Answers
Note that (1/12)^-2b is the same as 12^2b. When we add the exponents we get 2b-2b+2=2, hence 12² on the left.
Related Questions
A machine produces 584 units in 8 hours. how many units does it produce in 2 hours?
Answers
146 = 2 hours (divide each side by four)
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
584 units = 8 hours
1 hour = 73 units
2 hours = 146 units
The number of units produced in 2 hours is 146 units.
What is a unit rate?
It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
A machine produces 584 units in 8 hours.
This means,
584 units = 8 hours
Divide both sides by 8.
1 hour = 73 units
Now,
1 hour = 73 units
Multiply 2 on both sides.
2 hours = 146 units
Thus,
The number of units produced in 2 hours is 146 units.
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Scott drove to his friends house and back.on the trip there he drove 72km/h and on the return trip he went 60 km/h. How long did the trip there take if the return trip took six hours?
Answers
Because i had that question and i got it wrong
Kathryn draws three pairs of intersecting lines. In each figure, she measures a pair of angles. What is a reasonable conjecture for Kathryn to make by recognizing a pattern and using inductive reasoning? When a pair of lines intersect, the vertical angles are acute. When a pair of lines intersect, all of the angles formed are right angles. When a pair of lines intersect, the vertical angles are congruent. When a pair of lines intersect, all of the angles formed are congruent.
Answers
1) Vertical angles (or opposite angles) are congruent. In this case, vertical angles could be acute or obtuse depending on the position of the lines.
2) The second case is the exception when all the angles are equal. It means that the lines are perpendicular.
3) Again back to the first case, vertical angles are equal or congruent in other words.
4) And again back to the second case when the lines are perpendicular, then all the angles that formed are equal to each other.
You can observe all the cases in the picture attached below.
The reasonable conjecture for Kathryn to make by recognizing a pattern and using inductive reasoning is:
When a pair of lines intersect, the vertical angles are congruent.
Step-by-step explanation:The vertical angles are the opposite angles that are formed by the intersection of two lines. They are also known as Vertically opposite angles.
We know that when a pair of lines intersect then the vertical angles are always congruent.
However the measure of the angles may be acute or obtuse or right angle.
The same could be seen with the help of the figure attached to the answer.
PLEASE HELP.
On a road, a bike sign in the shape of an isosceles trapezoid is to be painted. The sign and its dimensions are shown below. What is the area of the sign?
A.24 square feet
B.28 square feet
C.30 square feet
D.32 square feet
Answers
½bh + LB + ½bh
= ½(1×4) + (7×4) + ½(1×4)
= 2 + 28 +2
= 32 square feet
D is ur answer
drag each label to the correct location on the table each label can be used more than once but not all labels will be used
Answers
this is the question...
factor 9x^2 -5 . using difference of squares
Answers
Which line is parallel to line r?
line p
line q
line s
line t
Answers
Hope this helps
In the accompanying diagram QRS is similar to LMN,RQ=30 ,QS=21 SR=27 and LN=7. What is the length of ML
Answers
Judy bought 2 cotton candies and 2 funnel cakes. Her total cost was $10. Wayne bought 3 cotton candies and 1 funnel cake. What was the total cost of Wayne's food?
a. too little
b. too much
Answers
Answer:
Too little
Step-by-step explanation:
A cube has an edge length of 9 centimeters. If the side length is increased by a factor of 3, how much larger is the perimeter of a face of the new cube?
Answers
Answer:
The perimeter of a face of the new cube is:
108 cm
Step-by-step explanation:
Original edge length of cube=9 cm
Increased edge length of the cube=9×3 cm
=27 cm
The perimeter of a face of a cube=4s
where s is the edge length of the cube
Perimeter of a face of new cube=4×27 cm
= 108 cm
Hence, the perimeter of a face of the new cube is:
108 cm
In a particular class of 31 students, 12 are men. What fraction of the students in the class are women
Answers
An organization founded by businesses in a specific industry for the purpose of collaboration between companies is called a(n):
Answers
Answer:
The answer is trade association.
Step-by-step explanation:
Such organizations are founded to encourage trade and collaboration between companies. These are also known as industry trade group or business association and is funded by businesses that operate in a particular industry.
Cassandra is trying to think of a good way to keep her financial records. She makes a lot of purchases, using cash, debit cards, and credit cards about equally. When she gets home every day, she tends to be very tired and doesn’t like to do a lot of organized thinking. She tends to lose individual pieces of paper if she doesn’t file them immediately. What might be a good method for Cassandra to use? a. Recording all of her daily expenditures in an organizational computer program. b. Keeping and collecting receipts for everything she buys. c. Tracking and collecting her bank and credit statements every month. d. Carrying a notebook and immediately recording all of her transactions in it.
Answers
Answer:
the answer is d
Step-by-step explanation:
everybody else keeps getting it wrong, the answer is d
The measure of one angle is three times the measure of its complement
Answers
First angle:x
Second angle:3x
x+3x=90
4x=90
x=22.5
The first angle is 22.5 degrees and the complement is 67.5
Given the function f(x)= x^4+6x^3-x^2-30x+4
Use the intermediate value Theorem to decide which of the following intervals contains at least one zero (there are 4 answers)
A) [-5,-4]
B) [-4,-3]
C) [-3,-2]
D) [-1,0]
E) [0,1]
F) [1,2]
Answers
The correct answers are a,b,e,f
By applying the Intermediate Value Theorem to the function f(x)=x^4+6x^3-x^2-30x+4, we find that the intervals containing at least one zero, or root, are [-4,-3], [-3,-2], [-1,0], and [0,1].
Explanation:In mathematics, particularly in calculus, the Intermediate Value Theorem (IVT) is used to show that a given interval has at least one zero, or root, of a function. In this case, the function is f(x)=x^4+6x^3-x^2-30x+4.
To apply IVT, we calculate the function value at the endpoints of the intervals. If the function values at the endpoints of an interval have different signs, then by IVT, there is at least one zero in that interval.
f(-5)=625+750-25+150+4=1504f(-4)=256+384-16+120+4=748f(-3)=81+162-9+90+4=328f(-2)=16+48-4+60+4=124f(-1)=1+6-1+30+4=40f(0)=4f(1)=1+6-1-30+4=-20f(2)=16+48-4-60+4=4A change in sign between the function values at the endpoints of an interval indicates there is at least one root in that interval. Thus, by checking the signs of the consecutive function values, we can conclude that the intervals which contain at least one root are [-4,-3], [-3,-2], [-1,0], and [0,1].
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Joey saved $2 today. if he doubles the number of dollars he saves each day, how many days, including today, will it take him to save more than $500?
Answers
1*2
2*2
4*2 by the third day, Joey has (2^2)*2 dollars
8*2 by the 4th day, Joey has (2^3)*2 dollars
16*2 by the 5th day, Joey has (2^4)*2 dollars
so by the nth day, he has 2^(n-1)*2, which is 2^n
2^n>500
n is about 9
By saving double the amount saved on the previous day starting with $2 in 8 days Joey will have $500.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
Given, Joey saved $2 today. If he doubles the number of dollars he saves each day.
This can be formed as a geometric sequence with common ratios(r) = 2.
a₁ = 2, We know the sum of a geometric series is [tex]S_n = \frac{a_1(r^n - 1)}{r - 1}[/tex].
∴ 500 = 2(2ⁿ - 1)/(2 - 1).
2ⁿ - 1 = 250.
2ⁿ = 251.
[tex]log_22^n = log_2251[/tex].
n = 7.97 Or approximately in 8 days.
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What is the coefficient of the fourth term in the expansion of (x + 3)4?
Answers
Final answer:
The coefficient of the fourth term in the expansion of (x + 3)⁴ is calculated using the binomial theorem, which results in a coefficient of 108.
Explanation:
To find the coefficient of the fourth term in the expansion of (x + 3)⁴, we can use the binomial theorem. The binomial theorem states that when a binomial is raised to a power, the expansion consists of terms in the form of [tex]C(n, k) \times a^{n-k} \times b^k[/tex], where C(n, k) is the binomial coefficient. In our case a = x and b = 3, and n = 4.
For the fourth term where k = 3, the term would be [tex]C(4, 3) \times x^{4-3} \times 3^3[/tex]. The binomial coefficient C(4, 3) is equal to 4 because there are four ways to choose three items out of four. Therefore, the coefficient is 4 × 3³ = 4 × 27 = 108. So, the coefficient of the fourth term in the expansion of (x + 3)⁴ is 108.
30 POINTS!!
Which construction correctly shows how to bisect ∠X?
Answers
An angle bisector is a ray, segment, or line that divides a given angle into two angles of equal measure. Therefore, the correct answer is option C.
What is an angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
An angle bisector is defined as a ray, segment, or line that divides a given angle into two angles of equal measures.
Steps to Construct an Angle Bisector:
Step 1: Draw any angle, say ∠ABC.
Step 2: Taking B as the center and any appropriate radius, draw an arc to intersect the rays BA and BC at, say, E and D respectively. (Refer to the figure below)
Step 3: Now, taking D and E as centers and with the same radius as taken in the previous step, draw two arcs to intersect each other at F.
Step 4: Join B to F and extend it as a ray. This ray BF is the required angle bisector of angle ABC.
Step 2: Taking B as the center and any appropriate radius, draw an arc to intersect the rays BA and BC at, say, E and D respectively. (Refer to the figure below)
Therefore, option C is the correct answer.
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What are the x and y intercepts of the line described by this equation? 4x-3y=12.3
Answers
4x-3(0)=12.3
4x=12.3
x=12.3/4
x=3.075 (x-intercept)
y-intercept is when x=0
4(0)-3y=12.3
-3y=12.3
y=12.3/-3
y=-4.1 (y-intercept)
Hope I helped :)
so; 4x - 3y = 12.3 will be
-3y = 12.3 - 4x
rearrange so it will be easy to isolate your y.
-3y = -4x + 12.3
divide both sides by -3
-3y/-3 = -4x/-3 + 12.3/-3
y = 4x/3 - 4.1
so: slope 'm' = 4x/3
y-intercept = -4.1
x-intercept = 0
In what time will $400 amount to $512 if the simple interest is calculated at 14% p.a.
Answers
The time is 2 years:
Important variables to know:
A= Amount
P = Principal
I = simple Interest
T = time in years
R = rate in years
Formulas:
A = P + I
I = PRT
What we have? Amount ($512), Principal ($400), Rate (14%)
What we need? Time and Interest (simple interest)
So, first let's find the interest.
512 = 400 + I
Subtract 400 from both sides.
I = 112
Then plug that into the second formula:
112 = 400*.14(T)
Multiply 400*.14= 56
112 = 56T
Divide both sides by 56
T = 2 years
Write an expression that represents "the difference of eight and two, added to x"
Answers
name the property or real numbers illustrated by the equation
Answers
The associative property of addition states that you can group the terms however you prefer and the result is the same. The parenthesis are used to indicate grouping a + b + c = (a + b) + c = a + (b + c).
Therefore, the answer is option A. Associative Property of Addition.
A photo 5 inches wide and 8 inches long is enlarged. How long is the new photo if it is (1)10 inches; (2)15 inches; (3)8 inches wide?
Answers
Answer:
1.16 in
2.24 in
3.12.8 in
Step-by-step explanation:
We are given that
Width of photo=5 in
Length of photo=8 in
We have to find the length of new photo in each case.
1. Let x represent the width and y represents the length of photo.
When width increase then length of photo is also increases then it is direct proportion.
[tex]\frac{x_1}{y_1}=\frac{x_2}{y_2}[/tex]
Substitute the values then we get
[tex]\frac{5}{8}=\frac{10}{y}[/tex]
[tex]y=\frac{10\times 8}{5}=16[/tex]
Hence, the length of photo=16 in
2.Width=x=15 in
Again using the formula
[tex]\frac{5}{8}=\frac{15}{y}[/tex]
[tex]y=\frac{15\times 8}{5}=24[/tex]
Hence, the length of new photo=24 in
3. Width =x=8 in
Substitute the values in the given formula
[tex]\frac{5}{8}=\frac{8}{y}[/tex]
[tex]y=\frac{8\times 8}{5}=\frac{64}{5}=12.8[/tex]
Hence, the length of new photo=12.8 in
BRAINLIESTTTTTT PLEASEEEEEE
Answers
Write the expression as a single natural logarithm.
3 ln 2 + 6 ln y
Answers
Answer:
[tex]ln(8y^{6})[/tex]
Step-by-step explanation:
3ln(2)+6ln(y)
= [tex]ln(2^{3} )+ln(y^{6})[/tex]
= [tex]ln(8 )+ln(y^{6})[/tex]
= [tex]ln(8*y^{6})[/tex]
= [tex]ln(8y^{6})[/tex].
Find the distance between A(-12,13) and B(-2,-11).
F. 6 units
G. 14 units
H. 26 units
J. 29 units
Answers
(-12, 13) and (-2, -11)
= √(-2 - -12)^2 + (-11 - 13)
= √(10^2) + (-24^2)
= √(100) + 576
= √676
= 26
hope this helps, God bless!
In a system of linear equations, the slope of one line is the negative reciprocal of the slope of the other line. Is this system independent, dependent, or inconsistent?
Answers
Final answer:
An independent system of linear equations has two lines that intersect at exactly one point. If the slope of one line is the negative reciprocal of the other, the lines are perpendicular, indicating they intersect once and the system is independent.
Explanation:
If the slope of one line in a system of linear equations is the negative reciprocal of the slope of the other line, this indicates that the two lines are perpendicular to each other. Perpendicular lines intersect at one point and therefore, the system of equations is independent. An independent system has a single unique solution, meaning that there is exactly one point where the two lines cross.
In terms of graphs and equations, the slope or 'm' in the equation y = mx + b represents the rate at which the dependent variable changes with respect to the independent variable. The negative reciprocal relationship between slopes of two lines means that one will rise (positive slope) and fall (negative slope) at the same rate but in opposite directions, ensuring they intersect just once unless the y-intercepts (b) are also identical, which would make them the same line (dependent system) rather than intersecting lines.
Ed counts 23 black cars, 9 red cars, 17 blue cars, 25 white cars and 21 silver cars during 20 minutes of watching. How many more white and blue cars are there than silver and red cars?*
Answers
9 red cars
17 blue cars
25 white cars
21 silver cars
(white cars + blue cars) - (sliver cars + red cars)
(25 + 17) - (21 + 9)
(42) - (30)
12 more blue and white cars
Tracy pays $8.50 of her monthly life insurance premium and her employer covers the rest of her monthly premium is $32.25 what is the annual value to Tracey of this benefit
Answers
Tracy pays $8.50/month = $102.
$387 - $102 = $285 that the employer pays
Final answer:
Tracy's employer pays $23.75 each month towards her life insurance premium. The annual value of this benefit to Tracy is $285, calculated by multiplying the monthly employer contribution by 12.
Explanation:
The question is asking to calculate the annual value of the benefit that Tracy receives from her employer for her life insurance. Tracy pays $8.50 monthly and her employer covers the remainder, making the total monthly premium $32.25. To find the annual value of the benefit, we need to first determine how much her employer pays each month and then multiply this by 12 to get the annual value.
First, we subtract Tracy's contribution from the total premium:
$32.25 - $8.50 = $23.75
This is the monthly contribution by the employer. Now, to find the annual value, we multiply the monthly employer contribution by 12:
$23.75 × 12 = $285. Therefore, the annual value of the benefit that Tracy receives is $285.
WHAT IS 6.4 DIVIDED BY 43.52
Answers
Final answer:
To divide 6.4 by 43.52, the approximate quotient is 0.09238.
Explanation:
To divide 6.4 by 43.52, you can simply perform the division operation. Here are the steps:
Set up the division problem as follows: 6.4 ÷ 43.52.Divide the decimal part of the dividend (6.4) by the divisor (43.52). The quotient will have the same number of decimal places as the dividend. In this case, divide 4 by 43, which equals approximately 0.09238.Therefore, 6.4 divided by 43.52 is approximately 0.09238.