Please help me with this Algebra I question.
Answer:
[tex]-\dfrac{b^2}{16a^4}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{(2a)^{-2}b^5}{-4a^2b^3}[/tex]
[tex]\textsf{Apply the exponent rule}\quad (ab)^c=a^c \cdot b^c:[/tex]
[tex]\implies \dfrac{2^{-2}a^{-2}b^5}{-4a^2b^3}[/tex]
Separate the variables:
[tex]\implies \dfrac{2^{-2}}{-4}\cdot \dfrac{a^{-2}}{a^2}\cdot \dfrac{b^5}{b^3}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies \dfrac{2^{-2}}{-4}\cdot a^{-2-2}\cdot b^{5-3}[/tex]
[tex]\implies \dfrac{2^{-2}}{-4}\cdot a^{-4}\cdot b^{2}[/tex]
[tex]\textsf{Apply the exponent rule}\quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies \dfrac{1}{-4(2^2)}\cdot \dfrac{1}{a^4}\cdot b^{2}[/tex]
[tex]\implies -\dfrac{1}{16}\cdot \dfrac{1}{a^4}\cdot b^{2}[/tex]
Simplify:
[tex]\implies -\dfrac{b^2}{16a^4}[/tex]
Arianna Hu has a family membership in her company's health insurance program. The total cost is $6,095 annually and her employer pays 75% of the total cost. She also pays the optional dental premium of $406.25 per year and the optional vision annual premium of $256.10. What is the total monthly premium for all her insurance?
Find the perimeter
simply Answer
The perimeter of the polygon of sides as 9/2, 17/2, 52/5, 52/5, 64/5, 59/4 is 1227 /20.
What is the perimeter of the polygon?The perimeter of the polygon is the measure of the sum of the sides of the given figure.
The sides are given as 9/2, 17/2, 52/5, 52/5, 64/5, 59/4
The perimeter of the polygon = 9/2 + 17/2 + 52/5 + 52/5 + 64/5 + 59/4
= 26/2 + 168/5 + 59/4
= 111/4 + 168/5
= 555 + 672 / 20
= 1227 /20
Thus, The perimeter of the polygon is 1227 /20.
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Which was a factor in explosive population growth in cities? Please help
Answer:
b
Step-by-step explanation:
what is the one piece?
trihh has a 3 1/2 foot long peice of ribbon she plans to cut into pieces to make boomarkets each bookmarkt will be 1/4 long how many bookmarks can she make
3 1/2 = 7/2
7/2 ÷ 1/4
7/2 × 4/1
14/2
7 pieces
hope it helps...!!!
There are 10 girls in an athletics club.
e ratio of girls to boys is 5:3.
w many boys are there?
Answer:
6Step-by-step explanation:
There are 10 girls in an athletics club.
e ratio of girls to boys is 5:3.
w many boys are there?
we can solve with an equation
10 : x = 5 : 3
x = 10 * 3 : 5
x = 30 : 5
x = 6
---------------
3tan² 45° - sin² 60 - cot 30 + sec² 45°
Answer:
[tex]4.25-\sqrt{3}.[/tex]
Step-by-step explanation:
1) tan45=1; sin60=√3/2; cot30=√3; sec45=√2, then
2) 3-0.75-√3+2=4.25-√3 (it is ≈2.5179492).
If log(16)=s, what is the value of 2/3 log(6400) - 1/3 log(1600) in terms of s?
The value of the given expression in terms of s will be [(s + 0.602)/3].
What is a logarithm?Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.
If [tex]\log(16) = s[/tex]
Then the value of the given expression in terms of s is given below.
[tex]\dfrac{2}{3} \times \log(6400) - \dfrac{1}{3} \times \log(1600)[/tex]
We know the property of the logarithm.
[tex]\log 100 = 2[/tex]
Then we have
[tex]\rm \rightarrow \dfrac{2}{3} \times \log(6400) - \dfrac{1}{3} \times \log(1600)\\\\\\\rightarrow \dfrac{2}{3} \times ( \log 16 + \log 4 + \log 100 ) - \dfrac{1}{3} \times (\log 16 + \log 100)\\\\\\\rightarrow \dfrac{2}{3} \times (s + 0.602+2) - \dfrac{1}{3} \times (s + 2)\\\\\\\rightarrow \dfrac{2}{3} \times (s + 2.602 ) - \dfrac{1}{3} \times (s + 2)\\\\\\\rightarrow \dfrac{2 (s + 2.602) - (s - 2)}{3} \\\\\\\rightarrow \dfrac{s + 0.602}{3}[/tex]
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A prism is completely filled with 540 cubes that have edge length of 13 cm. What is the volume of the prism? Enter your answer in the box.
Answer:
vp=1186380cm^3
Step-by-step explanation:
Number of cubes =540length of one edge=13cm[tex]volume \: of \: a \: cube = {l}^{3} \\ v = {(13cm)}^{3} \\ = {2197cm}^{3} \\ [/tex][tex]volume \: of \: prism \: = volume \: of \: cube \: \times \: nuber \: of \: cubes \\ volume \: of \: prism = ( {2197cm}^{3} )(540) \\ = 1186380 {cm}^{3} = 1.1864 {m}^{3} [/tex]Answer:
Step-by-step explanation: hi it’
Determine the value of x.
is it 20?
Answer:
X = 20
Step-by-step explanation:
The two angles are vertical.
62 = (2 + 3x)
60 = 3x
60/3 =
20
You were correct
What is the absolute value of negative 1/2
Answer:
The absolute value of negative 1/2 is 1/2
Step-by-step explanation:
The absolute value of a number is the positive form of the number
Javier loves flying kites. He flies his kite for 1 hour on Monday, 2 hours on Tuesday, 4 hours on Wednesday, and 3 hours on Thursday. How many more hours did Javier fly his kite on Wednesday and Thursday than Monday and Tuesday?
Answer:
4 more hours
Step-by-step explanation:
wednesday+thursday=7
monday+tuesday=3
7-3=4
if the simple interest on $1,000 for 4 years is $320, then what is the interest rate?
Answer:
8%
Step-by-step explanation:
assume simple interest rate = r
interest = 1000 * 4 * r = 320
r = 320/4000 = 0.08 = 8%
FIND THE DOMAIN AND RANGE
Answer:
B
Step-by-step explanation:
help me please! I'm confused
I couldn't take a pic of all of it but the top says
identify the scatter plots to shoe a positvive assosiation,a negative assosiation,or no assosiation.
Step-by-step explanation:
1 and 2 are negative
3 and 5 are none
4 and 6 are positive
the amount of water in a bottle is reduced by 85% to 120 millimeters. how much water was originally in the bottle?
A percentage is a way to describe a part of a whole. The amount of water in the bottle originally is 800 mm.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Let the water in the bottle at the very initial be x.
Given that after reduction the amount of water in the bottle is 120 millimetres, also, the water is reduced by 85%, therefore, the amount of water that will be in the bottle is 15% of the original.
Water in the bottle = 15% of x
120 mm = 0.15 × x
x = 800 mm
Hence, the amount of water in the bottle originally is 800 mm.
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Please i need your help
Answer: 475 Add 5 more.
Step-by-step explanation:
What is the domain of f?
Answer:
Step-by-step explanation:
f(x) = x/(x-7)
The domain is C
7/(7-7) = 7/0 = undefined
Which of the following package deals is a better buy according to unit price?
$5.73 for 3 cans
$11.44 for 8 cans
$13.55 for 5 cans
$14.28 for 6 cans
HELP PLS WILL GIVE BRAINLIEST
A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge s (in dollars) is given by the function S= 0.40M + 18.95 , where M is the number of miles driven.
The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function I = 0.25M + 5.70.
Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M . Simplify your answer as much as possible.
C= ?
Answer:
Simplified answer = C = $0.65m + $24.65
Step-by-step explanation:
Add the two initial charges together (from the insurance and the standard charge) and you get $24.65. Then add the two charges together for each mile which is $0.65 per mile. Therefore, the total charge on the car is $24.65 + 65 cents every mile driven.
Two electricians work 6 1/2 hours each per day for 5 days. Find the total number of hours worked.
Mixed format: 10 3/4 (with a space between the whole number and the numerator) Fraction format: 1/4 Reduce all fractions.
Answer:
32.5 hours
Step-by-step explanation:
Total hours
6.5 x 5
32.5 hours
Jo is pouring a driveway and he mixes cement and water in the correct ratio. X represents the cement and y represents the water. The graph includes (54,120) (108, 240) (162, 360) (216, 480). He says (63, 140) is included in the relationship of the graph. Is he correct?
Answer:
Yes.
Step-by-step explanation:
y/x = 2.22..... for all the 4 points given.
The graph is a straight line with slope 2.22....
140/63 = 2.2222... also so this is included in the realtionship
izzes
Two angles are complementary. The smaller angle is 24° less than the larger angle. Find the measures of
both angles.
Answer:
The bigger angle is 57 degrees
The smaller angle is 33 degrees
Step-by-step explanation:
complimentary is that two angles will add up to 90 degrees
Lets say one angle is x, and the other is y.
the smaller angle is x, so it is be x-24degrees
x+(x-24)=90
2x=114
x=57 degrees
y=33degrees
A rectangular prism and its net are shown below.
(All lengths are in yards.)
If the dimension of the rectangular prism will be 11 by 8 by 4. Then the volume of the rectangular prism will be 352 cubic yards.
What is a rectangular prism?A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.
A rectangular prism and its net are shown below.
Then the volume of the rectangular prism will be
Volume = LWH
where
Width (W) = 8 yd
Length (L) = 11 yd
Height (H) = 4 yd
Then the volume will be
Volume = 11 × 8 × 4
Volume = 352 yd³
Then the volume of the rectangular prism will be 352 cubic yards.
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If the geometric mean of a and 12 is 8root6, find the value of a.
The value of a, when the geometric mean of two numbers a and 12 is 8√6 is equal to the number 32.
How to find geometric mean?Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.
For Geometric sequence, the value of geometric mean can be found out using the following formula,
[tex]x=\sqrt{ab}[/tex]
Here, (a and b) are the two terms of geometric sequence.
The geometric mean of a and 12 is 8√6. Thus,
[tex]x=8\sqrt{6}[/tex]
[tex]b=12[/tex]
Put this value in formula to find the value of a,
[tex]8\sqrt{6}=\sqrt{a\times12}\\[/tex]
Square both side of equation,
[tex](8\sqrt{6})^2=(\sqrt{a\times12})^2\\64\times6=12a\\a=\dfrac{64\times6}{12}\\a=32[/tex]
Thus, the value of a, when the geometric mean of two numbers a and 12 is 8√6 is equal to the number 32.
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Use the drawing tools to form the correct answer on the graph. Plot function f on the graph. f(x)= 3, -9
The equation of the function f with solution 3, -9 is x²+6x-27 and the graph of this equation with the use of drawing tools is attached below.
What is the definition of a Function?A function assigns the value of each element of one set to the other specific element of another set.
A function has to be plot which has the value of f(x) as 3 and -9. Here, 3 and -9 are the solution of the function. Thus,
x=3
x-3=0
The second solution is,
x=-9
x+9=0
Multiply both factor for the function as,
f(x)=(x-3)(x+9)
f(x)=x²+9x-3x-27
f(x)=x²+6x-27
This is the required function. The graph of this function is attached below.
Thus, the equation of the function f with solution 3, -9 is x²+6x-27 and the graph of this equation with the use of drawing tools is attached below.
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The cost of downloading a movie from a website is $4.99. Which equation can be used to find c, the cost in dollars of downloading n movies? A. c = 4.99 +n = B. n = 4.990 C. n = 4.99 +c D. c = = 4.99n
Answer:- The answer is letter B, c=1.75n
Step-by-step explanation: Hope this helps.
complete this statement: A plolygon with all sides the same length is said to be
Answer:
it is said to be a regular polygon.
Step-by-step explanation:
A regular polygon is a polygon that has all angles of the same measure and all sides of the same length.
And environmental group would like a representative sample of its members to complete a survey. Which method gives the most representative sample?
a. Survey all the people who attended the month club meeting.
b. Survey every third person from the list of group members.
c. Survey the first five people who joined the club.
d. Survey every other person that went on the weekend nature walk.
Answer:
D.
Step-by-step explanation:
When you survey every 3rd person you will use that as a good sample for the survey. Hope this helps!
