To translate y = x + 7 one unit to the left, the expression becomes y = x + 8. To move y = 3x - 5 one unit to the right, it becomes y = 3x - 8. The translation shifts the graph parallel to the x-axis while maintaining its shape.
To translate the graph of the function y = x + 7 one unit to the left, we substitute x with (x + 1) because adding to the independent variable moves the graph to the left.
Therefore, the translated expression would be y = (x + 1) + 7 which simplifies to y = x + 8.
Similarly, to translate the graph of the function y = 3x - 5 one unit to the right, we substitute x with (x - 1) because subtracting from the independent variable moves the graph to the right.
The translated expression is y = 3(x - 1) - 5, which simplifies to y = 3x - 3 - 5 or y = 3x - 8.
The process of translating graphs involves shifting each point parallel to the x-axis, either to the left or right, by the desired number of units without altering the shape of the graph.
How much interest is earned on $140 at 7% for five years?
Answer:
49
Step-by-step explanation:
140*0.07*5= 49
what 3 numbers can be multiplied to make 106
Answer:
1 x 106 = 106
2 x 53 = 106
53 x 2 = 106
106 x 1 = 106
Step-by-step explanation:
(happy to help)
Answer:
1 x 106 = 106
2 x 53 = 106
53 x 2 = 106
106 x 1 = 106
Give me Brainliest Plz
Solve for d. 8d − 6 = 7d
Answer:1d
Step-by-step explanation:
Step-by-step explanation:
Bringing like terms on one side
8d - 7d = 6
d = 6
What would the equation be? First to ACTUALLY answer will be marked brainliest!! Plz and thank you
Answer:
y = 0.50 + 8
Step-by-step explanation:
The slope is .50 and the y-intercept is 8
y-int is the initial cost before adding toppings.
slope represents the cost of each topping.
Element X decays radioactively with a half life of 10 minutes. If there are 510 grams
of Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 21 grams?
Answer:
46 minutes
Step-by-step explanation:
A circle with radius of 5 cm sits inside a 11 cm x 11 cm rectangle.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
Answer:
The area of the shaded region is 42.46 cm2
Step-by-step explanation:
Answer:
5 x 5 = 25
25 x 3.14 = 78.5
11 x11 = 121 - 78.5 = 42.5
42.5 cm
Step-by-step explanation:
Please Help! 13. List all of the elements of each set
a) Set of integer solutions of x^2≤3
Answer:
S = {-1, 0, 1}
Step-by-step explanation:
First we need to solve the inequation x^2<=3
Using square root in both sides, we have:
|x| <= 1.73
Separating the module in two, we have:
x <= 1.73
x >= 1.73
So we have that -1.73 <= x <= 1.73
Solving this inequation only with integer values, we have:
x = -1, x = 0 or x = 1
So the set of integer solutions is S = {-1, 0, 1}
Consider the equation 2/x= 5/2x-1. Solve for x
Answer:
x=1.11651513…,−0.71651513…
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
A.P.E.X.
Which of the following relations is a function?
A.
(2, 1), (-2, 4), (-5, 1), (2, -5)
B.
(-5, 4), (-2, 6), (-5, 3), (7, 2)
C.
(-5, 1), (-2, -5), (2, 5), (7, 1)
D.
(-5, 1), (-2, 4), (2, -5), (-2, 6)
Answer:
the answer is C
Step-by-step explanation:
Please help on math.
Answer:
Total area= 207 ft^2
Step-by-step explanation:
You can divide the figure to make 2 big rectangles.
The first has a base of 15 ft and a height of 15 ft
A1 = b * h
A1= 15 ft * 9 ft A1= 135 ft^2
The second has a base of 12 ft and a height of 6 ft
A2= b*h
A2= 12 ft * 6 ft
A2= 72 ft^2
Total area= A1+A2= 135 ft^2 + 72 ft^2
Total area= 207 ft^2
What is the area length of a semi circle with the radius of2
Answer:
12.56
Step-by-step explanation:
If AC = 20 and BC = 17 what is the radius
The radius of the circle is 10.5.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
AC = 20 and BC = 17
From the figure,
We apply the Pythagorean theorem.
So,
AC² = BC² + AB²
Substituting,
20² = 17² + AB²
AB² = 400 - 289
AB² = 111
Now,
Radius = AB
So,
AB = √111
AB = 10.535
Rounding to the nearest tenth.
AB = 10.5
Thus,
The radius of the circle is 10.5.
Learn more about the Pythagorean theorem here:
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What is the value of x?
(3x – 14)
x
[4(x – 9)°
Enter your answer in the box.
Next
22
pretty sure we are doing the same test
y= 3x - 7
Complete the missing value in the solution to the equation.
(1, )
Answer:
(1, -4)
Step-by-step explanation:
y = 3x-7
Let x = 1
y = 3(1) -7
y = 3-7
y = -4
In the diagram, line x|| line y. Find the angle measures below.
Answer:
<1 = 95
<2 =85
Step-by-step explanation:
<1 = 95
They are alternate exterior angles and alternate exterior angles are equal when the lines are parallel
<1 + <2 = 180 since they form a straight line
95+ <2 =190
Subtract 95 from each side
95-95+<2 =180-95
<2 =85
Dean's class took a field trip to the art museum. They left school at 11:45 A.M. It took them 45 minutes to drive to the museum. They stayed at the museum for 1 hour and 30 minutes. What time was it when Dean's class left the museum?
Answer:
2:00 p.m.
Step-by-step explanation:
driving to the museum is 12:30
then they sped 1 hour and 30 minutes
Solve the system of equations.
y = 7x + 43
y= 2x + 13
a. (-6, 1)
b. (6, -1)
c. (6, 1)
d. No solution
Answer:
x=−6 and y=1
(a)
What is the slope of the line that contains these points?
Answer:
6
Step-by-step explanation:
The slope (m) can be found using the formula ...
m = (y2 -y1)/(x2 -x1)
Any pair of points will do. We can use the first two.
m = (2 -(-10))/(17 -15) = 12/2
m = 6
Part B:
The high temperature this Sunday is expected to be 5 degrees warmer than the high temperature this Saturday.
Using the line c = 2t - 89, how many more cups of lemonade should Lin expect to sell on Sunday than
Answer:
Lin should expect to sell 10 cups more
Step-by-step explanation:
The line c = 2t − 89 relates the cups Lin expect to sale (c) with the high temperature of the day (t)
If high temperature on Saturday is t1, then high temperature on Sunday is (t1+5)
Cups sold on Saturday are: 2t1 − 89
Cups sold on Sunday are: 2(t1+5) − 89 = 2t1 + 10 - 89
Cups sold on Sunday - Cups sold on Saturday:
2t1 + 10 - 89 - (2t1 − 89) = 2t1 + 10 - 89 - 2t1 + 89 = 10
A store sells two types of coffee: House blend and Premium blend. Each bag of House blend contains 3 pounds of Type A beans and 2 pounds of Type B beans. Each bag of Premium blend contains 7 pounds of Type A beans and 3 pounds of Type B beans. The store can use at most 105 pounds of Type A beans and at most 60 pounds of Type B beans. Each bag of House blend sells for $6 and each bag of Premium blend sells for $10. How many bags of each type of coffee should the store make in order to maximize its revenue? What is the maximum revenue?
Answer:
do 3 dived by 2 they the awnser times seven then add 105 then multiply 60 then carry the 3 then add 10 and 6 then add 16 to the awnser and boom!
Step-by-step explanation:
A bug is 1.2 cm up a wall and climbs up 1.7 cm each second. Another bug is 30 cm up the wall and climbs down 1.5 cm per second. After how many seconds will the bugs be the same height?
Seconds =
1.2 cm + ( 9 × 1.7 cm ) = 16.5 cm
30 cm - ( 9 × 1.5 cm ) = 16.5 cm
So the answer is 9 seconds!
Hope this helps :)
Let me know if my answer is incorrect or something :0
Willie had 55 baseball cards after trading with his friends. He traded 5 cards for one special card. Lee gave him 11 cards for a Mickey Mantel card. How many cards did Willie start with?
Answer:
49 baseball cards.
Step-by-step explanation:
First you want to add 5 cards to the 55 for the 5 he traded for the one. You get 60. Then subtract the 11 cards that he was given for the 1. You end up with 49 baseball cards.
Jennifer buys a block of clay for an art project. The block is shaped like a cube with edge lengths of 12 inches.
a. Jennifer uses one piece of the cube to make spheres that have a diameter of 4 inches. How many spheres can she make?
b. Jennifer wants to keep the other piece of the cube for a future project. What is the area of the newly exposed surface from the wire cut?
Answer:
Volume of block Jennifer bought:
V = side^3 = 12 x 12 x 12 = 1728 (in3)
Volume of sphere Jennifer wanted to make:
V = (4/3) x pi x radius^3 = (4/3) x pi x (4/2)^3 = 33.5 (in3)
a, The number of spheres she can make:
N = 1728/33.5 = 51.58 = ~51
b, The area of remaining clay after she made a sphere:
A = 1728 - 33.5 = 1694.5 (in3)
Hope this helps!
:)
The graph below shows the hours students spent studying and their science test scores.
Hours Spent Studying vs. Science Test Scores
A graph has hours spent studying on the x-axis and test score on the y-axis. A line has a regression equation of y = 3.1 x + 40.5.
A student gets a score of 70 on the test. Based on the trend line in the scatter plot, how much time did the student spend studying?
3.1 hours
4.5 hours
9.5 hours
40.5 hours
Answer:
(c) 9.5 hours
Step-by-step explanation:
The equation of the trend line predicts a score based on study hours. Here, we're asked for the inverse relation: finding a number of study hours based on a given score.
Inverse relationWe can solve the equation for x in terms of y:
y = 3.1x +40.5
y -40.5 = 3.1x . . . . subtract 40.5
(y -40.5)/3.1 = x . . . . divide by the coefficient of x
This tells us the number of hours spent studying for a particular score.
ApplicationUsing y=70, we find the number of study hours to be ...
x = (70 -40.5)/3.1 = 29.5/3.1 ≈ 9.516 ≈ 9.5
The student spent about 9.5 hours studying.
Which function is growing the fastest?
A) cubic C) linear
B) exponential D) quadratic
Answer: (C) the linear
Step-by-step explanation:
at x = 3 the y-value ... is growing
Answer:
Step-by-step explanation:
The rate of growth (the slope of the transformed curve) is first higher than for an exponential function, but later it goes down. ... Initially, the quadratic function grows much faster. The function x² grows from 0 to 1 in finite time, while the exponential function takes from minus infinity to 0.
can someone help me w #10 and #11
Answer:
10. Expanded vertically by 3, shifted left 2 and up 4.
11. Shifted right 6 and up 7.
Step-by-step explanation:
This sort of question involves matching patterns. You need to know what the various transformations look like, and what that means for a specific parent function.
Here are the transformations used in this problem:
f(x -a) . . . . shift f(x) to the right by "a" unitsf(x) +a . . . . shift f(x) up by "a" unitsa·f(x) . . . . . vertically scale f(x) by a factor of "a"For these problems, the parent function is f(x) = 1/x.
__
10. The multiplier of 3 in the numerator (3/x) means the function has been scaled vertically (expanded) by a factor of 3.
The replacement of x with x+2 means the function has been shifted to the right by -2 units. That is the same as shifted left 2 units.
The addition of 4 to the function value means the function has been shifted up by 4 units.
__
11. We note the numerator is still 1, so there is no vertical expansion. The replacement of x with x-6 means a right shift by 6 units. The addition of 7 to the function value means a shift up by 7 units.
U should rly help plz
Answer:
Final result :
(sorry if this is long)
a3 - 5a2 + 4a + 5
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((4a-(a3))-3)+(((2•(a3))-5a2)+8)
Step 2 :
Equation at the end of step 2 :
((4a-(a3))-3)+((2a3-5a2)+8)
Step 3 :
Checking for a perfect cube :
3.1 a3-5a2+4a+5 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: a3-5a2+4a+5
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 4a+5
Group 2: a3-5a2
Pull out from each group separately :
Group 1: (4a+5) • (1)
Group 2: (a-5) • (a2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(a) = a3-5a2+4a+5
Polynomial Roots Calculator is a set of methods aimed at finding values of a for which F(a)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers a which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 5.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,5
Hope it helps!!
hi help me right now i am dunb
If the perimeter of a square is 14d+28 centimeters, what is the length, in centimeters, of each side of the square?
Answer:
Each side is (7/2d +4) cm
Step-by-step explanation:
The perimeter of a square is given by
P = 4s where s is the side length
14d +28 = 4s
Divide each side by 4
14d/4 +28/4 = 4s/4
7/2d +7 = s
Each side is (7/2d +4) cm
The temperature at 4:00 P.M. was − 12°C. By 11:00 P.M. the temperature had dropped 14°C. What was the temperature at 11:00 P.M.?
Answer:
-26
Step-by-step explanation:
If the temperature dropped by 14 degrees than it decreased by 14, which means we subtract:
-12-14= -26