you can afford.
From the information given,
The charge per hour of work is $90. This means that the charge for h hours of work is
90 x h = 90h
The service fee is $190. This is a constant fee that must be paid irrespective of the number of hours. Thus, the total cost of h hours of work is
90h + 190
Again, you are on a budget and can afford no more then $460. This means that the amount that you can spend is less than or equal to $460. the symbol for representing 'less than or equal to' is '≤'
Therefore, the inequality that will be used to find the number of hours of work h you can afford is
90h + 190 ≤ 460
To solve the inequality, we would subtract 190 from both sides of the inequality. We have
90h + 190 - 190 ≤ 460 - 190
90h ≤ 270
We would divide both sides of the inequality by 90. We have
90h/90 ≤ 270/90
h ≤ 3
Given x = pi/3, what is the exact value of cos (pi+x)?
Answers
Using the unit circle above you can identify the cosine as the x-coordinate.
Then, the cosine of (4pi/3) is -1/2