Answers
(i) The vertex's x-coordinate is 25.
(ii) The maximum height of the cannonball is 12.48 meters.
(iii) Total horizontal distance that a cannon ball can travel is 50 meters.
(iv) Total horizontal distance that a cannon ball can travel with decreased angle is 22.5 meters.
(v) Distance the cannonball traveled before reaching the maximum height is 25 meters.
What is coordinate?
A pair of values is used to specify a point's placement on a coordinate plane using both horizontal and vertical distinctions from the two separate axes. usually represented by a pair of x-values and y-values (x,y).
(i) They are both at y = 4 and separated by (40-10) = 30
The symmetry line is halfway between 40 and 10
Consequently, the vertex's x-coordinate is 25.
(ii) y = -0.01x2 + 0.5x,
a = -0.01,
b = 0.5,
-b/2(a) = -0.5/(2X-0.01) = 0.5/0.02, and so on.
y=-0.01*2+0.5(25) =12.48 meters
The maximum height of the cannonball is 12.48 meters.
(iii) Total horizontal distance that cannon ball can travel is (0,0)-(50,0)= 50 meters.
(iv)Total horizontal distance that cannon ball can travel with decreased angle is (0,0)-(22.5,0) =22.5 metres
(v) Distance cannon ball travelled before reaching the maximum height is [(0,0)-(50,0)]/2 =25 meters
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Related Questions
Flan- servers 10 people; $10.85 per person 1/8 teaspoon salt.1(12 fluid once) 1 teaspoon vanilla1/4 cup brown sugar
Answers
Filling with the information given, we have:
Multiply the original recipe by 10 (Since we have to serve 10 people)
New recipe:
Salt: 1/8 x 10 = 10/8 = 5/4 (Multiplying fractions and simplifying)
5/4 = 1 1/4 ( Converting the fraction to a mixed number)
Evaporated milk : 1 x 10 = 10 cans.
Vanilla: 1 x 10 = 10 teaspoons.
Brown sugar: 1/4 x 10 = 10/ 4 = 5/2 (Multiplying fractions and simplifying)
5/2 = 2 1/2 (Converting the fraction to a mixed number)
The values of the new recipe are:
Salt: 1 1/4
Evaporated milk: 10 cans
Vanilla: 2 1/2 teaspoons
Brown sugar: 2 1/2 cups
i need help with this question
Answers
Answer:
58.29 cm^2
Step-by-step explanation:
The area of a trapezium is calculated with the following formula:
[tex] \frac{a + b}{2} \times h[/tex]
(a: base, b: base, h: height)
[tex] \frac{ 7 + (10.4)}{2} \times (6.7) \\ \\ \frac{17.4}{2} \times (6.7)[/tex]
get rid of fraction by dividing (17.4) with 2
(17.4)÷2 = 8.7 multiply this with height
(8.7) × (6.7) = 58.29
The area of the given trapezium is 58.29 cm².
What is a trapezium?In American and Canadian English, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid. A trapezium is a term used for a trapezoid in British and other varieties of English. These two terms were transposed due to a typo in Charles Hutton's mathematical dictionary.So, the area of the trapezium:
Formula: (a+b)/2 × hWhere, a = 7, b = 10.4 and h = 6.7.Solve as follows:
(a+b)/2 × h(7 + 10.4)/2 × 6.717.4/2 × 6.78.7 × 6.758.29 cm²Therefore, the area of the given trapezium is 58.29 cm².
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The ratio of 1.2 to 29 is the same as the ratio of 4.8 to
Answers
Answer:
116
Step-by-step explanation:
Given the ratio 1.2 : 29, you want x in the equivalent ratio 4.8 : x.
SetupEquivalent ratios can be written as a proportion:
1.2/29 = 4.8/x
SolutionMultiplying by 29x, we have ...
1.2x = 29(4.8)
Dividing by 1.2 gives ...
x = 29(4.8/1.2) = 29(4) = 116
The ratio is the same as 4.8 to 116.
__
Additional comment
A proportion like this can be written 4 ways. The solution takes only one step if the unknown is in the numerator.
[tex]\dfrac{1.2}{29}=\dfrac{4.8}{x},\quad\dfrac{29}{1.2}=\dfrac{x}{4.8},\quad\dfrac{1.2}{4.8}=\dfrac{29}{x},\quad\dfrac{4.8}{1.2}=\dfrac{x}{29}[/tex]
What is the value of x in the geometric sequence x, 3, — ‚ .A. -27B. -9C. -1D. -3
Answers
Recall that in a geometric sequence, whenever we take one value of the sequence and divide it by the next number of the sequence, we would get a constant number unique to that sequence. If we take the first and second numbers and calculate the ratio, we get
[tex]\frac{x}{3}[/tex]if we do that with the second and third numbers, we get
[tex]\frac{3}{\text{ -}\frac{1}{3}}=\text{ -}\frac{3\cdot3}{1\cdot1}=\text{ -9}[/tex]this two numbers should be equal. So we get
[tex]\frac{x}{3}=\text{ -9}[/tex]if we multiply both sides by 3, we get
[tex]x=3\cdot\text{ -9= -27}[/tex]so option A is the correct option.
Convert the angle \frac{13\pi}{4} 413π radians to degrees.
Answers
1 rad x 180/pi =57.296 deg
so the answer is 744.845
A 45 kg skydiver has a speed of 25 m/s at an altitude of 950 meters above the ground. Determine the
kinetic energy possessed by the skydiver.
Answers
The kinetic energy possessed by the skydiver is 14, 062. 5 Joules
What is kinetic energy?Kinetic energy of an object is defined as the energy possessed by an object due to its motion.
It is also described as the work that is required to accelerate a body of mass from rest to its given velocity.
The formula for calculating kinetic energy is expressed as;
Kinetic energy = 1/2 mv²
Where;
m is the mass of the objectv is the velocity of the objectNow, substitute the values
Kinetic energy = 1/2 (45)(25)²
Find the square
Kinetic energy = 1/2 (45)(625)
Find the product
Kinetic energy = 1/2(28125)
Find the quotient
Kinetic energy = 14, 062. 5 Joules
Hence, the value is 14, 062. 5 Joules
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(d) Find the domain of function R. Choose the correct domain below.
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Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
You need a 55% alcohol solution. On hand, you have a 150mL of a 45% alcohol mixture. You also have 80% alcohol mixture. How much of the 80% mixture will you need to add to obtain the desired solution?
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Let the equired amount of 80% alcohol mixture required be 'x' mL.
If C represents the concentration and V represents the correspon
PLS HELP ME WITH THIS QUESTION ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Solve for perimeter
Answers
Answer:
7x+9=8
Step-by-step explanation:
4-x+7x-1-8-5x+6x+13
=7x+8
:]
In a city in Ohio, the sales tax rate is 7.5%. If you buy a blanket for $22.00 and a pillow for $8.00, what is your total bill of the blanket and pillow including tax?
Answers
Name
1) The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to
24 rings each day using up to 80 total man-hours of labor. It takes 4 man-hours to make one VIP ring and 2
man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the
company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35?
Let V stand for the number of VIP rings made, S stand for the number of SST rings made.
State the Objective Function
Z=_
State the total ring constraint
State the man-hours constraint
Use the graph below to graph your constraints, label your Optimal Region points, and evalute them for the. Optimal solution using your
Z equation.
What is your Optimal Sales $'s.
How many VIP Rings
How many SST Rings
Answers
The combination that gives the most profit exists 12 VIP rings and 12 SST rings (900 / day).
How to maximize the company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35?This is a linear programming problem.
The objective function is profit R, which has to be maximized. [tex]$R=40 \mathrm{~V}+35 S$[/tex]
being V: number of VIP rings produced, and S : number of SST rings produced.
The restrictions are
Amount of rings (less or equal than 24 a day): [tex]$V+S \leq 24$[/tex]
Amount of man-hours (up to 60 man-hours per day):[tex]$3 V+2 S \leq 60$[/tex]
The number of rings of each type exists a positive integer: [tex]$V, S \geq 0$[/tex]
We get 3 points, in which 2 of the restrictions exists saturated. In one of these three points lies the combination of V and S that maximizes profit.
The points and the values for the profit function in that point are:
Point 1: V=0 and S=24
[tex]$R=40 \mathrm{~V}+35 S=40 \cdot 0+35 \cdot 24=0+840[/tex]
R = 840
Point 2: V=12 and S=12
R = 40 V+35 S [tex]=40 \cdot 12+35 \cdot 12=480+420[/tex]
R = 900
Point 3: V=20 and S=0
R = 40 V+35 S [tex]=40 \cdot 20+35 \cdot 0=800+0 \\[/tex]
R = 800
The combination that gives the most profit exists 12 VIP rings and 12 SST rings (900 / day).
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Miriam buys the chair shown. The tax rate is . How much was the tax on the chair?
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The tax on the chair is $7.50.
What is a tax?A tax is a mandatory financial charge or other sort of levy imposed by a governmental entity on a taxpayer in order to fund government spending and related public expenses.
The tax rate is the ratio at which a firm or individual is taxed in a tax system. A tax rate can be presented in numerous ways: statutory, average, marginal, and effective.
Let the cost of the chair be $150 and the assumed tax rate be 5%.
In this case, the tax on the chair will be:
= Tax rate × Cost of chair
= 5% × $150
= 0.05 × $150
= $7.50
Note that an overview was given as the information is incomplete.
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During a weight loss challenge, Ms. Norris went from 190 pounds to 160 pounds. percent of weight did she lose?
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the original weight is 190 pounds
the new weight is 160 pounds
so the percentage of weight loss is
[tex]=\frac{original\text{ weight - new weight}}{\text{original weight}}\times100[/tex][tex]\begin{gathered} =\frac{190-160}{190}\times100 \\ =\frac{30}{190}\times100 \\ =15.78 \end{gathered}[/tex]so she loss 15.78 per cent of the weight.
Which of the following are remote interior angles of Z1? Check all that apply51613/241O A. 23I B. 25O C. 26hO D. 22O E. 24O F. 21
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Given data:
The given figure of the triangle.
The remote interior angles of ∠1 are,
[tex]\angle4\text{ \& }\angle6[/tex]Thus, the options (C) and (E) are correct.
what is the sum?17.34 8.03+0.009
Answers
In order to add these numbers, first let's write all of them with the same number of decimal places:
17.34 = 17.340
8.03 = 8.030
0.009 = 0.009.
Then, let's add all algarisms that are in the same position in each number:
0 + 0 + 9 = 9
4 + 3 + 0 = 7
3 + 0 + 0 = 3
7 + 8 + 0 = 15 (5 plus 1 to next algarism)
1 + 0 + 0 (+ 1) = 2
So the final result is 25.379.
if once taxi fare was $7.65 how many miles did he travel in the taxi a taxi company charges $2.25 for the first mile and then $0.20 per mile for additional mile or f equals $2.25 + $0.20(m -1) where f is the fair and m is Adam's number of miles
Answers
Answer:
28 miles
Explanation:
The equation that describes the relationship between the fare and the number of miles is:
f = 2.25 + 0.20(m - 1)
Where f is the fare and m is the number of miles.
So, if the taxi fare was $7.65, we can replace f by 7.65. Then:
7.65 = 2.25 + 0.20(m - 1)
Therefore, we can calculate the number of miles by solving the equation for m. So, subtracting 2.25 from both sides:
7.65 - 2.25 = 2.25 + 0.20(m - 1) - 2.25
5.4 = 0.20(m - 1)
Dividing by 0.20, we get:
[tex]\begin{gathered} \frac{5.4}{0.20}=\frac{0.20(m-1)}{0.20} \\ 27=m-1 \end{gathered}[/tex]Finally, add 1 to both sides:
27 + 1 = m - 1 + 1
28 = m
So, he travels 28 miles in the taxi
A lifeguard is sitting in an observation chair at a pool. The lifeguard's eye level is 6.2. feet fromground. The chair is 15.4 feet from a swimmer. Calculate the measure if an angle forms when thelifeguard looks down at the swimmer.
Answers
We can represent this situation with a triangle, as shown below:
We need to calculate the angle that forms between the line of sight of the Life Guard and the swimmer. For that, we will have to use the tangent relation.
[tex]undefined[/tex]7. What is the value of z?t50°60°70°
Answers
Answer:
50 is next to 70 ,_(60) with the rest
Step-by-step explanation:
(50)_(60)+(70)
5. x^2+2x+1Factors:(__________________________)(_____________________)
Answers
Question: what are the factors of the expression:
[tex]x^2+2x+1[/tex]Solution:
Let the expression
[tex]x^2+2x+1[/tex]If we apply the quadratic equation:
[tex]\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]we get the zero of the polynomial
[tex]f(x)=x^2+2x+1[/tex]which is -1. Thus the polynomial can be factored in the following way
[tex]x^2+2x+1\text{ = (x+1)(x+1)}=(x+1)^2[/tex]then, we can conclude that the factors of the given polynomial are:
(x+1) and (x+1)
A trapezoid has bases 4 and 12 and area of 40m^2 find the height
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Step 1
State the formula for the area of a trapezoid
[tex]\begin{gathered} The\text{ area of a trapezoid=(}\frac{a+b}{2})\times height(h) \\ \text{Where a= base 1=4}m \\ b=\text{base 2=12m} \\ \text{The area of the trapezoid=40m}^2 \end{gathered}[/tex]Step 2
Find the height
[tex]\begin{gathered} 40=(\frac{4+12}{2})\times h \\ 40=\frac{16}{2}\times h \\ 80=16h \\ h=\frac{80}{16} \\ h=5m \end{gathered}[/tex]Hence, the height = 5m
Estimate the total cost of the following items from your dorm room rounded individual cost to the nearest $10 round your answer to the nearest dollar no sense
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First item= $159.55
Chair= $49.75
Cubes= $29.87
Lamp= $19.78
Rounding the individual cost to the nearest $10, we get:
First item= $160
Chair= $50
Cubes= $30
Lamp= $20
The total cost will be:
$160+$50+$30+$20= $260.
The answer is: $ 260.
Use the graph of y=f(x) shown below to graph the function GAnd then choose the correct graph
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Rule of dilation:
[tex](x,y)\rightarrow(4x,4y)[/tex]Find the coordinates of the points in g(x) following the rule above:
[tex]undefined[/tex]Ashe worked 8 hours every day for 10 days. If she made $620 for those 10 days she worked. What is her pay per hour?
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Answer:
$7.75 per hour
Step-by-step explanation:
10 days x 8 hours = 80 hours
$620/80 hours = $7.75 per hour
Answer:
$7.75 per hour
Step-by-step explanation:
8 x 10 =80
$620=80 hours
÷80 ÷80
$7.75=1 hour
8. (15 pts) Explain clearly why Graph A IS a function, while Graph B is NOT a function. (Youcan indicate where the graphs pass or fail and reference that in your explanation)
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We can see two graphs and we need to determine the reason why graph A IS a function, and graph B is NOT a function.
To achieve that, we can proceed as follows:
1. A function is a relation in which for each element of the domain we have only (exactly) one element of the range.
2. The domain of a function is the values for x for which the function is defined, and the range is those values for y that result when the function takes values for x and after following the rule of the function (the values for which the function is defined).
3. To determine if a graph is a function, we can use the vertical line test. Given the above definitions, this test tells us that if a vertical line passes through a graph at more than a point, then the relation is NOT a function.
4. Now we can use the Vertical Line Test on each graph as follows:
Graph A:As we can see from the graph, the vertical line passes through only one point (one value for y associated to x). We can see that the open circle indicates that the function is not defined for the value while the solid circle indicates that the function is defined for that value.
For instance, for x = -1 the value of the function is y = 0 (and not y = -1 - see the open circle). We have a similar case for x = 1 (y = 1) (not y = 0).
Therefore, graph A IS a function.
Graph B
In this case, we can say that the vertical line passes through more than one point in most of the values. However, we can say that there are some values where the line passes through one point - from x = -3 to x = -2 (included) -, and for values greater than 2 (x>2).
However, since the vertical line test indicates that the line passes through more than a point (there are more than a value, y, for each x) then Graph B is NOT a function.
Therefore, in summary, we can say that using the method of the vertical line test, Graph A IS a function, while Graph B is NOT a function.
the following equation is used by scientists to relate the pressure, volume, amount and temperature of gas solve for r in terms of p,v,n and t
Answers
The equation is PV = nRT.
What is a ideal gas law?The calculations for the ideal gas law are comparison of the Pressure and Volume of gas based upon amount and temperature.
The basic formula is PV = nRT where
P = Pressure in atmospheres (atm)
V = Volume in Liters (L)
n = number of moles (mol)
R = the Ideal Gas Law Constant
T = Temperature in Kelvin (K)
The value of n is the amount of the gas measured as moles.
One may need to convert a mass to moles by dividing the given mass of the gas by the molar mass of the gas to get moles.
Hence, The equation is PV = nRT.
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Which number is greater than 555,621,000?A.5.0 x 10*6B.6.2 x 10*7C.5.55621 x 10*7D.9.99 x 10*6
Answers
Given:
[tex]555,621,000[/tex]Consider the individual options and compare them with the given number.
A.
[tex]5.0\times10^9[/tex][tex]\text{Use }10^9=1,000,000,000.[/tex][tex]5.0\times10^9=5.0\times1,000,000,000[/tex][tex]5.0\times10^9=5,000,000,000[/tex]We know that
[tex]5,000,000,000>555,621,000[/tex]This option is correct.
B.
[tex]6.2\times10^7[/tex][tex]\text{Use }10^7=10,000,000.[/tex][tex]6.2\times10^7=6.2\times10,000,000[/tex][tex]6.2\times10^7=62,000,000[/tex]We know that
[tex]62,000,000<555,621,000[/tex]This option is not correct.
C.
[tex]5.55621\times10^7[/tex][tex]\text{Use }10^7=10,000,000.[/tex][tex]5.55621\times10^7=5.55621\times10,000,000[/tex][tex]5.55621\times10^7=55,562,100[/tex][tex]55,562,100<555,621,000[/tex]This option is not correct.
D.
[tex]9.99\times10^6[/tex][tex]\text{Use }10^6=1,000,000.[/tex][tex]9.99\times10^6=9.99\times1,000,000[/tex][tex]9.99\times10^6=9,990,000[/tex][tex]9,990,000<555,621,000[/tex]This option is not correct.
Final answer:
[tex]5.0\times10^9\text{ is greater than 555,621,000.}[/tex]Option A is correct.
-8 + 12x+7x+12= A19x4 B 24x-1 C 5x+20 D 5x+4
Answers
Given the expression:
-8 + 12x + 7x + 12
Let's simplify the expression.
To simplify the expression, combine all like terms.
We have:
-8 + 12x + 7x + 12
= 12x + 7x + 12 - 8
Add 12x and 7x
= 19x + 12 - 8
Add 12 and -8
= 19x + 4
ANSWER:
19x + 4
Solve the inequality for x.21 > x+2Simplify as much as posible.
Answers
The given inequality is 21>x+2.
The inequality can be solved as,
[tex]\begin{gathered} 21>x+2 \\ 21-2>x \\ 19>x \\ x\in(-\infty,19). \end{gathered}[/tex]Thus, the above expression gives the required solution for the inequality.
Signs are placed at regular intervals along a mountain road to indicate altitude. At Grinbrir Lodge, the sign indicates an elevation of 876 meters. But 17 kilometers down the road, another sign indicates that the elevation is 672 meters. What is the average elevation change per kilometer traveled from the Lodge
Answers
Answer:
-12 m/km
Step-by-step explanation:
You want to know the average elevation change per kilometer given the elevation changes from 876 meters to 672 meters over a distance of 17 kilometers.
Rate of changeThe average elevation change per kilometer is found by dividing the elevation change by the number of kilometers. The elevation change is the difference between the ending elevation and the starting elevation.
rate of change = ((end elevation) -(start elevation))/(distance)
= (672 m -876 m)/(17 km) = (-204 m)/(17 km) = -12 m/km
The average elevation change is -12 meters per kilometer traveled from the lodge.
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Additional comment
Expressing both dimensions in the same unit, we can find the average grade of the road to be ...
(-12 m)/(1000 m) = -0.012 = -1.2% . . . . . average grade of the road
Rachel earns $27 per hour at work. She worked 936 hours last year. How much did Rachel earn from working last year?
Answers
Answer: $25,272 is the answer hope it helps.
Answer:
25,272 dollars in total