a.
Function:
[tex]h(t)=-3t^2+12t+96[/tex]Factoring -3, we have:
[tex]\begin{gathered} h(t)=-3t^2+12t+96 \\ h(t)=-3(t^2-4t-32) \end{gathered}[/tex]Middle term facotizing the term inside parenthesis:
[tex]\begin{gathered} h(t)=-3(t^2-4t-32) \\ h(t)=-3(t-8)(t+4) \end{gathered}[/tex]This is the factored form.
b.
h(t) is the height.
When it lands on the ground, the height (h(t)) is 0, so we have:
[tex]\begin{gathered} h(t)=-3(t-8)(t+4) \\ 0=-3(t-8)(t+4) \end{gathered}[/tex]If we solve this equation for t, we get the line drone lands on the ground.
Let's do this:
[tex]\begin{gathered} -3(t-8)(t+4)=0 \\ t=8,-4 \end{gathered}[/tex]Time can't be negative, so the solution is t = 8 seconds.
Answer:
h(t) = -3(t-8)(t+4) and 8 minutes
Step-by-step explanation:
Enjoy ur answer have a great day please mark as brainliest :D !!!
Find the Area of the figure below, composed of a rectangle and one semicircle, with
another semicircle removed. Round to the nearest tenths place.
18
14
:C
PLEASE HELP 10 POINTS !!!!!!!!
Answer:
112
Step-by-step explanation:
8*14=112
3.14*4²=50.24
50.24/2=25.12
112-25.12+25.12=112
6x+1.6=58
i dont know the answer to this
The value of x in the given equation, 6x + 1.6 = 58, is x = 9.4
Determining the value of x in an equationFrom the question, we are to determine the value of x in the given equation.
The given equation is
6x + 1.6 = 58
To determine the value of x in the equation, we will determine the value of the unknown variable.
The unknown variable in the given equation is x.
Thus, we will determine the value of x.
Solving the equation for x
6x + 1.6 = 58
Subtract 1.6 from both sides of the equation
6x + 1.6 - 1.6 = 58 - 1.6
6x = 56.4
Divide both sides of the equation by 6
6x/6 = 56.4/6
x = 9.4
Hence, the equation solved for x gives x = 9.4
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Look at the simultaneous equations below.
x - 6y=10
3y² = 4x + 1
a) Show that 3y² - 24y - 41 0
=
b) Use part a) to solve the simultaneous
equations.
For x = 200, the equation 3y² - 24y - 410 is satisfied and there two possible solution sets A(66.68, 9.447) and B(1.31, - 1.447) for the given system of equations.
What is a expression? What is a mathematical equation? What is degree of a equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Degree of equation is the highest power of x in the given equation.An equation of second degree is of the form -f(x) = ax² + bx + c
It has two possible roots.Given is are the following equations -
x - 6y=10
3y² = 4x + 1
It is given that -
3y² - 24y - 41 ...Eq[1]
3y² = 4x + 1
y² = (4/3)x + (1/3)
So, we can write -
3{(4/3)x + (1/3)} - 24 × √{(4/3)x + (1/3)} - 410
Refer to the graph [1] attached. We can see that, for x = 200, the equation is fulfilled.
Now, refer to the graph [2] attached. It shows there two possible solution sets.
A(66.68, 9.447)
B(1.31, - 1.447)
Therefore, for x = 200, the equation 3y² - 24y - 410 is satisfied and there two possible solution sets A(66.68, 9.447) and B(1.31, - 1.447) for the given system of equations.
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What is the value of 0 in the following image
We will determine the value of theta as follows:
[tex]\begin{gathered} cos(\theta)=\frac{10}{21}\Rightarrow\theta=cos^{-1}(\frac{10}{21}) \\ \\ \Rightarrow\theta\approx61.6 \end{gathered}[/tex]So, the measurement of the angle is approximately 61.6°.
What is the Associative Property of Addition?The Associative Property of Addition states that when multiplying a number times the sum of two other numbers, that number can be multiplied by each of the numbers in the sum first and then added together.The Associative Property of Addition states that when adding three or more numbers, the order in which they are added is important.The Associative Property of Addition states that when adding numbers, the order can be reversed.The Associative Property of Addition states that when adding three or more numbers, they can be grouped in any way and the result will remain the same.
The associative property of addition states that when adding numbers, the order can be reversed.
The associative property of addition says that changing the grouping of the addends does not change the sum.
For example -
[tex](3+5)+4=3+(5+4)[/tex]Therefore, the given option (c) is correct.
In this coordinate plane, the slope of line a is equal to the opposite reciprocal of the slope of line b.
Blank 1: [tex]\frac{k}{m}[/tex]
Blank 2: [tex]-\frac{k}{n}[/tex]
Blank 3: [tex]\frac{k}{m}=\frac{n}{k}[/tex]
Blank 4: [tex]\frac{KL}{KM}=\frac{KN}{KL}[/tex]
Blank 5: SAS similarity theorem
Blank 6-9: The options are needed
Identify the graphs of y 2|x+2|-6 and y=-2 in the same coordinate plane
The graphs of the absolute value function y = 2|x + 2| - 6 and the horizontal line y = -2 are given on the image at the end of the answer.
How to build the graphs?The definition of the absolute value function is given as follows:
y = |x - h| + k.
In which the coordinates of the vertex are (h,k), representing the turning point of the graph of the absolute value function, the point in which the function makes the "V".
In this problem, the definition of the function is:
y = 2|x + 2| - 6.
Hence the coordinates of the vertex are:
(-2, -6).
The multiplication by 2 represents a vertical stretch but is not related to the vertex of the function.
y = -2 is a horizontal line, and the graph with these two functions is given by the image at the end of the answer.
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The sculptures at Mount Rushmore each measure about 60 feet from chin to forehead. For the average person, this distance is 9 inches. The average distance between a person’s ears is 6 inches. What is the ratio of a person’s chin to forehead distance compared to the distance between his ears?
The distance from the chin to the forehead is 1.5 times the distance between the ears.
The average person's chin-to-forehead distance is 9 inches, and the distance between human ears is 6 inches. You are asked to compare the distance from a person's chin to their forehead to the distance between their ears.
Calculation:-
We can express the given information as:9/6
9/6 = 1.5.
Average speed is calculated by dividing the total distance something has traveled by the total time it took to travel that distance. Velocity is how fast something is going at a given moment.
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I need to help with the page I attached below!
Nishnat can trade box tops only for printer.
Nishant keeps the box tops in 38 folders.
Each folder contains 80 box tops.
Number of box tops nishant has = number of folders x number of box tops in each folder
Number of box tops nishant has = 38 x 80
Number of box tops nishant has = 3040
For printer, he needs 1500 box tops
1500 < 3040
So, he can trade box tops for a printer.
For digital camera, he needs 3500 box tops
3500 > 3040
So, he can not trade box tops for a digital camera.
For tablet computer, he needs 5000 box tops
5000 > 3040
So, he cannot trade box tops for a tablet computer,
Therefore, Nishnat can trade box tops only for printer.
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2. The volume of a 3-D shape is 13 cubic feet. The shape is scaled up and the new volume is 832 cubic
feet. What was the scale factor?
Scale factor of given equation is 64 : 1
What is scale factor ?Scale Factor is used to scale the shape in various dimensions. In Geometry you will learn about different geometric shapes in 2D and 3D. A scale factor is a measure of similar figures that look the same but have different scales or measurements. Suppose two circles are similar but may have different radii. The scale factor indicates how much larger or smaller the figure is than the original figure. Scale allows you to scale the original shape up or down and draw it. The amount by which a shape is magnified or shrunk is called the scale factor. Used when you need to increase the size of 2D shapes such as circles, triangles, squares, and rectangles. Magnification is also well understood from the basic theorem of proportionality.Calculationinitial volume = 13 cubic feet
final volume = 832 cubic feet
scale factor = 832 / 13
= 64 : 1
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The price of Apple stock, A(X), over a 12 month period decreased and thenincreased according to the equation A(x) = x x 0, where x equals the number ofmonths. The 2 - 6 + 2 price of Baller stock B(x), increased according to theequation B(x) = 3x + 2 over the same 12-month period. When were both stockvalues the same?
The question is: When we're both stock values the same? Then all you have to do is match both equations and solve for x, like this
[tex]\begin{gathered} A(x)=x^2-6x+20 \\ B(x)=3x+2 \\ \text{ Matching you have} \\ x^2-6x+20=3x+2 \\ \text{Subtract 3x from both sides of the equation} \\ x^2-6x+20-3x=3x+2-3x \\ x^2-9x+20=2 \end{gathered}[/tex][tex]\begin{gathered} \text{Now subtract 2 from both sides of the equation} \\ x^2-9x+20-2=2-2 \\ x^2-9x+18=0 \end{gathered}[/tex]Factoring the trinomial you get
[tex]x^2-9x+18=(x-6)(x-3)=0[/tex]Which implies that
[tex]\begin{gathered} x-6=0 \\ x=6 \\ \text{ or} \\ x-3=0 \\ x=3 \end{gathered}[/tex]Therefore, since x corresponds to the number of months, then the values of the two shares were equal at 3 and at 6 months.
2) A recycling center was offering cash for different types of recyclables. For each pound of
paper recycled they offered $0.03, for each pound of aluminum they offered $1.32 and for
each pound of plastic they offered $0.07. Jerry took in 10 pounds of paper, 8 pounds of
aluminum and 7 pounds of plastic. How much money did he earn?
The money earned by Jerry at the recycling center is $11.35.
According to the question,
We have the following information:
For each pound of paper recycled they offered $0.03, for each pound of aluminum they offered $1.32 and for each pound of plastic they offered $0.07. Jerry took in 10 pounds of paper, 8 pounds of aluminum and 7 pounds of plastic.
Now, we have the following expression when multiplied with the cost of each pound:
10*0.03+8*1.32+7*0.07
Now, we will first use multiplication and then we will use addition:
0.3+10.56+0.49
$11.35
Hence, the money earned by Jerry at the recycling center is $11.35.
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The local seven digit telephone numbers in city A have 207 as the first three digits. How many different telephone numbers are possible in City A?
Given:
There are seven total digits.
The first 3 are already selected, so there is a choice for 4 digits.
There are 10 possible choices for each of the other 4 digits, so there are a total of 10×10×10×10 choices. Therefore:
[tex]10\times10\times10\times10=10000[/tex]Answer: 10000
Anna saved $40 each month from babbysitting for 1 and 1/4 years. She spends 70% of her savings on a computer
how much money does she have left
( write the answer as a decimal to 2 places.)
The money left for Anna is $180 which was earned by babysitting for 15 months.
What is meant by the term percentage?To calculate a percentage, divide the value by the total value and multiply the result by 100.For the given question;
Monthly saving of Anna is $40.
Total time of babysitting is 1 and 1/4 years.
Total time = 5/4 years = 15 months.
Total money saved = 15 × $40 = $600.
70% of the money is spent
Thus, 30 % money is left.
Find 30% of $600
= 30 × 600/ 100
= $180.
Thus, the money left for Anna is $180 which was earned by babysitting for 15 months.
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Select the correct answer.Which equation represents the line that is perpendicular to y = 1/4 and passes through (-6,-9)?A. x = -9B. X=-6C. y=-9D. y=-4
SOLUTIONS
Step-by-step explanation:
y = 1/4 is the equation of a horizontal line parallel to the x- axis.
A line perpendicular to it will be a vertical line parallel to the y- axis with equation
x = c
where c is the value of the x- coordinates the line passes through.
The line passes through (- 6, - 9 ) with equation
x = - 6 →
Option B
Answer:
B
Step-by-step explanation:
y = [tex]\frac{1}{4}[/tex] is the equation of a horizontal line, parallel to the x- axis and passing through all points with a y- coordinate of [tex]\frac{1}{4}[/tex]
A line perpendicular to it will be a vertical line parallel to the y- axis, with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (- 6, - 9 ) with x- coordinate - 6 , then
x = - 6 ← equation of perpendicular line
Micah has an electricity plan where he is charged a monthly fixed rate of $3.18 and a usage fee of $0.14 per kilowatt-hour. In the equation below, x represents the amount of electricity he used, and y represents the amount Micah was charged for electricity. y = $0.14x + $3.18 If Micah was charged $143.18 for electricity last month, how much electricity did he use? A. 140 kilowatt-hours B. 45 kilowatt-hours C. 1,023 kilowatt-hours D. 1,000 kilowatt-hours Reset Submit
Answer:
D. 1,000 kilowatt-hours
Step-by-step explanation:
Given:
[tex]y=0.14x+3.18[/tex]
If Micah was charged $143.18, then:
[tex]143.18=0.14x+3.18[/tex]
First, subtract 3.18 from both sides:
[tex]140.00=0.14x[/tex]
Then, divide both sides by 0.14:
[tex]1000=x[/tex]
Which angles are coterminal with -6pie/5
4π/5 and -16π/5 are Coterminal angles with -6π/5
What is Angle?an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle
Coterminal angles are angles that share the same initial and terminal sides. To find an angle coterminal to another you can do so by simply adding or subtracting any multiple of 360 degrees or 2 pi radians.
The given angle is -6π/5
We need to add 2π for finding coterminal angle
-6π/5+2π
4π/5
We need to subtract 2π for finding coterminal angle
-6π/5-2π
-6π-10π/5
-16π/5
Hence 4π/5 and -16π/5 are Coterminal angles with -6π/5
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It costs $2 to download a song and $12 to download an entire album. Jorge has $50 to spend on downloading music. Create an inequality that represents the number of songs (s ) and albums (a ) that Jorge could download.
I need a inequality
The inequality to represent the given situation is 2s+12a≤50.
Given that, it costs $2 to download a song and $12 to download an entire album.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Jorge has $50 to spend on downloading music.
Let the number of songs be s and the number of albums be a.
So, inequality to represent the given situation is
2s+12a≤50
Therefore, the inequality to represent the given situation is 2s+12a≤50.
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PLEASE HELP ASAP PLEASE!!!!!!!!!
Answer:
(4,-5)
Step-by-step explanation:
A spinner with 10 equally sized slices is shown below. (2 slices are red, 4 are blue, and 4 are yellow.) The dial is spun and stops on a slice at random. What is the probability that the dial stops on a slice that is not red?Write your answer as a fraction or a whole number.
We will have the following:
Since there are 8 slices that are not red, the probability will be given by:
[tex]p=\frac{8}{10}\Rightarrow p=\frac{4}{5}\Rightarrow p=0.8[/tex]So, the probability will be of 4/5, that is 80%.
Can someone answer this for me ill give a big reward
Answer:
carol
Step-by-step explanation:
Beth’s hair can be represented as 1 since everyone else is a fraction of her hair so we just convert the other 2 fractions to make them have the same denominator
4x3/5x3=12/15
2x5/3x5=10/15
10 is less than 12 so carol has the shortest hair
Hopes this helps please mark brainliest
To help visualize, let's say Beth's hair is 15 inches:
Beth = 15"
Abbey = 4/5 * 15" = 12"
Carol = 2/3 * 15" = 10"
Carol has the shortest hair.
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 10.8 seconds
Step-by-step explanation:
[tex]-16t^2 + 170t+40=10\\\\16t^2 -170t-30=0\\\\t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]
There are 6 mice in an attic. Their population is growing at a rate of12% per month.a. Write an exponential growth function to model this situation.
general equation of a population is
[tex]y=a(1+\frac{b}{100})^x[/tex]where a is the initial population and b the percent of growing
then replacing a=6 and b=12
[tex]y=6(1+\frac{12}{100})^x[/tex]and simplify
[tex]\begin{gathered} y=6(1+0.12)^x \\ y=6(1.12)^x \end{gathered}[/tex]What is the equation X+y>3 in the slope interceptform (ie y=mx+b)?
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
How many cups are in 8 quarts? EXPLAIN FOR 5 STARS AND MORE
Answer:
32 us cups
Step-by-step explanation:
yes yes. ik but I just know this. I ahd the same assignment
The selling price of a refrigerator, is $548.90. The markup value was 10%. How much was the refrigerator originally?
Let the original price be p.
Then
p + (10% of p) = 548.90
1.1p = 548.90
p = 548.9 / 1.1 = $499.00
Hence the refrigerator was $499.00 originally
1/16*1/8 in exponential form
The exponential form of 1/6 × 1/ 8 = 1/32 = 3.125 × [tex]10^{-5}[/tex]
The given numbers are 1/6 and 1/8
and exponential form means that we would have to write these numbers in such a way that the number can be expressed in the form 10 raised to the power of an integer.
When we solve 1/6
we will get 1/6 = 0.166
and when we solve 1/8 we will get
1/8 = 0.125
thus when we multiply 1/6 × 1/ 8 = 1/32
which when solved will give us
0.03125
this can be expressed as 3.125 × [tex]10^{-5}[/tex]
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3x + ( 8 )=4x ( 4 )
X=
Answer:
X = 8/13
Step-by-step explanation:
3x + 8 =4x 4
3x + 8 = 16x
3x + 8 - 8 = 16x - 8
3x - 16x - 8
X = 8/13
there 3 cups of ketchup for every 1/2 cup of mustard what is the rate in cups of per ketchup per mustard
There are 3 cups of ketchup for every 1/2 cup of mustard, then the rate in cups of ketchup per cup of mustard is:
3÷1/2 = 3*2 = 6 cups of ketchup per cup of mustard