After 2.57 hours, the distance between Steve and Elsie will be 25 miles.
What exactly is the distance?Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending point. Use the formula d = st, or distance equals speed times time, to find the distance. Since both represent a certain amount of distance per unit of time, such as miles per hour or kilometers per hour, rate and speed are comparable.So, let t (hours) represent the amount of time Elsie needs to travel before they are 25 miles apart.
Steve takes longer because he is 2 hours earlier, so his time is t + 2.
Steve travels x[tex]s_s=2(t+2)[/tex] miles to the north.Elsie travels a distance [tex]s_c=2.5 t[/tex] to the west.So, according to the formula the distance between Steve and Elsie will be:
[tex]\sqrt{s_s^2+s_c^2}=\sqrt{(2(t+2))^2+(2.5 t)^2}=25[/tex]Solve for t as follows:
[tex]\begin{aligned}&(2(t+2))^2+(2.5 t)^2=25^2=625 \\&4(t+2)^2+6.25 t^2=625 \\&4\left(t^2+4 t+4\right)+6.25 t^2=625 \\&10.25 t^2+16 t-609=0 \\&t=\frac{-b \pm \sqrt{t^2-4 a x}}{2 a} \\&t=\frac{-16 \pm \sqrt{(16)^2-4 *(10.25) *(-109)}}{2 *(10.25)} \\&t=\frac{-16 \pm 68.74}{20.5}\end{aligned}[/tex]
So, t = 2.57 or t = -4.13.
As we know that time can only be positive so it t = 2.57.Therefore, after 2.57 hours, the distance between Steve and Elsie will be 25 miles.
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The correct question is given below:
Steve and Elsie are camping in the desert, but have decided to part ways. Steve heads north, at 8 AM, and walks steadily at 2 miles per hour. Elsie sleeps in and starts walking west at 2.5 miles per hour starting at 10 AM. When will the distance between them be 25 miles?
Estimate the quotient of 72.4 ÷ 9.38.
8
9
10
11
Answer:
7.719
Step-by-step explanation:
Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $35 to come to his house and $50 for every hour they work. If the plumber charges Jerald a total of $190, how many hours did the plumber work?
Write and solve an equation to determine the number of hours worked by the plumber.
50x + 35 = 190; x = 3.1 hours
50x − 35 = 190; x = 4.5 hours
35x + 50 = 190; x = 4 hours
35x − 50 = 190; x = 6.9 hours
The equation to determine the number of hours worked by the plumber is 190 = 35 + 50x and the number of hours is 3.1 hours option (A) is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Jerald is having drain issues at his home and decides to call a plumber.
The plumber charges $35 to come to his house and $50 for every hour they work.
Let x be the number of hours:
190 = 35 + 50x
50x = 155
x = 3.1 hours
Thus, the equation to determine the number of hours worked by the plumber is 190 = 35 + 50x and the number of hours is 3.1 hours option (A) is correct.
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Explain why the statement line LR ≅ line RL and ∠CBA ≅ ∠ABC are both true by the Reflexive Property of Congruence.
The reflective Property of Congruence states that any figure is congruent with itself, therefore line LR ≅ line RL and ∠CBA ≅ ∠ABC.
What is congruence?If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence.
Reflexive Property of Congruence said that an angle line segment or any shape is congruent with itself.
For example, a line segment with a length of 5 meters will be the same as another line with 5 meters or a copy of that line so both will be congruent.
Line LR and RL are the same in length thus line LR ≅ line RL.
Angle CBA and angle ABC are the same thus ∠CBA ≅ ∠ABC.
Hence "The reflective Property of Congruence states that any figure is congruent with itself, therefore line LR ≅ line RL and ∠CBA ≅ ∠ABC".
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how many groups of 5/8 are in 15/16? Show all your work.
Simplify: 3√5•√10+11√5•√10-√5
choices:
A) 14√15-√5
B) 6√35
C) 26√50
D) 14√50-√5
The value of the numbers 3√5•√10+11√5•√10-√5 based on the information is D. 14✓50 - ✓5
How to illustrate the information?It should be noted that based on the information given, we simply want to simplify 3√5•√10+11√5•√10-√5.
This will be illustrated as:
= 3√5•√10+11√5•√10-√5
It should be noted that the numbers inside the square roots will be multiplied. This will be:
= (3√5•√10) + (11√5•√10) -√5
= 3✓50 + 11✓50 - ✓5
= 14✓50 - ✓5
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-w/5 + nine = thirteen
Answer:
w=-20
Step-by-step explanation:
-w/5+9=13
-w/5=-1/5w
-1/5w+9=13
Subtract 9 on both side
Multiply both sides by -5/1
w=-20
A local pizza shop has a membership program for frequent buyers. the membership costs $20 per month and members get a discounted price of $1.75 per slice of pizza. robert purchased a membership to this pizza shop. how much would robert have to pay the pizza shop if he bought 6 slices of pizza this month? what would be the monthly cost for xx slices of pizza?
Answer: $10.50
Step-by-step explanation:
Cot of 1 slice a pizza = $1.75
Cost of 6 slices of pizza = 6 × $1.75
=$10.50
Hence, Robert will pay $10.50 for the 6 slices of pizza and $20 for the membership.
2/3c - 2 = 2 + c
Solve for C.
Answer:
c=-12
Step-by-step explanation:
Let's solve your equation step-by-step.
2/3c−2=2+c
Step 1: Simplify both sides of the equation.
2/3c−2=2+c
2/3c+−2=2+c
2/3c−2=c+2
Step 2: Subtract c from both sides.
2/3c−2−c=c+2−c
−1/3c−2=2
Step 3: Add 2 to both sides.
−1/3c−2+2=2+2
−1/3c=4
Step 4: Multiply both sides by 3/(-1).
(3/−1)*(−1/3c)=(3/−1)*(4)
c=−12
Answer:
c=−12
Which of the following is the definition for permutation?
A. Selections of objects in which the order of the objects doesn't
matter.
B. The probability of an event where order doesn't matter when
selecting the objects.
C. Selections of objects in which the order of the objects matters.
D. The probability of an event where order matters when selecting
the objects.
SUBMIT
Estimate the quotient of 72.4 ÷ 9.38.
8
9
10
11
Answer: 80
Step-by-step explanation:
72.4 = 724/10
9.38=
938/10.
72.4/9.38
= 7.7
=8 approximately
The estimated quotient of 72.4 ÷ 9.38 is 8
Estimation is the process of calculating the approximate value to make the calculation easier and simple.
The rounding off a number is the process of putting a number up or down to the nearest whole number or the nearest tens, hundred, thousand, etc
First number is 72.4
Round the number to the nearest whole number
72.4 = 72
Second number is 9.38
Round the number to the nearest whole number
9.38 = 9
Divide the number 72 by 9
72/9 = 8
The quotient is 8
Hence, the estimated quotient of 72.4 ÷ 9.38 is 8
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simplify 3x + 5y - x +2y
Answer:
2x + 7y
Step-by-step explanation:
first we need to align the sample sympols
like this
3x -x + 5y + 2y
then you can easily calculate
Answer:
2x+7y
Step-by-step explanation:
3x-×=2x, 5y+2y=7y
2x+7y
could someone lend a hand... please?
The diagram prove that m ║n by the consecutive interior angles converse.
How to find angles?The diagram is to prove line m is parallel to line n.
Therefore,
m ║ n
Hence,
m∠1 = 115°, m∠2 = 65° is given.
m∠1 + m∠2 = m∠1 + m∠2 follows the reflexive property of equality.
The reflexive property of equality means that anything is equal to itself
m∠1 + m∠2 = 115° + 65° is the substitution property of equality
Supplementary angles add up to 180 degrees.
m∠1 + m∠2 = 180 is the definition of supplementary angles
∠1 and ∠2 are supplementary when simplify
m ║ n by consecutive interior angles converse.
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Someone please help me with this!!! (Will mark Brainliest)
Answer: 5/3
Step-by-step explanation:
The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.
We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.
Given the figure, find the total area of the shaded region.
-4
A
D
8.
6-
4-
2-
O
-2-
-4
2
G
S
B
The area of the shaded region is
R
6 8
-U
X
square units.
Answer:
what was one survival event you experienced
which lines are parallel if angle 4 = angle 5? justify your answer
r and s are the parallel lines, if ∠4 equals ∠5.
Given,
The figure with,
Four lines: Line r, Line s, Line l and Line m.
Angles: ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7 and ∠8
Here, we have to find the parallel lines when ∠4 = ∠5
Lets see:
Angle 1 and angle 4 are the same because the opposite angles created by two crossing lines are identical. As a result, angle 1 also equals angle 5.
The corresponding angles are identical when two parallel lines cross across a line. To put it another way, if r and s are parallel, the angles created when l intersects r and s are same. Angle 1 equals Angle 5, Angle 2 equals Angle 6, etc. We can infer that r and s are parallel since we know that angle 1 Equals angle 5.
So, we can conclude that if ∠4 equals ∠5, then r and s are the parallel lines.
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A dealer purchased an old car for 70,000. He spent 17,500 on its repair and painting. Due to lack of demand he had to dispose it at a loss of 12%. What was the selling price of the car?
The selling price of the car is 77,000.
First, let's define what a selling price is.
The selling price is the price the customer pays to purchase the good.
Selling price = Cost price – (100% Loss)/100
We are told that the car cost 70,000 and that 17,500 was lost (12%) in repairs and painting.
The car's total cost is equal to 70,000 + 17,500 = 87,500.
So, the car's cost price is 87,500.
Selling price = 100/12/100 x cost price
= 100/12/100 x 87,500
= 0.88 x 87,500
= 77,000
Consequently, the car is being sold for $77,000.
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Chloe had 3/4 of a pizza left. Addie ate 1/6 of Chloe's pizza. How much pizza did Addie eat?
Answer: 3/24 or 1/8 of the pizza
Step-by-step explanation:..
Frank is riding his bicycle for 6 hours at a speed of 9.6 kilometers per hour. For how many kilometers does he ride?
On a certain hot summer's day, 273 people used the public swimming pool. The daily prices are $1.25 for children and $2.50 for adults. The receipts for admission totaled $528.75. How many children and how many adults swam at the public pool that day?
The number of children is 123 and the number of adults is 150 for that day.
According to the question,
We have the following information:
273 people used the public swimming pool.
Price for children = $1.25
Price for adults = $2.50
The total amount received = $528.75
Now, let's take the number of children to be x and the number of adults to be y on that day.
So, we have the following expression:
x + y = 273
x = (273-y) .... (1)
1.25x + 2.50y = 528.75
Now, putting the value of x from equation 1:
1.25(273-y) + 2.50y = 528.75
341.25 - 1.25y + 2.50y = 528.75
341.25 + 1.25y = 528.75
1.25y = 528.75-341.25
1.25y = 187.5
y = 187.5/1.25
y = 150
Now, putting this value of y in equation 1, we will find the value of x:
x = 273-y
x = 273-150
x = 123
Hence, the number of children is 123 and the number of adults is 150 on that particular day.
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1. How would you subtract a negative fraction from a positive
decimal?
Answer:
you could either make the fraction a decimal or my personal like is to make the decimal a fraction
Step-by-step explanation:
convert the fraction to a decimal or decimal to fraction
Someone help with geometry please the answer I put isn’t correct
The △ABC is congruent to △DCB (△ABC ≅ △DCB) under the SAS condition.
What is the congruency of triangles?Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, rotate, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.So, △ABC ≅ △DCB:
CB = CB (Common line - Given)AC = DB (Similar lines - Given)∠ABC = ∠DCB = (Right angle - Given)So, △ABC ≅ △DCB is under SAS condition.
Therefore, the △ABC is congruent to △DCB (△ABC ≅ △DCB) under the SAS condition.
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GUYS PLSSS HELPPPPPP
Melissa is having a party. She has $126 to spend on ice cream. Each container of ice cream costs $6. How many containers of ice cream will she be able to purchase?
Answer: 21 containers of ice cream
Step-by-step explanation: simple problem, take 126 and divide it by 6 to get your answer
3x^2 + 36x + 11 = 0
Hello, could you please help me factorise this / complete the square?
Answer:
x = +/-[tex]\frac{\sqrt{291} }{3} -6[/tex]
Step-by-step explanation:
What is the value of x, when -9 (-5) = 1 + 22-¹/?
O A x=1³
I= 1²/
O B. X= 2/1/
OC x=2²/
OD x=2³/1
I can help you with this equation, if you type it out correctly :). The input you made doesn´t make sense.
Simplify 2/5(14–27)+2^5÷16.
We can simplify the numerical expression to get:
(2/5)*(14 - 27) + (2⁵/16) = -16/5
How to simplify the numerical expression?Here we have the expression:
(2/5)*(14 - 27) + (2⁵/16)
Let's simplify the term in the right first, we know that:
2⁵ = 2*2*2*2*2 = 4*4*2 = 16*2 = 32
Replacing that we get:
(2⁵/16) = 32/16 = 2
Then we get:
(2/5)*(14 - 27) + (2⁵/16) = (2/5)*(14 - 27) + 2
Now we can simplify the term in the left:
(2/5)*(14 - 27) = (2/5)*(-13) = -26/5
Replacing that we get:
(2/5)*(14 - 27) + 2 = -26/5 + 2 = -26/5 + 10/5 = -16/5
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Can anyone help me get through this problem I’ve tried using my knowledge but it’s not much. PLEASE HELP.
The scissor has intersecting lines with angles 1,2,3,4.The angles are ∠1=159° and ∠3 is 159°. We got the angle ∠2=21° and ∠4=21°.
Given that,
In the picture there is a scissor.
The scissor has intersecting lines with angles 1,2,3,4.
∠1=159° and ∠3 is 159°.
We have to find the angles ∠2 and ∠4.
Two straight lines that intersect at the same location are said to be intersecting lines. The junction point is the place where two intersecting lines meet. Four angles are created when two lines cross. The four angles added together always equal 360 degrees. There is a unique connection between the angles created when lines intersect.
The straight line has 180°
∠1+∠2=180°
159°+∠2=180°
∠2=180°-159°
∠2=21°
Now,
∠3+∠4=180°
159°+∠4=180°
∠4=180°-159°
∠4=21°
Therefore, the angle ∠2=21° and ∠4=21°.
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surface area of a cuboid with dimensions of 9cm 5cm and 7cm
Please help me I will give you extra points and the crown
Using the figure below, Maggie used the definition of vertical angles to help her solve for x. Since vertical angles are congruent, she set the two given expressions equal to each other. After solving for x, her teacher said she got the wrong value for x. Explain where Maggie made her mistake when solving for x.
Answer:
Maggie did not combine like terms correctly when she subtracted 7x from both sides of the equation. Here is a correct solution:
4x + 2 = 7x - 25
-3x + 2 = -25
-3x = -27, so x = 9, not -9
1. Check whether the following is closure under multiplication : 7×12 = 72
2. The sum of two integers is -38,one of them is -22.Find the other.
3. In a competitive exam, Gopi gets 4 marks for each correct answer and -2 for each wrong answer. If he gives 32 correct answers and 8 wrong answers, what will be his total score?
7 × 12 = 72 satisfies the closure property of multiplication, the other integer when the sum is - 38 and one integer is - 22 will be - 16 and the total score for Gopi will be 112 marks.
1)
Closure property of multiplication:
It states that if two real numbers a and b are multiplied, then the product will be a real number as well.
We have 7 × 12 = 72
7, 12 and 72 all are real numbers.
So, it is a closure property under multiplication.
2)
Sum = - 38
a = - 22
We need to find b
a + b = - 38
- 22 + b = - 38
b = - 38 + 22
b = - 16
3)
1 correct answer = 4 marks
1 incorrect answer = - 2 marks
Number of correct answers = 32
Number of incorrect answers = 8
Total score = 32 × 4 + (- 2) × 8
= 128 - 16
= 112 marks.
Therefore, we get that, 7 × 12 = 72 satisfies the closure property of multiplication, the other integer when the sum is - 38 and one integer is - 22 will be - 16 and the total score for Gopi will be 112 marks.
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