Can you help me please?A. How can Marc provide proof that his mighty shot actually hung in the air for 15 seconds? Or is this just another one of his lies?B. How long did the ball actually hang in the air?
Answers
The given formula for Marc's shot is:
[tex]h(x)=-16x^2+200x[/tex]a. To prove that the shot actually hung in the air for 15 seconds, we need to replace x=15 in the formula and solve for h, as follows:
[tex]\begin{gathered} h(15)=-16(15)^2+200(15) \\ h(15)=-16\times225+3000 \\ h(15)=-3600+3000 \\ h(15)=-600 \end{gathered}[/tex]As the height is negative, it means after 15 seconds the ball already hit the ground, because the ground is located at h=0. Then this result proves that this is just another one of Marc's lies.
b. To find how long the ball actually hung in the air, we need to find the x-values that makes h=0, as follows:
[tex]0=-16x^2+200x[/tex]We have a polynomial in the form: ax^2+bx+c=0, where a=-16, b=200 and c=0.
We can use the quadratic formula to solve for x:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-200\pm\sqrt[]{(200)^2-4(-16)(0)}}{2(-16)} \\ x=\frac{-200\pm\sqrt[]{40000+0}}{-32} \\ x=\frac{-200\pm\sqrt[]{40000}}{-32} \\ x=\frac{-200\pm200}{-32} \\ x=\frac{-200+200}{-32}=\frac{0}{-32}=0\text{ and }x=\frac{-200-200}{-32}=\frac{-400}{-32}=12.5 \end{gathered}[/tex]Then the two x-values are x=0 and x=12.5.
The starting time is 0 and the end time when the ball hit the ground is x=12.5.
The ball actually hung in the air 12.5 seconds.
Related Questions
Jupiter's orbital speed is approximately 52 kilometers in 4 seconds. At this rate, how many kilometers will Jupiter travel in 5 seconds?
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Jupiter's orbital speed is approximately 52 kilometers in 4 seconds.
In 4 seconds, she travel = 52km
i.e. in 1 minute she travel = 52/4
In one minutes she travel = 13 km
Distance travel in 5 seconds =
5 x 13 km = 65 km
At this rate Jupitar will travel 65 km in 5 seconds
Answer : Jupitar will travel 65 km in 5 seconds
if a pound of almonds cost eight dollars how many ounces can be bought for $3.80
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Proportions
A pound of almonds is said to cost 8 dollars.
But one pound is equivalent to 16 ounces, therefore:
16 ounces cost 8 dollars
Dividing by 8 we get that
2 ounces of almonds cost 1 dollar
Thus, for $3.80 we can buy 2*3.80 = 7.60 ounces of almonds
Graph the equationy = 6
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Since the equation has only the variable y and it is a constant value, that means this equation is represented by a horizontal line (the line contains all values of x and always the value of y is 6).
In order to graph this equation, we can graph two points that are on the line (for example, (0, 6) and (1, 6)) and then draw the line that passes through both of them.
So we have:
$75.00 is shared among 3 people in the ratio 2:4:9 how much is the largest share?
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The ratio is 2:4:9, so we can consider the total parts we are dividing the total as 2+4+9 = 15.
Then, the first person receives 2/15, the second receives 4/15 and the third receives 9/15.
As the total is 75, we can calculate each part as:
[tex]\begin{gathered} p_1=75*\frac{2}{15}=10 \\ \\ p_2=75*\frac{4}{15}=20 \\ \\ p_3=75*\frac{9}{15}=45 \end{gathered}[/tex]Then, the largest share correspond to the third person and is $45.00.
Answer: $45.00
For this assignment, leave all answers as simplified fractions.A bag contains letter tiles that spell the name of the state MISSISSIPPI. Find the theoretical probabilityof drawing one tile at random for each of the following.1. P(M)2. P(S)3. P)4. P(not M)5. P(not S)6. P(not 1)
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ANSWER
[tex]\begin{gathered} 1)\frac{1}{11} \\ 2)\frac{4}{11} \\ 4)\frac{10}{11} \\ 5)\frac{7}{11} \end{gathered}[/tex]EXPLANATION
From the given question;
MISSISSIPPI has 11 words
The number of M is 1
The number of S is 4
Hence;
1.
[tex]P(M)=\frac{1}{11}[/tex]2. P(S);
[tex]P(S)=\frac{4}{11}[/tex]4. P(not M) ;
[tex]\begin{gathered} 1-P(M) \\ =1-\frac{1}{11} \\ =\frac{10}{11} \end{gathered}[/tex]5. P(not S);
[tex]\begin{gathered} P(not\text{ S})=1-P(S) \\ =1-\frac{4}{11} \\ =\frac{7}{11} \end{gathered}[/tex]The slope of the line is 2 and goes through the point (-8,6)
Answers
Given:
Slope m=2
The point,
[tex](x_1,y_1_{})=(-8,-6)[/tex]Using point-slope formula,
[tex]y-y_1=m(x-x_1)[/tex]Therefore, we get the equation,
[tex]y-(-6)=2(x-(-8)_{})[/tex]HURRRYYY Given that AD is congruent to DC , find the length of XC.
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The length of XC is 20
What does congruence of triangle mean?Triangles are said to be congruent if the three angles and three sides of a triangle are equal to the corresponding angles and sides of another triangle.
To be congruent, two triangles must have the same size and shape. The two triangles under consideration must overlap. If you rotate, flip, and/or move the triangle, its position and appearance will look different. In this case, we need to identify the six parts of one triangle and the corresponding parts of the other triangle.
For the triangles ΔAXD and ΔCXD
AD = DC ( congruent sides)
∠XDA = ∠XDC = 90° ( XD is perpendicular to AC)
XD is the common side.
This proves that triangles ΔAXD and ΔCXD are congruent
So it concludes, that XD = XC
2m + 10 = 4m
10 = 4m - 2m
10 = 2m
m = [tex]\frac{10}{2}[/tex]
m = 5
XC = 4m
XC = 4 × 5 = 20
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What percentage of 3436 is 20
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Let x percent of 3436 be 20.
Recall, percentage is expressed in terms of 100. This means that
x/100 * 3436 = 20
34.36x = 20
Dividing both sides of the equation by 34.36, we have
34.36x/34.36 = 20/34.36
x = 0.582%
Thus, 0.582% of 3436 is 20
Please help me help help me please help help me
Answers
When we are given a polynomial of the form:
[tex]ax^n+bx^{n-1}+cx^{n-2}+..+d^{}[/tex]Then the number that is multiplied by no variable or contains no variables is called the constant of the polynomial. In the above example, it would be "d".
Therefore, in the given polynomial we have:
[tex]3x^9+4x+129[/tex]Therefore, the constant of the polynomial is 129.
Determine whether the event below is mutually exclusive. Then find the probability. Round to the nearest tenth of a percent, if necessary. Rolling a pair of dice and doubles or a sum of 6 is rolled.Not mutually exclusive.
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The given event is not mutually exclusive.
Remember that mutually exclusive events are those events that can't be both true, that is, if one event is true, then the other is false.
The probability of this event would be
[tex]P=\frac{6+5-1}{36}=\frac{10}{36}=\frac{5}{18}\approx0.28[/tex]Therefore, the probability is 0.28, or 28%, approximately.MATH HELP WILL MARK BRAINLEST
Answers
The equation of the parabola in the vertex form with vertex (6,-6) and passing through (8,6) is y = 3(x - 6)² - 6 , the correct option is (b) .
In the question ,
it is given that ,
the parabola passes through the point (8,6) .
the vertex of the parabola = (6,-6) .
We know that the equation of parabola in the vertex form with vertex (h,k) is
(y - k) = C.(x - h)²
we substitute the vertex and the point passing ,
we get ,
6 - (-6) = C.(8 - 6)²
6 + 6 = C(2)²
12 = 4C
C = 12/4
C = 3
So , the equation is (y - (-6)) = 3.(x - 6)²
y + 6 = 3(x - 6)²
y = 3(x - 6)² - 6
Therefore , The equation of the parabola in the vertex form with vertex (6,-6) and passing through (8,6) is y = 3(x - 6)² - 6 , the correct option is (b) .
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Please help!
1.) You are the crew chief of the Algebra 2 formula racing team. Your current task is to
determine fuel consumption of both cars. Car A travel x² + 3x miles and Car B travels 2x + 8 miles. Based upon tire wear (x), the cars will use x² + 4x gallons of fuel.
a.) What is the mileage
(miles/gallons) for each car?
Car A:
Car B:
b.) What is the total mileage for both cars in simplified form? (3 points)
Total:
2.)Solve for x: (5 points)
3r+3=−x+6
Answers
The mileage of Car A, Car B, and the average of is (x+3)/(x+4), 2/x and [tex]\frac{x^{2} +5x +8 }{x^{2} +4x}[/tex]
It is given that the distance traveled by the car A = x² + 3x
And the distance traveled by car B = 2x + 8
The mileage is given by mile/gallon.
So, the mileage of Car A = distance traveled by car A/gallons of fuel used.
Then,
Mileage of Car A = [tex]\frac{x^{2} +3x }{x^{2} +4x} =\frac{x(x +3)}{x(x+4)} = \frac{x+3}{x+4}[/tex] miles /gallons
Similarly, the mileage of Car B = distance traveled by car B/gallons of fuel used.
Then,
Mileage of Car B = [tex]\frac{2x+8}{x^{2} +4x} = \frac{2(x+4)}{x(x+4)} =\frac{2}{x}[/tex] miles/gallons
Now, the total mileage of A and B is the average of car A and car B,
Mileage of Car A + Mileage of Car B = [tex]\frac{x^{2} +3x }{x^{2} +4x} + \frac{2x+8}{x^{2} +4x} = \frac{x^{2} +5x +8 }{x^{2} +4x}[/tex]
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&Maps CClever | Portal e Learner Home e Learning Path - Eng... Mail- Makayla D. Submit Test R Pretest: The Real Number System rag the tiles to the boxes to form correct pairS. atch the pairs of equivalent expressions. (-1440)-1+ 46+ (54-26)+(28+) 8-15 -3-(8+6) -11 -10+8)+(76-5) -15 Dor Moxt
Answers
hello
to solve this question, we need to write out the expressio
The main printer in the Ivy Tech library can produce an average of 639copies every hour. For every 36 pages, it costs the college $0.06 forelectricity and supplies. If the library is open from 9AM to 9PM, howmuch money does the college use on printing each day?
Answers
You know that:
- An average of 639 copies per hour can be produced by the main printer.
- The cost for electricity and supplies is $0.06 for every 36 pages produced.
- The library is opened for 12 hours.
Let be "x"the cost (in dollars) for electricity and supplies for 639 copies produced in 1 hour.
You can set up the following proportion:
[tex]\frac{0.06}{36}=\frac{x}{639}[/tex]Solve for "x":
[tex]\begin{gathered} (\frac{0.06}{36})(639)=x \\ \\ x=1.065 \end{gathered}[/tex]Knowing that the cost for electricity and supplies for 639 copies produced in 1 hour is $1.065, youo can multiply it by 12, in order to calculate how much money the college uses on printing each day:
[tex](1.065dollars\text{)}(12)=12.78dollars[/tex]The answer is: The college uses $12.78 on printing each day.
The segments shown below could form a triangle.
9
A
C
C
B
4
B
A
15
True or false
Answers
No/False - there is a rule that state that the sum of two sides of a triangle must be greater than the 3rd side.
In light of the question -In geometry, a triangle is a closed two-dimensional figure with three sides, three corners, and three vertices.Triangles are considered polygons with the fewest sides. In this article, we will discuss in detail what a triangle is, its types, properties and formulas.Learn more about triangles here. In geometry, a triangle is a type of polygon with three sides and three vertices. A triangle is considered a three-sided polygon.The sum of the three angles of a triangle is 180°. A triangle is contained in a single plane. There are six types of triangles based on their side and angle measurements.A triangle has only three sides joined by corners. Therefore, no matter what kind of triangle it is, it always has three sides.CalculationNo - there is a rule that state that the sum of two sides of a triangle must be greater than the 3rd side.
While 9+15 >4
and 4+15 >9
9+4 is not greater than 15 - so this triangle cannot be made.
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E Which point is located at (4, -2)? 3 G 다
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The given coordinate tells us that when x = 4, y = - 2
Looking at the graph, the point where x = 4 and y = - 2 is point D
A small restaurant was purchased for 316000 with no down payment and a 6.6% loan for 10 year. Find the monthly payment
Answers
We will have the following:
First, we calculate the total payment per year:
[tex]p_y=316000\cdot0.066\Rightarrow p_y=20856[/tex]Now, we calculate the monthly payment:
[tex]316000=\frac{p}{0.0055}(1-\frac{1}{(1+0.066)^{120}})\Rightarrow1738=p(0.9995331951\ldots)[/tex][tex]\Rightarrow p=\frac{1738}{(1-\frac{1}{(1+0.066)^{120}})}\Rightarrow p=1738.811686[/tex]So, the monthly payment will be approximately $1738.811686.
the function g(x) was obtained by transforming f(x)=1/x Use the description of the transformation to write the equation representing g(x).f(x) Is vertically stretched by a factor of 2, reflected about the X axis, then shifted 5 units.
Answers
Since f(x) is vertically strectched by a factor 2, we get
[tex]f(x)\longrightarrow\frac{2}{x}[/tex]next, it is reflectec about the x-axis, then we have
[tex]\frac{2}{x}\longrightarrow-\frac{2}{x}[/tex]Finally, its shifted 5 units on x axis, then we have
[tex]-\frac{2}{x}\text{ --> }-\frac{2}{x+5}[/tex]which corresponds to option 2
PLEASE HELP! I WILL GIVE BRAINLIEST The sales tax rate is 50%. How much will it cost to buy a $7.59 panther figureine? (Panther $7.59 plus tax) $11.95$0.57$12.52$11.39
Answers
The sale tax of the product will be:
0.5(7.59)=3.795
then the final price for the panther figurine (with taxes) will be:
7.59+3.795=$11.39
The vertices of ACDE are C(-1, 1), D(3,5), and E(5. - 4). Translate ACDE using vectorr(3. – 1).Enter the correct ordered pair for C', D', and E'. Do NOT use any spaces in your answer.C'D'E
Answers
C (-1,1)
D (3,5)
E (5,-4)
now we are going to translate ACDE using vector r(3,-1)
C'(2,0)
D'(6,4)
E'(8,-5)
In the quadrilateral below. “Angle WXZ is congruent to Angle YZX." If Ricardo's conjecture is true, which of the following must be true for Quadrilateral WXYZ to be a parallelogram?
Answers
Answer:
∠YXZ ≅ ∠WZX
Explanation:
Given that “Angle WXZ is congruent to Angle YZX."
The angles are shown in the diagram below.
This means that angles WXZ and YZX are alternate angles and thus,
• WX is parallel to ZY.
Consider the diagram below:
Angles YXZ and WZX are congruent by alternate angles, and thus:
• WZ is parallel to XY.
So, we have shown that the opposite sides of the quadrilateral are parallel.
Therefore, in order for quadrilateral WXYZ to be a parallelogram, Angles YXZ and WZX must be congruent.
The first option (∠YXZ ≅ ∠WZX ) is correct.
A changes and8. The graph of y = cos z is transformed to y = a cos (2-c) + d by a vertical expansion by a factor of 2, then translated units right and 2 units up.The new equation is:y=2 cos (x + 5) - 2y= 2 cos (x - 1) +2y= {cos (x - 1) + 2y=2 cos ( - ) - 2
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Option 2 is correct.
I think I have the right answer but I would still like to be 100% sure that I understand i also have to show my work
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To solve this inequality, we can proceed as follows:
First: multiply both sides of the inequality by 9:
[tex]9\cdot\frac{x}{9}\leq9\cdot1\Rightarrow x\leq9[/tex]Then, the answer is x <= 9. In interval notation, we have that the answer is:
(-infinity, 9 ]. Or graphically:
If the radius of circle M is 7, and LK = 18, find JK
Answers
Answer:
JK = 24
Explanation:
If the radius of circle M is 7, we can say that MJ = 7 and ML = 7
So, the length of MK will be equal to:
MK = ML + LK
MK = 7 + 18
MK = 25
Now, we have a right triangle JMK, and we know the length of one leg MJ = 7 and the length of the hypotenuse MK = 25. Using the Pythagorean theorem, we can find the length of the other side JK, so
[tex]\begin{gathered} JK=\sqrt[]{MK^2-MJ^2^{}} \\ JK=\sqrt[]{25^2-7^2} \\ JK=\sqrt[]{625-49} \\ JK=\sqrt[]{576} \\ JK=24 \end{gathered}[/tex]Therefore, the value of JK is 24.
a. If Links printing store will make a 150 copies for the cost of $15.00, then what is theunit rate of price per copy?
Answers
ANSWER
$0.10
EXPLANATION
We have that 150 copies are made for a total cost of $15.00
The unit rate of price per copy is the price of each copy of the printing.
To find the unit rate of price per copy, we have to divide the total price by the total number of copies.
So, we have:
[tex]\frac{15}{150}\text{ = \$0.10}[/tex]This means that the unit rate of price per copy is $0.10
Miguel Rodriguez borrowed $500 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.2% a.) how much will the interest amount to ?b.) what amount must Miguel pay Julio at the end of 6 months ?
Answers
Given:
Miguel Rodriguez borrowed $500 from his brother Julio to pay for books and tuition.
He agreed to pay Julio in 6 months with simple annual interest at 6.2%
So, the interest = r = 6.2% = 0.062
the time = t = 6 months = 6/12 years = 1/2 year
a.) how much will the interest amount to?
The interest is given by the formula:
[tex]I=P\cdot r\cdot t[/tex]Substitute with the given values:
[tex]I=500\cdot0.062\cdot\frac{1}{2}=15.5[/tex]So, the interest = I = $15.5
b.) what amount must Miguel pay Julio at the end of 6 months?
So, Miguel will pay the amount that he borrowed and the interest
so, he will pay:
[tex]P+I=500+15.5=515.5[/tex]So, the answer will be: $515.5
use distributive property to fill in the blanks (4×7) - (4×3) = ___ × (7-3)
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okay I think your name was Mrs Huggins can you please help me with the rest of this fraction I'm really struggling and I accidentally signed off because of a network error I'm really sad please
Answers
In a previous session we worked on the subtraction of the mixed numbers 2 1/8 and 1 7/8 and reached the following result:
[tex]2\frac{1}{8}-1\frac{7}{8}=\frac{17}{8}-\frac{15}{8}=\frac{2}{8}[/tex]This fraction 2/8 can be simplified. Both values 2 and 8 are divisible by 2, so to simplify the fraction you have to divide the numerator and denominator of the fraction by 2:
[tex]\frac{2\div2}{8\div2}=\frac{1}{4}[/tex]Two farmers John and Harry cultivates twovarieties of rice namely Basmati and Naura.The sale price of these varieties of rice by boththe farmers are as follows:John sells Basmati at $5.00/kg and Naura at$3.50/kg. While Harry sells Basmati at$6.50/kg and Naura at $2.60/kg.Use the matrix to present the prices of rice bytwo farmers.
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Sales price for the rice varieties:
John:
Basmati cost = $5 per kg
Naura cost = $3.5 per kg
Harry:
Basmati cost = $6.5 per kg
Naura cost = $2.6 per kg
Writing in the form matrix:
[tex]\begin{gathered} let\text{ first column represent basmati rice} \\ let\text{ the 2nd column represent Naura rice} \\ In\text{ matrix, x and y can be represented as:} \\ \begin{bmatrix}{x\text{ column}} & {y\text{ column}} \\ {}{{x\text{ column}}} & {{y\text{ column}}}\end{bmatrix} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = Basmati, y = Naura} \\ \\ \begin{bmatrix}{5.00} & {3.50} \\ {6.50} & {2.60}\end{bmatrix}\text{ \lparen option B\rparen} \end{gathered}[/tex]what happens to F(x) when x is negative but approaches zero for the function F(x)=1/x whose graph is show below?*PHOTO*
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We have the following function:
[tex]F(x)=\frac{1}{x}[/tex]According to the graph, the function tends to minus infinity when x takes negative values close to zero.
Answer: B. F(x) is a negative number