Step-by-step explanation:
this is about the overall slope of the mountain road.
remember, the slope is (y change / x change). in this case it is elevation change / distance change.
getting from 2 to 4 miles the changes are
distance changes by +2
elevation changes by + 700 (from 5500 to 6200).
the slope is +700/+2 = 350/1 = 350.
the road begins at distance = 0.
the elevation of the begin of the road = x.
so going from 2 miles down again to 0 the changes are
distance changes by -2 (from 2 to 0)
elevation changes by x - 5500 (from 5500 to x).
the slope there must be the same as the slope further up (as it is said it has a constant rate) :
(x - 5500)/-2 = 700/2
(5500 - x)/2 = 700/2
5500 - x = 700
x = 5500 - 700 = 4,800 ft
the road started at an elevation of 4,800 ft above sea level.
At a constant temperature, the atmospheric pressure p in pascals is given by the formula p=101.3 e⁻⁰.⁰⁰¹h , where h is the altitude in meters. What is p at an altitude of 500 m ?
At an altitude of 500 meters, the atmospheric pressure (p) will be 61.46 pascals.
The exponential constant, denoted by the symbol e, is an essential mathematical constant. Its value is approximately equal to 2.718. This value occurs very frequently in mathematics when it is used to model physical and economic phenomena.
Here, we are given an exponential function- p = 101.3[tex]e^{-0.001h}[/tex]
where p = atmospheric pressure in pascals
h = altitude in meters.
If the altitude is 500m
h = 500
Then,
p = 101.3 [tex]e^{-0.001 * 500}[/tex]p
= 101.3 [tex]e^{-0.5}[/tex]p
= 101.3/ [tex]e^{-0.5}[/tex]p
= 101.3/ 1.648p
= 61.46
Thus, at an altitude of 500 meters, the atmospheric pressure (p) will be 61.46 pascals.
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Find the compound interest and the amount after twelve seconds if the interest is compounded
every three seconds.
Principal 20,000
Rate of interest = 800% per minute
=
Total amount =
Compound interest =
well, we know the rate is compounding at 800% per minute.
the elapsed time will be 12 seconds, and since a minute has 60 seconds, that'd be 12/60 minutes.
the compounding period is 3 seconds, and since a minute has 60 seconds, that means is compounds 60/3 times, or namely 20 times.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$20000\\ r=rate\to 800\%\to \frac{800}{100}\dotfill &8\\ n= \begin{array}{llll} \textit{times it compounds per minute}\\ \textit{twenty times} \end{array}\dotfill &20\\ t=minutes\to \frac{12}{60}\dotfill &\frac{1}{5} \end{cases}[/tex]
[tex]A=20000\left(1+\frac{8}{20}\right)^{20\cdot \frac{1}{5}} \implies A =20000(1.4)^4\implies A=76832[/tex]
Nathan is planning to ride his bike for 24 minutes if he rides at a rate of 5 miles per hour how far will he travel
The distance that Nathan can ride his bike is 2 miles.
What is the distance Nathan can ride?The rate is the total distance per time. Rate is determined by dividing the total distance travelled by the total time travelled.
Rate = total distance / total time.
Distance = rate x time
The rate is in miles per hour while the time given is in minutes. Thus, minutes has to be changed to hour. To do this, divide 24 minutes by 60.
60 minutes = 1 hour
24/ 60 = 2/5
Distance = 2/5 x 5= 2 miles
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Model with mathematics. Graph the fraction -1 2/5 on the number line.
The fraction -1 2/5 is modeled on the number line by: graph A.
What is a fraction?A fraction can be defined as a numerical quantity which isn't expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
In this scenario, we can reasonably infer and logically deduce that the fraction -1 2/5 is modeled on the number line by graph A because each interval increases by 2/5 or 0.4.
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The grid above shows the graph of the parent function f(x) = | x | and a translated functions graph.
Write the equation for the translated graph.
Please Hurry, I will give brainliest!
By using the principles of translation, the following equation can be derived for the graph of the translated text:
g(x) = |x + 2| + 1.
What is a translation?According to operations like multiplication or sum/subtraction either in its range (including values of y) or in its domain, a translation is represented by a change in the function graph (involving values of x).
Examples include shifts to the left, right, or bottom; compression or stretching along the vertical or horizontal axis; reflections across the x or y axes; and rotations of a degree measured around the origin.
From the graph, we have that the parent function was:
Shifted left 2 units, hence x -> x + 2.
Shifted up 1 unit, hence y -> y + 1.
Hence, considering the parent function f(x) = |x|, the equation for the translated graph is given by:
g(x) = |x + 2| + 1.
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What is the value of the expression 8 + (9 -1) \div÷ 4?
Answer:10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
8 + (9- 1) ÷ 4
Use PEMDAS to determine order of operations in a mathematical expression
The order of operations is
P = parentheses
E = exponent
M = multiplication
D == division
A = addition
S = subtraction
Note that multiplication and division have the same priority and we go from left to right that case. Because it does not affect the answer.
So 12 ÷ 4 x 6 = 12 x 6 ÷ 4
Same for addition and subtraction - same priority
Using PEMDAS
(9 - 1) is executed first giving 8
The expression becomes 8 + 8 ÷ 4
Next division is performed so 8 ÷ 4 is executed giving 2 as the answer
Finally 8 + 2 is executed giving 10
Manuel gave the cashier $20 to pay for 3 bottles of hand sanitizer. The cashier gave him $8.03 in change. Each bottle cost the same amount.
Answer:
Each bottle cost $3.99.
Step-by-step explanation:
$20-$8.03=11.97
Each bottle = $11.97÷3
=$3.99
So now each bottle cost$3.99
ײ + 5× - 11 + 3ײ - 11 × + 2
hello guys please solve and give a solution tthankyou
Step-by-step explanation:
start by collecting like terms
4x² - 6x -9
use quadratic equation, a=4, b= 6 and 9 = c.
x = 5,78 or x = -4,28
4r-4s+4t = -4
4r+s-2t= 5
-3r-3s-4t=-16
Answer:
1) R = 1 S = 3 T = 1
2) R = 1 S = 3 T = 1
3) R = 1 S = 3 T = 1
Step-by-step explanation:
Surprisingly each of the situations end up with 1, 3, 1. I double checked with a calculator and they all end up being true. Hope this helps. Have a great night. :)
I need help figuring out what 7x + 5 divided by x is
Answer:
The way you described this question was a bit confusing- but here is what I can provide based off of what you said.
Step-by-step explanation:
7x+5/x
Please provide a picture next time
Identify the number types that describe 7 squared
The square root value of 7 is 2.645.
Irrational number
All real numbers that are not rational are considered irrational numbers. In other words, it is impossible to describe an irrational number as the ratio of two integers.
Any square root number that cannot be represented as a fraction [tex]\frac{P}{Q}[/tex] for any integer p and q is said to be irrational.
A real number that cannot be expressed as a straight forward fraction is referred to as an irrational number. It cannot be described using a ratio. When p and q are integers and q is not equal to 0, N is not equal to [tex]\frac{P}{Q}[/tex] if N is irrational.
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One number is 19 greater than the other, the sum of these numbers is 97. What is the greater number?
Answer:
Greater number = 58
Step-by-step explanation:
The equation is,
→ (x + 19) + x = 97
Now the value of x will be,
→ (x + 19) + x = 97
→ 2x = 97 - 19
→ x = 78/2
→ [ x = 39 ]
Then the greater number is,
→ x + 19
→ 39 + 19 = 58
Hence, the answer is 58.
Answer:
58
Step-by-step explanation:
first number=x
second number= x+19
x+x+19= 97
thus, the two numbers are 39 and
Christmas tree lights are used not only for christmas trees, but sometimes to decorate college dorm rooms. Suppose that a string has 20 light bulbs. These lights are all wired in series, so that if one light bulb fails, the whole string fails. The probability that any one light fails is 0. 2. Each of the individual lights are independent of each other. What is the probability that the string will not fail?.
If a string has 20 light bulbs and these lights are all wired in series, so that if one light bulb fails, the whole string fails and the probability that any one light fails is 0.2 and each of the individual lights are independent of each other, then the probability that the string will not fail is 0.0115.
Probability in mathematics deals with the likelihood of an event to take place.
The probability that the string will not fail refers to when all 20 bulbs will not fail. As given in the conditions, each of the individual lights are independent of the other. Therefore;
the probability that any one of the lights will not fail is:
1 - probability that any one light fails = 1 - 0.2 = 0.8
And we need all 20 to be complete. The unity of events is a product of probabilities. Therefore the probability that the string will not fail is:
P = 0.8^20
P = 0.0115
Hence 0.0115 is the probability that the string will not fail.
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Lisa has a button collection and decided to measure her 12 favorite buttons to the nearest 1/8 inch. Her results are shown in the line plot below.
(look at photo attached)
If she took one of her smallest buttons, one of her largest buttons, and one of her most common-sized buttons and laid them side-by-side, what would be their combined length?
Answer:
2 3/4
Step-by-step explanation:
the Smallest is 1/2
the biggest is 1 1/2
the most common is 3/4
Adding them all up will give you 2 3/4 or 11/4
Answer:
2[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
the smallest button is [tex]\frac{1}{2}[/tex]
the most common button is [tex]\frac{3}{4}[/tex]
the largest button is 1 [tex]\frac{1}{2}[/tex]
add these buttons together
[tex]\frac{1}{2} + \frac{3}{4} + 1 \frac{1}{2} =[/tex]
find the LCD of the denominators
factors of 2: 2, 4, 6, 8, 10
factors of 4: 4, 8, 12, 16, 20
find the factor that is the same in the two rows
factors of 2: 2, 4, 6, 8, 10
factors of 4: 4, 8, 12, 16, 20
2*2 = 4
[tex]\frac{1}{2}[/tex]· 2 = [tex]\frac{2}{4}[/tex]
[tex]\frac{2}{4} + \frac{3}{4} + 1 \frac{2}{4} =[/tex]
1[tex]\frac{7}{4}[/tex]
[tex]\frac{7}{4} = 1 \frac{3}{4}[/tex] + 1
2[tex]\frac{3}{4}[/tex]
10)110
help me please
Answer:
If it is a division problem, then it is 11.
If it is a multiplication problem then it is 1100.
But it looks like division, so probably 11.
Answer:
011
Step-by-step explanation:
0 1 1
--------------------------------
1 /
0 1 1 0
− 0
1 1
− 1 0
1 0
− 1 0
0
Questions on the picture below or above
Answer:
hundred
million
hundredth
5800
2
460000
0.07
Step-by-step explanation:
Amy inputs 1÷17 in her calculator. The calculator displays 0.0588235294. Is the quotient a rational or an irrational number? Explain.
Answers with explanation please and thank you:))
The quotient of 1 ÷ 17 is a rational number.
In this question, Amy inputs 1÷17 in her calculator.
The calculator displays 0.0588235294
We need to check whether the quotient is a rational or an irrational number.
The quotient of 1 ÷ 17 is a rational number.
1 ÷ 17 can be written as 1/17, which is a rational number.
The quotient of 1 ÷ 17 is a decimal: the quotient a rational or an irrational number.
Therefore, the quotient of 1 ÷ 17 is a rational number.
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Work out
(3 × 10^−3)−(6 × 10^−5)
Give your answer in standard form.
Answer:
answer is
[tex] {2.94 \times 10}^{ - 3} [/tex]
Step-by-step explanation:
3*1/1000-6*1/100000=0.003-0.00006
=
[tex] {2.94 \times 10}^{ - 3} [/tex]
28:49 ratio in simplest form
Answer:
4:7
Step-by-step explanation:
thats the answer mate
Answer:
4 : 7
Step-by-step explanation:
28 : 49 ← divide both parts by 7
= 4 : 7 ← in simplest form
the ratio is in simplest form when no other value but 1 divides into the 2 parts of the ratio.
17 + x = 15
pls help
Answer:
x = -2
Step-by-step explanation:
The equation is,
→ 17 + x = 15
Now the value of x will be,
→ 17 + x = 15
→ x = 15 - 17
→ [ x = -2 ]
Hence, the value of x is -2.
Step-by-step explanation:
17+x=15
17+x-17=15-17
x=-2
Find the domain, points of discontinuity, and x - and y - intercepts of each rational function. Determine whether the discontinuities are removable or non-removable. y=3x-3 / x²-1
The domain of given points are :
IR x ≠ ±1
Points of discontinuity - x = -1 ( non removable / asymptote )
x = 1 ( removable / hole)
x - intercept = 1 , y - intercept = 3
What is rational functions ?Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. The domain of a rational function is the set of all numbers except the zeros of the denominator since polynomials are defined everywhere. First example: f(x) = x/ (x - 3).
CALCULATIONy=3x-3 / x²-1
= 3(x-1)/(x+1)(x-1)
The domain of given points are :
IR x ≠ ±1
Points of discontinuity - x = -1 ( non removable / asymptote)
x = 1( removable / hole)
x-intercept :
3(x-1)=0
3x-3=0
x=1
y - intercept :
3(0-1)/(0+1)(0-1)=3
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Please help
Which of the following lines is perpendicular to y = 1/4x -3. Select all that apply.
A. Y=4x+9
B. 8x-2y=3
C. 4x-y=-2
D. Y=-4x+6
E. Y=4x
The slope of a line is y=mx+c, where m is the slope. The lines is perpendicular to y = 1/4x -3 is Y=-4x+6.
What is slope intercept form?
The slope of a line is y=mx+c, where m is the slope.
The given line is y = 1/4x -3.
slope m1=1/4.
slope of second line=-(1/m)
=-(1/1/4)
=-4
point slope intercept form is y-y1=m(x-x1)
Equation of the perpendicular line passing through point (0,6) is
y-6=-4(x)
y=-4x+6
Therefore the line perpendicular to y = 1/4x -3 is Y=-4x+6.
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A women bought some large frames for $19 each and some small frames for $7 each at a closeout sale. If she brought 19 frames for $205, find how many of each type she bought
Answer:
the one I have found that would is
13 small frames
6 big ones
Step-by-step explanation:
not gonna lie I used trial and error
so I went for example 19 x 10 = 190
205 - 190 = 15 and then 15 / 7
I did this until I got an whole number on the divide by seven bit
The price of Stock A at 9 A.M. was $15.03. Since then, the price has been increasing at the rate of $0.05 each hour. At noon the price of Stock B was $15.53. It begins to decrease at the rate of $
0.14 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
After 1.842 hours the price of Stock A and Stock B will be the same using a set of linear equations.
A grouping of one or more linear equations containing the same variables is known as a system of linear equations.
For Stock A :
The initial price = $15.03
The rate of increase = $0.05
For Stock B :
The rate of decrease = $15.53
The rate of decrease per hour = $0.13
Then the price of stock A at noon will be:
$ 15.03 + $ (0.05 × 3) = $ 15.03 + $ 0.15 = $15.18
The period of time during which the stock price will remain constant:
15.18 + 0.05t = 15.53 - 0.14t
Simplifying the terms we get,
0.05t + 0.14t = 15.53 - 15.18
0.19t = 0.35
t = (0.35 ÷ 0.19) hours
t = 1.842 hours
Therefore, the stocks will be of equal price after 1.842 hours.
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Complete the identities.
csc θ =1/?
Answer:
? = sin θ
Step-by-step explanation:
csc θ =1/?
csc θ =1/sin θ
a to the power of 5 divided by a to the power of 3
Answer:
Step-by-step explanation: i thank the answer is 100 .
What is the approximate value of √8
Answer:
Close to 3 since 8 is close to 9.
The actual value was 2.8, so I approximated what was closest to it using rounding and the most logical explanation.
2x(4+1)+(3x+5)+(2x+1)
Triangle ABC with vertices A(–4, –4), B(–1, –2), C(3, –1) is rotated 180° about the origin. What are the coordinates of triangle A′B′C′?
Answer:
A(4, 4), B(1, 2), C(-3, 1)
Step-by-step explanation:
Because the triangle is rotated 180° about the origin you are just rotating it 2 quadrants, the size stays the same.
The rule for rotating 180° is if (x, y) is rotating 180° then the new position is (-x, -y).
So:
A(-4, -4), which then becomes B(-(-4), -(-4) ) = B(4, 4)
B(–1, –2) which becomes B(-(–1), –(-2) ) = B(1, 2)
C(3, –1) which becomes C(-3, –(-1) ) = C(-3, 1)
need help with inequality equations
Answer:
I and III
Step-by-step explanation:
I.
-6 - x ≤ 7
-6 - (-13) ≤ 7
-6 + 13 ≤ 7
7 ≤ 7
True
II.
-6 - x ≤ 7
-6 - (-14) ≤ 7
-6 + 14 ≤ 7
8 ≤ 7
False
III.
-6 - x ≤ 7
-6 - (-6) ≤ 7
-6 + 6 ≤ 7
0 ≤ 7
True
I hope this helps!