Answer:
The ball will hit the ground in 2 seconds
Step-by-step explanation:
The formula for throwing a baseball in the air is represented by :
h = -16t² + 12t + 40
where h is the height of the ball and t is the time in seconds
Now we need to find after how many seconds will the ball hit the ground
When the ball hits the ground the height of the ball is 0
⇒ -16t² + 12t + 40 = 0
⇒ 4t - 3t - 10 = 0
⇒ 4t² - 8t + 5t - 10 = 0
⇒ 4t(t - 2) + 5(t - 2) = 0
⇒ t cannot be negative so t = 2
Hence, The ball will hit the ground in 2 seconds
The ball will hit the ground after 2 seconds.
The formula for the height of a thrown baseball is given by:
h = -16[tex]t^{2}[/tex] + 12t + 40
where h is the height (in feet) and t is the time (in seconds).
To find the time when the ball hits the ground, we need to determine when the height h is equal to zero:
0 = -16[tex]t^{2}[/tex] + 12t + 40
Solving this quadratic equation using the quadratic formula:
The quadratic formula is: t = (-b ± √(b² - 4ac)) / 2a
For our equation, a = -16, b = 12, and c = 40. Plugging these values in:
b² - 4ac = 12² - 4(-16)(40) = 144 + 2560 = 2704t = ( -12 ± √2704 ) / 2(-16)t = ( -12 ± 52 ) / -32t = ( -12 + 52 ) / -32 = 40 / -32 ≈ -1.25 (negative time, not a valid solution)t = ( -12 - 52 ) / -32 = -64 / -32 = 2Thus, the ball will hit the ground at t = 2 seconds.
Note that we ignore the negative time value as it doesn’t represent a meaningful physical solution.
Explain two ways you can use a number line to order the integers –3, +1, and –10.
Answer:
-10,-3,1
1,-3,-10
Step-by-step explanation:
We are given that integers are -3,+1 and -10
We have to explain two ways in which we can use a number line to order the given integers.
The two ways are
1.Arrange in increasing order:From least to greatest
2.Arrange in decreasing order: From greatest to least
We know that when we go left side of zero on a number line then the value decreases and when we go right side of zero then the value increases.
1.-10 is smallest integer in the given integers and 1 is a largest integer.
Therefore, -10,-3,1.
2.In decreasing order
1,-3,-10
Use equations and inequalities to solve the following word problems.
3. Max is selling boxes of chocolate for a school fundraiser. He sold 12 boxes and earned $84. If all of the boxes have the same cost, how much does each box cost?
4. Anne donates at least $120 per month to charity. She has 4 favorite charities and divides her donations equally among them. How much does Anne donate to each of her favorite charities per month?
To find the cost of each box, we solve an equation: 12x = 84. To find the amount Anne donates to each charity, we set up an inequality: y ≥ 120/4.
Explanation:To solve the word problems, we can use equations or inequalities depending on the situation.
Question 3:
We are given that Max sold 12 boxes and earned $84. Let's assume the cost of each box is x dollars. The equation representing the given information is 12x = 84. To find the value of x, we divide both sides of the equation by 12: x = 84 / 12 = 7 dollars. Therefore, each box costs $7.
Question 4:
Anne donates at least $120 per month and divides her donations equally among 4 favorite charities. Let's assume the amount Anne donates to each charity is y dollars. The inequality representing the given information is y ≥ 120/4 = 30. Therefore, Anne donates at least $30 to each of her favorite charities per month.
PLz help me
Derek and Susan each open interest-bearing accounts in a bank and put the same amount of money into their accounts. Derek's account earns simple interest. The balance, in dollars, in Derek's account after t years is represented by the function D.
D(t)=500(1+2.5t)
Susan's account earns interest at a lesser rate than Derek's account, but the interest is compounded annually. The balance, in dollars, in Susan's account after t years is represented by the function
S. S(t)=500(1+1.8)^t
Which statement is true?
A. At first Derek's account balance will be greater, but eventually Susan's account balance will be greater.
B. Derek's account balance will always be greater than Susan's account balance.
C. Susan's account balance will always be greater than Derek's account balance.
D. At first Susan's account balance will be greater, but eventually Derek's account balance will be greater.
Answer:
Option A.
Step-by-step explanation:
we have
Derek's account
[tex]D(t)=500(1+2.5t)[/tex]
Susan's account
[tex]S(t)=500(1+1.8)^t[/tex]
Using a graphing tool
see the attached figure
At first Derek's account balance will be greater, but eventually Susan's account balance will be greater
Juan earns a monthly salary of $3,200. Federal withholding is 14.1% of his gross pay. Juan has a total of $244.80 deducted for Social Security and Medicare. Find his net pay.
Given is :
Monthly salary of Juan = $3200
Federal withholding is 14.1 % of 3200 = [tex]\frac{14.1}{100}*3200= 451.20[/tex]
Deductions for social security and medicare = $244.80
So, total deductions of Juan are = [tex]451.20+244.80=696[/tex]
So, Juan's monthly net pay is= [tex]3200-696=2504[/tex]
= $2504
Juan's net pay is calculated by first determining the federal withholding from his monthly salary and then subtracting the deductions for Social Security and Medicare. His net pay comes out to be $2,504 after all deductions.
To find Juan's net pay after deductions and taxes from his monthly salary of $3,200, we must first calculate the amount withheld for federal taxes, then subtract the fixed amount deducted for Social Security and Medicare. Juan's federal withholding is 14.1% of his gross pay, so we calculate 14.1% of $3,200 to find the federal withholding. Next, we subtract the total deduction for Social Security and Medicare from his gross salary.
The calculation for federal withholding is: $3,200 × 14.1% = $451.20
Therefore, the total deduction is: $451.20 (federal withholding) + $244.80 (Social Security and Medicare) = $696.
To find his net pay, we subtract the total deduction from the gross salary:
Net Pay = Gross Salary - Total Deduction = $3,200 - $696 = $2,504
Juan's net pay after all deductions is $2,504.
50Points Plato Help!!
The number of teams who entered in a 3-on-3 charity basketbal ournament can be modeled by function T, where x is the number of years since the tournament first started. T(x)=4x+24
The entry fee paid by each team to enter the tounament can be modeled by tunction F, where x is the number of years since the tounament fist started.
F(x)=5x+45
Which function, R, best represents the total entry lees collected in the year since the tournament first started?
A.R(x)=20x^2+300x+1080
B.R(x)=20x^2+1080
C.R(x)=9x+69
D.R(x)=9x^2+29x+69
T(x) calculates the number of teams and F(x) calculates the entry fees.
To find the total entry fee, you would add the entry fee for each team together, so you need to add T(x) and F(x) together.
The answer would be C. R(x) = 9x +69
Answer:
T(x) calculates the number of teams and F(x) calculates the entry fees.
To find the total entry fee, you would add the entry fee for each team together, so you need to add T(x) and F(x) together.
The answer would be C. R(x) = 9x +69
The winter coat I was looking at in January has now been marked down by 40%. It was going to cost me $120 in the winter, but if I buy it now it will only cost me $ .
Answer:
$72
Step-by-step explanation:
✯Hello✯
↪ First you need to work out what 40% of 120 is and that is 48
↪ Its been marked down by 40% so we need to do 120-48
↪ That is 72
↪ The coat is $72
❤Gianna❤
PLEASE HELP ASAP!!!
let f(x) = 2x^2 + x - 3 and g(x) = x - 1
find (g/f)(x) and state its domain.
ANSWER
[tex]( \frac{g}{f} )(x) = \frac{1}{ 2x+3} [/tex]
The domain is:
[tex]x \ne1 \: or \: x \ne - \frac{3}{2}[/tex]
EXPLANATION
The given functions are:
[tex]f(x) = 2 {x}^{2} + x - 3[/tex]
and
[tex]g(x) = x - 1[/tex]
[tex]( \frac{g}{f} )(x) = \frac{g(x)}{f(x)} [/tex]
[tex]( \frac{g}{f} )(x) = \frac{x - 1}{2 {x}^{2} + x - 3 } [/tex]
Factor the quadratic trinomial in the denominator.
[tex]( \frac{g}{f} )(x) = \frac{x - 1}{2 {x}^{2} +3 x - 2x- 3 } [/tex]
[tex]( \frac{g}{f} )(x) = \frac{x - 1}{ x(2x+3) -1 (2x + 3 )} [/tex]
[tex]( \frac{g}{f} )(x) = \frac{x - 1}{ (2x+3) (x-1)} [/tex]
Cancel the common factors,
[tex]( \frac{g}{f} )(x) = \frac{1}{ 2x+3} \: where \: x \ne1 \: or \: x \ne- \frac{3}{2} [/tex]
You work for a dress maker and your boss sends you to the fabric store to buy blue fabric. She tells you to buy the best deal. What is the best deal on fabric? A) 20 yards for $30.00 B) 40 yards for $45.00 C) 50 yards for $70.00 D) 65 yards for $85.00
Answer:
B 40 yards for $45 is the best deal at $1.13 per yard
Step-by-step explanation:
Break it down by finding the unit price per yard (divide cost by yardage)
A. 30/20 = $1.50 per yard
B. 45/40 = $1.125 per yard
C. 70/50 = $1.40 per yard
D. 85/65 = $1.30 per yard
Answer:a
Step-by-step explanation:
Please help me out!!!!!
Answer:
[tex]\frac{c}{a+b}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = A(0, 0) and (x₂, y₂ ) = C(a +b, c)
m = [tex]\frac{c-0}{a+b-0}[/tex] = [tex]\frac{c}{a+b}[/tex]
Answer:
[tex]\large\boxed{\dfrac{c}{a+b}}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points A(0, 0) and C(a + b, c). Substitute:
[tex]m=\dfrac{c-0}{a+b-0}=\dfrac{c}{a+b}[/tex]
If 2.5 is a root of the equation 2x^2+5x−q=0, what are the possible values of q?
Answer:
q = -25[tex]10 +5 = \pm \sqrt{5^2-4*2*q} \\ 225 = 25-8q \\\\8q = -200 \rightarrow q = -\frac {200}8 = -25[/tex]
Step-by-step explanation:
Grab the generic solution of the equation. [tex]\frac 52 = \frac{-5 \pm \sqrt{5^2-4*2*q}}{2*2}[/tex]. Let's isolate the radical, and square both sides.[tex]10 +5 = \pm \sqrt{5^2-4*2*q} \\ 225 = 25-8q \\\\8q = -200 \rightarrow q = -\frac {200}8 = -25[/tex]
Answer:
since we know that x1=2.5
we can just just use vieta's theorem
x1+x2=-b/a
x1*x2=c/a
Simplify the equation √8^17
The answer is 8^8 * /8
Find the angle of elevation of the sun when a 24 foot tree casts a shadow of 36 feet
ANSWER
37°
EXPLANATION
The angle of elevation of the sun is the angle through which one has to raise the head to see the sun.
When a 24 feet tree casts a shadow of 36 feet, we can obtain a right triangle as shown in the diagram to help us calculate the angle of elevation of the sun.
Let x be the angle of elevation of the sun, then
[tex] \tan(x) = \frac{24}{36} [/tex]
[tex]x = \tan ^{ - 1} ( \frac{2}{3} ) = 37.433[/tex]
Hence, the angle of elevation of the sun is 37° to the nearest degree.
Parallel lines e and f are cut by transversal b.
e=(2x+10)
f=(3x-15)
What is the value of x?
1
5
25
37
Answer:
25
Step-by-step explanation:
Answer:
the answer is 25. hope this helps
Describe the solution to the inequality p>4
Answer:
P is greater than 4
Step-by-step explanation:
so P could be anything from 5 to infinity
Final answer:
The inequality p > 4 is satisfied by any real number greater than 4. The solution is represented visually by shading the number line to the right of the open circle at 4.
Explanation:
The solution to the inequality p > 4 is all real numbers greater than 4. In other words, for any number p that is greater than 4, the inequality will hold true.
To visualize this solution on a number line, you would draw an open circle at 4 and shade all numbers to the right of 4, indicating that all those numbers are part of the solution set.
This is a basic concept in algebra, focusing on understanding and solving inequalities. The solution does not include the number 4 itself because the inequality is strictly greater than (not greater than or equal to).
Evaluate the log without a calculator ( Show your work )
[tex]log_{25} \frac{1}{5}[/tex]
Answer:
[tex]\log_{25}(\frac{1}{5})=-\frac{1}{2}[/tex]
Step-by-step explanation:
Let
[tex]\log_{25}(\frac{1}{5})=x[/tex]
We rewrite as an exponential equation to obtain;
[tex]\frac{1}{5}=25^x[/tex]
We rewrite both sides of the equation as an index number to base 5.
[tex]5^{-1}=5^{2x}[/tex]
Since the bases are the same, we equate the exponents to obtain;
[tex]-1=2x[/tex]
Divide both sides by 2;
[tex]x=-\frac{1}{2}[/tex]
Solve for x. 1/2x = -9
Answer:-18
Step-by-step explanation:x in (-oo:+oo)
(1/2)*x = -9 // + 9
(1/2)*x+9 = 0
1/2*x+9 = 0 // - 9
1/2*x = -9 // : 1/2
x = -9/1/2
x = -18
x = -18
brainliest please
What's is 5x2/3
A. 3 1/3
B 3 2/5
C 5 2/3
D 10/15
Answer:
The answer is A. 3 1/3
Step-by-step explanation:
Simplify:
10/3
Then, convert to a mixed fraction:
3 1/3
Hope this helped.
The mathematical expression 5x2/3 = 15/3 x 2/3 = 30/9 = 5 2/3.
Option C is correct.
How do we calculate?an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Step 1: Simplify 5x2/3
5x2/3 = (5 x 2)/3
5x2/3 = 10/3
Step 2: Simplify 10/3
10/3 = 3 + 2/3
10/3 = 5 2/3
An expression in math can also be described as a statement having minimum of two numbers, or variables, or both and an operator connecting them.
Therefore, the correct answer is C.
Learn more about mathematical expression at:
https://brainly.com/question/1859113
#SPJ6
Olympic volleyball player Bev Oden averaged 3.42 "kills" (spikes that end a rally) per game. Predict her number of kills in a 5 game match.
Answer: 17.1
Step-by-step explanation:
If she averages 3.42 kills per game, she should average that for each of the 5 games. You need to multiply 3.42 times 5 for the total of 5 games.
3.42 x 5 = 17,1
Bev Oden, achieve approximately 17 kills in a 5 game match .
To predict the number of kills Bev Oden will achieve in a 5 game match, we can use her average kills per game to make the calculation.
Given that Bev Oden averages 3.42 kills per game, we simply multiply her average by the number of games in the match.
Step-by-step calculation:
Average kills per game: 3.42Number of games: 5Total kills = 3.42 kills/game x 5 games = 17.1 killsTherefore, Bev Oden is predicted to achieve approximately 17 kills in a 5 game match.
Manjeet made a pizza for his family using their four favorite toppings - pepperoni, mushrooms, onions and olives. He put twice as many onions as pepperoni and half as many mushrooms as olives. If there are 39 individual toppings on the pizza how many of each topping did he use? How many different combinations can you come up with?
Answer:
Let
x = the number of pepperoni added to the pizza.
y = the number of mushrooms added to the pizza.
z = the number of onions added to the pizza.
u = the number of olives added to the pizza.
Twice as many onions as pepperoni
z = 2*x
Half as many mushrooms as olives
y = u/2
There are 39 individual toppings on the pizza
x + y + z + u = 39
We are dealing with a system of equation with 4 unknowns and only three equations.
2*x - z = 0
y - u/2 = 0
x + y + z + u = 39
This means that there are an infinite number of solutions for your problem
For example, here is one solution
x = 1
z = 2
1 + y + 2 + (2y) = 39
3y = 36
y = 12
u = 24
Find f^1(x) for f(x)= -3x+2 and state whether or not it is a function.
a : f^1(x)= -1/3x +2/3 ; function
b : f^1(x)= 1/3x -2/3 ; not a function
c : f^1(x)= 1/3x +2/3 ; function
d : f^1(x)= -1/3x -2/3 ; function
Answer:
A
Step-by-step explanation:
f^-1(x) is a common notation for the inverse of the function. An inverse of a function is a reflection over the line y=x. This results in the points (x,y) of the function becoming (y,x) for the inverse. Algebraically you find the inverse by switching the location of y and x in the equation of the function and solving.
y = -3x + 2
x = -3y + 2
x - 2 = -3y
-(x-2)/3 = y
-1/3x + 2/3 = y
The inverse of the function is a linear function because it follows the form y = mx+b for its equation. All lines are functions. The inverse is a function.
Answer: a : f^1(x)= -1/3x +2/3 ; function
Step-by-step explanation:
Kelie randomly chooses a number 1 to 10 what is the probability she chooses a number less than 3
Answer:
1/5
Step-by-step explanation:
She has 2 outcomes that satisfy a number less than 3. She can choose either 1, or 2.
There are 10 possible choices, so the probability is
2/10 = 1/5
Answer: [tex]=\dfrac{1}{5}[/tex]
Step-by-step explanation:
Given : The total numbers from which Kelie randomly chooses a number = 10
The numbers less than 3 = 1,2
Now, the probability she chooses a number less than 3 will be :-
[tex]=\dfrac{\text{Numbers less than 3}}{\text{Total numbers}}\\\\=\dfrac{2}{10}\\\\=\dfrac{1}{5}[/tex]
Hence, the probability she chooses a number less than 3 [tex]=\dfrac{1}{5}[/tex]
I'm thinking of a mystery number. Seventeen more than five times the number is equal to four times the number, decreased by nine. What's my mystery number? Good luck!
[tex]5x + 17 = 4x - 9\Leftrightarrow x = - 26[/tex]
The mystery number satisfying the equation 5x + 17 = 4x - 9 is -26. To find this, we subtract 4x and then 17 from both sides of the equation.
The student is asking to find the mystery number that satisfies the equation: 17 more than five times the number is equal to four times the number, decreased by nine.
Let's represent the mystery number as x. The equation based on the given statement is then:
5x + 17 = 4x - 9.
To solve for x, we need to isolate the variable. Here's the step-by-step solution:
Subtract 4x from both sides of the equation: 5x - 4x + 17 = 4x - 4x - 9, which simplifies to x + 17 = -9.Subtract 17 from both sides of the equation: x + 17 - 17 = -9 - 17, which simplifies to x = -26.Therefore, the mystery number is -26.
A figure is translated horizontally 4 units. Which drawing shows a correct translation? A B C D
Answer:
The Answer is C!! (With two L's pointing right)
Step-by-step explanation:
Answer:
Give the other person brainliest they deserve it!
Step-by-step explanation:
Given 1+tan x/ 1+ cot x= 2 , find a numerical value of one trigonometric function of x
[tex]b. \tan(x) = 2[/tex]
Academy Sports buys baseball bats for $40. If they increase the price 75%, how much will the bats cost?
Answer:
$70
Step-by-step explanation:
$40x.75=30
30+40=$70
Juan threw a dart onto the board. Which of the following is most likely? Answers in pic
Answer:
I think its at least 2, but im not so sure
Answer:
At least 2 points
Step-by-step explanation:
If he throws the dart onto the board, the lowest possible score he can get is two, and if he hits the 4 or 8 point circles, it is still at least 2.
A third grade party two groups each had their own pizza each had their own pizza the blue group ate 7-8 the green group ate 2-8 pizza which group ate more of their pizza
Answer:
The blue group ate 5/8 more pizza than the red group.
Step-by-step explanation:
7/8 - 2/8 = 5/8
Answer:
So what I had yesterday was yogurt, turkey, cheese, honey wheat bread, sandwich and eggs and bacon and biscuits
Yogurt=dairy
turkey=protien
cheese=dairy
bread=garin
eggs=protien
bacon=protien
bicuits=grain
milk=dairy
Step-by-step explanation:
Ella and her brother are driving between 2 cities that are 330 miles apart at a rate of 55 mph.How long will it take them to make the trip
Answer:
6 hours
Step-by-step explanation:
1. Divide the total miles (330) by the speed (55)
330/55 = 6
A circle is divided into 20 equal parts. What is the angle measure of three of those left parts?
Answer:
54
Step-by-step explanation:
A circle is 360 degrees
We divide it into 20 parts
360/20 = 18
Each part is 18 degrees
We want the angle means of 3 of the parts
3*18 = 54
Three of the parts measures 54 degrees
Tommy has a pet monkey every day his monkey eats 4 apples in the morning. The monkey also eats two bananas for every banana that Tommy eats. Write an equation to describe this situation where X is the number bananas Tommy eats and y is the total number of fruits the monkey eats
Answer:X*2+4=y
Step-by-step explanation:Ok, so, we can pull four different points from this equation.
The monkey eats 4 apples each morning
The monkey eats 2 bananas for each 1 Tommy has
The number of bananas Tommy eats is marked as X
The number of fruits the monkey eats is marked as y
Let's start with Tommy.
X
Tommy eats X amount of bananas. Next the monkey.
X=y
The monkey eats y amount of bananas, but if you notice, he eats double to amount Tommy eats. So let's double Tommy's bananas.
X*2=y
You'll also notice, the monkey eats four apples everyday. Now, we're looking for the monkey's FRUIT intake, where as we're only looking at Tommy's BANANA intake. So, let's add that to the equation.
X*2+4=y
And there's the equation right there.