The solution of the equation found by completing the square are;
x = 7 - √(53) and 7 + √(53)
What is the completing the square method?Completing the square method involves writing the quadratic expression of the form a·x² + b·x + c as (x + d)² + e, where d and e are constants.
Moving the constant to one side of the equation, we get;
x² - 14·x = 4
We complete the square on the left side of the equation by adding and subtracting the square of the half the coefficient of x term inside the parenthesis. Therefore, we add and subtract (-14/2)² = 49, as follows;
(x² - 14·x + 49) - 49 = 4
Therefore; (x - 7)² - 49 = 4
The -49 is moved to the right side of the equation to get;
(x - 7)² = 4 + 49 = 53
Taking the square root of both sides, we get;
x - 7 = ± √(53)
Therefore; x = 7 ± √(53)
The solution is; x = 7 + √(53) and 7 - √(53)
Learn more on the completing the square method here: https://brainly.com/question/21507540
#SPJ6
What are the sine, cosine, and tangent of Θ = 3 pi over 4 radians?
sin Θ = square root 2 over 2; cos Θ = negative square root 2 over 2; tan Θ = -1
sin Θ = negative square root 2 over 2; cos Θ = square root 2 over 2; tan Θ = 1
sin Θ = square root 2 over 2; cos Θ = negative square root 2 over 2; tan Θ = 1
sin Θ = negative square root 2 over 2; cos Θ = square root 2 over 2; tan Θ = -1
Why Are Mr. and Mrs. Number so Happy?
Mr. and Mrs. Number are so happy because they are both prime numbers, which are natural numbers greater than 1 that have no positive divisors other than 1 and themselves.
For example:
Mr. Number could be 2, as it is divisible only by 1 and 2.
Mrs. Number could be 3, as it is divisible only by 1 and 3.
Prime numbers have unique properties and are considered special in mathematics. They play a fundamental role in number theory and various mathematical algorithms. Additionally, prime numbers are essential in cryptography, ensuring secure communication and data encryption.
So, Mr. and Mrs. Number are happy because they share the special quality of being prime numbers, making them quite unique and valuable in the mathematics.
Learn more about Prime here:
https://brainly.com/question/34250415
#SPJ6
289 + 456 x 789 / 489 - 746 + 2457 x 3453 / 3646 =
Which of the following options best describes an algebraic fraction?
Select All That Apply.
1.) Common denominators
2.) a variable in the numerator
3.) a variable in the denominator
4.) a variable with an exponent.
I already know 4 for sure is one...
Answer:
Option 1,2 and 3.
Step-by-step explanation:
An algebraic expression is such a mathematical representation of variables
Algebra is relation with variables a,y,z and so on
So, Option 2 is correct that is it will contain variable in numerator.
Similarly, Option 3 is correct that is it will contain variable in denominator.
Option 4 is incorrect because if it contains variable with an exponent then it will not be algebraic it will become exponent function.
Option 1 is correct because it may have common denominator an algebraic fraction will have common denominator.
When you sign up for a movie service, you get three free months of movies. Then you are charged $15 per month to rent movies. If you pay $90, how many months of use do you get?
Answer:
9 months!!
Step-by-step explanation:
(25ab^3)^1/3 divided by (ab)^-1/2
The value of a van depreciates at the rate of 20% per year. Gary buys a new van for £27500. After n years the value of the van is £11264. Find the value of n.
Answer:
n = 3years
Step-by-step explanation:
If Gary buys a van £27500 and sell the van at a value of the £11264 after n years, depreciation will give us;
£27500-£11264 = £16236
If the van depreciates by 20% each year, yearly depreciation will be;
20% of £27500 = £5500
To get the total number of years n it takes the van to depreciate to £11264 will give total depreciation amount/yearly depreciation amount which gives;
£16236/£5500 = 2.9years
This means that the van has depreciate from £27500 to £11264 after 3years
The Florida tourism board surveyed people on their favorite vacation cities. Half of the people said Orlando, 1/4 said Miami, 1/8 said Kissimmee, 1/16 said Fort Lauderdale, 1/32 said Key West, and the rest said Tampa. If 22 people said Tampa, how many people responded Orlando?
To find out how many people responded Orlando, we need to add up the fractions for Miami, Kissimmee, Fort Lauderdale, Key West, and Tampa and then set up a proportion to find the number of people who said Orlando. The answer is approximately 47 people.
Explanation:To find out how many people responded Orlando, we need to add up the fractions for Miami, Kissimmee, Fort Lauderdale, Key West, and Tampa since the rest said Tampa. The fractions we need to add are 1/4, 1/8, 1/16, and 1/32. Let's calculate each fraction to get a common denominator.
1/4 = 8/32, 1/8 = 4/32, 1/16 = 2/32, 1/32 = 1/32.
Now we can add them up: 8/32 + 4/32 + 2/32 + 1/32 = 15/32.
Since the remaining fraction is Tampa, which corresponds to 22 people, we can set up a proportion: 15/32 = 22/x to find out how many people said Orlando. Cross-multiply and solve for x: 32 * 22 = 15x, 704 = 15x, x = 704/15, x ≈ 46.93.
Therefore, approximately 47 people responded Orlando.
HELPPPPPP
A person can order a new car with a choice of 10 possible colors, with or without air conditioning, with or without automatic transmission, with or without power windows, and with or without a CD player. In how many different ways can a new car be ordered with regard to these options?
Final answer:
To find the number of different ways a new car can be ordered with various options, multiply the number of choices for each option.
Explanation:
To find the number of different ways a new car can be ordered with regard to the given options, we need to multiply the number of choices for each option. There are 10 possible colors, 2 choices for air conditioning (with or without), 2 choices for automatic transmission, 2 choices for power windows (with or without), and 2 choices for a CD player (with or without).
Therefore, the total number of different ways a new car can be ordered is:
10 colors × 2 choices for air conditioning × 2 choices for automatic transmission × 2 choices for power windows × 2 choices for a CD player = 10 × 2 × 2 × 2 × 2 = 160
What is the sum of 58 76?
"The sum of 58 and 76 is 134.
To find the sum of two numbers, one simply needs to add them together. In this case, the numbers are 58 and 76.
The addition can be performed as follows:
[tex]\[ 58 + 76 = 134 \][/tex]
Thus, the correct answer to the question ""What is the sum of 58 and 76?"" is 134."
During renovation, a pillar is supported by two braces as shown in the diagram. Based on the diagram, at what height should the short brace touch the pillar to ensure that the short brace is parallel to the long brace?
10 feet
12 feet
15 feet
17 feet
The answer is A. 10 feet, on Plato.
At the city museum child admission is $5.70 and the adult admission is $9.60 on Thursday,186 ticket were sold for a total sales of $1399.50. How many child tickets were sold that day?
Describe the angle formed by the hands of a clock at 3:00 in the term of degrees and radians ...?
Answer:
90 degree and [tex]\frac{pi}{180}[/tex] radians.
Step-by-step explanation:
Given : Angle formed by the hands of a clock at 3:00
To find : Write in term of degrees and radians ...
Solution : We have given that a clock show the time 3 :00
We know that at 3 : 00 clock show hour hand at 3 and minute hand at 12.
Angle formed by the minute hand at 12 and hour hand at 3 is 90 degree.
90 degree = [tex]\frac{pi}{180}[/tex] radian.
Therefore, 90 degree and [tex]\frac{pi}{180}[/tex]radians.
Anna has put her money into various investments. Which of the three Cs of credit do these investments fall into?
A. Capital
B. Character
C. Capacity
The correct answer is:
A) Capital.
Explanation:
Capital is any valuable assets that you have such as real estate, personal property, or savings and investments that you could possibly use to repay credit debts if necessary.
Anna has put her money into various investments. These are Anna's capital.
A capital amount is the money that is needed to start any business venture or investment. Capital is also an asset of any person. Apart from personal money, capital also include funds in ones deposit accounts, tangible things like machinery used for production purposes etc.
1) Is it possible to have a function f defined on [ 2 , 4 ] and meets the given conditions?
f is continuous on [ 2 , 4 ), minimum value f(4)=2, and no maximum value.
2) Is it possible to have a function f defined on [ 4 , 5 ] and meets the given conditions?
f is continuous on [ 4 , 5 ], takes on no rational values.
3) Is it possible to have a function f defined on [ 2 , 5 ] and meets the given conditions?
f is continuous on [ 2 ,5 ] and the range of f is an unbounded interval.
The possibility statements are:
PossiblePossibleNot possibleStatement 1
The function is defined on [2.4]
The above means that, the minimum is 2, and the maximum is 4
However, since the function is continuous at [2,4), the close bracket ")" means that the function extends indefinitely i.e. no maximum.
Hence, this statement is possible
Statement 2
The function is defined on [4.5]
The above means that, the minimum is 4, and the maximum is 5
However, since the function is continuous at [4,5], the close brackets "[" and "]" mean that the function have finite values
Hence, this statement is possible
Statement 3
The function is defined on [2,5]
The above means that, the minimum is 2, and the maximum is 5
However, since the function is continuous at [2,5], the close brackets "[" and "]" mean that the function have finite values and it has bounded intervals
Hence, this statement is not possible
Read more about continuous functions at:
https://brainly.com/question/20089539
32/50 in simplest form
Please help! I'm really confused.
Angle A = 8x - 2, angle B = 2x - 8, and angle C = 94 - 4x. List the sides of triangle ABC in order from shortest to longest.
Options: (all are line segments)
o AC, AB, BC
o AC, BC, AB
o AB, AC, BC
o AC, BC, AB
Answer:
First option is correct.
Step-by-step explanation:
In triangle ABC, [tex]\angle A=8x-2[/tex], [tex]\angle B=2x-8[/tex] and [tex]\angle C=94-4x[/tex].
According to angle sum property of a triangle, the sum of interior angles of a triangle is 180 degree.
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]8x-2+2x-8+94-4x=180[/tex]
[tex]6x+84=180[/tex]
[tex]6x=96[/tex]
Divide both sides by 6.
[tex]x=16[/tex]
Therefore the value of x is 16. The measure of angles are
[tex]\angle A=8(16)-2=126[/tex]
[tex]\angle B=2(16)-8=24[/tex]
[tex]\angle C=94-4(16)=30[/tex]
The opposite angle of shortest side is always smallest interior angle. Similarly the opposite angle of longest side is always largest interior angle.
[tex]\angle B<\angle C<\angle A[/tex]
[tex]AC<AB<BC[/tex]
Therefore option 1 is correct.
What does this mean:
Harriet is comparing the costs of calling cards. To use card A, the cost is $1.00 to connect and then $0.04 per minute. To use card B, it costs $0.65 to connect and then $0.06 per minute. For what number of minutes does it cost the same amount to use each card for a single call?
Answer: There are 17.5 minutes for which it costs the same amount to use each card for a single call.
Step-by-step explanation:
Let the number of minutes be x
To use card A, the cost is $1.00 to connect and then $0.04 per minute.
So, our expression becomes,
[tex]1+0.04x[/tex]
To use card B, the cost is $0.65 to connect and then $0.06 per minute.
So, our expression becomes,
[tex]0.65+0.06x[/tex]
According to question, if it cost the same amount to use each card for a single call, then it will be
[tex]1+0.04x=0.65+0.06x\\\\1-0.65=0.06x-0.04x\\\\0.35=0.02x\\\\\frac{0.35}{0.02}=x\\\\17.5=x[/tex]
Hence, there are 17.5 minutes for which it costs the same amount to use each card for a single call.
Solve for b2 in A = 1/2 h(b1+b2), if A = 16, h = 4, and b1 = 3. 16= 1/2* 4(3+b2) =6+2b2 or, b2= [16-6]/2= 5
PLEEEAAASE HEEEELP
what is the cube root of -729a^9 b^6
-9a3b2
-9a2b3
Explain how you would know log3100 is between 4 and 5 without the use of a calculator.
...?
*Will give brainliest. $1,500 is invested into an account with an interest rate of 6.75%. How many years will it take for the account to reach $7,300? Round to the nearest hundredth
Using the compound interest formula, it will take approximately 24.53 years for an initial investment of $1,500 to grow to $7,300 at an annual interest rate of 6.75%. This is calculated by solving for t in the rearranged compound interest formula.
To determine how many years it will take for your $1,500 investment to reach $7,300 with an interest rate of 6.75% compounded annually, we use the formula for compound interest:
[tex]A = P(1 + r/n)^{(nt)[/tex]
Where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money, $1,500).r is the annual interest rate (decimal, so 6.75% becomes 0.0675).n is the number of times that interest is compounded per year (since it's annual, n = 1).t is the number of years.We rearrange the formula to solve for t:
t = (log(A/P) / log(1 + r/n)) / n
Plug in the known values:
t = (log(7300/1500) / log(1 + 0.0675)) / 1
Calculate the logarithms:
t ≈ (log(4.8667) / log(1.0675))
t ≈ (0.6887 / 0.0281)
t ≈ 24.53
It will take approximately 24.53 years for the investment to grow to $7,300.
Solve for x. x - 8 = -10 x = 2 x = -2 x = 18 x = -18
Answer:
x = -2
Step-by-step explanation:
1. Determine which ratio forms a proportion with 9/5 by finding a common multiplier.
a. 54/30 b. 45/50 c. 45/40 d. 90/20 2. Determine which ratio forms a proportion with 15/8 by using cross products.
a. 25/16 b. 30/12 c. 60/32 d. 75/32 3. Solve 3/27 = w/54 a. 2 b. 6 c. 9 d. 18 4. In a survey, 3 out of 10 people names blue as their favorite color. 1 out of 5 named red. If 1,200 people were included in the survey, how many named blue or red as their favorite color?
a. 700 people b. 800 people c. 600 people d. 400 people 5.Solve the proportion using cross products. Round to the nearest hundredth if necessary.
12 miles/27 hours = 4 miles/ h hours a. 28 b. 12 c. 9 d. 18 6. LA is about 385 miles from San F. How far apart would the cities be on the map with a scale of 1 inch = 15 miles. If necessary, round to the nearest hundredth.
a. 26.33 in. b. 25.67 in. c. 24.33 in. d. 27.50 in
Final answer:
To find the ratio that forms a proportion with 9/5, we can find a common multiplier for each option and check if the resulting ratios are equal to 9/5.
Explanation:
If we want to determine which ratio forms a proportion with 9/5, we can find a common multiplier. We can multiply both the numerator and denominator of each ratio by the same number and check if the resulting ratios are equal to 9/5.
Let's check each option:
a. 54/30: multiplying by 6 gives us 54/30 = 9/5, so this ratio forms a proportion with 9/5.b. 45/50: multiplying by 10 gives us 450/500 = 9/10, so this ratio does not form a proportion with 9/5.c. 45/40: multiplying by 8 gives us 360/320 = 9/8, so this ratio does not form a proportion with 9/5.d. 90/20: multiplying by 2 gives us 180/40 = 9/2, so this ratio does not form a proportion with 9/5.Therefore, the ratio 54/30 (option a) forms a proportion with 9/5.
The formula D = rt gives the distance traveled in time T at rate R. A bicyclist rides at a constant rate of 15 miles per hour. How many miles will she travel in 3.5 hours?
A. 52.5
B. 4.3
C. 23.3
D. 18.5
90 in fraction form show your work
I have three numbers. The biggest one is twice the middle one, and the biggest one plus the middle one is four times the smallest one. The smallest one plus the middle one is two less than the biggest one. What are the numbers? ...?
Let
x------> the biggest number
y------> the middle number
z------> the smallest number
we know that
[tex]x=2y[/tex] -------> equation [tex]1[/tex]
[tex]x+y=4z[/tex] -------> equation [tex]2[/tex]
[tex]z+y=x-2[/tex] -------> equation [tex]3[/tex]
substitute equation [tex]1[/tex] in equation [tex]2[/tex] and equation [tex]3[/tex]
[tex][2y]+y=4z[/tex] ------> [tex]3y=4z[/tex] ------> equation [tex]4[/tex]
[tex]z+y=[2y]-2[/tex] ----> [tex]z+2=y[/tex] ------> equation [tex]5[/tex]
using a graph tool-----> to resolve the system of equations
see the attached figure
the solution is the point [tex](6,8)[/tex]
[tex]z=6\\y=8[/tex]
Find the value of x
[tex]x=2y[/tex]
[tex]x=2*8=16[/tex]
therefore
the answer is
the biggest number is [tex]16[/tex]
the the middle number is [tex]8[/tex]
the smallest number is [tex]6[/tex]
a bowling ball is dropped from a height of 24 feet. write a function that gives the height h (in feet) of the bowling ball after t seconds
Answer:
[tex]h=16t^2[/tex]
Step-by-step explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration due to gravity = 32 ft/s²
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow h=ut+\frac{1}{2}32\times t^2\\\Rightarrow h=ut+16t^2[/tex]
Here, u = 0 so,
[tex]h=0t+16t^2\\\Rightarrow h=16t^2[/tex]
The equation is [tex]h=16t^2[/tex]
[tex]24=16t^2\\\Rightarrow t=\sqrt{\frac{24}{16}}\\\Rightarrow t=1.22\ s[/tex]
Time taken by the ball to hit the ground is 1.22 seconds
The maximum distance D(h) in kilometers that a person can see from a height h kilometers above the ground is given by the function D(h)=111.7 times square root of h. Find the height that would allow a person to see 50 kilometers.
To find the height that allows a person to see 50 kilometers, we set the given function equal to 50 and solve for h. This calculation gives us the height as approximately 0.2 kilometers.
Explanation:The question requires us to find the height h that would allow a person to see 50 kilometers, given the function D(h)=111.7 * sqrt(h).
We can solve this by setting the function equal to 50 and then solving for h. Like so: 50 = 111.7 * sqrt(h).
To isolate sqrt(h), we divide both sides of the equation by 111.7: sqrt(h) = 50 / 111.7.
Then we square both sides of the equation to solve for h: h = (50 / 111.7)^2.
Upon calculating the right side of this equation, we find that the height is approximately 0.2 kilometers.
Learn more about Height here:https://brainly.com/question/32418014
#SPJ12
The answer for this question is 0.2 Kilometers or 200 meters(approx.)
The detailed explanation is as follows :
The maximum distance D(h) in kilometers that a person can see from a height h kilometers above the ground is given by the function D(h)=111.7 times square root of h. We need to find the height that would allow a person to see 50 kilometers.
To solve this problem, we need to find the height h that allows a person to see a distance of 50 kilometers. We start with the given function:
D(h) = 111.7 * sqrt(h)
We set D(h) to 50 kilometers:
50 = 111.7 * sqrt(h)
To isolate sqrt(h), we divide both sides by 111.7:
sqrt(h) = 50 / 111.7
Next, we calculate the division:
sqrt(h) ≈ 0.4475
Now we square both sides to find h:
h = (0.4475)^2 ≈ 0.2002
Therefore, the height that allows a person to see 50 kilometers is approximately 0.2002 kilometers, or 200.2 meters above the ground.
Hence the required answer is 0.2 kilometers or 200 meters(approximately)