Answer:
g(x) = 7x^2
Step-by-step explanation:
Given a function f(x), the function kf(x) is stretched by a factor of k. In this case, if we stretch the function f(x) = x^2 by a factor of seven, the new function is going to be the base function multiplied by 7, as follows:
g(x) = 7x^2
Which expression is equivalent to ((2a^-3 b^4)^2/(3a^5 b) ^-2)^-1
Answer:
[tex]\large\boxed{\dfrac{1}{36a^4b^{10}}}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac{\left(2a^{-3}b^4\right)^2}{\left(3a^5b\right)^{-2}}\right)^{-1}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\=\dfrac{\left(3a^5b\right)^{-2}}{\left(2a^{-3}b^4\right)^2}\qquad\text{use}\ (ab)^n=a^nb^n\\\\=\dfrac{3^{-2}(a^5)^{-2}b^{-2}}{2^2(a^{-3})^2(b^4)^2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{3^{-2}a^{(5)(-2)}b^{-2}}{4a^{(-3)(2)}b^{(4)(2)}}=\dfrac{3^{-2}a^{-10}b^{-2}}{4a^{-6}b^8}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}[/tex]
[tex]=\dfrac{3^{-2}}{4}a^{-10-(-6)}b^{-2-8}=\dfrac{3^{-2}}{4}a^{-4}b^{-10}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{3^2}\cdot\dfrac{1}{4}\cdot\dfrac{1}{a^4}\cdot\dfrac{1}{b^{10}}=\dfrac{1}{36a^4b^{10}}[/tex]
Answer:
1 / 36a^4 b^10
Step-by-step explanation:
Which statements about the graph of the function Fx=-x2-4x+2 are true check all that apply
Step-by-step explanation:
Just graph it and see if the descriptions fit the graph
(see attached)
A. We can see from the graph that the possible x-values are -∞ ≤ x ≤ +∞ . Hence limiting to domain to x≤ -2 this is obviously not true.
B. We can see from the graph that the vertex is y = 6 and that the entirety of the graph is under this point, hence range y<6 is true
C. We can see that the vertex is located at x=-2. Every part of the graph to the left of this point has a positive slope, hence the function is increasing for negative infinity to this point x=-2 is true
D) We can see that for the interval -4<x<∞, the graph actually increases between -4<x<-2, and then decreases after that. Hence this statement is not true.
E. it is obvious that the y intercept is y=2 which is positive. Hence this is true.
The graph of F(x)=-x^2-4x+2 is a downward-opening parabola with its vertex serving as the local and global maximum. There are no asymptotes for this quadratic function. The shape of the graph is best understood by examining its behavior over a range of x-values and by sketching it with the vertex and axis of symmetry.
The graph of the function F(x) = -x^2 - 4x + 2 represents a parabola opening downward because the coefficient of x^2 is negative. To understand the nature of the graph, we evaluate its characteristics by identifying the vertex, the axis of symmetry, and whether it has local or global extrema. The vertex of this parabola can be found using the formula -b/2a, which gives us the x-coordinate, and by substituting that back into the function for the y-coordinate. The axis of symmetry will be a vertical line passing through the vertex's x-coordinate.
Since this is a quadratic function, it does not have asymptotes because it extends indefinitely in both the positive and negative directions of the y-axis. Instead, the parabola will have a maximum point at the vertex, which is a local and global maximum because the parabola opens downward. Moreover, we should evaluate the function for a range of x-values to understand its behavior for large negative x, small negative x, small positive x, and large positive x.
Sketching the graph of this function would involve plotting the vertex, drawing the axis of symmetry, and selecting a few points around the vertex to determine the shape of the parabola.
Which of the following lists of ordered pairs is a function
Answer:
A
Step-by-step explanation:
A function can't have the same number more than once, so the answer is A since there are no repeating numbers.
10 points for this! btw it’s really easy to some people so yea
Answer:
C
step-by-step explanation:
you just have to subtract them 9/16-1/4=8/12
can someone help me pls?
Answer:
graph c
Step-by-step explanation:
there is no slope since it doesn't go up/down by anything or over by anything. meaning there is no increase or decrease.
Which terms could be used as the first term of the expression below to create a polynomial written in standard form? Check all that apply.
+ 8r2s4 – 3r3s3
s5
3r4s5
–r4s6
–6rs5
Answer:
[tex]3r^{4}s^{5}\\-r^{4}s^{6}[/tex]
Step-by-step explanation:
The standard form of a polynomial is when its term of highest degree is at first place.
In this case, we have two variables. The grade of each term is formed by the sum of its exponents. That means both given terms have a degree of six. So, the right answers must have a higher degree.
Therefore, the right answers are the second and third choice, because their degrees are 9 and 10 respectively.
simplify (2x^4y^3) x (6x^3y^2)
Answer:
[tex]\large\boxed{(2x^4y^3)(6x^3y^2)=6x^7y^5}[/tex]
Step-by-step explanation:
[tex](2x^4y^3)(6x^3y^2)\\\\=(2)(3)(x^4x^3)(y^3y^2)\qquad\text{use}\ a^na^m=a^{n+m}\\\\=6x^{4+3}y^{3+2}\\\\=6x^7y^5[/tex]
Which graph shows the solution to the inequality |x+3| >2
Answer:
The answer is B, given the module of a number has always a positive value
Answer:
Answer is B.
SECOND NUMBER LINE
Step-by-step explanation:
identify the transformation taking place in this function. y = x^2 +8. a. translation down 8 units. b. translation left 8 units. c. translation right four units. d. translation up 8 units.
Answer:
D. if we are describing how to get from y=x^2 to y=x^2+8.
Step-by-step explanation:
If we are describing how to get from y=x^2 to y=x^2+8, then the transformation is just a translation of 8 units up.
If the equation was y=x^2-8, it would have been down 8 units.
If the equation was y=(x-8)^2, it would have been right 8 units.
If the equation was y=(x+8)^2, it would have been left 8 units.
true or false
x=3 when 5*6\x=10
Mark is playing soccer. He is 150 yards from the center goal. When he kicks the ball it goes 145 yards at an angle of 2 degrees off to the right. How far is the ball from the goal?
Answer:
8 yards
Step-by-step explanation:
This can be illustrated from drawing it. (Attachment)
Scale- Real : Map
10 yard : 1 cm
150 yard : 15 cm
145 yard : 14.5 cm
Step 1: Draw a 7.5 cm line from origin to Point A
Step 2: Form a 2 degree angle from the origin
Step 3: Draw a 7.25 cm line 2 degree angle from the origin to Point B
Step 4: Measure the distance in cm from Point A to Point B
Step 5: Convert the distance from Point A to Point B in yards.
Therefore, the ball is 8 yards far from the goal.
!!
Answer:
The ball is 7.176 yards away from the center of the goal.
Step-by-step explanation:
Given distance between the center goal and Mark is AB = 150 yards
Distance traveled by ball at angle 2 degree off to the right from Mark is
AC = 145 yards
We have to find the distance BC in triangle ABC
Using cosine rule
[tex]BC^{2}=AB^{2}+AC^{2}-2AB\times AC\times \cos \Theta[/tex]
=>[tex]BC^{2}=[150^{2}+145^{2}-2\times 150\times 145\times \cos (2^{\circ})] yards^{2}[/tex]
=>BC^{2}=51.5 yards^{2}
=>[tex]BC=\sqrt{(51.5 yards^{2})}=7.176yards[/tex]
Thus the ball is 7.176 yards away from the center of the goal.
Which of the following reveals the minimum value for the equation 2x2 − 4x − 2 = 0?
2(x − 1)2 = 4
2(x − 1)2 = −4
2(x − 2)2 = 4
2(x − 2)2 = −4
Answer:
[tex]2(x-1)^{2}=4[/tex]
Step-by-step explanation:
we have
[tex]2x^{2} -4x-2=0[/tex]
This is the equation of a vertical parabola open upward
The vertex is a minimum
Convert the equation into vertex form
Group terms that contain the same variable and move the constant to the other side
[tex]2x^{2} -4x=2[/tex]
Factor the leading coefficient
[tex]2(x^{2} -2x)=2[/tex]
[tex]2(x^{2} -2x+1)=2+2[/tex]
[tex]2(x^{2} -2x+1)=4[/tex]
Rewrite as perfect squares
[tex]2(x-1)^{2}=4[/tex] -----> this is the answer
The vertex is the point (1,-4)
A garden has an area of 240 ft. Its length is 8 ft more than its width. What are the dimensions of the
garden?
Answer:
w=12
l=20
Step-by-step explanation:
The area can be found using the following equation:
[tex]A=lw[/tex]
Given the information provided, we are also told the following:
[tex]l=w+8[/tex]
Therefore, we can plug in our length and our area:
[tex]240=w(w+8)\\240=w^2+8w\\\\w^2+8w-240=0[/tex]
We can solve by using the quadratic formula.
[tex]w=\frac{-8+\sqrt{8^2-4(1)(-240)} }{2(1)}=12 \\\\[/tex]
w=12, so w+8=20.
The average car sold from Dealership A is $25,700. If the sales person receives 1.5% commission on the price of the car, how much commission is made on average per car sold?
Answer:
385.5 USD
Step-by-step explanation:
If an average car is sold for 25,700 USD, and the sales person gets 1.5% commission of it, we can easily get to the amount of money that the sales person managed to get from each sale.
The 25,700 should be divided by 100, as that is number of total percentage:
25,700 / 100 = 257
So we have 1% being 257 USD, but we need 1.5%, so we should multiple the 257 USD by 1.5%:
257 x 1.5 = 385.5
So we get a result of 385.5 USD, which is the amount the sales person makes from commissions on average per sold car.
Multiply (9-4i)(2+5i)
(9 - 4i)(2 + 5i)
To solve this question you must FOIL (First, Outside, Inside, Last) like so
First:
(9 - 4i)(2 + 5i)
9 * 2
18
Outside:
(9 - 4i)(2 + 5i)
9 * 5i
45i
Inside:
(9 - 4i)(2 + 5i)
-4i * 2
-8i
Last:
(9 - 4i)(2 + 5i)
-4i * 5i
-20i²
Now combine all the products of the FOIL together like so...
18 + 45i - 8i - 20i²
***Note that i² = -1; In this case that means -20i² = 20
18 + 45i - 8i + 20
Combine like terms:
38 - 37i
^^^This is your answer
Hope this helped!
~Just a girl in love with Shawn Mendes
what is the area of a rectangle that is 3/5 of a meter long and 7/12 of a meter long
Answer:
7/20 m^2
Step-by-step explanation:
A = l*w
=3/5 * 7/12
Multiplying the numerators
3*7 =21
Multiplying the denominators
5*12= 60
Putting the numerator over the denominator
21/60
Divide the top and bottom by 3
7/20
Answer:
7/20
Step-by-step explanation:
In ΔBCA, CA = 15 cm, CF = 7 cm, BH = 3 cm. Find the perimeter of ΔBCA.
25 cm
35 cm
36 cm
46 cm
Answer:
The perimeter of the triangle is equal to 36 cm
Step-by-step explanation:
we know that
The inscribed circle contained in the triangle BCA is tangent to the three sides
we have that
BF=BH
CF=CG
AH=AG
step 1
Find CG
we know that
CF=CG
so
CF=7 cm
therefore
CG=7 cm
step 2
Find AG
we know that
CA=AG+CG
we have
CA=15 cm
CG=7 cm
substitute
15=AG+7
AG=15-7=8 cm
step 3
Find AH
Remember that
AG=AH
we have
AG=8 cm
therefore
AH=8 cm
step 4
Find BF
Remember that
BF=BH
BH=3 cm
therefore
BF=3 cm
step 5
Find the perimeter of the triangle
P=AH+BH+BF+CF+CG+AG
substitute the values
P=8+3+3+7+7+8=36 cm
The perimeter of ΔBCA (triangle BCA) is 36 cm
Perimeter of a triangle
The perimeter of a triangle is the sum of the length of the three sides.
The inscribed circle contained in the triangle BCA is tangent to the three sides
Therefore,
BF = BH = 3 cm
CF = CG = 7 cm
AH = AG = 15 - 7 = 8 cm
Therefore,
perimeter = CA + BC + BA
perimeter = 15 + 3 + 7 + 3 + 8
Therefore,
perimeter = 15 + 10 + 11
perimeter = 15 + 21
perimeter = 36 cm
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how many solutions does the following equation have?
13 - |3x-9| = 2
It has _____ solutions
[tex]13 - |3x-9| = 2\\|3x-9|=11\\3x-9=11\vee 3x-9=-11\\3x=20 \vee 3x=-2\\x=\dfrac{20}{3} \vee x=-\dfrac{2}{3}[/tex]
TWO
Answer:
2
Step-by-step explanation:
[tex]13-|3x-9|=2[/tex]
Subtract 13 on both sides.
[tex]-|3x-9|=2-13[/tex]
Simplify right hand side.
[tex]-|3x-9|=-11[/tex]
Take the opposite of both sides (also known as multiply both sides by -1).
[tex]|3x-9|=11[/tex].
Let u=3x-9.
Since we have |u|=positive, we will have two solutions for x.
If we had |u|=negative, we will have no solutions for x.
If we had |u|=0, we would have one solution for x.
A box contains 90 coins, only dimes and nickels. The amount of money in the box is $6.00. How many dimes and how many nickels are in the box?
The number of dimes is
The number of nickels is
Answer:
60 nickles and 30 dimes
Step-by-step explanation:
60 $0.05=3.00
30 $.10=3.00
60+30=90
In the box, there are 30 dimes and 60 nickels, as determined by solving a system of equations based on the total number of coins and their value.
Explanation:The box contains both dimes and nickels, totaling an amount of money of $6.00. Because a dime is worth $0.10 and a nickel is worth $0.05, we can set up a system of equations to solve this problem.
Let's denote the number of dimes as x and the number of nickels as y. Thus, our equations are x + y = 90 (since the total number of coins is 90) and 0.10x + 0.05y = 6 (since the total value of the coins is $6.00).
Solving these equations will give us the number of dimes and nickels in the box. Doubling the second equation gives us 0.20x + 0.10y = 12. We can subtract the first equation from this to solve for x, giving us x = 30. Substituting x=30 into the first equation, y = 90 - 30, so y = 60. So, there are 30 dimes and 60 nickels in the box.
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Sheila is looking at some information for the obstacle course she is interested in completing. The x-coordinate is the number of the obstacle, while the y-coordinate is the average time to complete the obstacle, measured in minutes.
(1, 8.25), (2, 9.075), (3, 9.9825), (4, 10.98075)
Help Sheila use an explicit formula to find the average time she will need for the 8th obstacle.
f(8) = 8.25(1.1)^8; f(8) = 17.685
f(8) = 8.25(1.1)^7; f(8) = 16.077
f(8) = 1.1(8.25)^7; f(8) = 2861345
f(8) = 1.1(8.25)^8; f(8) = 23606102
Answer:
f(8) = 8.25(1.1)^7; f(8) = 16.077
Step-by-step explanation:
In order to calculate the explicit formula we need to look at the y coordinates. All the options list the formula of a Geometric Sequence, so we will find which sequence defines the given coordinates:
The sequence is:
8.25, 9.075, 9.9825, 10.98075
f(1) = First term of the Sequence = 8.25
r = Common Ratio = Ratio of two consecutive terms = [tex]\frac{9.075}{8.25}[/tex] = 1.1
The explicit formula for a geometric sequence is:
[tex]f(n)=f(1)(r)^{n-1}[/tex]
Using the values, we get:
[tex]f(n)=8.25(1.1)^{n-1}[/tex]
For 8th term, we have to replace n by 8:
[tex]f(8)=8.25(1.1)^{8-1}\\\\ f(8)=8.25(1.1)^{7} \\\\ f(8)=16.077[/tex]
So, second option gives the correct answer: f(8) = 8.25(1.1)^7; f(8) = 16.077
Answer:
B // f(8) = 8.25(1.1)^7; f(8) = 16.077
Step-by-step explanation:
I'm Pretty Sure She's Got It ^^^
Make y the subject of:
X=5y+4/2y-3
Step-by-step explanation:
I have answered ur question
To make y the subject, distribute and simplify the equation, then isolate y on one side by performing the necessary operations.
Explanation:To make y the subject of the equation X = 5y + 4/2y - 3, we need to isolate y on one side of the equation.
Distribute the 5 to both terms within the parentheses: X = 5y + 2 - 3.Combine the constants: X = 5y - 1.Move the constant term to the other side of the equation by subtracting 1 from both sides: X + 1 = 5y.Divide both sides of the equation by 5: (X + 1)/5 = y.Therefore, y = (X + 1)/5 is the solution.
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A bank features a savings account that has an annual percentage rate of r=5.2% with interest compounded quarterly. Marcus deposits $8,500 into the account.
The account balance can be modeled by the exponential formula S(t)=P(1+rn)^nt, where S is the future value, P is the present value, r is the annual percentage rate written as a decimal, n is the number of times each year that the interest is compounded, and t is the time in years.
(A) What values should be used for P, r, and n?
P= _____ , r=______ , n=________
(B) How much money will Marcus have in the account in 7 years?
Answer = $______ .
Round answer to the nearest penny.
Answer:
Part A)
[tex]P=\$8,500\\ r=0.052\\n=4[/tex]
Part B) [tex]S(7)=\$12,203.47[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]S(t)=P(1+\frac{r}{n})^{nt}[/tex]
where
S is the Future Value
P is the Present Value
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
Part A)
in this problem we have
[tex]P=\$8,500\\ r=5.2\%=5.2/100=0.052\\n=4[/tex]
Part B) How much money will Marcus have in the account in 7 years?
we have
[tex]t=7\ years\\ P=\$8,500\\ r=0.052\\n=4[/tex]
substitute in the formula above
[tex]S(7)=8,500(1+\frac{0.052}{4})^{4*7}[/tex]
[tex]S(7)=8,500(1.013)^{28}[/tex]
[tex]S(7)=\$12,203.47[/tex]
In this problem, we find that Marcus should use the values P = $8,500, r = 0.052 and n = 4 for the given savings account. After calculating, we conclude that Marcus would have approximately $11,713.69 in the account after 7 years.
Explanation:This problem involves the concept of compound interest in mathematics. Let's break it down:
For part (A), we are given that the initial deposit or the present value P is $8,500, the annual percentage rate, r, is 5.2% (but for the formula we need to use this as a decimal, so divide by 100: r = 0.052), and the interest is compounded quarterly, or 4 times a year so n = 4.For part (B), we need to find out the future value S of the deposit after 7 years.We use the formula S(t)=P(1+rn)^(nt):
S(7) = 8500(1 + 0.052/4)^(4*7)
By calculating the above, we find the balance after seven years to be approximately $11,713.69 when rounded to the nearest penny.
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Select the correct answer from each drop-down menu.
A rope is cut into three pieces. The lengths are given as 2ab(a − b), 3a2(a + 2b), and b2(2a − b).
The expression representing the total length of the rope is .
If a = 2 inches and b = 3 inches, the total length of the rope is inches.
math
Answer:
1) [tex]3 a^3 + 8 a^2 b - b^3[/tex]
2) 93 inches
Step-by-step explanation:
1) We know that the lenghts are given by these expressions:
[tex]2ab(a - b)\\\\3a^2(a + 2b)\\\\b^2(2a - b)[/tex]
Then, we need to add them in order to find the expression that represents the total length of the rope:
- Apply Distributive property.
- Add the like terms.
Then:
[tex]=2ba^2-2ab^2+3a^3+6ba^2+2ab^2-b^3\\\\=3 a^3 + 8 a^2 b - b^3[/tex]
2) Knowing that:
[tex]a=2in\\\\b=3in[/tex]
We must substitute these values into [tex]3 a^3 + 8 a^2 b - b^3[/tex] in order to caculate the total lenght of the rope. This is:
[tex]3 (2in)^3 + 8 (2in)^2 (3in) - (3in)^3=93in[/tex]
Audrey has .x pounds of red grapes and y pounds of
green grapes. She has less than 5 pounds of grapes in
Which are reasonable solutions for this situation?
Check all that apply.
(-1,2)
(1.3.5)
(2, 2)
(4.5, 0.5)
(5,0)
Answer: (1,3,5) & (2,2)
Step-by-step explanation:
Which functions has the graph shown?
Answer:
C.
Step-by-step explanation:
Let's identify some points here that are on the graph:
(0,0), (pi/2,-1), (pi,0).
Let's see if this is enough.
We want to see which equation holds for these points.
Let's try A.
(0,0)?
y=cos(x-pi/2)
0=cos(0-pi/2)
0=cos(-pi/2)
0=0 is true so (0,0) is on A.
(pi/2,-1)?
y=cos(x-pi/2)
-1=cos(pi/2-pi/2)
-1=cos(0)
-1=1 is false so (pi/2,-1) is not on A.
The answer is not A.
Let's try B.
(0,0)?
y=cos(x)
0=cos(0)
0=1 is false so (0,0) is not on B.
The answer is not B.
Let's try C.
(0,0)?
y=sin(-x)
0=sin(-0)
0=sin(0)
0=0 is true so (0,0) is on C.
(pi/2,-1)?
y=sin(-x)
-1=sin(-pi/2)
-1=-1 is true so (pi/2,-1) is on C.
(pi,0)?
y=sin(-x)
0=sin(-pi)
0=0 is true so (pi,0) is on C.
So far C is winning!
Let's try D.
(0,0)?
y=-cos(x)
0=-cos(0)
0=-(1)
0=-1 is not true so (0,0) is not on D.
So D is wrong.
Okay if you do look at the curve it does appear to be a reflection of the sine function.
Audrey has x pounds of red grapes and y pounds of
green grapes. She has less than 5 pounds of grapesin
all.
Which are reasonable solutions for this situation?
Check all that apply.
D(-1,2)
(1.3.5)
D (2, 2)
(4.5, 0.5)
(5,0)
Answer:
(2,2)
Step-by-step explanation:
can someone plz help me plz
Answer:
[tex]\large\boxed{C.\ y=2+x^4}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of linear function:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
============================
[tex]A.\\\\9y+3=0\qquad\text{subtract 3 from both sides}\\\\9y=-3\qquad\text{divide both sides by 9}\\\\y=-\dfrac{3}{9}\\\\y=-\dfrac{1}{3}\to m=0,\ b=-\dfrac{1}{3}[/tex]
[tex]B.\\\\y-4x=1\qquad\text{add}\ 4x\ \text{to both sides}\\\\y=4x+1\to m=4,\ b=1[/tex]
[tex]C.\\\\y=2+x^4\qquad\text{nonlinear, because}\ x\ \text{is in fourth power}[/tex]
[tex]D.\\\\x-2y=7\qquad\text{subtract}\ x\ \text{from both sides}\\\\-2y=-x+7\qquad\text{divide both sides by (-2)}\\\\y=\dfrac{1}{2}x-\dfrac{7}{2}\to m=\dfrac{1}{2},\ b=-\dfrac{7}{2}[/tex]
[tex]E.\\\\\dfrac{x}{y}+1=2\qquad\text{subtract 1 from both sides}\\\\\dfrac{x}{y}=1\to y=x\to m=1,\ b=0[/tex]
Which is the graph of the equation y = -3x- 1
Neither of those two graphs do the trick, but if I saw the rest of the answer choices, then I would be happy to assist you.
John was 40 years old in 1995 while his father was 65.In what year was John exactly half his father's age?
Answer:
1980.
Step-by-step explanation:
John was born in 1995 - 40 = 1955.
His father was born in 1995 - 65 = 1930.
Let x be Johns age and his father 2x
1955 + x = 1930 + 2x
1955 - 1930 = 2x - x
x = 25
So the year is 1955 + 25 = 1980..
In that year John was 25 and his father was 50.
Today, Jana picked 15 flowers from her garden. This is 5 more than what she picked yesterday. How many flowers did Jana pick yesterday? F. 10. G. 20. H. 25. I. 30.
Answer:
F. 10
Step-by-step explanation:
She had 15 flowers today
So if she had 5 more than yesterday
You subtract the 5 to get how much she had yesterday
15-5=10
Answer:
F. 10
Step-by-step explanation:
Today: 15 flowers
: 5 more than yesterday
more than means add
15 = 5+ yesterday
Subtract 5 from each side
15-5 = 5+ yesterday -5
10 = yesterday