Let's suppose that the hole is at y = 0m, where x is the time variable.
we know that:
The vertex is (-1s, 8m).
(i suppose x in seconds and y in meters)
At x = 1s, the ball reaches the hole, so we also have the point:
(1s, 0m).
Remember that the vertex of a quadratic equation y = a*x^2 + b*x + c is at:
x = -b/2a,
then we have:
-1 = -b/2a.
Then we have tree equations:
8m = a*(-1s)^2 + b*-1s + c
0m = a*(1s)^2 + b*1s + c
-1s = -b/2a.
First we should isolate one variable in the third equation, and then replace it in one of the other two:
1s*2a = b.
So we can replace b in the first two equations bi 1s*2a.
8m = a*1s^2 - 1s*2a*1s + c
0m = a*1s^2 + 1s*2a*1s + c
We can simplify both equations and get:
8m = a*( 1s^2 - 2s^2) + c = -a*1s^2 + c.
0m = a*(1s^2 + 2s^2) + c = a*3s^2 + c.
Easily we can isolate c in the second equation and then replace it into the first equation:
c = -a*3s^2
The first equation becomes:
8m = -a*1s^2 - a*3s^2 = -a*4s^2
a = 8m/-4s^2 = -2m/s^2.
Now with a, we can find the values of c and b.
c = -a*3s^2 = -(-2m/s^2)*3s^2 = 6m.
b = 1s*2a = 1s*(-2m/s^2) = -2m/s.
Then the equation is:
y = (-2m/s^2)*t^2 + (-2m/s)*t + 6m
An architect is making a floor plan for a rectangular gymnasium. If the gymnasium is 80 feet
long and 60 feet wide, what will the distance be between opposite corners?
feet
Answer:
160
Step-by-step explanation:
the length betwenn side to side woukd be 160
Answer:
The answer is 100
Step-by-step explanation:
a² + b² = c²
80²+60²=c²
6,400+1,200=c²
√6,400=√c²
subtract 1,200 - 6,400= 5,200
c2=72.1
Solve using the quadratic formula: 2x^2 + 5x + 1
Answer:
x = -0.22 or x = -2.28
Step-by-step explanation:
2x^2 + 5x + 1 = 0
You use the quadratic formula: -b ±√5² - 4 x 2 x 1 ÷ (2 x 2)
-5 +√17 ÷ 4 = -0.22
-5 - √17 ÷ 4 = -2.28
Here are the marks of a student in four exams. 65 80 76 69 The student takes a fifth exam. His mean mark for the five exams is 70 Work out his mark in the fifth exam
Answer:
mark of the fifth exam = 60
Step-by-step explanation:
Mean = sum of all marks / number of exam
Mean = 70
Number of exam = 5
Let x =
Mean = sum of all marks / number of exam
70 = (65 + 80 + 76 + 69 + x) / 5
Cross product
70 × 5 = (290 + x)
350 = 290 + x
350 - 290 = x
x = 60
mark of the fifth exam = 60
solve the system
y=x+5
y=-3x+1
The solution is (__,__)
(WILL GIVE BRIANLIEST TOO FOR THE CORRECT ANSWER!)
TRUE OR FALSE FOR EACH QUESTION
1. The units for mass are based on Newtons.
2. The units for length are based on meters.
3. Area = width x length
69 points!
Aisha purchases a hot chocolate each for $5.87. How much would she paid after 3.5 weeks
Tim’s age is nine more than his sister, Jill. Twice his age added to twice Jill’s age is 330.
Answer:
jill age is 78 and tim's age is 87
Step-by-step explanation:
let jill age be x then, tim's age is 9+x
by the question,
2(9+x) + 2x = 330
or,18 + 2x + 2x = 330
or,4x = 330-18
or, x = 312÷4
x = 78
9+x= 9+78=87
The equation 4x + 2 has a domain of {0,3,6), what is the range
Domain is basically an input while Range is an output. Domain is the set of all x-values while Range is the set of y-values.
[tex]\large \boxed {domain} = > \large \boxed{range}[/tex]
From input to output. That means from if we substitute domain in the equation, we would get range.
Substitute x = 0,3 and 6 in the equation.[tex]f(x) = 4x + 2 \\ f(0) = 4(0) + 2 = 0 + 2 = 2 \\ f(3) = 4(3) + 2 = 12 + 2 = 14 \\ f(6) = 4(6) + 2 = 24 + 2 = 26[/tex]
We input the value of x that are given and we get the value of f(x) which is the output at the specified domain.
AnswerRange[tex] \large \boxed{2, 14, 26}[/tex]
Math. Help I really need this giving brainliest to the person with the correct answer, please explain your answer........
Answer:
65-n
Step-by-step explanation:
"less than" means you will subtract the second number by the first, therefore 65 less than a number is 65-n.
Tell whether the triangle is right or not
Answer: Solved below...
Answer: Yes, that is a right triangle.
Step-by-step explanation:
To tell whether this is a right triangle or not you use a^2 + b^2= c^2
c is the hypotenuse the hypotenuse is the longest side of a right triangle, opposite the right angle. A and B can be either of the triangles sides.
To get this answer: 80^2+39^2 = 89^2
6400 + 1521 = 7921
7921=7921
Since they are the same this IS a right triangle. Here is a little help for if the a question asks if you have a right acute or obtuse. To tell if you have an acute triangle the sign will be a greater than sign for ex) 180 > 169. If you have a obtuse triangle the sign would be a less than sign for ex) 120 < 200.
Here is a problem like that if you do not understand:
6^2 +12^2 = 13^2 ( remember c is the hypotenuse)
36+144= 169
180 > 169
Have a nice day!
function or not a function? justify your answer
domain:
range:
(please help!!! for both please!!!)
Answer:
function
Step-by-step explanation:
I got that answer correct on ed2020
8.73x10^-4 in standard form
Answer:
here you go I hope this is right
round to the hundredth 3.5262
A piece of wood is 0.9 metres long.
It is cut into three unequal pieces.
The first piece is 0.2 metres longer than the second piece.
The third piece is 23 hundredths of a metre shorter than the second piece.
How long is each piece of wood?
Answer:
The length of the first piece is 0.51 m
The length of the second piece is 0.31 m
The length of the third piece is 0.28 m
Step-by-step explanation:
The question is a simultaneous equation with word problem
The total length of the wood = 0.9 m
The number of pieces the wood is cut into = 3
The length of the first piece = 0.2 m + The length of the second piece
The length of the third piece = The length of the second piece - 0.23 m
Let "y" represent the length of the second piece, let "x" represent the length of the first piece, and let "z" represent the length of the third piece, we have;
x = 0.2 + y...(1)
z = y - 0.23...(2)
x + y + z = 0.9...(3)
Therefore, by substitution, we have;
0.2 + y + y + y - 0.23 = 0.9
3·y - 0.03 = 0.9
3·y = 0.9 + 0.03 = 0.93
y = 0.93/3 = 0.31
y = 0.31
The length of the second piece = y = 0.31 m
From equation (1), we have;
x = 0.2 + y = 0.2 + 0.31 = 0.51
x = 0.51
The length of the first piece = x = 0.51 m
From equation (2), we have;
z = y - 0.23
z = 0.51 - 0.23 = 0.28
z = 0.28
The length of the third piece = z = 0.28 m.
A tree casts a shadow that is 7 feet long. A person nearby casts a shadow that is 3.5 feet long. The person is
5 feet tall. What is the height of the tree?
In quadrilateral PQRS, the exterior angle at Q measures 155 and PS = QR. What measure of ∠PSR would confirm that PQRS is a parallelogram?
Answer:
The measure confirming that PQRS would be 25
Step-by-step explanation:
It's easier if you draw it down.
1. We need to make this shape a parallelogram and the way we will do that is by making angle Q and angle S the same, because in parallelograms those opposite angles are required to be the same.
\
155 \
P \ -------------------------\ Q
\ 25 \
\ \ so that's your shape
S \______________\ R
2.We were given that the exterior angle of Q measures 155, and since exterior and interior angles combined make 180, then we can assume that the interior angle of Q is 25.
3. As mentioned before, in a parallelogram, opposite angles are the same and therefore PSR (which is just asking for the middle letter, S) is equal to 25 because Q is also 25.
6 in.
4in.
8in.
find the area
Answer:
192 in 2. multiply all of the numbers together
Step-by-step explanation:
6x4x8=192
ILL MARK U BRAINLIEST
At Kroger, milk costs $3.27 per gallon. Which equation best represents y, the total cost of x gallons of milk?
a. x = 3.27 + y
b. y = 3.27 + x
c. y = 3.27x
d. x = 3.27y
Answer:
C y=3.27x
Step-by-step explanation:
total cost = £3.27 times by the gallons
Step-by-step explanation:
B its B I had the same work and its B
Consider the system of equations: y=3x & y=3x+12. How many solutions does the system have?
A) One Solution
B) No Solution
C) infinite Solutions
PLS PLS HELP ILL GIVE U ALL MY POINTS PLUS BRAINLIEST!! i need this to be right !! asap
Answer:
D
Step-by-step explanation: So, multiplying two rationals is the same as multiplying two such fractions, which will result in another fraction of this same form since integers are closed under multiplication. Thus, multiplying two rational numbers produces another rational number.
Answer:
The product of a rational number and an irrational number is irrational.
Step-by-step explanation:
The product of a rational number and an irrational number is irrational. For example, let p= 1 be a rational number and q= 3.567be an irrational number if multiplied together the result would be 3.567, which is an irrational number.
Hope this helped!
The three angles of a triangle measure x+37, 90, and x+67. Find the measurement of the smallest angle in degrees.
Please help!!!
Answer:
The first angle is the smallest
Step-by-step explanation:
Step one:
given data
Angle 1= x+37
Angle 2= 90
angle 3= x+67
We know that the sum of angle in a triangle is 180
so
x+3+90+x+67= 180
collect like terms
2x+160= 180
2x=180-160
2x= 20
divide both sides by 2
x= 10
Step two:
so
Angle 1= 10+37= 47 °
Angle 2= 90= 90
angle 3= 10+67= 77 °
What is the image of the point (9, – 7) after a rotation of 270° counterclockwise
about the origin?
Answer:
The image if the point is (-7, -9)
Step-by-step explanation:
If The point (x, y) rotated about the origin by angle 90° counterclockwise, then its image is (-y, x)If the point (x, y) rotated about the origin by angle 180° counterclockwise, then its image is (-x, -y)If the point (x, y) rotated about the origin by angle 270° counterclockwise, then its image is (y, -x)∵ The given point is (9, -7)
∴ x = 9 and y = -7
∵ The given point is rotated 270° counterclockwise about the origin
→ By using the third rule above
∴ The image of the point is (y, -x)
→ That mean change the sign of x-coordinate, then switch them
∵ x = 9 and y = -7
∴ The image if the point is (-7, -9)
1 23/24 as an improper fraction
Answer:
47/24
Step-by-step explanation:
24x1 = 24
24+23 = 47
47/24
Answer:
47/24
Step-by-step explanation:
just add 24 to the 23 and you'll get your answer.
ayo someone help me please
Answer:
B. [tex]y= \left \{ {{x^{2}+4,\,x< 2 } \atop {-x+4,\,x \ge 2}} \right.[/tex]
Step-by-step explanation:
The piecewise function consists in two functions:
(i) A vertical parabola directed in the +x direction and centered at [tex]V(x,y) = (0, 4)[/tex] for all [tex]x \in (-\infty, 2)[/tex]. That is:
[tex]y = x^{2}+4[/tex], [tex]x < 2[/tex]
(ii) A line with negative slope for all [tex]x \in [2, +\infty)[/tex].
[tex]y = -x+4[/tex], [tex]x \ge 2[/tex]
The correct answer is B.
Fin in the table to convert the units of measure from milliliters to liters or liters to milliliters.
Milliliters. Liters
1
9
1,000
350
1 millilitre = 0.001 litre
1 litre = 1000 millilitres
9 millilitres = 0.009
9 litres = 9000 millilitres
1,000 millilitres = 1 litre
1,000 litres = 1e+6
350 millilitres = 0.35 litres
350 litres = 350000 millilitres
Help ASAP please help
Answer:
Step-by-step explanation:
b/c this is an isosceles triangle we know that either leg is the same length.. so we can use many trig functions :)
SOH CAH TOA to remember how trig functions fit on the triangle...
we know the hypotenuse and the angle and we want to find the adjacent leg ( which for this triangle is also the opposite leg )
use Cos = Adj / Hyp
Hyp*Cos(45) = adj
16* [tex]\sqrt{2}/2[/tex] = adj
8*[tex]\sqrt{2}[/tex] = adj
each leg is the same [tex]8\sqrt{2}[/tex]
I PROMISE TO MARK BRAINLIESTTTTT
Answer:
D!
Step-by-step explanation:
What is the equation ?
Answer:
[tex]y=1/3x[/tex]
Step-by-step explanation:
It's positive, and it goes up once for every three times it goes to the right.
Can someone plz help!!!! :(
Answer:
60 degress
Step-by-step explanation:
How I got it:
1. Find out the angel of each side. 360 divded by 6 = 60
2. Get the answer of 60
Advice:
-Make an polygon using paper and rotate it. (Use protractor and ruler if your gonna do it)
Which of the following is equivalent to 7^-2?
Answer:
C
Step-by-step explanation:
Answer:
C. [tex]\frac{1}{49}[/tex]
Step-by-step explanation:
When one puts a number to a negative exponent, such as;
[tex]a^{-b}[/tex]
One is essentially doing;
[tex]\frac{1}{a^{b}}[/tex]
Applying that knowledge;
[tex]7^{-2} \\= \frac{1}{7^{2}}\\= \frac{1}{49}[/tex]