Given:
A student says that the graph of the equation [tex]y = 3(x + 8)[/tex] is the same as the graph of [tex]y = 3x[/tex], only translated upwards by 8 units.
To find:
Whether the student is correct or not.
Solution:
Initial equation is
[tex]y=3x[/tex]
[tex]f(x)=3x[/tex]
Equation of after transformation is
[tex]y=3(x+8)[/tex]
[tex]g(x)=3(x+8)[/tex]
Now,
[tex]g(x)=f(x+8)[/tex] ...(i)
The translation is defined as
[tex]g(x)=f(x+a)+b[/tex] ...(ii)
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
From (i) and (ii), we get
[tex]a=8\text{ and }b=0[/tex]
Therefore, the graph of [tex]y=3x[/tex] translated left by 8 units. Hence, the student is wrong.
DESARROLLO:
Un capital de $5000 está depositado en un banco y produce un interés anual simple del 2% Recuerde: I = C. T.t
I = Interés
C = Capital.
T = Porcentaje como número decimal.
t = Tiempo en años.
Con esta información determine:
a) Escriba la función que representa el problema.
Calcule
b) ¿Cuánto dinero hay al cabo de un año?
c) ¿Cuánto dinero hay al cabo de dos años?
d) ¿Cuánto dinero hay al cabo de n años?
e) Realice una tabla de valores y su gráfico.
f) ¿Qué tipo de función representa la gráfica?
Answer:
C.¿Cuanto dinero hay al cabo de n anos
(a^2 - b^2)/(2 + d^3)
a stands for 6, b stands for 4, d stands for 1 over 2, i need explanation too
Answer:
Solving the equation [tex]\frac{a^2-b^2}{2+d^3}[/tex] by putting a=6, b=4 and d=1/2 we get [tex]\frac{160}{17}[/tex]
Step-by-step explanation:
We are given formula: [tex]\frac{a^2-b^2}{2+d^3}[/tex]
and values a=6, b=4 and d=1/2
We need to put the values of a, b and d in the given equation [tex]\frac{a^2-b^2}{2+d^3}[/tex] and find their result
Putting values in the equation:
[tex]\frac{a^2-b^2}{2+d^3}\\=\frac{(6)^2-(4)^2}{2+(\frac{1}{2})^3}\\=\frac{36-16}{2+\frac{1}{8}}\\=\frac{20}{\frac{2*8+1}{8}}\\=\frac{20}{\frac{17}{8}}\\=\frac{20*8}{17}\\=\frac{160}{17}[/tex]
So, solving the equation [tex]\frac{a^2-b^2}{2+d^3}[/tex] by putting a=6, b=4 and d=1/2 we get [tex]\frac{160}{17}[/tex]
x/a + b = c solve for x
Answer:
x = a(c-b)
Step-by-step explanation:
x/a + b = c
-b -b
x/a = c - b
times a times a
x = a(c-b)
Answer:
The answer should be x=ac-bc.
Step-by-step explanation:
You should start with multiplying the both sides a+b. The left hand side of the equation will cancel out and we'll be left with, x. At the right hand side, we have c.(a+b), which is equal to ac+bc and this value is equal to x.
I thought that the question was [tex]\frac{x}{a+b}=c[/tex].
The correct solution is, may be because of the question's second look of mine is, x=a(c-b). You subtract b from the both sides, then you'll multiply both sides with a, and the answer will be x=ac-ab.
Does the equation: -x + 6y = -7 represent direct variation?
Answer:
The equation -x + 6y = -7 does not represent direct variation.
Step-by-step explanation:
The form of the linear equation is y = m x + b, where m is the slope of the line which represents the equation and b is the y-interceptThe direct variation is a linear relation, and represented graphically by a line passes through the origin, which means the y-intercept is (0. 0), then (b = 0)The equation of the direct variation is y = m xLet us solve the question
∵ The equation is -x + 6y = -7
→ Substitute x by 0 to find the value of y-intercept
∵ x = 0
∴ 0 + 6y = -7
∴ 6y = -7
- Divide both sides by 6 to find y
∴ y = [tex]-\frac{7}{6}[/tex]
∴ The y-intercept of the equation is (0, [tex]-\frac{7}{6}[/tex] )
∵ The y-intercept of the direct variation is (0, 0)
∴ The equation -x + 6y = -7 does not represent direct variation.
Please helpp!
Find the difference. Use a number line. Enter your answer as a simplified mixed number.
Answer:
2[tex]\frac{7}{9} \\[/tex]
Step-by-step explanation:
-(2/9) + 3
= 27/9 - 2/9
= 25/9
= 2[tex]\frac{7}{9} \\[/tex]
A football team lost 12 yards on the first play, gained 5 yards on the 2nd play and
lost 3 yards on the final play. What have they done in all?
Answer:
they have lost 10 yards
Step-by-step explanation:
12-5+3=10
The label on the car's antifreeze container claims to protect the car between −40°C and 125°C. To convert Fahrenheit temperature to Celsius temperature, the formula is C = 5 over 9 (F − 32). Write and solve the inequality to determine the Fahrenheit temperature range at which this antifreeze protects the car.
Answer:
The antifreeze protects the car between -40°F and 257°F
Step-by-step explanation:
Inequalities
The range of Celsius temperatures the car's antifreeze protects the car is
[tex]-40 \le ^\circ C \le 125[/tex]
To convert °C to °F we use the formula:
[tex]\displaystyle ^\circ C=\frac{5}{9}(^\circ F-32)[/tex]
To find the equivalent range of temperatures in °F, substitute the formula:
[tex]\displaystyle -40 \le \frac{5}{9}(F-32) \le 125[/tex]
Multiply by 9, divide by 5:
[tex]\displaystyle -40*9/5 \le F-32 \le 125*9/5[/tex]
Operating:
[tex]\displaystyle -72 \le F-32 \le 225[/tex]
Adding 32:
[tex]\displaystyle -72+32 \le F \le 225+32[/tex]
Operating, we get the range of temperatures in °F:
[tex]\displaystyle -40 \le F \le 257[/tex]
The antifreeze protects the car between -40°F and 257°F
TIMED TEST WILL GIVE BRAINLIEST
During an algebra class, a teacher asks for examples of non-prime numbers. Jake says 51, Teresa says 41, and Liu says 21. Which student(s) are correct in their response?
Answer:
D. Jake and Liu
Step-by-step explanation:
41 is prime so Teresa is wrong. The other two are not prime.
Find the airthmetic mean of prime numbers between 20 and 50
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Prime numbers between 20 and 50 are :
[tex]23 \: , \: 29 \: , \: 31 \: , \: 37 \: , \: 41 \: , \: 43 \: , \: 47[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Arithmetic mean is :
[tex] \frac{23 + 29 + 31 + 37 + 41 + 43 + 47}{7} = \frac{251}{7} = 35.857 \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Answer:
23 , 29 , 31 , 37 , 41 , 43 , 47
HELP:( I know I’m slow and all asking all these question today but...
Second answer
Step-by-step explanation:
The Lakewood wildcats won 5 of their first 7 games this year.There are 28 games in the season.About how many games would you expect the Wildcats to win this season?
Answer:
7 equal to 5
1 equal to 5/7
28 equal to 5/7*28=20
Step-by-step explanation:
Dan has £100. Colin takes £. How much is left
Answer:
Maybe 99£
Step-by-step explanation:
Please give me brainliest
Answer:
i think 99 because theres no number after the symbol
Step-by-step explanation:
Can somebody please help me
Answer:
26/24
Step-by-step explanation:
you multiply 1 by 8 and 6 by three as well as 3 by 8 and 8 by three to get 8/24 and 18/24 . now that you have a common denominator, you can add the two together to get 26/24
Can someone please solve this with explanation?
Answer: 67/9 or 7 4/9
Step-by-step explanation:
If f(x) = x2 + 2x + 3, what is the average rate of change of Rx) over the interval (-4, 6]?
Answer:
Step-by-step explanation:
The average rate of change of a function over an interval is simply the slope over the interval because:
[tex]let \: g(x)=f'(x)\\\frac{\int\limits^b_a {g(x)} \, dx }{b-a}(the\:average\:value\:of\:g)=\frac{f(b)-f(a)}{b-a}[/tex]
We have to know f(6) and f(-4)
[tex]f(x) = x^2 + 2x + 3\\f(6) = 6^2 + 2(6) + 3\\f(6) = 36 + 12 + 3\\f(6) = 51\\\\f(-4) = (-4)^2 + 2(-4) + 3\\f(-4) = 16 - 8 + 3\\f(-4) = 11\\\\\frac{f(6)-f(-4)}{6-(-4)} = \frac{51-11}{10} = \frac{40}{10} = 4[/tex]
6) Select the best method to solve the system.
5x-4y=7
4x-4y=12
*elimination
*substitution
Answer:
Elimination
x=-5 and y=-8
Step-by-step explanation:
-(5x-4y=7) <--- Multiply by a negative so that y can cancel out
4x-4y=12
=-5x+4y=-7
4x-4y=12
=-x=5
x=-5
5(-5)-4y=7 <--- plug x back in to solve for y
-25-4y=7
+25 +25
-4y/-4=32/-4
y=-8
Question 1 of 10
If f(x) = 4x - 12, what is f(2)?
A. -20
B. 8
C. 4
D. -4
Evaluate the expression | -4| -10| =
Answer:
test? is it? if it is i can't tell you
Step-by-step explanation:
egadar amd fred share cupcakes in the ratio 3:1 if edgar gets 9 cakes how many does fred get(pleez someone anwer my question
Answer:
3
Explanation:
For every 3 cupcakes that Edgar gets, Fred gets 1. So, if Edgar gets 9, Fred gets 3.
Simplify the expression:
7p+6q-2p+q
Answer:
5p+7q
Step-by-step explanation:
Answer:
5p+7q
Step-by-step explanation:
You add common terms together.
(7p-2p)+(6q+q)
5p+7q
Hope I helped!
y
4+
3+
2+
1
+
-4
-3
-2
-1
2
3
4
-2
-3+
-4
What is the slope of the line?
Answer:
the slope is 3/4
Step-by-step explanation:
Randomly pick two points
point 1 (0, -1)
point 2 (4, 2)
gradient = (y2-y1)/(x2-x1)
m = (2-(-1))/(4-0)
m = 3/4
Write or describe the function that flips over the x-axis, shifts right .5
units, and up 12 units. *
Which expression is equivalent to 2(3x + 4)(x - 1)(x – 3)?
Answer:
Step-by-step explanation:
The manager of an art supply store decides to hold a Buy 2, Get 1 Free sale on tubes of watercolor paints. The sale is held for one week and a total of 280 tubes of paint were sold (not including the ones given away for free). If each tube of watercolor paint cost the store $7.25, how much money did the store lose by giving away the free tubes of paint?
Answer:
$1015
Step-by-step explanation:
280 divided by 2 140 times $7.25 is $1015
The amount of money that the store lose by giving away the free tubes of paint is $1015.
Since the manager held Buy 2, Get 1 Free sale on tubes of watercolor paints, then when 280 tubes of paints are sold, 1/2 × 280 = 140 tubes of paints will be given out for free.
Therefore, the amount lost will be calculated by multiplying the number of paints given out by the price. This will be:
= 140 × $7.25
= $1015
Therefore, the amount of money that the store lose by giving away the free tubes of paint is $1015.
Read related link on:
https://brainly.com/question/18874560
REWRITE THE EQUATION{ TEN LESS THAN 3 TIMES A NUMBER IS THE SAME AS THE NUMBER PLUS 4
Help!! I do not get it, you have to find the ratio and put it in simplest form all I need to do is letter (W)!!
Answer:
24
Step-by-step explanation:
ratios are just like fractions. The ratio would be 1200:50 but think of it like [tex]\frac{1200}{50}[/tex]
To simplify find common factors of each number
1200 and 50 can both be divided by 50 so divide each by 50
1200 ÷ 50 =24
50 ÷ 50 = 1
now your new ratio is 24:1 or just 24
Answer:
Step-by-step explanation:
24 students to every 1 teacher 24:1
1200/50= 24
La familia Quispe para mejorar su casa que está deteriorada por los inclemencias de la naturaleza Busca financiar un préstamo de 4000 soles en dos entidades la entendidad "el emprendedor" Se ofrece un préstamo de $4000 por un período de 18 meses , a una tasa de interés del 20% anual capitalizable semestralmente. La entidad tu apoyo ofrece un préstamo de 4000 por "un período" de 18 meses a una tasa de interés del 5% trimestral capitalizable trimestralmente¿ En cuál de las entidades financieras le conviene solicitar el préstamo a la familia quispe"? ¿por qué?
T-shirts and More Print Shop will print any image on a mouse pad for a cost of $2 per mouse pad and a one-time charge of $12 to set up the mouse pad design. The total cost of an order was $562. How many mouse pads were printed?
A:47
B:275
C:550
D:281
Answer: 275
Step-by-step explanation:
A function f(x)is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
Enter your answer in the box.
f(x)=
Answer:
[tex]f(x)=2x+1[/tex]
Step-by-step explanation:
At x=0, the y is at 1
at x=1, y went up to 3
the change between 3 and 1 is 2 therefore the equation is
[tex]f(x)=2x+1[/tex]
I hope this helps you and good luck!
Solve for x
-18x +21 > -15
OR
20x-13>27
Choose 1 answer:
Answer:
x<2
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x < 2 the answer your welcome
