The type of model best fits the given situation is a quadratic equation
Quadratic equationQuadratic equations are equation that has a leading degree of 2.
From the given question, the motion of the rocket from the launch point to the landing point will be parabolic in nature and since the graph of a quadratic function is a parabola, hence the type of model best fits the given situation is a quadratic equation
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The ground temperature at sea level is 60 degrees F. For every 100-foot increase in elevation, the temperature rises 1/10 of one degree. At an altitude of 2,000 feet, what will be the likely temperature? A. 58 degrees F B. 62 degrees F C. 72 degrees F D. 80 degrees F Show ALL work please!!
====================================================
Explanation:
x = elevation in feet
y = temperature in fahrenheit
The temperature goes up 1/10 = 0.1 degrees for every 100-foot increase of elevation. So the slope is 0.1/100 = 0.001, which tells us how fast the temperature is increasing. In other words, the temperature goes up 0.001 degrees each time the elevation goes up by 1 foot.
The ground temperature is 60 degrees, which is our starting temperature. It's the value of y when x = 0. Therefore, 60 is the y intercept.
We have a slope of m = 0.001 and a y intercept of b = 60. The equation y = mx+b becomes y = 0.1x+60
Now plug in x = 2000 to find the temperature at this elevation
y = 0.001x+60
y = 0.001*2000+60
y = 2+60
y = 62
Answer:
B.62
Step-by-step explanation:
60 + (2000/100) We find 20 is the answer to the division
60 + (20 * 1/10) We find 2 is the answer to the multiplication
60 + (2)
We can then + for elevation or - or depression or decrease.
= 62
= 62 degrees.
What is the prime factorization of 10? Enter your answer as a product of prime numbers, like 2x3 or as a single prime number, like 17
Answer:
2 × 5
Step-by-step explanation:
We want to split the number 10 into its prime numbers.
A good way to start is divide the number by 2, if it's even. 10 is even, so we can divide by 2.
[tex]10\div2=5[/tex]
So the current factors are 2 and 5. We would keep going if one of these numbers was composite, but 2 and 5 or both prime numbers, so we can end the factorization here.
Therefore, the prime factorization of 10 is 2 × 5.
Hope this helped!
The prime factorization of 10 is 2 x 5.
What is the prime factorization of 10?Prime factorization is when you figure out the prime numbers that you can multiply together to get a certain number.
To figure out the prime factors of 10, we begin by dividing it by the lowest prime number, which is 2. Because 10 can be divided evenly by 2, we can say that 10 is equal to 2 multiplied by 5.
The numbers 2 and 5 are special because they can only be divided by 1 and themselves. This makes them prime numbers. The prime factorization of 10 is the result of multiplying the prime factors 2 and 5 together.
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Use the graph of the parabola to identify the domain and range of the function.
Question 18 options:
A) Domain: (–∞, ∞), range (–∞,–3]
B) Domain: (–∞, ∞), range (–∞,3]
C) Domain: (–∞,3], range (–∞, ∞)
D) Domain: (–∞,3], range (–∞, –3)
Answer:
B
Step-by-step explanation:
It's domain is side from side and so it can't be c or d. and it range goes to a positive number so it has to be B.
Please help with this.
Answer:
g(1)=-72; g(n)=g(n-1)*(1/6)
Step-by-step explanation:
g(1)= -72*(1/6)^(1-1)=-72*(1/6)^0=-72*1=-72
g(2)=-72*(1/6)^(2-1)=-72*(1/6)^1=-72*(1/6)=-12
g(2)=g(1)*(1/6)
g(n)=g(n-1)*(1/6)
How does 4D Shape look like? and, do (4 < n)D are possible?
ANSWER:
4d shape LOOKS LIKE THIS
Calculate the height of the cylinder shown.
Answer:
37.3
Step-by-step explanation:
If you want to solve it.
Cylineder Formula: Volume = π(radius)²(height)
Isolate height by diving πr² on both sides.
height = (volume/πr²)
height = (300/π(1.6^2))
Answer:
h = 36.2 cm
Step-by-step explanation:
lets make it short and simple
vol of cylinder + volume of hemisphere = 300 cu.cm.
Vc + Vh = 300 --- eq.1
cylinder radius = 1.6 cm.
since it says NOT TO SCALE
let the radius of hemisphere is the same as cylinder.
vol of cylinder = πr²h
vol of hemisphere = 2/3 πr³
using eq.1
πr²h + 2/3 πr³ = 300
π (1.6²) h + 2/3 π (1.6³) = 300
h = 36.2 cm
check:
Vc + Vh = 300
π (1.6²) 36.2 + 2/3 π (1.6³) = 300
300 cu.cm = 300 cu.cm. ----OK
A grocery store recently sold a bag of peanuts for $0.76 and a bag of Pikachu's for $3.68 at the end of the day 50 bags of peanuts and Pikachu's were sold for a total of 128 point 52 how many bags of each were sold
Answer:
31 Pikachu bags were sold.
19 peanut bags were sold.
Step-by-step explanation:
Let's set up an equation of the total revenue of the day, where x is the number of Pikachu's sold.
We know that the number of Peanuts sold is 50-x (as the total needs to be 50)
We know that the total revenue is:
Number of Pikachus * Cost per Pikachus + Number of Peanuts * Cost per Peanuts
Using our definitions above:
Total Revenue = x * $3.68 + (50-x) * $0.76
We know that the revenue needs to be $128.52.
$128.52 = x * $3.68 + (50-x) * $0.76
Let's remove the $ signs.
128.52 = x * 3.68 + (50-x) * 0.76
Multiplying both 50 and -x with 0.76, "expanding" the parenthesis.
128.52 = x*3.68 + 50*0.76 - x*0.76
128.52 = x*3.68 + 38 - 0.76*x
Subtracting 38 from both sides
90.52 = 3.68*x - 0.76*x
We can simplify the right side.
90.52 = 2.92*x
We can divide both sides by 2.92:
31 = x
And flip it:
x = 31
So 31 Pikachus were sold (remember we claled that x), and as we know, the number of peanut bags sold is
50-x = 50-31 = 19
31 Pikachu bags were sold.
19 peanut bags were sold.
[tex] \LARGE{ \boxed{ \rm{ \pink{Solution:}}}}[/tex]
Let the number of peanut bags be x
Then, Number of pikachu bags = 50 - x
Given,
Cost of each peanut bag = $0.76Cost of each pikachu bag = $3.68Then,
⇛ Total cost he gets from peanut bag = $0.76 × x
⇛ Total cost he gets from pikachu bag = $3.68(50 - x)
According to question,
⇛ $0.76x+ $3.68(50 - x) = $128.52
Solving this equation,
⇛ 0.76x + 184 - 3.68x = 128.52 (Removed $ symbol)
⇛ 184 - 2.92x = 128.52
⇛ 184 - 128.52 = 2.92x
⇛ 55.48 = 2.92x
Flipping the equation,
⇛ 2.92x = 55.48
⇛ x = 55.48 / 2.92
⇛ x = 19
Then,
⇛ 50 - x = 50 - 19 = 31
[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: peanut \: bags = 19}}}}}[/tex]
[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: pikachu \: bags = 31}}}}}[/tex]
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Create diagrams to represent the possible cases for common tangents between two circles. Your diagram can be created using multimedia sources or drawn by hand. They should not be copied and pasted from a website. Explain why your diagrams satisfy the given criteria. One Common Tangent (10 points) Diagram: Justification:
Answer:
draw 2 lines and draw 2 circles in the lines with the edge touching the line
Step-by-step explanation:
In between two circles, there might be 0, 1, 2, 3, and 4 tangents are there.
What is the tangent of a circle?"A tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior.
1. When one circle is in between another and one circle does not touch the other one, then tangent is not possible.
2. When one circle is in between another and one circle touches the other one at a point inside the circle, then only one tangent is possible.
3. When one circle intersects the other one, then two tangents are possible.
4. When one circle touches the other one at a point outside, then three tangents are possible.
5. When one circle neither intersects the other one nor inside the other one, then four tangents are possible.
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The Varners live on a corner lot. Often, children cut across their lot to save walking distance. The children’s path is represented by a dashed line. Approximate the walking distance that is saved by cutting across their property instead of walking around the lot. Hypotenuse: 32 ft , Short leg: x , Long leg: x+6
Answer:
[tex]x= \sqrt{503}-3[/tex]
Step-by-step explanation:
Hypotenuse = 32 feet
Short leg = x
Long leg = x+6
We will use Pythagoras theorem
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
[tex]32^2=x^2+(x+6)^2[/tex]
[tex]1024=x^2+x^2+36+12x[/tex]
[tex]2x^2+12x-988=0[/tex]
[tex]x=-3-\sqrt{503}, \sqrt{503}-3[/tex]
Since the distance cannot be negative
So,[tex]x= \sqrt{503}-3[/tex]
Type the correct answer in each box. If necessary, use / for the fraction bar.
Complete the statements about series A and B.
Series A: 10 + 4 +8/5 + 16/25 + 13/125 + ...
Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...
Series (a or b) has an r value of (blank) where 0<|r|<1. So, we can find the sum of the series. The sum of the series is (blank)
Answer:
Step-by-step explanation:
Given two series A and B;
Series A: 10 + 4 +8/5 + 16/25 + 13/125 + ...
Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...
Both series are geometric series since they have the same common ratio. Given the geometric series T₁, T₂, T₃, T₄..., the common ratio r is expressed as [tex]\frac{T_2}{T_1} =\frac{T_3}{T_2} =\frac{T_4}{T_3} = r[/tex].
a) For series A, Given T₁ = 10, T₂ = 4, T₃ = 8/5 and T₄ = 13/125
Its common ratio is expressed as [tex]\frac{4}{10} =\frac{8/5}{4} =\frac{13/125}{8/5} = 2/5[/tex]
Hence the common ratio of series A is 2/5
The sum to infinity of the geometric series will be expressed as [tex]s_\infty = \dfrac{a}{1-r}[/tex]
Note that the sum to infifnity is used since the series is tending to infinity.
a is the first term if the series = 10
r - 2/5
On substituting this values into the formula;
[tex]s_\infty = \dfrac{10}{1-2/5} \\\\s_\infty = \dfrac{10}{3/5} \\\\s_\infty = 10* 5/3\\s_\infty = 50/3[/tex]
Hence the sum of the series is 50/3
b) For the series B;
Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...
The common ratio of the series is expressed as shown;
[tex]\frac{3/5}{1/5} =\frac{9/5}{3/5}= \frac{27/5}{9/5 } = r\\ r = (3/5 * 5/1) = 9/5*5/3 = 27/5*5/9 = 3[/tex]
Hence its common ratio is 3.
Sun of the series is expressed similarly as:
[tex]s_\infty = \frac{a}{1-r}\\ s_\infty = \frac{1/5}{1-3}\\\\s_\infty = \frac{1/5}{-2}\\\\[/tex]
[tex]s_\infty = 1/5 * -1/2\\s_\infty = -1/10[/tex]
Hence the sum of series B is -1/10
Evaluate the expression. *
23 – (12 + 6) + 8
Please help
Answer:
13
Step-by-step explanation:
23-(12+6)+8
23-18+8
31-18
13
answer is 13
Step-by-step explanation:
Using the BODMAS rule,bracket of division or multiplication, addition or subtraction.
This applies the rule:
therefore,
23- (12+6)+8 ,calculate within bracket first
=23-(18)+8
now remove the bracket,by multiply by the -1
=23-18+8
the start calculate from the left to right
=23-10
=13
therefore the answer is 13
what is x? Please explain how you got it so I can understand for future questions.
Answer:
[tex]\boxed{x = 40}[/tex]
Step-by-step explanation:
Hey there!
Well angles like 142 and 2x + 22 equal each other because they are across from each other.
So we can set up the following,
142 = 3x + 22
Single out x
-22 to both sides
120 = 3x
Divide both sides by 3
x = 40
Hope this helps :)
Answer:
x=40
Step-by-step explanation:
142=3x+22
3x+22-22=142-22
3x=120
120/3=40
5. Find the measures of the following. Round to the nearest whole number
Answer:
a - HT = 17
b - ∠T = 62
c - ∠H = 28
Which equation represents the graphed function?
a)–3x + 2 = y
b) –2/3 x + 2 = y
c) 3/2 x – 3 = y
d) 2x – 3 = y
Answer: C is your answer.
Step-by-step explanation:
For the equation, determine whether the equation is true for all, some, or no values of x.
Explain how you know.
−3x=x×−3
Answer:
nothing can be further done with this topic. please check the expression entered or submit a picture for futher understanding
Step-by-step explanation:
These cones are similar. Find the volume
of the smaller cone. Round to the
nearest tenth.
Answer:
19.5
Step-by-step explanation:
The Volume of a cone is h/3(r²)[tex]\pi[/tex]
That means, for the larger cone,
66=h/3(3²)([tex]\pi[/tex])
66=h/3*9[tex]\pi[/tex]
66/9[tex]\pi[/tex]*3=h
h=7, so the height of the larger cone is seven
Since the cones are similar, it has to have the same ratio. 7/3 of 2 is 4.6666. So the height of the smaller cone is 4.66666.
Putting that in the formula,
V=(4.66666/3)(2²)[tex]\pi[/tex]
V=1.555555*4*[tex]\pi[/tex]
V=19.547
Answer:
19.6
Step-by-step explanation:
I have acellus too, and honestly, I typed in 19.5, which didn't work, so I typed in 19.6 and it worked. Hope this helps!
Given: UR ∥ ST ∠R, ∠T right angles Prove: ∆RSU ≅ ∆TUS
What you will get:
25 pts
Brainliest
Here
Angle R = Angle T
UR = ST
US = SU
So using RHS conguerence criteria Triangle RSU conguerent to Triangle TUS
While the currency of the United States is dollars, the currency of England is pounds. When Robin visited London, she exchanged $225 for 150 pounds. What was the exchange rate of pounds to dollars in decimal form? Round your answer to the nearest hundredth
Answer:
0.67
Step-by-step explanation:
We have to find out the exchange rate for pounds to dollars
150 pounds divided by 225 dollars
We get 0.6(6) the 6 in parenthesis for the repeating number.
Since we round to the nearest hundred we get 0.67.
How do I determine if -3x+y =8 is a function?
You need to see if it passes the vertical line test, then graph it to see if it is but is a function tho.
Graph the line with the slope 1/3 that contains the point (-4, -3)
Answer:
So, 1 point is on (-4, -3)
Other point is on (-4, -7)
Step-by-step explanation:
Slope = y/x - y1/x1
=> -3 / -4 - ? = 1/3
=> -3 / -4 - 1/3 = ?
=> -3 -1 / -4 - 3
=> -4 / -7
So, -3 / -4 - (-4 / -7)
=> -3 +4 / -4 + 7
=> 1/3
So 1 point is on (-4 , -3)
Other point is on (-4, -7)
Answer:no
Step-by-step explanation:
No
Solve the simultaneous equations. You must show all your working to find x and y. 1/2x -3y = 9 5x y + y = 28
The right question is:
[tex]\frac{1}{2}x - 3y = 9[/tex]
[tex]5x + y = 28[/tex]
Answer:
[tex]x = 6[/tex]
[tex]y = -2[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{2}x - 3y = 9[/tex]
[tex]5x + y = 28[/tex]
Required
Solve for x and y
Make y the subject of formula in the second equation
[tex]y = 28 - 5x[/tex]
Substitute [tex]y = 28 - 5x[/tex] in the first equation
[tex]\frac{1}{2}x - 3(28 - 5x) = 9[/tex]
Open the bracket
[tex]\frac{1}{2}x - 3*28 - 3*- 5x = 9[/tex]
[tex]\frac{1}{2}x - 84 + 15x = 9[/tex]
Collect Like Terms
[tex]\frac{1}{2}x + 15x = 9+ 84[/tex]
[tex]\frac{x}{2} + 15x = 9+ 84[/tex]
[tex]\frac{x+30x}{2} = 93[/tex]
[tex]\frac{31x}{2} = 93[/tex]
Multiply both sides by 2
[tex]2 * \frac{31x}{2} = 93 * 2[/tex]
[tex]31x = 186[/tex]
Divide both sides by 31
[tex]\frac{31x}{31} = \frac{186}{31}[/tex]
[tex]x = \frac{186}{31}[/tex]
[tex]x = 6[/tex]
Recall that [tex]y = 28 - 5x[/tex]
So;
[tex]y = 28 - 5 * 6[/tex]
[tex]y = 28 - 30[/tex]
[tex]y = -2[/tex]
Hence;
[tex]x = 6[/tex] and [tex]y = -2[/tex]
pls help… I don’t understand this stuff
Find the conjugate of 2 - 5i and then calculate the product of the given complex
number and its conjugate. (1 point)
O The conjugate is –2 + 5i and the product is -4 - 201 - 2522.
The conjugate is 2 + 5i and the product is 4 -
2522
O The conjugate is -2 + 5i and the product is - 29.
The conjugate is 2 + 5i and the product is 29.
JUST ONE MORE !! PLS
Answer:
The conjugate is 2+5i and the product is 29.
Step-by-step explanation:
The conjugate of a complex number [tex]a+bi[/tex] is [tex]a-bi[/tex]
Our complex number is 2-5i.
Here, a = 2 and b = -5
Thus, the conjugate of 2-5i is
[tex]2-(-5i)=2+5i[/tex]
Using this rule:
[tex](a+b)(a-b)=a^{2}-b^{2}[/tex]
And the fact that [tex]i^{2} = -1[/tex]
We can find the product of any complex number and its conjugate:
[tex](a+bi)(a-bi)=a^{2} - (bi)^{2}=a^{2} - b^{2} i^{2} = a^{2} + b^{2}[/tex]
As our complex number is [tex]2-5i[/tex], the product with its conjugate will be
[tex]2^{2} + (-5)^{2} =4+25=29[/tex]
Select the equation of the line that passes through the point (5.7) and is perpendicular to the line x = 4.
Factor the following expression completely:
32
z
4
+
8
z
3
−
4
z
2
Answer:
40z + 5
Step-by-step explanation:
I'm assuming you need to factor 32z + 4 + 8z + 3 - 4 + 2
32z + 8z ( since they both have the same variable ) = 40z4 + 3 - 4 + 2 ( since they have to variables ) = 5Hope this helped
Answer:
The factored expression for the given equation is 4(8z⁴ + 2z³ - z²)
Step-by-step explanation:
In the problem, we a re given an equation.
32z⁴ + 8z³ - 4z²
We can factor out this equation by finding the common factor between all of the coefficients which are 32, 8, and 4.
A common factor between them is 4 because each number can be easily divided by 4. Each number is also a multiple of 4. So, when we are factoring, we will divide each number by 4 because 4 will be on the outside of the parentheses in the final answer.
4(8z⁴ + 2z³ - z²)
So, this is your factored expression from the given equation.
Please help I suck at math
Answer: 12
Step-by-step explanation:
Find the difference between the first and second points.
Since the x-coordinates are the ones changing, find the difference between them.
2 - (-3)
= 5
Then find the distance between the second and the third points.
Here, the y coordinates are the only ones changing, so we subtract them/or find the distance between them.
2-(-5)
=7
Now add the distances (5+7) and you get 12.
hope this helps!!:)
Find the measure of b+d.
Answer:
=90
Step-by-step explanation:
because d=32° and b=58°
this is because corresponding angles are equal
Answer:
Step-by-step explanation:
b+d =90 degree
hope it helps
Nine-tenths of a 70 foot long driveway has already been paved. How many
feet of the driveway have been paved so far?
Answer:
63
Step-by-step explanation:
becuase when you divide 70 by 10, you will get 7 which then when you mutiply it by 9, you will get 63
Write the equation for the following table:
0 2
1 7
2 13
3 20
Answer:
Step-by-step explanation:
for each positive integer m, so that la - r2m-ll and la - r2m I are both less than
1 1
Ir2m - r2m-ll .:::: 42(m-l) Ir2 - rll = 24m - 3 ·
It follows that limn--->oo rn = limn--->oo rn-l = a. Taking limits in the recursion in
(d) leads to
1
a=I+--
l+a
which reduces to a 2 = 2. Since rn > 0 for each n, a > O.
What is the value of m in the equation 1/2m-3/4n=16, when n=8?
20
32
44
48
Answer:
44
Step-by-step explanation:
1/2m-3/4n=16 , m when n=8
1/2m-3/4n=16
1/2m - 3/4(8) = 16
1/2m - (8 x 3)/4 = 16
1/2m - (24/4) = 16
1/2m - 6 = 16
1/2m = 16 + 6
1/2m = 22
m = 22 x 2
m = 44