Answer:
1) 3.25 units
2) 4.875 seconds
3) 98.3125 units
4) 2.4375 seconds
Step-by-step explanation:
1) The given equation of motion of the soft ball is y = -16·x² + 78·x + 3.25
Where;
y = The height of the softball
x = The time in seconds after it is hit
Therefore, the initial height of the softball is given by the value of y when x = 0 as follows;
y₀ = -16 × 0² + 78 × 0 + 3.25 = 3.25
Therefore, the initial height of the softball is 3.25 units
2) Given that the initial height of the soft ball is 3.25 ft., we have;
y = -16·x² + 78·x + 3.25 = x·(-16·x + 78) + 3.25
Therefore, the times at which the level of the softball is at 3.25 unit height, are;
x = 0 and ((-16·x + 78) = 0 which gives x = -78/(-16) = 4.875) 4.875 seconds
Therefore, from start time x = 0, the softball was in the air for 4.875 seconds
3) Given that the equation of motion of the softball is the equation of a parabola, the maximum height of the ball is given by the x-coordinate value at the top of the curve where the slope is zero as follows;
d(-16·x² + 78·x + 3.25)/dx = -32·x + 78 = 0
x = -78/(-32) = 39/16 = 2⁷/₁₆ = 2.4375 seconds
The maximum height of the softball is therefore;
[tex]y_{max}[/tex] = -16 × 2.4375² + 78 × 2.4375 + 3.25 = 98.3125
The maximum height of the softball is 98.3125 units
4) From the calculation for the maximum height, the time it took the softball to reach maximum height = 2.4375 seconds
Solve the system of equations -8x-6y=58 and x-y=9
Answer:
[tex](-\frac{2}{7},-\frac{65}{7} )[/tex]
Step-by-step explanation:
By steps in the image:
Step 1:
To eliminate, you need one of the coefficients to be the same in both equations. We will use the term "-6x" found in the first equation.
To get this, multiply the entire second equation by 6 and simplify using the distributive property. The new equation is:
[tex]6x-6y=54[/tex]
Step 2:
Now you need to subtract the first equation and the new version of the second equation. By doing this, the "-6x" in both equations will cancel each other out.
Step 3:
Solve for x in the given equation by:
Dividing both sides by -14Simplify the value of x by dividing top and bottom by 2Step 4:
Solve for y by:
Substitute the value of x into the second equationMultiply both sides of the equation by 7Add 2 to both sides of the equationDivide both sides of the equation by -7Solution:
[tex](-\frac{2}{7},-\frac{65}{7} )[/tex]
:Done
The lunch special at Omar's Restaurant is a sandwich, a drink and a dessert. There are sandwiches, drinks, and desserts to choose from. How many lunch specials are possible?
Answer:
the question is incomplete, so I looked for similar questions:
There are 3 sandwiches, 4 drinks, and 2 desserts to choose from.
the answer = 3 x 4 x 2 = 24 possible combinations
Explanation:
for every sandwich that we choose, we have 4 options of drinks and 2 options of desserts = 1 x 4 x 2 = 8 different options per type of sandwich
since there are 3 types of sandwiches, the total options for lunch specials = 8 x 3 = 24
If the numbers are different, all we need to do is multiply them. E.g. if instead of 3 sandwiches there were 5 and 3 desserts instead of 2, the total combinations = 5 x 4 x 3 = 60.
The sum of three consecutive odd integers is -99. Find each integer.
Answer:
-35, -33, -31
Step-by-step explanation:
Let the 3 consecutive odd integers be x+1,x+3,x+5
Given, x+1+x+3+x+5=-99
3x+9=-99
3x=-108
x=-36
The 3 odd integers are x+1 = -35, x+3=-33, x+5=-31
Find the slope given the two points below
(-1, 5) and (7,3)
Answer:
-1/4
Step-by-step explanation:
Write an equations to describe the linear relationship.
Anne has $250 in a savings account. She withdraws $5 per month
Answer:
Step-by-step explanation:
espera y termino y te ayudo vale que me falta poco
Answer:
250-5x=y. is the answer
250 is the y intercept
5 is the slope
Marta made a batch of stole for her family , but she decided it wasn't sweet enough
5 -x < 8; x = -3 Great gratitude if you helped!
Answer:false 5-(-3)<8
Step-by-step explanation:
8 is not less than 8
Sophia’s math test is worth 130 points and has 40 problems. Each problem is worth either 4 points or 3 points. How many of each question type were on the test? The test had 30 4-point questions and 10 3-point questions. The test had 10 4-point questions and 30 3-point questions. The test had 28 4-point questions and 12 3-point questions. The test had 25 4-point questions and 10 3-point questions.
Answer:
b
Step-by-step explanation:
The test had '10' 4-point questions and '30' 3-point questions in the math test.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Sophia’s math test is worth 130 points and has 40 problems.
And, Each problem is worth either 4 points or 3 points.
Now,
Let number of 4 point questions = x
And, Number of 3 point questions = y
Since, There are 40 problems.
So, We get;
x + y = 40 .... (i)
And, Each problem is worth either 4 points or 3 points.
So, We can formulate;
4x + 3y = 130 .... (ii)
Solve equation (i) and (ii) as;
Multiply by 4 in equation (i), we get;
4x + 4y = 160
Subtract from equation (ii),
y = 30
And, x + y = 40
x = 40 - 30
x = 10
Thus, The test had '10' 4-point questions and '30' 3-point questions in the math test.
Learn more about the mathematical expression visit:
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which equation is represented by this line?
Answer:
y= -5/2x +3 (always look at where the line passes at X=0 to get your Y intercept and count the boxes to get your slope)
Step-by-step explanation:
Need a quick answer for this homework
Answer:
clothes are expensive
Step-by-step explanation:
the hypothesis is at the beginning of the sentence followed by the conclusion
Which relation is NOT a function?
Answer:
A
Step-by-step explanation:
when you are finding a function you look to see if there are any of the same x-vaules meaning a repitation of a number .
PLEASE HELP FIRST TO ANSWER ACCURATELY AND WITH A GOOD EXPLANATION GETS BRAINLIEST!
Well is it 8 3/4? Because i got no idea
Answer:
8 3/4
Step-by-step explanation:
The reason is because on the graph the most common size was 1 3/4, so you count how many x's there was. There were 5 x's so you multiply 1 3/4 by 5 and you get 8 3/4
Hope this helps! :) Plz mark as brainliest!
"Write two equations so that each have variables on both sides and a solution of 1/2?
Marisa and her brother 2/3 of a gallon of lemonade to sell at their lemonade stand. They divided the lemonade equally among 4 paper cups. How much lemonade was in each paper cup?
Answer: 0.16
Step-by-step explanation:
The formula for percentage increase I (given as a decimal) of an investment is I=S−PP I = S − P P , where P P is the purchase price and S S is the sale price. You sell a stock at a price of $91, earning a percentage increase of 30%. What was the purchase price of the stock?
Answer:
$130
Step-by-step explanation:
Given:
I = (S − P) / P
where,
P = purchase price and
S = sale price.
What was the purchase price of the stock?
I = 30%
S = $91
I = (S − P)/P
30% = (91 - P) / P
0.3 = (91 - P) / P
Cross product
0.3P = 91 - P
0.3P + P = 91
0.7P = 91
P = 91 / 0.7
P = $130
What is the equation of this line?
Y=3/2x
Y= -2/3x
Y= 2/3x
Y= -3/2x
Answer:
y = (2/3)x
Step-by-step explanation:
Note that (0, 0) and (3, 2) are both points on this line. The change in y as we go from (0, 0) to (3, 2) is +2 and the change in x is +3.
The slope of this line is this m = rise/run = 2/3
and so the desired equation is y = (2/3)x
What might be 3 reasons that a grocery store would have higher prices on items than another store
Answer:
Different Distributor Pricing. Supermarkets pay different prices for the same product through distributors.The difference in Quality.Different Supplier Deals.Please help!! I need help I don’t understand this!
Answer:its d because im smart
Step-by-step explanation:
Answer:
The answer is B
Step-by-step explanation:
The answer is B because the line doesn't pass through the origin (0,0)
4x - 5
Зу +1
3х + 11
solve for x
Answer:
this can be the answer
because in given question there is no relation between equations
Alexa's babysitting business charges a flat rate of $40 per month, plus $10 per hour that she babysits. Nick's babysitting service does not charge a monthly fee, but does charge $50 per hour that he babysits. Write an equation to find the number of hours h for which Alexa and Nick would charge the same amount
Let, after h hours both would charge the same amount.
Money charged by Alexa in h hours :
A = 40 + 10h .... 1)
Money charged by Nick in h hours :
N = 0 + 50h .... 2)
For equal charge :
A = N
40 + 10h = 50h
40h = 40
h = 1 hour
Therefore, Alexa and Nick would charge the same amount at first hour.
Hence, this is the required solution.
What passes through the points (5.4) and (2,-2)
(-18) - (-16) =
A -2
B 3
C -3
Answer:
A
Step-by-step explanation:
-18-(-16) is -2
PLEASE HELP ME COMPLETE THIS EQUATIONS!!!thanks
7/8-(-2+3/4)=(____)+(____)+7/8
Answer:
-2 and 3/4 because of the reflective postualte
Step-by-step explanation:
what is 300,000 times 45,000
Answer:
13,500,000,000
Answer:
13500000000
Step-by-step explanation:
Round to the nearest hundredth. 23.70 ÷ 1.8
Answer:
13.17
Step-by-step explanation:
Answer:
13.16
If this is not the answer you are looking for plz let me know
You know: 13 + 7 = 20. Therefore: 13 + 7 + 2 = 20 + 2. Which Property of Equality was illustrated?
A. Subtraction Property of Equality
B. Multiplication Property of Equality
C. Division Property of Equality
D. Addition Property of Equality
Answer:
Addition Property
Step-by-step explanation:
Because since there are the plus sign there is no x - or a ÷sign so its Addition Property
13 + 7 = 20 ⇒ 13 + 7 +2 = 20 + 2 represents addition property of equality.
What is Equality ?
" Equality means representation of any two quantities using mathematical expression with the sign of 'equals to'."
According to the question,
Given,
13 + 7 = 20
Add '2' both the side of the given equality we get,
⇒ 13 + 7 + 2 = 20 + 2
Add both the sides represents addition property of equality.
Hence, Option(D) is the correct answer.
Learn more about addition property of equality here
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What is the answer to this question
Answer:
Angle 1 and Angle 5
Step-by-step explanation:
Since we know that a straight angle is 180 degrees this means that angle 2+5+1 is 1/2 of a full angle. We also know that angle 2 is 90 degrees or a right angle, we can subtract 180 - 90 which equals 90 degrees. Since two complementary angles add up to 90 degrees. This 100% assures us that angle 1 + angle 5 are the two complementary angles.
Hope this Helps!!! :)
Let me know if I should change anything or if it is helpful in the comments.... thx!!!
Use the linear equations to answer the question. Information y equals StartFraction 2 over 3 EndFraction x minus 3 y equals StartFraction negative 3 over 2 EndFraction x plus 2 Question Which statement about the lines is true? Answer options with 4 options A. The lines are the same. B. The lines are parallel. C. The lines are perpendicular. D. The lines intersect but are not perpendicular.
Answer:
C. The lines are perpendicular.Step-by-step explanation:
Given the equation of the lines expressed as:
L1: y = 2/3 x - 3 and L2: y = -3/2 x +2
Comparing to the standard form of equation of a line y= mx+c
The slope of L1 is m1 = 2/3
The slope of line L2 is -3/2
Since their slope are not the same, therefore the lines are not parallel to each other.
For two lines to be perpendicular, the product of their slope is -1.
Let's check for both lines:
Check the product of their slope;
m1m2 =2/3 * -3/2
m1m2 = -6/6
m1m12 = -1
Since the product of their slope is -1, hence the lines are perpendicular to each other.
Option C is correct
Answer:
Option C is correct
Step-by-step explanation:
2 can got into 18 how many times
Answer:
9
mark me brainliest plz
Step-by-step explanation:
What is -6/20+1.5 I really need help.
Answer:
1.2
Step-by-step explanation:
Divide then add.
Answer:
1.2
Step-by-step explanation:
-6/20 + 1.5 = 1.2
Hope this helps☺️