Given:
The function is
[tex]g(x)=(\dfrac{1}{5})^x[/tex]
To find:
The correct ordered pairs.
Solution:
We have,
[tex]g(x)=(\dfrac{1}{5})^x[/tex]
For x=3,
[tex]g(3)=(\dfrac{1}{5})^3[/tex]
[tex]g(3)=\dfrac{1}{125}[/tex]
So, the ordered pair is [tex](3,\dfrac{1}{125})[/tex].
For x=-2,
[tex]g(-2)=(\dfrac{1}{5})^{-2}[/tex]
[tex]g(-2)=(5)^2[/tex] [tex][\because (\dfrac{a}{b})^{-n}=(\dfrac{b}{a})^n][/tex]
[tex]g(-2)=25[/tex]
So, the ordered pair is [tex](-2,25)[/tex].
For x=1,
[tex]g(1)=(\dfrac{1}{5})^1[/tex]
[tex]g(1)=\dfrac{1}{5}[/tex]
So, the ordered pair is [tex](1,\dfrac{1}{5})[/tex].
For x=-1,
[tex]g(-1)=(\dfrac{1}{5})^{-1}[/tex]
[tex]g(-1)=(5)^1[/tex] [tex][\because (\dfrac{a}{b})^{-n}=(\dfrac{b}{a})^n][/tex]
[tex]g(-1)=5[/tex]
So, the ordered pair is (-1,5). This is the correct answer.
Therefore, the correct option is D.
A ladder leans against a wall creating a 58 angle. The ladder reaches 4.5m up the wall. Calculate how long the ladder is
Answer:
Follow the steps above
(3 + 3) x 5
explain yo answer
Answer:
30
Step-by-step explanation: you add 3+3 and multiply 5 and get 6x5 is 30
What is the image point of (4,-7)(4,−7) after a translation right 4 units and up 5 units?
The new coordinate of point (4,−7) after a translation right 4 units and up 5 units is (8,-2).
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
Given the point (4,-7)
If we transformed any point (x,y) to 4 units right then it will add in x so x + 4, and 5 units up then it will add in y so y + 5.
So,
4 units right → 4 + 4 = 8
5 units up → -7 + 5 = -2
So the new coordinate will be (8,-2)
Hence "The new coordinate of point (4,−7) after a translation right 4 units and up 5 units are (8,-2)".
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Work out the size of angle x.
Answer:
13 degrees.
Step-by-step explanation:
First we calculate the other 2 angles of the triangle of which < x is a part.
The bottom angle = 85 (vertical angles are equal).
The top one = 180 - 98 = 82. ( corresponding and adjacent angles).
So angle x = 180 - (85 + 82).
= 180 - 167
= 13 degrees.
How do you read the following rate "25 miles/hour"*
Answer:
you read it as 25 miles per hour
Simplify: −2(5) + 2 =
Answer:
-8
Step-by-step explanation:
-2(5) + 2
-10 + 2
-8
Translate the figure 4 units left and 3 units down.
Step-by-step explanation:
Check the photo
~~~~~~~~~~~~~~
The translated equation of line 7y = 4x + 24 is given as 7y = 4x + 3, and the figure is attached below.
What is translation?A shape is translated when it is moved to the left, right, up, or down without turning. Congruence is demonstrated by the fact that the translated shapes (or the image) seem to be the same size as the original ones. Simply said, they have changed their path or directions.
Given:
The figure is shown, The line is passing through (1, 4) and (8, 8),
The equation of the line in the given question can be written as,
y - 8 = (8 - 4) / (8 - 1) (x - 8)
y - 8 = 4 / 7 (x - 8)
7(y - 8) = 4(x - 8)
7y - 56 = 4x - 32
7y = 4x - 32 + 56
7y = 4x + 24
The slope of the line is 4 / 7
The translated equation can be written as,
y - (-3) = 4 / 7 (x - (-4))
y + 3 = 4 / 7 (x + 4)
Thus, the (1, 4) coordinate will become (-3, 1) and the (8, 8) coordinate will become (4, 5), The figure is attached below.
To know more about translation:
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A constant volume of pizza dough is formed into a cylinder with a relatively small height and large radius. The dough is spun and tossed into the air in such a way that the height of the dough decreases the radius increases, it retains its cylindrical shapeAt time of the dough 1/3 inch, the radius of the dough is 12 inches, and the radius of the dough is increasing at a rate of 2 inches per minute at the area of the circular surface of the dough increasing with respect to time? Show answer and numerical answer and units of measure.
Answer:
The rate of change of each circular surface of the dough is approximately 150.796 in.²/minute
Step-by-step explanation:
The given parameters are;
When the radius of the dough, r = 12 inches, the radius is increasing at 2 inches per minute
Therefore, we have;
dr/dt = 2 in./min
The area of the circular surface of the dough, A = π·r²
The rate of change of each (top or bottom) circular surface area of the dough dA/dt is given as follows;
dA/dt = d(π·r²)/dt = π·2·r·dr/dt
Where;
r = 12 in.
dr/dt = 2 in./min
Substituting, we have;
dA/dt = π·2·r·dr/dt = π × 2 × 12 in. × 2 in./min ≈ 150.796 in.²/minute.
The rate of change of each circular surface of the dough = dA/dt ≈ 150.796 in.²/minute.
On a particular day, the Dow Jones had a rate of change of -2.1%. Which of the following statements must also be true?
A. The S&P 500 increased.
B. Every stock in the Dow Jones decreased
C. The Nasdaq decreased
D. The average of the 30 stocks in the Dow Jones decreased
Answer:D
Step-by-step explanation: the average of the 30 stocks in the Dow Jones increased
solve this inequality for x: -46 -8x >22.
Answer:
Step-by-step explanation:
The key to answering this is to know that the only time you'll change the direction of the sign is when you multiply or divide by a negative number.
-46 - 8x > 22
-8x > 22 + 46
-8x > 68
x < 68/-8 (we divided by -8 so the inequality changed direction)
x < -17/2
Step-by-step explanation:
-46 - 8x > 22: Original problem
-46 - 8x + 46 > 22 + 46: Bringing all the constants to one side of the inequality
-8x > 68: Simplification
x < 68/-8 : You have to flip the inequality symbol because you are dividing by
a negative number..
x< -8.5 : The answer!!!!!
Checking your answer....
-46 - 8x > 22 : Original problem
-46 - 8(-8.5) > 22 : Substitution
-46 + 68 > 22 : Simplification
22 > 22 : Answer check successful!!!
(22 is not greater than 22 but we know that the answer cannot be -8.5 because the inequality states that x is less -8.5. This process was only for the purpose of checking not for the purpose of proving)
Hope this helps!!!!
25. A bag contains colored tiles.
• 3 tiles are red
• 6 tiles are green
• 3 tiles are blue
Atile will be randomly selected from the bag. What is the probability in decimal
form that the tile selected will be green?
When we're talking about a
chemical equation, what do we
mean when we say products and
reactants?
Answer:
The reactantsare the what is used to solve for the products.
Step-by-step explanation:
For example if you the chemical equation C+Ph=CPh C and Ph are the reactants and CPh is the product.
What is the cosine of angle B? Can anyone help with this please? ❤️
Answer:
a
Step-by-step explanation:
It took Sebastian 10 years to repay a loan of $30,000, paying $296.66 per month. Jana paid off a loan for the same amount at the same interest rate in 5 years by paying $545.75 per month. How much more did Sebastian pay in interest than Jana?
Answer:
$2,854.2
Step-by-step explanation:
For Sebastian
It took Sebastian 10 years to repay a loan of $30,000, paying $296.66 per month.
1 year = 12 months
10 years = x
Cross Multiply
x = 10 × 12 = 120 months
He pays $296.66 monthly
Hence, the total amount he paid in 10 years =
$296.66 × 120
= $35,599.2
The loan he took was $30,000.
Hence, the interest Sebastian paid on his loan = $35,599.2 - $30,000
= $5,599.2
For Jana
Jana paid off a loan for the same
amount at the same interest rate in 5 years by paying $545.75 per month.
1 year = 12 months
5 years = x
Cross Multiply
x = 10 × 5 = 60 months
He pays $545.75 monthly
Hence, the total amount he paid in 5 years =
$545.75 × 60
= $32,745
The loan she took was $30,000.
Hence, the interest Sebastian paid on his loan = $32,745 - $30,000
= $2,745
How much more did Sebastian pay in interest than Jana?
This is calculated as:
The interest Sebastian paid - The Interest Jana paid
= $5,599.2 - $2,745
= $2,854.2
Therefore, Sebastian paid $2,854.2 more than Jana
find the equation of the circle with center at (3 -2) and radius of 3.
Answer:
(x - 3)² + (y + 2)² = 9
General Formulas and Concepts:
Pre-Calculus
Equation of a Circle: (x - h)² + (y - k)² = r²
(h, k) is centerr is radiusStep-by-step explanation:
Step 1: Define
Center (3, -2)
h = 3k = -2Radius r = 3
Step 2: Write Equation
Substitute [EC]: (x - 3)² + (y + 2)² = 3²Exponents: (x - 3)² + (y + 2)² = 9Help with number 2 please
Answer:
3 in a half miles
Step-by-step explanation:
Elevator 1 in a building moved from ground position to a final position of +13 feet. Elevator 2 in the same building moved from ground to a final position of −10 feet. Which statement best describes the final positions of these two elevators?
Answer:
Elevator 1: (0, 0) to (0, 13)
Elevator 2: (0, 0) to (0, -10)
Vertically, the two elevators are now 23 feet apart.
Step-by-step explanation:
I just used the coordinate plane for this. Did it help?
6 is 16% of what number?
Answer:
37.5
Step-by-step explanation:
Answer:
6 is 16% of the number 37.5
Step-by-step explanation:
We have, 16% × x = 6
or, 16/100 × x = 6
Multiplying both sides by 100 and dividing both sides by 16,
we have x = 6 × 100/16
x = 37.5
what is 8 x 23
+ 6
3 + 2
Answer:
8x23 +6+3+2 = 195
Step-by-step explanation:
used PEMDAS <3 hope this helps
Which of the following is a point-slope equation for a line with the point
(-2, 4) and a slope of 3?
OA. y- 4 - 3(x+2)
OB. y+2 = 3(x- 4)
OC. y-2 - 3(x- 4)
OD. y- 4 - 3(x- 2)
Answer:
A. y - 4 = 3(x + 2)
Step-by-step explanation:
Point slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line
Plug in the slope and given point:
y - y1 = m(x - x1)
y - 4 = 3(x + 2) is the equation
So, A is the correct answer.
Please I need help
What is the perimeter of the parallelogram
A staffing agency for in-home nurses and support staff places necessary personnel at locations on a daily basis. Each placed nurse works 240 minutes per day at a daily rate of $90. Each support staff employee works 360 minutes per day at a daily rate of $120.
A. On a given day, 3000 total minutes are worked by then nurses and support staff that were placed. Write an equation that represents this relationship
B. On the same day, earnings for placed nurses and support staff totaled $1050. Write an equation that represents this relationship.
C. Solve the system of equations, and interpret the solution in the context of the situation.
assignment
1 of
POSSIBLE POINTS: 2
Two students, Brian and Alexa, both broke their chromebooks. Brian has $50 in his bank account and makes 12 dollars for every driveway
that he shovels. Alexa has 10 dollars in her bank account but makes $20 for every driveway that she shovels. The graph is shown below
20
Answer:
8267
Step-by-step explanation
The function g(x) is a transformation of the cube root parent function, f(x) = 3/x . What function is g(x) help
Me
The function g(x) is a transformation of the cube root parent function f(x) = ∛x will be g(x) = ∛(x - 4) - 3. Then the correct option is D.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The function g(x) is a transformation of the cube root parent function that will be given below.
f(x) = ∛x.
If we subtract h in the variable of the function then the function shifts toward the left by h units.
And if we subtract k in the function then the function shifts downward by k units.
Then the function g(x) will be
g(x) = ∛(x - 4) - 3
Then the correct option is D.
More about the function link is given below.
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HELP!!!Will Give Brainliest to correct answer!!! 40 POINTS!!!
Answer:
115
Step-by-step explanation:
The person above is right your ratio is the key to divide all the sizes.
(15 POINTS!!!) Solve 4 two-step equations:
1. 2x + 12 = 4
2. -5c + 9 = -16
3. -12 = -7 + x/4 (<-- x divided by 4)
4. -n/6 + 4 = 3
What is the slope (1,5),(10,2)
Answer:
m=-1/3
Step-by-step explanation
y2=2,y1=5 , x2=10 , x1= 1
m=y2-y1/x2-x1
m=2-5/10-1
m=-1/3
3/9 because if u plot the 2 points on a graph it will be 3 up and 9 over.
Does the graph represent an arithmetic sequence or geometric sequence?
Group of answer choices
Geometric sequence because the graph models a linear function.
Arithmetic sequence because the graph models an exponential function.
Geometric sequence because the graph models an exponential function.
Geometric sequence because the graph models a quadratic function.
Arithmetic sequence because the graph models a linear function.
Arithmetic sequence because the graph models a quadratic function.
Answer:
it is geometric because it multiplies by a factor of 3
help me with the question in the image please help me out :)
Step-by-step explanation:
(7 + x) / 3 = 2x - 5
7 + x = 3(2x - 5) (multiply 3 on both sides)
7 + x = 6x - 15 (distributive property)
5x = 22 (arrange like terms)
x = 4.4 (divide 5 on both sides)
2(x-6)+3x+4=
Helpppppp.
Answer:
5x + (-8)
Step-by-step explanation:
2(x-6)+3x+4=
Distribute:
(2)(x)+(2)(−6)+3x+4
=2x+−12+3x+4
Combine Like Terms:
(2x+3x) + (-12+4)
= 5x+(-8)