Answers
We are given an equation that represents the path of the longest shot put by the women's track team as:
[tex]h(x)=-0.017x^2\text{ + 1.08x + 5.8}[/tex]Where x represents the horizontal distance from the start and h(x) is the height of the shot put above the ground.
Solution:
(a) The vertex of the model:
Method 1: We can plot the model on a graph and identify the vertex from the graph. The vertex is the lowest/highest point on the curve.
The graph is shown below:
From the graph, we can see that the vertex of the model is : (31.765, 22.953)
Method 2: The vertex of the model can also be calculated using the formula:
First, we find the x-coordinate using the formula:
[tex]x\text{ = -}\frac{b}{2a}[/tex]Substituting, we have:
[tex]\begin{gathered} x\text{ = -}\frac{1.08}{2\text{ }\times\text{ -0.017}} \\ x\text{ = 31.765} \end{gathered}[/tex]The y-coordinate of the vertex can be obtained by substituting the x-coordinate into the model. So, we have the y-coordinate to be:
[tex]\begin{gathered} y\text{ = h(31.765)} \\ y=-0.017(31.765)^2\text{ + 1.08(31.765) + 5.8} \\ y\text{ = 22.953} \end{gathered}[/tex]Hence, the vertex is : (31.765, 22.953)
(b) The maximum height
The horizontal distance of the maximum height of the shot put from the starting point is :
From the plot, the starting point is -4.98
[tex]\begin{gathered} \text{Horizontal distance = 31.765 + 4.98} \\ =\text{ 36.745 f}eet \end{gathered}[/tex]The maximum height of the shot put is 22.953 feet, 36.745 feet away from the starting point.
(c) The vertical intercept
The vertical intercept is the point where the curve cuts the y-axis.
From the graph, the point is (0, 5.8).
At this point where the horizontal distance is 4.98 feet away from the starting point, the shot put is 5.8 feet above the ground.
(d) The distance from the starting point to when the shot-put stikes the ground is:
From the plot, the intercepts on the x-axis are (-4.98, 0) and (68.509, 0).
Hence, the distance is:
[tex]\begin{gathered} =\text{ 68.509 + 4.98} \\ =\text{ 73.489} \\ \cong\text{ 73.49 f}eet\text{ (2.d.p)} \end{gathered}[/tex]
Related Questions
[tex]k(x) = 3(2) {}^{x} - 8[/tex]. Is the function linear, quadratic, exponential or neither?
Answers
An exponential function is defined as a function of the form:
[tex]f(x)=a(b)\placeholder{⬚}^x+c[/tex]where a, b and c are constants.
We notice that the function given has this form, therefore the function given is an exponential function.
find the equation of the line that contains the point (6,4) and is perpendicular to the line y=3x-5
Answers
The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .
What is a equation of line?The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. Key Point. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.
Given that,
equation of given line with a slope of m = 3
y=3x-5
A line perpendicular to that line will have a slope that is the negative reciprocal of 3.
The reciprocal of 3 is 1/3. So the negative reciprocal of 3 is -1/3.
Therefore, we want to write the equation of a line with slope, m = -1/3, and passes through the point (6, 4) = (x, y).
y = mx + b
4 = (-1/3)(6) + b
(we've set up the equation with only one unknown, b, that we can now solve for)
4 = -2 + b
b = 6
With a slope, m = -1/3, and a y-intercept, b = 6, the equation of our line relating x and y is:
y = (-1/3)x + 6
Hence, The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .
To learn more about equation of line from the given link:
https://brainly.com/question/13763238
#SPJ9
please look at screenshots
Answers
When the linear correlation coefficient is 1 there is a perfect positive linear relation between the two variables. Scatter diagram would contain points that all lie on a line with a positive slop.
What is coefficient coorelation?A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively linked, the value either rises or falls together.
A correlation coefficient is a metric that expresses a correlation, or a statistical link between two variables, in numerical terms. Two columns of a specific data set of observations, sometimes referred to as a sample, or two parts of a multivariate random variable with a known distribution may serve as the variables.
The strength and direction of the linear links between two sets of variables are evaluated using correlation coefficients. Use Pearson's correlation coefficient if both variables are regularly distributed; otherwise, use Spearman's correlation coefficient.
To learn more about coefficient coorelation refer to:
https://brainly.com/question/11811889
#SPJ13
Answer To this question so that we can move onto the next question so that we can get done with all this homework so we can go play
Answers
We need to transform a number that is written in scientific notation to the standard notation. For that we have to move the dot to the right, because the exponent of the power is positive, every time we do that we will subtract one from the exponent. When there is no more dot we will add zeros. This is done below:
[tex]\begin{gathered} 2.07\cdot10^5 \\ 20.7\cdot10^4 \\ 207\cdot10^3 \\ 2070\cdot10^2 \\ 20700\cdot10 \\ 207000 \end{gathered}[/tex]The correct answer is 207,000.
a salad dressing recipe calls for 3/4 cup of olive oil for every 1/2 cup of vinegar is needed for 2 cups of olive oil?
Answers
the answer is 1 1/4 cups of vinegar
Step-by-step explanati
can someone please help me find the value of x to this equation
Answers
SOLUTION
This is a right-triangle problem.
We will use the SOHCAHTOA principle.
In this triangle, we will relate the opposite side and the hypotenuse side to get the value of x. That will be the CAH relationship.
[tex]\begin{gathered} \cos \theta=\frac{adjacent}{hypotenuse} \\ \cos \theta=\frac{5}{18} \\ \cos \theta=0.27778 \\ \theta=\cos ^{-1}(0.27778) \\ \theta=73.872^o \\ \theta=73.87^o \end{gathered}[/tex]The final answer is 73.87 degrees.
you deposit $3,300 in account with an annual interest of 3.3% for 20 years. what is the amount of money you'll have at the end of the 20 years?
Answers
Given data:
The given principal is P=$3,300.
The given rate of interest is r=3.3%.
The given time is t=20 years.
The expression for the final amount of money is,
[tex]A=P+\frac{P\times r\times t}{100}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} A=(3,300)+\frac{3,300\times3.3\times20}{100} \\ =3,300+2,178 \\ =5,478 \end{gathered}[/tex]Thus, the final amount after 20 years is 5,478.
work out the sale has been decreased
20% of 120
Answers
The current amount of the sale is 96
How to find the current amount of the sale ?The sale is 120
It was decreased by 20%
20/100 × 120
= 0.2 × 120
= 24
The amount of the current sale is
120-24
= 96
Hence the amount of the current sale which is calculated by subtracting 24 from 120 is 96
Read more on sale here
https://brainly.com/question/27614521
#SPJ1
solve the triangle. round to the nearest tenth A B 16 14 С
Answers
According the question
Side AC of the triangle = 16
Side BC = 14
The opposite side of the triangle is AC = 14
The adjacent side of the triangle is BC = 16
Using SOH CAH TOA
[tex]\begin{gathered} \text{Tan }\theta\text{ = }\frac{opposite}{\text{adjacent}} \\ \text{Tan }\theta\text{ = }\frac{14}{16} \\ \text{Tan }\theta\text{ = 0.875} \\ \theta\text{ = arc tan of 0.875} \\ \theta=tan^{-1}(0.875) \\ \theta\text{ = 41. 18 degre}es \\ To\text{ the nearest tenth} \\ \theta\text{ = 41.2 degre}es \end{gathered}[/tex]Evaluate 14xy if x=−23 and y=35 . Write your answer as a fraction in simplest form.
Answers
Answer: -11270
Step-by-step explanation:
14xy = -11270 x=-23 y=35
14(-23)(35) = -11270
In the expression below, what operation should be done first?
4 + 8 ÷ 2
Answers
Answer:
Division
Step-by-step explanation:
Using the tool PEMDAS, you will see the order that you must complete an equation in, P=Parenthesis E=Exponents M=Multiplication D=Division Addition S=Subtraction
Explanation and answer for both Part A and B please
Answers
(2x - 21) + x = 90°
So after factorising:
(2x + x) -21 = 90°
And simplify:
3x -21 = 90°
Do some moving around:
3x = 90° + 21°
3x = 111°
Then divide by 3 on both sides:
x = 37°
Then, because we know what x is, we can substitute it into the formulas for each complimentary angle:
So:
(2x -21) = (2 times 37) - 21 = 53°
And:
x°= 37°
In the questions format:
∠SOT = 37 °
∠SOR = 53°
Hope this helps!
If you have any questions, ask them here!
A circle has a center at (4, -7) and a radius of 4 units. What is the equation of this circle?
O (4)² + (y + 7)² = 16
O (x + 4)² + (y + 7)² = 4²
O(x-4)² + (y - 7)² = 16
O(x + 4)² + (y - 7)² = 4²
Answers
the equation for the circle with radius, r = 4 units and center =(4,-7)
will be (x-4)² + (y+7)² = (4)².
When the center and radius of a circle are known, how do you determine its equation?
Use the formula (x-a) ² + (y-b) ² = r ² to determine a circle's equation when you are aware of its radius and center. Here, stands for the circle's center, and is its radius. This equation is essentially a variant way of writing the general equation for a circle.
In this question,
we are given the center of our circle to be,
(4,-7) ≈ (a,b)
thus we are given,
a = 4
and b = -7
and we are given the radius to be 4units
substituting these values in the above equation,
(x-4)² + (y-(-7))² = (4)²
= (x-4)² + (y+7)² = (4)²
Hence the equation for the circle with radius, r = 4 units and center =(4,-7)
will be (x-4)² + (y+7)² = (4)².
to learn more about
to learn more about the above-mentioned concept visit:
https://brainly.com/question/27507801
#SPJ9
Which of the following best describes AD?17D17сA. MedianB. AltitudeC. Perpendicular bisectorD. Angle bisector
Answers
The median of a triangle is a line segment joining a vertex to the midpoint of the opposite side thus bisecting that side.
Hence, Median best describes the line.
Option A is the correct option,
Give the name (monomial,binomial, trinomial etc.) anddegree of the polynomial.
Answers
12x^3
Name: Monomial , because it has only 1 term
Degree: 3, exponent of the monomial
A shirt costs ₹(a2 –ab -b2 ) , a pair of trousers cost ₹(2a2 +8ab-2b2 ) and a pair of shoes cost ₹(a2 –3ab+4b2 ) .After collecting these three items from the store, Ranjan paid ₹(2a+b )2 .What balance will Ranjan receive from the cashier ?
Answers
The balance Ranjan will receive from the cashier is ₹ 0
How to determine the balanceBased on the information given, we have that;
shirt costs ₹(a² –ab -b² ) pair of trousers cost ₹(2a² +8ab-2b² ) pair of shoes cost ₹(a² –3ab + 4b² ) Ranjan paid ₹(2a+b )2Now, expand the bracket for the payment, we have;
(2a+b )²
(2a +b) (2a + b)
Multiply through
4a² + 2ab + 2ab + b²
Add like terms
4a² + 4ab + b²
Now, let's add the amount for the items bought
a² –ab -b² + 2a² +8ab-2b² + a² –3ab + 4b²
add like terms
4a² + 4ab + b²
Now, subtract the amounts
4a² + 4ab + b² - 4a² + 4ab + b²
₹ 0
Hence, the balance is ₹ 0
Learn more about cost here:
https://brainly.com/question/19104371
#SPJ1
Assessment
Time Remaining: 2:33:21 | Question 16
Charmaine spent $21 on fruit at the grocery store. She spent a total of $70 at the store. What percentage of the total did she spend on fruit?
%
Answers
The slope of a line which passes through the vertex and the y-y− intercept of the quadratic equation x^2 + 10x - 5x
2
+10x−5 is
Answers
The slope of the line passing through the y intercept and the vertex of the quadratic x²+10x-5 is 5.
The provided quadratic equation is,
y = x²+10x-5
The vertex of a quadratic equation,
(-b/2a, -D/4a)
Where,
a = 1,
b = 10,
c = -5,
D = (b²-4ac)
D = (10²-4(-5)(1))
D = 100+20
D = 120,
Putting all the values to find the vertex of the equation,
(-10/2,-120/4)
(-5,-30)
So, the vertex are now known,
To find the y intercept, putting x = 0 and solving the equation for y,
y = (0)²+10(0)-5
y = -5
The y intercept is,
(0,-5)
If there are two points on the line, let say (a,b) and (c,d), then the slope of the line is,
M = (d-b)/(c-a)
Now, we know two points,(-5,-30) and (0,-5).
We can now find the slope of line,
M = (-5+30)/(0+5)
M = 25/5
M = 5
To know more about slope of line, visit,
https://brainly.com/question/3493733
#SPJ9
The table below represents the snacks that Sidney and Erica purchased at the movies last month. Write a system of equations to determine the price of each candy and each drink.
Answers
SOLUTION:
Case: System of equations
Given: A table of value of snacks and drinks for Sidney and Erica
Required: Write a system of equations to determine the price of each candy and each drink.
Method:
Step 1: Assume the price of snacks be represented by s and drinks by d
Step 2: Equation for Sidney
[tex]\begin{gathered} 2s+1d=13.50 \\ 2s+d=13.50.........equation(1) \end{gathered}[/tex]Step 3: Equation for Erica
[tex]\begin{gathered} 3s+1d=12.85 \\ 3s+d=12.85.......equatiion(2) \end{gathered}[/tex]Final answer:
The system of equations is:
[tex]\begin{gathered} 2s+d=13.50 \\ 3s+d=12.85 \end{gathered}[/tex]A table is on sale for $589, which is 24% less than the regular price.
What is the regular price?
Answers
$589 + $141.36 = $730.36
Regular price was $730.36
what is the median value?if another 5 is added, which statement must be true the mean would increase the mean would decrease the median would increaseboth the median and mean will stay the samehow many people made 3 or less trips to the movie
Answers
Solution
We have the following data:
0, 0, 0, 0, 1, 1, 1, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5
And the mean would be:
Mean = 2.958
And the median
Median = 4
Then if we add a 5 then the median would be the same 4
And the mean = 3.04
then the solution is:
The mean would increase
And for the other part of the question
we have:´
4+3+1+2 = 10 people made 3 or less trips to the movie
Describe in extension each of the following sets:a) A is the set of positive integers less than 8.C) C is the set of digits of the number 12353888D) D is the set of courses you are enrolled in.
Answers
a. All positive integers are greater than 0,
we can express this as a set which positive integers less than 8, A = {1, 2, 3, 4, 5, 6, 7}.
This is a Finite Set.
b. The number 12353888 has a set of digits, 1, 2, 3, 5 and 8 and can be expressed as C = {1, 2, 3, 5, 8}
This is also a Finite Set.
c. The set of courses you are enrolled depends on the number of courses. We can express this as
D = {course1, course2, course3, ...}
This is Universal Set.
Translate to a system of equations and solve:Priam has a collection of nickels and quarters, with a total value of $9.30. The number of nickels is six less than three times the number of quarters. How many nickels and how many quarters does he have?
Answers
The value of a nickel is 5 cents
The value of the quarter is 25 cents
Since Priam has a total of 9.30 dollars = 930 cents, then
[tex]5n+25q=930[/tex]Simplify the equation by dividing all terms by 5
[tex]\begin{gathered} \frac{5n}{5}+\frac{25q}{5}=\frac{930}{5} \\ n+5q=186\rightarrow(1) \end{gathered}[/tex]Since he has 6 nickels less than 3 times the quarters, then
[tex]n=3q-6\rightarrow(2)[/tex]Substitute n in equation (1) by equation (2)
[tex](3q-6)+5q=186[/tex]Add the like terms on the left side
[tex]\begin{gathered} (3q+5q)-6=186 \\ 8q-6=186 \end{gathered}[/tex]Add 6 to both sides
[tex]\begin{gathered} 8q-6+6=186+6 \\ 8q=192 \end{gathered}[/tex]Divide both sides by 8
[tex]\begin{gathered} \frac{8q}{8}=\frac{192}{8} \\ q=24 \end{gathered}[/tex]The number of quarters is 24
Substitute q by 24 in equation 2 to find n
[tex]\begin{gathered} n=3(24)-6 \\ n=72-6 \\ n=66 \end{gathered}[/tex]The number of nickels is 66
He has 66 nickels and 24 quarters
Solve Step by step
8 = x/7 + 9
Answers
Answer:
[tex]x=\frac{-1}{7}[/tex]
Step-by-step explanation:
[tex]8=x/7+9\\[/tex]
Subtract 9 from both sides
[tex]-1=x/7[/tex]
Multiply both sides by 7
[tex]\frac{-1}{7} =x[/tex]
Swap the order because you're a smart person
[tex]x=\frac{-1}{7}[/tex]
Can somebody please help me right now??? i’m stuck and i need help with this bad
Answers
Answer:
Step-by-step explanation:
The answer is B!
Ai Mi was out at a restaurant for dinner when the bill came. Her dinner came to $9. After adding in a tip, before tax, she paid $11.79. Find the percent tip.
Answers
Answer:
I don't know if it is the answer
Find the length of the hypotenuse if the length of the legs are 6 inches and 9 inches. Round to two decimal places.The length of the hypotenuse is ___ inches.
Answers
The hypotenuse (longest side) of a right angled triangle can be derived using the Pythagoras' theorem as shown;
[tex]\begin{gathered} AC^2=AB^2+BC^2 \\ \text{Where AC is the hypotenuse, you now have;} \\ AC^2=6^2+9^2 \\ AC^2=36+81 \\ AC^2=117 \\ \text{Add the square root sign to both sides} \\ AC=\sqrt[]{117} \\ AC=10.8166 \\ AC=10.82\text{ (To 2 decimal places)} \end{gathered}[/tex]The answer is 10.82 inches, to 2 decimal places
The table below represents the total weight, in pounds, of a set ofstone blocks.<
Answers
k=12
1) Gathering the data, and setting this table:
Blocks | Pounds
5 60
6 72
7 84
8 96
2) Since we have this table, and a proportional relationship means a linear function without linear coefficient, i.e. y =mx
Then we can write:
y =12x
3) So, as we can write it y=kx, then the constant of proportionality k =12 because the weight in pounds is 12 times the number of blocks.
5 x 12 = 60
6 x 12 =
I need help on this also could you check if the first 3 questions are correct
Answers
We have two parallel lines intersected by other line.
We have to relate the angles.
We will take the angle with measure 17° as reference (red angle).
The angle <1 has a measure that is supplementary to the red angle, as <1 is supplementary to the <4, which is a corresponding angle to the red angle.
[tex]m\angle1=180-17=163\degree[/tex]It has no direct relationship with the red angle.
The angle <2 is supplementary to <1, so it will have the same measure as the red angle (m<2 = 17°).
The relationship with the red angle is that they are alternate exterior angles.
Angle <3 has no direct relationship with the red angle. As it is vertical with <1 it has the same measure (m<3 = 163°) and is supplementary to the red angle.
Angle <4 and the red angle are corresponding angles.
They have the same measure, so they are congruent.
Angle <5 and the red angle form a linear pair, so they are supplementary. The measure of <5 is then m<5 = 163°.
Angle <6 and the red angle are vertical angles, so they have the same measure.
Angle <7 and the red angle form a linear pair, so they are supplementary. The measure of <7 is then m<7 = 163°.
Answer:
Angle <1:
Measure = 163°
Relationship: No name for relationship and supplementary.
Angle <2:
Measure = 17°
Relationship: Alternate exterior and congruent.
Angle <3:
Measure = 163°
Relationship: No name for relationship and supplementary.
Angle <4:
Measure = 17°
Relationship: Corresponding and congruent.
Angle <5:
Measure = 163°
Relationship: Linear pair and supplementary.
Angle <6:
Measure = 17°
Relationship: Vertical and congruent.
Angle <7:
Measure = 163°
Relationship: Linear pair and supplementary.
Select the correct figures
Answers
The correct answer is the figure