Solve the following problem.
1. If a is indirectly proportional to b, then a=k/b, where k is a constant or fixed number. If a=8 when b=6, find the value of k.
Using the value of k in number 1, find:
2. a if b=3
3. a if b=4
4. a if b=12
5. a if b=1.5
6. a if b=3.6
7. a if b=4.8
8. b if a=3
9. b if a=4
10. b if a=4.5
11. b if a= 4.8
12. b if a=3.6
13. b if a=6
Answer:
see explanation
Step-by-step explanation:
given the equation
a = [tex]\frac{k}{b}[/tex]
to find k use the given condition a = 8 when b = 6 , then
8 = [tex]\frac{k}{6}[/tex] ( multiply both sides by 6 to clear the fraction )
48 = k
a = [tex]\frac{48}{b}[/tex] ← equation of variation
2
if b = 3
a = [tex]\frac{48}{3}[/tex] = 16
3
if b = 4
a = [tex]\frac{48}{4}[/tex] = 12
4
if b = 12
a = [tex]\frac{48}{12}[/tex] = 4
5
if b = 1.5
a = [tex]\frac{48}{1.5}[/tex] = 32
6
if b = 3.6
a = [tex]\frac{48}{3.6}[/tex] = 13.3333.. = 13 [tex]\frac{1}{3}[/tex]
7
if b = 4.8
a = [tex]\frac{48}{4.8}[/tex] = 10
for the remaining questions, rearrange the equation with b as the subject
a = [tex]\frac{48}{b}[/tex] ( multiply both sides by b )
ab = 48 ( divide both sides by a )
b = [tex]\frac{48}{a}[/tex]
8
if a = 3
b = [tex]\frac{48}{3}[/tex] = 12
9
if a = 4
b = [tex]\frac{48}{4}[/tex] = 12
10
if a = 4.5
b = [tex]\frac{48}{4.5}[/tex] = 10.666... = 10 [tex]\frac{2}{3}[/tex]
11
if a = 4.8
b = [tex]\frac{48}{4.8}[/tex] = 10
12
if a = 3.6
b = [tex]\frac{48}{3.6}[/tex] = 13.333... = 13 [tex]\frac{1}{3}[/tex]
13
if a = 6
b = [tex]\frac{48}{6}[/tex] = 8
5. Standard form of 15240000 is :
Answer:
1.524×10^7
Step-by-step explanation:
move the "comma" from the back till you get a number less than 10, the 7 is how many times you've moved the comma
In the equation 12u + 3v = 0, if u = 1, find the value of v.
Answer:
v = -4.
Step-by-step explanation:
Replace the u in the equation by 1, so we have:
12*1 + 3v = 0
3v = -12
v = -1/3 = -4.
Use Pascal's Triangle to expand (5z + 5x²)³. Express your
answer in simplest form.
The simplest form is 15z+ 15x²
How to simplify the given expression ?In algebra, a triangle-shaped grouping of integers known as Pascal's triangle provides the coefficients for the expansion of any binomial formula, such as (x + y)n. Although it is much older, it bears the name of the French mathematician Blaise Pascal from the 17th century.
Because it has so many patterns that can be used to greatly simplify complex calculations, Pascal's triangle is significant.
Given,
(5z+5 x²)3
15z+15x² by simplifying,
3(5z+5 x²)
apply the distributive formula :a (b + c) =ab + ac
3(5z+5 x²) = 5x+3 * 5x²
By simplifying 3 5z+3 , 5x², 15z+15x²
we get
15z+ 15x²
Therefore the simplest form is 15z+ 15x² .
To learn more about pascal triangle refer to :
https://brainly.com/question/13670757
#SPJ1
Luke randomly selects 25 students from his school and asks each of them how many minutes they read each night to find out how much, on average, students at his school read. This represents which type of data collection?
A: Census
B: Experiment
C: Observation
D: Sample
I'm pretty sure it's census
3 tenths and 24 hundredths, after regrouping, there are
3 tenths and 24 hundredths, after regrouping gives 0.54
What does Regroup Mean?In math, regrouping can be defined as the process of making groups of tens when carrying out operations like addition and subtraction with two-digit numbers or larger. To regroup means to rearrange groups in place value to carry out an operation. We use regrouping in subtraction, when digits in the minuend are smaller than the digits in the same place in the subtrahend.
Given here, 3 tenths and 24 hundredths after regrouping we get
(3 tenths + 24 hundreths) = 0.54
Hence, 3 tenths and 24 hundredths after regrouping gives 0.54
Learn more about regrouping in decimals here:
https://brainly.com/question/11903168
#SPJ1
pls answer all questions
Spiders are arachnids with eight legs, as do all arachnids. Spiders differ from insects in that they have only six legs.
Do spiders have 6 or 8 legs?Crabs and prawns are also members of the phylum Arthropoda, which includes spiders. Spiders walk on eight legs, but they also have two additional legs that they utilise as hands. The front legs are called pedipalps, or palps for short.
Proteins are secreted by glands on spiders, which aid in the formation of the web. For a number of objectives, including prey capture, prey detection, tunnel lining, egg sacs, and prey wrapping, spiders can create a variety of webs or silks.
Spiders are venomous carnivores who hunt their prey with poison.In Everglades National Park, arachnids such as spiders, scorpions, mites, ticks, whip scorpions, and pseudoscorpions are all common.
To learn more about spider refer to:
https://brainly.com/question/885563
#SPJ1
10. What is the value of x?
A 47.5
0.50.5
2
D. 105
Answer:
A
Step-by-step explanation:
2x + 10 = 105
2x = 95
x = 47.5
A radioactive compound with mass 320 grams decays at a rate of 27% per hour. Which equation represents how many grams of the compound will remain after 7 hours?
Answer:
320 grams ÷ 27% = 8.3 grams
Step-by-step explanation:
mark brainliest plss
How many times larger than 3 x 10^4 is to 15 x 10^8
Answer:
149970000
Step-by-step explanation:
1500000000-30000=149970000
Answer:
1499970000
Step-by-step explanation:
3 x 10^4 = 30,000
15 x 10^8 = 1500000000
1500000000 - 30,000 = 1499970000
Please help! I have a barrel of apples. 70% are red and 30% is green but 24% of all green apples are damaged. What is the remaining percentage of green apples?
Answer:
6
Step-by-step explanation:
Answer:
22.8% ≈ 23%
Step-by-step explanation:
Since we don't know the number apples, I just turned the percentages into decimals
30% = 0.3
24% = 0.24
1.00 - 0.24 = 0.76 *Since 24% of green apples are damaged, then 76% are not damaged*
0.3 x 0.76 = 0.228 = 22.8% ≈ 23%
The length of a rectangle is 7cm more than twice the width. When just the width is tripled, the perimeter of the resulting rectangle is 74cm. What are the original dimensions of the rectangle?
Answer:
Length = 27cm
Width = 10cm
Step-by-step explanation:
Let the length of the rectangle be x
Let the width be y
If the length of a rectangle is 7cm more than twice the width, then;
x = 2y + 7
Since P = 2(x+y)
P = 2(2y+7+y)
P = 2(3y+7)
P = 6y+14
If the width is tripled, P = 74
74 = 6y+14
6y = 74-14
6y = 60
y = 10
Since x = 2y+ 7
x = 2(10) + 7
x= 20+7
x = 27
Hence the original dimension is 27cm by 10cm
Solve for x (Will get brainliest award)
Answer:
X = 21
Step-by-step explanation:
We know that's 90 degrees in total so we add both angles and equal them to 90 to solve for x
x + 4 + 3x + 2 = 90 Combine like terms
4x + 6 = 90
- 6 -6 subtract 6
4x = 84
/4 /4 isolate x
x = 21
We know 5. 3 = 15. Which 2 of the following statements must also be true? (You need to select 2 answers) 9 5 is a factor of 15. 3 is a multiple of 15. 15 is a multiple of 3.
Answer: 5 is a factor of 15.
15 is a multiple of 3.
Step-by-step explanation:
A Factor, is a number that can divide another number without a remainder. For example, 5 is a factor of 15 ad it can divide 15 evenly.
A multiple is simply a times table. For example, the multiples of 3 are 3, 6, 9, 12, 15, 18, 21 ......
Therefore, the correct option from the answers given are:
5 is a factor of 15.
15 is a multiple of 3.
Two shipping companies charge different amounts to ship a package. Company A charges a fee of $6.50 and $0.35 for each pound. Company B charges a fee of $7.25 and $0.25 for each pound. Write an equation that could be used to find p, the number of pounds each package would have to weigh for the total cost of shipping the packages to be the same.
The number of pounds each package would have to weigh for the total cost of shipping the packages to be the same will be 7.50 pounds.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The cost to transport an item varies between two shipping providers. The price charged by Company A is $6.50 plus $0.35 per pound. Charges from Company B are $7.25 plus $0.25 per pound.
Let 'p' be the number of pounds and 'T' be the total cost of shipping. Then the equations are given as,
T = 0.35p + 6.50
T = 0.25p + 7.25
If the total cost of shipping the packages is to be the same. Then the number of pounds is given as,
0.35p + 6.50 = 0.25p + 7.25
0.35p - 0.25p = 7.25 - 6.50
0.10p = 0.75
p = 7.50 pounds
The number of pounds each package would have to weigh for the total cost of shipping the packages to be the same will be 7.50 pounds.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ1
-50 POINTS-
Don’t need to explain
A.)
B.)
C.)
Answer:
C
Step-by-step explanation:
Find the length and width of the actual room, shown in the scale drawing. Then find the area of the actual room. Round the final answer, if necessary, to the nearest tenth.
The actual dimensions are 9.75 feet and 7.5 feet. The area will be 73.125 square feet.
What is the scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). The scale factor is defined as the proportion of the new image's size to that of the previous image.
Here the scale factor for the given image is 2 inch = 3 ft.
The measure of the actual dimensions will be calculated as,
2 in = 3 ft
1 in = 3/2 ft
6.5 in = 6.5 x 3 / 2 = 9.75 ft
5 in = 5 x 3 / 2 = 7.5 ft
The actual area will be calculated as,
Area = 9.75 x 7.5
Area = 73.125 square feet
To know more about scale factors follow
https://brainly.com/question/2826496
#SPJ1
What is the angle of turn clockwise from South East to North?
N
A 45°
B 135°
C 225°
D 315°
The angle of a turn clockwise from South East to North is Option B 135°.
When determining the angle of turn, it is important to consider the direction of rotation (in this case, clockwise) and the starting and ending points (in this case, South East to North).
If we imagine the compass as a clock, with North at the 12 o'clock position, South at the 6 o'clock position, East at the 3 o'clock position, and West at the 9 o'clock position. Then South East would be at the 4:30 position and the North would be at the 12 o'clock position. To rotate from 4:30 (South East) to 12 o'clock (North) in a clockwise direction, we would have to rotate 135 degrees. Thus, the angle of a turn clockwise from South East to North is 135 degrees.
To learn more about the angle, visit:
brainly.com/question/13954458
#SPJ4
Need this done in a square root method and show me all the steps.
Answer:
d=i√7, -i√7
Step-by-step explanation:
-2d^2 -4=10 add 4 to both sides
-2d^2 = 14 divide each term by -2
d^2= -7 take the square root of each side to get rid of the exponent
d= = √-7 ( put a slash(short line above that = sign ) in the second equal sign)
d = =i√7
5. Maria writes the expression below.
21 + 3 + 6 + 9 − 3
Which expression could be shown to be equivalent to Maria's expression based on the commutative property of addition?
Answer:
35+1
Step-by-step explanation:
They both equal 36 according to the commutatative property of addition.
These tables correspond to inputs and outputs. Which of these input and output tables could represent a function rule, and which ones could not?
Table A is a function.
Table B is not a function.
Table C is a function.
Table D is not a function.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
We know a relation is a function if it is one-to-one or many-to-one.
But a relation is not a function if it is one to many.
Table A is a function and it is a many-to-one function.
Table B is not a function as input 1 leads to two different outputs 1, - 1.
Table C is a function and it is a one-to-many function.
Table D is not a function as one input leads to 3 different outputs.
learn more about functions here :
https://brainly.com/question/12431044
#SPJ2
Help me pleaseeeeeeeee!!!
0.08/0.2 and 0.2/0.8 are not proportional.
What is proportionality?A proportion is an equality of two ratios. We write proportions to help us establish equivalent ratios and solve for unknown quantities.
Given are two numbers, 0.08/0.2 and 0.2/0.8
Checking for if they are proportional or not,
0.08/0.2
Multiplying denominator and numerator by 100,
8/20 = 2/5
And,
0.2/0.8 = 1/4
Since, 0.08/0.2 ≠ 0.2/0.8
Hence, 0.08/0.2 and 0.2/0.8 are not proportional.
Learn more about proportional, click;
https://brainly.com/question/3254974
#SPJ1
Recall that there are 2π radians in one full rotation and 360 degrees in one full rotation.
Suppose an angle has a measure of 2. 1 radians.
This angle (with a measure of 2. 1 radians) is what percent of a full rotation?
 %
Use your work in part (i) to determine the measure of the angle in degrees.
 degrees
If there are [tex]2\pi[/tex] radians and [tex]360 \textdegree[/tex] in one full rotation and an angle has a measure of [tex]2.1 radians[/tex] then the angle is 33.4 percent of a full rotation , and the measure of the angle in degrees is [tex]120.2\textdegree[/tex] .
we know that in 1 full rotation , the radians is 2π ;
and in 1 full rotation , the degree is 360 degree ;
We know that the relation between the degree and the radian measure is
⇒ [tex]1 radian = \frac{180\textdegree}{\pi }[/tex] ;
Part(i) ;
we have to express the 2.1 radians as a percent of full rotation ;
we get ; ⇒ [tex]\frac{2.1}{2\pi } \times 100\%[/tex]
on simplifying further ,
we get ; [tex]\approx 33.4\%[/tex] .
Part(ii) ;
we have to determine the measure of the angle in degrees.
from part(i) , we find the percent is [tex]33.4\%[/tex] ,
So , [tex]33.4\%\times 360\textdegree[/tex]
On simplifying ,
⇒ [tex]\frac{33.4}{100} \times 360\textdegree[/tex]
[tex]\approx 120.2\textdegree[/tex] .
Learn more about Angles here
https://brainly.com/question/21506238
#SPJ4
10. Find the solution set for the following
y=x²-3x-4
y-x=-4
Answer:
I have no idea tbh I need help with this too
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!
What is a real value number?
Real value numbers are both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc are all real numbers.
What is a real number in mathematics?The real number that consist of different types of numbers for example prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc. These numbers can be expressed in the form of figures.Any number that we can think except complex numbers is a real number.
How many types of real numbers?Real numbers encompass three classifications of numbers.Whole numbers, rational numbers, and irrational numbers are all real numbers.Even counting and natural number are all real numbers.
To learn more about real number visit;
https://brainly.com/question/551408
#SPJ4
What is an inverse variation graph called?
The graph of the inverse variation equation is called a rectangular hyperbola.
A form of proportionality called inverse variation occurs when one number falls as the other rises or the other way around. This suggests that if one number rises while the other decreases, the magnitude or absolute value of the first quantity will decrease, resulting in a constant product. The constant of proportionality is another name for this item.
An inverse variation is a relationship between two variables in which the product is constant; as a result, while one of the variables changes, the other changes correspondingly to maintain the same value of the product. This connection has the form of a hyperbola.
To know more about inverse variation visit: brainly.com/question/11592410
#SPJ4
A pound of strawberries costs $3.28 and a pound of apples costs $4.63. What is the combined cost of 0.7 pound of strawberries and 1.4 pounds of apples
The combined cost of 0.7 pound of strawberries and 1.4 pounds of apples is $8.778.
What is called a pound?The Latin word "poundus," which means "weight," is whence its name originates.
Any of the many weight and mass units. especially: a measurement that is commonly used by English-speaking peoples and equals 16 ounces (about 0.454 kilograms) see measurement. the United Kingdom's fundamental monetary unit. known also as the pound sterling.
Given that A pound of strawberries costs $3.28
and a pound of apples costs $4.63
So the combined cost of 0.7 pound of strawberries and 1.4 pounds of apples is
cost = $3.28(0.7) + $1.4(4.63)
cost = $2.296 + $6.482
cost = $8.778
Therefore, the answer is $8.778.
To learn more about pound refer to:
brainly.com/question/26233980
#SPJ4
ngl i forgot whats 23+41
Answer:
64
Step-by-step explanation:
23
41
____
6 4
Serena paid $194.99 for a game system and then bought two equally-priced games. She spent a total of $284.97.
Answer:
Serena paid $194.99 for a game system and then bought two equally-priced games. She spent a total of $284.97.
Step-by-step explanation:
The perimeter of a rectangle is 84cm and it's length is 6cm longer than it's breadth. Find the length and breadth of the rectangle
Answer:
Step-by-step explanation:
The perimeter of a rectangle is the sum of all its sides. Since the perimeter is given as 84 cm, we can set up the following equation to represent the problem:
2l + 2b = 84
Where l is the length of the rectangle and b is the breadth.
We are also told that the length is 6 cm longer than the breadth. We can represent this relationship with the equation:
l = b + 6
Substituting the second equation into the first equation, we get:
2(b + 6) + 2b = 84
Expanding the left side of the equation gives:
2b + 12 + 2b = 84
Combining as terms gives:
4b + 12 = 84
Subtracting 12 from both sides gives:
4b = 72
Dividing both sides by 4 gives:
b = 18
Substituting this value back into the equation l = b + 6 gives us:
l = 18 + 6
l = 24
Therefore, the length of the rectangle is 24 cm and the breadth is 18 cm.