Deon rented a truck for one day. there was a base fee of $16.95, and there was an additional charge of 75 cents for each mile driven. Deon had to pay $220.20 when he returned the truck. For how many miles did he drive the truck?
A quadratic equation is shown below: 9x2 − 16x + 60 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 4x2 + 8x − 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
Need help solving this equation please 5w+8-12w=16-15w
A fair sortition trial is carried out, and one of the candidates is assigned the number 32,041. If each digit can be chosen from 0-4, and if each of the possible sequences is assigned to a candidate, how many candidates are there?
Answer: 3125
Step-by-step explanation:
Given: A fair sortition trial is carried out, and one of the candidates is assigned the number = 32,041
If each digit can be chosen from 0-4, and if each of the possible sequences is assigned to a candidate, then the number of candidates (repetition of digits allowed)=[tex]5\times5\times5\times5\times5[/tex]
[tex]=3125[/tex]
Hence, the number of candidates there are = 3125.
If one store is selling 3/4 of a bushel of apples for $9, and another store is selling 2/3 of a bushel for $9, which store has the better deal? Explain you answer
Justin is redoing his bathroom floor with tiles measuring 6 in. By 13 in. The floor has an area of 8500 in.². What is the least number of tiles he will need
How is the goal of solving equations with the variable on each side the same as solving multi-step equations?
Final answer:
The goal of solving equations with variables on both sides or multi-step equations is to isolate and solve for the variable. Operations such as addition, subtraction, multiplication, and division are used to maintain equation balance and eliminate terms, which is necessary for solving any algebraic equation. The process involves careful step-by-step simplification, including dealing with multiple variables when necessary.
Explanation:
The goal of solving equations with the variable on each side is essentially the same as solving multi-step equations because in both scenarios, we aim to isolate the variable to find its value. When we encounter an equation with variables on both sides, we usually perform operations to get all variable terms on one side and constant terms on the other. This often involves addition or subtraction to eliminate terms and then the use of multiplication or division to isolate the variable. This process aligns with the steps taken in solving multi-step equations, where we also combine like terms, use inverse operations, and apply the distributive property if necessary.
Multiplication or division by the same number on both sides of an equation maintains equality, which is a fundamental principle in algebra. For an equation with more than one term on either side, it is important to enclose the side with more terms in brackets before applying a multiplication or division operation to ensure the operation is distributed to each term within the brackets. By doing so, we preserve the balance of the equation while simplifying it step by step toward finding the unknown value.
When faced with an equation containing more than one variable, our objective is to use algebra to determine the remaining unknowns. This could involve solving simultaneous equations or manipulating a single equation to isolate the variable of interest. In more complex scenarios involving several unknowns, finding a set of equations that each contain only one unknown becomes essential, and careful consideration of physical principles or context may guide us in selecting the right equations to solve for the variables in question.
Choose the correct simplification of (5xy7)2(y2)3.
The simplified form of the given expression is [tex]25 x^{2} y^{20}[/tex].
What is the simplified form of the expression?Simplifying expressions mean rewriting the same algebraic expression with no like terms and in a compact manner.
What are the exponent rules?The different Laws of exponents are:
[tex]x^{m} .x^{n} =x^{m+n}[/tex][tex]\frac{x^{m} }{x^{n} } = x^{m-n}[/tex][tex](x^{m} )^{n} = x^{m\times n}[/tex][tex]x^{0} =1[/tex][tex]x^{-1} = \frac{1}{x}[/tex]According to the given question.
We have an expression [tex](5xy^{7} )^{2}(y^{2} )^{3}[/tex]
To simplify the above expression we use the exponent rules.
Therefore,
[tex](5xy^{7} )^{2}(y^{2} )^{3}[/tex]
[tex]= 5^{2}x^{2} y^{7\times2} y^{2\times3}[/tex]
[tex]= 25 x^{2} y^{14} y^{6}[/tex]
[tex]= 25 x^{2} y^{14+6}[/tex]
[tex]= 25 x^{2} y^{20}[/tex]
Therefore, the simplified form of the given expression is [tex]25 x^{2} y^{20}[/tex] .
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Which value must be added to the expression x2 + 16x to make it a perfect-square trinomial?
Answer:
[tex]\text{64 must be added to the expression }x^2 + 16x\text{ to make it a perfect-square trinomial}[/tex]
Step-by-step explanation:
Given the expression
[tex]x^2+16x[/tex]
we have to tell which value must be added to the above expression to make it a perfect-square trinomial.
Expression: [tex]x^2+16x[/tex]
By completing the square method,
The square of half of the coefficient of x must be added , we get
[tex]x^2+16x+64[/tex]
[tex]x^2+8x+8x+64[/tex]
[tex]x(x+8)+8(x+8)[/tex]
[tex](x+8)^2[/tex]
which is a perfect square.
[tex]\text{Hence, 64 must be added to the expression }x^2 + 16x\text{ to make it a perfect-square trinomial}[/tex]
9 1/4 - 6 2/3
Write answer as mixed number with fractional part in lowest terms.
To subtract the mixed numbers 9 1/4 and 6 2/3, first convert them to improper fractions, find a common denominator, and then perform the subtraction. The result is expressed as the mixed number 2 7/12 with the fractional part in lowest terms.
Explanation:Subtracting Mixed Numbers
The question involves subtracting mixed numbers, specifically 9 1/4 (nine and one quarter) from 6 2/3 (six and two thirds). First, we need to convert these mixed numbers into improper fractions for easier subtraction.
Convert 9 1/4 to an improper fraction: (9 × 4) + 1 = 36 + 1 = 37/4.Convert 6 2/3 to an improper fraction: (6 × 3) + 2 = 18 + 2 = 20/3.To subtract, we need a common denominator. Multiplying the denominators 4 and 3 gives us 12, the LCD.Adjust the fractions: 37/4 becomes 111/12 (since 37 × 3 = 111) and 20/3 becomes 80/12 (since 20 × 4 = 80).Now subtract the numerators: 111 - 80 = 31. So, the difference is 31/12.Finally, convert 31/12 back into a mixed number, which is 2 7/12 (since 31 divided by 12 is 2 with a remainder of 7).The answer is 2 7/12.
To subtract mixed numbers, find a common denominator. Subtract the fractional part by subtracting the numerators. Subtract the whole numbers as usual. The answer is 8 7/12.
Explanation:To subtract mixed numbers, we first need to find a common denominator. In this case, the common denominator is 12. Then, we can subtract the fractions by subtracting the numerators and leaving the denominator the same.
For the whole numbers, we simply subtract them as usual.
So, 9 1/4 - 6 2/3 = 8 7/12.
PRE-ALG HELP ASAP !!!!!!!!
PART A) the initial value of the function is 150 at 0
weeks, that means that there are still 150 songs to be downloaded at the
beginning.
The rate of change is -30 songs each week, that is because the amount of songs
left to be downloaded decrease by 30 each week.
PART B:
lets use 2 points of the graph p1(0, 150), p2(1, 120)
calculate the slope:
m = (y2- y1)/(x2 - x1) = (120 - 150)/(1 - 0)
m = -30
and now use line equation in form point-slope:
y - y1 = m(x - x1)
y - 150 = -30(x - 0)
y = -30x + 150
2nd picture: for bushels of corn
Part A, looking at the line in the graph, you can see the line falls on 2 bushes cost $16, 4 bushels cost $31, etc., using that information you can calculate that 1 bushel of corn costs $8, ( 16/2 = 8, 32/4 = 8)
PART B
using the table for previous years you can calculate corn cost $6 a bushel ( 12/2=6)
so corn cost $2 more this year.
red die and a black die are rolled at the same time. The probability of getting a 6 on the red die is 16, and the probability of getting a 3 on the black die is 16. Given that the two events are independent, what is their combined probability?
it should be 1/6 not 16
there are 6 numbers on a die so to get a number you have a 1/6 probability
so 1/6 x 1/6 = 1/36
the probability of getting both a 6 and a 3 is 1/36
Huilan's age is two times Thomas's age. The sum of their ages is
54
. What is Thomas's age
Jane Peter and Simon have $395 which they wish to divide between them Jane gets $20 more than Peter and Peter gets $15 more than Simon how much does each get
There are 42 boys and girls participating in an essay-writing competition. Of the competitors, 21 are in seventh grade, 14 are in eighth grade, and 7 are in ninth grade. What is the probability of an eighth grader winning the competition? Which simulation(s) can be used to represent this situation?
Answer: Our required probability is 0.34.
Step-by-step explanation:
Since we have given that
Number of seventh grade student s= 21
Number of eight grade students = 14
Number of ninth grade students = 7
Total number of boys and girls = 42
Probability of an eigthth grader winning the competition would be
[tex]\dfrac{14}{42}\\\\=\dfra{1}{3}\\\\=0.3333333..................\\\\\approx 0.34[/tex]
Hence, our required probability is 0.34.
If x2 = 60, what is the value of x?
Help me and show work if needed. Only 24 and 25
25.
answer is B since it is adding he amount of the bill with the amount of the tip.
the other 3 will all calculate just the amount of the tip
26
3x-4 needs to equal or be below 8
rearrange the formula to 3x,=8+4
so 3x<=12
12/3 = 4
so x <= 4 to satisfy the inequality
so answer is A
How do you do 8.75 Times 38
The height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function mc002-1.jpg. Which expression could be used to determine the average rate at which the object falls during the first 3 seconds of its fall?
Answer:
the answer on edge is D) h(3)-h (0)/3
And, the answer to the equation is 156.
Which property of equality should Wade use to solve the equation x/6=3
Answer:
I believe it is The Multiplication Property of Equality
Step-by-step explanation:
Since "x" is being divided by 6, we need to do the opposite!
Answer:
multiplication
Step-by-step explanation:
since x/6 is a fraction and fractions represent division we would havw to do the opposite to isolate the x variable. pLeAsE mArK bRaInLiEsT
If sin Θ = negative square root 3 over 2 and π < Θ < 3 pi over 2, what are the values of cos Θ and tan Θ?
Answer: The values are
[tex]\cos\theta=-\dfrac{1}{2},~~\textup{and}~~\tan\theta=\sqrt3.[/tex]
Step-by-step explanation: For an angle [tex]\theta[/tex],
[tex]\sin \theta=-\dfrac{\sqrt3}{2},~\pi<\theta<\dfrac{3\pi}{2}.[/tex]
We are given to find the values of [tex]\cos\theta[/tex] and [tex]\tan \theta[/tex].
Given that
[tex]\pi<\theta<\dfrac{3\pi}{2}\\\\\\\Rightarrow \theta~\textup{lies in Quadrant III}.[/tex]
We will be using the following trigonometric properties:
[tex](i)~\cos \theta=\pm\sqrt{1-\sin^2\theta},\\\\(ii)~\tan\theta=\dfrac{\sin\theta}{\cos\theta}.[/tex]
The calculations are as follows:
We have
[tex]\cos\theta=\pm\sqrt{1-\sin^2\theta}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\left(-\dfrac{\sqrt3}{2}\right)^2}\\\\\\\Rightarrow \cos\theta=\pm\sqrt{1-\left(\dfrac{3}{4}\right)}\\\\\\\Rightarrow \cos\theta=\pm\sqrt{\left(\dfrac{1}{4}\right)}\\\\\\\Rightarrow \cos\theta=\pm\dfrac{1}{2}.[/tex]
Since [tex]\theta[/tex] is in Quadrant III, and the value of cosine is negative in that quadrant, so
[tex]\cos\theta=-\dfrac{1}{2}.[/tex]
Now, we have
[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{-\frac{\sqrt3}{2}}{-\frac{1}{2}}=\sqrt3.[/tex]
Thus, the values are
[tex]\cos\theta=-\dfrac{1}{2},~~\textup{and}~~\tan\theta=\sqrt3.[/tex]
Since the given theta lies in third quadrant, then you can use the fact that only tangent and cotangent are positive in third quadrant, rest are negative.
The value of cos and tan for given theta is:
[tex]cos(\theta) = -\dfrac{1}{2}\\\\ tan( \theta) = \sqrt{3}[/tex]
How to find if the angle given lies in third quadrant?If angle lies between 0 to half of pi, then it is int first quadrant.
If angle lies between half of pi to a pi, then it is in second quadrant.
When the angle lies between [tex]\pi[/tex] and [tex]\dfrac{3\pi}{2}[/tex], then that angle lies in 3rd quadrant.
And when it lies from [tex]\dfrac{3\pi}{2}[/tex] and 0 degrees, then the angle is in fourth quadrant.
Which trigonometric functions are positive in third quadrant?Only tangent function and cotangent functions.
In first quadrant, all six trigonometric functions are positive.
In second quadrant, only sin and cosec are positive.
In fourth, only cos and sec are positive.
We can continue as follows:
[tex]sin(\theta) = -\dfrac{\sqrt{3}}{2}\\ sin(\theta) = sin(\pi + 60^\circ)\\ \theta = \pi + 60^\circ[/tex]
Thus, evaluating cos and tan at obtained theta:
[tex]cos(\pi + 60^\circ) = -cos(60) = -\dfrac{1}{2}\\ tan( \pi + 60^\circ) = tan(60) = \sqrt{3}[/tex]
Learn more about trigonometric functions and quadrants here;
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A rectangle with a width of 2.5 cm and a length of 3 cm is dilated by a scale factor of 4. Which statements about the new rectangle are true?
Check all that apply.
The dimensions of the new rectangle will be 10 cm by 12 cm.
The dimensions of the new rectangle will be 40 cm by 48 cm.
The new perimeter will be 4 times the original perimeter.
The new perimeter will be 16 times the original perimeter.
The new area will be 4 times the original area.
The new area will be 16 times the original area.
The new perimeter will be 44 cm.
The new area will be 30 square cm
Answer:
The dimensions of the new rectangle will be 10 cm by 12 cm.The new perimeter will be 4 times the original perimeter.The new area will be 16 times the original area.The new perimeter will be 44 cm.Step-by-step explanation:
Given dimensions of original rectangle , length(l)=3 cm and width(w)=2.5 cm
We know that after dilation with scale factor (k), the dimension of new figure = k times the original dimensions.
Thus width of new rectangle=[tex]4\times2.5=10\ cm[/tex]
length of new rectangle=[tex]4\times3=12\ cm[/tex]
∴The dimensions of the new rectangle will be 10 cm by 12 cm.
Now, Perimeter of original rectangle=[tex]2(l+w)=2(3+2.5)=2(5.5)=11\ cm[/tex]
Thus, Perimeter of new rectangle=[tex]2(4l+4w)=2(12+10)=2(22)=44\ cm[/tex]
⇒ Perimeter of new rectangle=44 cm=[tex]4\times11\ cm[/tex]
∴The new perimeter will be 4 times the original perimeter.
Now, Area of original rectangle=[tex]lw=3\times2.5=7.5\ cm^2[/tex]
Thus, Area of new rectangle=[tex]4l\times4w=12\times10=120\ cm^2[/tex]
Area of new rectangle=[tex]16lw=16(lw)[/tex]
⇒The new area will be 16 times the original area.
Please answer question,
My Family went hiking through a cave. To help us track where we were and make out way back out, we left a trail. We left a light flare every 20 feet of the hike. We hiked 2 miles through the cave before turning back. How many flares did we pick up on the way back out of the cave?
1 light flare every 20 feet. Hiked 2 miles.
Thanks Guys!
The answer is 22 add
What is the mean of the data set?
41, 32, 39, 47, 55
Find the least number between 200 and 500 which leaves a reminder of 3 in each case when divide by 8,10,12 and 30
Identify the number that does not belong with the other three. Explain your reasoning.
-10/2, -13.4, square root of 18, 22.7 repeating
List the discontinuities for the function f(x) = cot(2x over 3)
Answer:
Step-by-step explanation:
cot(x) can be written as
[tex]cot(x) =\frac{cosx}{sinx}[/tex]
Here we have [tex]cot(\frac{2x}{3}[/tex]
so It will be undefined whenever
[tex]sin(\frac{2x}{3}) = 0[/tex]
As we cannot have a 0 in the denominator .
so to point all the discontinuties we need to identify the x values where
[tex]sin (\frac{2x}{3} ) = 0[/tex]
[tex]\frac{2x}{3} = 0 + \pi k[/tex] where k is any integer
[tex]x= \frac{3\pi }{2} k[/tex]
It means f(x) is discontinuous at all the values of [tex]x = \frac{3\pi }{2}k[/tex]
for k = 0 , 1 ,2.....
Can you please help me
Solve for ×. show your work
30×-40=80
A car dealership decreased the price of a certain car by 4%. The original price was
$45,400.
(a) Fill in the blank to write the new price in terms of the original price.
New Price = ? x Original price.
(b) Use your answer in part (a) to determine the new price.
New price $?
Answer:
(a) [tex]\text{New Price}=0.96\times \text{Original Price}[/tex]
(b) The new price of car is $43584.
Step-by-step explanation:'
(a)
The original price of car is $45400.
It is given that the car dealership decreased the price of a certain car by 4%.
[tex]\text{New Price}=\text{Original Price}-\frac{4}{100}\times \text{Original Price}[/tex]
[tex]\text{New Price}=(1-\frac{4}{100})\times \text{Original Price}[/tex]
[tex]\text{New Price}=\frac{96}{100}\times \text{Original Price}[/tex]\
[tex]\text{New Price}=0.96\times \text{Original Price}[/tex]
(b)
Using part (a), we get
[tex]\text{New Price}=0.96\times \text{45400}[/tex]
[tex]\text{New Price}=43584[/tex]
Therefore the new price of car is $43584.
The formula for the new price is New Price = 0.96 x 45400, while the value of the new price of the car is $43,584
The formula for the new priceFrom the question, we have:
Original price = $45,400
Rate decreased = 4%
The new price would be calculated using:
New Price = (1 - Rate) x Original price.
So, we have:
New Price = (1 - 4%) x Original price
Express the percentage as decimal
New Price = (1 - 0.04) x Original price.
So, we have:
New Price = 0.96 x 45400
The new priceIn (a), we have:
New Price = 0.96 x 45400
Evaluate
New Price = 43584
Hence, the new price of the car is $43,584
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