Step-by-step explanation:
1. The equation graph is a parabola, so the maximum height will be the vertex of the parabola. You can find the vertex coordinate t using the formula:
t = -b/2a
t = -18/2•(-4.9)
t = -18/-9.8
t = 1.84 seconds
2. The height of the ground is 0, so the balls hit the ground when the equation result is 0:
0 = -4.9t²+18t+10
Now you solve it using Bhaskara:
Δ = b² -4ac
Δ = 18² -4•(-4.9)•10
Δ = 520
t = (-b ±√Δ)/2a
t = (-18 ± √520)/2•(-4.9)
t1 = (-18 - 20.8)/-9.8
t1 = 3.96 seconds
t2 = (-18 +20.8)/-9.8
t2 = -0.28
Doesn't exist negative time, so we pick the first value found, t = 3.96 seconds
3. Now you just need to put 3 in place of t to find the result:
h = -4.9•3² +18•3 +10
h = -4.9•9 + 54 + 10
h = -44.1 + 64
h = 19.9 meters
4. You just need to put 1 in place of t to find the height:
h = -4.9•1²+12
h = -4.9+12
h = 7.1 meters
what is the decimal expansion of -11/15
Answer:
−0.73333333333333
Step-by-step explanation:
This is the decimal form of -11/15
Find tan a Picture included
Answer:
5/12
Step-by-step explanation:
We know its a right angled triangle because of phythogorean theorem,
h^2=p^2+b^2
Take angle A as reference,
13^2=12^2+5^2
or,169=144+25
169=169
Now,
We know,
Tanx=p/b
As we took angle A as reference,
p=5
b=12
h=13
Put that in tanx=p/b
We get,
tanx=p/b=5/12
Answer:
Step-by-step explanation:
[tex]tan \ A = \frac{opposite \ side}{adjacent \ side}\\\\tan \ A = \frac{5}{12}[/tex]
Is this a function or no ?
Evaluate the expression shown below and write your answer as a fraction in simplest form(1/10-2/3) ÷ 0.5
Answer:
[tex]\frac{-17}{15}[/tex]
Step-by-step explanation:
When solving this problem you must follow PEMDAS, so parentheses should go first. To solve 1/10 - 2/3, first, find the common denominator. In this case, that is 30. Then, subtract, [tex]\frac{3}{30} - \frac{20}{30}[/tex]. This equals -17/30. Finally, divide by 0.5. To do this remember that dividing by half is the same as multiplying by 2. Doing [tex]\frac{-17}{30} *2[/tex] equals [tex]\frac{-17}{15}[/tex].
Each month a manufacturing plant makes 14500 light bulbs. last month, a random sample of 200 bulbs found that 2.5% were defective. Estimate the number of defective bulbs that were produced last month.
PLEASE HELP ASAP I WILL GIVE BRAINLIEST
Answer:
363
Step-by-step explanation:
Of 2.5% of 200 is 5 so we can scale that up to 14500 we get 362.5 and then we round it up to 363.
Please help I don’t understand math
Answer:
x = 12
Step-by-step explanation:
The sum of the two smaller angles is 140
80+5x = 140
Subtract 80 from each side
80+5x-80 =140-80
5x = 60
Divide each side by 5
5x/5 = 60/5
x = 12
Given the function g(x) = x^2 + 5x + 14, determine the average rate of change
of the function over the interval 1 < x < 7.
Answer:
13
Step-by-step explanation:
The average rate of change is
f(7) - f(1)
---------------
7-1
f(7) = 7^2 + 5*7 +14 = 49 +35 +14=98
f(1) = 1^2 +5(1)+14 = 1+5+14=20
98-20
--------
7-1
78/6
13
Please help!! 20 points
(-78) + 69 =
Answer:
-9
Step-by-step explanation:
Since the signs are different, subtract the two numbers and take the sign of the larger number
78 - 69
9
Since 78 is the larger number and it was negative
-9
Answer:
-9
Step-by-step explanation:
-78+69
=-9
happy to help
1. What property could you use to show that triangles ACT and ODG are congruent?
Answer:
SSS
Step-by-step explanation:
We do not know any of the angles, and we also do not know if the triangles are right triangles. Thus, SSS is the only option left. We know that all three sides are congruent anyway.
Answer:
SSS
Step-by-step explanation:
AC = OD
AT = OG
CT = DG
You have three congruent sides making ΔACT & ΔODG congruent by SSS.
calculate w reasons the size of the unknown angles
Answer:
a= 75°
β= 30°
Step-by-step explanation:
α = 75° This is because triangle PQR isosceles. Thus two of its angles are equal and these two are angle α and the one labelled 75.
β = 30° This is because angles in a triangle sum up to 180°. We already know two of these angles. To find β you say 180 - ( 75 × 2)
The answer becomes 30°.
HOPE THIS HELPED
Which question can be answered using the expression 1/3 ÷ 3/4 ?
Answer:
0.4444444
Step-by-step explanation:
yes
(81/16)1/4 +(81/16)0
Answer:
should be 0.28125
Step-by-step explanation:
If the range of the function f(x) =5x + 8 is 18, find its domain.
Step-by-step explanation:
f(X) = 5x+18= 18
so,
18 = 5x+18
18-18 = 5x
X= 0
so domain of the function is 0
find the surface area. Leave your answer in terms of pi
Answer:
210*pi
Step-by-step explanation:
Surface area=2*pi*r*(r+h)
=2*pi*5*(21)=210*pi
When the movies is half over , popcorn sells for half price. Full price popcorn is $3.50 and drinks are $1.35 . Determine the cost for purchasing 3 orders of popcorn and 3 drinks when the movie is half over
Answer:
The total price is $9.30
Step-by-step explanation:
Price of the orders of popcorn= $5.25
Price of the drinks= $4.05
find the slope and y intercept
Answer:
slope = -1
y intercept (0,-2)
Step-by-step explanation:
We can use the two points to find the slope
(-4,2) and (1,-3)
m = ( y2-y1)/(x2-x1)
= (-3 -2)/(1 - -4)
= -5 /(1+4)
= -5/5
- 1
The y intercept is where it crosses the y axis
y intercept is (0,-2)
What is the most dangerous country
Answer:
Iceland
Step-by-step explanation:
answer for brainiest
Answer:
Hello
answer :B and C
Step-by-step explanation:
√25=5 is an integer
b) is not an integer
c) is not an integer=0.75
d) is an integer
Pls pls pls help me
Answer:
48
Step-by-step explanation:
AC = 10
DC² = 10² - 6² = 64
DC = 8
[tex]A_{ABCD}[/tex] = 6 × 8 = 48
2/4.7+2/7.10+2/10.13+2/13.16+.....+2/49.52
tính giá trị biểu thức
It looks like you're trying to evaluate the sum,
[tex]\displaystyle \frac2{4\times7} + \frac2{7\times10} + \frac2{10\times13}+\cdots+\frac2{49\times52}[/tex]
which can be written as
[tex]\displaystyle \sum_{n=1}^{16} \frac2{(3n+1)(3n+4)}[/tex]
Split up the summand into partial fractions:
[tex]\displaystyle \frac2{(3n+1)(3n+4)} = \frac a{3n+1} + \frac b{3n+4} \\\\ \implies 2 = a(3n+4)+b(3n+1) \\\\ \implies 2 = (3a+3b)n+4a+b[/tex]
so that
3a + 3b = 0, or a = -b
4a + b = 2
Solve for a and b :
4a + (-a) = 3a = 2 ==> a = 2/3 ==> b = -2/3
So the sum is
[tex]\displaystyle \frac23 \sum_{n=1}^{16} \left(\frac1{3n+1} - \frac1{3n+4}\right)[/tex]
Write out the first terms and observe that several terms cancel with each other:
2/3 (1/4 - 1/7)
+ 2/3 (1/7 - 1/10)
+ 2/3 (1/10 - 1/13)
+ …
+ 2/3 (1/43 - 1/46)
+ 2/3 (1/46 - 1/49)
+ 2/3 (1/49 - 1/52)
So the sum collapses and simplifies to
[tex]\displaystyle \sum_{n=1}^{16} \frac2{(3n+1)(3n+4)} = \frac23 \left(\frac14 - \frac1{52}\right) = \boxed{\frac2{13}}[/tex]
A car left Sydney at 9 am and arrived in
Melbourne at 6 pm. The distance travelled
was 711 km. Find the car's average speed.
km/h
Answer:
average speed = distance/ time
711/9
79km/h
4. Given the diagram below what is the length of RS or the distance across a body of water?
Answer:
62 ft
i know its a late answer but i just did the test
If the length of ST is 62 feet the length of RS or the distance across a body of water will also be 62 feet.
What is the congruent triangle?Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅. When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.
It is given that the length of s ST is 62 feet and PS = PQ.
The measurements of the sides and angles of two or more triangles determine their congruence. A triangle's size is determined by its three sides, and its shape is determined by its three angles. If the pairs of corresponding sides and angles of two triangles are equal, they are said to be congruent.
Since the one angle in both triangles is 90° and the two sides are equal the two triangles are equal.
The ratio of the sides is equal if the triangle is congruent. As a result,
PS / PQ = RS / ST
1 = RS / ST
RS = ST
RS = 62 feet
Thus, if the length of ST is 62 feet the length of RS or the distance across a body of water will also be 62 feet.
Learn more about the congruent triangle here:
brainly.com/question/12413243
#SPJ5
ji and jl are opposite rays
Two sides of a triangle are 12 and 18 cm. Complete the inequality to show the possible lengths of the third side.
Let a = 12 and b = 18 be the two given sides
Let c be the unknown third side
Due a modified form of the triangle inequality theorem, we know that,
b-a < c < b+a
18-12 < c < 18+12
6 < c < 30 which is the final answer
This says c is between 6 and 30, but cannot equal either endpoint.
In ΔRST, m∠R = 92° and m∠S = 71°. Which list has the sides of ΔRST in order from shortest to longest?
Answer:
RS, RT, ST
Step-by-step explanation:
We require the third angle in the triangle
∠ T = 180° - (92 + 71)° = 180° - 163° = 17°
The shortest side is opposite the smallest angle
∠ T = 17° → opposite side RS
The longest side is opposite the largest angle
∠ R = 92° → opposite side ST
Then sides from shortest to longest is
RS, RT, ST
whats does it me study the exercises in which both addends are negative.what do you notice about the sum
Answer:
Jsjiaghajqkkooo898iiwiqiooopwpppwopfokejejieieieieiie
what is the the value of ∣9∣
Hey there! I'm happy to help!
This symbol is an absolute value symbol. It means that we are looking for that number's distance from 0. There is no such thing as a negative distance; the distances are all positive, so both ∣9∣ and ∣-9∣ have a value of 9.
Have a wonderful day and keep on learning! :D
LCM of two even number is 220, find their sum
Answer:
Two consecutive even terms and LCM = 180
Let’s assume the two terms:
1st term : 2x
2nd term : 2x + 2
There is a rule which states that
If ‘a’ and ‘b’ are two numbers, then their product is equal to the product of their LCM and HCF.
i.e,
a∗b=HCF∗LCM - (i)
We can logically say that the HCF of any two consecutive even numbers is always equal to ‘2’ provided that the smallest no. is at least ‘2’.
i.e.,
HCF of ‘2x’ and ‘2x + 2’ is ‘2’ - (ii)
Therefore,
from (i) and (ii),
2x∗(2x+2)= HCF * LCM
2x∗(2x+2)=2∗180
x∗(2x+2)=180
2x2+2x−180=0
Solving the quadratic equation we get,
x=9,−10 (we discard -10 since it is negative)
Therefore, the numbers are
2∗9=18 (1st no.)
2∗9+2=18+2=20 (2nd no.)
Answer : 18,20
Step-by-step explanation:
How much money will be in a bank account after 3 years if $9 is deposited at an interest rate of 5% compounded annually? Round to the nearest tenth.
Answer:
Step-by-step explanation:
$13.1
If you know the answer please help me
Answer:
2/7
Step-by-step explanation:
This is basically asking how many 7/10 's fit in 1/5. Or 1/5 divided by 7/10.
1/5 divided by 7/10 is the same as 1/5 times the reciprocal, 10/7. Therefore it is 1/5*10/7, or 10/35.
That simplifies to 2/7.