If a road was made directly from his home to his place of work, its distance will be 16.6 mi.
If a man drives east from his home, makes a left turn at an intersection, and then travels north to his place of work, then the path he travels resembles the sides of a right triangle (see attached photo).
if a road was made directly from his home to his place of work, then this path will be the hypotenuse of the triangular path.
Using Pythagorean theorem, we can solve for the distance of the road.
c^2 = a^2 + b^2
where c is the distance of the road
a is the distance he travels to the east
b is the distance he travels up north
c^2 = a^2 + b^2
c^2 = (14 mi)^2 + (9 mi)^2
c^2 = (196 + 81) mi^2
c^2 = 277 mi^2
c = 16.64331698 mi
distance of the road = c = 16.64331698 mi
Rounding off to the nearest tenth of a mile:
distance of the road = 16.6 mi
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Determine the smallest integer that makes -3x + 7 -5x < 15 true.
Step-by-step explanation:
-3x+7-5x<15
-5x-3x+7<15
-8x+7<15
-8x<15-7
-8x<8
The smallest integer is -3x.
Which graph represents 7x - 2y < 5?
Suppose when you study 4 hours for an exan, your mark is 80 percent. and if you study for an extra hour, your mark is 85 percernt. the marginal benefir from studying one more hour is:_________
The marginal benefit from studying one extra hour is 5 percent.
What is marginal benefit?The maximum sum of money a consumer will spend on an additional commodity or service is known as the marginal benefit. As spending rises, customer contentment tends to decline.Now,
Given:
Marks scored on studying 4 hours = 80 percentMarks scored on studying 1 hour extra = 85 percentTo find: Marginal benefit on studying one hour extra.
Finding:
Now, marks scored on studying 4 hours is 80 percent and 5 hours is 85 percent.
Thus, the extra percentage that is scored is because of the 1 hour of extra studying.
The extra percentage = marginal benefit of studying extra = 85 - 80 = 5 percent.
Hence, the marginal benefit from studying one extra hour is 5 percent.
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Write an explicit formula for an, the nth term of the sequence 26, 24, 22
we get that the nth term of the arithmetic sequence is given by aₙ = 28 - 2 n.
We are given an arithmetic sequence:
26, 24 , 22 ....
We need to find the nth term of this sequence (aₙ)
We will first find the common difference between the terms:
Common difference = d = 24 - 26 = - 2
also, we know that initial term = a = 26.
We know the formula for aₙ is given by:
aₙ = a + ( n - 1 ) d
Substituting the values, we get that:
aₙ = 26 + ( n - 1 ) ( - 2 )
aₙ = 26 - 2 n + 2
aₙ = 28 - 2 n
Therefore, we get that the nth term of the arithmetic sequence is given by aₙ = 28 - 2 n.
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f(x) = -x² - 8x - 16; Find ƒ(-3)
f(-3) = -1
Step-by-step explanation:We can find an unknown y-value by plugging an x-value into a given function.
Function Notation
Before we answer this question, we need to understand the notation of the equation. In function notation, the equation is given in terms of f(x).
"f(x)" represents the y-value of a function at the point "x".For example, f(-3) represents the value of y when x = -3.
Finding f(3)
As stated above, to find f(-3) we need to plug -3 in for x. *Remember to use PEMDAS when solving.* This creates the new equation:
f(-3) = -(-3)² - 8(-3) - 16Then, distribute the exponent.
f(-3) = -9 - 8(-3) - 16Next, multiply.
f(-3) = -9 - (-24) - 16Distribute the negative.
f(-3) = -9 + 24 - 16Finally, add the remaining terms.
f(-3) = -1This means that when x = -3, y or f(-3) = -1.
Square root of 750 ..?
Answer: 27.3861278753
Step-by-step explanation:
√750 = 27.3861278753
PLEASE HELP THIS IS SO CONFUSING TO ME!!!
According to the American Sleep Disorders Association, the average teenager needs around 9.5 hours of sleep per night, possibly because of hormones that are critical. Yet studies show that teenagers generally get an average of only 7.4 hours a night or less. Calculate the number of seconds of sleep that an average teenager is lacking for the 180 days of school in one year.
Answer:
A
Step-by-step explanation:
The two sentences relate like They establish a contrast. As American Sleep Disorders Association is considering the teenager sleep and adult sleep.
What is sleeping disorder?
Sleep Disorders are mostly common nowadays as people are more busy in their scheduling, they don't get proper and sufficient time to sleep. This creates many problems in the human body.
The common type of sleeping disorder are insomnia, restless toughnesses' syndrome, narcolepsy and sleep apnea.
Thus, option A is correct.
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A rectangle is 15 cm wide. Find the area and the perimeter of the rectangle if its width is 3/5 of its length
The area and perimeter of the rectangle are 80 cm and 375 cm² respectively.
How to find area and perimeter of a rectangle?The rectangle is 15 cm wide.
The width is 3 / 5 of its length
Therefore, the area and the perimeter of the rectangle can be found as follows:
area of a rectangle = lw
where
l = lengthw = widthTherefore,
w = 15 cm
15 = 3 / 5 × l
cross multiply
75 = 3l
l =75 / 3
l = 25 cm
Therefore,
area of the rectangle = 25 × 15 = 375 cm²
Perimeter of the rectangle = 2l + 2w
Perimeter of the rectangle = 2(l + w)
Perimeter of the rectangle = 2(25 + 15)
Perimeter of the rectangle = 2(40)
Perimeter of the rectangle = 80 cm
Therefore, the area and perimeter of the rectangle are 80 cm and 375 cm² respectively.
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HELP ASAP!!!!!
Write a function g whose graph represents the indicated transformation of the graph of f.
f(x)=4x+1; translation 2 units left.
HELP PLEASE
Answer:
The translation of 2 units left in function f (x) = 4x + 1 is 4x + 3.
Here,
Function is given as, f(x)=4x+1
And, translation 2 units left.
We have to find the function after translation.
Now,
Function is given as, f(x)=4x+1
After translation 2 units left the function is;
f (x) = 4x + 1 + 2
f (x ) = 4x + 3
Hence, the function after translation 2 units is f (x) = 4x + 3
Two trains leave stations 240 miles apart at the same time and travel toward each other. One train travels at 70 miles per hour while the other travels at 80
miles per hour. How long will it take for the two trains to meet?
Answer: get a verified 340
Step-by-step explanation:
simplify the equation 12-2/6+4
i need help asap !!!!
Answer:
47 / 3 ( Or 1 if you typed it wrong)
Step-by-step explanation:
When simplifying an equation like this, we always want to do our multiplication and division before addition and subtraction.
So for the first step, let's simplify the expression down to only addition and subtraction...
12 - 2 / 6 + 4 =
12 - (2 / 6) + 4 =
12 - 1/3 + 4
Now we can combine everything together from left to right...
(12 - 1/3) + 4 =
35/3 + 4 =
47 / 3
However...
If the original equation was:
[tex]\frac{12-2}{6+4}[/tex]
Then you would just simplify the top and bottom separately before dividing the two numbers, treating the fraction as parentheses.
So...
(12 - 2) = 10
(6 + 4) = 10
And since 10 / 10 = 1
The answer to the fraction simplification is 1.
The solution of the expression would be 47/3.
Given that,
The expression is,
[tex]12 - \dfrac{2}{6} + 4[/tex]
Now simplify the expression by applying the BODMAS rule,
[tex]12 - \dfrac{2}{6} + 4[/tex]
[tex]12 - \dfrac{1}{3} + 4[/tex]
[tex]16 - \dfrac{1}{3}[/tex]
[tex]\dfrac{(48 - 1)}{3}[/tex]
[tex]\dfrac{47}{3}[/tex]
Therefore, the solution of the expression is 47/3.
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Two friends are playing with water balloons. They each start at the bucket of balloons and walk in opposite directions before tossing their balloons at each other. Joy walked 14 steps forward, and Shaunte walked 5 steps backwards. Which expression correctly represents the distance between the friends? 14 + |−5| = 19 steps 14 + 5 = 19 steps |−14| + |−5| = 19 steps |−14| + 5 = 19 steps
The number expression will be 14 + |-5| = 19 if Joy walked 14 steps forward, and Shaunte walked 5 steps backward option (A) is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It is given that:
Two friends are playing with water balloons. They each start at the bucket of balloons and walk in opposite directions before tossing their balloons at each other.
Joy walked 14 steps forward, and Shaunte walked 5 steps backward.
Let forward direction be the positive
The backward direction is negative.
The number expression can be represented;
The distance between two friends:
14 + |-5| = 14 + 5 = 19
14 + |-5| = 19
Thus, the number expression will be 14 + |-5| = 19 if Joy walked 14 steps forward, and Shaunte walked 5 steps backward.
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A painting service charges $65 for a project in addition to $11 per hour. if they charge you a total of $263, how many hours did it take to complete the project?
Answer:
18 hours.
Step-by-step explanation:
Subtract $65 from the total.
263 - 65 = 198
Divide by 11.
198 ÷ 11 = 18
Answer:
18 hours
Step-by-step explanation:
$263-$65=$198
$198÷$11=18 hours
Find the mode(s) for the given sample data. (if there are more than one, enter the largest value for credit. if there is no mode, enter 0 for credit.) 42, 25, 86, 30, 25, 15, 42, 42
For the given sample data, 42, 25, 86, 30, 25, 15, 42, 42, the mode is 42.
In statistics, the mode, denoted by Mo, refers to the most frequent value or values in the data set. If all the numbers in the data set appears only once, then the data set has no mode.
For the given sample data,
42, 25, 86, 30, 25, 15, 42, 42
the number 42 appears thrice, 25 appears twice and the rest appears only once.
The number 42 appeared the most frequent among all the other data.
Hence, the mode of the data set that contains 42, 25, 86, 30, 25, 15, 42, 42 is 42.
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2help me PLEASE THIS IS WORTH SO MANY POINTS PLEAS EHELP ME
Answer:
I would say A
Step-by-step explanation:
Because just because a quadrilateral has 4 congruent sides, does not make it a rhombus. Because a square has 4 congruent sides too.
(3-x)² what is the standard form
Answer:
here is my answer........
Step-by-step explanation:
(3-x)^2 = 9 - 3x - 3x + X2
= X2 - 6x +9
Find the volume of a cube with a side that measures 0.01 cm. (Hint: V = s ³).
Answer: V=[tex]\frac{1}{1000000}[/tex] cm^3
Step-by-step explanation:
V = s³
V = (0.01)³
V=(1/100)³
V=[tex]\frac{1}{1000000}[/tex] cm^3
the volume of cube with a side that measures 0.01 cm is answer v = a3
what's the answer? It's difficult to understand and my teacher doesn't really teach.
Step-by-step explanation:
So for questions 1 through 4, you're basically finding the number in the middle of the two letters. In question 1, D is above 7 on the number line and E is above 11. The mid-point would be 9.
For 5 and 6, we'll be using this formula: [tex](\frac{x_{1} + x_{2}}{2},\frac{y_{1} + y_{2}}{2})[/tex]
And now we just plug in the numbers from question 5 but it works the same way on 6 as well.
[tex](\frac{3 + 5}{2},\frac{1 + 3}{2})[/tex] => (8/2, 4/2)
Coordinate of the midpoint would be (4, 2).
Lastly, we follow this system in order to get the final answers:
(Answer below shown for question 7)
(x + 2)/2 = 5
x + 2 = 10
x = 8
(y + 0)/2 = 2
y + 0 = 4
y = 4
Missing endpoint is (8, 4)
Find the area of the region that lies inside both curves. r = 9 sin(), r = 9 cos()
The area of the region inside both curves r = 9 sin(θ) and r = 9 cos(θ) is 11.56 square units.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
The curves are:
r = 9 sin(θ) and
r = 9 cos(θ)
On graphing the above curves:
From the graph:
A = (1/2)∫(9sin(θ))2dθ + (1/2)∫(9cos(θ)2dθ
The region is symmetrical about π/4,:
A = 81∫sin2(θ)dθ from 0 to π/4
After solving:
= 11.56 square unit
Thus, the area of the region inside both curves r = 9 sin(θ) and r = 9 cos(θ) is 11.56 square units.
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a sporting event coordinator has 200 mini foam fingers she gives 2 foam fingers to each student in attendance. there are 26 left. how many students are in attendance?
thank u <3
The total number of students which are there in the sporting events are 87.
The total number of mini foam fingers which the sporting event coordinator has is 200. Since he gives 2 foam fingers to each student present in the event therefore each student has 1 pair of mini foam fingers.
So, in total there are 200/2 = 100 pairs of mini foam fingers.
The total number of mini foam fingers left after distribution is equal to 26.
So total pairs of mini foam fingers left = 26/2 = 13
Therefore, the number of students which are present in attendance is given by:
Total pairs of foam fingers - total pairs of foam fingers left
=> 100-13 = 87
Therefore, total number of students in attendance are 87.
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When applying PEMDAS, always work from left to right. True or False?
Answer:
False
Step-by-step explanation:
Sometimes, multiplication can occur after addition. For example, in 3+4*7, you don't add 3 and 4 first. You multiply 4 and 7 first since that's following the PEMDAS rule. After multiplying 4 and 7, then you add 3 to get a total of 31. ==> 3+4*7=3+28=31.
Please help with. Scale Factors
Answer:
5×8=40
x=7×8
=56
Step-by-step explanation:
5×8=40
x=7×8
=56
What is 0.29 as a fraction in simplest form ?
Answer:
Step-by-step explanation:
0.29 as a fraction is 29/100. Anytime you have a decimal, just turn it into a whole number and simplify it. However, 29/100 is already in its simplest form.
Write a rule for the function:
1 6
2 11
3 16
4 21
Answer:
4 21
Step-by-step explanation:
Its probably the answer you are looking for
median and mode of 4.3,4.5,4.2,5
Check the picture below.
Jamal loves his dog, Rupert. On sunny days, Jamal keeps Rupert on a 12-foot leash
in the backyard. He secures the leash to a stake in the ground.
> Answer each question and use 3.14 for T.
1 Determine the diameter, circumference, and area of Rupert's play area.
Diameter = 24 foot, circumference = 75.36 foot, Area = 452.16 square foot
As the leash is 12 feet, and dog Rupert will form a circle in the backyard.
As the leash is of 12 feet, so it is the radius(r) of the circle.
Diameter = 2r
= 2×12
= 24 foot
Circumference = 2πr
=2×3.14×12
= 75.36 foot
Area of the circle = π[tex]r^{2}[/tex]
= 3.14×[tex]12^{2}[/tex]
=3.14 × 144
= 452.16 [tex]foot^{2}[/tex]
Therefore we get diameter = 24foot, circumference = 75.36 foot and area = 452.16 square foot.
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Find the general solution of the given higher-order differential equation. y(4) y''' y'' = 0
The homogeneous linear ODE
[tex]y^{(4)} + y''' + y'' = 0[/tex]
has characteristic equation
[tex]r^4 + r^3 + r^2 = r^2 (r^2 + r + 1) = 0[/tex]
with a double root at [tex]r=0[/tex] and two complex roots
[tex]r^2 + r + 1 = 0 \implies r = -\dfrac{1 \pm i\,\sqrt3}2[/tex]
Hence the characteristic solution is
[tex]y = C_1 e^{0x} + C_2x e^{0x} + C_3 e^{((-1/2)-i(\sqrt3/2))x} + C_4 e^{((-1/2)+i(\sqrt3/2))x}[/tex]
[tex]y = C_1 + C_2x \\\\ ~~~~~~~~~~ + C_3 e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) - i\, \sin\left(\dfrac{\sqrt3}2x\right)\right) \\\\ ~~~~~~~~~~ + C_4 e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) + i\,\sin\left(\dfrac{\sqrt3}2x\right)\right)[/tex]
[tex]y = C_1 + C_2x + C_3 e^{-x/2} \cos\left(\dfrac{\sqrt3}2x\right) + C_4 e^{-x/2} \sin\left(\dfrac{\sqrt3}2x\right)[/tex]
which of the following ordered pairs make this question true y=2x-4?
Answer:
There is not a single ordered pair which is a solution to y=2x−4 .
What's the GCF of 30,60 and 78
Answer:
6
Step-by-step explanation:
Answer: 6
Step-by-step explanation:
First, take the prime factorization of all 3 numbers.
30: 15*2 ==> 5*3*2
60: 30*2 ==> 15*2*2 ==> 5*3*2*2
78: 39*2 ==> 13*3*2
Notice any common factors? That's the GCF.
GCF: 3*2=6
GCF: 6
Solve for the system:
-w+3z=18
5w+6z=15