Answer:
105 seconds
Step-by-step explanation:
To solve this, we can set up an equation.
First, let's find how far ahead Jillian is.
15*6=90
Jillian is 90 feet ahead.
Let's name the time that Samantha walks x.
7x is the distance Samantha walks.
90+6x is the distance Jillian walks.
We want to find how many seconds they have walked when the distance is equal.
So let's form an equation.
7x=90+6x
Subtract 6x from both sides.
x=90
Samantha needs to walk 90 seconds.
Jillian started 15 seconds before that.
90+15=105
Jillian had been walking for 105 seconds when the two girls had walked the same distance.
Hyperbola Question:
Two neighbors who live one mile apart hear an explosion while they are talking on the telephone. One neighbor hears the explosion two seconds before the other. If sound travels at 1100 feet
per second, determine the equation of the hyperbola on which the explosion was located.
(i know the answer is
[tex] \frac{ {x}^{2} }{1210000} - \frac{y {}^{2} }{5759600} = 1[/tex]
but i don't understand how you get it)
Answer:
[tex]\dfrac{x^{2}}{1210000 } - \dfrac{y^{2}}{5759600} = 1[/tex]
Step-by-step explanation:
A hyperbola is a curve for which the difference of the distances |d₂ - d₁| of any point P from the foci is constant.
The definition leads to the equation
[tex]\dfrac{x^{2}}{a^{2}} - \dfrac{y^{2}}{b^{2}} = 1[/tex]
1. Calculate the value of a²
Assume the neighbours are at the foci A and B.
The explosion is farther from B than from A, so it occurred on the right branch of the hyperbola.
Then AB = 1 mi = 5280 ft
and the distance from the focus to the y-axis is
c = 2640
The vertices are (±a,0).
The speed of sound is 1100 ft/s, so B is 2200 ft further from the explosion.
The distance from A to the vertex V₁ is c - a. Then
AB = 2200 + 2(c - a) = 2200 -2(2640 - 2a) = 2200 +5280- 2a = 5280
2a = 2200
a = 1100
a² = 1 210 000
2. Calculate the value of b²
[tex]\begin{array}{rcl}a^{2} + b^{2} & = & c^{2}\\1100^{2} + b^{2} & = & 2640^{2}\\b^{2} & = & 2640^{2} - 1100^{2}\\& = & 6969600 - 1210000\\& = & \mathbf{5759600}\\\end{array}[/tex]
3. Write the equation for the hyperbola
[tex]\mathbf{\dfrac{x^{2}}{1210000 } - \dfrac{y^{2}}{5759600}} = \mathbf{1}[/tex]
The equation of the hyperbola is [tex]\frac{x^2}{1210000} -\frac{y^2}{5759600^2} = 1[/tex]
How to determine the equation of the hyperbolaThe equation of an hyperbola is represented as:
[tex]\frac{x^2}{a^2} -\frac{y^2}{b^2} = 1[/tex]
The given parameters are given as:
AB = 1 mile
a = 1100 feet
Express the distance AB as feet
AB = 5280 ft
So, the distance AB from the foci is:
[tex]c = \frac{AB}2[/tex]
This gives
[tex]c = \frac{5280}2[/tex]
[tex]c = 2640[/tex]
The value of b is calculated as:
[tex]a^2 + b^2 = c^2[/tex]
So, we have:
[tex]1100^2 + b^2 = 2640^2[/tex]
This gives
[tex]b^2 = 2640^2 -1100^2[/tex]
Evaluate
[tex]b^2 = 5759600[/tex]
Recall that:
[tex]\frac{x^2}{a^2} -\frac{y^2}{b^2} = 1[/tex]
So, we have:
[tex]\frac{x^2}{1100^2} -\frac{y^2}{5759600^2} = 1[/tex]
[tex]\frac{x^2}{1210000} -\frac{y^2}{5759600^2} = 1[/tex]
Hence, the equation of the hyperbola is [tex]\frac{x^2}{1210000} -\frac{y^2}{5759600^2} = 1[/tex]
Read more about hyperbola at:
https://brainly.com/question/19395889
At a zoo, youth tickets cost $5 and adult tickets cost $9. A group that purchased x youth tickets and y adult tickets spent $90 on tickets. What is the domain of the relationship
Answer:
0 ≤ x ≤ 18
Step-by-step explanation:
Let 'x' be the number of youth tickets purchased at the zoo and 'y' be the number of adult tickets purchased at the zoo.
At a zoo, youth tickets cost $5 and adult tickets cost $9. A group spent a total of $90 on tickets. We can write as
5x + 9y = 90
to find x we divide both side by 5
x = (90-9y)/5 => 90/5 - 9y/5
x = 18 - 9y/5
The domain of the relationship is the possible set of values of x and y that satisfies the equation. The domain of this relationship is
0 ≤ x ≤ 18
At x = 0, it means only adult tickets were purchased.
At x = 18, it means only youth tickets were purchased.
Answer:
0 ≤ x ≤ 18
Step-by-step explanation:
got it correct on pluto
solve 8x+6=5(x+1)+2
please help me with this
Does anyone know how to find a in this please ??
Answer:
Step-by-step explanation:
180 - 67 = 113
180 - 113 - 42 = 25
α = 25º
it’s cut off but it says “about how many of them would you expect to be marked with a white dot.”
Answer:
Assuming that the person does not account for probability changes when counters are not replaced, the answer is 20 counters.
Step-by-step explanation:
Please refer to the picture above.
Disclaimer: Probability is not used to deduce the question. The knowledge of fraction is used instead to avoid excess complexity.
Assuming the number of dabbed counters follow the ratio of 1/4 as deduced from the number of dabbed counters in 200 counters, you would expect the number of dabbed counters in 80 counters to follow the same ratio of 1/4. Hence the answer is 20.
Tell which variable you would choose to eliminate when solving the system by elimination. Then solve the system by elimination.
2x+y=−5
Equation 1
−2x+y=8
Equation 2
Answer: 1.y= -2 2. y=2
Step-by-step explanation:
Find the zeros
of y= x2 - 6x- 4 by completing the square.
A. X=-3+ 13
B. X=3+ 13
C. X = +3
D. X = 31.5
Step-by-step explanation:
answer is (b) x=3+√13
-
Stuck on this help !
Answer:
9/16
Step-by-step explanation:
Total of 16 combinations:
1:2
1:3
1:4
1:5
2:2
2:3
2:4
2:5
3:2
3:3
3:4
3:5
4:2
4:3
4:4
4:5
Total is 5 or less
1:2
1:3
1:4
2:1
2:2
2:3
3:1
3:2
4:1
I got 9/16
Can anyone help w/ this?
Answer:
[tex]170in^3[/tex]
Step-by-step explanation:
[tex]V=\pi r^2h=\pi *3^2*6=169.646\\=170in^3[/tex]
find the values of a, b, and c.
Answer:
94°, 120°, 152°
Step-by-step explanation:
78°=(b+36°)/2 ⇒ b/2=78°-18° ⇒ b/2=60° ⇒ b=120°87°=(120°+x)/2 ⇒ x/2=86°-60° ⇒ x= 52°c=360°-(120°+52°+36°)= 152°a=(152°+36°)/2=94°a pet shelter has a verity of pets for adoptions whats the probability of geting a cat or a dog. show ur work
cat: 1/4 dog 2/5
Answer:
The probablility of getting a cat is 1/4 or 25%
The probability of getting a dog is 2/5 or 40%
Step-by-step explanation:
1/4 = .25 = 25%
2/5 = .4 = 40%
Please help! I really need help with this
Answer:
As shown in table, the probability that a person selected at random is going to city B is:
P = number of responses to city B/total number of people answered survey
= 36/100 = 0.36
Hope this helps!
:)
A.48
B.54
C.102
D.105
Answer:
D
Step-by-step explanation:
i did this one
Tara, Brett, Kerri, and Will bought 3_4pound of raspberries. They are sharing the raspberries equally. How many pounds of raspberries will each receive? A 3 B 1/4 C 3/16 D 1/16
Answer:
C 3/16
Step-by-step explanation:
C 3/16
How is the product of 2 and -5 shown on a number line?
4
3
7
2
-1 0 1
4 5 6 7 8 9 10
-10 -3 78 51
-2
-- 0 1 2 3 4 5 6 7 8 10
N
--10-9-6--6-5-4-3 -2 -1 0 1 2 3
4
$
8
8
10
-1 0 1
6 67
w
Answer:
the answer is -10
Step-by-step explanation:
2 × -5 =-10
The procedure for representing products 2 and -5 is described as follows:
Draw the distance of the first negative number then Extend the distance by the magnitude of the second negative number.
What is a number line?Integers are arranged at equal intervals along horizontal straight lines called number lines. A number line can be used to represent every number in a series. The endpoints of this line go on forever.
This refers to those as closed number lines. Number lines might be alternatively left empty or blank.
In the number line, negative numbers represent leftward distances. The product of a negative number and a positive number will be equal to the distance of the negative one by the number of times such distance is repeated.
The procedure is described as follows:
Draw the distance of the first negative number then Extend the distance by the magnitude of the second negative number.
And Draw the distance of the reflection of the result found in 2.
Learn more about number line here:
brainly.com/question/13425491
#SPJ7
Which inequality is shown in the graph?
Answer: D
Step-by-step explanation:
I don’t know how to explain this to you step by step but when it comes to questions like this try to think more “logically” (if that makes sense) especially if you’re not familiar with the topic, like me. Think about it, if it was the first one the line on the graph would be above the middle line (its addition plus its greater than y so that wouldn’t be correct). Now the second one is subtraction but its less than y and everything thats coloured goes up not down so it has to be greater than y. C is not the correct answer because its a regular equation and thats not what the question wants plus its the only question out of the the 4 answers which is completely the odd one out so you can just cancel that out. Mow we come to the last answer which is the correct answer because it follows all the right “points” I mentioned earlier. I hope this makes sense to you, sorry I couldn’t explain it better!
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!!
Kwame must earn more than 16 1616 gold pieces per day to afford living in the City of Gold. Write an inequality that describes G GG, the number of gold pieces Kwame must earn per day to afford living in the City of Gold.
Answer:
G > 16
Step-by-step explanation:
The expression "more than" 16 gold pieces per day means that the number of gold pieces Kwame earns each day (G) must be greater than 16. In order to represent that as an inequality, we should use the greater-than sign: >.
The inequality that describes the number of gold pieces Kwame must earn per day is G > 16.
In a quadrilateral A B C D angle d is
equal to 150° and angle a = angle b=angle c
Eind angle A, angle b, and angle c
Answer:
Step-by-step explanation:
Let ∠A = x
Therefore, ∠A = ∠B = ∠C = x
The sum of all angles of a quadrilateral is 360
∠D + ∠A + ∠B + ∠C =360
150 +x + x + x =360
150 + 3x = 360
3x = 360 - 150
3x = 210
x = 210/3
x = 70
∠A = ∠B = ∠C = x = 70°
UN NUMERO SE PUEDE ESCRIBIR COMO 2 POR 2 POR 3 POR 5.SI MULTIPLICAS ESTE NUMERO POR 6,¿CUAL SERA SU FACTORIZACION EN PRIMOS?¿Y SI LO MULTIPLICAS POR 8?
Answer:
2,880
Step-by-step explanation:
La facturación en primas sería de 2,880
PLEASE HELP --Which of the following best describes the figure?
concave pentagon
not a polygon
regular pentagon
Sophia is selling quarts of tomatoes at a road-side stand. The graph shows the amount Sophia earns by selling a certain number of quarts of tomatoes.
How much will Sophia earn if she sells 20
20
quarts of tomatoes?
Answer:
$80
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
She gets 16.00 for every 4 quarts she sells
The dollar amount increases by 16.00 after 4 quarts
Simplify 5^3/5^7 leaving your anwser in index form
Steps:
Simplify:
5³/5⁷
= 5³/5⁷
= 5*5*5/ 5*5*5*5*5*5*5
=1/5⁴
=1/625 (Decimal: 0.0016)
Steps by Step:
5³/5⁷
=125/5⁷
=125/78125
=1/625
Answer: =1/625 (Decimal: 0.0016)
Please mark brainliest
Hope this helps.
???? Anyone know the answer ASAP
Answer:
YES
Step-by-step explanation: I DID IT
Answer:
6 minutes
Step-by-step explanation:
First convert the hours into minutes to give you 60 minutes.
0.1 of 1 hour is also 0.1 multiplied by 1 hour, so you change the 0.1 into a fraction which is [tex]\frac{1}{10}[/tex] and multiply it with the 60 minutes
[tex]\frac{1}{10} * 60\\= 6mins[/tex]
Write 28 as a product of its prime factors
Answer:
2*2*7
Step-by-step explanation:
28 = 2*2*7
Answer:
2 x 2 x 7
Step-by-step explanation:
Jasmine is going to put $20 worth of gasoline in her car. She goes to the gas station where she pays a price of p-dollars per gallon for gas and gets g-gallons for it. Which of these two variables, the price or the gallons, is the dependent variable? Explain.
Answer:
I say p because in order to see how many dollars she pays, she needs to find how gallons are there.
Step-by-step explanation:
Correct me if I am wrong
Which point on the number line represents the rational number -2 3/5
Answer:
Step-by-step explanation:
A number line is a line that can be used to show the position of directed numbers. It has the negative numbers to its left ( i.e before zero) and positive number to the right (i.e after zero).
Rational numbers are positive or negative integers, fractions or decimals.
The rational number -2[tex]\frac{3}{5}[/tex] = -[tex]\frac{13}{5}[/tex] = -2.6 can be shown on the number line as indicated in the image attached to this answer.
Answer:A
Step-by-step explanation: i did the assignment on edge
A population of 100 frogs has a growth rate of 1.25% each month. At this growth rate,
the function f(x) = 100(1.25)* gives the population in x months. In how many months
will the population first reach 500?
Answer: 7.2 months
Step-by-step explanation:
Hi, to answer this question we have to substitute f(x) =500 in the equation given:
f(x) = 100(1.25)^x
500= 100(1.25)^x
Solving for x (number of months)
500/100 = 1.25^x
5 = 1.25^x
log 5 =log 1.25^x
log 5 =x (log 1.25)
log 5 /log 1.25 =x
x = 7.2 months
Feel free to ask for more if needed or if you did not understand something.
Prove that the difference of the squares of 2 consecutive numbers is always the sum of the 2 numbers
Answer:
see explanation
Step-by-step explanation:
let the 2 consecutive numbers be n and n + 1
sum = n + n + 1 = 2n + 1
and
(n + 1)² - n² ← difference of the squares
= n² + 2n + 1 - n²
= 2n + 1 = sum of 2 numbers
A steel hex nut has two regular hexagonal bases and a cylindrical hole with a diameter of 1.6 centimeters through the middle. The apothem of the hexagon is 2 centimeters. A cylinder is cut out of the middle of a hexagonal prism. The hexagon has an apothem with a length of 2 centimeters and base side lengths of 2.3 centimeters. The prism has a height of 2 centimeters. The cylinder has a diameter of 1.6 centimeters. The equation for the area of a regular hexagon = one-half (apothem) (perimeter). What is the volume of metal in the hex nut, to the nearest tenth? Use 3.14 for π. 21.1 cm3 23.6 cm3 27.6 cm3 31.6 cm3
Answer:
[tex]V=V_p-V_cV=27.712 cm^3 - 4.019 cm^3V=23.693 cm^3V=23.6 cm^3[/tex]
Step-by-step explanation:
Given that:
Diameter of the cylinder: d=1.6 cm
Apothem of the hexagon: a=2 cm
Assuming the thickness of the steel hex nut: t=2 cm
Volume of metal in the hex nut: V=?
[tex]V=V_p-V_c[/tex]
[tex]\texttt {Volume of the prism}: V_p\\\\\texttt {Volume of the cylinder}: V_c[/tex]
Prism:
[tex]V_p=Ab h[/tex]
Ab=n L a / 2
Number of the sides: n=6
Side of the hexagon: L
Height of the prism: h=t=2 cm
Central angle in the hexagon: A=360°/n
A=360°/6
A=60°
[tex]\tan \frac{A}{2} =\frac{L}{2} / a[/tex]
[tex]\tan \frac{60}{2} =\frac{L}{2} / 2cm[/tex]
[tex]\tan 30 =\frac{L}{2} / 2cm[/tex]
[tex]\frac{\sqrt{3} }{3} =\frac{\frac{L}{2} }{2}[/tex]
[tex]2\frac{\sqrt{3} }{3} =\frac{L}{2}[/tex]
[tex]L=4\frac{\sqrt{3} }{3}[/tex]
[tex]Ab=n *L *\frac{a}{2}[/tex]
[tex]Ab=6(4\frac{\sqrt{3} }{3} )(2cm)/2[/tex]
[tex]=24\frac{\sqrt{3} }{3} cm^2\\\\=8\sqrt{3} cm^2[/tex]
[tex]V_p=Ab h[/tex]
[tex]=(8\sqrt{3} )cm^2(2cm)\\\\=16\sqrt{3} cm^3\\\\=16(1.732)cm^3\\\\=27.712cm^3[/tex]
Cylinder:
[tex]V_c=\pi\frac{d^2}{4} L[/tex]
π=3.14
d=1.6 cm
Height of the cylinder: h=t=2 cm
[tex]V_c=3.14\times\frac{1.6^2}{4} \times2\\\\=3.14\times\frac{2.56}{4} \times 2\\\\=2.0096\times2\\\\=4.019cm^3[/tex]
[tex]V=V_p-V_cV=27.712 cm^3 - 4.019 cm^3V=23.693 cm^3V=23.6 cm^3[/tex]
Answer:
23.6
Step-by-step explanation:
Edge 2020