Answer:
The circle has radius = 9 units, and its equation is:
[tex]x^2+y^2=81[/tex]
The parabola has equation of the form:
[tex]y=a\,x^2+9[/tex]
with [tex]a[/tex] being a positive number
Step-by-step explanation:
Given the characteristics of the two figures (circle and parabola) as described,
since the parabola intersects the circle at a single point (it vertex) then the radius of the circle centered at the origin must be 9. that makes the equation of the circle to have the following standard form;
[tex]x^2+y^2=9^2\\x^2+y^2=81[/tex]
Since there is no other info regarding the parabola, the most one can say about the equation of the parabola, is that in vertex form, the parabola's equation must be of the form:
[tex]y=a\,(x-x_{vertex})^2+y_{vertex}\\y=a\,(x-0)^2+9\\y=a\,x^2+9[/tex]
with [tex]a[/tex] being a positive number.
Which data set could be represented by the box plot shown below?
Answer:
16
Step-by-step explanation:
Can someone please help with questions 4 and 5 and explain it to me I’ll appreciate!
Answer for number 4:
4. It will take them 3.5 hours on the fourth day.
Alright, so this is a multistep problem.
1. We need to calculate how many miles they have already traveled.
In order to do that, we multiply the number of hours by the average speed on each day.
- On day 1, they drove 5 hours at an average of 70 mph. 5 * 70 = 350, so they drove 350 miles on the first day.
- On day 2, they drove 7 hours at an average of 65 mph. 7 * 65 = 455, so they drove 455 miles on the second day.
- 350 miles + 455 miles = 805 miles, so they've driven 805 miles so far.
2. We need to figure out how far they have left to travel.
They started out with 1,050 miles, so they've got 245 miles left. 1,050 - 805 = 245.
3. We need to figure out how many hours they've got left to drive.
On the third day, they drive at an average speed of 70 mph, and they've got 245 miles left. to find the amount of time they need to drive, we divide the distance by the speed.
245 miles ÷ 70 mph = 3.5 hours. Therefore, it will take them 3.5 hours to reach their friend's home.
Answer For Number 5:
10 gallons of water will leak out in 30 hours.
This question involves unit rates.
1. We need to figure out how much water leaks out per hour.
- Since 7 gallons of water will leak out in 21 hours, we divide the amount of water by the amount of time it took for it to leak out. The answer will be how much water leaks out in an hour.
- 7 gallons ÷ 21 hours = 1/3 gallon of water. Now we have our unit rate. Every hour, 1/3 gallon of water leaks out.
2. We need to figure out how much water will leak out in 30 hours.
- Since we know how much water leaks out in 1 hour, we can easily figure out how much water leaks out in 30 hours. All we need to do is multiply how much water leaks out in one hour by 30!
- 1/3 gallon * 30 hours = 10 gallons of water.
Therefore, 10 gallons of water will leak out in 30 hours.
I hope this helps!
help could u guys add an explanation on how u got the answer too? thanks!
Answer:
15
Step-by-step explanation:
f(x) = x^2+1
f(2) = 2^2+1 = 4+1 = 5
g(x) = 3x+1
g(3) = 3(3)+1 = 9+1 = 10
f(2)+g(3) = 5+10 =15
Answer:
15
Step-by-step explanation:
I'm just guessing though.
A building casts a 33-m shadow when the sun is at an angle of 27° the vertical. How tall is the building to the
nearest meter? How far is it from the top of the building to the tip of the shadow?
Answer:
1. EF = 65m
2. DF = 73m
Step-by-step explanation:
1. EF = height of the building = h = 33 / tan 27 = 65m
2. DF = sqrt (65² + 33²) = 73m
The building is 64.76 meters long and 73 meters far from the top of the building to the tip of the shadow.
From the triangle DEF, we find the value of EF by using tan function.
tan function is a ratio of opposite side and adjacent side.
tan(27)= 33/FE
0.5095 = 33/FE
Apply cross multiplication:
FE=33/0.5095
FE=64.76
Now DF is the hypotenuse, we find it by using pythagoras theorem.
DF²=DE²+EF²
DF²=33²+64.76²
DF²=1089+4193.85
DF²=5282.85
Take square root on both sides:
DF=72.68
In a triangle the the sum of three angles is 180 degrees.
∠D + 27 +90 =180
∠D + 117 =180
Subtract 117 from both sides:
∠D =63 degrees.
Hence, the building is 64.76 meters long and 73 meters far from the top of the building to the tip of the shadow.
To learn more on trigonometry click:
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You buy a new computer for $1,500. The value of the computer decreases by 6%
every year. How much is the computer worth after 4 years?
$999.80
$1,171.05
$1,008.50
$1,225.35
Answer:
$1171.05
Step-by-step explanation:
1500 × (1-(6 / 100))⁴
Answer:
Hey there!
Each year, the computer is (100-6), or 94% of it's original value.
Thus, we have:
Original: 1500
First year: 1500(0.94)
Second year: 1500(0.94)(0.94)
Third year: 1500(0.94)(0.94)(0.94)
Fourth year: 1500(0.94)(0.94)(0.94)(0.94)
Fourth year: 1171 dollars.
Hope this helps :)
TheOriginal tragedy of the commons concern grazing cows and sheep’s and 14 century England, space choose the theme in about the tragedy of the commons that is correct
Answer:
The tragedy of the commons in fourteenth-century England was overcome by the common lands being enclosed and privatized.
Step-by-step explanation:
The Commons tragedy refers to a popular economic narrative that explains why common assets appear to be overused from a social point of view. The story-line is focused on the premise that each person tries to get as much profit as possible from the available resource. As per the question, the land available for grazing was limited and solution can be opted through enforcing regulations, auctioning out a limited number of licenses, or transforming the common good into a private good.
Mr. Blake's biology class is divided into three secrions. The same test is given to each section. The table above shows both the lowest score and the range of scores on this rest for each section
What is the overall range of all scores in all three sections?
Answer:
25
Step-by-step explanation:
The overall range of all scores in all three sections is 25.
What is Average?In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
Given:
The range of 3 sections is 28, 25 and 22.
So, the overall range of all scores in all three sections
= (28+ 25+ 22)/ 3
= 75/3
= 25
Hence, the overall range of all scores in all three sections is 25.
Learn more about average here:
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5•1000000 is how many times as large as 5•10000
Answer:
100 times
Step-by-step explanation:
5•1000000 has 2 more zeros than 5•10000 so that means the first number is 100 times larger than the second number! hope this helps and please mark as brainiest
Find an equation of the line with the slope m= 3/2 that passes through the point (8,-3). Write the equation in the form Ax+By = C.
Answer:
work is shown and pictured
Please help with 2 and 3 for maths
Answer:2-4=
Step-by-step explanation:y-16-(-42)
y-16+16
y-32
y-16-(-22)
y-16+4
y-20
y-16-(02)
y-16
y-16-(42)
y-0
Answer:
The answer is 2-4
Step-by-step explanation:
If -1< y< 0, which of the following has the greatest value?
Answer:
[tex]\boxed{\sf B}[/tex]
Step-by-step explanation:
-1 < y < 0
The value of y is negative.
Let’s take the number -0.5.
(-0.5)² = 0.25
1 - (-0.5) = 1.5
1 + (-0.5) = 0.5
2(-0.5) = -1
The greatest value is 1.5.
The answer is 1 - y.
Can someone do this?
PLEASE HEEELPPP 15 POINTS PLESSEE
If In a = 2, In b = 3, and Inc = 5, evaluate the following:
(a) In
(b) In V63c4a-2
(c)
In(a+b-3)
In(be)"
3
(d)
Answer:
-20/343
Step-by-step explanation:
What happened that caused Nollie's housemate, Katrien, to arrive at the ten Boom's house in an emotional state?
Answer:
Nollie told the police that Annaliese was a Jew
Step-by-step explanation:
Add.
8/9+2/3+1/6
11/18
11/15
1 13/18
1 2/9
Answer:
1 13/18
Step-by-step explanation:
Get a common denominator of 18
8/9+2/3+1/6
8/9 *2/2 + 2/3 *6/6 + 1/6 *3/3
16/18 + 12/18 + 3/18
31/18
18/18+13/18
1 13/18
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{The Lowest Common Denominator (LCD) of these fraction is: \bf 18}[/tex]
[tex]\mathsf{\dfrac{8}{9}+\dfrac{2}{3}+ \dfrac{1}{6}}\\\\\mathsf{= \dfrac{8\times2}{9\times2}+\dfrac{2\times6}{3\times6}+ \dfrac{1\times3}{6\times3}}\\\\\mathsf{8\times2=\bf 16}\\\mathsf{2\times6=\bf 12}\\\mathsf{1\times3 = \bf 3}\\\\\mathsf{9\times2=\bf 18}\\\mathsf{3\times6= \bf 18}\\\mathsf{6\times3 = \bf 18}\\\\\mathsf{\dfrac{16 + 12 + 3}{18}}\\\\\mathsf{16+12+3}\\\mathsf{= 28 + 3}\\\mathsf{=\bf 31}\\\\\\\mathsf{ = \bf 1 \dfrac{13}{18}}\\\\\\\boxed{\huge\textsf{Answer: \boxed{\mathsf{1 \dfrac{13}{18}}}}}}[/tex] ☑
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
PLEASE HELP!!!!! I BEG OF EVERYONE. FIRST CORRECT WILL GET BRALIEST!!!!!!! How far have I travelled if I biked at 10mph for hhrs, I walked at 3mph for twice as long as I biked, and ran at 10mph for one quarter as long as I walked?
Answer:
32 miles/4 hours.
Step-by-step explanation:
can somewon help me plz can somewon help me
Hey there! I'm happy to help!
Let's look at our diameters.
[tex]1*10^2^1\\5*10^2^2[/tex]
We want to see how many times greater the diameter of the IC 1101 is than the Milky Way. So, we will divide it's diameter by the diameter of the Milky Way.
[tex]\frac{5*10^2^2}{1*10^2^1} \\[/tex]
We divide the numbers without exponents, giving us 5. Then, we divide the 10s with exponents. When dividing exponents, you subtract the numbers in the exponent to get your result. For example, x³÷x²=x
[tex]\frac{5*10^2^2}{1*10^2^1} = 5*10=50[/tex]
Therefore, your answer is 50.
Have a wonderful day! :D
determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither. 3x-4y=-5 8x+6y=-5 show full work please and thank you
what is the equation
Answer: -12 - 3 = -15
Explanation:
We start at -12 which goes in the first box.
Moving to the left 3 units means we subtract off 3, so that's why 3 goes in the second box.
The arrow is pointing at -15 as the final destination, which goes in the final third box.
Determine whether the lines given by the vector equations r1=2i+3j+k+s(4i−k) and r2=2i+3j+k+t(2i+2j+k) intersect. If they intersect, give the coordinates of their point of intersection.
They do. the initial point is same in both lines.
formally,
[tex] \vec{r_1}=(2\hat i+3 \hat j+\hat k)+s(4\hat i-\hat k)[/tex]
$\vec{r_2}=(2\hat i +3 \hat j +\hat k)+t(2\hat i+2\hat j +\hat k)$
if they intersect then $\begin{vmatrix} 4 & 0 & -1 \\ 2 & 2 & 1 \\ (2-2) & (3-3) & (1-1) \end{vmatrix}=0$
(which obviously is zero)
Simplify (−3c3w5)3. −9c6w8 −9c9w15 −27c6w8 −27c9w15
Answer:
-6723cw
Step by Step:
(-3c * 3w * 5) * 3 - 9c * 6w* 8 - 9c * 9w * 15 - 27c * 6w * 8 - 27c * 9w * 15
Help ASAP please and thanks
How are you? Heres the question of the day! 138 + 76 x 94 =
Answer:
7282
Step-by-step explanation:
To answer this use PEMDAS
First, we need to multiply: 76 x 94 = 7144
Then we add: 7144 + 138 = 7282
Answer:
[tex]\boxed{7282}[/tex]Step-by-step explanation:
Using PEMDAS rule:
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
Now, let's solve:
[tex] \mathsf{138 + 76 \times 94}[/tex]
Multiply the numbers
[tex] \mathsf{ = 138 + 7144}[/tex]
Add the numbers
[tex] \mathsf{7282}[/tex]
Hope I helped!
Best regards!
The figure shows a parallogram inside a rectangle outline: What is the area of a parallogram? (1/25) (11/25) (3/25) (4/25)
Answer:(3/25)
Step-by-step explanation: just had this question
The members of a film crew are at least 75 miles from their camp and must carry equipment back to camp before a storm arrives. The storm is scheduled to begin in 24 hours. They plan to travel as far as possible by truck and then walk the rest of the way. The truck can travel at a rate of 10 miles per hour through the terrain, and the team can travel 2 miles per hour on foot. Which system represents the number of hours the crew can travel by truck, x, and on foot, y, to reach camp before the storm? x + y < 24 2x + 10y ≥ 75 x + y > 24 2x + 10y ≥ 75 x + y < 24 10x + 2y ≥ 75 x + y > 24 10x + 2y ≥ 75
Answer:
I DONT UNDERSTAND ANY OF THIS
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
d) Use your knowledge of scale drawings and image sizes to fill in the missing
information in the table. (3 points)
Empire State Building
Original
Image
Actual Height
(in feet)
1,450
1,450
1,450
Reduced
Image
Model Height
(in blocks)
145
1
1
Scale Factor
25
50
Answer:
Your table is filled in below.
Step-by-step explanation:
The scale factor is the ratio of image size to original size. In part (d), the image height is "blocks" while the original height is "feet". So, the units of the scale factor are "blocks/ft".
Sometimes a scale factor has units, like this, and sometimes it is expressed as a pure number. A map scale factor might be the pure number ratio 1 : 62500, or it could also be expressed with units as 1 in : 1 mile.*
__
* actually, these are slightly different scales. 1:62500 is about 0.98643 inches per mile.
Answer: Image
Step-by-step explanation:
took the test
The sum of 4 consecutive integers is 130 what is the third number in the sequence
PLZ HELP!!!
Answer:
33
Step-by-step explanation:
We can write an equation:
x+x+1+x+2+x+3=130
x represents the smallest number of the consecutive integers
By the way, an example of consecutive would be 2, 3, 4, 5 or 10, 11, 12, 13
We can combine like terms from our equation:
4x+6=130
4x=124
x=31
The smallest number is 31. The second number would be 31+1=32, which means the third number is 33!
Hope this helps! :) :)
Answer:
[tex]\huge\boxed{3rd\ number = 33}[/tex]
Step-by-step explanation:
Let the consecutive numbers(Coming one after another) be x, x+1, a+2 and x+3
So,
x+x+1+x+2+x+3 = 130
4x + 6 = 130
Subtracting 6 to both sides
4x = 130-6
4x = 124
Dividing both sides by 4
x = 32
So,
1st number = x = 31
2nd Number = x+1 = 31+1 = 32
3rd number = x+2 = 31+2 = 33
4th number = x+3 = 31+3 = 34
A bag contains red, white, and blue marbles. If 1/4 of the marbles are red and 2/3
of the marbles are white, what fractional part of the marbles are blue?
Answer: 1/12
Step-by-step explanation: 1/4=3/12. 2/3=8/12. 3/12+8/12=11/12. The remaining 1/12 is blue.
Find the surface area of the square pyramid shown below.
Answer:
179.38 sq.units
Step-by-step explanation:
answer is in the pic