The height of 3 meter to the left of the center of arch is -2.7 meters which is found by the evaluation of the given equation when x = -3.
We can solve it through
The Height at x = -3 meters on the left of the center = [tex](1/10)(-3^2 - 36) [by Substituting x = -3]= (1/10)(9 - 36)= (1/10)(-27)= -2.7 meters[/tex]
At the end height of the arch at 3 meters to the left of the center when x = -3 is -2.7 meters. This negative value means the point is actually below the ground level at that position. So the height is -2.7 meters where - insists negative value.
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Please answer these I’m so confused
The solution set of the inequality 2.5x ≥ 20 is x ≥ 8 and as such, Sebastian is incorrect based on his graph.
The graph of the solution set of -48 < -8t is shown below.
What is a number line?In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
Next, we would determine the solution to the given inequality as follows;
2.5x ≥ 20
x ≥ 20/2.5
x ≥ 8 (Sebastian was wrong)
-48 < -8t
-48/-8 < -8t/-8
6 < t
t > 8
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what are two numbers have a product of 20 and a sum of 9
Answer:
Step-by-step explanation:
Find the volume of this sphere.
Use 3 for TT.
V≈ [?]cm³
V = πr³
6 cm
The volume of the sphere with a diameter of 6cm is 108 cm³.
What is the volume of the sphere?A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.
The volume of a sphere is expressed as:
Volume = (4/3)πr³
Where r is the radius of the sphere and π is the mathematical constant pi
Given the data in the question:
Diameter d = 6cm
Radius is half of diameter
Radius r - 6cm/2
Radius r = 3cm
Also, π = 3
Plug the given values into the above formula.
Volume = (4/3)πr³
Volume = (4/3)π3³
Volume = (4/3)(3)(27)
Volume = 108 cm³
Therefore, the volume is 108 cm³.
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The temperature on Tuesday was -5 Celsius the temperature in Wednesday was 5 Celsius
The temperature of Srinagar on Wednesday was -3°C.
If the temperature was -5°C on Monday and dropped by 2°C on Tuesday, we can subtract 2 from -5 to get:
-5°C - 2°C = -7°C
So the temperature of Srinagar on Tuesday was -7°C.
If the temperature on Wednesday rose by 4°C from the temperature on Tuesday, we can add 4 to -7°C to get:
-7°C + 4°C = -3°C
So the temperature of Srinagar on Wednesday was -3°C.
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The complete question:
At Srinagar temperature was -5°C on Monday and then it dropped by 2°C on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4°C. What was the temperature on this day?
MODELING REAL LIFE A hemisphere-shaped mole has a diameter of 5.7 millimeters and a surface area of about
51 square millimeters. The radius of the mole doubles. Estimate the new surface area of the mole. Round your
answer to the nearest whole number.
The new surface area is square millimeters.
The new surface area of the hemisphere-shaped mole would be = 102mm².
How to calculate the new surface area for the hemisphere-shaped mole?A hemisphere-shaped mole has a shape that has one surface that is curved and the other surface a flat circular base.
Since the surface area of one hemisphere has been given, the second hemisphere can be determined.
To calculate the new surface area of the hemisphere-shaped moles the following is carried out;
Radius of the initial mole = 5.7/2 = 2.85 mm
If 2.85mm radius = 51 mm²
2(2.85mm) radius = x
Make X the subject of formula;
X = 2×2.85 × 51/2.85
= 102 mm²
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Use the binomial theorem to find specified term of the given power of binomial ( remember that r starts at 0 in the binomial theorem so finding say the second term means that r=1)
The fourth term in the expanded form of (x - 1)⁶ is -20x³.
What is the fourth term in the expanded form of (x - 1)⁶?The fourth term in the expanded form of (x - 1)⁶ using the binomial theorem is calculated as follows;
The expanded form of (x - 1)⁶ using the binomial theorem is;
(x - 1)⁶ = 1x⁶ + (-6)x⁵ + 15x⁴ + (-20)x³ + 15x² + (-6)x + 1
(x - 1)⁶ = x⁶ -6x⁵ + 15x⁴ -20x³ + 15x² -6x + 1
To find the fourth term, we look for the fourth term from the left side to right side, which is -20x³.
Therefore, the fourth term in the expanded form of (x - 1)⁶ is -20x³.
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The city council voted on a new tax. The council has 60 members and 70% of the council members voted in favor of the new tax. How many members voted in favor of the tax?
BJ won the lottery and decided to invest some of his money in an account
that will be compounding continuously. The account he chose earned
5.2%. He invested $27,000. How much money will he have after 18 years,
when his newborn will graduate from high school?
Answer:
$68,796.57
Step-by-step explanation:
approx $68,796.57 at 18 years
a = 19.5 cm, b = 12.5 cm and c = 5.5 cm for the triangle shown below.
X
X =
- C
Work out the value of a rounded to 1 DP.
The diagram is not drawn to scale.
cm
a
- b----
The value of x rounded to 1 decimal place is 15.9 cm.
What is Pythagorean theorem?In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):
x² + y² = z²
Where:
x, y, and z represents the length of sides or side lengths of any right-angled triangle.
How to determine the value of x?First of all, we would determine length of sides or side lengths of the opposite side of the ight-angled triangle as follows;
12.5² + y² = 19.5²
156.25 + y² = 380.25
y² = 224 cm.
y = √224 cm
Now, we can determine value of x;
x² = (√224)² + (5.5)²
x² = 224 + 30.25
x = 15.9 cm.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Write the product as a product of a whole number and a unit fraction. 3 x 2/4=
Answer:
1 whole and 2/4
Step-by-step explanation:
2/4+2/4=1
1+2/4=1 whole and 2/4
A city official would like to know if there is public support for increasing funding for arts programs. To collect data, the city official stands outside a concert hall after a show and surveys every 25th person to exit and asks their opinion about raising funds for the arts. Which of the following describes the population in this scenario?
A. all residents of the city
B. the members of the city council
C. all city residents who support the arts
D. the people surveyed by the city official
All city residents who support the arts. Therefore, the option C is the correct answer.
As the city official would lie to know that if public support for increased funding of arts programs. By collecting data the officials show the survey after every 25 persons and ask for their opinion.
They also tend to raise a fund that states the population in the scenario of a city resident that supports the arts.
The population in this scenario is the people surveyed by the city official. The city official is conducting a survey outside a concert hall after a show, which means they are targeting people who have just attended a show. Since the city official is asking every 25th person to exit their opinion about raising funds for the arts, these are the people who are included in the population being surveyed.
Therefore, the option C is the correct answer.
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How many anagrams of CADERNO have vowels before consonants?
There are 264 anagrams of the word CADERNO that have vowels before consonants.
We have,
To count the number of anagrams of the word CADERNO that have vowels before consonants, we can use the following steps:
Count the number of vowels in the word.
In this case, there are three vowels: A, E, and O.
Count the number of consonants in the word.
In this case, there are four consonants: C, D, R, and N.
Determine the possible arrangements of vowels and consonants that satisfy the condition of having vowels before consonants.
Since there are three vowels and four consonants, there are two possible arrangements that satisfy this condition:
a) Vowel - Consonant - Vowel - Consonant - Vowel - Consonant - Consonant
b) Vowel - Consonant - Vowel - Consonant - Consonant - Vowel - Consonant
Calculate the number of ways to arrange the vowels and consonants in each of the possible arrangements determined in step 3.
We can use permutations to calculate this.
For arrangement a):
There are 3 ways to choose the first vowel (A, E, or O)
There are 4 ways to choose the first consonant (C, D, R, or N)
There are 2 ways to choose the second vowel (whichever is left out of the two remaining vowels)
There are 3 ways to choose the second consonant (whichever is left out of the three remaining consonants)
There is 1 way to choose the third vowel (the remaining vowel)
There is 1 way to choose the fourth consonant (the remaining consonant)
There is 1 way to choose the fifth consonant (the remaining consonant)
The total number of arrangements for this case is: 3 x 4 x 2 x 3 x 1 x 1 x 1 = 72
For arrangement b):
There are 3 ways to choose the first vowel
There are 4 ways to choose the first consonant
There are 2 ways to choose the second vowel
There are 2 ways to choose the second consonant (whichever is left out of the two remaining consonants)
There are 2 ways to choose the third consonant (whichever is left out of the two remaining consonants)
There is 1 way to choose the third vowel
There is 1 way to choose the fourth consonant
The total number of arrangements for this case is: 3 x 4 x 2 x 2 x 2 x 1 x 1 = 192
Add up the total number of arrangements for both cases to get the final answer:
72 + 192 = 264
Therefore,
There are 264 anagrams of the word CADERNO that have vowels before consonants.
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Use substitution!!!
Pt. a
truck a costs $20,345. You can expect to pay an average of $1230 per year for repairs. truck b costs about 16,000. It will cost an average of $1425 for repairs per year. After how many years are the total costs for cars the same?
(I can solve it, can you just turn the words into an equation for me?)
Pt. B
You have 56 coins that are all nickles and dimes. The value of the coins is $2.05. Find the number of nickels and dimes.
(Can you also just make an equation out of this for me?)
The system of equations are t = 22.28 years , number of nickles and dimes are solved
Given data ,
a)
Let the number of years be represented as t
For truck A, the total cost (including the initial cost and average yearly repair cost) after "t" years can be represented as:
Total cost for truck A = 20345 + 1230t
For truck B, the total cost (including the initial cost and average yearly repair cost) after "t" years can be represented as:
Total cost for truck B = 16000 + 1425t
when the total costs are equal , we get
20345 + 1230t = 16000 + 1425t
On simplifying , we get
195t = 4,345
t = 22.28 years
b)
Let the number of nickels be n and number of dimes be d
The total value of nickels is 0.05n (since the value of one nickel is $0.05) and the total value of dimes is 0.10d (since the value of one dime is $0.10)
The total value of the coins = $ 2.05
And , the total number of coins = 56
0.05n + 0.10d = 2.05
And , n + d = 56
Hence , the system of equations are solved
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Ten upright dominos of increasing height are lined up to be knocked down. The dominos are numbered 0 to 9. The smallest domino, #0, is 3.00 inches tall and will be toppled by a person to start the chain reaction. Each subsequent domino is 15% taller than the one before. What is the height of domino #9?
Answer:
8.604 in.
Step-by-step explanation:
We can use the formula for compound interest to find the height of domino #9:
A = P(1 + r)^n
where A is the final amount, P is the initial amount, r is the growth rate, and n is the number of compounding periods. In this case, P is the height of domino #0, r is 15% or 0.15, and n is 9 (since we want to find the height of domino #9).
Substituting the given values:
A = 3.00 in * (1 + 0.15)^9
Simplifying:
A = 3.00 in * 2.86797199
A ≈ 8.604 in
Therefore, the height of domino #9 is approximately 8.604 inches.
Use the drop downs to determine which symbols
would complete the inequality for the domain.
-4_____(a)______x______(b)______4
(a)
(b)
DONE✔
The domain of the function in the graph can be written as: -4 ≤ x < 4
or [-4, 4)
How to write the domain of the function?To identify the domain look at the horizontal axis. Remember that the domain is the set of the inputs, and the inputs go in the horizontal axis (or the x-axis)
You can see that there is a closed dot (which means that the value belongs to the domain) at x = -4, and there is a open dot (which means that the value does not belong to the domain) at x = 4.
Then the domain of the graph is:
-4 ≤ x < 4
Or, written in interval form, it is [-4, 4)
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determine the volume of the oblique cylinder below. leave your answer in terms of pi and round to the hundredths place if needed.
The volume of the oblique cylinder can be calculated as:
833π cm³
How to Find the Volume of an Oblique Cylinder?The formula that would be used to find the volume of any given oblique cylinder can be expressed as:
Volume = πr²h, where:
radius of the cylinder = r
height of the cylinder = h
π is a constant
We are given the values for the cylinder as:
r = 14/2 = 7 cm
h = 17 cm
Volume of the oblique cylinder = πr²h = π × 7² × 17
Volume of the oblique cylinder = 833π cm³
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find the misding values in the ratio table then write the equivalent ratios forks 16 8 spoons 10, 30
The missing number in the ratios of numbers are 16:10 8:20 and 0:30
How to determine the missing numbers?Ratios are quantitative relationships between two numbers that describe how many times one value can contain another
the given parameters are
Forks 16 8 ----
Spoons 10 --- 30
The numbers are written in ascending order of magnitude
Using AP,
for forks: a = 16, 2nd term = 8
common difference = 8-16 - -8
For spoons a = 10, 3rd term = a + 2d = 30
30 = 10 + 2d
30 -10 = 2d
d= 20/2 = 10
Therefore the 2nd term = 10+10=20
The table reappears as follows
Forks 16 8 0
Spoons 10 20 30
Therefore the equivalent ratios are 16:10 8:20 and 0:30
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The position (in meters) of a particle per respect to time (in seconds) is defined by the
following functions (t)=t4-16t³+72t² +5. Find the maximal and minimal value for
the speed of the particle for t E [1, 7].
The maximum of 1,159 m/s occurs when t = 7, and the minimum of 16 m/s occurs when t = 6.
How to calculate the valueIt should be noted that upon deriving v(t), an equation of 12t² - 96t + 144 is produced. Subsequently, v'(t) must be set to zero, resulting in a quadratic equation of 12t² - 96t + 144 = 0, requiring division of both sides by 12 to produce t² - 8t + 12 = 0.
The quadratic can now be factored to obtain (t - 2)(t - 6) = 0, indicating that critical points lie on the values t = 2 and t = 6.
After calculating these values— v(1) = 100 m/s, v(2) = 64 m/s, v(6) = 16 m/s and v(7) = 1159 m/s—it is clear that the maximum of 1,159 m/s occurs when t = 7, and the minimum of 16 m/s occurs when t = 6.
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geometry please helpp
Answer:
(1)
Step-by-step explanation:
11111111111111111111111
Add 2x+ 3 y + 7 and 4x-7y-8 PLLSSS QUICKKK
Answer:
3
Step-by-step explanation:
h(1) = 23 meters and h(a) = 34.25 meters.
The average rate of change of the height of the rocket is 11.25/(a - 1)
Estimating the average rate of change of the height of the rocketFrom the question, we have the following parameters that can be used in our computation:
h(1) = 23 meters and h(a) = 34.25 meters.
The average rate of change of the height of the rocket is
Rate = Change in height /Time
So, we have
Rate = (34.25 - 23)/(a - 1)
Evaluate
Rate = 11.25/(a - 1)
Hence, the rate = 11.25/(a - 1)
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Complete question
Melissa launches a rocket from a 3-meter-tall platform. The height, h, of the rocket, in meters, can be modeled by the given graph.
Melissa knows that h(1) = 23 meters and h(a) = 34.25 meters.
What is a reasonable estimate of the average rate of change of the height of the rocket, in meters per second
The volume of this rectangular prism is 199.68 cubic yards. What is the value of z?
Answer:
z=199.68
Step-by-step explanation:
PLEASE HELP ME WITH THIS MATH! XC
Answer:
The answer is
1) x²=5²+6²
2)Volume
3)39.7ft
Step-by-step explanation:
KL=4-(-1)=5
KJ=3-(-3)=6
JL=x
using pythagoras theorem
x²=5²+6²
3)using pythagoras theorem
opp²=hyp²-adj²
let opp be y
y²=40²-5²
y²=1600-25
y²=1575
y=39.7ft
Here are some integers where a
a
b
C
d
d
d
The mode of the integers is 9
The median of the integers is 8
The range of the integers is 4
Work out the value of a, the value of b, the value of c and the value of d
We know that the mode of the integers is 9, which means that 9 occurs more frequently than any other number in the set of integers.
How to explain the mediWe also know that the median of the integers is 8, which means that when the integers are arranged in order from smallest to largest, the middle number is 8.
Finally, we know that the range of the integers is 4, which means that the difference between the largest and smallest integers in the set is 4.
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Graham has 1/3 of 3/4 dollar, and Frank has 3/5 of 1/2 dollar. Who has more money
Here cuz:
Frank got more cuz you see Graham has 1/3 and 3/4 and frank got 3/5 and 1/2 so he got more.
Hope This Helps Cuz!
I need help with this please
Answer: C
Step-by-step explanation:
Right angles (or 90 degree angles) are indicated by little squares in the corners of the figures that have them.
A radioactive element has a half-life of 18 years. We start with 40mg. Assuming the decay is occurring continuously, the appropriate model is...
Identity P0.
Solve for k.
What amount of the element remains after 10 years?
When with 10mg be remaining?
1) The decay constant is 0.0385
2) The amount after ten years is 27.2 mg
3) The time taken for 10 mg to remain is 36 years.
What is the half life of a radioactive isotope?We know that;
P = Poe^-kt
Given that the half life is 18 years;
20=40e^-18k
20/40=e^-18k
0.5 =e^-18k
ln0.5 = -18k
k = -0.693/-18k
k = 0.0385
After 10 years we have;
P = 40e^-10(0.0385)
P = 27.2 mg
10 mg will remain when;
10 = 40e^-0.0385t
10/40 =e^-0.0385t
0.25 = e^-0.0385t
ln0.25 = -0.0385t
t = -1.386/-0.0385
t = 36 years
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new car is purchased for 18700 dollars. The value of the car depreciates at
14.25% per year. To the nearest year, how long will it be until the value of the
car is 3000 dollars?
The minimum time required to depreciate the value of the car is 12 years.
Let us assumed the time to be t. Representing the formula for calculation of time-
Final value = Principal value × [tex] {(1 - rate of depreciation)}^{t} [/tex]
Keeping the values in formula to find the time period
3000 = 18700 × [tex] {(1 - 14.25%)}^{t} [/tex]
Solving the expression
[tex] {(0.8575)}^{t} [/tex] = 3000/18700
Cancelling zeroes common in numerator and denominator
3000/18700 = [tex] {(0.8575)}^{t} [/tex]
Taking log on both sides of the equation
t log 0.8575 = 30/187
Keep the value
t = log 0.8575 30/187
t = 12 years
Hence, it will take 12 years for value depreciation.
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Rotations : If the point (6,2) was on a figure that was rotated 180 degrees clockwise what would be the coordinates of the new point on this figure
The coordinates of the new point is (-6, -2)
What would be the coordinates of the new pointFrom the question, we have the following parameters that can be used in our computation:
Point = (6, 2)
Rule: 180 degrees rotation
The rule of 180 degrees rotation is
(x, y) = (-x -y)
Substitute the known values in the above equation, so, we have the following representation
image = (-6, -2)
Hence, the image is (-6, -2)
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A pyramid has a square base with an area of 144 ft. Mark each statement as true or false and correct any false statements.
T/F? - The length of one side of the pyramids base can be found using the equation s^2=144.
T/F? - The Length of one side of the pyramids base is 72 feet.
A = s^2, where A is the area and s is the length of one side of the square gives the area of a square base. The correct option is true
If s^2 = 144, then s = √144 = 12 feet. The correct option is false
What is pyramid ?A pyramid is a polyhedron that is created by joining an apex and a polygonal base. A triangle known as a lateral face is formed by each base edge and apex.
Therefore, s^2 = 144 is a valid equation to find the length of one side of the base. The correct option is true
Therefore, one side of the pyramid's base is 12 feet, not 72 feet.
The correct option is false
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