The ball when thrown at initial velocity of 40ft/sec is 10 ft above the moon's surface after approximately 0.09 seconds and 14.73 seconds .
When an item is moving, its velocity is the rate at which its direction is changing as seen from a certain point of view and as measured by a specific unit of time.
The given equation for the height of the ball from the surface after t seconds is given by :
s=-2.7t²+40t+6.5
The initial velocity is 40ft/second.
the height of the ball is 10 ft from the surface.
therefore: s=10
Substituting the value in the equation we get:
10=-2.7t²+40t+6.5
or, -2.7t²+40t-3.5=0
This is a quadratic equation in t . Solving by the quadratic formula we get:
We know that for a equation: ax²+bx+c=0
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}[/tex]
So using the above equation we get:
[tex]{\displaystyle x={\frac {-40\pm {\sqrt {40^{2}-4(-2.7)(-3.5)}}}{2(-2.7)}}}[/tex]
either x=14.726... or x= 0.088...
Therefore x≈14.73 and x≈ 0.09
So the ball will be 10 ft above the moon's surface after approximately 0.09 seconds or 14.73 seconds .
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Evaluate the problem
Answer:
400
Step-by-step explanation:
Change the 16 and the 64 in the numerator to exponents
2^4 x 10^2 x 4^3/2^4 x 4^2
Simplify
10^2 x 4
100 x 4
evaluate -4 - 5+4+(-5)
Colton bought some strings of beads. The number of strings was 10 more than the number of beads on each string. There were 119 beads in all. How many strings of beads did Colton buy?
Answer: 17 strings
Step-by-step explanation:
let the number of strings be a
let the number of beads on each string be b
a − b = 10 (first equation)
a × b = 119 (second equation)
From the first equation:
a = 10 + b
substitute first equation into second equation
b × (10 + b) = 119
10b + b² − 119 = 0
b = 7 or b = -17 reject -17
a − 7 = 10
a = 17
Last year, Suzie's salary was $76,000. This year, she is getting a 8% raise. What will her new salary be?
[tex]76000\times1.08=\boxed{82,080}[/tex]
Answer:
82,080
Step-by-step explanation:
To increase a number by it's percentage, you must first extract what 8% of 76,000 is (6080). Then, you must add the original number to what is 8% of it, to get 82,080, and that, is the final answer.
During a person's commute to school, she spends 12 minutes driving 35 mph and 3 minutes stopped at red lights. What is the person's average
speed during her commute?
Step 1 of 2: First, find the distance of her commute.
The average speed of person during her commute is 28 miles/ hour.
What do you mean by average speed ?
The entire distance that an object travels in a given amount of time is defined as the average speed for that object.
Total time of driving is 12 minutes.
This can be written as hours which will be :
= 12 / 60
= 1/5 hour
Time of stopping at red lights is 3 minutes and speed is 35 miles per hour.
So , the total distance using the formula will be :
Total distance = Speed × time
Here , the time taken will be equal to :
= [(12 + 3) / 60]
= 15 / 60
= 1/4 hour
So ;
Total distance = 35 × (1/4 hour)
Total distance = 7 miles
And the average speed will be ;
Average speed = Distance / Time
or
Average speed = 7 miles / (1/4) hour
Average speed = 7 × 4 miles/hour
Average speed = 28 miles / hour
Therefore , the average speed of person during her commute is 28 miles/ hour.
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Please help what is 8.9 divided
by 0.4
Answer:
8.9 ÷ 0.4 = 22.25
so the answer is 22.25
hope this helps
Answer:
22.25 is your answer
Step-by-st
What is the justification for each step in the solution of the equation?
23x−13=2(x+2)
23x−13=2(x+2) Given
2x−1=6(x+2)
2x−1=6x+12
2x=6x+13
−4x=13
x=−134
The justification for each step in the solution of the equation are as follows:
2/3x − 1/3 = 2(x + 2) -- GivenBy the multiplication property of an equation: 2x − 1 = 6(x + 2)By the distributive property of an equation: 2x − 1 = 6x + 12Collect and evaluate the like terms: 2x = 6x + 13By the subtraction property of an equation: −4x = 13By the division property of an equation: x =−13/4How to determine the justification for each step in the solution of the equation?The equation is given as
23x − 13 = 2(x + 2)
Based on the solutions, we can rewrite the given equation as follows
So, we have
2/3x − 1/3 = 2(x + 2)
So, the justification for each step in the solution of the equation are as follows:
2/3x − 1/3 = 2(x + 2) -- Given
By the multiplication property of an equation, we have
2x − 1 = 6(x + 2)
By the distributive property of an equation, we have
2x − 1 = 6x + 12
Next, we collect and evaluate the like terms
2x = 6x + 13
By the subtraction property of an equation, we have
−4x = 13
By the division property of an equation, we have
x =−13/4
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There are 6 black marbles and 4 red marbles in a jar. If you add 4 red marbles to the jar, how many black marbles do you need to add to keep the ratio of black marbles to red marbles the same?
You need to add 6 red marbles for the ratio to stay the same
How many black marbles do you need to add?The given parameters are:
Black = 6
Red = 4
Represent as ratio
Ratio = Red : Black
This gives
Red : Black = 4 : 6
When you add 4 red marbles, we have:
4 + 4 : 6 + x = 4 : 6
Where x represents the additional number of black marbles
This gives
8 : 6 + x = 4 : 6
Multiply 4 : 6 by 2
So, we have:
8 : 6 + x = 8 : 12
By comparing both sides, we have
6 + x = 12
This gives
x = 6
Hence, you need to add 6 red marbles for the ratio to stay the same
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A company spends $20 million dollars for an office building. Over what period should
the cost be written off?
Answer:The cost should be 300,000 dollars
Step-by-step explanation:
9. The graph represents the path of a football kicked by a player, where x is the horizontal
distance (in yards) and y is the height (in yards). The player kicks the ball a second time
so that it travels the same horizontal distance, but reaches a maximum height that is 6
yards greater than the maximum height of the first kick. Write a function that models
the path of the second kick.
y=-0.02(x - 30)2 + 18
The function that models the path of the second kick is y = -0.02(x - 0.30)^2 + 24
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to write a function that models the path of the second kick?The function that models the path of the first kick is given as
y = -0.02(x - 0.30)^2 + 18
A quadratic function is represented as
y = a(x - h)^2 + k
Where
Vertex = (h, k)
In this case, the interpretation of the vertex is
Vertex = (Horizontal distance, Maximum height)
Using the above as a guide, we have
Vertex = (30, 18)
This means that
Horizontal distance = 30
Maximum height = 18
For the second ball, we have
Same horizontal distanceMaximum height is 6 yards greater than the maximum height of the first kickThis means that
Horizontal distance = 30
Maximum height = 18 + 6
Evaluate
Horizontal distance = 30
Maximum height = 24
So, the function that models the path of the second kick is y = -0.02(x - 0.30)^2 + 24
Hence, the function that models the path of the second kick is y = -0.02(x - 0.30)^2 + 24
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Given the equation y = 3x + 7, which word(s) best describes the 3? Select all that apply.
*
A. slope
B. y-intercept
C. x-intercept
D. coefficient
E. constant
The slope ( option A) best describes the number 3.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=7x+2. Where:
a= the slope. It can be calculated for [tex]\frac{\Delta y}{\Delta x}[/tex].
b= the constant term that represents the y-intercept.
For the given example: a=7 and b=2.
The equation of the question is y=3x+7, when you compare this equation with the standard form for the linear equation is: y= ax+b. You find that a=3, where a represents the slope.
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(x-5)/3=21 What is equal to x
Answer: x=68
Step-by-step explanation:
(x-5)/3=21
(x-5)*3/3=21*3 ==> Multiply both sides by 3 to remove fractions
x-5=21*3
x-5=63
x+5-5=63+5 ==> Add 5 on both sides to isolate the x variable
x=63+5
x=68
Let's solve the problem,
→ (x - 5)/3 = 21
→ x - 5 = 21 × 3
→ x = 63 + 5
→ [ x = 68 ]
Hence, the value is 68.
A small plant is 212 inches tall. How tall will it be in 3 weeks if it grows 34 inch each week? Which method will NOT give the correct number of inches?
The small will grow 19/4 inch in 3 weeks and the method which will not give the correct inches will be the first option which is
multiply [tex]2\frac{1}{2} * 3[/tex] and then add 3/4.
According to the question we have been given that
The height of the small plant = [tex]2\frac{1}{2}[/tex] inch
In 1 week the plant grows = [tex]\frac{3}{4}[/tex] inch
We need to find the height of the small plant after 3 weeks.
For that we will first find how much tall it will be in 3 weeks using unitary method that is,
1 week = [tex]\frac{3}{4}[/tex] inch
3 week = [tex]\frac{3}{4}[/tex] * 3 inch
= 9/4 inch
Therefore the height of the small plant after 3 weeks will be
[tex]=2\frac{1}{2} + \frac{9}{4} \\= \frac{5}{2} + \frac{9}{4}\\= \frac{10+9}{4} \\= \frac{19}{4}[/tex]
hence the height is 19/4 inch
And the method which will not give the correct number of inches is the first option which is
multiply [tex]2\frac{1}{2} * 3[/tex] and then add 3/4.
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The sum of two consecutive even integers is 46. Find the integers.
Answer:
22, 24
Step-by-step explanation:
Hello!
Consecutive integers are integers that come after each other. We want to find two consecutive even integers that when added give us 46.
Let the first consecutive even integer be x. Since even integers come every 2 integers (even, odd, even), the second even integer should be x + 2.
Solve for xx + x + 2 = 462x + 2 = 462x = 44x = 22That means x + 2 should be 24.
The two numbers are 22 and 24.
The area of a right triangle is 5 in 2. If the length of a leg is x, write the function h(x) that describes the length of the hypotenuse.
The length of the hypotenuse is given by the function h(x) = √[x² + (10/x)²]
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The area of the right triangle is 5 in², the length of the leg is x, hence:
Area = (1/2) * base * height
5 = (1/2) * x * height
height = 10/x
hypotenuse = √[(leg)² + (height)²]
h(x) = √[x² + (10/x)²]
The length of the hypotenuse is given by the function h(x) = √[x² + (10/x)²]
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Mark and Heather Starr are celebrating their 25th anniversary by having a reception at a local reception hall. They have budgeted $3,500 for their reception. If the reception hall charges a $50 cleanup fee plus $30 per person, find the greatest number of people that they may invite and still stay within their budget
What is the slope of the line that contains these points?
Answer: Slope=5/3
Step-by-step explanation:
my teacher said
The sidewalk around a lake is 9/10 mile long. You walk 3 laps Around the lake in the morning and 2 laps in the evening. Your friend walks the same total distance as you on a 1 1/2 mile track. How many laps does your friend walks?
The total laps your friend runs is 3.
How many laps does your friend run?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below.
A proper fraction is a fraction where the numerator is less than the denominator. A mixed fraction is a fraction that is made up of a whole number and a proper fraction.
The first step is to determine the total miles you run
Total miles run = length of the side walk x total number of laps
9/10 x (3 + 2)
9/10 x 5 = 45 / 10 = 4.5 miles
The second step is to determine the total number of laps she runs:
4.5 miles / 1 1/2 miles
4.5 / 1.5 = 3 laps
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what is the parent function f(x)=2x^2+3x-4
Answer:
x^2
Step-by-step explanation:
it's a quadratic equation so the parent function is x^2.
At a basketball game, 54% of people attending were supporting the home team, while 46% were supporting the visiting team. If 1566 people attending the game supported the home team, what was the total number of people attending the game? HELPP FASTT
Evaluate (a - 4b)2 + 2a if a = 15 and b = 3.
Answer:
9
Step-by-step explanation:
(a-b)^2=a^2-2ab+b^2
(15-12)^2=9
Answer: 96
Step-by-step explanation:
Plug in a and b. so, (15-4(3))2+2(15). so (15-12)2+30. (3)32. Answer is 96.
The difference between the square of c and the total of c and 14
The given statement written as a mathematical expression is c² - c + 14
Writing an expressionFrom the question, we are to write the given statement as a mathematical expression
The given statement is
"The difference between the square of c and the total of c and 14"
The square of c is
c²
and
The total of c and 14 is
c + 14
Thus,
The statement becomes
c² - c + 14
Hence, the given statement written as a mathematical expression is c² - c + 14
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Given g(x)=-4x-4g(x)=−4x−4, find g(-2)g(−2)
How do I factor 5X = 3(X+6)
Answer:
Step-by-step explanation: 5x=3(x+6)
5x=3x+18
5x-2x=18
3x=18
x=18/3
x=6
How much money do you save by purchasing the vanilla cupcakes in a dozen Pak versus buying 12 individual cupcakes? $11.53 for dozen pack and twelve individual cupcakes is $2.15
Answer:
You save $ 14.27
Step-by-step explanation:
12 dozen = 11.53
2.15 x 12 = 25.80
25.80 - 11.53 = 14.27
Can someone please help me :(?
Simplify and combine like
terms:
-2 x+14-20-8x
Answer:
-10x-6
Step-by-step explanation:
and simplify and add
PLS ANSWER 50 POINTS Simplify 6-3/6-4
The expression 6-3/6-4 after simplification will look like 1.5.
Given that the expression is 6-3/6-4.
We are required to find the value after simplification.
Simplification or simplify fractions basically means to simplify a complicated mathematical expression to get a single or direct answer.
We have to use BODMAS rule for the simplification. The full form of BODMAS is Brackets, Open, Division, Multiplication,Addition and Subtraction. Simplication is nothing but to reduce the expression.
The expression is 6-3/6-4.
We have to do division first.
6-3/6-4 =6-0.5-4
Now we have to do subtraction now.
6-0.5-4=5.5-4=1.5
Hence the expression 6-3/6-4 after simplification will look like 1.5.
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Mrs. Thomas needs
to set up 5 rows of 3
marsh mellows. She
has 12 marsh C EX
mellows. Does she
have enough marsh
mellows?
A. No, she needs 20 marsh mellows
B. No, she needs 15 marsh mellows
C. Yes, she needs 10 marsh mellows
D. Yes, she needs 8 marsh mellows
A manufacturer of household items has total revenue given by the function R=16.5x and has total cost given by C=14x+400, where
x is the number of items produced and sold. Use graphical methods to find the number of units at which the manufacturer will break
even for the product.
The number of units that gives break even for the product is
(Simplify your answer.)
If total revenue given by the function R=16.5x and has total cost given by C=14x+400, where x is the number of items produced and sold then the number of units that gives break even for the product is 160.
What is function?In mathematics, a function is an expression, rule, or law that specifies a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are commonplace in mathematics and are required for expressing physical relationships in the sciences. The present concept of function was proposed by German mathematician Peter Dirichlet in 1837.
If a variable y is so tied to a variable x that there is a rule that determines a unique value of y whenever a numerical value is assigned to x, then y is referred to as a function of the independent variable x.
If the manufacturer will break even for the products then
Revenue = Cost
F(R) = F(C)
14x+400 = 16.5x
On solving the equation
16.5x - 14x = 400
2.5x = 400
x = 400/2.5
x = 160
In the graph the value of x is 160 as well
Thus, to break the product even the number of units =
160
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The coldest temperature ever recorded in Mathville was -19°F. This happened on January 30th, 1955. The normal low for that day is 10°F.
How much colder was the record temperature than the normal low temperature?
Answer:
-29⁰F
Step-by-step explanation:
Because -19-10=-29.
