Answer:
It will take the boulder approximately 4.28 seconds to hit the road
Step-by-step explanation:
The given height of the cliff from which the boulder falls, h = 90 feet
The equation that can be used to find the time it takes the boulder to fall is h = u·t + (1/2)·g·t²
Where;
h = The height of the cliff = 90 ft.
u = The initial velocity of the boulder = 0 m/s (The boulder is assumed to be at rest when it falls)
g - The acceleration due to gravity ≈ 9.81 m/s²
t = How long it will take for the boulder to hit the road below
Plugging in the values gives;
90 = 0 × t + (1/2)×9.81×t² = 4.905·t²
∴ t = √(90/4.905) ≈ 4.28
The time it takes the boulder to hit the road, t ≈ 4.28 seconds.
You and your friend are selling magazine subscriptions for a fundraiser. After w weeks, you have sold (2w+9) subscriptions and your friend has sold (6w+3) subscriptions.
Answer:
3/2 weeks
Step-by-step explanation:
The question: find the number of weeks you and your friend sells equal number of magazine
You = 2w + 9
Your friend = 6w + 3
Equate both equations
2w + 9 = 6w + 3
Collect like terms
2w - 6w = 3 - 9
- 4w = - 6
w = -6/-4
w = 3/2 weeks
Joey is running an experiment with a mass on a spring. Joey models the height of the mass above the table he is working on using the equation h(t)=6.85cos(3.42t)+9, where the height is in inches and the time, t, is in seconds since he let the mass free. How many seconds, to the nearest tenth, will it take for the mass to return to its original position?
Answer: 1.8 s
Step-by-step explanation:
Given
The height of the spring mass system above the table is given by
[tex]h(t)=6.85\cos (3.42t)+9[/tex]
The mass is performing S.H.M with frequency [tex]\omega =3.42[/tex]
and [tex]\omega T=2\pi[/tex]
[tex]\therefore T=\dfrac{2\pi }{\omega}[/tex]
time when mass returns to its original position
[tex]T=\dfrac{2\pi }{3.42}\\\\T=1.8\ s[/tex]
The number of seconds, to the nearest tenth, will it take for the mass to return to its original position is 1.8 seconds.
Calculation of the time in seconds:Since the equation h(t)=6.85cos(3.42t)+9, where the height is in inches and the time, t, is in seconds
So here the time should be
[tex]= 2\pi \div 3.42\\\\= 2\times 3.14\div 3.42[/tex]
= 1.8 seconds
Therefore, The number of seconds, to the nearest tenth, will it take for the mass to return to its original position is 1.8 seconds.
Learn more about time here: https://brainly.com/question/24308516
Jada walks up to a tank of water that can hold up to 10 gallons how many more minutes will it take for the tank to drain completely explain or show your reason
Answer:
7.5 minutes
Step-by-step explanation:
Given
See attachment for complete question
Let
[tex]t \to time[/tex]
[tex]y \to capacity[/tex]
From the question, we have the following points
[tex](t_1,y_1) = (0,7)[/tex] --- When he first sees it
[tex](t_2,y_2) = (3,5)[/tex] --- 3 minutes later
First, we calculate the rate (m)
[tex]m = \frac{y_2 -y_1}{t_2 -t_1}[/tex]
[tex]m = \frac{5 -7}{3 -0}[/tex]
[tex]m = -\frac{2}{3}[/tex]
The discharge rate is 2/3 gallons per minute
To calculate the additional minute, we simply consider the capacity of the tank at the later time. i.e. 5 gallons
To calculate time (t), we have:
[tex]Rate * Time = Capacity[/tex]
[tex]\frac{2}{3} * t = 5[/tex]
Solve for t
[tex]t = 5 *\frac{3}{2}[/tex]
[tex]t = \frac{15}{2}[/tex]
[tex]t = 7.5[/tex]
what are the roots of the quadratic equation below? 3x^2+15x-5=0
Answer:
X1 = [tex]\frac{=15+\sqrt{285} }{6}[/tex] and X2 = [tex]\frac{-15-\sqrt{285} }{6}[/tex]Step-by-step explanation:
To find the roots of a quadratic equation, you need to solve the quadratic equation by using the quadratic formula.
OR
You can use the (Equation/Function) mode on the calculator.
[tex]\frac{-b+-\sqrt{b^{2} -4ac } }{2a} x \neq 0[/tex]
For this equation,
a = 3
b = 15
c = -5
X1 = [tex]\frac{-15+\sqrt{15^{2} -4(3)(-5) } }{2(3)} x \neq 0[/tex]
X2 = [tex]\frac{-15-\sqrt{15^{2} -4(3)(-5) } }{2(3)} x \neq 0[/tex]
Solving this on the calculator and you should get
X1 = [tex]\frac{=15+\sqrt{285} }{6}[/tex] X2 = [tex]\frac{=15-\sqrt{285} }{6}[/tex]
a, b, c = constants, where a ≠ 0
x = the unknown
Can someone answer this for me?
Answer:
sin = opposite / hypotenuse
cos = adjacent/hypotenuse
sin U = 4/5
cos U = 3/5
sin T = 3/5
cos T= 4/5
I need help with it one plz
Answer:
- 2/5
Step-by-step explanation:
(3/5 + 1/5) + (4/5 - 2/5) = 6/5
6/5 - (9/5-1/5) = - 2 /5
A rectangle has length (x+3)cm and width (x-2).Given that it's area is 50cm2,find the dimensions of the rectangle
Answer:
length- 10cm, width- 5cm
Step-by-step explanation:
You want to convert this into an algebraic equation.
Since a=lw, in this case, 50=lw. Subbing (x+3) for l and (x-2) for w, we get the equation (x+3)(x-2)=50.
Using FOIL, we can expand the brackets to make x²-2x+3x-6=50 and collect like terms to x²+x-6=50.
We want all the numbers on one side (to use the null factor law), so we subtract 50 from both sides. This gives x²+x-56=0.
From there, we factorise it, which becomes (x-7)(x+8)=0. (I used the cross method for this)
With the null factor law, one of the brackets must be equal to 0, meaning x-7=0 or x+8=0. This gives x as either 7 or -8.
With measurement, units must be positive, meaning it has to be 7. We can sub this for x in the 2 equations (length and width) to get the answers.
Length=x+3 becomes 7+3, which is 10cm.
Width=x-2 becomes 7-2, which is 5cm.
**This content involves writing, expanding, and factorising quadratic equations, and the null factor law which you may wish to revise. I'm always happy to help!
help help help :)))))))
Answer:
✓✓ Area of traingle = 1.2 cm^2 ✓✓
Step-by-step explanation:
Hello mate (◕ᴗ◕✿)
=>> In above traingle, height and hypotenuse are given
=> height = 12 cm
=> Hypotenuse = 14 cm
✓✓ Area of traingle = 1/2(base*height) ✓✓
we need to find base of above traingle
Base = √Hypotenus - √Perpindicular
Base = √14 - √12
Base = 3.7 - 3.4
Base = 0.2 cm
Now, we can find area of traingle
Area of traingle = 1/2(Base*Height)
Area of traingle = 1/2(0.2*12)
Area of traingle = 6*0.2
Area of traingle = 1.2 cm^2
Hope it helps you mate (. ❛ ᴗ ❛.)
Answer :
➢ 43.3 cm²
Explanation :
let the missing side be c
a = 12 cm
b = 14 cm
Pythagoras theorem :
➢ a² + c² = b²
➢ 12² + c² = 14²
➢ 144 + c² = 196
➢ c² = 196 - 144
➢ c² = 52
➢ c = √52
➢ c = 7.21
Area = 1/2 × a × c
➢ 1/2 × 12 × 7.21
➢ 6 × 7.21
➢ 43.26 cm²
➢ 43.3 cm² [ round off to 1 decimal place ]
Figure ABCD is rotated clockwise about the origin through 360 degrees. Identify the transformed figure.
Answer: 360 is a complete circle meaning the figure will be back where it was originally
Step-by-step explanation:
r=x(a+b) solve for A
Answer:
Step-by-step explanation:
r=x(a+b)/x
r/x=a+b-b
r/x-b=a
PLSSS ANSWER FASTTT
If angle ACB is 34 degrees, what is the measure of angle ADB?
A
Answer:
34 because the shape is split.
Step-by-step explanation:
Someone pls help me ill hive out brainlist pls don’t answer if you don’t know
Answer:
B. 14 and 15
hope this helps
have a good day :)
Step-by-step explanation:
the square root of 200 is 14.14213562 so it has to be between 14 and 15
Write the system and
Brian sold fruit at his stand. Apples cost $0.40 and pears cost $0.50 each. In an afternoon he
sold 52 pieces of fruit and made $24. How many of each did he sell?
Answer:
20 apples, 32 pears
Step-by-step explanation:
Using a for number of apples and p for number of pears, you get a+p=52 (amount) and 0.4a+0.5p=24 (cost).
One way of solving simultaneous equations is using like terms and adding/subtracting them to remove a variable. There aren't any like terms here, but we can create some by multiplying terms.
Multiplying the second equation by 2 gives 0.8a+p=48, so that makes a like term.
Since the symbols are the same in front of the like term, we subtract the second term from the first one. This gives 0.2a=4.
Dividing by 0.2 gives a=20.
We can sub this into either equation to get the value of p.
a+p=52, so 20+p=52, meaning p=32.
**This content involves simultaneous equations, which you may want to revise. I'm always happy to help!
What are the possible steps involved in solving the equation shown? Select three options.
3.5 + 1.2(6.3 - 7x) = 9.38
O Add 3.5 and 1.2.
O Distribute 1.2 to 6.3 and -7x
O Combine 6.3 and -7x
O Combine 3.5 and 7.56.
D Subtract 11.06 from both sides.
Answer:
Distribute 1.2 to 6.3 and -7x
Combine 3.5 and 7.56
suhtract 11.06 from both sides
If my box plot is ranged from 60-64 in height and inches what is the data value is the upper quartile ( q3)
Answer:
[tex]Q_3 = 64[/tex]
Step-by-step explanation:
Given
Box of a box plot with the range: 60 - 64
Required
The upper quartile
To do this, we simply identify the endpoint of the range
Given that the range of the box is 60 to 64.
We have:
[tex]Start = 60[/tex]
[tex]End = 64[/tex]
Hence:
[tex]Q_3 = 64[/tex]
help pls. cant figure it out.
[tex]\longrightarrow{\green{a\:=\:2}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\purple{Step-by-step\:explanation}}{\purple{:}}}}}[/tex]
➡[tex]\:4a + 1 = a + 7[/tex]
Combining like terms, we have
➡[tex]\:4a - a = 7 - 1[/tex]
➡[tex]\:3a = 6[/tex]
➡[tex]\:a = \frac{6}{3} [/tex]
➡[tex]\:a = 2[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
➪ [tex] \: 4 \times 2 + 1 = 2 + 7[/tex]
➪ [tex] \: 8 + 1 = 9[/tex]
➪ [tex] \: 9 = 9[/tex]
➪ [tex] \: L.H.S.=R. H. S[/tex]
Hence verified.
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]
Maria rolls a six sided die. What is the possibility that she rolls a prime number?
1/6
1/3
1/2
2/3
Answer:
1/2
Step-by-step explanation:
2, 3, and 5 are the prime numbers. Therefore, it would be 3/6 or 1/2 chance she rolls a prime number.
If two side of a right angle triangle is 25cm and 15cm what is the length of the unknown side
Answer:
29.2 cm
Step-by-step explanation:
The two leg lengths are 15 and 25 cm and we are to find the length of the hypotenuse. The Pythagorean Theorem applies here because this is a right triangle.
a^2 + b^2 = c^2 becomes 15^2 + 25^2 = 225 + 625 = 850
The hypotenuse length is thus √850 ≈ 29.2 cm
ASAP what is the answer?
Answer: The ASAP Math program provides an opportunity for additional small group instruction for students who find the math program challenging. Students in grades 1 to 4 will come to the ASAP room two to three times a week during the math block.
PLZ HELP!!!!! ASAP!!!!!!!!!!!! NO FILES!
Answer:
A' (1, -4)
B' (-4, -2)
C' (-5, 4)
D' (-2, 1)
Step-by-step explanation:
When reflecting a point across the x-axis, the x-coordinate remains the same, but the y-coordinate becomes its additive inverse.
The additive inverse of a number is simply the opposite of a number.
So, to reflect this quadrilateral across the x-axis, we must change the coordinates.
Remember: When reflecting a point across the x-axis, the x-coordinate remains the same, but the y-coordinate becomes its additive inverse.
Point A: (1, 4) ⇒ A' (1, -4)
Point B: (-4, 2) ⇒ B' (-4, -2)
Point C: (-5, -4) ⇒ C' (-5, 4)
Point D: (-2, -1) ⇒ D' (-2, 1)
The attachment will help as well.
HCF of smallest 2 digit composite number and smallest 3 digit prime number is?
Answer:
HCF = 1
Step-by-step explanation:
Smallest 2 digit composite number = 10
Smallest 3 digit prime number = 101
Factors of 10 = 1 , 2 , 5
Factors of 101 = 1 , 101
HCF = 1
What is the equation of the parabola, in vertex form, with vertex at (-2,-4) and
directrix x = -6?
O A. (x+2) = 8(y+4)
B. (y+4)2 = - 8(x+6)
O c. (y+4)2 = 16(x+2)
O D.(x+4)² = 8(y+2)
Answer:
Step-by-step explanation:
The distance between the vertex and the directrix is 4 units, that means that p = 4 in the equation
[tex](y-k)^2=4p(x-h)[/tex] and h and k are the coordinates of the vertex. Filling in:
[tex](y+4)^2=4(4)(x+2)[/tex] which simplifies to
[tex](y+4)^2=16(x+2)[/tex] choice C
Option C is correct, (y+4)² = 16(x+2) is the the equation of the parabola, in vertex form, with vertex at (-2,-4) and directrix x = -6
What is Parabola?A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
The focus of the parabola is at a point that is equidistant to the vertex and the directrix.
Since the directrix is x = -6, the focus is at (-2+4,-4) = (2,-4).
The vertex form of the equation of a parabola is given by:
(y - k)² = 4p(x - h)
where (h, k) is the vertex and p is the distance between the vertex and focus.
In this case, (h, k) = (-2,-4) and the focus is at (2,-4). Therefore, p = 4.
Substituting the values into the vertex form equation, we get:
(y + 4)² = 4(4)(x + 2)
Simplifying, we get:
(y + 4)² = 16(x + 2)
Hence, (y+4)² = 16(x+2) is the the equation of the parabola, in vertex form, with vertex at (-2,-4) and directrix x = -6
To learn more on Parabola click:
https://brainly.com/question/31142122
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Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
The answer is C≈49.64
Answer:
C=2πr=2·π·7.9≈49.63716
Step-by-step explanation:
brainliest??
I AM GOING TO FAIL THIS EXAM L M A F O
Answer:
x = 4
Step-by-step explanation:
The line in the triangle is an angle bisector and divides the opposite sides into segments that are proportional to the other 2 sides, that is
[tex]\frac{x+6}{20}[/tex] = [tex]\frac{x}{8}[/tex] ( cross- multiply )
20x = 8(x + 6) = 8x + 48 ( subtract 8x from both sides )
12x = 48 ( divide both sides by 12 )
x = 4
cual es la distancia entee los siguientes puntos R ( 6,-10) M (5,4) C(7,3) H (8,6) M (-4,9)
Answer:
M ( -4,9)
Step-by-step explanation:
What is the degree of the monomial 4x^2y^5
Answer:
5
Step-by-step explanation:
The highest power is 5 so the degree of the monomial is also 5.
i need help in this assignment
Given:
A figure of a rectangular prism with length l, width w and height h.
To find:
The surface area of the rectangular prism.
Solution:
The product of twice of the length l and the width w is:
[tex]2\times l\times w=2lw[/tex] ...(i)
The product of twice of the length l and the height is:
[tex]2\times l\times h=2lh[/tex] ...(ii)
The product of twice of the width w and the height h is:
[tex]2\times w\times h=2wh[/tex] ...(iii)
The surface area of the prism is the sum of (i), (ii) and (iii). So, the expression for the surface area is:
[tex]A=2lw+2lh+2wh[/tex]
[tex]A=2(lw+lh+wh)[/tex]
Therefore, the required expression is [tex]2(lw+lh+wh)[/tex].
Help!!!!!! I Don’t Know The Answer It’s Hard
Answer:
D
Step-by-step explanation:
Have a great summer :)
Answer:
C
Step-by-step explanation:
The slope is negative, so we can exclude the graph A and D
If we substitute y with 2 and x with -3 we have
2 = -4/3 (-3) -2
2 = 4 - 2
2 = 2
the equality is verified so C is the answer
Write all subsets of set {1, 2, 3}
The set {1, 2, 3} has 8 subsets.
A set with 'n' elements in it can have 2n subsets.
the correct answer
A school bus has 25 seats, with 5 rows of 5 seats, 15 students from the first grade and 5 students from the second grade travel in the bus. How
many ways can the students be seated if all of the second grade students occupy the first row?
ОА 2P20
OB gPg 20115
oc. gg* 25 C14
OD. SPg ISPIS
Ol. 9Pg x 2g Cis
Answer:
5P5 × 20P15
Step-by-step explanation:
i think...
sorry if im wrong
good luck
