Answer:
[tex]\boxed{-4.1x-11y}[/tex]
Step-by-step explanation:
[tex](-12.7y-3.1x) + 5.9y-(4.2y + x)[/tex]
Expand brackets.
[tex]-12.7y-3.1x+ 5.9y-4.2y - x[/tex]
Combining like terms.
[tex]- x-3.1x-12.7y+ 5.9y-4.2y[/tex]
[tex]-4.1x-11y[/tex]
Answer:
[tex] \boxed{\red{ - 11y - 4.1x}}[/tex]
Step-by-step explanation:
[tex] (- 12.7y - 3.1x) + 5.9y - (4.2y + x) \\ - 12.7y - 3.1x + 5.9y - 4.2y - x \\ - 12.7y + 5.9y - 4.2y- 3.1x - x \\ = - 11y - 4.1x[/tex]
Can any kind soul help me
Answer:
a) 4.50m/s²
b) v= 21
c) 11.25m/s
Step-by-step explanation:
a) rate of change of speed in first 2 seconds
= gradient of graph from t=0s to t=2s
The two points are (0,0) and (2,9).
[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]
Rate of change of speed
[tex] = \frac{9 - 0}{2 - 0} \\ = \frac{9}{2} \\ = 4.50m/ {s}^{2} [/tex]
Total distance= area under graph
Distance travelled for first 6s
= area of traingle +area of rectangle
= ½(2)(9) +(6-2)(9)
= 9 + 4(9)
= 9 +36
= 45m
Distance travelled from t=6s to t=12s
= 135 -45
= 90m
Area under graph from t=6s to t=12s =90
Area of trapezium= 90
½(A +B)(h)= 90
½(9+ v)(6)= 90
3(9 +v)= 90 (simplify)
9 +v= 30 (÷3 throughout)
v= 30 -9
v= 21
c) Average speed
= total distance ÷total time
= 135 ÷12
= 11.25 m/s
The number of bacteria in a culture is increasing according to the law of exponential growth. There are 105 bacteria in the culture after 2 hours and 325 bacteria after 4 hours. (a) Find the initial population. (Round your answer to the nearest whole number.) bacteria (b) Write an exponential growth model for the bacteria population. Let t represent the time in hours. y
a) The number of bacteria in the initial population is 34.
b) The exponential growth model is y = 34 * e^(kt)
Given data:
(a) To find the initial population, we can use the exponential growth formula:
y = A * e^(kt)
Where:
y = population at time t
A = initial population
k = growth rate
t = time
Given that there are 105 bacteria after 2 hours, so plug in these values into the formula:
105 = A * e^(k*2)
Similarly, given that there are 325 bacteria after 4 hours:
325 = A * e^(k*4)
We now have a system of equations:
105 = A * e^(2k)
325 = A * e^(4k)
To solve for A, divide the second equation by the first equation:
325/105 = e^(4k)/e^(2k)
Simplifying further:
325/105 = e^(2k)
Taking the natural logarithm of both sides:
ln(325/105) = ln(e^(2k))
ln(325/105) = 2k
Solving for k:
k = 0.56493
Substitute it back into one of the original equations to solve for A. Let's use the first equation:
105 = A * e^(2k)
Substituting k = ln(325/105) / 2:
105 = A * e^(2 * ln(325/105) / 2)
Simplifying:
105 = A * (325/105)
A = 105 * (105/325)
A ≈ 34 (rounded to the nearest whole number)
Hence, the initial population is approximately 34 bacteria.
(b) Now that we have the initial population, A, and the growth rate, k, we can write the exponential growth model for the bacteria population:
y = 34 * e^(kt)
where t represents the time in hours.
Hence, the exponential equations are solved.
To learn more about exponential growth factor, refer:
https://brainly.com/question/13674608
#SPJ4
An old wheat-grinding wheel in a museum actually works. The sign on the wall says that the wheel has a rotational acceleration of 180 rad/s 2 as its spinning rotational speed increases from zero to 1700 rpm. How long does it take the wheel to attain this rotational speed?
Answer:
It will take 0.989 second to attain this speed
Step-by-step explanation:
In this question, we want to calculate the time it will take for the wheel of the machine to attain the given rotational speed
We proceed as follows;
From the question, we can identify the following parameters
Rotational acceleration of the wheel is, α = 180 rad/s^2
Initial spinning rotational speed of the wheel is, ω= 0 rpm
1 rpm = (1/60) revolution per second = 2π * (1/60) rad/s
Thus,
initial rotational speed ωi = 0 rad/s
Final spinning rotational speed ωf of the wheel is, = 1700 rpm =178.02 rad/s
Now, from the equations of motion (for rotational motions),
ωf = ωi + αt
where t is the time taken by the wheel to attain its final rotational speed.
178.02= 0 + 180 * t
t = 178.02/180
t = 0.989 second
PLEASE HELP
A hire purchase agreement offers gym equipment, with a marked price
$897, for $87 deposit and $46.80 a month payable over 2 years.
Calculate :
a) the total hire-purchase price
b) the amount of
amount of interest charged
Answer: a) $1,210.20 b) $313.20
Step-by-step explanation:
a) $87 down + $46.80(24 months) = $1,210.20 total paid
b) $1,210.20 - $897.00 = $313.20 interest paid
Help :(
Yun was trying to factor 7x^2- 14x. He found that the greatest common factor of these terms was 7x and made an area model:
What is the width of Yun's area model?
Answer:
If the question is saying that length is 7x, then the answer (width) is x-2
URGET PLEASE HELP QUICKLY
Find the constant of variation k for the direct variation. x f ( x ) 0 0 2 –1 4 -2 7 -3.5
Answer: -0.5.
Step-by-step explanation:
The constant of variation k for the direct variation is given by:-
[tex]k= \dfrac{f(x_2)}{x_2}=\dfrac{f(x_1)}{x_1}[/tex]
The given table:
x f( x )
0 0
2 -1
4 -2
7 -3.5
Then,
[tex]k=\dfrac{-1}{2}=\dfrac{-2}{4}=\dfrac{7}{-3.5}=-0.5[/tex]
Hence, the constant of variation k for the direct variation is -0.5.
If a watch store paid $125 per watch for a shipment of watches, and sold all but 15 watches from the shipment for $150 per watch, then, in terms of the number of watches in the shipment, y, what function describes the watch store’s profit, P, from the sales?
A) P(y) = 125(y – 15) – 150y
B) P(y) = 15(125 – y) – 150y
C) P(y) = 150(y – 15) – 125y
D) P(y) = 15(150 – y) – 125y
Answer: C) P(y) = 150(y – 15) – 125y
Step-by-step explanation:
Hi, to answer this question we have to write an equation:
Profit = revenue - cost
Cost: a watch store paid $125 per watch for a shipment of watches
Cost = 125 y
Where y is the number of watches in the shipment
Revenue: sold all but 15 watches from the shipment for $150 per watch
Revenue = 150(y-15)
Profit(y) = 150(y – 15) – 125y
So, the correct option is:
C) P(y) = 150(y – 15) – 125y
Feel free to ask for more if needed or if you did not understand something.
In the figure ABCD is a parallelogram. P, Q, R and S are the midpoint of the sides of the parallelogram. Prove that PQ = RS and QR = PS.
Answer:
ΔRCQ = ΔAPS
QR = PS (CPCTC)
ΔSRD ≅ ΔQPB
PQ = RS (CPCTC)
Step-by-step explanation:
Given that ABCD is a parallelogram, we have;
AD = BC, and DC = AB (Definition of a parallelogram)
AD = AS + SD Given S is midpoint of AD
Similarly,
DC = DR + RC
BC = BQ + QC
AB = AP + PB
RC = DR = AP = PB
BQ = QC = QC = BQ segments on either sides of midpoint
∠BCA = ∠DAB (opposite interior angles of a parallelogram)
ΔRQC ≅ ΔSPA
ΔRCQ = ΔAPS (Side Angle Side SAS rule of congruency)
Therefore, segment QR = segment PS (QR = PS) (Corresponding Parts of Congruent Triangles are Congruent CPCTC)
Similarly we have;
∠CDA = ∠CBA (opposite interior angles of a parallelogram)
ΔSRD ≅ ΔQPB (opposite interior angles of a parallelogram)
Therefore, segment PQ = segment RS (PQ = RS) (Corresponding Parts of Congruent Triangles are Congruent CPCTC).
Maya is on a game show. To win $1,000,000, she must answer this question: What key features are necessary-and how are the features used-to create the sketch of a polynomial function? What is Maya's winning answer? Explain in complete sentences
Answer:
To create the sketch of a polynomial function there are key features are necessary and these are the vertex, axis of symetry, x and y intercepts
Step-by-step explanation:
To create the sketch of a polynomial function there are key features are necessary and these are the vertex, axis of symetry, x and y intercepts
One of the key features arte the vertex and this shows where it changes concativity.
While the x and y intercepts give you a couple of points of reference.
Also, the axis of symetry is only applicable to even degree polynomials
You want to buy a new sweater. The regular price was
$48 dollars. The sale price was $34. What was the
percent of discount to the nearest percent?
Answer:
29%
Step-by-step explanation:
48-34 = 14 dollar saving
14/48 = 29.17 % = 29% saving
Answer:
29%
Step-by-step explanation:
48-34= 14 dollar saving
14/48 = 29.17% = 29% saving
what is 92.5% of 200
Answer:
185
Step-by-step explanation:
All you have to do is multiply 200 by 92.5/100 (because it is 92.5%). This gives you 185.
Hope this helps!
Answer:
185
We know 92.5% of 100 is 92.5%, so 92.5 of 200 is just 92.5×2.
Ms. delilio borrowed 1,200 from a bank for 3 months at 12% annual interest. How much interest did she pay?
Answer: $36
Step-by-step explanation:
When taking a loan from a bank, we have to pay interest. The Simple Interest Formula is:
Simple Interest (I) = Principal (P) × Interest Rate (r) × Time (t)
Principal (P) is the borrowed amount.
Interest Rate (r) is the percent of the principal to be paid.
Time (t) is the length of time that money is borrowed.
If Ms. Delilio borrowed $1,200 at an interest rate of 12% per year, for 3 months:
First, we have to convert 3 months into years
3 months = 3/12 =0.25 years
Then, find the interest by using the formula
Simple Interest (I) = Principal (P) × Interest Rate (r) × Time (t)
In this example
P = $1200
I = 12%
t = 0.25 years
Then:
I = 1200 × 0.12 × 0.25
I = 36
Answer: $36
Step-by-step explanation:
3/12x1200x0.12=36
SIMPLE INTEREST FORMULA
TIME(ALWAYS IN YEARS)FOR EXAMPLE 4 MONTH WOULD BE 4/12 SINCE THERE ARE 12 MONTH IN 1 YEAR
DIVIDE BY 100 FOR INTEREST SHOWN
AND MULTIPLY TO SOLVE
1
English
TIME REMAINING
58:10
The radius of the large sphere is double the radius of
the small sphere.
How many times is the volume of the large sphere than
the small sphere?
O 2
4
6
08
Answer
2
Step-by-step explanation
The radius of the large sphere is double the radius of the small sphere
The probability that a plane departs on time at a certain airport is .87 The probability that a plane arrives on time given it departed on time is .93 Find the probability that a plane departed and arrived in time. Write answer to four decimals. 3 points
Answer:
0.9355
Step-by-step explanation:
What we will use here is conditional probability formula.
let A be the event that the plane departs on time
and B be the event that it arrives on time
P(A) = 0.87
P(B|A) = 0.93
P(B) = ?
P(A n B) = ?
Mathematically;
P(B|A) = P(B nA)/P(A)
0.93 = 0.87/P(A)
P(A) = 0.87/0.93
P(A) = 0.935483870967742
which is 0.9355 to four decimal places
ZE is the angle bisector of AngleYEX and the perpendicular bisector of Line segment G F. Line segment G X is the angle bisector of AngleYGZ and the perpendicular bisector of Line segment E F. Line segment F Y is the angle bisector of AngleZFX and the perpendicular bisector of Line segment E G. Point A is the intersection of Line segment E Z, Line segment G X, and Line segment F Y.Which must be true? Point A is the center of the circle that passes through points E, F, and G but is not the center of the circle that passes through points X, Y, and Z. Point A is the center of the circle that passes through points X, Y, and Z but is not the center of the circle that passes through points E, F, and G. Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z. Point A is not necessarily the center of the circle that passes through points E, F, and G or the center of the circle that passes through points X, Y, and Z.
Answer:
Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.
Step-by-step explanation:
A is the intersection of angle bisectors, so is the incenter of triangle EFG. It is also the intersection of the perpendicular bisectors of the sides of triangle EFG, so is the circumcenter.
The altitudes at X, Y, and Z are perpendicular to sides EF, EG, and FG, and pass through the incenter, so X, Y, Z are points on the incircle.
A is the center of circles through E, F, and G, and through X, Y, and Z.
Answer:
Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.
C on edg2020
Match each quadratic graph to its respective function
Answer:
f(x) = (x - 3)(x + 1) → Corresponds with the first (raised higher ) ∪ shaped graph
f(x) = -2(x - 1)((x + 3) → Corresponds with the ∩ shaped graph
f(x) = 0.5(x - 6)((x + 2) → Corresponds with the second (lower) ∪ shaped graph
Step-by-step explanation:
For the function f(x) = (x - 3)(x + 1)
We have;
When x = 0, y = -3
When y = 0 x = 3 or -1
Comparing with the graphs, it best suits the first ∪ shaped graph that rises here than the other ∪ shaped graph
For the function;
f(x) = -2(x - 1)((x + 3)
When x = 0, y = 6
When y = 0, x = 1 or -3
Which corresponds with the ∩ shaped graph
For the function;
f(x) = 2(x + 6)((x - 2)
When x = 0, y = -24
When y = 0, x = -6 or 2
Graph not included
For the function;
f(x) = 0.5(x - 6)((x + 2)
When x = 0, y = -6
When y = 0, x = 6 or -2
Which best suits the second ∪ shaped graph that is lower than the other (first) ∪ shaped graph
For the function;
f(x) = 0.5(x + 6)((x - 2)
When x = 0, y = -6
When y = 0, x = -6 or 2
Graph not included
For the function;
f(x) = (x + 3)((x - 1)
When x = 0, y = -3
When y = 0, x = -3 or 1
Graph not included
Answer:
The guy above me was right. i accidently put in the answers in the wrong order so i thought it was wrong and rated it 1 star
Step-by-step explanation:
Find the value of f(g(-2))
Answer:
The correct ans is 3.
g(-2) = 2(-2) + 5
=-4 + 5 = 1
f(g(-2)) = 4 - (1)^2
= 4 - 1
=3
Step-by-step explanation:
Which equation is true for the value b = 10? A. 2(b + 4) = 16 B. 2(b + 2) = 40 C. 3(b – 2) = 24 D. 2(8 + b) = 42 E. 3(b – 4) = 20
Answer:
C is the correct answer
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
have a good day
HELP PLEASE! Thank you
Answer:
2000
Step-by-step explanation:
Hello,
A or C means 2 ways
and then a digit means 10 ways 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
so in total we have 2*10*10*10 = 2000 possible codes
Hope this helps
If Andrew has $72 in his wallet, what is the largest number of bags of sugar he can afford? (Each bag of sugar costs $6.33)
Answer:
11 bags
Step-by-step explanation:
$72/6.33=11.3744075829 or 11.4
11.4 estimate= 11
Answer:
11 bags of sugar
Step-by-step explanation:
In order to find the answer to this question simply divide the amount of money Andrew has by the amount of money it cost per bag of sugar.
[tex]S=6.33[/tex]
[tex]W=72[/tex]
[tex]72\div6.33=11.3744075829[/tex]
Round:
[tex]=11[/tex]
Hope this helps.
Which statement about the function is true?
The function is positive for all real values of x where
x > –4.
The function is negative for all real values of x where
–6 < x < –2.
The function is positive for all real values of x where
x < –6 or x > –3.
The function is negative for all real values of x where
x < –2.
Answer:
b
Step-by-step explanation:
The function is positive for all real values of x where
x < –6 or x > –3.
The function is negative for all real values of x where
x < –2.
HELPPPPPPPPPPPPPPPPPPPPP
Answer:
its 147
Step-by-step explanation:
yes
Which expression can be used to find the surface area of the following square pyramid?A 16+16+55+55+8816+16+55+55+8816, plus, 16, plus, 55, plus, 55, plus, 88 (Choice B) B 10+10+55+55+8810+10+55+55+8810, plus, 10, plus, 55, plus, 55, plus, 88 (Choice C) C 8 +8+55+55+888+8+55+55+888, plus, 8, plus, 55, plus, 55, plus, 88 (Choice D) D 16+8816+8816, plus, 88
Answer:
4 + 3+3+3+3
Step-by-step explanation:
We add up all the areas to find the surface area
The bottom is
2*2 = 4
The sides are all the same
The area of one side is
A = 1/2 bh = 1/2 (2*3) = 3
There are 4 triangular side
SA = 4 + 3+3+3+3
Answer:
4 + 3 + 3 + 3 + 3
Step-by-step explanation:
The base is a square.
Find area of a square.
2² = 4
Find the area of one triangle.
2 × 3 × 1/2 = 3
There are 4 triangles.
3 + 3 + 3 + 3
Add all the areas:
4 + 3 + 3 + 3 + 3
Consider the line . y = 7/3x +2 Find the equation of the line that is parallel to this line and passes through the point . (-9,4) Find the equation of the line that is perpendicular to this line and passes through the point (-9,4)
Answer:
parallel lines have the same slope. so your new equation will be y = 7/3x + b
to find b, plug in the (x, y) values of (-9, 4) since the line has to pass through this point.
a. 4 = (7/3)(-9) + b
b. 4 = -21 + b
c. b = 4 +21
d. b = 25
your equation is y = 7/3x + 25
perpendicular lines have reciprocated slopes. so your new equation will be y = -3/7x + b
to find b, plug in the (x, y) values of (-9, 4) since the line has to pass through this point.
a. 4 = (-3/7)(-9) + b
b. 4 = (27/7) + b
c. b = 4 - (27/7)
i. (112/28) - (108/28) = 4/28
d. b = 1/7
your equation is y = -3/7x + 1/7
hope this helps :)
Which phrase refers to the legal act of lowering an individual’s tax liability?Which phrase refers to the legal act of lowering an individual’s tax liability?
Answer:
Tax avoidance - legal
Tax evasion - illegal
What is the approximate length of arc s on the circle below? Use 3.14 for Pi. Round your answer to the nearest tenth.
5.8 ft
6.3 ft
27.5 ft
69.1 ft
Answer:
69.1 ft
Step-by-step explanation:
A circle has 360 degrees.
The arc we are finding the length of is 330 degrees.
Its length is 11/12 of the circle's total circumference. (330/360=33/36=11/12)
Let's find the circumference of the entire circle.
Circumference is πd.
The radius of the circle is 12ft.
Diameter is double of radius.
12*2=24
The diameter is 24.
Plug that in.
24π=75.36 when using 3.14 for π
Multiply that by 11/12.
11/12*75.36=69.08
Round 69.08 to nearest tenth.
69.1
Keywords:
Circle
Circumference
Arc
Diameter
Radius
Learn more about arc length here:
https://brainly.com/question/16930503
Based on the diagram , P, Q, R and S are four vertices of a regular polygon with centre O.
1)Given OP is perpendicular to OS,determine the number of sides of the regular polygon.
Answer:
Is it 12?Yes,I think it's 12.
HELP IF YOURE GOOD IN MATH AND CAN DO THIS PLEASEEEE. THANK YOU SM
Answer:
Period : 2π
Maximum: 2
Minimum: -4
y-intercept: (0,-1)
Amplitude: 3
When does the max occur: x=π/2
When does the min occur: x =3π/2
Equation of Axis: y = -1
Which properties would you use to simplify the following expression? log (17x3)
Answer:
Step-by-step explanation:
Did you mean log (17*3)? If so, your log (17x3) becomes log 17 + log 3.
Did you mean log 17^3? If so, log 17^3 = 3 log 17.
Did you mean log 17*x*3? If so, this equals log 17 + log x + log 3
Answer:
C: 1 and 3
Step-by-step explanation:
EDGE2021
Plz.. Help me.. True or false?
Answer:
[tex]\boxed{\mathrm{False}}[/tex]
Step-by-step explanation:
[tex](p-q)^2[/tex]
[tex](p-q)(p-q)[/tex]
Use FOIL method.
[tex]p^2-pq-pq +q^2[/tex]
[tex]p^2-2pq +q^2[/tex]