Question AA baseball is hit, following a path represented by x = 135t and y = 3.3 + 38t − 16t 2 for 0 ≤ t ≤ 3.Part A: Find the ordered pairs, (x, y) when t = 0.2, 1.2, and 2.2.Part B: The fence, which is 10 feet tall, lies 320 feet away from home plate. Does the baseball travel over the fence? Justify your answer mathematically.Part C: Write a rectangular equation to represent the plane curve.
Answers
Explanation
For the given question, we have the following
[tex]\begin{gathered} x=135t \\ y=3.3+38t-16t^2 \end{gathered}[/tex]Part A
find the ordered pairs (x,)
[tex]\begin{gathered} when \\ t=0.2 \\ \\ x=135(0.2)=27 \\ y=3.3+38(0.2)-16(0.2)^2=10.26 \\ \\ when\text{ t=0.2} \\ (x,y)=(27,10.26) \\ \end{gathered}[/tex][tex]\begin{gathered} when \\ t=1.2 \\ x=135(1.2)=162 \\ y=3.3+38(1.2)−16(1.2)^2=25.86 \\ \\ (x,y)=(162,25.86) \end{gathered}[/tex][tex]\begin{gathered} when \\ t=2.2 \\ x=135(2.2)=297 \\ y=3.3+38(2.2)−16(2.2)^2=9.46 \\ \\ (x,y)=(297,9.46) \end{gathered}[/tex]Related Questions
Hi I need help with this question please thank you!
Answers
To answer this question we will factorize each term.
Notice that:
[tex]20x^4y=5xy(4x^3),[/tex][tex]10x^3y^3=5xy(2x^2y^2),[/tex][tex]5xy^2=5xy(y).[/tex]Therefore, the greatest common factor of the terms is:
[tex]5xy\text{.}[/tex]Answer:
[tex]5xy\text{.}[/tex]
7/8 = X/16 X=how do I solve it
Answers
x= 14
1) Let's solve this equation considering that we're dealing with two ratios.
Then we can cross multiply and simplify them this way:
[tex]\begin{gathered} \frac{7}{8}=\frac{x}{16} \\ 8x=16\cdot7 \\ \frac{8}{8}x=\frac{16\cdot7}{8} \\ x=2\cdot7 \\ x=14 \end{gathered}[/tex]2) So the answer is x= 14
Drag and drop numbers into the equation to complete the equation of the line in slope-intercept form.The line passes through (8, 19) and (5, 1).
Answers
we are given two points
(8,19) and (5,1)
firstly, we need to calculate the slope
slope = y2 - y1 / x2 - x1
from the points
x1 = 8, y1 = 19, x2 = 5, y2 = 1
slope = 1 -19 / 5 - 8
slope = -18/-3
negative will cancel each other
slope = 18/3
slope = 6
slope intercept equation is
y - y1 = m(x - x1)
m = slope = 6
y1 = 19 and x1 = 8
y - 19 = 6(x - 8)
open the parentheses
y - 19 = 6*x - 6*8
y - 19 = 6x - 48
make y the subject of the formula
y = 6x - 48 + 19
y = 6x - 29
y = 3x ÷ 9 and x = -6 what is the output?
Answers
y = 3x ÷ 9 and x = -6
y = 3(-6) ÷ 9 = -18 ÷ 9 = -2
y = -2
Answer:
y = -2
1 5/6 - (-2 4/5)[tex]1 \frac{5}{6} - ( - 2 \frac{4}{5} )[/tex]
Answers
We have the following:
[tex]1\frac{5}{6}-(-2\frac{4}{5})[/tex]solving:
[tex]\begin{gathered} 1\frac{5}{6}=\frac{11}{6} \\ 2\frac{4}{5}=\frac{14}{5} \\ \frac{11}{6}+\frac{14}{5}=\frac{11\cdot5+14\cdot6}{30}=\frac{55+84}{30}=\frac{139}{30} \\ \frac{139}{30}=4\frac{19}{30} \end{gathered}[/tex]The answer is 4 19/30
Determine if each of the following relationships form a function.(1,1), (3,2), (5,4), (-9,6)
Answers
Determine if each of the following relationships form a function.
(1,1), (3,2), (5,4), (-9,6)
we know that
A relationship between x and y form a function, if for one value of x there is only one value of y
In this problem we have that
for one value of x there is only one value of y
therefore
Yes, form a function
The hallway of an apartment building is 44 feet long
and 6 feet wide. A landlord has 300 square feet of carpet. Does she have
enough carpet to cover the hallway? Explain.
Answers
Answer:
Yes, there is enough carpet to cover the hallway. We know this because the area of the floor is shown as 44 times 6, which equals 264 feet. With 300>264, there is enough feet of carpet to cover
Step-by-step explanation:
44 times 6 = 264
Evaluate with no calculator sin(sin^-1(3/8))
Answers
Since the sine ratio is opposite side/hypotenuse
Then in
[tex]\sin (\sin ^{-1}\frac{3}{8})[/tex]This means the angle has opposite side 3 and hypotenuse 8 in a right triangle
Then use this rule to evaluate without a calculator
[tex]\sin (\sin ^{-1}\frac{a}{b})=\frac{a}{b}[/tex]Because sin will cancel sin^-1
[tex]\sin (\sin ^{-1}\frac{3}{8})=\frac{3}{8}[/tex]The answer is 3/8
Kevin went for a drive in his new car. He drove for 377.6 miles at a speed of 59 miles per hour. For how many hours did he drive ?
Answers
We know that the average speed (v) can be calculated as the quotient between the distance D and the time t.
As v = 59 mi/h and D = 377.6 mi., we can calculate the time as:
[tex]v=\frac{D}{t}\longrightarrow t=\frac{D}{v}=\frac{377.6\text{ mi}}{59\text{ mi/h}}=6.4\text{ h}[/tex]Answer: he drove for 6.4 hours.
Which of the following statements about the Real Number System is always true?A Rational numbers include irrational numbers.B A number that is an integer is also a whole number and a natural number.C A number that is a whole number is also an integer and a rational Fimber.Tmber.D A number that is a whole numbers is also a natural number.
Answers
C
1) Let's draw a sketch to better understand this:
2) So, based on that we can say that
A number that is a Whole number is also an integer and a Rational Number.
Whole numbers are counting number with the 0 included
Integers numbers are whole numbers and the negative numbers
Rational numbers are any number that can be written as a ratio like 2, (2/1), 3/2, 5, 6/7, etc.
So whole numbers are integer numbers and rational ones simultaneously.
For example 2, 3, etc.
which of tje following proportion are true16/28=12/216/16=4/1430/40=24/3510/15=45/30
Answers
Notice that:
1)
[tex]\frac{16}{28}=\frac{4\cdot4}{7\cdot4}=\frac{4}{7}=\frac{4\cdot3}{7\cdot3}=\frac{12}{21}\text{.}[/tex]2)
[tex]\frac{6}{16}=\frac{2\cdot3}{2\cdot8}=\frac{3}{8}\ne\frac{2}{7}=\frac{2\cdot2}{2\cdot7}=\frac{4}{14}\text{.}[/tex]3)
[tex]\frac{30}{40}=\frac{10\cdot3}{10\cdot4}=\frac{3}{4}\ne\frac{2}{3}=\frac{12\cdot2}{12\cdot3}=\frac{24}{36}.[/tex]4)
[tex]\frac{10}{15}=\frac{5\cdot2}{5\cdot3}=\frac{2}{3}\ne\frac{9}{10}=\frac{5\cdot9}{5\cdot10}=\frac{45}{50}.[/tex]Answer: The only proportion that is true is the first one.
I need to find out which ones are true and which ones I have to change to get the answers correct please help me.
Answers
Solution
- In order to solve this question, we need to apply the following rules:
[tex]\begin{gathered} Given \\ f(x)=ax^2+bx+c \\ \\ |a|>1:\text{ } \\ \text{ The graph gets narrower the larger }|a|\text{ gets} \\ \\ 0<|a|<1: \\ \text{ The graph gets wider the closer }|a|\text{ is to zero} \\ \\ a<0: \\ \text{ The graph has a peak} \\ \\ a>0: \\ \text{ The graph has a valley} \end{gathered}[/tex]- Applying this rule, we can proceed to solve this question.
- Based on these rules above, we can select the correct options as follows:
If ST = x + 4, TU = 10, and SU = 9x + 6, what is ST?
Answers
Given:
[tex]\begin{gathered} ST=x+4 \\ \\ TU=10 \\ \\ SU=9x+6 \end{gathered}[/tex]Find-:
The value of "x."
Explanation-:
The line of property
[tex]SU=ST+TU[/tex]Put the value is:
[tex]9x+6=x+4+10[/tex][tex]\begin{gathered} 9x+6=x+14 \\ \\ 9x-x=14-6 \\ \\ 8x=8 \\ \\ x=\frac{8}{8} \\ \\ x=1 \end{gathered}[/tex]So, the value of "x" is 1.
A regular plot of land is 70 meters wide by 79 meters long. Find the length of the diagonal and, if necessary, round to the nearest tenth meter
Answers
Given :
The length is given l=79 m and width is given w=70m.
Explanation :
Let the length of diagonal be x.
To find the length of diagonal , use the Pythagoras theorem.
[tex]x^2=l^2+w^2[/tex]Substitute the values in the formula,
[tex]\begin{gathered} x^2=79^2+70^2 \\ x^2=6241+4900 \\ x^2=11141 \\ x=\sqrt[]{11141} \\ x=105.55m \end{gathered}[/tex]Answer :
The length of the diagonal is 105.6 m.
The correct option is D.
What is the volume of this rectangular prism? 5/3 cm 1/4 cm 3/2 cm
Answers
The volume of the prism can be determined as,
[tex]\begin{gathered} V=\frac{5}{3}cm\times\frac{1}{4}cm\times\frac{3}{2}cm \\ V=\frac{5}{8}cm^3 \end{gathered}[/tex]Thus, the required volume is 5/8 cubic centimeters.
does any know how to find the variance using n=122 p= 0.64
Answers
The formula to find the variance of a binomial distribution given the values n and p is:
[tex]\begin{gathered} \sigma^2=n\cdot p\cdot q \\ \text{ Where} \\ q=1-p \end{gathered}[/tex]In this case, you have:
[tex]\begin{gathered} n=122 \\ p=0.64 \\ q=1-p \\ q=1-0.64 \\ q=0.36 \end{gathered}[/tex]Then
[tex]\begin{gathered} \sigma^2=n\cdot p\cdot q \\ \sigma^2=122\cdot0.64\cdot0.36 \\ \sigma^2=28.11 \\ \text{ Rounding to the nearest tenth} \\ \sigma^2=28.1 \end{gathered}[/tex]Now, the standard deviation is the square root of the variance. So, you have
[tex]\begin{gathered} \sigma=\sqrt[]{\sigma^2} \\ \sigma=\sqrt[]{28.1} \\ \sigma=5.3 \end{gathered}[/tex]Therefore, the variance and standard deviation of the binomial distribution with the given values n y p are
[tex]\begin{gathered} \sigma^2=28.1\Rightarrow\text{ Variance} \\ \sigma=5.3\Rightarrow\text{ Standard deviation} \end{gathered}[/tex]General MathematicsProblem:What interest rate would yield ₱1,200 interest on ₱10,000 in 2 years?
Answers
Answer
Interest rate = 6%
Explanation
From the information given in the question,
Interest, I = ₱1,200
Principal, P = ₱10,000
Time, T = 2 years
Interest rate, R = ?
Using Simple Interest formula:
[tex]I=\frac{PRT}{100}[/tex]Since I, P and T are know, we shall substitute these values into the formula to get R.
[tex]\begin{gathered} 1200=\frac{10000\times R\times2}{100} \\ 1200=200R \\ \text{Divide both sides by 200} \\ \frac{1200}{200}=\frac{200R}{200} \\ R=6 \end{gathered}[/tex]Therefore, the interest rate is 6%
One friend claims that to find the height of the platform, you need to use the tangent ratio. Explain why her approach is or is not a reasonable approach to finding the height of the platform.
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the trigonometric ratios
[tex]\begin{gathered} \sin\theta=\frac{opposite}{hypotensue} \\ \cos\theta=\frac{adjacent}{hypotenuse} \\ \tan\theta=\frac{opposite}{adjacent} \end{gathered}[/tex]STEP 2: Analyze the given scenario to get the details given
We were given the length of the piece of wood needed to make the ramp as 3.5m long, this implies that the length of the side is 3.5m. From the given image, this is the hypotenuse.
[tex]hypotenuse=3.5m[/tex]The angle of elevation is 28 degrees,
[tex]\theta=28\degree[/tex]The height of the platform from the image will be opposite since it is the side that is facing the angle 28 degrees.
[tex]opposite=height\text{ }of\text{ }platform[/tex]Joining all these together, we have a right-angled triangle given below:
From the given ratios in step 1, since we know tha hypotenuse and the opposite and also the theta, therefore the correct ratio to use is:
[tex]\begin{gathered} \sin\theta=\frac{opposite}{hypotenuse} \\ \\ \sin28=\frac{height}{3.5} \\ height=3.5\times\sin28 \end{gathered}[/tex]Therefore, the given claim of needing tangent ratio to find the height of the platform is not a reasonable approach because the adjacent which is the base is not given.
PLESSS HELP I NEED HELP PLESS HELP I NEEED HELP
Answers
For this exercise you need to remember that the area of a triangle can be calculated with the following formula:
[tex]A=\frac{bh}{2}[/tex]Where "b" is the base of the triangle and "h" is the height of the triangle.
Analyzing the information given in the exercise, you can identify that, in this case:
[tex]\begin{gathered} b=x=11units \\ h=7units \end{gathered}[/tex]Then, knowing these values, you can substitute them into the formula and then evaluate, in order to find the area of the triangle. This is:
[tex]\begin{gathered} A=\frac{(11units)(7units)}{2} \\ \\ A=\frac{77units^2}{2} \\ \\ A=38.5units^2 \end{gathered}[/tex]The answer is: Option B.
Hi , i need help with this question: what is the anwser to the division problem. 9÷4590
Answers
Problem
what is the anwser to the division problem.
9÷4590
Solution
We have the following number given:
[tex]\frac{9}{4590}[/tex]The first step would be simplify the fraction and we can divide both numbers by 9 and we got:
[tex]\frac{9}{9}=1,\frac{4590}{9}=510[/tex]So then our fraction becomes:
[tex]\frac{1}{510}[/tex]And if we convert this into a decimal we got 0.00196.
Write an equation for the line that contains (-32, -12) and is perpendicularto the graph -8x + 10y = 40Can anyone that KNOWS the answer help?
Answers
The first step is finding the slope of the equation -8x + 10y = 40.
To do so, let's put this equation in the slope-intercept form: y = mx + b, where m is the slope.
So we have:
[tex]\begin{gathered} -8x+10y=40 \\ -4x+5y=20 \\ 5y=4x+20 \\ y=\frac{4}{5}x+4 \end{gathered}[/tex]Then, since the line we want is perpendicular to this given line, their slopes have the following relation:
[tex]m_2=-\frac{1}{m_1}[/tex]So, calculating the slope of the line, we have:
[tex]m_2=-\frac{1}{\frac{4}{5}}=-\frac{5}{4}[/tex]Finally, our equation has the point (-32, -12) as a solution, so we have:
[tex]\begin{gathered} y=mx+b \\ y=-\frac{5}{4}x+b \\ -12=-\frac{5}{4}\cdot(-32)+b \\ -12=-5\cdot(-8)+b \\ -12=40+b \\ b=-12-40 \\ b=-52 \end{gathered}[/tex]So our equation is y = (-5/4)x - 52
ubtract. - B the model to help
Answers
As you can see in the model
[tex]\frac{1}{2}=\frac{4}{8}[/tex]Then
[tex]\frac{5}{8}-\frac{1}{2}=\frac{5}{8}-\frac{4}{8}=\frac{5-4}{8}=\frac{1}{8}[/tex]This is the same as if you removed 4 pieces of 1/8 from the 5 pieces of 1/8, resulting in 1 piece of 1/8.
Therefore, the result of the subtraction is
[tex]\frac{1}{8}[/tex]f(x)=x^3-4x^2+x+6 find all the real zeros of the function
Answers
The zeroes of the polynomial f(x)= x³ - 4x² + x + 6 = 0 are x - 1, x = 2
and x = 3.
We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, f(x)= x³ - 4x² + x + 6 = 0.
Now, zeroes of the polynomial should be factors of 6 they are ±1, ±2. ±3, ±6.
Now at x = 1 f(x) = 4 so not a zero, at x = - 1, f(x) = 0 so x = - 1 a zero
at x = 2 f(x) = 0 so x = 2 is a zero,
at x = 2 f(x) = so x = 3 is a zero.
learn more about polynomials here :
https://brainly.com/question/20121808
#SPJ2
Find the remaining zer Degree 3; zeros: 5, 7- i The remaining zero(s) of f is
Answers
Answer:
The remaining zero is;
[tex]7+i[/tex]Explanation:
Given that two of the zeros of a polynomial are;
[tex]\begin{gathered} 5 \\ 7-i \end{gathered}[/tex]to get the remaining zero.
Recall that according to complex conjugates, complex roots/zeros comes in pairs;
[tex]\begin{gathered} a+bi \\ \text{and} \\ a-bi \end{gathered}[/tex]where a and b are real numbers.
Applying the rule to the given roots.
Since we have a complex root;
[tex]7-i[/tex]we must also have the other pair of the complex root;
[tex]7+i[/tex]Therefore, the remaining zero is;
[tex]7+i[/tex]What are the solutions to the following system?{-2x+y=-5y=-3x2 + 50 (0, 2)O (1, -2)o (12.-1) and (- 12.-1):o 15.-10) and (-75-10
Answers
Answer:
[tex](\sqrt[]{2\text{ }},-1)\text{ and (-}\sqrt[]{2\text{ }}\text{ ,-1)}[/tex]Explanation:
Here, we want to solve the system of equations
Since we have y in both equations, let us start by rewriting the second equation to look like the first
We have that as:
[tex]\begin{gathered} -2x^2+y\text{ = }-5 \\ y+3x^2\text{ = 5} \end{gathered}[/tex]Subtract equation ii from i
We have it that:
[tex]\begin{gathered} -5x^2=\text{ -10} \\ 5x^2=10 \\ x^2=\text{ 2} \\ \\ x\text{ = }\pm\sqrt[]{2} \end{gathered}[/tex]when x = positive root 2, we have it that:
[tex]\begin{gathered} -2x^2+y\text{ = -5} \\ -2(\sqrt[]{2\text{ }})^2+y\text{ = -5} \\ -4+y\text{ = -5} \\ y\text{ = -5+4} \\ y\text{ = -1} \end{gathered}[/tex]when x = negative root 2:
We will still get the same answer as the square of both returns the same value
Thus, we have the solution to the system of equations as:
[tex](\sqrt[]{2\text{ }},-1)\text{ and (-}\sqrt[]{2\text{ }}\text{ ,-1)}[/tex]Fergus gets paid $5.25 an hour with time-and-a-half for overtime(over 40 hours). How much did he earn one week when he worked 48hours?a. $63.04b. $190.90c. $210d. $273.04
Answers
The correct answer is d. $273
Fergus worked 48 hours in the week. This means that for 40 hours he was paid $5.25 per hour; And for 8 hours he was paid 150% of the normal (150% is one and a half time)
Then for the regular paid hours:
$5.25 per hour by 40 hours => 5.25*40= $210
Now for the 8 remaining hours we need to calculate how much Fergus is paid by hour.
Then 50% of $5.25 is the same as 5.25 divided by 2: 5.25/2 = $2.625
Then the 150% is equal to 100% + 50%. The 100% is $5.25 and the 50% is $2.625
5.25 + 2.625 = $7.875
This is what Fergus gets paid for every overtime hour. This week he worked 8 overtime hours.
Then, $7.875 * 8 = $63
Now the total earning of the week is equal to $210 + $63 = $273 and that's option D.
1 + xThe function g is defined by g(x)=7+2xFind g(a+5).
Answers
The function is given as:
[tex]g(x)=\frac{1+x}{7+2x}[/tex]We need to find the expression g(a + 5).
This means that we are going to plug in "a + 5" into "x" of the function. So, substituting, it gives us,
[tex]\begin{gathered} g(x)=\frac{1+x}{7+2x} \\ g(a+5)=\frac{1+(a+5)}{7+2(a+5)} \end{gathered}[/tex]Now, we need to simplify the expression. Steps are shown below:
[tex]\begin{gathered} g(a+5)=\frac{1+(a+5)}{7+2(a+5)} \\ =\frac{1+a+5}{7+2a+10} \\ =\frac{6+a}{17+2a} \end{gathered}[/tex]Answer[tex]\frac{6+a}{17+2a}[/tex]Graph the following:X>y^2 + 4y
Answers
Solution:
Given the inequality;
[tex]x>y^2+4y[/tex]The graph of inequality without an equal sign is done with broken lines,
The y-intercept is;
[tex]\begin{gathered} 0>y^2+4y \\ \\ 0>y(y+4) \end{gathered}[/tex]Thus, the graph is;
Below is a model of the infield of a baseball stadium. How long is each side of the field Hurry pleaseee
Answers
We have the following:
[tex]\begin{gathered} A=s^2 \\ s=\sqrt{A} \end{gathered}[/tex]A = 81, replacing:
[tex]A=\sqrt{81}=9[/tex]therefore, each side measures 9 in
Drag and drop a phrase to make the statement true. TrianglesABC and DEF are Response area.similar or not similar
Answers
Solution:
Given two triangles;
Triangle ABC and DEF are similar only if;
[tex]\begin{gathered} \angle A\cong\angle D \\ \angle B\cong\angle E \\ \angle C\cong\angle F \end{gathered}[/tex]Thus, we have;
[tex]\begin{gathered} \angle A=180^o-80^o-60^o \\ \angle A=40^o=\angle D \end{gathered}[/tex]Also,
[tex]\angle B=\angle E=80^o[/tex]Also,
[tex]\begin{gathered} \angle F=180^o-80^o-40^o \\ \angle F=60^o=\angle C \end{gathered}[/tex]FINAL ANSWER: Triangle ABC and DEF are similar triangles