Using Pythagoras theorem
[tex]\\ \Large\sf\longmapsto P^2=H^2-B^2[/tex]
[tex]\\ \Large\sf\longmapsto P^2=17^2-8^2[/tex]
[tex]\\ \Large\sf\longmapsto P^2=289-64[/tex]
[tex]\\ \Large\sf\longmapsto P^2=225[/tex]
[tex]\\ \Large\sf\longmapsto P=\sqrt{225}[/tex]
[tex]\\ \Large\sf\longmapsto P=15ft[/tex]
Answer:
Applying the Pythagorean theorem we have :wall length is : a²-b²=c²⇒17²-8²=c²⇒c=15(c>=0)Step-by-step explanation:
we have : the length of the ladder is the hypotenuse of the triangle ; the length of the ladder, which is far from the wall, is the right angle side of the triangle (draw your own illustration)
Find 3rd and 5th form by using nth term formula tn=a+(n-1)d when tn=a+(n-1)d when a=2 and d=3.
Answer:
t3 = 8, t5 = 14
Step-by-step explanation:
t3 = 2 + (3-1) × 3
t3 = 2 + (2) × 3
t3 = 2 + 6
t3 = 8
t5 = 2 + (5-1) × 3
t5 = 2 + (4) × 3
t5 = 2 + 12
t5 = 14
9.
A rocket is launched from the top of a 76-foot cliff with an initial velocity of 135 ft/s. a. Substitute the values into the vertical motion formula h = –16t2 + vt + c. Let h = 0. b. Use the quadratic formula to find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
A. 0 = –16t2 + 135t + 76; 0.5 s
B. 0 = –16t2 + 76t + 135; 9 s
C. 0 = –16t2 + 76t + 135; 0.5 s
D. 0 = –16t2 + 135t + 76; 9 s
Answer:
The answer is 2.)
Step-by-step explanation:
Given initial velocity=135 ft/s
& cliff=76 foot
Given quadratic equation
⇒ (let h=0 it is given)
⇒
⇒
⇒ t=8.96≈9 s (the other root is negative)
Hence, rocket will take 9 s to hit the ground after launched.
Answer: Choice D
0 = 16t^2 + 135t + 76; 9 s
==============================================
Explanation:
The equation we start with is
[tex]h = -16t^2 + vt + c\\\\[/tex]
where v is the starting or initial velocity, and c is the starting height.
We're told that v = 135 and c = 76
We let h = 0 to indicate when the object hits the ground, aka the height is 0 ft.
That means the equation updates to [tex]0 = -16t^2 + 135t + 76\\\\[/tex]
Based on that alone, the answer is between A or D
-------------------
We'll use the quadratic formula to solve for t
We have
a = -16b = 135c = 76So,
[tex]t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\t = \frac{-135 \pm \sqrt{135^2 - 4(-16)(76)}}{2(-16)}\\\\t = \frac{-135 \pm \sqrt{23,089}}{-32}\\\\t \approx \frac{-135 \pm 151.9506}{-32}\\\\t \approx \frac{-135 + 151.9506}{-32} \ \text{ or } \ t \approx \frac{-135 - 151.9506}{-32}\\\\t \approx \frac{16.9506}{-32} \ \text{ or } \ t \approx \frac{-286.9506}{-32}\\\\t \approx -0.52971 \ \text{ or } \ t \approx 8.96721\\\\[/tex]
We ignore the negative t value because a negative time duration makes no sense.
The only practical solution here is roughly 8.96721 which rounds to 9.0 or simply 9 when we round to the nearest tenth (one decimal place).
In short, the object will hit the ground at the 9 second mark roughly. Or put another way: the object is in the air for about 9 seconds.
From this, we can see that the final answer is choice D.
Keep in mind that we aren't accounting for any wind resistance. Considering this variable greatly complicates the problem and requires much higher level mathematics. So we just assume that there is no wind at this moment.
Isobel is pulling water up from an old-fashioned well. She lifts the bucket of water at a rate of 4 ft/s, and after 1 s, the bucket is 1 ft below the top of the well. Select the equation in point-slope form for the line that represents the height of the bucket relative to the top of the well.
A. y + 1 = 4x – 1
B. y – 1 = 4x + 1
C. y – 1 = 4(x + 1)
D. y + 1 = 4(x – 1)
find the inequality represented by the graph
would I write it y is more than or equal to -2x-5 ?
Answer:
y ≥ -2x-5
you use the greater than and equals to sign
can you help me please.
Answer:
45
Step-by-step explanation:
1st term is 2
2nd term is 3
3rd term is 4
.
.
.
nth term is (n+1)
because common difference is 1, so 1st term = 1 + common difference = 1+1 = 2, for any term, we take n + common difference, so n+1
putting n = 44,
44th term is 44+1 = 45
Answered by GAUTHMATH
I NEED HELP PLEASE.....................................
Answer:
No
Step-by-step explanation:
The Rectangle A is occupied by 5 unit Squares on its length and 3 unit Squares on its width .....and we know one unit square in a grid is equal to 1 cm
hence.......A=L×W
Area = 5 unit Squares ×3 Unit Squares
Area of A= 15 unit Squares .
The Square B is occupied by 3 unit Square on each side thus.....Area =S×S
Area of B = 3 unit Squares × 3 Unit Squares
Area of B = 9 unit Squares.
Hence the answer is no ....9 isn't the double of 15
cho x,y thuộc n thoả mãn x hia 3 dư 1,y chia 3 dư 2.hỏi x.y chia 3 có số dư bằng bao nhiêu
Answer:
2
Step-by-step explanation:
x÷3 dư 1-->x=3a+1
y÷3 dư 2-->y=3b+2
x×y=(3a+1)×(3b+2)
=9ab+6a+3b+2
Mà 9ab, 6a, 3b chia hết cho 3, 2 chia 3 dư 1
==>x×y chia 3 dư 2
Solve the compound inequality. Graph your solution. 2x – 2 < –12 or 2x + 3 > 7
Answer:
09
Step-by-step explanation:
√a²-b² +√2ab-b² >a giúp với huuuuuuuuuuuuuuuuuuuuuuu
Step-by-step explanation:
버터처럼 부드럽게
What is the estimate for 312+138+207
Answer:
657
Step-by-step explanation:
312 + 138 + 207
= 450 + 207
= 657
Answer:
600
Step-by-step explanation:
To round your answer, you check the tenths place to see if it is under 5 or above 5. If it is under 5, your answer will stay in the number the hundreds place is in currently. If it is above 5, you will add one to the hundreds place.
312: there is one in the tenths place, so it will stay as 300.
138: there is three in the tenths place, so it will stay as 100.
207: there is a zero in the tenths place, so it will stay as 200.
If you are doing it with the one's place, it is the same method. Either round up or down.
300 + 100 + 200 = 600
The answer is 600.
Solve the equation for all values of x.
(22 – 16)(x2 + 49) = 0
Please help
Answer:
-24.5 or 7i or -71 (see below)
Step-by-step explanation:
Im gonna guess that you mean (22-16)(2x+49)=0
Therefore, since one of the brackets must be equal to 0 and 22-16 is 6, 2x+49=0 so x is -24.5
However, if you meant (22-16)(x^2+49)=0
then x^2+49=0 so x^2 =-49
Therefore, the answer is complex and therefore 7i or -7i
What is the simplest radical form of the expression? (8x^5y^3)^(2/3)
Step-by-step explanation:
(8x⁵y³)^(2/3)
= 8^(2/3)×(x^(5×2/3))×(y^(3×2/3))
= 4×x^(10/3)×y^(2)
= 4y²(³√x¹⁰)
2cos5xcos3x+sinx=cos8x
It looks like your equation (it's not an identity) is
2 cos(5x) cos(3x) + sin(x) = cos(8x)
Recall that
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
cos(x - y) = cos(x) cos(y) + sin(x) sin(y)
==> 2 cos(x) cos(y) = cos(x + y) + cos(x - y)
so that
2 cos(5x) cos(3x) = cos(8x) + cos(2x)
Then the equation simplifies to
cos(8x) + cos(2x) + sin(x) = cos(8x)
cos(2x) + sin(x) = 0
Also recall that
cos(2x) = 1 - 2 sin²(x)
so the equation is quadratic in sin(x) and can be factorized:
1 - 2 sin²(x) + sin(x) = 0
2 sin²(x) - sin(x) - 1 = 0
(2 sin(x) + 1) (sin(x) - 1) = 0
Solve for x :
2 sin(x) + 1 = 0 or sin(x) - 1 = 0
sin(x) = -1/2 or sin(x) = 1
[x = arcsin(-1/2) + 2nπ or x = π - arcsin(-1/2) + 2nπ] or x = arcsin(1) + 2nπ
(where n is any integer)
x = -π/6 + 2nπ or x = -5π/6 + 2nπ or x = π/2 + 2nπ
What is the value of x?
Enter your answer in the box.
x =
Answer:
x = 26
Step-by-step explanation:
x and 64 are complementary angles so their sum is 90
x+64 = 90
x = 90-64
x = 26
Answer:
26
Step-by-step explanation:
90-64=26
~~~~~~~~~~
I don’t get itttttttttt
Answer:
<1 = 65
Step-by-step explanation:
Exterior angle thm:
40 + 3x = 5x - 10
3x - 5x = -10 - 40
-2x = -50
x = 25
5x - 10
5(25) - 10
125 - 10
115
180 - 115
65
Answer:
65
Step-by-step explanation:
The sum of the measures of the angles of a triangle equals 180°.
3x + 40 + m<1 = 180
3x + m<1 = 140
<1 and the angle measuring 5x - 10 are supplementary angles, so the sum of their measure is 180°.
m<1 + 5x - 10 = 180
Solve for m<1 and substitute in equation above.
m<1 = 190 - 5x
3x + 190 - 5x = 140
-2x = -50
x = 25
m<1 = 190 - 5x
m<1 = 190 - 5(25)
m<1 = 190 - 125
m<1 = 65
1. A soccer team is to be selected from a group of 24 players. Of them, one-third is below 16 years of age, one-fourth is in the age group 16 to 18 years and the remaining are above 18 years.
(a) What fraction of players is above 18 years of age?
(b) If all players of age above 18 are selected, how many players are above 18 years of age?
Answer:
(a).5/12
(b).10 players
Step-by-step explanation:
a.
⅓+¼=7/12
Remaining=5/12
b.5/12of 24 =10 players
Set up the appropriate trigonometric ratio to determine the value of the safety angle.
Step-by-step explanation:
sin/cos=tan theta.It is the value of the safety angle
Pls help me with my work
Answer:
A).
1) A
2) U
3) S
4) J
5) T
6) M
7) H
8) B
9) Y
10) L
s(-5,-1)
k(-3,1)
f(0,5)
p(5,1)
also the value of L is (-4,4)
E (-2,-3)
N(2,1)
mark is making a square pen for his puppy. he wants the puppy to have 36 square feet of space to play in. he can use square roots to determine the length of one side of the square section so that he can be sure to purchase enough fencing for the pen. how is the side of the square pen related to the area ?
how long is one side of the square pen ?
how much fencing will mark need to purchase ?
someone please help me lol
Answer:
see below
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length
36 = s^2
Taking the square root of each side
sqrt(36) = sqrt(s^2)
6 = s
The side length of the pen is 6 ft
To find the perimeter of a square
P = 4s
P = 4*6 = 24
He will need 24 ft of fencing
Use the drop-down menus to identify the values of the
parabola.
Vertex = (-3, -5), (-2, 0),
(0, 4), or (2, 0)
Domain = x < 0, x > 0, y > 0, or x is a real number
Range = {y| y < 0, 2, 4, or 6}
Answer:
Vertex= (0,4)
Domain= x: all real number
Range: ( - ∞, 4] or y ≤ 4
OAmalOHopeO
Teresa has $451 in a personal bank account,and then withdraws $10 per week.Andrew has $10 in a personal bank account,and then deposits $53 earned from dog grooming each week.After how many weeks will they have the same amount of money in the bank.
Given:
Teresa has $451 in a personal bank account,and then withdraws $10 per week.
Andrew has $10 in a personal bank account,and then deposits $53 each week.
To find:
After how many weeks will they have the same amount of money in the bank.
Solution:
Let x be the number of weeks after which they have the same amount.
Teresa has $451 in a personal bank account,and then withdraws $10 per week. So, the amount in Teresa's account is:
[tex]\text{Teresa's account}=451-10x[/tex]
Andrew has $10 in a personal bank account,and then deposits $53 each week. So, the amount in his account is:
[tex]\text{Andrew's account}=10+53x[/tex]
They have equal amount after x weeks. So,
[tex]451-10x=10+53x[/tex]
Isolate variable terms.
[tex]451-10=10x+53x[/tex]
[tex]441=63x[/tex]
Divide both sides by 63.
[tex]\dfrac{441}{63}=x[/tex]
[tex]7=x[/tex]
Therefore, they will have the same amount of money in the bank after 7 weeks.
. She lets numbers from 1 to __ represent defective batteries, and __ to __ represent working batteries. She generates this list: 120, 413, 472,564, 38, 266, 344, 476, 486, 177, 26, 331,358,131,352, 227, 31, 253, 31, 277
Answer:
Since 50 out of the 600 batteries are defective, She lets numbers from 1 to 50 represent defective batteries, and 51 to 600 represent working batteries
~OAmalOHopeO~
41
Ivan has just opened a small coffee shop. He paid a copy store 50.10 percopy to make
1,428 copies of the flyer to announce the opening of the shop an is having 14
distribute all 1 428 flyers, and he is paying them 50.25 tot sath Syer shey der He suure
each friend the same number of flyers
What is the total amount Ivan is paying each friend to
disor
Show your work
Answers
Answer:
41
Ivan has just opened a small coffee shop. He paid a copy store 50.10 percopy to make
1,428 copies of the flyer to announce the opening of the shop an is having 14
distribute all 1 428 flyers, and he is paying them 50.25 tot sath Syer shey der He suure
each friend the same number of flyers
What is the total amount Ivan is paying each friend to
disor
Show your work
Answers
Help fast pleaseeeeeeee
Answer:
Multiply 800 by 1.022^7 because 1.022^(n-1)
Step-by-step explanation:
Series and sequences.
A. What are the approximate coordinates of the point of intersection of the two
graphs? What does this mean in terms of the two mold populations?
B. The area of mold A is given by the function Ad) = 100 -0.25 .When will this
mold cover 1000 square millimeters? Explain your reasoning.
The two mold populations are equal after 4.5 years and the number of days is 9.2
Calculating the approximate coordinates of intersectionFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the point of intersection to be
(x, y) = (4.5, 3)
The means that the two mold populations are equal after 4.5 years
Estimating when the moid will cover 1000 sq mlGiven that
A(d) = 100e⁰.²⁵ᵇ
We have
100e⁰.²⁵ᵇ = 1000
Divide by 100
e⁰.²⁵ᵇ = 10
So, we have
0.25d = ln(10)
Evaluate
0.25d = 2.3
Divide
d = 9.2
Hence, the number of days is 9.2
Read more about exponential functions at
https://brainly.com/question/2456547
#SPJ1
The dot plot below represents this set of data:
8, 7, 5, 5, 4, 2, 3, 3, 4, 6, 5, 4, 5, 5
Answer:
False
Step-by-step explanation:
There isnt two eights
Full working out for this question please.
Answer:
(0. - 11 )
Step-by-step explanation:
To find the y- intercept let x = 0 and solve for y, that is
y = - 3(0)² - 7(0) - 11 = 0 - 0 - 11 = - 11
y- intercept = (0, - 11 )
prime factorization of 44
231 give the serious
answer
Answer:
11,4021
Step-by-step explanation:
the steps are simply ,
44231
11^4021
Answer:
The Prime Factorization is:
11 x 4021
In Exponential Form:
111 x 40211
CSV Format:
11, 4021
All Factors of 44231:
1, 11, 4021, 44231
hope it helps
please mark Brainliest
Suppose you roll a die. Find the probability of the given event. Simplify your answer. P(a number less than 7)
Answer:
1/6
Step-by-step explanation:
There are 6 faces on a die, and you can only roll one face only. So, the denominator will be 6 because there are 6 faces, and 1 as the numerator because that's the equal proportion for each face (unless you use two dice)
(10^2+8^2+6^2+4^2+2^2)- (9^2+7^2+5^2+3^2+1^2)
55
you know you can just use a calculator or a search engine for that, right?
Answer:
i got 69 it should be right
Step-by-step explanation:
