This is confusing very much, I’m having a lot of problems at the moment and I’m in a lot of pain.
. Waipio Rd in Honokaa, Hawaii, is one of the steepest roads in the world. It rises 450 ft over a horizontal distance of 1,000 ft. a. What is the percentage grade of this hill? Round to the nearest tenth of a percent.
Answer: 50%
Step-by-step explanation:
From the question, we're given the information that Waipio Rd in Honokaa, Hawaii, is one of the steepest roads in the world and that it rises 450 ft over a horizontal distance of 1,000 ft.
Therefore, the percentage grade of this hill will be calculated as the height over the length and this will be:
= 450/1000 × 100
= 45%
= 0.45
= 0.5 to nearest tenth
= 50% to nearest tenth.
A large container is partially filled with n liters of water. Ito adds 10 liters of water to the container, making it 60% full. If Ignacio adds 6 more liters of water, the container will be 75% full.
What is the value of n?
Answer:
[tex]14\text{ liters}[/tex]
Step-by-step explanation:
Let the total amount of water the container can hold be [tex]t[/tex]. Currently, there are [tex]n[/tex] liters in the container. If Ito adds 10 liters of water, the container will be 60% full. We can express this statement in the following mathematical equation:
[tex]n+10=0.6t[/tex]
Next, we're given that if we add 6 more liters to this, the container will be 75% full.
Therefore, we have:
[tex]n+10+6=0.75t,\\n+16=0.75t[/tex]
This is a system of equations:
[tex]\begin{cases}n+10=0.6t,\\ n+16=0.75t\end{cases}[/tex]
Subtract both equations to conveniently get rid of [tex]n[/tex]:
[tex]10-16=0.6t-0.75t,[/tex]
Combine like terms:
[tex]-6=-0.15t[/tex]
Divide both sides by -0.15:
[tex]t=\frac{-6}{-0.15}=40[/tex]
Now substitute [tex]t=40[/tex] into any equation (I'll choose the first):
[tex]n+10=0.6(40),\\n+10=24[/tex]
Subtract 10 from both sides:
[tex]n=24-10=\boxed{14\text{ liters}}[/tex]
The equation a[tex]x^{2}[/tex]+b[tex]x[/tex]+c=0 has roots α, β. Express (α+1)(β+1) in terms of a, b and c.
Answer:
[tex]\displaystyle \left(\alpha+1\right)\left(\beta + 1\right) = \frac{a+c-b}{a}\:\: \left(\text{ or } 1+\frac{c-b}{a}\right)[/tex]
Step-by-step explanation:
We are given the equation:
[tex]ax^2+bx+c=0[/tex]
Which has roots α and β.
And we want to express (α + 1)(β + 1) in terms of a, b, and c.
From the quadratic formula, we know that the two solutions to our equation are:
[tex]\displaystyle x_1 = \frac{-b+\sqrt{b^2-4ac}}{2a}\text{ and } x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]
Let x₁ = α and x₂ = β. Substitute:
[tex]\displaystyle \left(\frac{-b+\sqrt{b^2-4ac}}{2a} + 1\right) \left(\frac{-b-\sqrt{b^2-4ac}}{2a}+1\right)[/tex]
Combine fractions:
[tex]\displaystyle =\left(\frac{-b+2a+\sqrt{b^2-4ac}}{2a} \right) \left(\frac{-b+2a-\sqrt{b^2-4ac}}{2a}\right)[/tex]
Rewrite:
[tex]\displaystyle = \frac{\left(-b+2a+\sqrt{b^2-4ac}\right)\left(-b+2a-\sqrt{b^2-4ac}\right)}{(2a)(2a)}[/tex]
Multiply and group:
[tex]\displaystyle = \frac{((-b+2a)+\sqrt{b^2-4ac})((-b+2a)-\sqrt{b^2-4ac})}{4a^2}[/tex]
Difference of two squares:
[tex]\displaystyle = \frac{\overbrace{(-b+2a)^2 - (\sqrt{b^2-4ac})^2}^{(x+y)(x-y)=x^2-y^2}}{4a^2}[/tex]
Expand and simplify:
[tex]\displaystyle = \frac{(b^2-4ab+4a^2)-(b^2-4ac)}{4a^2}[/tex]
Distribute:
[tex]\displaystyle = \frac{(b^2-4ab+4a^2)+(-b^2+4ac)}{4a^2}[/tex]
Cancel like terms:
[tex]\displaystyle = \frac{4a^2+4ac-4ab}{4a^2}[/tex]
Factor:
[tex]\displaystyle =\frac{4a(a+c-b)}{4a(a)}[/tex]
Cancel. Hence:
[tex]\displaystyle = \frac{a+c-b}{a}\:\: \left(\text{ or } 1+\frac{c-b}{a}\right)[/tex]
Therefore:
[tex]\displaystyle \left(\alpha+1\right)\left(\beta + 1\right) = \frac{a+c-b}{a}[/tex]
which is the equation of the line with slope 0 passing through the point (-1,-2)?
The answer is A.
Because it goes 2 down
A firework is launched into the air from ground level with an initial velocity of 128 ft/s. If acceleration due to gravity is –16 ft/s2, what is the maximum height reached by the firework?
Answer:
h = 256 feet
Step-by-step explanation:
Given that,
The initial velocity of firework, v = 128 ft/s
The acceleration due to gravity is-16 ft/s².
We need to find the maximum height reached by the firework.
The equation for the firework is :
[tex]h(t) = -16t^2 + 128t[/tex]
To find the vertex's x-coordinate, we can use
[tex]t=\dfrac{-b}{2a}\\\\t=\dfrac{-128}{2\times (-16)}\\\\t=4\ s[/tex]
Put all the values in the expression for h (t).
[tex]h(t) = -16(4)^2 + 128(4)\\\\h(t)=256\ ft[/tex]
So, the maximum height reached by the firework is 256 feet.
help again geometry similarity transformations
1. 2
2. The X axis
3. 3 right and 1 up (3, 1)
Answer:
2 or A
x-axis or y = 0
I'm not sure the answer choices for the third one so I'm heading out.
Step-by-step explanation:
If your device is capable of taking screenshots from your laptop/desktop, then take a screenshot, like on Windows OS, it's Windows Key + Shift + S, and on Mac OS, it's Command + Control + Shift + 4, I think.
Taking a picture from a phone takes longer to upload and has bad quality since it's from a further distance and the individual pixels are more spread out.
25. Several functions represent different savings account plans. Which functions are linear?
A. y = 3.6 x2
B. y = 5.25 x
c. y = 0,5 Х
D.y = 2.5 x +7
E. y = 2.50(1.3)*
NEED HELPP
Answer:
b, c, d
Step-by-step explanation:
y=kx+b
or
y=kx
so y=5,25x-right
y=0,5x-right
y=2,5x+7-right
Hey can anyone help me with this question
Mary wants to buy a mobile phone; the least expensive one she's spotted so far is $15. Mary has $4.25 saved for a mobile phone. If Mary works at a rate of $2.15 per hour, how many hours (H) will she have to work in order to afford a mobile phone?
Answer:
Mary would have to work 5 hours to afford a mobile phone.
Step-by-step explanation:
$15-$4.25= $10.75 that Mary would need to save.
2.15 x 5= 10.75
A woman deposits 100 EUR in her daughter's bank account on her first birthday. On every subsequent birthday, she deposits 10 EUR more than she deposited the previous year, so on her second birthday, she deposits 110 EUR, and on her third birthday she deposits 120 EUR.
By the time her daughter is 21 years old, how much money has been deposited in her account?
Answer:
By the time her daughter is 21 years old 300 EUR will have been deposited into the account.
Step-by-step explanation:
Since a woman deposits 100 EUR in her daughter's bank account on her first birthday, and on every subsequent birthday, she deposits 10 EUR more than she deposited the previous year, so on her second birthday, she deposits 110 EUR, and on her third birthday she deposits 120 EUR, to determine, by the time her daughter is 21 years old, how much money has been deposited in her account, the following calculation must be performed:
100 + (20 x 10) = X
100 + 200 = X
300 = X
Therefore, by the time her daughter is 21 years old 300 EUR will have been deposited into the account.
Classify each number as rational or irrational.
Answer:
π - irrational
0.04053.. - irrational
0.76 - rational
3.565565565 - irrational
-17 - rational
3.275 - rational
Step-by-step explanation:
rational = can express as fraction
irrational = cannot
Find the values of x and y that make these triangles congruent by the HL Theorem.
Answer the following (a) find an angle between 0 and 2 that is coterminal with 27/10 (b) find an angle between 0 and 360 That is conterminous with 775
Answer:
I have no clue sorry my bad bro
assume abc=def. if ab=5, ac=9 and ef=7, what is the length of bc?
Answer:
bc= 7
Step-by-step explanation:
Tess created a Pythagorean triple of (24, 32, 40) by multiplying the known Pythagorean triple 3, 4, and 5 by 8. Is Tess correct? Can a Pythagorean triple be created using multiples of a known Pythagorean triple.
Yes, as long as each number in the Pythagorean triple is multiplied by the same whole number.
Yes, as long as each number in the Pythagorean triple is multiplied by a different whole number.
No, Pythagorean triples only exist with small numbers.
No, multiplying a known Pythagorean triple by a whole number will not create a Pythagorean triple.
Answer:
Hello,
Answer A
Yes, as long as each number in the Pythagorean triple is multiplied by the same whole number.
Step-by-step explanation:
(a,b,c) is a Pythagorien triple : c²=a²+b²
and k is a naturel.
[tex](ka)^2+(kb)^2\\\\=k^2*a^2+k^2*b^2\\\\=k^2(a^2+b^2)\\\\=k^2c^2\\\\=(kc)^2\\[/tex]
Answer:
Yes, as long as each number in the Pythagorean Triple is multiplied by the same whole number.
General Formulas and Concepts:
Pre-Algebra
Equality PropertyTrigonometry
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
a is a leg b is another leg c is the hypotenuseStep-by-step explanation:
In order for it to remain a Pythagorean triple, we must follow the equality rules. To make it the exact same expression, all parts of an equation must be multiplied or divided by the same number. If this is done, then it would also remain a Pythagorean triple, and hence we arrive at our answer.
Find the value of each variable. Lines that appear tangent are tangent, and the dot is the center. (Answer in the form a=? b=? c=? d=?)
Answer:
a = 60°/2 = 30°
b = 84/2 = 42°
c = (100+60)/2 = 80°
d = 360-100-60-84 = 116°
Answered by GAUTHMATH
what is the ratio for the surface areas of the rectangular prisms shown below, given that they are similar and that the ratio of
their edge lengths is 8:5
Answer:
B. 64:25
Step-by-step explanation:
the ratio of the surface areas =
(8)² : (5)² = 64 : 25
URGENT PLS HELP. pls but why or why not thank you:))
Answer:
No the relation is not a function
Step-by-step explanation:
A function by definition will have a unique output for every input, so there should be no repeating outputs, however, the clinic cares for 2 legged animals (birds) as well as 4 legged animals (cats and dogs). With this being said, if a clinic has 2 animals(input), the amount of legs(output) could be 8 if two dogs, or it could be 4 if two birds, or even six if a dog and bird.
If this were a function, the clinic would undeniably have different amounts of legs having two animals opposed to one animal, but this isn't true. if the clinic has 2 birds(input), there'd be 4 legs(output). but the clinic would also have 4 legs(output) if it had 1 dog(input). the output is the same for two different inputs
This shows the output is varying depending on the type of animal since the amount of legs changes, rather than the amount of animals.
Hope this helps :)
find the missing length indicated
Answer:
240
Step-by-step explanation:
We are given a right triangle. Based on the leg rule, the following equation shows how the length of a leg in a right triangle relates with the segments connected to the hypotenuse:
Hypotenuse/leg = leg/part
Where,
Hypo = 400
Leg = x
Part = 144
Substitute
400/x = x/144
Cross multiply
400*144 = x*x
57,600 = x²
√57,600 = x
240 = x
x = 240
What is the domain of g(x)
X is a real number
Answer:
The doing would be x
Step-by-step explanation:
since you are calculating domain for a specific value it would be the corresponding g(x) value which is the domain
Given the distance between (x,1) and (-2,5) is 2 root 7, find the the value of x. Leave your answer in simplified exact form
Answer:
Step-by-step explanation:
Distance = the square root of (x2-x1)2 + (y2-y1)2Added:Distance Formula: Given the two points (x1, y1) and (x2, y2), the distance between these points is given by the formula:square root of x2-x1 squared +y2-y1 squared
The value of x is (√12) - 2, when the distance between (x,1) and (-2,5) is 2√7 units.
What is the length of any line on the graph?The distance or length of any line on the graph,
[tex]d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
where,
d = distance/length of the line between point 1 and 2,
(x₁ , y₁) = coordinate of point 1,
(x₂ , y₂) = coordinate of point 2,
Given that the distance between (x,1) and (-2,5) is 2√7 units. Therefore we can write,
[tex]d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
[tex]2\sqrt7= \sqrt{(x + 2)^2 + (1-5)^2}[/tex]
Squaring both the sides of the equation,
[tex](2\sqrt7)^2= (\sqrt{(x + 2)^2 + (1-5)^2})^2[/tex]
4 × 7= (x + 2)² + (-4)²
28 = (x+2)² + 16
28 - 16 = (x+2)²
12 = (x+2)²
x+2 = √12
x = (√12) - 2
Hence, the value of x is (√12) - 2.
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What does the greater unit rate or slope mean in terms of the situation? What can you conclude from this?
Answer:
Bruce's tiles covered more area than Felicia's, so this means Bruce has the greater unit rate.
Step-by-step explanation:
Got it right
Is a decimal less than a whole number?
The Chesapeake Bay holds about 18 trillion gallons of water. The bay covers 4,480 square miles or 2,867,200 acres. Each acre can hold 750,000 oysters. Each oyster can filter 50 gallons of water each day. Can there be enough oysters to filter the whole Chesapeake Bay in one day
Answer:
There are enough oysters
Step-by-step explanation:
Given
[tex]Volume = 18\ trillion\ gallon[/tex]
[tex]Area = 2867200\ acre[/tex]
[tex]1\ acre = 750000\ oysters[/tex]
[tex]1\ oyster = 50\ gallons[/tex]
Required
Determine if there is enough water for a day
We have:
[tex]1\ oyster = 50\ gallons[/tex]
Convert to oysters: multiply both sides by 750000
[tex]750000 * 1\ oyster = 50\ gallon *750000[/tex]
[tex]750000\ oysters = 37500000\ gallons[/tex]
Given that:
[tex]1\ acre = 750000\ oysters[/tex]
So, we have:
[tex]1\ acre= 37500000\ gallons[/tex]
Convert to acre: Multiply by 2867200
[tex]2867200 * 1\ acre= 37500000\ gallons * 2867200[/tex]
[tex]2867200\ acres= 107520000000000\ gallons[/tex]
By comparison:
[tex]18000000000000\ gallons < 107520000000000\ gallons[/tex]
i.e. the volume of water in the bay is less than the capacity of the oysters. Hence, there are enough oysters.
What is the answer please help
Answer:
i don't know sorry
Answer:
a
Step-by-step explanation:
-5 shifts the y-intercept down, and it needs to be outside of the modulus as if its in the modulus, the graph would shift 5 units to the right instead
Which of the following statements is false?
B. A parallelogram is a rectangle.
When a weed solution is added to a lawn, the number of weeds can be represented by the function W(d)=1500(.75)^d where d is the number of days since application. By what percent does the population of weeds decrease each day
Number of weeds is represented by the function,
[tex]W(d)=1500(0.75)^d[/tex]
[tex]W(d)=1500(1-0.25)^d[/tex] -------(1)
Here, [tex]d=[/tex] Number of days since application
Function representing the exponential decay is,
[tex]A(t)=A(1-r)^t[/tex] --------(2)
[tex]A=[/tex] Initial value
[tex]r=[/tex] Percentage decay
[tex]t=[/tex] duration
By comparing both the functions (1) and (2),
[tex]r=[/tex] 0.25 ≈ [tex]\frac{25}{100}[/tex]
Or [tex]r=[/tex] 25%
Therefore, population of weeds will decrease 25% each day.
Learn more about exponential decay,
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Find the area of the following composite figure. Assume angles that look like they are a right angle are
right angles.
14 in
14 in
Q
Leave your answer in terms of . For example your answer might to 98 + 107.
square inches
NOTE: Figures are NOT to scale.
Answer:
7π + 7π + 196 ( could also be 14π + 196)
Step-by-step explanation:
14 is the length of the square. However it is also the diameter of the circle.
If you do diameter x π you will get the circumfrance. Which in this case is 14π. If your trying to find half of the circumfrance you would do 14π ÷ 2 which is 7π.
After finding 7π for one half a circle you do the same for the other and also get 7π
After finding the 2 half circles find the square which is 14 x 14 = 196
196 + 7π + 7π if you don't want bother pi's there it could also be seen as 196+ 14 π
What is the volume of the rectangular prism.
A. 16in. 3
B. 22 1/2in. 3
C. 200 in. 3
D. 212 1/2in. 3
Answer:
C: 200
Step-by-step explanation:
Just multiply 12.5 x 8 x 2 to get the answer.
Answer:
C. 200 in.^3
Step-by-step explanation:
The volume is given by
V = l*w*h
V = 12 1/2 * 8*2
V = 25/2 *8*2
= 25*8
= 200 in ^3
