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.
how to find the trigonometric ratio
Answer:
tanZ° = 3/4
General Formulas and Concepts:
Trigonometry
[Right Triangles Only] tanθ = opposite over adjacentStep-by-step explanation:
Step 1: Identify Variables
Angle θ = Z
Opposite Leg XY = 21
Adjacent Leg YZ = 28
Step 2: Find Trig Ratio
Substitute [tangent]: tanZ° = 21/28Simplify: tanZ° = 3/4A school library has 160 DVDs in its collection. Given that 45% of the DVDs are about science and 40% are about history, how many of the DVDs are about other subjects?
Answer:
24 DVDs
Step-by-step explanation:
45% of 160 = 72
40% of 160 = 64
72+64=136
160-136=24
24 DVDs
May you please help me with this question!
Answer:
9/4x to the power of one plus 12y to the power of one
Step-by-step explanation:
You can add the top numbers for 9, but cant add the bottoms since they are different variables.
Answer:
[tex]\frac{6y+7x}{12xy}[/tex]
Step-by-step explanation:
i hope this helps :)
Need help ASAP!!!!!!!
The second of two numbers is two more than the first.
The sum is 40. Find the numbers.
Answer:
19 + 21 = 40.
Step-by-step explanation:
BRAINLYEST
Answer:
:)
Step-by-step explanation:
i think it's MODE 21........
The surface area "S" of a sphere of radius ris given by the forma
S=4pir^
Find (i) the surface area of a sphere whose radius is 5 cm.
The scale factor from the large triangle to the small triangle is 3:1 What is the length of side x of the smaller triangle CAN SB PLEASE HELP ME OUT!
Answer:
x = 10
Step-by-step explanation:
From what we can see in the diagram, the smaller triangle dimensions were dilated by a factor of 3
So to get the dimensions of the smaller from the bigger or larger triangle, we proceed to divide what we have on the larger triangle by 3
Kindly note that we do this for the comparable sides
Mathematically, we can have x as;
30/3 = 10
Write the sum, and then write an equivalent expression by collecting like terms and removing parentheses whenever possible.
d. The opposite of - 10t and t - 10t
Answer:
The answer is t.
Step-by-step explanation:
We need to find the sum of opposite of - 10t and t - 10t.
Opposite of -10t = 10 t
So,
10t + (t-10t)
Grouping the numbers,
(10t+(-10t)) + t
= 0 + t
= t
Hence, the answer is t.
37.
An express train travelled at a certain average speed from Town X to Town Y which was
150 km away. It then continued its journey to Town Z at an average speed 20 km/h faster than
its initial average speed. Town Ywas 200 km from Town Z. If it took the same time to travel for
both parts of the journey, what was the train's average speed for the first part of the journey?
Answer:
60 km/hr
Step-by-step explanation:
Let the speed at the initial average speed from Town X to Town Y be a.
We are told that it journeyed to Town Z at an average speed 20 km/h faster than its initial average speed. Thus, its average speed here is (a + 20) km/hr.
Town Y was 200 km from Town Z.
Thus, time spent here is;
t_2 = 200/(a + 20)
Time from X to Y is; t_1 = 150/a
We are told that it took the same time to travel for both parts of the journey.
Thus; t_1 = t_2
150/a = 200/(a + 20)
Cross multiply to get;
150(a + 20) = 200a
150a + 3000 = 200a
200a - 150a = 3000
50a = 3000
a = 3000/50
a = 60 km/hr
Find all possible solutions for x and y such that △ABC is congruent to △DEF.
△ABC: sides of length 19, 25, and 3x − 3.
△DEF: sides of length 25, 15, and 5 − y.
△ABC ≅ △DEF when x is ___ and y is ___.
Answer:
Step-by-step explanation:
it means the ABC And DEF have side lengths of 15,19, 25
so 3x-3 = 15
x = 6
5-y = 19
so y = -14
What is 2/9+1 1/2= What
What is the slope of the line that passes through the points (4,5) and (12,7)?
Answer:
(2,8)
Step-by-step explanation:
If we plot both points on the graph and start at (4,5) we count up (rise) 2 and to the right (run) 8. This means they are both positive numbers as it goes up and to the right.
*Down or to the left would be negative.
Edward plans to put $75 into a savings account. He can place his money into an account represented by b(x) = 7x + 75, or into another account represented by c(x) = 75(1.06)x. Which account has the highest value in 2 years? Which account has the highest in 12 years?
Answer:
the answer is the option B
b(x) has the highest value in years; b(x) has the highest value in years
Step-by-step explanation:
x------> the time in years
b(x)----> the value in dollars of a saving account
c(x)----> the value in dollars of another account
we know that
Step 1
Find the value of each account for
so
----> b(x) has the highest value in years
Step 2
Find the value of each account for
so
----> b(x) has the highest value in years
Which expression is equivalent to 12(4m−2n+4)?
1.2m−n+2
2.2m−2n+4
3.8m−4n+4
4.8m−4n+8
Answer:
1. 2m - n + 2
Step-by-step explanation:
12×4m - 12×2n + 12×4. ( because 12 is multipled by whole bracket)
48m - 24n + 48.
2m - n + 2. (by finding common factor 24)
The volume of the world's oceans is nearly 1.5⋅10^9 cubic kilometers. Write this number in scientific notation.
Answer:
"The World Ocean." The Columbia Encyclopedia. CD-ROM. 2007, 6th Ed. New York: Columbia University Press. "The World ocean has an area of about 361 million sq km (139,400,000 sq mi), an average depth of about 3,730 m (12,230)
Viau, Elizabeth Anne. World Builders: Water on Earth. California State University Los Angeles. 2003.
There are two origins of water: comets (extraterrestrial bombardment) and out gassing (condensation of steam from early volcanism). These processes are continuing today.
Step-by-step explanation:
Please help me due today
Find the exact length of the third side.
35
28
Answer:
44.821869662
Step-by-step explanation:
If x = 2, y = -1, Simplify and find the value of x(2) - 3 (x(2) + y(2) - 4).
Answer:
I think it would be -4x-6y+12
Answer:
10
Step-by-step explanation:
Plug in the values to "x" and "y" and solve.
Solve:
2(2) - 3(2(2) - 1(2) - 4)
2(2) - 3(4 - 1(2) - 4)
2(2) - 3(4 - 2 - 4)
2(2) - 3(-2)
4 - 3(-2)
4 + 6
10
Your answer would be 10.
Which of the following would be a possible solution to the system of inequalities given below?
(3,-3)
(1,-7)
(6,4)
(-5,0)
Answer:
(3, -3)
Step-by-step explanation:
A point qualifies as a solution to a system of inequalities if it is true when both of its x and y values are substituted into the both inequalities. Knowing this, let's plug in the first option, (3, -3), into both inequalities.
Let's try 6x + 3y > 3 first. Substitute 3 for x and -3 for y:
[tex]6 (3) + 3 (-3) > 3\\18 - 9 > 3\\9 > 3[/tex]
9 is bigger than 3, so (3, -3) is a solution to that inequality.
Let's try [tex]x -y \geq 4[/tex]. Do the same, substituting the same values:
[tex]3 - (-3) \geq 4\\3 + 3 \geq 4\\6\geq 4[/tex]
6 is bigger than 4, so (3, -3) is a solution to that inequality too.
Since (3, -3) is a solution to both inequalities, it must be the answer.
SOME ONE HELP PLS Jenny has finished 15 of the 20 lessons in her piano book. Liam has finished the same percent of lessons from his piano book. His book contains 40 lessons. How many lessons has Liam finished?
Answer:
30
Step-by-step explanation:
15/20 is 75%
75% of 40 is 30
Can someone also help me with this one?
Answer:
120
Step-by-step explanation:
4p - 7 + 6p + 10 how do you do this i put 10p + 3 but I don't know if it correct
Answer:
10p + 3
Step-by-step explanation:
4p+6p+10-7
10p + 3 is correct :)
What is the solution to the
y = 4x – 10
y = 2
O (3, 2)
O (2, 3)
O (-2, 2)
O (2,-2)
Answer:
this is the answer. (3,2)
Background
Layout-
Theme
Testos
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Freda bought 6 gallons of gasoline for $19.14
What was the unit price of this gasoline?
What is one of the greatest problems in Brazil?
O education
O language
O transportation
Answer:
c transportation
Step-by-step explanation:
Half the area of the rectangle shown is 24 inches. Write and solve an equation to find the value of 'x'
Answer:
The answer will b 4
Step-by-step explanation:
Answer:
12
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?
Simplify the expression given below.
X+2/x^3+2x^2-9x-18 divided by 3x+1 / x^2-9
A. 1 / (x+3)(x-3)
B. 3x +1
C. 1 / 3x+1
D. 3x + 1 / (x+3) (x-3)
Answer:
D
Step-by-step explanation: your welcome have a good day
Answer:
C. [tex] \dfrac{1}{3x + 1} [/tex]
Step-by-step explanation:
[tex] \dfrac{x + 2}{x^3 + 2x^2 - 9x - 18} \div \dfrac{3x + 1}{x^2 - 9} = [/tex]
Factor all polynomials.
[tex] = \dfrac{x + 2}{x^2(x + 2) -9(x + 2)} \div \dfrac{3x + 1}{(x + 3)(x - 3)} [/tex]
[tex] = \dfrac{x + 2}{(x^2 - 9)(x + 2)} \div \dfrac{3x + 1}{(x + 3)(x - 3)} [/tex]
[tex] = \dfrac{x + 2}{(x + 3)(x - 3)(x + 2)} \div \dfrac{3x + 1}{(x + 3)(x - 3)} [/tex]
To divide by a fraction, multiply by its reciprocal.
[tex] = \dfrac{x + 2}{(x + 3)(x - 3)(x + 2)} \times \dfrac{(x + 3)(x - 3)}{3x + 1} [/tex]
Cancel out common factors in the numerator and denominator.
[tex] = \dfrac{1}{3x + 1} [/tex]
Solve 5x+3=3x+11
Please can someone answer this.