What expression is equivalent to x^2+2x-24/3x+18
The equivalent expression to [tex]x^2 + 2x - 24 / (3x + 18([/tex] is (x - 4) / 3, after factoring and simplifying the common terms.
The question is asking for an expression equivalent to [tex]x^2 + 2x - 24 / (3x + 18[/tex].
This expression can be factored and simplified.
First, notice that the quadratic expression in the numerator can be factored into (x + 6)(x - 4).
Similarly, the denominator can be factored as 3(x + 6). After factoring, we have:
= (x + 6)(x - 4) / 3(x + 6)
We can now simplify the expression by canceling out the common factor of (x + 6):
= (x + 6)(x - 4) / 3(x + 6) = (x - 4) / 3
So the equivalent expression is (x - 4) / 3.
17 ÷ 4520= what is the product
The student's question is related to dividing 17 by 4520. This is performed by a straight division resulting in a small decimal quotient, not a product. The calculation is best done using a calculator and rounding to the proper number of significant figures.
The equation given, 17 by 4520, is asking for the result of dividing 17 by 4520. To compute this, we simply perform the division, recognizing that since 4520 is much larger than 17, the answer will be a very small decimal value. The term 'product' in the student's question seems to be a mistake, as they are likely referring to the quotient obtained from the division.
When attempting to perform the computation mentally and simplify the process, one might attempt to find numbers that are more easily divisible or apply scientific notation to simplify calculations, much like re-expressing numbers to make them more manageable. However, for this division, no mental math trick simplifies it effectively, and using a calculator might be the best option.
When going through this process, it is also important to consider significant figures when giving the final answer, rounding as necessary based on the precision of the data provided.
110% of 90 is what number a?
What does is a?
please help me, solve for y 2x-y=5
A relation is plotted as a linear function on the coordinate plane starting at point E at
(0, 27)
and ending at point F at
(5, −8).
What is the rate of change for the linear function and what is its initial value?
The rate of change and the initial value are given as -5 and 27 respectively.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
Given that,
The points for the given linear function are given as (0, 27) and (5, -8) respectively.
The rate of change is equivalent to the slope of the straight line and is given as,
(-8 - 27)/(5 - 0) = -35/7 = -5
Now, the equation of the function can be written as,
(y - 27)/(x - 0) = -5
=> y - 27 = -5x
=> y = -5x + 27
The initial value is given at x = 0 as below,
y = -5 × 0 + 27
= 27
Hence, the rate of change for the function is -5 and its initial value is 27.
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derivative of the (sqrt of t/4t-3)
Answer:
[tex]\displaystyle \frac{dy}{dt} = \frac{-3}{2(4t- 3)^2\sqrt{\frac{t}{4t - 3}}}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \sqrt{\frac{t}{4t - 3}}[/tex]
Step 2: Differentiate
Basic Power Rule [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = \frac{1}{2\sqrt{\frac{t}{4t - 3}}} \cdot \frac{d}{dt} \bigg[ \frac{t}{4t - 3} \bigg][/tex]Derivative Rule [Quotient Rule]: [tex]\displaystyle y' = \frac{1}{2\sqrt{\frac{t}{4t - 3}}} \cdot \frac{(t)'(4t - 3) - t(4t - 3)'}{(4t - 3)^2}[/tex]Basic Power Rule [Derivative Properties]: [tex]\displaystyle y' = \frac{1}{2\sqrt{\frac{t}{4t - 3}}} \cdot \frac{(4t - 3) - 4t}{(4t - 3)^2}[/tex]Simplify: [tex]\displaystyle y' = \frac{-3}{2(4t- 3)^2\sqrt{\frac{t}{4t - 3}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
erica bougfht 3 1/2 yards of fabric if she uses 2/3 of the fabric for a curtain.how much will she have left?
a pail hold 6 3/4 gallon of water. how much is this in cups
The required, there are 108 cups of water in the pail as a pail hold 6 3/4 gallon of water.
What is a unit of measurement?Unit of measurement is defined as every entity having its measures in dimensions, weight, and time. Such as for length we have a meter, for liquid we have liters, and so on.
Here,
To convert 6 3/4 gallons to cups, we can use the fact that there are 16 cups in one gallon.
So, we can start by multiplying 6 (the number of whole gallons) by 16 to get the number of cups in those gallons:
6 gallons × 16 cups/gallon = 96 cups
Next, we need to convert the 3/4 of a gallon to cups. To do this, we can multiply the fraction by the number of cups in one gallon:
3/4 gallon × 16 cups/gallon = 12 cups
So, the total amount of water in the pail is:
96 cups + 12 cups = 108 cups
Therefore, there are 108 cups of water in the pail.
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simplify and reduce. show the work. ^= an exponent of 2 and 0
(-2 3/4 + 1 2/3)^2 - (-7/9)^0
The sides of a triangle measure 76 mm, 8 CM, and 10 CM..What is the lengths of the two shorter sides
A closet measure 5 feet by 3 feet does the measurement of 15 square feet show the volume inside the closet
If you are adding two fractions that are both less than 1/2, What must be true about the sum? Give three examples to support your thinking.
if both fractions are less than 1/2 then the sum has to be less than 1
1/8 + 3/8 = 4/8 = 1/2 , less than 1
7/16 + 1/4 = 11/16, less than 1
3/16 + 1/16 = 4/16 = 1/4, less than 1
A recipe makes 6 2/3 cups the serving size is 5/6 cup how many servings does the recipe make
The recipe can make serving 8 cups.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Here, given that,
A recipe makes 6 2/3 cups
=20/3 cups
And, the serving size is 5/6 cup
So, the recipe can make serving = 20/3÷ 5/6 cups
=20/3 × 6/5 cups
=8 cups
Hence, the recipe can make serving 8 cups.
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Elizabeth has $252.00 in her account on Sunday. Over the next week, she makes the following changes to her balance via deposits and purchases: Day Debit ($) Credit ($) Monday 114.60 150.00 Tuesday 79.68 --- Wednesday 161.39 --- Thursday 57.40 --- Friday 22.85 75.00 Saturday 140.55 --- On what day does Elizabeth first get charged an overdraft fee?
Given:
Elizabeth has $252.00 in her account on Sunday and a table is given of her deposits and purchases over the following week.
To Find:
The day Elizabeth first gets charged an overdraft fee.
Answer:
Thursday's expenditure of $57.40 exceeds her bank balance at the time of transaction, and therefore Thursday is the day Elizabeth would first get charged with an overdraft fee.
Step-by-step explanation:
Elizabeth would first get charged with an overdraft fee when her expenditure exceeds her bank balance, i.e., the amount that is debited is more than what is in her bank account at that particular time.
So we analyse her transactions one by one.
On Sunday, we are given that she has $252.
On Monday, $114.60 is debited. So the remaining balance would be
$252 - $114.60 = $137.4
But on the same day, $150 is also credited to her account. So her balance would then be
$137.4 + $150 = $287.4
Next, on Tuesday, $79.68 is debited so the balance she is left with would be
$287.4 - $79.68 = $207.72
On Wednesday, $161.39 is debited so the balance she is left with would be
$207.72 - $161.39 = $46.33
On Thursday, $57.40 is debited so the balance she is left with would be
$46.33 - $57.40 = -$11.07
Thus, we see that Thursday's expenditure of $57.40 exceeds her bank balance and therefore Elizabeth would be charged with an overdraft fee as her bank balance after the transaction would be -$11.07.
factor the expression 10x−25y
Final answer:
To factor the expression 10x-25y, we find the greatest common factor, which is 5, and write the expression as 5(2x - 5y).
Explanation:
To factor the expression 10x−25y, we need to find the greatest common factor (GCF) that both terms share. In this case, both terms are divisible by 5. When we factor out the GCF, we get:
Identify the GCF of 10x and 25y, which is 5.
Divide both terms by the GCF: 10x/5 = 2x and 25y/5 = 5y.
Write the factored expression: 5(2x - 5y).
Thus, the expression 10x−25y factored is 5(2x - 5y)
A bicycle went 120 miles in 5 hours. A motorcycle is three times as fast as the bicycle. Find the speed of motorcycle.
Answer:
Step-by-step explanation:
120 x 5 = 600
The motorcycle is 3 times as fast.
600 x 3 = 1800
Can anyone help me Plot a parabola through the points? Cause i dont understand what to do
A 6-ounce can of frozen juice costs 84. Give the unit price in cents per ounce.
For a normal distribution, the proportion in the tail beyond z = 0.30 is p = 0.1179.
a. True
b. False
Using the normal distribution, it is found that the statement is False, thus the correct option is b.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.The area on the tail beyond z is the proportion that is above z, that is, 1 subtracted by the p-value of z.For this problem, z = 0.3 has a p-value of 0.6554.
1 - 0.6554 = 0.3446
The proportion in the tail beyond z = 0.30 is p = 0.3446, thus, the statement is False.
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5 less than a third of a number is at most 15
The temperature, t, in Burrtown starts at 32°F at midnight, when h = 0. For the next few hours, the temperature drops 2 degrees every hour.Which equation represents the temperature, t, at hour h?
Answer: We find the equation that represents the temperature (t) at hour (t) using the slope-intercept form and it is:
t = -2 h + 32
Solution:
The temperature, t, in Burrtown starts at 32°F at midnight, when h = 0. This represents the y-interception of the right line, when h=0 hours, t=32 °F:
Point=(h,t)→Point=(0,32)=(0,b)→b=32
For the next few hours, the temperature drops 2 degrees every hour. This represents the slope of the line (m): m=-2, negative because the temperature drops.
Slope-Intercept form:
y=mx+b; y=t, m=-2, x=h, b=32
Replacing the values:
t=-2h+32
Answer:
t=-2h+32
Step-by-step explanation:
What is cos θ if sec θ = 2?
Answer:
the value of cos θ is [tex]\frac{1}{2}[/tex].
Step-by-step explanation:
Since, [tex] cos\theta=\frac{1}{sec\theta}[/tex]
we are given with sec θ = 2
To find the value of cos θ , we use this fact [tex] cos\theta=\frac{1}{sec\theta}[/tex]
put sec θ = 2 in [tex] cos\theta=\frac{1}{sec\theta}[/tex]
[tex] cos\theta=\frac{1}{2}[/tex]
Therefore, the value of cos θ is [tex]\frac{1}{2}[/tex].
Evaluate each expression. Click on undefined as needed
Compare the decimals 17.20 and 17.2. Which comparison is correct? A. 17.20 > 17.2 B. 17.20 < 17.2 C. 17.20 = 17.2
Draw a garden with up to 5 rows and that has the same number of flowers in each row . Then two equation that match your array .
Simply (8xto4) (4x to 3) \ 7x to 2
hich sentence is a run-on sentence?
A.
Dogs and hamsters are both fun pets, they relate to people in different ways.
B.
Dogs enjoy human contact; they love to fetch and chase.
C.
My hamster likes to run in his wheel, and he does not like to be held.
D.
When I try to pick up my hamster, he looks for a place to hide.
Which expression shows the result of applying the distributive property to 3(2x−6) ?
A. 2x−18
B. 6x−18
C. 6x−6
D. 5x−3
Answer:
b
Step-by-step explanation:
He for got his pin code. 20% of his pin code was 246.8. What was his pin code?
Over a two hour time period a snail moved 76 inches. How far is this in yards? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Final answer:
The snail moved a total distance of 2 1/9 yards after converting 76 inches to yards using the conversion factor of 1 yard equals 36 inches.
Explanation:
To convert the distance a snail moved from inches to yards, we use the conversion factor that 1 yard equals 36 inches. Given that the snail moved 76 inches, we divide this number by 36 to find the distance in yards.
76 inches ÷ 36 inches/yard = 2 yards and 4 inches.
Since there are 36 inches in a yard, the remaining 4 inches must be converted to a fraction of a yard by dividing by 36:
4 inches ÷ 36 = 1/9 yard.
Therefore, the snail moved 2 yards and 1/9 yard, or 2 1/9 yards in total.