No, (4, -3) is not a solution to the system of equations
Explanation:If (4, -3) is a solution to the given system of equations, then
for x = 4, and y = -3, both of the equations are satisfied.
x - y = 4 - (-3)
= 4 + 3
= 7
This is not 4, so the first equation is not satisfied
2x + y = 2(4) + (-3)
= 8 - 3
= 5
This equation is satisfied
It is sufficient to conclude that (4, -3) is not a solution to the system of equations since it doesn't satisfy the first equation
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}
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]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 7204. 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
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]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]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
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.
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
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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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
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.
Find the equation for the line that passes through the point (-4,1), and that is perpendicular to the line with the equation
EXPLANATION
Given:
Point ( - 4, 1)
⇒x = -4 and y = 1
Perpendicular equation
3/4 x + y = -5/4
We need to re-write the above equation in the form y = mx + b
y = -3/4 x -5/4
Compare the above with y=mx + b where m is the slope and b is the intercept.
slope(m) = -3/4
Slope of vertical lines are inverse of one another.
This implies that the slpe of our new equation is:
[tex]m=\frac{-1}{m}=\frac{-1}{-\frac{3}{4}}=\frac{4}{3}[/tex]Next, is to find the intercept of the new equation.
We can find this by substituting m = 4/3 , x = -4 and y = 1 into y=mx + b and then solve for b.
That is;
[tex]\begin{gathered} 1=\frac{4}{3}(-4)+b \\ \\ 1=-\frac{16}{3}+b \\ \\ 1+\frac{16}{3}=b \\ \\ b=\frac{3+16}{3} \\ \\ b=\frac{19}{3} \end{gathered}[/tex]We can proceed to form the new equation by simply substituting the values of m and b into y=mx + b
Hence, the equation is:
[tex]y=\frac{4}{3}x+\frac{19}{3}[/tex]What is the answer 5 +5
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
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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11. 9 Reason Abstractly Explain why astudent who runs 3/4 mile in 6 minutes isfaster than a student who runs 1/2 mile in5 minutes.
hello
to solve this question, need to calculate their speeds and compare
student A ran 3/4 miles in 6 mins
[tex]\text{speed}=\frac{dis\tan ce}{time}[/tex]now we can substitute the values into the equatio
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
A circle has a radius of 20 inches. Find the length of the arc intercepted by a central angle of 45°. Leave answers in terms of π.A. 5π/2 inchesB. 5π inchesC. 5 inchesD. 4π inches
radius = 20 inches
angle = θ= 45°
We would apply length of an arc:
[tex]length\text{ of an arc = }\frac{\theta}{360\text{ }}\text{ }\times2\pi r[/tex][tex]\begin{gathered} \text{length of the arc = }\frac{45}{360}\times2\times\pi\times20 \\ =\text{ }\frac{1}{8}\times\text{ 40}\pi \end{gathered}[/tex]Since the options is in terms of π, the answer will be in that form
[tex]\text{length of }arc\text{ = 5}\pi\text{ inches (option B)}[/tex]25÷2 3/8 please help
25÷2 3/8
Let's remember how to convert
[tex]a\frac{b}{c}=\frac{(a\cdot c)+b}{c}[/tex]Step 1
convert
[tex]\begin{gathered} 2\frac{3}{8}=\frac{(2\cdot8)+3}{8} \\ 2\frac{3}{8}=\frac{19}{8} \\ \end{gathered}[/tex]Step 2
now , we have 25 divided by 19/8
[tex]\begin{gathered} 25\text{ divide by 19/8=}\frac{\frac{25}{1}}{\frac{19}{8}} \\ 25\text{ divide by 2 3/8=}\frac{25\cdot8}{19\cdot1}=\frac{200}{19} \\ 25\text{divide by 2 3/8=}\frac{200}{19} \\ \end{gathered}[/tex]so, the answer is 200/19
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
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.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.
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
What type of sequence and how to write the explicit rule.
The Solution:
Given the sequence below:
[tex]26,18,10,2,\ldots[/tex]We are required to identify the type of sequence and to find the explicit rule for the given sequence.
Step 1:
To determine the type of sequence, we shall run the following check:
[tex]\begin{gathered} a_2-a_1=a_3-a_2\text{ then it is an Arithmetic sequence} \\ \text{ but if} \\ \frac{a_2}{a_1}=\frac{a_3}{a_2}\text{ then it is a Geometric sequence.} \end{gathered}[/tex]So,
[tex]\begin{gathered} 18-26=10-18 \\ -8=-8 \\ \text{ Then it follows that the sequence is an Arithmetic sequence.} \end{gathered}[/tex]Thus, the sequence is an arithmetic sequence.
Step 2:
To find the explicit rule, we shall use the formula below:
[tex]a_n=a_1+(n-1)d[/tex]In this case,
[tex]\begin{gathered} a_1=\text{ first term=26} \\ n=\text{ number of terms=?} \\ d=\text{ co}mmon\text{ difference=18-26=-8} \end{gathered}[/tex]Substituting these values in the formula, we get
[tex]\begin{gathered} a_n=26+(n-1)(-8) \\ a_n=26-8(n-1) \end{gathered}[/tex]Therefore, the explicit rule of the sequence is :
[tex]a_n=26-8(n-1)[/tex]Hi, I am having trouble with this. Could you help? This month a band plays 3 private parties, each of which pays them the same amount. However, the band also has $200 in travel expenses. Taking those expenses into account, they make a total of $2500. The following month, the band has 5 bar gigs and 2 private parties, plus they make an additional $800 (total) by selling merch, and have a total of $350 in travel expenses. With all expenses factored in, they make a total of $4125. How much, on average, is the band payed per bar gig? (assume they are paid the same amount per party this month as they were last month). Write 2 algebra equations then solve.
We have two cases. The first month, they played in 3 private parties that payed the same. They had a cost of $200 in travel and, in the end, they made $2500. Let "p" be the paid amount of each party. Since there were 3, they were payed 3*p. If we then substract their expenses of $200, we get the final amount, that should be equal to $2500.
In an equation, this is:
[tex]\begin{gathered} 3p-200=2500 \\ 3p=2500+200 \\ 3p=2700 \\ p=\frac{2700}{3} \\ p=900 \end{gathered}[/tex]So, each party payed $900.
In the second month, they worked on 5 bar gigs and 2 private parties. We already know that each private party pays $900, so, if "b" is the average amount they made in each bar gig, then "5b" will be the total they made in bar gigs and, adding the party amount, we have, in the second month:
[tex]5b+2p=5b+2\cdot900=5b+1800[/tex]The had $350 travel expenses, so we need to substract this and we should end up with the total they made, that was $4125:
[tex]\begin{gathered} 5b+1800-350=4125 \\ 5b+1450=4125 \\ 5b=4125-1450 \\ 5b=2675 \\ b=\frac{2675}{5} \\ b=535 \end{gathered}[/tex]Thus, on average, they were payed $535 per bar gig.
-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
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
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