Using FOIL (First, Outer, Inner, Last):
(x+3)(x-4)
FIRST: multiply x times x to get x^2.
OUTER: multiply x times -4 to get -4x.
INNER: multiply 3 times x to get 3x.
LAST: multiply 3 times -4 to get -12.
Your expression now looks like:
x^2-4x+3x-12
Combine like terms.
x^2-x-12
The answer is D. x^2-x-12.
I hope this helps :)
Which of the following sets of ordered pairs in the form (x,y) represent a function of x?
3 points
{(2,4), (-2,4), (5,3), (7,4)}
{(3,5),(-1,1),(3,2), (-6,2)}
{(9,2), (-3,4), (-3,1), (7,-4)}
{(5,1),(-2,-1),(5,-4), (6,1)
Show work please
Answer:
Option A is right.
Step-by-step explanation:
For answering this question we must understand what is a function.
A function is different from mapping.
Mapping is just a subset of AxB where A and B are two sets.
But function is constrained to the point that elements of I set will have unique image in second set.
We find From the options
in option A, each of 2,-2, 5 and 7 have unique images. Hence it is a function.
But in option B,, we find that 3 has two images 5 and 2. i.e. 3 does not have unique image. Hence not a function.
Similarly in option C,, we find that -3 has two images 4 and 1. i.e. -3 does not have unique image. Hence not a function
and in option D,, we find that 5 has two images 1 and -4. i.e. 5 does not have unique image. Hence not a function.
Only first option is a function.
The graph of function g is a vertical stretch of the graph of function f by a factor of 3. Which equation describes function g?
A. g(x)=3f(x)
B. g(x)=f(3x)
C. g(x)=f(x3)
D. g(x)=13f(x)
What transformation takes the graph of f(x)=3x+8 to the graph of g(x)=3x+6 ?
A. translation 2 units up
B. translation 2 units left
C. translation 2 units down
D. translation 2 units right
Answer:
Step-by-step explanation:
A vertical stretch by a factor of k means that the point (x, y) on the graph of f (x) is transformed to the point (x, ky) on the graph of g(x), where k <1.
If k =1, then same graph we obtain and if k>1 we get a vertically shrink graph.
In our question, there is a vertical stretch of 3. This means new graph would have points as (x,y/3)
i.e. instead of f(x) = y, we have now f(x) = y/3
So transformation is g(x) = 3f(x)
Option A is correct.
2) Here f(x) = 3x+8 is transformed to g(x) =3x+6
i.e. y intercept is reduced by 2 units. Hence there is a translation of 2 units down.
I did not have the answer to the second question but here is the first.
Which expression is equivalent to 46 ⋅ 4−8?
42
414
That is 176 my friend not 42 or 414!
Herky was given the following system of equations to solve.
3x-2y=17
x-3y=1
What is the solution to the system?
(2,7)
(20/7,67/7)
(7,2)
(67/7,20/7)
Answer:
Option 3 (7,2) is right answer.
Step-by-step explanation:
Given two equations
3x-2y=17 ... i
x-3y=1 ... ii
We can solve this by elimination.
coefficients of x are 3 and 1 with LCD = 3
Hence multiply ii equation by 3
3x-9y = 3 ... iv
3x-2y = 17 ... i
Subtract i from iv
-7y = -14
Divide by -7
y =2
Substitute in ii
x-3(2) = 1
x=7
Hence solution is (7,2)
Verify:
We can verify our solution by substituting in i and ii.
3(7)-2(2) = 17 and 7-6 =1
Verified
you invest $2,500 in an account that grows 5% each year. what will be your investment amount after 6 years?
a. $2,699.72
b. $3,374.65
c. $15,769.07
d. $13,272.96
Answer: b. $3,374.65
Step-by-step explanation:
The exponential equation of growth (continuously) is given by :-
[tex]y=Ae^{rx}[/tex], where A is the initial amount, r is the rate of growth ( in decimal) and x is the time period.
Given : You invest $2,500 in an account that grows 5% each year.
i.e. A= $2,500 and r= 5%=0.05
Then, the equation model this situation will be :-
[tex]y=2500e^{0.05x}=2500(1.05)^x[/tex]
Now, At x= 6
[tex]y=2500e^{0.05\times6}\\\\\Rightarrow\ y=2500e^{0.3}=3374.64701894\approx3374.65[/tex]
Hence, the investment amount after 6 years will be $3,374.65.
The amount of the investment after 6 years is $3,374.65
How to determinet the amount after 6 yearsFrom the question, we have the following parameters that can be used in our computation:
Inital value, a = $2500
Rate of increase, r = 5%
Using the above as a guide, we have the following:
The function of the situation is
f(x) = a * (1 + r)ˣ
Substitute the known values in the above equation, so, we have the following representation
f(x) = 2500 * (1 + 5%)ˣ
So, we have
f(6) = 2500 * (1 + 5%)⁶
Evaluate
f(6) = $3,374.65
Hence, the amount is $3,374.65
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A local grocery store, a 16 ounce bottle of apple juice cost $3.20. What is the cost of the apple juice per ounce?
answer=3.20/16=0.20 is cost per ounce
Fill in the blank.
The ____ is used to determine the left-hand and right-hand behavior of the graph of a polynomial function.
Choices:
Vertical line test (wrong btw)
Horizontal line test (wrong too)
Leading coefficient test
Distinct zero test
Even degree test
Polynomial test
Behavior test
Odd degree test
The ____ is used to determine the left-hand and right-hand behavior of the graph of a polynomial function.
When largest exponent of the polynomial is even and leading coefficient is positive , then left hand and right hand ends of the graph goes up
When largest exponent of the polynomial is even and leading coefficient is negative , then left hand and right hand ends of the graph goes down
When largest exponent of the polynomial is odd and leading coefficient is positive , then left hand graph goes down and right hand ends of the graph goes up
When largest exponent of the polynomial is odd and leading coefficient is negative , then left hand graph goes up and right hand ends of the graph goes down
Hence, Leading coefficient test is used to determine the left-hand and right-hand behavior of the graph of a polynomial function.
The leading coefficient test is used to determine the left-hand and right-hand behavior of the graph of a polynomial function.
Explanation:The correct choice to fill in the blank is Leading coefficient test.
The leading coefficient, which is the coefficient of the highest power term in a polynomial function, helps determine the behavior of the graph. If the leading coefficient is positive, the graph will have an upward (right-hand) behavior, while if the leading coefficient is negative, the graph will have a downward (left-hand) behavior.
For example, in the polynomial function f(x) = 3x^3 - 2x^2 + 5x - 1, the leading coefficient is 3. Therefore, the graph of this function will have an upward (right-hand) behavior.
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What is the value of the correlation coefficient r of the data set? Please Help!!!?
Will give Brainliest answer :)
I am so lost
Options:
-1
-0.81
0.66
0.81
The formula for the correlation coefficient is quite messy. I suggest checking some websites discussing this and am also attaching the formula how to calculate it by hand (the ∑'s mean summation over all the elements listed.
But unless your teacher does not allow using online calculators, you can use them. I used python's function to process the data in the table and the result is approximately -0.81. So that's your answer.
Negative value like -0.81 means that the variables x and y are quite "anit-correlated" meaning the value behave like opposites: when x is small, y tends to be large, and vice versa.
Answer:
-0.81
Step-by-step explanation:
x y xy
12 6 72
13 21 273
14 14 196
6 28 168
25 2 50
31 1 31
1 67 67
Total 857
Mean 14.57142857 19.85714286 214.25
Std dev 10.37396007 23.06099572
Cov (x,y) -75.09693878
Correlation coefficient is obtained by the formula
r = {E(xy)-E(x)E(y)}/(std dev x )(std dev y)
From the data we find x bar=14.57 and y bar = 19.86
STd dev of x = 10.37 and y = 23.06
E(xy) = average of product x and y = 214.25
Hence substitute to get r = -0.81
consider the type of equations
5x+y=31
-3x+4y=37
solve the first equation as y in terms of x
like y=.....
You just have to isolate the y term for both equations so the first one would be y=31-5x because you have to subtract x from both sides.
The second one would be y=3+3x and all of that over 4 because to get the y isolated, you have to add 3x to both sides and then divide by 4 to get 4 y to just be y.
Determine the sum of the first 9 terms in the geometric series where r = -0.25 and a1 = 256
A) -256
B) -204.8
C) 204.8
D) 0
Answer:b
Step-by-step explanation:
Apply. Streets A and L run parallel to each other. Boulevard N forms a 75 degree angle with Street L south of (below) their intersection. What angle does Boulevard N make with Street L north of (above) their intersection. Justify your answer
Answer:
There are two street A and L which run parallel to each other.
Suppose the point of intersection of Boulevard N and Street L is 75°south of below their intersection.
Let their point of intersection is S.
Taking a point P and Q on opposite side of L and R and T on opposite side of Line N,
then either ∠PSR=75° or ∠ QSR=75°
Case 1. If ∠PSR=75°,
then ∠PSR + ∠PST=180°[ linear pair]
75°+ ∠PST=180°
∠PST=180°- 75°
∠PST=105°
∠QST = ∠PSR=75° [ Vertically opposite angles]
2. If ∠ Q S R =75°
∠ Q S R + ∠ Q S T=180°[linear pair]
75° +∠ Q S T=180°
∠ Q S T=180°-75°
∠ Q S T= 105°
∠Q SR = ∠P ST = 75° [ Vertically opposite angles]
MATH PLEASE HELP!
Identify the vertex and the y-intercept of Y=-2(x+3)^2+2the graph of the function .
A.vertex: (−3, 2); y-intercept: −16
B.vertex: (−3, −2); y-intercept: 11
C.vertex: (3, 2); y-intercept: −16
D. vertex: (3, −2); y-intercept: −18
Identify the vertex and the y-intercept of the graph of the function Y=-2(x+2)^2+2
A.vertex: (−2, 2); y-intercept: −6
B.vertex: (2, 2); y-intercept: −6
C. vertex: (−2, −2); y-intercept: 6
D. vertex: (2, −2); y-intercept: −8
A and A
the equation of a parabola in vertex form is
y = a(x - h)² + k
where ( h, k ) are the coordinates of the vertex and a is a multiplier
y = - 2(x + 3)² + 2 is in this form
with vertex = ( - 3, 2)
To find the y-intercept let x = 0
y = - 2(3)² + 2 = - 18 + 2 = - 16
Similarly
y = - 2(x + 2)² + 2 is in vertex form
vertex = ( - 2 , 2)
x = 0 : y = - 2(2)² + 2 = - 8 + 2 = - 6 ← y- intercept
An appliance repair service charges a flat fee of $75 per service call with an additional $55 per hour. If h represents the number of hours it takes to do the repair, which function models this situation?
The function that models the total cost of the repair service as a function of the number of hours, [tex]\( h \),[/tex] is given by: [tex]\[ C(h) = 75 + 55h \][/tex]
In this situation, the appliance repair service charges a fixed amount of [tex]75[/tex] for making a service call, regardless of how long the repair takes. This is the flat fee component of the cost. Additionally, the service charges [tex]55[/tex] for each hour of work performed by the technician. This is the hourly rate component of the cost.
To model the total cost as a function of the number of hours [tex]h[/tex] that the repair takes, we start with the flat fee of [tex]75[/tex]. We then add the product of the hourly rate [tex]55\\[/tex] and the number of hours [tex]\( h \)[/tex]. This gives us the total cost function:
[tex]\[ C(h) = \text{Flat Fee} + (\text{Hourly Rate} \times h) \][/tex]
[tex]\[ C(h) = 75 + 55h \][/tex]
Here, [tex]\( C(h) \)[/tex] represents the total cost in dollars as a function of the number of hours [tex]\( h \)[/tex] spent on the repair. The term [tex]\( 75 \)[/tex] is the fixed cost, and [tex]\( 55h \)[/tex] represents the variable cost that depends on the number of hours worked.
This linear function correctly models the total cost of the repair service based on the given rates and the time spent on the repair.
A rectangle measures 14cm x 7cm what is the area
area = 98 cm²
the area of a rectangle = length × width
here length = 14 and width = 7
area = 14 × 7 = 98 cm²
How many possible numbers of solutions are there to the system of equations? 0 1 2 3 4 infinite
Answer:
0,1 and 2 on edg
Step-by-step explanation:
3/2n-8/3=-29/12
Please show work
please help asap 25 pts
[tex]\text{The formula of a perimeter of a rectangle:}\\\\P=2(w+l)\\\\\text{we have}\\w:l=3:2\to w=\dfrac{3}{2}l,\ P=55\ cm\\\\\text{substitute}\\\\55=2\left(\dfrac{3}{2}l+l\right)\\\\55=2\cdot\left(\dfrac{3}{2}l+\dfrac{2}{2}l\right)\\\\55=2\cdot\dfrac{5}{2}l\\\\55=5l\ \ \ \ \ |:5\\\\l=11\ cm\\\\w=\dfrac{3}{2}\cdot11=\dfrac{33}{2}=16.5\ cm\\\\Answer:\ b.\ 11\ cm,\ 11\ cm,\ 16.5\ cm,\ 16.5\ cm[/tex]
The answer is B hope this helped
The first four numbers of the pattern are shown below, what would be the 6th number in the pattern.
0.08,0.4,2,10
A.450
B.250
C.5
D.50
The 6th number is in the pattern 0.08, 0.4, 2, 10 is 250 because the sequence represents a geometric sequence option (B) is correct.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is given that:
The first four numbers of the pattern are shown below:
0.08, 0.4, 2, 10
The above sequence represents the geometric sequence.
The common ratio = second term/first term
The common ratio = 0.4/0.08
The common ratio = 5
The nth term of the geometric sequence:
a(n) = a(r)ⁿ⁻¹
a(n) = 0.08(5)ⁿ⁻¹
Plug n = 6 in the above expression:
a(6) = 0.08(5)⁶⁻¹
After calculating:
a(6) = 250
Thus, the 6th number is in the pattern 0.08, 0.4, 2, 10 is 250 because the sequence represents a geometric sequence.
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what's the numerator of the following expression u/v+9/v=?/v
The correct answer is u/v+9/v= 9u/v
The formula for the area of a square is s2, where s is the side length of the square. What is the area of a square with a side length of 6 centimeters? Do not include units in your answer
36
area of square = s²
given s = 6 , then
area = 6² = 36
Length of a side is considered to calculate area of a square. The area of a square can be defined as the number of square units needed to fill a square.
The formula to calculate Area of square is:
[tex]\rm Area\: of\:square = \rm side^2[/tex]
We need to calculate area of a square with sides [tex]\rm\\6 \:centimetres[/tex].
As per above stated formula:
Area of square is square of length of its sides.
[tex]\begin{aligned}\rm Area\:of\: square &= \rm side^2\\&= 6^2\\&= 36\end[/tex]
Therefore, the area of square with side 6 is 36.
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15 POINTS!!!!! PLEASE ANSWER AS SOON AS POSSIBLE
Given: AB = AC
AH = AK
m∠BAK = m∠CAH
Prove: m∠K = m∠H
△BAH≅△_____ by reason_______
In △BAH and △CAK
AB = AC (Given congruent sides of triangle)
m∠BAK = m∠CAH ( Given congruent angles)
AH = AK (Given congruent sides of triangle)
Therefore, triangle △BAH congruent to triangle △CAK.
△BAH ≅ △CAK by (Side Angle Sngle or SAS triangle congruency postulate).
Therefore, m∠K = m∠H (Congurent parts of the congruent triangles are congruent).
A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. Choose a possible description for the rows and columns.
A) Column: In a Band, Play a Sport; Row: Not in a Band, Do Not Play a Sport
B) Column: Not in a Band, Play a Sport; Row: In a Band, Do Not Play a Sport
C) Column: In a Band, Do Not Play a Sport; Row: Not in a Band, Play a Sport
D) Column: In a Band, Not in a Band; Row: Play a Sport, Do Not Play a Sport
Answer:
D) Column: In a Band, Not in a Band; Row: Play a Sport, Do Not Play a Sport
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
Number of students in the band = 48
Number of students both play in the band and play a sport = 24
Number of students who are not in band and do not play a sport = 22
Total number of students = 80
so, we will make a table:
In a band Not in a band
Play a sport 24 10
Don't play a sport 24 22
-------------------------------------------------------------------------------
Total 48 (80-48) = 32
So, Column: In a Band, Not in a Band; Row: Play a Sport, Do Not Play a Sport.
Hence, Option 'D' is correct.
A ship has 1400 people on board. There are 200 more adults than children. How many children are on the ship?
PLEASE HELP!!!!!!!!!!
So,
1400 people in total. Though, subtract 200 for the amount of extra adults. This makes 1200. Divide that by two. You get 600
You need to add 200 to the 600 to get the amount of adults. The amount of adults on board is 800.
The amount of children on board is 600.
600 plus 800 equals 1400, it makes sense. :P
To find the number of children on the ship, we can set up an equation based on the given information and solve for x. The number of children can be represented as x, and the number of adults can be represented as x + 200.
Explanation:Let's use x to represent the number of children on the ship. Since there are 200 more adults than children, the number of adults can be represented as x + 200. We know that the total number of people on board is 1400, so we can set up the equation: x + (x + 200) = 1400.
Combining like terms, we get 2x + 200 = 1400. Subtracting 200 from both sides gives us 2x = 1200. Dividing both sides by 2, we find x = 600.
Therefore, there are 600 children on the ship.
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Mary has 10$ in savings she owes her parents 50$ she also gets 25$ for her birthday from her grandmother. Dose Mary have enough money to pay her parents what she owes them how much money does she need
If red oak lumber weighs 63 pounds per cubic foot, how much does one cord of red oak weigh? (A cord is a measurement for bulk wood—8 feet long, 4 feet wide, and 4 feet high.)
A. 8,192 pounds
B. 7,936 pounds
C. 8,064 pounds
D. 4,032 pounds
Answer: Option C. 8,064 pounds
Solution:
Unit weight: U=63 pounds/foot^3
Total Weight: W=?
W=U*V
Volume: V
Length: l=8 feet
Width: w=4 feet
Height: h=4 feet
V=l*w*h
Replacing the knwon values in the formula above:
V=(8 feet)*(4 feet)*(4 feet)
V=128 feet^3
Replacing in the formula of total Weight:
W=U*V
W=(63 pounds/foot^3)*(128 feet^3)
W=8,064 pounds
Final answer:
To calculate the weight of one cord of red oak, multiply the cord's volume (128 cubic feet) by the density of red oak (63 pounds/cubic foot), which results in 8,064 pounds.
Explanation:
To answer this question, we will calculate the weight of one cord of red oak by multiplying the volume of a cord by the weight per cubic foot.
Determine the volume of a cord: 8 feet long, 4 feet wide, and 4 feet high. Volume = length × width × height = 8 ft × 4 ft × 4 ft = 128 cubic feet.Multiply the volume by the weight per cubic foot: 128 cubic feet × 63 pounds/cubic foot = 8,064 pounds.Therefore, one cord of red oak weighs 8,064 pounds, which matches option C.
I need help with this is there anyone
Which is the graph of the sequence defined by the function f(x + 1) = f(x) if the initial value of the sequence is 108?
answer is
f (x) = 108. (2/3)x
Answer:
The correct graph is graph C
Step-by-step explanation:
Given that a sequence defined by the function f(x + 1) =[tex]\frac{2}{3}[/tex] f(x)
Also given that initial value is 108
i.e. f(0) = 108
Applying the recurrence formula given we get
f(0+1) = 2/3 f(0) = 2/3 (108) = 72
Hence (1,72) should be next point
Now we have
f(2) = f(1+1) = 2/3 f(1) = 2/3 (72) =48
(2,48) is next point
f(3) = f(2+1) = 2/3 f(2) = 2/3 (48) = 32
(3,32) is the next point
The graph covering all these points is the graph C
Hence answer is graph C
Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink. What fraction of the bouquet is pink roses? There are 12 roses in a dozen.
Answer:
Angelica's bouquet has 7/12 pink roses.
Step-by-step explanation:
A dozen is defined to be a set of 12 in number or group pf anything. Here, in this case we have roses so a dozen of roses means '12 roses'.
5 of the roses in the bouquet are white roses, so the fraction of white roses will be 5 divided by the total number of roses i.e. 12:
White roses = [tex]\frac{5}{12}[/tex]
Rest of the roses are pink, so we can simply subtract 5 from 12 to get the number of roses which will be 12 - 5 = 7
Or
we can subtract the fraction of white roses from 1 to get the fraction of pink roses in the bouquet:
Pink roses = [tex]1 - \frac{5}{12}[/tex] = [tex]\frac{7}{12}[/tex]
Patrick was born with 1/7 of his faults and acquired the rest during his teenage years. if we was born with 326 faults, how many does he have in total?
Remark
How does this poor soul survive?
Solution
Let the number of faults he has in his teens = x
1/7 of (of means multiply) those faults were there at birth.
1/7 x = 326 Solve for x by multiplying by 7
7* (1/7 x) = 326 * 7
x = 2282 is the number of faults Patrick has. Answer
Leo has 32 coins and wants to make equal groups with 8 coins each.What does the answer tell him?
There would be 4 groups of 8 coins. 32/8=4 Hope I could help!!!