From the question, we are given the following;
Cost of entering the state fair = $10
Amount of each ride = $2
For us to determine the amount it will cost Evan to go to the fair and ride 5 rides, the equation y = $10 + 2x will be used where;
x is the total ride taken = 5 rides
y is the amount it cost evan to enter the state fair and ride 5 rides
Substitute x = 5 into the equation and get y;
y = $10 + 2x
y = $10 + $2(5)
y = $10 + $10
y = $20
Hence it will cost Evans $20 to go to the fair and ride 5 rides
In your own words, explain what you know about a number that satisfies theequation x2 = -1.
The number that satisfies the equation is
[tex]x^2=-1[/tex]Doing the square root on both sides
[tex]x=\pm\sqrt{-1}[/tex]On complex number we use the definition:
[tex]i=\sqrt[]{-1}[/tex]Therefore, the number that satisfies the equation is
[tex]x=\pm i[/tex]That means that a solution is a complex number.
Complex numbers have two parts, the complex part and the real part:
[tex]z=a+bi,\quad a,b\in\mathbb{R}[/tex]Look that a and b are real coefficients, but z is a complex number because we have b multiplying i, the complex unit.
But why complex numbers are so important?
• Complex numbers can be used to solve polynomial equations, that we couldn't solve before
,• Complex numbers can connect exponential function with trigonometric functions
[tex]e^{ix}=\cos (x)+i\sin (x)[/tex]Complex numbers are a powerful set that we can use to solve many complex problems in physics and mathematical, it may seem hard but they actually make things easier, sometimes working with complex numbers is way easier than working with real numbers.
which e q u a t i o n s the correct
The given statement is Four less than a number is nine.
Remember that "less than" refers to subtraction. "A number" refers to a variable x. "is" refers to equality. So, the expression would be
[tex]x-4=9[/tex]C is the answer.Write the place of the underlined digit then write its value. what is the value?
EXPLANATION
2) 812: The place of the underlined digits corresponds to UNITS.
VALUE --> 812: eight hundred twelve
Find a linear function h, given h(3)=-2 and h(-3)=16. Then find h(5).
You have to find the equation of the linear function h(x), given that you know two points of the said function.
h(3)=-2 → this notation indicates the ordered pair (3,-2)
h(-3)=16 → this notation indicates the ordered pair (-3,16)
The first step to determine the equation of any line or linear function is to calculate its slope. To do so you have to use the following formula:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]Where
(x₁,y₁) are the coordinates of one point of the line
(x,₂,y₂) are the coordinates of a second point of the line
Using the ordered pairs:
(3,-2) as (x₁,y₁)
(-3,16) as (x,₂,y₂)
Calculate the slope as follows:
[tex]\begin{gathered} m=\frac{(-2)-16}{3-(-3)} \\ m=\frac{-18}{3+3} \\ m=-\frac{18}{6} \\ m=-3 \end{gathered}[/tex]So the slope of the linear function is m=-3
To determine the equation you can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]Where
m represents the slope
(x₁,y₁) are the coordinates of one point of the line
I will use the point (3,-2) and the slope m=-3 to determine the equation but you can use either ordered pair to do so.
[tex]\begin{gathered} y-(-2)=-3(x-3) \\ y+2=-3(x-3) \end{gathered}[/tex]Now, what's left is to write the equation in slope-intercept form:
-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} y+2=(-3)\cdot x-(-3)\cdot3 \\ y+2=-3x-(-9) \\ y+2=-3x+9 \end{gathered}[/tex]-Pass "+2" to the right side of the equal sign by applying the opposite operation to both sides of the equal sign "-2"
[tex]\begin{gathered} y+2-2=-3x+9-2 \\ y=-3x+7 \end{gathered}[/tex]The equation of the linear function is:
[tex]h(x)=-3x+7[/tex]To find the value of h(5), you have to replace the equation of the function with x=5 and calculate the corresponding h(x) value
[tex]\begin{gathered} h(x)=-3x+7 \\ h(5)=-3\cdot5+7 \\ h(5)=-15+7 \\ h(5)=-8 \end{gathered}[/tex]So:
[tex]\begin{gathered} h(x)=-3x+7 \\ \text{and} \\ h(5)=-8 \end{gathered}[/tex]What is an equation of the line that passes through the point (3,1) and is parallelto the line 4x + 3y=15
Explanation
two lines are parallel when their slopes are equal,
Step 1
convert the equation to the form
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope} \end{gathered}[/tex]to easily find m
[tex]\begin{gathered} 4x+3y=15 \\ \text{subtract 4x in both sides} \\ 4x+3y-4x=15-4x \\ 3y=15-4x \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{15}{3}-4x \\ y=-4x+5 \end{gathered}[/tex]Hence
[tex]\begin{gathered} y=-4x+5\Rightarrow y=mx+b \\ m=\text{slope}=-4 \end{gathered}[/tex]Step 2
Now we have this info to find the equation of the line
[tex]\begin{gathered} P1(3,1) \\ m_1=m_2=-4 \end{gathered}[/tex]apply the formula
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{replacing} \\ y-1=-4(x-3) \\ y-1=-4x+12 \\ \text{add 1 in both sides} \\ y-1+1=-4x+12+1 \\ y=-4x+13 \end{gathered}[/tex]I hope this helps you
x of Lixin's classmates plan to buy her a birthday gift. The cost of the birthday gift is $36 (i) Given that 5 of Lixin's classmate decided not to contribute to the birthday gift, the rest of her classmates will have to pay an additional $0.24 to make up for the difference. Write down an expression, in terms of x, for the amount which each of the remaining classmates will now have to pay. (ii) Form an equation in x and show that it reduces to x square- 5x - 750 = 0. (i) Find the number of classmates Lixin has.
Lixin has x number of classmates and plan to buy her a birthday gift worth $36.
So basically, they need to contribute 36/x dollars each in order to buy the gift.
But 5 of them will not contribute and it cost them to add $0.24 each
So from 36/x dollars, it become (36/x + 0.24) dollars each
Multiply this individual contribution by the number of her classmates which was reduced by 5. (x - 5)
The equation will be :
[tex]\begin{gathered} \text{contribution}\times\text{ number of classmates}=36 \\ (\frac{36}{x}+0.24)(x-5)=36 \end{gathered}[/tex]Simplify the equation :
[tex]\begin{gathered} (\frac{36}{x}+0.24)(x-5)=36 \\ \frac{36}{x}(x-5)+0.24(x-5)=36 \\ (36-\frac{180}{x})+(0.24x-1.2)=36 \end{gathered}[/tex]Multiply both sides by x to remove the denominator.
[tex]\begin{gathered} x(36-\frac{180}{x})+x(0.24x-1.2)=36x \\ 36x-180+0.24x^2-1.2x=36x \end{gathered}[/tex]Rearrange and combine like terms :
[tex]\begin{gathered} 0.24x^2+36x-1.2x-36x-180=0 \\ 0.24x^2-1.2x-180=0 \end{gathered}[/tex]Divide both sides by 0.24 to make the coefficient of x^2 become 1 :
[tex]\begin{gathered} \frac{0.24x^2}{0.24}-\frac{1.2x}{0.24}-\frac{180}{0.24}=0 \\ x^2-5x-750=0 \end{gathered}[/tex]Solve by factoring completely :
[tex]\begin{gathered} x^2-5x-750=0 \\ (x-30)(x+25)=0 \end{gathered}[/tex]Equate both factors to 0, then solve for x :
x - 30 = 0
x = 30
x + 25 = 0
x = -25
Neglect negative value since there is no negative value for the number of persons.
The answer is x = 30
To summarize :
i Expression in terms of x :
[tex](\frac{36}{x}+0.24)(x-5)=36[/tex]ii Equation in x that reduces to x^2 - 5x - 750 = 0
[tex]\begin{gathered} 0.24x^2-1.2x-180=0 \\ \Rightarrow x^2-5x-750=0 \end{gathered}[/tex]iii Number of classmates Lixin has.
x = 30
Answer:
this is 50. i = 50
Step-by-step explanation:
hope it helps you
1. What is the unit price for each detergent? Brand Size (oz) Price ($) Brand A: $ per ounce A 32 4.80 Brand B: $ per ounce B 48 5.76 Brand C: $ per ounce C с 128 17.92 2. Which detergent is the best buy?
To determine the unit price for each detergent, i.e. the price per ounce, you have to divide the cost of the detergent by the number of ounces the container has.
Detergent A
Has 32 ounces
Costs $4.80
The unit price can be calculated as:
[tex]\frac{4.80}{32}=0.15[/tex]Detergent A costs $0.15/ounce
Detergent B
Has 48 ounces
Costs $5.76
The unit price can be calculated as the quotient between the price and the amount of detergent:
[tex]\frac{5.76}{48}=0.12[/tex]Detergent B costs $0.12/ounce
Detergent C
Has 128ounces
Costs $17.90
Calculate the unit price by dividing the price by the number of ounces of the container:
[tex]\frac{17.90}{128}=0.139\approx0.14[/tex]Detergent C costs $0.14/ounce.
The best detergent to buy is the one that has the lower unit price, so to determine which one is it you have to compare their price per ounce.
In this case, detergent B has the lower price per ounce and thus it is the best detergent to buy.
What is the answer 5 +5
4. Ash is three years older than ShawnCrystal is four times as old as Shawn. Oscaris twice as old as Ash. Altogether their agestotal 49. Find each person's age.
Shawn's age = 5 years
Ash's age = 8 years
Crystal's age = 20 years
Oscar's age = 16 years
Explanations:Let Ash's age be represented by A
Let the Shawn's age be represented as S
Let the Crystal's age be represented as C
Let Oscar's age be represented as O
Ash is three years older than Shawn
A = S + 3.....................(1)
Crystal is 4 times as old as Shawn
C = 4S................................(2)
Oscar is twice as old as Ash
O = 2A.................................(3)
Altogether, their ages total 49
A + S + C + O = 49 ...............(4)
First, to get Oscar's age in terms of Shawn's age, substitute equation (1) into equation (3)
O = 2 ( S + 3)
O = 2S + 6..................(5)
Substitute equations (1), (2), and (5) into equation (4)
(S + 3) + S + (4S) + (2S + 6) = 49
S + S + 4S + 2S + 3 + 6 = 49
8S + 9 = 49
8S = 49 - 9
8S = 40
S = 40 / 8
S = 5
Shawn's age = 5 years
To get Ash's age, substitute the value of S into equation (1)
A = S + 3
A = 5 + 3
A = 8
Ash's age = 8 years
To get Crystal's age, substitute the value of S into equation (2)
C = 4S
C = 4(5)
C = 20
Crystal's age = 20 years
To get Oscar's age, substitute the value of A into equation (3)
O = 2A
O = 2(8)
O = 16
Oscar's age = 16 years
A baseball league has ten teams. How many different end-of-the-season ranking first, second, and third place are there.
Find out the permutation 10P3
[tex]10P3=\frac{10!}{(10-3)!}=720[/tex]The answer is 720Y=x^2 how does Y= (x-4^2) andY = (x+3) differ from theParent function and each other?what causes this to change?
The parent function is:
y = x²
This is a quadratic function
The child functions are:
y = x - 4² whcih can be written as
y = x - 16
The second child function is
y = x + 3
The two child functions are linear functions while the parent function is a quadratic function.
The parent and child functions also differ in their ranges and domains
For y = x²Domain = ( -∞ , ∞ )
Range = [0 , ∞ )
For y = x - 4² and y = x + 3:Domain = ( -∞ , ∞ )
Range = (-∞ , ∞ )
The difference between y = x - 4² and y = x + 3 is their intercepts on the y axis .
For y = x - 4², the y - intercept is -16
For y = x + 3, the y - intercept 3
This change is due to transformation (basically translation) on the x and y axes
1. The endpoints of line PQ on a real number line are -.5 and .72. What is the coordinate of the midpoint of line PQ?
We are given the endpoints of a line PQ
[tex]-0.5\text{ and }0.72[/tex]We are asked to find the midpoint of line PQ.
Let us first find the distance of line PQ
[tex]\begin{gathered} d=|x_2-x_1| \\ d=|0.72_{}-(-0.5)_{}| \\ d=|0.72_{}+0.5| \\ d=|1.22| \\ d=1.22 \end{gathered}[/tex]Recall that the midpoint is at the halfway of the line PQ so divide the distance by 2
[tex]midpoint=\frac{1.22}{2}=0.61[/tex]I have tried 4 tutors who could not answer this question. Someone, please help me.
The expected return of the stock portfolio is 9.3%.
From the properties of stock portfolio we know that,
Expected return of a portfolio = RF + BP ( RM - RF )
E(RP) = RF + BP ( RM - RF )
RF= risk free rate =3%
RM = expected market return = 10%
BP = beta of portfolio
BP = ∑(Wi × Bi)
Wi is weight of stock i and Bi is the beta of stock i .
Wi= investment in stock / total investment
Beta of portfolio(BP)
=(0.5×1) + (0.35×0.2) + (0.33)
= 0.50 +0.07+0.33
=0.9
E(RP)
= RF + BP ( RM - RF )
= 0.03 + 0.9(0.30-0.03)
= 0.03 +0.063
= 0.093
Hence the expected rate = 0.093 × 100% = 9.3%
The stock market portfolio of an investor consists of stocks, funds, and possibly other market-traded securities. In general, cash and bond assets are often present in investment portfolios. Various assets with different sizes, industries, and other characteristics are included in a varied portfolio.
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I have to send the picCalculate the Area of the figure
The area of the figure is 24 cm²
The figure is divided into two blocks, one is rectangle having the dimensions, length as 5cm and width as 4 cm, another is a square having side of 2 cm.
The area of the figure is the summation of the area of the rectangle and the area of the square.
area of the rectangle = length x width = 4 x 5 = 20cm²
area of the square = side² = 2² = 4cm²
area of the figure = area of rectangle + area of the square
= 20 + 4
area of the figure is 24 cm²
Therefore, the area of the figure is 24 cm²
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Jeff picks a number with 2 tens 42 ones. victor picks a number with 3 tens 51 ones. what number does each child pick?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Jeff = 2 tens 42 ones
Victor = 3 tens 51 ones
what number is = ?
Step 02:
Jeff = 2 tens 42 ones
2 * 10 = 20
42 * 1 = 42
----------
Victor = 3 tens 51 ones
Answer:
Jeff: 62
Victor: 81
Step-by-step explanation:
Jeff has a number with 2 tens, and 42 ones. We can write out our 2 tens like this: 10 + 10 = 20
Next, he has 42 ones. This is just another way of saying '42'
So, jeff picked a number that is 20 + 42 = 62
Now, Victor. Victor has a number with 3 tens. This is saying: 10 + 10 + 10 which is 30. He has 51 ones, which is just the number 51.
So, Victor's number is 30 + 51 = 81
Find the area of a regular nonagon (9-sided polygon) if the apothem is 4 cm long, and each side is14 cm.
Answer:
[tex]252\text{ cm}^2[/tex]Explanation:
Here, we want to find the area of the polygon
Mathematically, we have that calculated as:
[tex]A\text{ = }\frac{n\times b\times a}{2}[/tex]where:
n is the number of sides of the polygon which is 9
b is the length of a side which is 14 cm
a is the length of the apothem which is 4 cm
Substituting the values, we have it that:
[tex]A\text{ = }\frac{9\times14\times4}{2}\text{ = 252 cm}^2[/tex]Determine the relationship between the two triangles and whether or not they can be proven to be congruent. + The two triangles are related by so the triangles Submit Answer
Given data:
The given triangles.
The given triangles are congruent by side-angle-side (ASA) rule.
Thus, the given triangles are congruent by ASA.
-99G =2 7-759 -6-5 3-4 -9C4 -1-10 013 -7-8 104[G] + 2[C]
.Explanation:
we are given the following matrices
To compute
[tex]4|G|+2|C|[/tex]We will simply multiply the entries of G by 4 and C by 2
Thus, we will have
The final step will be to add the terms together
Thus, we will have
From the Graph, find the constant of proportionality and write the direct variation equation
In this case the answer is very simple. .
We must use the graph to find the answers.
Step 01:
Data
For x = 2 ===> y = 1
Step 02:
Direct variation equation
y = k * x
Constant of proportionality
x = 2 , y = 1
[tex]\text{ y = k }\cdot\text{ x}[/tex][tex]\begin{gathered} 1\text{ = k }\cdot\text{ 2 } \\ \frac{1}{2}\text{ = k } \\ \end{gathered}[/tex]The solution is:
Constant of proportionality = k
k = 1/2
Direct variation equation
y = k * x
y = (1/2) * x
There are three novels on Keisha's reading table: Scoop, Light, and Lanark. On her next trip, she can choose to take some or none, but not all, of these novels. In the braces below, list all the possible sets of novels that Keisha can take.Write each set in your list in roster form..
She could take
1.- {x|x Scoop}
2.- {x|x Light}
3.- {x|x Lanark}
4.- {x|x Scoop, Light}
5.- {x|x Scoop. Lanark}
6.- {x|x Light, Lanark}
In 2018 it was estimated that approximately 41% of the American population watches the Super Bowl yearly. Suppose a sample of 118 Americans is randomly selected. After verifying theconditions for the Central Limit Theorem are met, find the probability that the majority (more than 50%) watched the Super Bow.
We would test if np and n(1 - p) is at least 10
p = sample proportion
p = x/n
where
x = number of success
n = sample size
From the information given,
p = 41% = 41/100 = 0.41
n = 118
np = 48.38
n(1 - p) = 118(1 - 0.41) = 69.62
Both values are greater than or equal to 10. Thus, the distribution is approximately normal.
The mean of the distribution = p = 0.41
Standard deviation = √(p(1 - p)/n
By substituting the values,
standard deviation = √(0.41(1 - 0.41)/118 = √0.00205 = 0.045
We want to find P(p ≥ 0.5)
We would standardize 0.5 into a z score by applying the formula,
z = (x - mean)/standard deviation
z = (0.5 - 0.41)/0.045 = 2
From the normal distribution table, the probability value corresponding to a z score of 2 is 0.9773
P(p ≥ 0.5) = 1 - 0.9773
P(p ≥ 0.5) = 0.023
the probability that the majority (more than 50%) watched the Super Bow is 0.023
8. Find the volume of a cone with a diameter of 10 meters and a height of 5.1 metersUse - (π = 3.14)
Answer:
133.45 m^3
Explanation:
Given:
Diameter of the cone (d) = 10 meters
Then the radius(r) of the cone will be d/2 = 10/2 = 5 meters
Height of the cone (h) = 5.1 meters
Pi = 3.14
We'll go ahead and use the below formula to determine the volume of the cone(V);
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ =\frac{1}{3}*3.14*5^2*5.1 \\ =\frac{1}{3}*3.14*25*5.1 \\ =133.45\text{ m}^3 \end{gathered}[/tex]So the volume of the cone is 133.45 m^3
Westin Trading normally nets $6 million per month. The table shows the variance from the average for five months.Sales Above/Below Average (Millions)AprilMayJuneJulyAug.–2.5Negative 2 and one-half3.1–1.62 and two-thirdsWhich comparison is true? Use the number line to help.A number line going from negative 6 to positive 6 in increments of 1. June < AugustApril = MayMay > JulyMay = August
We have:
April --> -2.5
May --> Negative 2 and one-half = - 2 + 1/2 = -2.5
June --> 3.1
July --> - 1.6
Aug --> 2 and two-thirds = 2 + 2/3 = 2.67
We place them on the number line
Therefore,
June > August
April = May
May < July
May ≠ August
Answer: The true comparison is April = May
Pam and Rachel buy books at the bookstore where Rachel works. As an employee, Rachel pays only 75% of the advertised price. How many books could each purchase and spend the same amount for the same number of books?
Answer:
0, that is not possible
Step-by-step explanation:
Since she gets a discount she will always pay less
which of these situations cannot be represented by the number -10 ?A) A loss of 10 yeards.B) 10 degrees below zero.C) A withdrawal of $10.D) gaining 10 points.
The correct option is D
gaining 10 points cannot be represented by the number -10
Explanation:-10 can represent all the given situations except gaining 10 points.
Because that will be an increase (+10), and not a decrease (-10)
Answer is: A withdrawal of $10.
Sample Data48262191036984391035414135264238472947512227421220143514138142710482529331220229149943521413Computations(Round the mean and sample standard deviation to values to FIVE decimal places)Sample Mean = 25.42Sample Standard Deviation = 14.25724(Round the lower/upper limits and margin of error to THREE decimal places). #1. 80% Confidence Interval: 80% Confidence Interval Margin of Error:What does this confidence interval mean given the data?#2. 95% Confidence Interval:95% Confidence Interval Margin of Error: #3. 99% Confidence Interval:99% Confidence Interval Margin of Error:#4. Make up YOUR OWN Interval.50% Confidence Interval:50% Confidence Interval Margin of Error:
The given information is:
- Sample mean = 25.42
- Standard deviation = 14.25724
Part 1.
We have a confidence interval (C.I.) of 80%.
We need to find the z-score for this C.I., so, let's see a diagram:
We have a two-sided confidence interval. So, we need to find the z-score for a cumulative probability of 80+10=90%=0.9.
By using a standard normal table, we can see that z-score for 0.9 is:
By using an online calculator, we find the exact z-score is 1.282.
The confidence interval is given by the formula:
[tex]C.I=\bar{x}\pm z_c\frac{s}{\sqrt{n}}[/tex]Where x is the mean of the sample, Zc is the z-score for the given confidence level, s is the standard deviation and n is the number of elements in the sample n=50.
By replacing the known values, we obtain:
[tex]\begin{gathered} 80\%C.I.=25.42\pm1.282\frac{14.25724}{\sqrt{50}} \\ \\ C.I.=25.42\pm1.282\times2.016 \\ C.I.=25.42\pm2.585 \end{gathered}[/tex]So, the lower and upper limits are:
[tex]\begin{gathered} lower:25.42-2.585=22.835 \\ upper:25.42+2.585=28.005 \end{gathered}[/tex]The margin of error is equal to half the width of the entire confidence interval, and it is also the value we add and subtract to the mean to find the confidence interval, so the margin of error is 2.585.
Forest rangers wanted to better understand the rate of growth for younger trees in the park. They took measurements of a random sample of 50 young trees in 2009 and again measured those same trees in 2019. The data below summarize their measurements, where the heights are in feet.
Year Mean SD n
2009 11.4 3.6 50
2019 24.3 8.8 50
Difference 12.9 5.52 50
Round all calculated values to 4 decimal places as appropriate.
1. Construct a 90 confidence interval for the mean difference between the height of trees in the park in 2009 and in 2019.
2. What conditions must be met if we want to perform a hypothesis test and answer the question of the management? Select all that apply:
A. Large samples and no extreme outliers.
B. There must be at least 3 levels of the categorical variable.
C. np^≥10 and n(1−p^)≥10
D. Independently sampled pairs.
1. The 90% confidence interval for the mean difference between the height of trees in the park in 2009 and in 2019 is given as follows:
(11.59, 14.21)
2. The conditions for the confidence interval are of:
A. Large samples and no extreme outliers.D. Independently sampled pairs.What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 50 - 1 = 49 df, is t = 1.6766.
The remaining parameters are given as follows:
[tex]\overline{x} = 12.9, s = 5.52, n = 50[/tex]
Then the lower bound of the interval is of:
12.9 - 1.6766 x 5.52/sqrt(50) = 11.59.
The upper bound of the interval is of:
12.9 + 1.6766 x 5.52/sqrt(50) = 14.21.
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Find the exact solutions to x2-3x+1-0 by using the Quadratic Formulal
Given
[tex]x^2-3x+1=0[/tex]Find
Exact solution by quadratic formula
Explanation
Quadratic formula is given by
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]here a = 1 , b = -3 and c = 1
substitute the values in quadratic formula ,
[tex]\begin{gathered} x=\frac{-(-3)\pm\sqrt{(-3)^2-4\times1\times1}}{2\times1} \\ \\ x=\frac{3\pm\sqrt{9-4}}{2} \\ \\ x=\frac{3\pm\sqrt{5}}{2} \end{gathered}[/tex]Final Answer
Therefore , the correct option is 4.
Jose Is cooking a roast. The table below gives the temperature (1) of the roast (In degrees Celsius), at a few timest (In minutes) after he removed it from theoven.Timet Temperature R (1)(minutes)(c)010305070226.6205.6157.6119.661.6(a) Find the average rate of change for the temperaturefrom 0 minutes to 10 minutes.0 °C per minute(b) Find the average rate of change for the temperaturefrom 30 minutes to 50 minutes.[ °C per minute
(a). From the given table,
R(0)=226.6
R(10)=205.6
The average rate of change for the temperature from 0 minutes to 10 minutes is
[tex]\begin{gathered} A=\frac{R(10)-R(0)}{10-0} \\ =\frac{205.6-226.6}{10} \\ =-2.1 \end{gathered}[/tex](a) The average rate of change for the temperature from 0 minutes to 10 minutes is -2.1 (in degree centrigrade)
Minus sign implies that the temperature is deacreasing with increasing time
(b). Again,
R(30)=157.6
R(50)=119.6
The average rate of change for the temperature from 30 minutes to 50 minutes is
[tex]\begin{gathered} A=\frac{R(50)-R(30)}{50-30} \\ =\frac{119.6-157.6}{20} \\ =-1.9 \end{gathered}[/tex](b) The average rate of change for the temperature from 30 minutes to 50 minutes is -1.9 (in degree centrigrade)
Minus sign implies that the temperature is deacreasing with increasing time
1.3(2y-7)2.-(x+4)3.2/3 (1/4x-6)4. 6(x+1) -5 (x+2)
In this expression, we can solve it by applying the distributive property
3(2y-7)
6y-21
So, factor 3 multiplies each term inside the parentheses.
2)-(x+4)
The minus outside the bracket works like a -1 multiplying it
-(x+4)
-x-4
3) For this one, remember the rule for multiplying fractions and then simplifying:
[tex]\begin{gathered} \frac{2}{3}(\frac{1}{4}x-6) \\ \frac{2}{12}x\text{ -}\frac{12}{3} \\ \frac{1}{6}x-4 \end{gathered}[/tex]4) 6( x+1) -5(x+2)
6x+6 -5x-10
6x-5x+6-10
x-4