[tex]S=4+64t-16t^2\implies \stackrel{\textit{at a height of 32}}{32=4+64t-16t^2}\implies 16t^2-64t-4+32=0 \\\\\\ 16t^2-64t+28=0\implies 4(4t^2-16t+7)=0\implies 4t^2-16t+7=0 \\\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{4}t^2\stackrel{\stackrel{b}{\downarrow }}{-16}t\stackrel{\stackrel{c}{\downarrow }}{+7}=0 \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]
[tex]t= \cfrac{ - (-16) \pm \sqrt { (-16)^2 -4(4)(7)}}{2(4)} \implies t = \cfrac{ 16 \pm \sqrt { 256 -112}}{ 8 } \\\\\\ t= \cfrac{ 16 \pm \sqrt { 144 }}{ 8 }\implies t=\cfrac{16\pm 12}{8}\implies t= \begin{cases} \frac{1}{2}&\textit{on the way up}\\\\ \frac{7}{2}&\textit{on the way down} \end{cases}[/tex]
Write and solve an equation for this problem. First represent the number of each item and the total cost for each item.
Kawan buys some protein bars at $0.80 each and bottled water at $0.90 each for a group hike. He buys twice as many bottles of water as protein bars. If he spends $52 in total, how many bottles of water and protein bars does he buy?
Let x = the number of protein bars
When he spends $52 in total, the number of bottles of water and protein bars that he buys will be 40 and 20 respectively.
How to calculate the equation?It should be noted that an equation is used to show the relationship between the variables.
In this case, Kawan buys some protein bars at $0.80 each and bottled water at $0.90 each for a group hike and he buys twice as many bottles of water as protein bars.
Let x = the number of protein bars
Table waters = 2x
Therefore, the equation will be:
0.8x + 0.9(2x) = 52
0.8x + 1.8x = 52
2.6x = 52
Divide
x = 52/2.6
x = 20
The number of proteins bars is 20.
The number of water will be:
= 2x.
= 2 × 20 = 40
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
Manuel's younger brother Ricky loves hot
wheels. Ricky has 28 boxes of toy cars. Each
box holds 16 cars. Ricky gives his brother
Manuel 15 cars. How many cars does Ricky
have now?
Answer:
29
Step-by-step explanation:
Add 28 + 16=44
Subtract 44 - 15=29
You and a group of friends participate in a game where you must use clues to escape from a room. You have a limited amount of time to escape and are allowed 3 free clues. Additional clues may be requested, but each removes 5 minutes from your remaining time. Whatinteger represents the total change in the time when you use 5 clues?
Integer represents the total change in the time when you use 5 clues with the condition of using 3 free clues is equal to 10 minutes.
As given in the question,
Number of free clues =3
Total number of clues used to escape from a room = 5clues
Out of these 5 clues, 3 clues are free to use. Hence these 3 clues do not result in any time change.
Hence total time elapsed after usage of 3 clues = 0
Each removes 5 minutes from your remaining time
Integer represents the total change in the time for the usage of 4th and 5th clue = 10 minutes
So overall change in timeline after consuming 5 clues = 10 minutes since each of the 4th and 5th clue results in decrease of 5 minutes each; thus effecting 10 minutes total time change (reduction)
Therefore, integer represents the total change in the time when you use 5 clues with the condition of using 3 free clues is equal to 10 minutes.
Learn more about integer here
brainly.com/question/15276410
#SPJ1
Which of the following is equivalent to sin 37°?Group of answer choicescos 37°cos 53°sin 53°sin 63°
Recall that:
[tex]sin\theta=cos(90^{\circ}-\theta).[/tex]Therefore:
[tex]sin37^{\circ}=cos(90^{\circ}-37^{\circ}).[/tex]Simplifying the above result, we get:
[tex]sin37^{\circ}=cos53^{\circ}.[/tex]Answer: [tex]\begin{equation*} cos53^{\circ}. \end{equation*}[/tex]Find the axis of symmetry using the formula. X = -b/2a
x = 2
Explanation:f(x) = -2x² + 8x - 9
Comparing this function with f(x) = ax² + bx + c
a = -2, b = 8, c = -9
The axis of symmetry is given by the formula:
x = -b/2a
Substitute a = -2 and b = 8 into the formula:
[tex]\begin{gathered} x=\frac{-8}{2(-2)} \\ \\ x=\frac{-8}{-4} \\ \\ x=2 \end{gathered}[/tex]x = 2
question is in box and you don’t need to show work if you don’t want to
ANSWER:
8 square meters
STEP-BY-STEP EXPLANATION:
To calculate the area of the sector, we must first calculate the area of the entire circle and then by means of a proportion, knowing that the entire area is 360° and the sector is 45°, we could determine the area we need.
Just like this:
[tex]\begin{gathered} A_c=\pi\cdot r^2 \\ \\ \text{ We replacing:} \\ \\ A_c=\pi\cdot8^2=64\pi \\ \\ \text{ Therefore, we calculate the value of the area of the sector as follows:} \\ \\ A_s=64\pi\cdot\frac{45\degree}{360\degree} \\ \\ A_s=8\pi\text{ square meter} \end{gathered}[/tex]The area of the sector is 8 square meters
A certain insecticide kills 70% of all insects in laboratory experiments. A sample of 10 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 6 insects will die? Round your answer to four decimal places.
The required probability that exactly 6 insects will die is 60%.
Given that,
A certain insecticide kills 70% of all insects in laboratory experiments. A sample of 10 insects is exposed to the insecticide in a particular experiment. The probability that exactly 6 insects will die is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
here,
Total number of sample spaces = 10
Total number of favorable outcomes = 6
probability can be given as,
= 6 / 10
= 0.6 or 60%
Thus, the required probability that exactly 6 insects will die is 60%.
Learn more about probability here:
brainly.com/question/14290572
#SPJ1
What is the answer
Three friends ate at a restaurant. They ordered nachos for $18.85 and jalapeno poppers. Each friend paid $9.98, not including sales tax or tip, which was one third of the total. Determine the cost of the jalapeno poppers.
The cost of the jalapeno poppers is $11.09 .
In the question ,
it is given that
Cost of the nachos = $18.85
amount paid by each friend = $9.98
amount paid by three friends = 9.98*3 = $29.94
let the cost of jalapeno poppers = $x
So according to the question
the total amount paid by three friends = cost of nachos + cost of jalapeno poppers
Substituting the values from above , in the equation we get
29.94 = 18.85 + x
simplifying further , we get
x = 29.94 - 18.85
x = 11.09
Therefore , the cost of the jalapeno poppers is $11.09 .
Learn more about Equations here
https://brainly.com/question/28678883
#SPJ1
please help me graph
Answer:
A
Step-by-step explanation:
See that the slope of the parabola changes at x=4
And left of x=4, the slope is positive, meaning the value is increasing (you can also see it directly from the graph)
Right of x=4, the slope is negative, meaning the value of the graph is decreasing. Thus the answer is A
Consider the equation 3x3 + 14x2 – 14x + 60 = 0. The real solution is –6. What are the nonreal solutions?
Negative 2 i StartRoot 26 EndRoot, 2 i StartRoot 26 EndRoot.
4 minus 2 i StartRoot 26 EndRoot, 4 + 2 i StartRoot 26 EndRoot.
StartFraction negative 2 + i StartRoot 26 EndRoot Over 3 EndFraction, StartFraction negative 2 minus i StartRoot 26 EndRoot Over 3 EndFraction.
StartFraction 2 + i StartRoot 26 EndRoot Over 3 EndFraction, StartFraction 2 minus i StartRoot 26 EndRoot Over 3 EndFraction.
Using the polynomial expression, the non-real solutions are x = (2 + i√26)/3 and x = (2 - i√26)/3
What are polynomial expressions?Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the non-real solutions?The equation of the polynomial expression is given as:
3x^3 + 14x^2 - 14x + 60 = 0
From the question, we have
Real solution = -6
Rewrite the above equation as
x = -6
Add 6 to both sides of the equation
So, we have
x + 6 = 0
The next step is to divide the polynomial equation 3x^3 + 14x^2 - 14x + 60 = 0 by x + 6 = 0
This is represented as
3x^3 + 14x^2 - 14x + 60/x + 6
Using a graphing calculator, we have
3x^3 + 14x^2 - 14x + 60/x + 6 = 3x^2 - 4x + 10
Next, we determine the solution of the quadratic expression 3x^2 - 4x + 10 using a quadratic formula
So, we have
x = (-b ± √(b² - 4ac))/2a
This gives
x = (4 ± √((-4)² - 4 * 3 * 10))/2 * 3
So, we have
x = (4 ± √-104)/6
This gives
x = (4 ± 2√-26)/6
Divide
x = (2 ± √-26)/3
Rewrite as
x = (2 ± i√26)/3
Split
x = (2 + i√26)/3 and x = (2 - i√26)/3
Hence, the non-real solutions of the polynomial expression are x = (2 + i√26)/3 and x = (2 - i√26)/3
Read more about polynomial expression at
https://brainly.com/question/17517586
#SPJ1
The net of a rectangular prism with a square base is shown. Use the net to find the surface area of the prism. PLEASE HELP!!!
Answer:
B
Step-by-step explanation:
the surface area is the sum of all individual side areas.
a prism (like a cube that is a special prism) has 6 sides.
top-bottom
left-right
front-back
in our case top and bottom are 5×5 squares.
and the other 4 sides are equal 5×20 rectangles.
so, we get
top-bottom : 2× 5×5 = 50 cm²
left-right : 2× 20×5 = 200 cm²
front-back : 2× 20×5 = 200 cm²
in total we have
200 + 200 + 50 = 450 cm²
I need help with this question.
Given:
There is a graph given in the question
Required:
We want to find the solution of the given graph
Explanation:
As we can see that, both lines are parallel so there is no chance for intersection
now if there is no intersection point means there is no solution
Final answer:
No solution
a segment drawn from the center of the circle to which letter creates a terminal side that forms a central angle of 2pi/3 radians?
2pi/3 radians=120 degrees
F is 90 degree.
j is 180 degree
midpoint of F and J is 150 degree.
H is 150 degree
Hence,
G is 120 degree
The function g is defined by the following rule.
g(x) = (1/2)x
Find g(x) for each x-value in the table.
-1
0
1
2
3
Answer:
g(-1)=2, g(0)=1, g(1)=1/2, g(2)=1/4, g(3)=1/8
Step-by-step explanation:
Rational Numbers - Part 1
Which statements about the opposite of -12 are true?
Select each correct answer.
The opposite of the opposite of -12 is -12.
0-12 and its opposite are on located on the same side of zero on a number line.
The opposite of -12 is -1/2
0-12 and its opposite are located the same distance from zero on a number line
The correct statement for the rational number is the opposite of the opposite of -12 is -12.
What is rational number?
Rational numbers are those numbers which include natural numbers, whole numbers as well as integers. And it is written in the form of a/b where a and b are integers. Sometimes, the values of the denominator is one then the given number is not fraction.
According to the question, rational number are those numbers which takes positive integers, negative integers as well as zero.
Therefore, on a number line, the opposite of (-12) is 12. And again the opposite of 12 is (-12). Therefore the first statement is correct.
Hence, the correct statement for the rational number is the opposite of the opposite of -12 is -12.
To learn more about the rational number from the given link:
https://brainly.com/question/22221295
#SPJ9
Given the equation below, find the x and y−intercepts by completing the table.What is the problem with using these intercepts to graph the equation in #7?The ordered pair (x, y) you found in #7 is called the
In order to find the x-intercept we need to make y=0
[tex]-4x+2(0)=0[/tex]Then we isolate the x
[tex]-4x=0[/tex][tex]x=0[/tex]x y Ordered Pair type of intercept
0 0 (0,0) x-intercept
Now for the y-intercept we need to make x=0
[tex]-4(0)+2y=0[/tex]we isolate the y
[tex]2y=0[/tex][tex]y=0[/tex]0 0 (0,0) y-intercept
ANSWER
0 0 (0,0) x-intercept
7. AXYZ with X(-2, 2), Y(4,2), and Z(1, -5); rotate 180° clockwise. 73 a. What are the vertices of the image after the transformation? 76 b. Graph the original triangle and its image. у
The given coordinate of the vertices of triangle XYZ is X(-2,2), Y(4,2) and Z(1,-5).
a). When rotates 180 degrees clockwise the new coordinate of the triangle can be determined as,
[tex]\begin{gathered} X^{\prime}(2,-2) \\ Y^{\prime}(-4,-2) \\ Z^{\prime}(-1,5) \end{gathered}[/tex]b). The original and the new coordinates of the triangle can be drawn as,
The original and the new triangles can be drawn as,
1) A gallon jug of milk is 3/4 full. After breakfast the jug is 1/12 full. How much milk did your family have at breakfast?
well, your family really ate "x" for breakfast, was pretty good with cereal and strawberries btw.
let's keep in mind that the LCD of the denominators 4 and 12 is "12", so we'll use that to do away with the denominators.
[tex]\stackrel{\textit{before breakfast}}{\cfrac{3}{4}}~~ - ~~\stackrel{for~breakfast}{x}~~ = ~~\stackrel{leftover}{\cfrac{1}{12}} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{3}{4}-x \right)~~ = ~~12\left( \cfrac{1}{12} \right)}\implies 9-12x=1 \\\\\\ 9=12x+1\implies 8=12x\implies \cfrac{8}{12}=x\implies {\Large \begin{array}{llll} \cfrac{2}{3}=x \end{array}}[/tex]
How can you transform the equation 8x - 10 + 10 + 4x = -10 + 6x + 6x + 10 into the form of a = a, where a is a number, to show that the equation has an infinite number of solutions? Select all that apply.
A. by adding 12x to both sides of the equation and then simplifying
B. by subtracting 8x to both sides of the equation and then simplifying
C. by subtracting 12x from both sides of the equation then simplifying
D. by subtracting 20 from both sides of the equation then simplifying
E. by dividing 6x from both sides of the equation and then simplifying
Step-by-step explanation:
Simplifying
8x + -10 + 10 + 4x = -10 + 6x + 6x + 10
Reorder the terms:
-10 + 10 + 8x + 4x = -10 + 6x + 6x + 10
Combine like terms: -10 + 10 = 0
0 + 8x + 4x = -10 + 6x + 6x + 10
8x + 4x = -10 + 6x + 6x + 10
Combine like terms: 8x + 4x = 12x
12x = -10 + 6x + 6x + 10
Reorder the terms:
12x = -10 + 10 + 6x + 6x
Combine like terms: -10 + 10 = 0
12x = 0 + 6x + 6x
12x = 6x + 6x
Combine like terms: 6x + 6x = 12x
12x = 12x
Add '-12x' to each side of the equation.
12x + -12x = 12x + -12x
Combine like terms: 12x + -12x = 0
0 = 12x + -12x
Combine like terms: 12x + -12x = 0
0 = 0
Solving
0 = 0
Couldn't find a variable to solve for.
This equation is an identity, all real numbers are solutions.
Simplifying
8x + -10 + 10 + 4x = -10 + 6x + 6x + 10
Reorder the terms:
-10 + 10 + 8x + 4x = -10 + 6x + 6x + 10
Combine like terms: -10 + 10 = 0
0 + 8x + 4x = -10 + 6x + 6x + 10
8x + 4x = -10 + 6x + 6x + 10
Combine like terms: 8x + 4x = 12x
12x = -10 + 6x + 6x + 10
Reorder the terms:
12x = -10 + 10 + 6x + 6x
Combine like terms: -10 + 10 = 0
12x = 0 + 6x + 6x
12x = 6x + 6x
Combine like terms: 6x + 6x = 12x
12x = 12x
Add '-12x' to each side of the equation.
12x + -12x = 12x + -12x
Combine like terms: 12x + -12x = 0
0 = 12x + -12x
Combine like terms: 12x + -12x = 0
0 = 0
Solving
0 = 0
Couldn't find a variable to solve for.
This equation is an identity, all real numbers are solutions.
Determine if the relation is a function. { ( − 2 , 4 ) , ( − 1 , 7 ) , ( 0 , − 6 ) , ( 5 , 3 ) , ( 7 , 5 ) } {(−2,4),(−1,7),(0,−6),(5,3),(7,5)} Determine if the relation is a function. { ( − 2 , 4 ) , ( − 1 , 7 ) , ( 0 , − 6 ) , ( 5 , 3 ) , ( 7 , 5 ) } {(−2,4),(−1,7),(0,−6),(5,3),(7,5)} The relation is not a function. The relation is a function
Based on the given ordered pairs, yes, the relation is a function.
What is a function?A function simply refers to a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for uniquely mapping an input variable to an output variable.
Based on the ordered pairs shown above, we can reasonably infer and logically deduce that these ordered pairs represent a function because the elements of the set of "x" are uniquely mapped to the elements of the set of "y" as shown below:
x y__
-2 ↔ 4
-1 ↔ 7
0 ↔ -6
5 ↔ 3
7 ↔ 5
Read more on function here: brainly.com/question/3632175
#SPJ1
<
A local restaurant ordered 81 cans of tomato paste. Each can contains 18 ounces of paste. Write an
equation using compatible numbers to estimate the total number of ounces of paste ordered.
OA. 81 x 18 = 1,458
OB. 80 x 20 = 1,600
OC. 85 x 20 = 1,700
OD. 100 x 20 = 2,000
Answer:
It would be A because they ordered 81 cans and in each can there 18 ounces so if you multiply it you can get the Total amount.
When Bob runs at 4 miles an hour, it takes him 20 minutes to run the path around the
park. If he ran instead at 5 miles an hour, how long would it take him to run that path
around the park?
Time taken to cover path around the park if he runs at speed 5miles/hour is 15.96min
What is Speed ?
Speed indicates how quickly something or someone is moving. If you know how far something has traveled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance x time.
Given that,
Time taken when Bob runs 4miles/hour = 20min
Time taken when Bob runs 5miles/hour = ?
First we have to find the distance of the path around the circle
Distance = speed x time
= 4 x 20/60
= 4/3 miles
= 1.33 miles
Now to calculate the time when he ran 5 miles/hours:
Time = distance / speed
= 1.33 / 5
= 0.266hours
0r
= 0.266 x 60 min
= 15.96 min
Hence, its will take 15.96min to cover the path around the park
To learn more about Speed click on the link
https://brainly.com/question/13943409
#SPJ9
Pat and Terry believe the color yellow attracts hummingbirds. They decided to test their hypothesis by doing an experiment in which they set up four hummingbird feeders with the same amount of food and placed them in locations only hummingbirds could reach. One feeder was yellow, one was red, one was blue, and one was clear. Each day for one week, Pat and Terry measured and recorded the amount of food left in each of the feeders. At the end of the experiment the red feeder had the least amount of food left in it. What conclusion should Pat and Terry reach?
Step-by-step explanation:
red feeder is smarter
Help
Albie is comparing the ratio of students in her class that are wearing the color green to the total number of students in her class. She finds out of 30 students in her class, 7 are wearing green. What kind of ratio relationship is she using?:
A: Part-to-part relationship
B: Whole relationship
C: Part-to-whole relationship
D: Part relationship
Answer:
C
Step-by-step explanation:
Beacuse part to whole means describing a specific part of a group to the whole group, in our case students wearing green : students
PLS HELP MEEEEEEEEEEEEEEEEEEEEE PLS I BEG U
how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
A graph of a proportional relationship can be used to find any ratio in the proportional relationship when the graph passes through the origin.
How to illustrate the information?A connection is proportional if its graph is a line that goes through the origin. The ratio is not proportionate if it is not a line or ray that doesn't accomplish this. K = y/x is the equation for the proportionality constant. The equation for the slope of a straight line with respect to the origin is the same as this.
A relationship is proportionate if its graph is a line or ray that passes through the origin. It is not proportionate if the line or ray does not go through the origin. Additionally, something is not proportionate if it is not linear.
Learn more about graph on:
https://brainly.com/question/19040584
#SPJ1
Which of these equations describe a line that is parallel to the y-axis, and passes through (-2.3) A. y=-2x+3 B. Y=3 C. X= -2 D. x=3
The y-axis it's a vertical line, so is represented by x=0.
Then, a parallel line to this one has to be vertical too, and if it passes thorugh (-2, 3). The equation of the parallel line would be x=-2.
Let me explain with a graph:
PLEASE ANSWER QUICKLY WILL GIVE BRAINLIEST IF RIGHT
Answer:
Domain:
{−4,1,6,7}
Range:
{5,3,8,−4}
Step-by-step explanation:
Use the given information to answer the question. The distance s that an object falls varies directly with the square of the time, t , of the fall. If an object falls 16 feet in one second, how long will it take for it to fall 48 feet? Round your answer to two decimal places.
The time that it will take for it to fall 48 feet will be ✓3 seconds.
How to illustrate the information?From the information, the distance s that an object falls varies directly with the square of the time, t , of the fall and an object falls 16 feet in one second.
This will be:
s = kt²
s = distance
k = constant
t = time
s = kt²
16 = 1²k
k = 16
Therefore, the time that it will take for it to fall 48 feet will be:
s = kt²
48 = 16t²
t² = 48 / 16
t² = 3
t = ✓3
Learn more about time on:
brainly.com/question/26046491
#SPJ1
pls help me solve this with steps
The solution of the given inequality for the value of x, x ≥ 1/2.
Define inequality.In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than. Both mathematical phrases, equations, and inequalities are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols >,<,≥,≤,≠ or indicate that the two expressions in inequality are not always equal.
Given Data
Equation
[tex]\frac{4x -7}{2}[/tex] ≥ 4.5
4x - 7 ≥ 9
4x≥2
x ≥ [tex]\frac{1}{2}[/tex]
For the value of x, x ≥ [tex]\frac{1}{2}[/tex]
To learn more about inequality, visit:
https://brainly.com/question/15064057
#SPJ13
3. It takes a Ferris wheel 1.5 minutes to complete one full rotation. If a ride lasts for 6 minutes, how many full rotations does the Ferris wheel make? O O T= 9 rotations T= = 4 rotations O Or = 7.5 rotations T = 4.5 rotations
Answer:
Four.
Step-by-step explanation:
6 divided by 1.5 is 4. We do that because if it takes 1.5 mins to make a full rotation and it takes 6 minutes to do blank rotations, the answer is 4 bc we either ti.es 1.5 by 4 to get 6, or do 6 divided by 1.5 to get 4. Sorry if that was confusing.