It is given that, Altitude above sea level =Positive Values
=Positive Integer{1,2,3,4,5,6,7,8,.......}
Altitude below sea Level=Negative values
=Negative Integer{-1,-2,-3,-4,-5,-6,.......}
Now, The situation given is
A hiker in Death Valley stopping at an altitude of 0 feet
Zero(0)= The Point 0, means neither Positive nor Negative, that is additive Identity with respect to Addition of Integers.That is when two integers having Opposite sign, means additive Inverse of each other, are added together it yields Zero.
For example
-2 + 2=0
2 and -2 are Additive Inverse of each other.
Which of the following is true about the expression given below?
9>2
A.9 is to the left of 2 on a horizontal number line.
B.9 is the opposite of 2 on a horizontal number line.
C.9 is to the right of 2 on a horizontal number line.
D.9 is at the same place as 2 on a horizontal number line.
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
9 > 2
i.e. 9 is to the right of 2 on a horizontal number line
As we know that in the Cartesian plane, upper most is for y- positive coordinate, lower most is for y- negative coordinate
Similarly, right most is for x-positive coordinate and left most is for x- negative coordinate.
And we have 9>2
Both 2 and 9 are positive numbers so, both numbers must be in the right part of axis.
And 9 is always right of 2 on a horizontal number line.
Hence, Option 'C' is correct.
Which is the solution to (x-2)(x+10)=13
The solution to (x-2)(x+10)=13 is x can be either 3 or -11, therefore the problem has 2 solutions.
Answer:
x = 3 or x = -11
Hope This Helps!
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How do you find the domain an range and how do you graph it
Divide 46 on both sides to get f(x)=((x+2)^3-3)/46. The domain ranges from negative infinity to infinity. The range ranges from -infinity to infinity as well because the exponent is 3, so the resulting number may be negative.
Remember, when graphing cubics, there is always two turns. The following graph is from Desmos.
Pleaseeeee helppppp lol
Answer:
2/4 I believe
Step-by-step explanation:
2/4
Step-by-step explanation:
use the quadratic formula to solve -5x^2-12x+8=0
[tex]\text{The quadratic formula:}\\\\ax^2+bx+c=0\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a};\ x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\--------------------------------\\\text{We have}\ -5x^2-12x+8=0\\\\a=-5,\ b=-12,\ c=8\\\\\text{Substitute:}\\\\b^2-4ac=(-12)^2-4(-5)(8)=144+160=304\\\\\sqrt{b^2-4ac}=\sqrt{304}=\sqrt{16\cdot9}=\sqrt{16}\cdot\sqrt{19}=4\sqrt{19}\\\\x_1=\dfrac{-(-12)-4\sqrt{19}}{2(-5)}=\dfrac{12-4\sqrt{19}}{-10}=\boxed{-\dfrac{6-2\sqrt{19}}{5}}\\\\x_2=\dfrac{-(-12)+4\sqrt{19}}{2(-5)}=\dfrac{12+4\sqrt{19}}{-10}=\boxed{-\dfrac{6+2\sqrt{19}}{5}}[/tex]
Please help me I’m begging someone I really need help !!!!!!! I will mark brainlest!!!!!
Answer:
I can be little confident because if it was just 0.7 then it would be I am not confident at all. This decimal is more than 0 so it would be a little and not a lot.
Step-by-step explanation:
A line includes the points (-1, -10) and (1, 0). What is its equation in slope-intercept form?
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-1, -10) and (1, 0). Substitute:
[tex]m=\dfrac{0-(-10)}{1-(-1)}=\dfrac{10}{1+1}=\dfrac{10}{2}=5[/tex]
y = 5x + bPut the coordinates of the point (1, 0) to the equation of line:
[tex]0=5(1)+b[/tex]
[tex]0=5+b[/tex] subtract 5 from both sides
[tex]-5=b\to b=-5[/tex]
Answer: y = 5x - 5For the line's equation, calculate the slope from the provided points to get 5, and use one point to find the y-intercept, which is -5. The line's equation is y = 5x - 5.
To find the equation of a line in slope-intercept form, which is y = mx + b.
We need to determine the slope (m) and the y-intercept (b).
Given two points on the line, (-1, -10) and (1, 0), we can calculate the slope using the formula
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}\\ m = \frac{0-(-10)}{1-(-1)}\\ m = 5[/tex]
Next, we use one of the points to find the y-intercept, b. If we use the point (1, 0), we can substitute the slope and the coordinates into the slope-intercept equation:
0 = (5)(1) + b, which simplifies to b = -5.
Thus, the equation of the line is y = 5x - 5.
what is the sum 12 1/4+ 5 5/6 reduce to lowest terms
Answer:
is it 2/21 i hope im right cuz i just looked it up
Step-by-step explanation:
To find the sum, convert the fractions to have the same denominator. Add the whole numbers and the fractions separately. The sum of 12 1/4 and 5 5/6 reduced to lowest terms is 17 13/12.
Explanation:To find the sum of 12 1/4 and 5 5/6, we need to convert the fractions to have the same denominator. The common denominator for 4 and 6 is 12. So, we can rewrite 12 1/4 as 12 3/12 and 5 5/6 as 5 10/12. Now we can add the whole numbers, 12 and 5, which gives us 17. Then, we add the fractions, 3/12 and 10/12, which equals 13/12. Therefore, the sum of 12 1/4 and 5 5/6 reduced to lowest terms is 17 13/12.
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If the current exchange rate is 1.35261 US dollars for each Euro, how many dollars would be exchanged for 285 Euro?
Answer:
$385.49
Step-by-step explanation:
285x1.35261=385.49385
round to the nearest cent and you get $385.49
To exchange 285 Euros for US dollars at an exchange rate of 1.35261, you would receive 385.80785 US dollars.
Current exchange rate = 1.35261 US dollars
To calculate how many dollars would be exchanged for 285 Euros at an exchange rate of 1.35261 US dollars per Euro:
Set up a simple multiplication problem: 285 Euros multiplied by 1.35261 US dollars per Euro.
Multiply the two numbers to get the total amount in US dollars.
So, 285 Euros x 1.35261 = 385.80785 US dollars would be exchanged for 285 Euros.
Rule; y=5x
Table:
x | y
2
4
6
Triangle ABC is reflected over the y-axis. The coordinates of Point A are (–3, –1). What are the coordinates of Point A', the reflected image, using an algebraic representation?
Answer:
A'(3, - 1)
Step-by-step explanation:
Under a reflection in the y-axis
a point (x, y) → (- x, y), hence
A (- 3, - 1) → A'(3, - 1)
The coordinate A(-3,-1) on reflection across y-axis transforms to (3,-1)
what is the Cartesian coordinate system?A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates.
Given here: The coordinate of a Triangle A as (-3,-1)
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Thus The vertex of the triangle (-3,-1) it changes to (3,-1)
The algebraic representation for the transformation is given by '
(x,y)⇒(-1×x,1×y)
⇒(-x, y)
Hence, The coordinate A(-3,-1) on reflection across y-axis transforms to (3,-1)
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A quadratic equation is shown below:
9x^2 - 16x + 60 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work
Part B: Solve 4x^2 + 8x - 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you choose the method used.
the solutions to a general quadratic equation is
X=-b±√b²-4ac/2a ,, When ax²+bx+c=0
the discriminant is the expression under the radical b²−4ac
Part A:
discriminant is (-16)² - 4(9)(60) = -1904
there are two complex solutions
Part B:
4x² + 8x − 5 = 0
4x² + 10x -2x - 5=0
2x ( 2x + 5) - 1(2 x + 5) =0
(2x + 5)(2x-1) = 0
/ \
/ \
2x+5 = 0 2x-1 =0
x = -5/2 x = 1/2
hawick is 15 miles south of abbostford and kelso is 17 miles east of abbotsford. what is the distance from Hawwick to kelsi?
Answer:
22.7 miles
Step-by-step explanation:
You are gonna use a^2 + b^2 = c^2 because the cities make a right triangle and you are trying to find the hypotenuse (c). C^2 ends up being 517 and the square root.
Answer:
22.7
Step-by-step explanation:
Given the equation, y = x - 4, what is the slope and the y-intercept?
m = 4 and b = 1/3
m = -4 and b = 1/3
m = 1/3 and b = 4
m = 1/3 and b = -4
Answer:
the answer would be m=1/3 and b=-4
Step-by-step explanation:
Y=X-4
the X= 1 almost all the time in an equation unless otherwise your given an equation for "x". so x is automatically 1/3 which would be your slope, and then then looking at the equation the end part of the equation is your starting point.so you look at the end of the equation and the -4 is were youd start your point on the graph.
How do odd or even exponents influence polynomial exponents?
(x + y)^0 = 1
(x + y)^1 = x + y
(x + y)^2 = x^2 + 2x + y
(x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3
(x + y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4
.
.
.
1
1 + 1
1 + 2 + 1
1 + 3 + 3 + 1
1 4 6 4 1
.
.
.
I hope I helped you.
Odd exponents ensure at least one real root for polynomials, while even exponents may result in no real roots. Multiplying even functions together, or odd functions together, results in an even function. These properties have applications in areas like quantum mechanics.
Odd and even exponents greatly influence the behavior of polynomial functions. For polynomials with odd exponents, they will always have at least one real root. This is because polynomials of odd degree tend to positive infinity as x goes to positive infinity and negative infinity as x goes to negative infinity, therefore they must cross the x-axis at some point. A polynomial like x³ - x + 17 exemplifies this behavior.
On the other hand, polynomials with even exponents may not have any real roots, as they never need to cross the x-axis; for example, x² + 1 is always positive for any real value of x and thus has no real roots.
Even functions and odd functions also display characteristic properties when multiplied. An even function times an even function yields an even function (e.g., x² e⁻²), and an odd function times another odd function results in an even function (e.g., x sin x).
In contrast, an odd function times an even function gives an odd function. These properties are particularly useful in fields such as quantum mechanics where symmetry plays an important role in solving equations like Schrödinger's equation.
Determine wether the binomial is a facor of f(x).
F(x)=4x^3-15x^2-30x+25; x-5
Typo free question:
Determine whether the binomial is a factor of F(x).
Answer:
Yes.
Step-by-step explanation:
Method one: evaluate F(5). If F(5) is zero then x-5 is a factor.
Method two: use long polynomial division to divide F(x) by (x-5). If the remainder is zero then (x-5) is a factor.
if you deposit $1,000 in an account that pays 6% annual interest compounded continuously what will the balance be after 5 years
a.$1,232.06
b.1,349.86
c.29,803.91
d.1,932.06
Answer:
[tex]1000 {e}^{.06 \times 5} = 1349.86[/tex]
The correct answer is B.
After 5 years with continuous compounding at 6%, $1,000 will grow to approximately $1,349.86.
Explanation:To find the future value of an account with continuous compounding, we use the formula:
A = Pe^(rt)
where:
A is the amount of money accumulated after n years, P is the principal amount (the initial amount of money), e is the number approximately equal to 2.71828, r is the annual interest rate (in decimal form), and t is the time in years.
In your case:
P = $1,000, r = 6% (or 0.06 in decimal form), and t = 5 years.
So plug these values into the formula:
A = $1,000 * e^(0.06*5)
After you calculate this, you'll find that the value of A is approximately $1,349.86. Therefore, after 5 years, your balance would be $1,349.86 so the answer is (b).
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A 24 ounce can of Fanta cost $1.75.How many does it cost per ounce round to the nearest cent
If 24 ounce can of Fanta cost $1.75 then it cost 13.71 per ounce.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that a 24 ounce can of Fanta cost $1.75.
We need to find the how many does it cost per ounce.
To find this we need to divide twenty four by one point seven five.
Cost per ounce is twenty four by one point seven five
Cost = 24/1.75
Cost per ounce=13.71
So a 24 ounce can of Fanta cost $1.75 can cost 13.71 per ounce.
Hence, if 24 ounce can of Fanta cost $1.75 then it cost 13.71 per ounce.
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If your starting salary is $40,000 and you receive a 3% increase at the end of every year, what is the total amount, in dollars, you will earn over the first 16 years that you work?
Round your answer to the nearest whole dollar, and express your answer without using commas.
Answer:
SEE BELOW PLEASE GIVE BRAINLIEST
Step-by-step explanation:
YEAR 1: 40000 X .03 = 1200 40,000 + 1200 = 41200
YEAR 2: 41,200 X .03 = 1236 41,200 + 1236 = 42436
YEAR 3: 42436 X .03 = 1273.08 42436 + 1273.08 = 43709.08
YEAR 4: 43709.08 x .03 = 1311.27 43709.08 + 1311.27 = 45020.35
YEAR 5: 45020.35 X .03 = 1350.61 45020.35 + 1350.61 = 46370.96
YEAR 6: 46370.96 X .03 = 1391.13 46370.96 + 1391.13 = 47762.09
YEAR 7: 47762.09 X .03 = 1432.86 47762.09 + 1432.86 = 49194.95
YEAR 8: 49194.95 X .03 = 1475.85 49194.95 + 1475.85 = 50670.80
YEAR 9: 50670.80 X .03 = 1520.12 50670.80 + 1520.12 = 52190.92
YEAR 10: 52190.92 X .03 = 1565.73 52190.92 + 1565.73 = 53756.65
YEAR 11: 53756.65 X .03 = 1612.70 53756.65 + 1612.70 = 55369.35
YEAR 12: 55369.35 X .03 = 1661.08 55369.35 + 1661.08 = 57030.43
YEAR 13: 57030.43 X .03 = 1710.91 57030.43 + 1710.91 = 58741.34
YEAR 14: 58741.34 X .03 = 1762.24 58741.34 + 1762.24 = 60503.58
YEAR 15: 60503.58 X .03 = 1815.11 60503.58 + 1815.11 = 62318.69
YEAR 16: 62318.69 X .03 = 1869.56 62318.69 + 1869.56 = $64,188.25 = $64188
$806275, hope this helps!
fill in the missing reasons for the proof below.
Complete the equation of the graphed linear function in point-slope form. y – (–2) = (x – ) The graph of the function goes through point 1, negative 2 and point 2, 2.
Answer:
[tex]y+2=4(x-1)[/tex]
Step-by-step explanation:
we know that
The equation of the line into point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
Let
[tex]A(1,-2), B(2,2)[/tex]
Find the slope of the line AB
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{2+2}{2-1}[/tex]
[tex]m=\frac{4}{1}[/tex]
[tex]m=4[/tex]
With the point A and the slope m find the equation of the line
[tex]y-(-2)=4(x-1)[/tex]
[tex]y+2=4(x-1)[/tex]
What step should you perform to bisect an angle drawn on tracing paper
Answer:
Step-by-step explanation:
• Suppose the angle is PQR where Q is the midpoint.
• Keep the compass at angle vertex Q and adjust some wide setting (the width is not important).
• Without changing the compass, draw an arc across each leg of the angle
• Now keep the compasses on the point drawn on each leg, and draw an arc in the interior of the angle.
• Using a ruler, draw a line through the vertex to the point where the arcs cross
Answer: fold the paper through the vertex so that the rays lie on top of each other.
Step-by-step explanation: apex
artaud noticed that if he takes the opposite of his age and adds 40, he gets the number 28. how old is artaud?
let's say Artaud's age is "x", its opposite will then be -x, so
[tex]\bf \stackrel{\textit{opposite of his age plus 40}}{-x+40}~~\stackrel{is}{=}~~28\implies -x+40-28=0 \\\\\\ -x+12=0\implies \boxed{12=x}[/tex]
Answer:
12 years old
Step-by-step explanation:
28 - 40 = -12
Note that -12 is the opposite of 12.
Artaud is 12
Given 3X=-15
Prove X =-5
Answer:
X = -5
Step-by-step explanation:
3X=-15
Lets solve the equation for x. We will isolate x by dividing each side by 3
3X/3 = -15/3
X = -5
Method 1:
Solve the equation
3x = -15 divide both sides by 3
3x : 3 = -15 : 3
x = -5
Method 2:
Put the value of x to the equation:
L = 3(-5) = -15
R = -15
L = R CORRECT
Mike has two containers, One container is a rectangular prism with width 2 cm, length 4cm, and height 10cm. The other is a cylinder with a radius of 1cm and height 10cm. Both containers sit on flat surfaces. Water has been poured into two containers so that the height of the water in two containers is 80 cubed cm, then the height of the water in each container is?
so, we know both the rectangular prism and the cylinder got filled up to a certain height each, the same height say "h" cm.
we know the combined volume of both is 80 cm³, so let's get the volume of each, sum them up to get 80 then.
[tex]\bf \stackrel{\stackrel{\textit{volume of a}}{\textit{rectangular prism}}}{V=Lwh}~~ \begin{cases} L=length\\ w=width\\ h=height\\[-0.5em] \hrulefill\\ L=4\\ w=2\\ \end{cases}~\hspace{2em}\stackrel{\textit{volume of a cylinder}}{V=\pi r^2 h}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=1 \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \stackrel{\textit{prism's volume}}{(4)(2)(h)}~~+~~\stackrel{\textit{cylinder's volume}}{(\pi )(1)^2(h)}~~=~~80 \\\\\\ 8h+\pi h=80\implies h(8+\pi )=80\implies h=\cfrac{80}{8+\pi }\implies h\approx 7.180301999[/tex]
Final answer:
To find the height of the water in each container, we must calculate the volumes of the rectangular prism and the cylinder, set equations based on their volumes that add up to 80 cm³, and solve for the heights of the water in each container.
Explanation:
To solve this, the volume of the containers and then the height of the water in each container must be determined.
The volume of the rectangular prism can be found with the formula:
Volume = length × width × height. So, the volume = 4cm × 2cm × height of water for the rectangular prism.
The volume of the cylinder is calculated using the formula: V = πr²h, where 'r' is the radius and 'h' is the height of water for the cylinder. Given the radius is 1 cm, the formula simplifies to V = π × 1 cm × height of water.
Knowing the combined volume of the water is 80 cm³, we set up the equations considering the volume of water held by each container and solve for the heights of water in both the rectangular prism and the cylinder. The calculations will provide the individual heights of water, ensuring they add up to the total volume of 80 cm³.
Help me find the slope of the line please
Answer: 3/4
Step-by-step explanation:
Given 4x = a + b/
8c
, rearrange the equation for a, in terms of b, c, and x
Answer:
B) a = 32cx − b
Step-by-step explanation:
i just did it
Hello! I kinda need a little help with this...
Lines m contains (6,8) and (-1,2). Lines n contains (-1,5) and (5,y). What is the value of y if line m is perpendicular to line n?
Can someone please help? The Maths is not something I'm too good at. :D
I honestly don't know or I would have replied. Sorry :(
Answer: y = -2
========================================
Explanation:
Find the slope of line m using the slope formula
slopeM = (y2-y1)/(x2-x1)
slopeM = (2-8)/(-1-6)
slopeM = -6/(-7)
slopeM = 6/7
The slope of line m is 6/7. The perpendicular slope is -7/6. We flip the fraction (aka reciprocal) and flip the sign (from positive to negative). The phrase "flip the fraction and flip the sign" is a handy way to think of "negative reciprocal", at least in my opinion. Note how the two slopes 6/7 and -7/6 multiply to -1 to prove they are perpendicular slopes
We'll use the slope formula again to set up the slope for line n. We don't know y, but we can set the fraction equal to -7/6 and solve for it.
slopeN = (y2-y1)/(x2-x1)
slopeN = (y-5)/(5-(-1))
slopeN = (y-5)/(6)
-7/6 = (y-5)/6
-7*6 = 6(y-5)
-42 = 6y-30
6y-30 = -42
6y = -42+30
6y = -12
y = -2
So in short, if y = -2, then line n goes through (-1,5) and (5,y) = (5,-2). The slope of line N is computed to be...
slopeN = (y2-y1)/(x2-x1)
slopeN = (-2-5)/(5-(-1))
slopeN = (-2-5)/(5+1)
slopeN = -7/6
which is the proper slope value we want.
If you multiply two even numbers where the product be even or odd explain with an example
Answer:
Even
Step-by-step explanation:
Any two numbers you multiply together that are both even will always result in an even number. For example 48x24=1152. You can use any two even numbers and you will always get and even product.
What is the solution set of the quadratic inequality x^2+x-2>0?
Answer:
The solution set is { x | x[tex]\leq[/tex] -2 or x[tex]\geq[/tex] 1}
Step-by-step explanation:
The given inequality is
[tex]x^{2} +x-2>0[/tex]
Let us factor [tex]x^{2} +x-2[/tex]
so we have
[tex](x+2)(x-1)>0[/tex]
Let us find zeros of [tex](x+2)(x-1)[/tex]
[tex](x+2)(x-1)=0[/tex]
[tex]x+2=0[/tex] or [tex]x-1 =0[/tex]
[tex]x= -2[/tex] or [tex]x=1[/tex]
so we have intervals (-∞ , -2) , (-2 , 1) and (1, ∞)
we need to find in which interval is [tex]x^{2} +x-2[/tex] is greater than 0
so we will assume the value of x in each interval and will plug it in [tex]x^{2} +x-2[/tex] and will check if we get negative or positive value
Let us check the sign of [tex]x^{2} +x-2[/tex] in (-∞ , -2)
we can take x=-3 and plug it in [tex]x^{2} +x-2[/tex]
so we have
[tex](-3)^{2} +(-3)-2= 9-3-2= 4[/tex] ( which is greater than 0)
This shows (-∞, -2) is one of the solution set
similarly we can check the sign of [tex]x^{2} +x-2[/tex] in (-2,1)
we take x= 0 , so we have
[tex]0^{2} +0-2=-2[/tex] ( which is less than 0)
This shows (-2,1) is not the solution set
now we check the sign of [tex]x^{2} +x-2[/tex] in (1 ,∞)
we can assume x= 2, so we have
[tex]2^{2} +2-2 = 4[/tex] ( which is greater than 0)
This shows (1 ,∞) is the solution set
Hence the solution set in interval notation (∞ ,-2)∪(1,∞)
we can write this as { x | x[tex]\leq[/tex] -2 or x[tex]\geq[/tex] 1}
Answer:
A on edge
Step-by-step explanation: