Answer:
The ball lands 18 feet from where it is kicked.
Step-by-step explanation:
Given : The path of a ball kicked from the ground can be modeled by the equation [tex]y=-\frac{1}{3}(x-3)(x-21)[/tex], where x and y are measured in feet. The x-axis represents the ground.
To find : How far does the ball land from where it is kicked?
Solution :
According to question,
The value of y is zero as it is kicked from ground.
So, [tex]0=-\frac{1}{3}(x-3)(x-21)[/tex]
Applying zero product property,
[tex]a\cdot b\cdot c=0\Rightarrow a=0\text{ or }b=0\text{ or }c=0[/tex]
i.e. [tex]-\frac{1}{3}\cdot (x-3)\cdot (x-21)=0[/tex]
[tex]x-3=0[/tex]
[tex]\Rightarrow x=3[/tex]
[tex]\text{ or }x-21=0[/tex]
[tex]\Rightarrow x=21[/tex]
The distance the ball land from where it is kicked is d=21-3=18.
Therefore, the ball lands 18 feet from where it is kicked.
The ball lands 18 feet from where it is kicked.
To find out how far the ball lands from where it is kicked, we need to determine the horizontal distance traveled by the ball when it hits the ground again. The x-axis represents the ground, so we are looking for the x-coordinate of the point where the ball lands, which is when y = 0.
Given the equation of the path of the ball:
[tex]\[ y = -\frac{1}{3}(x - 3)(x - 21) \][/tex]
We set y to 0 to find the x-coordinates where the ball touches the ground:
[tex]\[ 0 = -\frac{1}{3}(x - 3)(x - 21) \][/tex]
This equation can be factored to:
[tex]\[ 0 = (x - 3)(x - 21) \][/tex]
Setting each factor equal to zero gives us two solutions for x:
[tex]\[ x - 3 = 0 \quad \text{or} \quad x - 21 = 0 \][/tex]
[tex]\[ x = 3 \quad \text{or} \quad x = 21 \][/tex]
These solutions represent the x-coordinates where the ball is kicked (x = 3) and where it lands (x = 21). To find the distance between these two points, we subtract the smaller x-coordinate from the larger one:
[tex]\[ \text{Distance} = 21 - 3 = 18 \text{ feet} \][/tex]
However, since the ball is kicked from the ground and lands back on the ground, the distance it travels horizontally is the absolute value of the difference between the two x-coordinates:
[tex]\[ \text{Horizontal distance} = |21 - 3| = |18| = 18 \text{ feet} \][/tex]
Please help. I'll mark you as brainliest if answered correctly. :)
Two complex numbers are represented by c + di and e-fi, where c, d, e, and f are positive real numbers. In what two quadrants may the product of these complex numbers lie? Explain your answer in complete sentences.
Answer:
What are the quadrants? if the quadrants are c,d,e, and f then it would be c and d because both of the numbers lie on a y complex.
Step-by-step explanation:
⭐ Answered by Kash ʕ •㉨• ʔ⭐
⭐ Brainliest would be appreciated!⭐
⭐ If you have questions, leave a comment, I'm happy to help! ⭐
Convert each degree measure into radians.
1) -290°
Answer:
-290/180 × pi
-29pi/18
Or, -5.06
A medication states that the odds of having an allergic reaction are 1 in 50. What is that probability states as a percent?
1/5
1/10
1/20
1/500
As a percent, the odds of having an allergic reaction would be 2%.
This is because 1 in 50 of a chance, is equal to 1/50, and to make this a percent out of 100, just multiply both parts of the fraction by 2.
None of the choices equal 1/50, so let's just make it a percentage anyway.
1/50 ---> 0.02
0.02 ---> 2%
The answer is 2%, or 1/50 as a fraction.
WILL MARK BRAINLIEST
Each of the college students shown below has been chosen to represent their club on campus. One of the students will be selected at random to attend a special dinner with the president of the college.
Enter all fractions in reduced form.
A. Use the picture to complete the following table.
Long Sleeves Short Sleeves Rolled-up Sleeves
Male
Female
B. What is the probability that the student selected will be a female with long sleeves?
C. What is the probability that the student selected will be a male with rolled-up sleeves?
B. Probability of long sleeve female is zero.
C. Probability of rolled-up male is 1/4.
Step-by-step explanation:
A. The table from the picture :
Long Sleeves Short Sleeves Rolled-up Sleeves
Male 3 0 2
Female 0 3 0
B. The probability that the student selected will be a female with long sleeves :
From the table,
It is determined that no female are with long sleeve.
So, the probability of choosing female with long sleeve is 0.
C. The probability that the student selected will be a male with rolled-up sleeves :
From the table,
The number of males with rolled-up sleeves = 2
Total number of students = 8
P(rolled-up male) = 2/8 = 1/4.
The probability of selecting a female with long sleeves is 0, and the probability of selecting a male with rolled-up sleeves is 1/4.
Let's first complete the table...
1. Long Sleeves:
Male: 3Female: 02. Short Sleeves:
Male: 0Female: 33. Rolled-up Sleeves:
Male: 2Female: 0Probability Calculations
Total number of students = 3 (Male, Long Sleeves) + 0 (Female, Long Sleeves) + 0 (Male, Short Sleeves) + 3 (Female, Short Sleeves) + 2 (Male, Rolled-up Sleeves) + 0 (Female, Rolled-up Sleeves) = 8.
Probability of Selecting a Female with Long Sleeves
P(Female with Long Sleeves) = Number of Females with Long Sleeves / Total Students = 0/8 = 0.
Probability of Selecting a Male with Rolled-up Sleeves
P(Male with Rolled-up Sleeves) = Number of Males with Rolled-up Sleeves / Total Students = 2/8 = 1/4.
Therefore, the probability of selecting a female with long sleeves is 0, and the probability of selecting a male with rolled-up sleeves is 1/4.
Complete question: Each of the college students shown below has been chosen to represent their club on campus. One of the students will be selected at random to attend a special dinner with the president of the college.
Enter all fractions in reduced form.
A. Use the picture to complete the following table.
Long Sleeves Short Sleeves Rolled-up Sleeves
Male 3 0 2
Female 0 3 0
B. What is the probability that the student selected will be a female with long sleeves?
C. What is the probability that the student selected will be a male with rolled-up sleeves?
17. (-3, y) and (1, -7); m = -4
y-y1=m(x-x1) where (x1, y1)=(1, -7)
y+7=-4(x-1)
y+7=-4x+4
y+7=(-4x+4)*4
y+7=-x+16
y=-x+9
-----------------
y=9−x
y−9=−x
−y+9=x
9−y=x
x=9−y
-----------------
x=9−y
y*x=9 put 1 in for x
y=9
The value of [y] in the coordinate (-3, y) through which the line passes is 9 units.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
Where -
m is the slope of the line.
c is the y - intercept
Given is a line that passes through the points (-3, y) and (1, -7). The slope of this line is m = -4.
We can write from the above data -
The coordinates through which the line passes are → (-3, y) and (1, -7)
Now, the general equation of line -
y = mx + c
So -
- 7 = -4 x 1 + c
- 7 = -4 x 1 + c
- 7 = - 4 + c
c = - 7 + 4
c = - 3
Therefore, we can write, for coordinate (-3, y) as -
y = -4 x -3 - 3
y = 12 - 3
y = 9
The value of [y] will be 9 units.
Therefore, the value of [y] in the coordinate (-3, y) is 9 units.
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The equation of a parabola is y=x^2-10x+27. Write the equation in vertex form
Answer:
[tex]\large \boxed{y = (x - 5)^{2} + 2 }[/tex]
Step-by-step explanation:
y = x² - 10x + 27
y = ax² + bx + c
This is the general form of the equation for a parabola.
We must convert it to the vertex form
y = (x - h)² + k, where (h,k) are the coordinates of the vertex.
We can do this by completing the square.
[tex]\begin{array}{rcll}y & = & x^{2} - 10x + 27 & \\y - 27 & = & x^{2} - 10x & \text{Subtracted 27 from each side}\\y - 27&= & x^{2} - 10x + 25 - 25 & \text{Added and subtracted (b/2)}^{2}\\y - 27&= & (x - 5)^{2} - 25 & \text{Wrote the first three terms as the square of a binomial}\\y& = & \mathbf{(x - 5)^{2} + 2} & \text{Added 27 to each side}\\\end{array}\\\text{The vertex form of the parabola is $\large \boxed{\mathbf{y = (x - 5)^{2} + 2 }}$}[/tex]The figure below shows that your parabola has its vertex at (5,2).
For problem 2, f(2) =
A. 8
B. 16
C. 124
Hello! Remember you have to write complete question in order to get good and exact answers. Here you haven't provided any function, so I'll help you providing this one:
[tex]f(x)=3x^2+5x-6[/tex]
So [tex]f(2)[/tex] means that you need to evaluate the function when [tex]x=2[/tex]. In other words:
[tex]f(2)=3(2)^2+5(2)-6 \\ \\ f(2)=3(4)+10-6 \\ \\ f(2)=12+12-6 \\ \\ \boxed{f(2)=16}[/tex]
In this context:
Correct option is B. 16
Simplify the expression.
6m +10 - 10m =
Which expression is equivalent to 8x - 2y + x + x?
4x
6x -2y
8x
10x - 2y
Answer:
Problem 1
6m + 10 - 10m
4m + 10
Answer: 4m + 10
Problem 2
8x - 2y + x + x
8x + 2x - 2y
10x - 2y
Answer: Option D, 10x - 2y
Linear equation 1+2x=5x+3
Answer:x=-2/3
Step-by-step explanation:
(5.2x10^-1)(1.5x10^-5)
Answer:
(10^-6) (5.2x1.5 )=10^-6 x 7.8 = 7.8 x10^-6
Step-by-step explanation:
0.000001 x7.8=0.0000078
Heather flipped a coin five times, and each time it came up heads. Heather flips the coin one more time. Which is the theoretical probability that it will come up tails?
Answer:
1/2
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
The prior flips have no influence on the outcome of the 6th flip. its still a 50-50 chance to flip tails
what is 4x + 3x if x=2
Answer:
14
Step-by-step explanation:
Step 1: Plug in 2 for x
4(2) + 3(2)
8 + 6
14
Answer: 14
Answer:
14
Step-by-step explanation:
[tex]4(2) + 3(2)[/tex]
[tex]8 + 6[/tex]
[tex]14[/tex]
PLEASE HELP ASAP!!
Three-fifths of the days last year were sunny. If there were 365 days in the year, Answer
of them were sunny.
Answer:219
Step-by-step explanation:
Write down the square number between 26 and 63 that is odd?
Ans is 49.
If we multiply 7*7 then we can get 49 as result.49 is the square number of 7.
HOPE THIS WILL HELP U..✌
The square number between 26 and 63 that is odd will be 49.
What is the number pattern?A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.
The number is between 26 and 63.
26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63
From the given numbers,
49 is the square number between 26 and 63 which is odd.
Here, 7 × 7 = 49
Therefore, the square number between 26 and 63 is 49
odd is 49 as 7 × 7 = 49.
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If 1/2 cup of fruit cocktail 13g of sugar, then 1 1/4 cup of fruit cocktail contains how many grams of sugar?
Answer: 32.5g of sugar
Step-by-step explanation:
if 1/2 cup of fruit cocktail is 13g of sugar then half of that, or 1/4 cup is going to be 6.5g of sugar. With that in mind, multiplying our 1/2 by 2 to give us one full cup of fruit cocktail will tell us that there is 26g of sugar in one cup. Adding our 1/4 cup to our whole cup will give us 32.5g of sugar in 1 1/4 cups of fruit cocktail.
Answer: There are 32.5g of sugar in 1 1/4 cup of fruit cocktail.
Step-by-step explanation:
13/2= 6.5
1/4 cups = 6.5g of sugar
6.5x5= 32.5g
Hope this helps!
A factory sells backpacks for $35 each. The cost to make 1 backpack is $15. In addition to the cost of making backpacks, the factory has operating expenses of $11,000 per week. The factory's goal is to make a profit of at least $7,800 per week. Write and solve an inequality that represents the number of backpacks, x, that need to be sold? *
Answer:9400 backpacks
[tex]\geq[/tex]Step-by-step explanation
since the number of packs to be sold in a is represented by x,
selling price for 1 week = 35x
cost price for 1 week = 15x
profit = 35x-15x = 20x
additional cost of production = 11,000
this implies that 20x - 11,000 [tex]\geq[/tex] 7800
20x - 11,000 [tex]\geq[/tex] 7,800
20x [tex]\geq[/tex] 7800+ 11000
20x [tex]\geq[/tex] 18,800
x [tex]\geq[/tex] 18800/2
x [tex]\geq[/tex] 9,400
at least 9,400 packs have to be sold each week to make a profit of $7800
When solving this system of equations by elimination, which could be the resulting equation when a variable has been eliminated?
3x - 2y = 10
5x + y = 4
Answer:
Step-by-step explanation:
3x-2y=10
5x+y=4
15x-10y=50
15x+3y=12
-13y=38
y=-38/13
Substitute for y
x=54/39
8 yo the power of 2 ÷4×(2+3)-9
Which linear equation represents the data given in the table?
A) y = 6x + 6
B) y = 2x + 6
C) y = 6x − 6
D) y = 2x − 6
Answer:
the equation is C: y=6x-6
Answer:
Step-by-step explanation:
(1,0) (2,6)
(6-0)/(2-1)
6/1= 6
y - 0 = 6(x -1)
y = 6x - 6
answer is c
Each notebook contains 60 sheets
try using photo math
I hope it helps
Help please like hurry!!
Answer: 36 square inches
Step-by-step explanation: The trapezoid is divided into three triangles.
The formula for the area of a triangle is 1/2(b*h). Replace the variables with the values in the drawing.
1/2(4*6)
= 1/2(24)
=12
There are 3 triangles, so multiply the area of 1 triangle (which is 12) by 3.
12*3
=36
Label the final answer.
36 square inches
What is (3x+2)+(−4x+4)
Answer:
-x + 6
Step-by-step explanation:
(3x + 2) + (-4x + 4)
Distribute + into the bracket (-4x + 4). When you do so, + sign becomes -
3x + 2 - 4x + 4
Rearrange the expression
3x - 4x + 2 + 4
-x + 6
solve the inequality
2r^2-13x+15<0
Answer:
x > 2r^2/13 + 15/13
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
x > 2r^2/13 + 15/13
Answer: [tex]\bold{\dfrac{3}{2}<x<5\quad \rightarrow \quad \text{Interval Notation}: \bigg(\dfrac{3}{2},5\bigg)}[/tex]
Step-by-step explanation:
First, factor the inequality and solve for x to find the zeros.
Then, choose test points on the outside of those values and between them.
Plug them in to determine which one(s) yield a negative (< 0).
2x² - 13x + 15 < 0
(2x - 3)(x - 5) < 0
2x - 3 = 0 and x - 5 = 0
x = 3/2 and x = 5
I choose the left test point of 0 (2(0) - 3) × (0 - 5) > 0 (+)
I choose the between test point of 2 (2(2) - 3) × (2 - 5) < 0 (-)
I choose the right test point of 6 (2(6) - 3) × (6 - 5) > 0 (+)
Illustration of Graph:
+ --- +
←----|----------o----------------|---------------o--------------|----→
0 3/2 2 5 6
Since the "between" test point is the only one that yielded a negative, then the solution is the values between 3/2 and 5.
What are the steps of adding and subtracting a fraction?
Step-by-step explanation: To add and subtract fractions with the same denominator, or bottom number, place the 2 fractions side by side. Add or subtract the numerators, or the top numbers, and write the result in a new fraction on the top. The bottom number of the answer will be the same as the denominator of the original fractions.
An international company has 12,700 employees in one country. If this represents 27.1% of the company's employees, how many employees does it have in total?
The international company has 46864 employees in total.
Step-by-step explanation:
Given that,
An international company has 12,700 employees in one country.
And, this 12,700 employees represents 27.1% of the company's employees.
Therefore, the total number of employees can be found by calculating the 100% of the employees.
Let us assume that the total number of the employees be 'x'.
From the x number of employees, 12,700 employees were 27.1%
Now, framing the above statement in the equation form to solve for x :
⇒ 27.1 % of x = 12700
⇒ (27.1 / 100) x = 12700
⇒ 0.271 x = 12700
⇒ x = 12700 / 0.271
⇒ x = 46863.5 (which is approximately 46864 employees)
Therefore, the total number of employees is 46864.
In a small U.S. city, the ratio of people to cars is approximately 1.85 : 1. If 12,100 people live in
the city, to the nearest 100 cars, approximately how many cars are in the city?
Answer:
[tex]6,500\ cars[/tex]
Step-by-step explanation:
Let
x ---> the number of people
y ---> the number of cars
we know that
The ratio of people to cars is approximately 1.85 : 1
so
[tex]\frac{x}{y}=\frac{1.85}{1}[/tex]
[tex]x=1.85y[/tex] -----> equation A
12,100 people live in the city
so
[tex]x=12,100[/tex]
substitute the value of x in the equation A
[tex]12,100=1.85y[/tex]
solve for y
[tex]y=6,540.54\ cars[/tex]
to the nearest 100 car
[tex]y=6,500\ cars[/tex]
Final answer:
To find the number of cars in the city, divide 12,100 by the ratio of people to cars (1.85:1), resulting in approximately 6,540.05 cars. Rounded to the nearest hundred, the city has about 6,500 cars.
Explanation:
The question is about finding the number of cars in a small U.S. city given the ratio of people to cars is approximately 1.85:1 and there are 12,100 people living in the city. To solve this, we divide the total number of people by the given ratio to find the approximate number of cars. Firstly, find the proportion of cars to people by taking the reciprocal of 1.85, which gives us approximately 0.5405. Then, multiply this proportion by the total population to estimate the number of cars.
Calculation:
Number of cars = Total population × Proportion of cars to people
Number of cars = 12,100 × 0.5405 ≈ 6,540.05
Rounded to the nearest hundred, the city has approximately 6,500 cars.
Brain and Zach went to village grille for lunch. Brian's lunch cost $4 less than 3 times Zach's. The total cost for lunch was $25.How much did each boy spend on lunch?
Answer:
The cost for Zach's lunch is 12, and for Brain's lunch it cost 8.
Step-by-step explanation:
Since, I am sorry, you can answer from here in out. ;)
Zach spent $6 on lunch and Brian spent $19 on lunch.
Explanation:To solve this problem, we need to create an equation based on the given information.
Let's assume Zach's lunch cost x dollars.
According to the problem, Brian's lunch cost $4 less than 3 times Zach's lunch, which can be expressed as 3x - 4 dollars.
The total cost for lunch was $25, so we can write the equation: x + (3x - 4) = 25.
Solving this equation, we find that Zach spent $6 on lunch and Brian spent $19 on lunch.
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Pleaseeee helppppp me
Answer:
Step-by-step explanation:
Good luck
4x - 5y = 14
If y = 2, what value of x satisfies the given equation?
A) 6
B) 8
C) 10
D) 24
Answer:
A
Step-by-step explanation:
Given
4x - 5y = 14 ← substitute y = 2 into the equation and solve for x
4x - 5(2) = 14, that is
4x - 10 = 14 ( add 10 to both sides )
4x = 24 ( divide both sides by 4 )
x = 6 → A
Rewrite the equation B - 7,536 = 2t as a function of t.
Answer:
B = 2t + 7,536
Step-by-step explanation:
B - 7,536 = 2t
Add 7,536 to both sides.
B = 2t + 7,536