Answer with explanation:
[tex]\rightarrow \frac{\frac{2y^2-6 y-20}{4 y+12}}{\frac{y^2+5 y+6}{3 y^2+28 y+27}}\\\\\rightarrow \frac{\frac{y^2-3y-10}{2 y+6}}{\frac{(y+2)(y+3)}{3 y^2+28 y+27}}\\\\\rightarrow \frac{\frac{(y-5)(y+2)}{2 (y+3)}}{\frac{(y+2)(y+3)}{3 y^2+28 y+27}}\\\\\rightarrow \frac{(y-5)(y+2)}{2 (y+3)}} \times {\frac{3 y^2+28 y+27}{(y+2)(y+3)}}\\\\ \rightarrow\frac{(y-5)\times(3 y^2+28 y+27)}{2 (y+3)^2}}[/tex]
→y²+5y+6
=y²+3 y+2 y+6
=y×(y+3)+2×(y+3)
=(y+2)(y+3)
→y² -3 y-10
=y² -5 y+2 y -10
=y×(y-5)+2×(y-5)
=(y+2)(y-5)
Answer:
B. 3(y-5)/2 on edge
Step-by-step explanation:
A patient takes a medication with a half life. Initially, there are 20 milligrams of the medication in the patient's system. After 8 hours there are 12 milligrams. How many milligrams will there be after 10 hours? Round your answer to the nearest hundredth, and do not include units
Answer:
At 10 hours there will be 10 milligrams
Step-by-step explanation:
On a graph your slope would be y= -1x+20 because there where 20 mill at 0 hours and 12 mill at 8 hours. 20-8=12 meaning 1 mill would be deluded every hour. Hope this helps.
Final answer:
Using the exponential decay formula, we can find the half-life of the medication from the initial and given 8-hour amounts and then use it to calculate the amount of medication remaining after 10 hours.
Explanation:
To determine the remaining medication after a given number of hours, we will apply the exponential decay formula which accounts for substances with a half-life. Thus, given that there are initially 20 milligrams of the medication and that it decreases to 12 milligrams after 8 hours, we need to calculate the half-life and then use it to predict the amount remaining after 10 hours.
First, finding the half-life 't1/2' can be done using the formula A = A0×2−t/t1/2, where A is the remaining amount (12 mg), A0 is the initial amount (20 mg), and t is the time elapsed (8 hours). Solving for the half-life gives us t1/2 as the unknown in this equation.
12 mg = 20 mg ×2−(8 hours)/t1/2
Reducing this equation, we find that:
t1/2 = 8 hours / (log2(20 mg/12 mg))
After finding 't1/2', we can then determine the amount remaining after 10 hours. The calculation would be as follows:
A = 20 mg ×2−(10 hours)/t1/2
This will give us the final amount of medication left in the system at the 10-hour mark, rounded to the nearest hundredth.
Hector paid $68 for a taxi ride. This driver has a sign above his mirror that recommends a 20% tip. Estimate the amount the driver expects to be tipped to the nearest dollar.
Answer:
Answer:
The answer is 14
Step-by-step explanation:
IT IS NOT 82 I JUST TOOK THE TEST AND IT WAS WRONG...THE ANSWER IS 14!
The driver expects to be tipped approximately $14.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Hector paid $68 for a taxi ride. This driver has a sign above his mirror that recommends a 20% tip.
The amount recieved as a tip is given as -
20% of 68
20/100 x 68
13.6
Therefore, the driver expects to be tipped approximately $14.
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Solve h2-42 = -h using the quadratic formula.
A) h = 0 or h = 7
B) h = -6 or h = 7
C) h = 6 or h= -7
D) h = -6 or h = -7
Answer: Option C
h = 6 or h= -7
Step-by-step explanation:
We have the expression
[tex]h^2-42 = -h[/tex]
To solve add h on both sides of the equality
[tex]h^2+h-42 = -h+h[/tex]
[tex]h^2+h-42 = 0[/tex]
For an equation of the form [tex]ah^2 +bh +c[/tex] the quadratic formula is
[tex]h=\frac{-b \± \sqrt{b^2 -4ac}}{2a}[/tex]
In this case
[tex]a = 1\\b= 1\\c =-42[/tex]
[tex]h=\frac{-1 \± \sqrt{1^2 -4(1)(-42)}}{2(1)}[/tex]
[tex]h_1=6[/tex]
[tex]h_2=-7[/tex]
The answer is the option C
What factor is used to convert feet per minute into miles per hour?
To convert feet per minute into miles per hour, use the conversion factor of 5280 feet in 1 mile and 60 minutes in 1 hour. Divide the given value by 5280 to get the number of miles, then divide the result by 60 to convert minutes to hours.
Explanation:To convert feet per minute into miles per hour, you need to use the conversion factor of 5280 feet in 1 mile and 60 minutes in 1 hour. Here's the step-by-step calculation:
First, determine the number of miles in the given feet per minute by dividing the given value by 5280.Next, divide the result by 60 to convert minutes to hours.The final result will be the given value in feet per minute converted to miles per hour.For example, if you have a speed of 300 feet per minute:
300 feet per minute / 5280 feet per mile = 0.056818 miles per minute.0.056818 miles per minute / 60 minutes per hour = 0.000947 miles per hour.Therefore, 300 feet per minute is equal to 0.000947 miles per hour.Learn more about Unit Conversion here:https://brainly.com/question/19420601
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a right prism has a square base, a surface area of 512 inches squared, and a height of 12 inches. Find the length of the square base
Answer:
8 inches
Step-by-step explanation:
Surface area of a prism is:
S = 2A + Ph
where A is the area of the base, P is the perimeter of the base, and h is the height of the prism.
The base is a square, so A = s² and P = 4s:
S = 2s² + 4sh
Given that S = 512 and h = 12:
512 = 2s² + 4s(12)
512 = 2s² + 48s
256 = s² + 24s
0 = s² + 24s - 256
0 = (s + 32) (s - 8)
s = -32, s = 8
Since s must be positive, s = 8 inches.
Follow below steps;
To find the length of the square base of the right prism:
First, calculate the lateral surface area: 512 in² = 4s * 12 where s is the side length of the square base.
Then, solve for s: 512 = 48s, s = 512 / 48 = 10.67 in.
Therefore, the length of the square base is 10.67 inches.
find the prime factorization of following the number: 56
Answer:
2×2×2×7=56
Step-by-step explanation:
Find the multiples that goes into 56
Each number that goes into 56 put then from least to greatest and you got your prime numbers
When is a lower annual interest fee better than a low annual fee
Answer: a lower annual interest fee is better than a low annual fee if you expect to pay your balance in full during most months
Final answer:
A lower annual interest fee is generally better than a low annual fee when it leads to significant savings over time, especially with large amounts or long-term financial products. Interest rates dictate the overall cost of borrowing more than annual fees, particularly for longer terms or larger sums. However, for small, short-term borrowing, a low annual fee might be more beneficial.
Explanation:
When comparing a lower annual interest rate versus a low annual fee, it is essential to consider the specific financial situation and the amount of money involved. As a general rule, a lower interest rate is beneficial when it leads to significant savings on the overall interest paid throughout the loan or credit product term. This is often the case for larger amounts or longer terms where the interest accumulates considerably over time.
For example, financial investors who choose a Certificate of Deposit (CD) earn a higher interest rate compared to savings accounts, as they agree to leave the money deposited for a fixed period, forgoing liquidity. However, if interest rates rise after a loan is made, the existing loan with the lower interest rates becomes less attractive. On the other hand, if the economy experiences a fall in interest rates, the value of the loan with the previously fixed lower rate increases.
Therefore, while a low annual fee can seem attractive, it's the annual interest that ultimately has a more significant impact on the cost of borrowing, especially over longer periods or with larger sums of money. Conversely, for small short-term loans or when the outstanding balance is frequently paid off, a low annual fee might be more advantageous than a lower interest rate, as the interest charges could be minimal.
Estimate the x-coordinates at which the relative maxima and relative minima occur for the function.
f(x) = 3x3 + 9x2 – 1
ANSWER
Relative minimum occurs at x=0
Relative maximum occurs at x=-2
EXPLANATION
The given function is;
[tex]f(x) = 3 {x}^{3} + 9 {x}^{2} - 1[/tex]
We take the first derivative to get:
[tex]f'(x) = 9 {x}^{2} + 18x[/tex]
At turning point f'(x)=0
[tex] 9 {x}^{2} + 18x = 0[/tex]
[tex] 9x(x + 2) = 0[/tex]
[tex]x = 0 \: or \: x = - 2[/tex]
We take the second derivative to get
[tex]f''(x) = 18x + 18
[/tex]
[tex]f''(0) = 18(0) + 18 = 18 \: > \: 0[/tex]
Relative minimum occurs at x=0
[tex]f''( - 2) = 18( - 2)+ 18 = - 18 \: < \: 0[/tex]
Relative maximum occurs at x=-2
Answer:
Relative minimum occurs at x=0
Relative maximum occurs at x=-2
Step-by-step explanation:
What is the simplified form expression 2(x-5)?
Answer:
2x-10
Step-by-step explanation:
original equation: 2(×-5)
distributive property: 2(x) 2(-5) =2x-10
Answer:
2x-10
2(x-5)
2*x=2x
2*5=10
What is the output of the following function for x 1? F(x)=-x^3-2x^2+7x-10
Answer:
-6
Step-by-step explanation:
Let x =1
F(x)=-x^3-2x^2+7x-10
F(1) = - (1)^3 -2(1)^2 +7(1) -10
= -1 -2 +7-10
= -3+7-10
=-6
The output of the given function F(x)=-x^3-2x^2+7x-10 when x equals 1 is -6. We substituted x=1 into each term to calculate this.
Explanation:The given function is F(x)=-x^3-2x^2+7x-10. To find the output of the function when x equals 1, you substitute '1' in place of 'x' in the equation. So let's calculate:
For -x^3, substituting x=1, we get: -1^3 = -1For -2x^2, substituting x=1, we get: -2*(1^2) = -2For 7x, substituting x=1, we get: 7*1 = 7Lastly, -10 remains the same as there's no x to substituteNow, add all the results together: -1 - 2 + 7 - 10 = -6. Therefore, when x equals 1, the output of the function F(x) is -6.
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Solve the equation:
5 - 20 =
– 15
Enter answer below
Enter your response
Answer:
15
Step-by-step explanation:
First add 20 to both sides to get x/3 = 5
Then multiply both sides by 3 to get 15.
You can check it by substituting it into the equation
15/3 - 20 = -15
5 - 20 = -15
-15 = -15
Step-by-step explanation:
x/3 - 20 = -15
x/3 = -15 + 20
x/3 = 5
x = 15
what is the sum of -36 4/9 - (10 2/9) - (18 2/9)
let's firstly convert the mixed fractions to improper fractions and then add them up.
[tex]\bf \stackrel{mixed}{36\frac{4}{9}}\implies \cfrac{36\cdot 9+4}{9}\implies \stackrel{improper}{\cfrac{329}{9}} \\\\\\ \stackrel{mixed}{10\frac{2}{9}}\implies \cfrac{10\cdot 9+2}{9}\implies \stackrel{improper}{\cfrac{92}{9}}~\hfill \stackrel{mixed}{18\frac{2}{9}}\implies \cfrac{18\cdot 9+2}{9}\implies \stackrel{improper}{\cfrac{164}{9}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf -\cfrac{329}{9}-\cfrac{92}{9}-\cfrac{164}{9}\implies \stackrel{\textit{using the LCD of 9}}{\cfrac{-329-92-164}{9}}\implies -\cfrac{585}{9}\implies -65[/tex]
helpp me plz respond
A car race lasted 2.07 hours. How many seconds did the race last? If
necessary, round your answer to the nearest tenth of a second.
1 hour = 60 minutes
1 minute = 60 seconds
therefore 2.07 hours = (2.07*60*60) seconds
=7452 seconds
Answer:
7452
Step-by-step explanation:
There are 3600 seconds per hour
60*60= 3600
To find how many seconds are in 2.07 hours you need to multiply 3600 by 2.07
2.07* 3600 = 7452 seconds
Hope This helps
if you shift the linear parent function, f(x)=x, up 13 units, what is the equation of the new function?
Answer:
f(x) = x + 13
Step-by-step explanation:
Given f(x) then f(x) + c represents a vertical translation
• If c > 0 then vertical shift up ↑ of c units
• If c < 0 then vertical shift down ↓ of c units
here c = + 13, hence
f(x) = x + 13
which of the following equations is of a parabola with a vertex at (1,2)
answer choices
1. y=(x-1)^2 - 2
2 . y=(x-1)^ 2 + 2
3 . y=(x+1)^2 - 2
4 . y=(x+1)^2 + 2
ANSWER
The choice is correct.
[tex]y = {(x -1)}^{2} + 2[/tex]
EXPLANATION
The equation of a parabola in vertex form is given by:
[tex]y = a {(x -h)}^{2} + k[/tex]
where (h,k) is vertex of the parabola and 'a' is the leading coefficient of the parabola.
From the given options, the leading coefficient must be a=1.
We also have the vertex of the parabola at (1,2). This implies that h=1 and k=2.
We substitute these values into the formula to get,
[tex]y = {(x -1)}^{2} + 2[/tex]
The second option is correct.
Write a function for p(x), the profit from selling x necklaces.
The revenue from selling x necklaces is r(x) = 10x. The cost of buying x necklaces is c(x) = 4x + 15. The profit from selling x necklaces is p(x) = r(x) – c(x)
ANSWER
[tex]p(x) = 6x - 15[/tex]
EXPLANATION
The revenue from selling x necklaces is
[tex]r(x) = 10x[/tex]
The cost of buying x necklaces is
[tex]c(x) = 4x + 15[/tex]
The profit from selling x necklaces is
[tex]p(x) = r(x) - c(x)[/tex]
We substitute the functions to get;
[tex]p(x) = 10x- (4x + 15)[/tex]
[tex]p(x) = 10x- 4x - 15[/tex]
[tex]p(x) = 6x - 15[/tex]
Therefore the function for the profit is
[tex]p(x) = 6x - 15[/tex]
To the nearest hundredth of a centimeter, what is the length of a leg of the triangle?
[1] cm
84.6 cm
Answer:
The length of a leg of the triangle = 59.83 cm
Step-by-step explanation:
Points to remember
If a right angled triangle with angles 45°, 45° and 90° then the sides are in ratio 1 : 1 : √2
It is given a right angled triangle with 45°, 45° and 90° and hypotenuse = 84.6 cm
To find the length of a leg
Let 'x' be the length of each leg,
From the figure we can write,
1: 1 : √2 = x : x : 84.6
Therefore x = 84.6/√2
= 59.83 cm
Therefore the length of a leg of the triangle = 59.83 cm
ANSWER
59.82
EXPLANATION
The given right angle is an isosceles right triangle.
Let the length of a leg be x cm.
Then by the Pythagoras Theorem,
[tex] {x}^{2} + {x}^{2} = 84.6 ^{2} [/tex]
[tex]2 {x}^{2} = 7157.16[/tex]
Divide both sides by 2.
[tex]{x}^{2} = \frac{7157.16}{2} [/tex]
[tex]{x}^{2} = 3578.58[/tex]
Take positive square root of both sides to get,
[tex]x = 59.82123369[/tex]
Hence the length of a leg is 59.82 to the nearest hundredth.
Solve the following system of equations using the substitution method.
-X + 9y = -5
x - 5y = 1
Answer: x=8.5 y=1.5
Step-by-step explanation:
Use the second problem and get X by itself. X= 5y+1. Now plug that equation into the 1st equation.
-(5y+1) +9y =-5.
-5y-1+9y=-5.
-5y+9y= 1+5
4y= 6
Y=1.5
Now that you know what is the value of Y you can plug that into any equation.
5(1.5) +1
7.5+1
X=8.5
For this case we have the following system of equations:
[tex]-x + 9y = -5\\x-5y = 1[/tex]
We clear "x" from the second equation and replace it in the first:
[tex]x = 1 + 5y[/tex]
Substituting in the first equation:
[tex]- (1 + 5y) + 9y = -5\\-1-5y + 9y = -5[/tex]
We have similar terms:
[tex]-1 + 4y = -5[/tex]
Adding 1 to both sides of the equation:
[tex]4y = -5 + 1\\4y = -4\\y = \frac {-4} {4}\\y = -1[/tex]
We look for the value of "x":
[tex]x = 1 + 5 (-1)\\x = 1-5\\x = -4[/tex]
Answer:
[tex](x, y): (- 4, -1)[/tex]
-1/64 has what value
Answer:
If you're looking for the absolute value, its 1/64
Step-by-step explanation:
The absolute value is the distance a number is from 0.
1/64 is 1/64th away from 0/64
So, the answer would be 1/64
I hope this helped you! :)
1. On delivery, eggs should be rejected if:
A. There is only one USDA inspection stamp on each carton
B. The shells of the eggs have cracks in them
c. The shells vary in color
D. The eggs are odorless
When eggs are delivered, if one notices that B. The shells of the eggs have cracks in them, the eggs should be rejected.
Eggs that have cracks in them can be potentially dangerous to people because microorganisms like bacteria can enter through those cracks and either spoil the egg or make it harmful for consumption.
It is therefore best that an egg that has a crack, be rejected upon delivery.
Other options are incorrect because:
One USDA inspection stamp is good enough proof that the eggs are good Shell color has no effect on whether an egg is bad or not Eggs are supposed to be odorlessIn conclusion, if an egg has a crack in it upon delivery, it should be rejected.
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Kira walks 8 and a half blocks in 17 minutes. If Kira continues to walk at a steady pace, how many blocks will she walk each minute
Answer:
Half a block ( 0.5 or 1/2 )
Step-by-step explanation:
8 1/2 blocks can also be written as 8.5 blocks.
If Kira walks 8.5 blocks in 17 minutes [and continues to walk at this steady pace], divide 8.5 by 17.
8.5/17 = 0.5
So, Kira walked 0.5 or 1/2 blocks in a minute.
I hope this helps! :)
Kira walks at a rate of 0.5 blocks per minute when she walks 8 and a half blocks in 17 minutes.
Kira walks 8 and a half blocks in 17 minutes. To find out how many blocks she will walk each minute, we need to calculate the rate by dividing the total number of blocks by the total number of minutes:
Rate = Total Blocks Walked / Total Minutes
Rate = 8.5 blocks / 17 minutes
Rate = 0.5 blocks per minute.
Therefore, at a steady pace, Kira will walk half a block every minute.
what is the y-interceptof the line shown?
Answer:
y- intercept = 4
Step-by-step explanation:
The y- intercept is the value of the y- coordinate where the line crosses the y- axis.
Here the y- intercept = 4 or (0, 4) ← coordinates of point
Answer:
( 0 , 4 )
Step-by-step explanation:
The y - intercept of the line is where the line hit's or crosses the y - axis and in the case since the line goes through 4 on the y - axis
What is the greatest common factor of 42a5b3, 35a3b4, and 42ab4?
For this case we have that by definition, the Greatest Common Factor (GCF) is the largest factor that 2 numbers have in common.
So, we have the following expressions:
[tex]42a ^ 5b ^ 3\\35a ^ 3b ^ 4\\42ab ^ 4[/tex]
We look for the positive integers that divide to 35 and 42 without leaving residue:
42: 1,2,3,6,7,14,21
35: 1,5,7
Thus, the GCF of 42 and 35 is 7
Then, the GCF of the three expressions is:
[tex]7ab ^ 3[/tex]
Answer:
[tex]7ab ^ 3[/tex]
Answer:
A) 7ab^3
Step-by-step explanation:
EDG2021
An unknown number x is at most 10. Which graph best represents all the values of x? Number line graph with closed circle on 10 and shading to the right. Number line graph with open circle on 10 and shading to the right. Number line graph with open circle on 10 and shading to the left. Number line graph with closed circle on 10 and shading to the left.
Answer:
Step-by-step explanation:
The question does say at most 10. That includes 10. So the circle on 10 should indicate it is closed or fully filled in.
The shading should go left. It should indicate less than 10.
please help Solve (x-5)^2=3
Answer:
x = 5 + √3, 5 - √3
which is 6.73 , 3.27 to the nearest hundredth.
Step-by-step explanation:
(x - 5)^2 = 3
Take the square root of both sides:
x - 5 = +/- √3
x = 5 + √3, 5 - √3
Answer:
x = 5 + √3 or x = 5 - √3
Step-by-step explanation:
Equation: (x - 5)² = 3
Square root: x - 5 = ±√3 <-- the square root of a number can be positive or negative.
Subtract: x = 5 + √3 or x = 5 - √3
How many 5-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is not allowed?
Answer:
2520
Step-by-step explanation:
7×6×5×4×3 = 2520
Imagine □□□□□
For the 1st □, there are 7 choices
For the 2nd □, there are 6 choices (since 1 out of the 7 numbers is already used)
For the 3rd □, there are 5 choices (since 2 out of the 7 numbers are used)
And so on...
The total number of 5-digit numbers that can be formed with the digits 1 to 7, without repetition, is 2520.
Explanation:Your question pertains to the concept of permutations - the number of ways items can be arranged without repetition. In this case, you are considering how many 5-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 without repeating any digit.
A helpful way to think about this is to think of the 5 places for our 5-digit number (i.e., _ _ _ _ _). For the first position, you have 7 choices (the digits 1 to 7) to choose from. Once you have chosen a digit, you are left with 6 choices for the second position, 5 for the third position, 4 for the fourth, and finally 3 for the fifth. So, the total number of 5-digit numbers you can form is 7 × 6 × 5 × 4 × 3 = 2520.
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Combine the radicals -2/13 + 19/13
Answer:
17/13
Step-by-step explanation:
Answer:
Step-by-step explanation:
" / " indicates "division" and should not be used in this context.
If you meant: -2 square root 13 plus 19 square root 13, the simplest result would be 17 square root 13.
Note that if you click on the "omega" symbol (below), a menu of symbols will appear, including the square root symbol √.
Then: -2√13 + 19√13 = 17√13.
The polynomial (x - 2) is a factor of the polynomial 4x2 - 6x-4. True or false?
In 2014, there were approximately 900,000 sworn law enforcement officers serving in the U.S. Approximately 12% of those officers were female. How many officers were females?
Answer:
108,000 females
Step-by-step explanation:
12% of 900,000 is 108,000.
Therefore, there are 108,000 female officers in the U.S.
Answer: 108,000
Step-by-step explanation:
In 2014, 900,000 sworn law enforcement officers who were serving in the United States and 12% of those officers were female. To find the number of females that were law enforcement officers, we multiply the percentage of females by the total number of law enforcement officers. This will be:
= 12% of 900000
= 12/100 × 900000
= 0.12 × 900000
= 108,000
There were 108,000 females as law enforcement officers serving in the United States.