The equation of the parabola, in vertex form, that represents the ball's distance, y, from the hole, x seconds after the ball is hit is
y = (-2m/s^2)t^2 + (-2m/s)t + 6m
Define quadratic equation.ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given,
Assume for the moment that the hole is located at y = 0m, where x represents the time variable.
We are aware of:
The vertices are (-1s, 8m).
x in seconds and y in meters, I presume
The ball enters the hole at time x = 1s, hence we also have the following point:
(1s, 0m).
The vertex of the quadratic equation y = ax2 + bx + c is located at:
x = -b/2a,
Next, we have:
-1 = -b/2a.
Next, we have equations for trees:
8m = a(-1s)2, b(-1s), and c
0m = (a(1s)2) + (b(1s)2) + (c)
-1s = -b/2a.
The third equation should have one variable isolated first, and then it should be substituted in one of the other two:
1s2a = b.
Therefore, we can change b to bi 1s2a in the first two equations.
8m = 1s×2a×1s - a×1s2a1s + c
0m = 1s×2a×1s + a×1s×2a + c
We can combine the two equations to get:
8m is equal to a(1s2 - 2s2) + c, or a×1s2 - c.
0m is equal to a(1s2 + 2s2) + c, or a×3s2 + c.
We may quickly remove c from the second equation and then substitute it in the first equation:
c = -a3s^2
The initial equation is now:
8m is equal to -a×1s2 - a×3s2 - a×4s2.
a = 8m/-4s^2 = -2m/s^2.
We can now determine the values of c and b using a.
c = -(-(-2m/s2)*3s2)*3s2 = 6m.
B is equal to 1s*2a = 1s*(-2m/s2) = -2m/s.
The equation is then:
y = (-2m/s^2)t^2 + (-2m/s)t + 6m
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what is x if 4x+2=6 wwwwwwwwwwwwwwwwwwwwwwwww
Answer:
x=1
Step-by-step explanation:
in photo
im so confused right now
Answer:
The solution is A. 183
Step-by-step explanation:
112-38×14÷14+109
= 74×1+109
= 74+109
= 183
5. Find TR if PR = 10m and QT=7 m
Explain correctly and will give brainlist
The correlation coefficient between two quantitative variables is approximately 0. 2. What does the value of this correlation coefficient indicate about how well the model fits the data?.
As per the concept of correlation coefficient "tell us" that the model in question does not fit the data well, in whose case we need to find another that can do it.
Correlation coefficient:
Correlation coefficient refers the a statistical measure of the strength of a linear relationship between two variables. And its values can range from -1 to 1.
Given,
The correlation coefficient between two quantitative variables is approximately 0. 2.
Here we need to find the value of this correlation coefficient indicate about how well the model fits the data
While we looking into the given question, a correlation coefficient of 0.02 is near to zero. In this case, the correlation coefficient is "telling us" that the two variables do not follow the cases 1 and 2 above described. Instead, it follows the case 3.
Therefore, the model in question does not fit the data well, in whose case we need to find another that can do it.
Therefore, it is important to remember that the correlation coefficient does not tell us anything about that one variable causes the other variable, only behaviors as described above.
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Find the slope of the line
We have that the data is: (x₁ = 2, y₁ = 2) and (x₂ = 6, y₂ = 3).
The formula to calculate the slope of the line is:
m = y₂ - y₁/x₂-x₁
m = 3 - 2/6 - 2 = 1/4
The slope through the points (2,2) and (6,3) is 1/4Find the least common denominator of 1/6 and 11/9
Answer:
LCD is 18
Step-by-step explanation:
1/6 = 3/18
11/9 = 22/18
(b) suppose you were going to construct an 89% confidence interval from this population. what critical value should you use? (3 decimal places)
Using the theories of confidence interval, we got that 0.945 is critical value which should we use for constructing an 89% confidence interval from this population.
In statistics, a confidence interval is the range of values that is determined through the use of the observed data, calculated at a desired confidence level that may contains the true value of the parameter being studied.
Assuming this is asymmetrical confidence interval we have the diagram, and dealing with a Normal distribution
from the diagram we see that
P(Z<z)=0.89+0.055=0.945
Hence, if I were going to construct an 89% confidence interval from this population, critical value should use is 0.945
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Which equation has the solution x = 9? Select each correct answer. Responses x3+7=8 x over 3 end fraction plus 7 equals 8 4 + 5x = 18 4 + 5, x, = 18 81x−3=6 81 over x end fraction minus 3 equals 6 24−2x=13 24 minus 2 x equals 13 2x−3=15 2 x minus 3 equals 15 3x + 2 = 25 3, x, + 2 = 25
The equation be which has the solution x = 9 are:
81/x - 3 = 62x - 3 = 15Which equation has the solution x = 9?x/3 + 7 = 8
substract 7 from both sides
x/3 = 8 - 7
x/3 = 1
cross product
x = 3
4 + 5x = 18
Subtract 4 from both sides
5x = 18 - 4
5x = 14
divide both sides by 5
x = 14/5
x = 2.8
81/x - 3 = 6
Add 3 to both sides
81/x = 6 + 3
81/x = 9
cross product
81 = 9x
divide both sides by 9
x = 81/9
x = 9
24 - 2x = 13
Subtract 24 from both sides
-2x = 13 - 24
-2x = -11
divide both sides by -2
x = -11/-2
x = 5.6
2x - 3 = 15
Add 3 to both sides
2x = 15 + 3
2x = 18
divide both sides by 2
x = 18/2
x = 9
3x + 2 = 25
Subtract 2 from both sides
3x = 25 - 2
3x = 23
divide both sides by 3
x = 23/3
x = 7.67
So therefore, the equations 81/x - 3 = 6, 2x - 3 = 15 has x = 9 as the solution.
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Your team win 16 medal at a competition. The medal are gold, ilver, and bronze in a ratio of 6 : 1 : 1. How many of each medal did your team win?
In a concrete mixture, the ratio of cement to sand is 1 to 4. At this ratio, how many shovelfuls of cement would be needed to be mixed with 80 shovelfuls of sand?
Answer: 20 shovelfuls of cement would be needed to be mixed with 80 shovelfuls of sand.
Step-by-step explanation:
First, we'd find out 4 divided by 1. This would equal 4.
Because we knew the amount of sand we had, we'd divide instead.
80 divided by 4
(If we had known the amount of cement we had, we would multiply)
This equals 20. This is how we get our answer, 20 to 80
Rule of x and / is.
If we use a × b, then it means that a is b times more than a and if we use a/b it means that we are making parts of a by the factors of b.
What is meant by multiplication and division?A mathematical expression that specifies the objects to be multiplied, known as a factor, produces a product. The other operations are multiplication, addition, and subtraction. When two natural numbers are divided with a remainder, or in the Euclidean method, the result is an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains after computing the quotient.
Rule of Division and Multiplication of Integers
Multiplication:
Rule 1: A positive integer and a negative integer cannot be added together.
Rule 2: A positive number is the result of two positive integers.
Rule 3: It states that the sum of two negative integers is positive.
Examples:
Rule 1: 1. (+4) x (-2) = -8 2. (-2) x (+5) = -10
Rule 2: 1. (+6) x (+8) = +48 2. (+6) x (+2) = +12
Rule 3: 1. (-6) x (-8) Equals +48 2. (-2) x (-4) = +8
Division:
Rule 1: A positive integer and a negative integer cannot be multiplied together.
Rule 2: A positive number is the quotient of two positive integers.
Rule 3: A positive number is the quotient of two negative integers.
Examples:
Rule 1: 1. (-8) / (+4) = -2 2. (-12) / (+6) = -2
Rule 2: 1. (+6) / (-3) = -2 2. (+24) / (-6) = -4
Rule 3. 1. (+9) / (+3) = +3 2. (+16) / (+4) = +4
Rule 4: 1. (-6) / (-2) = +3 2. (-42) / (-7) = +6
This is the summary of multiplication and division rules.
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Which of the following best describes the solution to the equation below?
9x + 5 = 9x + 5
Answer:
x is undefined
Step-by-step explanation:
Mario is setting up a new tent during a camping trip the tech game was 7 feet of rope the instructions are to use 34.5. Inches of rope to tie a tarp on top of the tack then the remaining rope should be cut into 8 1/4 in section 2 times the 10th two steaks in the ground Mario will use all the rope as instructed right and solve an equation to determine the number of 8 1/4 inch sections of Mario can come from the rope
If Mario will use all the rope as instructed right the number of 8 1/4 inch sections of Mario that can come from the rope is: 6.
How to find the inches?First step is to convert the 7 feet rope to inches
7 feet robes = 84 inches
Second step is to find the inches of rope left
Inches of rope left =84 inches - 34.5 inches
Inches of rope left = 49.5 inches
Now let find the number of 8 1/4 inch sections
Number of 8 1/4 inch sections =49.5 / 8.25
Number of 8 1/4 inch sections =6
Therefore 6 is the number of 8 1/4 inch sections .
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Riley has $200 she spends 60 on a video game what percent of her money does Riley spend?
Answer:
30%
Step-by-step explanation:
60/200 = 3/10 = 30%
three different methods for assembling a product were proposed by an industrial engineer. to investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 10 workers. the number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. the following results were obtained: sst
The p-value is found to be 0.0006 by using the f-ratio.
Given that ,
SST = 10, 800 , SSTR = 4560
Sum of Square error SSE = SST- SSTR = 10800- 4560
SSE = 6240
df for treatment K= 1, where K are the level of treatment and given that K=3.
df treatment = k-1 = 3 - 1 = 2.
df error = n-k = 30- 3=27.
df total = n- 1 = 30 - 1= 29 .
Mean Square for treatment = SSTR / If treatment
=4560/ 2 = 2280
MSTR = 2280
MSE = SSE/ df error = 6240/27 = 231.11
F-ratio = MSTR/ MSE = 2280 / 231.11
= 9.8654 -=9.87 ( rounded to 2 decimal )
F ratio = 9.87
By using F-table the value of P-value in
F = 9.87 , and df1 = 2, df2=27 , with Significance level =0.05 , then the value is
P-value = 0.0006 .
Therefore, The p-value is 0.0006
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Estimate 76.94 - 44.478 by first rounding each number to the nearest whole number.
Estimating 76.94 - 44.478 by first rounding each number to the nearest whole number gives 33
How to estimate the subtraction problemRounding to the nearest whole numbers the figures are written s follows
rounding to the nearest whole is achieved by checking the number following the decimal.
If the number is up to 5 a number is added to the last number before the decimal as in here
76.94 = 77 (to the nearest whole number)
/when the number following the decimal is less than 5 is number is neglected as in here
44.478 = 44 (to the nearest whole number)
The subtraction is continued as follows
= 77 - 44
= 33
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The equation 5x + (–2y) = 8 relates the amount spent, y, to the number of picture frames purchased, x, after a discount for buying two or more frames is applied to the total cost of the frames. How much is the discount?
The equation for straight line can be used to plot it on the graph. The amount of discount is 4.
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
The given equation is as follows,
5x + (–2y) = 8
Here, x is the number of picture frames purchased after discount.
And, y is the total amount spent.
In order to find the discount, write the equation in terms of y as,
5x + (–2y) = 8
=> 2y = 5x - 8
=> y = 5 / 2 x - 4
The above equation can be plotted as a graph which is shown below,
It is found from the graph that slope is 5 / 2 which is the rate of per picture.
Since the frames are being purchased after the discount, from the above graph discount can be obtained as 4.
Hence, the discount on the picture frames is given by 4.
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03:Pretest
CR Algebra 1 A (GP) 22-23/3:Identifying and Using Properties
2. You roll a blue number cube and a green number cube. Find P a number less than 2 on the blue cube and an odd number on the green cube.
The probability P (a number less than 2 on the blue cube and odd number on the green cube) is 1/12.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
For the probability,
The sample space of a die is, S = {1,2,3,4,5,6}
The probability of getting a number less than 2 is P(x < 2) = 1/6
The probability of getting an odd number is P(Odd) = 3/6
The required probability is calculated as:
P = 1/6 * 3/6
P = 1/12
Hence, the value of P (a number less than 2 on the blue cube and odd number on the green cube) is 1/12.
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You decide to buy a car that costs $19,000. You've heard that the car may
depreciate at a rate of 14% per year. At that rate, what will the car be worth
in six years?
Answer:
$7,686.77744
Step-by-step explanation:
19000-14%=16340
16340-14%=14052.4
14052.4-14%=12085.064
12085.064-14%=10393.155
10393.155-14%=8938.1133
8938.1133-14%=7686.77744
In triangle ABC, which side is the longest if these are the measures of the angles?
mzA= 60°, mzB = (3x - 2)°, mzC = (2x + 7)°
Applying the triangle sum theorem and the angle-side relationship, the longest side of triangle ABC is: side AC.
What is the Triangle Sum Theorem?The triangle sum theorem states that if we add all three interior angles of a triangle, the sum we get would be equal to 180 degrees.
What is the Angle-Side Relationship of a Triangle?The angle-side relationship of a triangle explains that the longest side of a triangle is always opposite to its largest angle, the medium side is opposite to the medium angle, and the shortest side is to the smallest angle of the triangle.
Given that triangle ABC has the following angle measures:
m∠A = 60°
m∠B = (3x - 2)°
m∠C = (2x + 7)°
Therefore:
m∠A + m∠B + m∠C = 180
Substitute:
60° + (3x - 2)° + (2x + 7)° = 180
60 + 3x - 2 + 2x + 7 = 180
Combine like terms:
65 + 5x = 180
5x = 180 - 65
5x = 115
x = 23
Find the measure of each of the angles by plugging in the value of x:
m∠B = (3x - 2)° = 3(23) - 2 = 67°
m∠C = (2x + 7)° = 2(23) + 7 = 53°
The largest angle is m∠B = 67°.
AC is opposite to angle B, therefore, AC is the longest side of the triangle.
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A supervisor records the repair cost for 17 randomly selected TVs. A sample mean of $94.57 and standard deviation of $20.65 are subsequently computed.
Determine the 80 % confidence interval for the mean repair cost for the TVs. Assume the population is approximately normal.
Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
The 80 % confidence interval for the mean repair cost for the TVs will be [87.873,101.266] and the critical value that should be used in constructing the confidence interval is ±1.337 for 80% interval.
What is confidence interval?An area created using fixed-size samples of data from a population (sample space) that follows a particular probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability.
Here,
df = 17-1=16
critical value = ±1.337 for 80% interval
lower end value,
-1.337=(x-94.57)/[20.65/√17]
x = 87.87
higher end value,
1.337=(x-94.57)/[20.65/√17]
x = 101.27
hence, 80% interval:[87.87 101.27]
The range of values within which the mean repair cost for TVs falls within an 80% confidence interval is [87.873,101.266], and a critical value of ±1.337 should be used to construct the confidence interval.
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through: (-4, 1) and (1, -3) how do u write the point slope form of the equation of the line through the given points ?
Answer:
through: (-4, 1) and (1, -3) how do u write the point slope form of the equation of the line through the given points ?
Step-by-step explanation:
to find slope you do delta y over delta x meaning 3 - 1 over 1 - (-4) you get 2/5 that is slope then you do to find b you take one of the points and you plug in for y = mx + b doesn't matter which one so -3 = 2/5 (1) + b
-3 = 2/5 + b
subtract 2/5 from both sides you get
-17/5 = b
so the equation is
y = 2/5x - 17/5
Describe the sequence of transformation that maps quadrilateral ABCD onto quadrilateral A'B'C'D'.
The sequence of transformation that maps quadrilateral ABCD onto quadrilateral A'B'C'D' is A'(3,-1) , B'(3,2), C'(4,3) and D'(4,0)
From the graph:
A(-4,5) , B(2,5) , C(4,3) ,D(-2,3)
transformations:
A'(-4+7,5-6)
= A'(3,-1)
B'(2+1,5-3)
= B'(3,2)
C'(4,3)
D'(-2+6,3-3)
= D'(4,0)
Therefore the sequence of transformation that maps quadrilateral ABCD onto quadrilateral A'B'C'D' is A'(3,-1) , B'(3,2), C'(4,3) and D'(4,0).
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Hey! i need help please!
The expression [tex]\sqrt[5]{36\cdot t^6\cdot w^{17}}[/tex] in simplified radical form obtained by using the laws of indices is presented as follows;
[tex]2\cdot t \cdot w^3\times t^{\frac{1}{5} }\cdot w^\frac{2}{5} = 2\cdot t \cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]
What are the laws of indices?The laws of indices are a set of rules that can be used to simplify expressions of variables and numbers that consists of powers that have the same base.
The expression is; [tex]\sqrt[5]{36\cdot t^6\cdot w^{17}}[/tex]
The laws of indices which can be used to evaluate the expression includes;
xᵃ × xᵇ = xᵃ⁺ⁿxᵃ ÷ xᵇ = xᵃ⁻ᵇ(xᵃ)ⁿ = [tex]x^{a\times b}[/tex]x⁻ⁿ = 1/xⁿx⁰ = 1[tex]x^\frac{n}{m} =\sqrt[m]{x^n}[/tex]Expressing the index in terms of 5, we get;
[tex]\sqrt[5]{32\cdot t^6\cdot w^{17}} = \sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2}[/tex]
[tex]\sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2} = 2\cdot t\cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]
The expression, [tex]\sqrt[5]{36\cdot t^6\cdot w^{17}}[/tex] in the simplified form is [tex]2\cdot t\cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]
A second method evaluating the expression is presented as follows;
[tex]\sqrt[5]{32\cdot t^6\cdot w^{17}} = \sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2}[/tex]
[tex]\sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2} = 2^\frac{5}{5} \cdot t^\frac{5}{5} \times t\cdot w^{\frac{15}{3} } \times w^\frac{2}{5}[/tex]
[tex]2^\frac{5}{5} \cdot t^\frac{5}{5} \times t^{\frac{1}{5} }\cdot w^{\frac{15}{3} } \times w^\frac{2}{5} = 2\cdot t \cdot w^3\times t^{\frac{1}{5} }\cdot w^\frac{2}{5}[/tex]
[tex]2\cdot t \cdot w^3\times t^{\frac{1}{5} }\cdot w^\frac{2}{5} = 2\cdot t \cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]
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what are the solutions?
sandeep visited green glen apple orchard yesterday. he picked a basket of fresh apples in the field. he also got 3 pounds of pre-picked apples at the farm stand because they were overripe and perfect for making applesauce. the farm charges $4 a pound for apples, regardless of whether they're fresh or pre-picked. sandeep paid $30 in all. which equation can you use to find f, the number of pounds of fresh apples sandeep picked? how many pounds of fresh apples did sandeep pick? write your answer as a whole number or a decimal.
Sandeep picked up 4.5 pounds of fresh apples from the field
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the standard form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.
Pounds of pre-picked apples picked up by Sandeep = 3 pounds
Charges per pound = $4
The total amount paid by Sandeep = $30
Let x be the pounds of fresh apples picked up by Sandeep
In the formulation of the equation we get the following:
Pounds of pre-picked apples*Charges per pound + Pounds of fresh apple picked*Charges per pound = Total amount paid by Sandeep
= 3*4 + x*4 = 30
12 +4x = 30
4x = 18
x = 4.5
So, fresh apples = 4.5 pounds
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A line has a slope of 2 and passes through the point (1, 5). What
is its equation in slope-intercept form?
Answer:
Y= 2x+3
Step-by-step explanation:
Slope = (y-y1)/(x-x1)
2= (y-5)/(x-1)
Cross multiply
Y-5= 2x-2
Collect like terms
Y= 2x+3
The square has an area of
196. It contains two
overlapping squares; the larger
of these squares has an area 4
times that of the smaller and the area of their
overlap is 1. What is the total area of the
shaded regions?
The total area of the shaded regions is 72 unit sq.
What is the area of a square?The area of a square can be calculated as the square of the sides of a given figure.
The area of a square = side x side
Given that square has an area of 196.
The region contains two overlapping squares that is the larger of these squares has an area 4 times that of the smaller and the area of their overlap is 1.
We can come up with equations as;
Since the area of their overlap is 1 then the side length is 1 unit.
Let the length of the smaller square is x.
The length of the larger square is 2x.
Therefore,
x + 2x - 1 = 3x - 1
Thus, 3x - 1 = 14
x = 5
The area of larger square = 100
The smaller one is 25
The area of shaded region;
196 - 124 = 72.
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a certain machine can process 6,000 letters in 1 hour. at this rate, how many letters can the machine process in 1/12 hour?
Calculate the quotient below and give your answer in scientific notation.
180
9 × 10^-5
=?
It take the speed of 299 m to travel 30 cm .
What is speed?
Speed is what it means. the speed at which an object's position changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed only has a direction and no magnitude, it is a scalar quantity.
Let us convert cm to m for distances
C = 2.998× 10^8 ms
The relationship between distance, speed, and time is
T =1 ×10^6/8
Because in this case you are being asked how long or time it takes, make it the subject.
Rounding the quotient produces.
Adjust it again to fit the scientific notation.
The result is -
d= c×t
d=2.998×10^8 m/s 10^6 m/s
d=2.998
As a mathematical expression, the time taken for light is 2.998
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