Index notations are as follows:
a) 2³
b) 3²
c) 6³ * 8³
d) 3³ * 4²
What are Exponents?A number's exponent demonstrates how many times we are multiplying a given number by itself. 3^4, for instance, indicates that we are multiplying 3 by four. 3*3*3*3 is its expanded form. The power of a number is another name for an exponent. A whole number, fraction, negative number, or decimal are all acceptable.
Let's break down the given index notation one by one:
a) 2 is taken 3 times = 2³
Similarly,
b) 3²
c) 6³ * 8³
d) 3³ * 4²
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A line has a slope of 1/5 and passes through the point (3,10). What is its equation in point-slope form? Use the specified point-slope form.
The equation of a line that has a slope of 1/5 and passes through the point (3, 10) is y= (1/5)x + (47/5).
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is that a line has a slope of 1/5 and passes through the point (3, 10)
We can write the slope of the line as -
m = 1/5
For the point (3, 10), we can write -
y = (1/5)x + c
10 = (1/5) x 3 + c
c = 10 - 3/5
c = 47/5
Therefore, the equation of a line that has a slope of 1/5 and passes through the point (3, 10) is y= (1/5)x + (47/5).
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−
50
67
1. 5−100%=minu, tart fraction, 67, divided by, 50, end fraction, plu, 1, point, 5, minu, 100, percent, equal
Enter the anwer a an exact decimal or implified fraction
The answer as an exact decimal = -0.84 and simplified fraction = −21/25.
What is simplified fraction?Simplifying a fraction is the process of reducing a fraction to its most basic form. If the numerator and denominator of a fraction have no common factors other than one, the fraction is in its simplest form.
When solving fraction problems, we must first simplify them. Even if we simplify them, the fraction's value will remain unchanged. This means that the simplified and actual fractions are equivalent fractions.
Given that
-67/50 + 1.5 − 100% = ?
Lets solve
= -67/50 + 1.5 − 100%
= -67/50 + 1.5 − (100 × 0.01)
= -67/50 + 3/2 - 1
= -67/50 + 75/50 - 50/50
= (-67 + 75- 50)/50
= −42/50
= −21/25
= -0.84
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Derek owns a snack shop where he sells tins of buttered and caramel popcorn. The table shows the number of each type of popcorn sold over w weeks.
Popcorn Sales
Popcorn Cost ($)
Number Sold
Over w Weeks
Buttered 11 8w+9
Caramel 11 6w−1
After 12 weeks, how much more will he have made in sales of buttered popcorn than the sales of caramel popcorn?
In the transaction, he will receive $374 more in sales of buttered popcorn than caramel popcorn.
What are mathematical operations?An operation, often known as an "operand" or "argument," is a function in mathematics that converts zero or more input values into a clearly defined output value. In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.
Given, Derek owns a snack shop where he sells tins of buttered and caramel popcorn. The table shows the number of each type of popcorn sold over w weeks.
Popcorn Sales Popcorn Cost ($) Number Sold Over w Weeks
Buttered 11 8w+9
Caramel 11 6w−1
After 12 weeks of total buttered popcorn, he will make the sale
= $11 * (8*12 + 9)
= 11 * (96 + 9)
= $1,155
After 12 weeks of total caramel popcorn, he will make the sale
= $11 * (6*12 - 1)
= $11* (71)
=$781
In the sale, he will get more sales in buttered popcorn than sales in caramel popcorn by 1,155 - 781 = $374
Therefore, He will make $374 more in sales of buttered popcorn than caramel popcorn during the sale.
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I really need help on this one too
The solution is Option C and Option D.
The exponential function is given by f ( x ) = 2 ( 3 )ˣ
The exponential function is given by f ( x ) = 800 / 4ˣ
What are the laws of exponents?
When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
Let the x values be x = { 0 , 1 , 2 , 3 }
Let the y values be y = { 7 , 19 , 31 , 43 }
The equation of line is y = 12x + 7
This is a linear equation
b)
Let the x values be x = { 0 , 1 , 2 , 3 }
Let the y values be y = { 5 , 10 , 15 , 30 }
The equation is a quadratic equation
c)
Let the x values be x = { 0 , 1 , 2 , 3 }
Let the y values be y = { 2 , 6 , 18 , 54 }
The equation is y = 2 ( 3 )ˣ
This is an exponential function
d)
Let the x values be x = { 0 , 1 , 2 , 3 }
Let the y values be y = { 800 , 200 , 50 , 12.5 }
The equation is f ( x ) = ( 800 / 4ˣ )
This is an exponential function
Hence , the exponential equations are solved
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Put these numbers in order from least to greatest.
-8.52
-8.15
8.25
0.55
Answer:
-8.52, -8.15, 0.55, 8.25
Step-by-step explanation:
The lowest of negatives goes first, and the highest of positives goes last.
Answer:
from the least to the highest which is:
-8.52
-8.15
0.55
8.25
I'm need help asap! i dont get the question, i would appreciate it if somebody could help me( giving brainilest & 20 points)!!!
Look at picture below
Answer:
215/100
Step-by-step explanation:
it is asking for improper fraction
improper fractions are just the bottom number multiplied by the number outside of the fraction so in this case it is
2*100 which is 200 then add that to the top number
which leaves you with 215/100
Subtract (9x-12)-(5x-7)
Answer:
Step-by-step explanation:
(9x-12)-(5x-7)=9x-12-5x+7=9x-5x-12+7=4x-5
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Luc is investigating dilations of scale factor 2 of the line y = -4x +3. He claims that for some centers of dilation, the line will remain the same. Which centers of dilation could be used to support Luc's claim? Select ALL that apply.
Luc is correct in stating that the line will remain the same with certain dilation centers, such as the origin (0, 0) and the point (3, -4). These centers of dilation will cause a scale factor of 2, but the line will remain the same.
To check if Luc is correct, we can calculate the points of the dilation with scale factor 2.
For the origin (0, 0):
Point A: (x, y) = (0, 3)
Point B: (x, y) = (-4, -3)
Dilated Point A: (x, y) = (0, 6)
Dilated Point B: (x, y) = (-8, -6)
Equation of the dilated line: y = -4x + 6
This shows that the line is dilated with scale factor 2, but is the same line.
For the point (3, -4):
Point A: (x, y) = (3, -1)
Point B: (x, y) = (-1, -7)
Dilated Point A: (x, y) = (6, -2)
Dilated Point B: (x, y) = (-2, -14)
Equation of the dilated line: y = -4x + 3
This shows that the line is dilated with scale factor 2, but is the same line.
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Are isosceles triangles always 90?
No, isosceles triangles do not always have to have 90-degree angles.
An isosceles triangle is a triangle with two sides of equal length. While the two sides are equal, they can be of any length. This means that the angles of the isosceles triangle can vary, and the triangle does not always have to have 90-degree angles. In fact, an isosceles triangle can have angles that range from 0 to 180 degrees. The only requirement for an isosceles triangle is that it must have two sides of equal length. As such, an isosceles triangle can have angles that are greater than 90 degrees, angles that are less than 90 degrees, or even angles that are equal to 90 degrees.
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How do you solve an inequality equation?
There are four fundamental types of inequality: less than ( < ), larger than( > ), less than or equal to ( ≤ ), and more than or equal to( ≥ ).
What is an inequality?The term "inequality" in mathematics refers to a connection between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus. The majority of the time, size comparisons between two numbers on the number line are made.
The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity. Comparatively speaking, some people in the healthcare system receive better and more skilled care. For these services, they are also likely to pay more.
Steps to solve the inequality:
First, get rid of all fractions by multiplying all terms by the fractions' lowest common denominator. (There is no difference when we multiply by a positive number.)Second, simplify the inequality by merging like words on either side. The sameThird To get the unknown on one side and the numbers on the other, add or subtract the appropriate amounts. The sameFourth, multiply each term in the inequality by the unknown coefficient. The inequality will not change if the coefficient is positive. Inequality will also be reversed if a negative coefficient exists. The crucial distinction between equations and inequalities is this.To know more about inequalities refer to:
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One-fifth of a bread loaf was shared equally among Herb, Dara, Mark, and Lily. What fraction of the original bread loaf did each person get?
Using the provided values and information, The answer is each person would receive 1/5 of the original bread loaf.
What do you mean by proportion?A proportion is a mathematical statement that compares two ratios. It is an equation that states that two ratios are equal, such as "a/b = c/d." Proportions are often used to solve problems involving fractions, decimals, and percentages. For example, if you know that a particular recipe calls for two cups of flour for every one cup of sugar, you can use this proportion (2/1 = x/3) to figure out how much sugar you need if you want to triple the recipe. The proportion can also be written as 2:1 = x:3.
What do you mean by ratio?A ratio is a mathematical comparison of two or more quantities, typically represented as a fraction. It is a way to compare the size of two or more things. For example, if a recipe calls for 2 cups of flour to 1 cup of sugar, the ratio of flour to sugar is 2:1. This means that for every 2 units of flour, there is 1 unit of sugar. Ratios can also be written using the colon symbol (:) or the word "to". For example, the ratio 2:1 can also be written as 2/1 or 2 to 1. Ratios can be simplified by dividing both the numerator and denominator by a common factor and can be used to compare quantities in different units.
Each person would get 1/5 of the original bread loaf. If the bread is divided equally among four people, then each person would receive 1/4 of the total amount. Since 1/5 is the same as 4/20, and 4 people are receiving the bread, then each person would receive 1/5 of the original bread loaf.
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400 people are asked if they drink tea. [tex]\frac{7}{10}[/tex] say Yes and 20% of the people who say Yes drink at least 3 cups each day.
I really need help on a) Complete the frequency tree, I don't know how to work that one out.
The missed value in the frequency tree is 224.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that 400 people are asked if they drink tea.
7/10 say Yes and 20% of the people who say Yes drink at least 3 cups each day
7/10 of 400 is 280
Which means 280 people drink tea.
The remaining people does not drink tea.
Remaining =400-280=120.
Now let us find 20% of 280
20/100×280
0.2×280=56
So 56 drink at least 3 cups each day.
280-56=224
So 224 people drink tea but not three cups.
Hence, the missed value in the frequency tree is 224.
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In the Himalaya Mountains along the border of Tibet and Nepal, Mount Everest reaches a record height of 29,035 feet. How high is Mt. Everest in miles
The height of the mt. Everest in miles exists 5.499 miles.
What is meant by unit conversion?By changing the unit of measurement, a quality can be expressed differently. In contrast to distance, which can be stated in miles, kilometers, feet, or any other unit of length, time can also be expressed in minutes rather than hours.
By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. The right conversion factor to an equal value must be used when a conversion is required. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet.
The height of the mt. Everest is : 29035 feet.
The unit conversion is given as :
5280 feet = 1 mile
1 feet = 1/5280 mile
So, 29035 feet =29035 × 1/5280 miles
29035 feet = 29035/5280 miles
29035 feet = 5.499 miles
So, the height of the mt. Everest in miles is 5.499 miles.
The complete question is:
In the Himalaya mountains along the border of Tibet and Nepal, mount Everest reaches a record height of 29,035 feet. how high is mt. Everest in miles? use the conversion equivalency of 1 mile = 5280 feet.
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Answer: The height of the Mount Everest in miles is 5.499 miles
Step-by-step explanation:
1 miles = 5,280 feet
For feet to miles conversion, you should multiply your length value by 0.0001894: mi = ft × 0.0001894 .For miles to feet conversion, you should multiply your length value by 5,280: ft = mi × 5,280 .1 feet = 1/5280 mileso So, 29035 feet = 29035×1/528029035 feet = 29035/5280in the given question, 29035 feet = 5.499 milesSo, the height of the mt. Everest in miles is 5.499 mileTo learn more about it refer to:
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A large plane cruises at 530 miles per hour. What is the ratio, Unit Rate, and Rate?
Answer:
For this example they are all the same thing.
530:1 or 530 mph
Step-by-step explanation:
A unit rate is when the denominator is 1. In this case, the denominator is already 1 hour.
Write the standard equation of the circle.
PLEASE HELP DUE TN 01/06
GEOMETRY B
Answer:
Center: = (-1,-3)
Radius: = 1
Step-by-step explanation:
Practice 2-2 Using number sense to solve Equations (PLEASE HELP)
The solutions for all the equations would be
1. p = 30
2. h = 99
3. t = 31.4
4. r = 57
5. t = 5
6. w = 8
7. y = 9
8. p = 7
9. a = 13
10. w = 12
11. h = 24
12. g = 128
13. a = 21
14. y = 39
15. d = 16
16. w = 25
What is an equation?
An equation is a statement that asserts the equality of two expressions. The expressions on either side of the equation are separated by an equals sign (=), and they must have the same value for the equation to be true.
1) 30p = 900
p = 900/30
p = 30
2) h/9 = 11
h = 9 * 11
h = 99
3) t + 32.4 = 62
t = 62 - 32.4
t = 31.4
4) r - 17 = 40
r = 40 + 17
r = 57
5) 5t = 25
t = 25/5
t = 5
6) 8w = 64
w = 64/8
w = 8
7) 9y = 81
y = 81/9
y = 9
8) p + 5 = 12
p = 12 - 5
p = 7
9) a + 2 = 15
a = 15 - 2
a = 13
10) w + 8 = 20
w = 20 -8
w = 12
11) h/6 = 4
h = 6 * 4
h = 24
12) g/8 = 16
g = 16 * 8
g = 128
13) a/7 = 3
a = 3 * 7
a = 21
14) y - 11 = 28
y = 28 + 11
y = 39
15) d - 4 = 12
d = 12 + 4
d = 16
16) w - 10 = 15
w = 15 + 10
w = 25
Hence, solutions for all the equations would be
1. p = 30
2. h = 99
3. t = 31.4
4. r = 57
5. t = 5
6. w = 8
7. y = 9
8. p = 7
9. a = 13
10. w = 12
11. h = 24
12. g = 128
13. a = 21
14. y = 39
15. d = 16
16. w = 25
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M(2,4) is the midpoint
between the points A(-2,9)
and B.
Find the coordinates of B.
The coordinates of B are (6,0).
The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the segment. For a line segment with endpoints (x1, y1) and (x2, y2), the midpoint is given by the coordinates:
((x1 + x2) / 2, (y1 + y2) / 2)In this problem, we're given that the midpoint is (2, 4) and we need to find the coordinates of point B. Since we know the coordinates of the midpoint, we can set up the equation:
((x1 + x2) / 2, (y1 + y2) / 2) = (2, 4)We know that point A = (-2,9) is one endpoint, so we can substitute it into the equation
((-2 + x2) / 2, (9 + y2) / 2) = (2, 4)Solving for x2 and y2, we get x2 = 6 and y2 = 0 which is the coordinates of point B.
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Tim's phone service charges $24.20 plus an additional $0.17 for each text message sent per month. If Tim's phone bill was $28.45, which equation could be used to find how many text messages, x, Tim sent last month? A. $0.17x + $24.20 = $28.45 B. $0.17x - $24.20 = $28.45 C. $24.20x + $0.17 = $28.45 D. $24.20x - $0.17 = $28.45
Answer:
A
Step-by-step explanation:
each text message is .17 text messages are x the total bill is 28.45. the service charges are 24.20.
.17x + 24.50 = 28.45
I really need help!! Find the value of..
Answer:488441
Step-by-step explanation:
Please help me!
Will give you brainlist!!!!
Sydney says that if all of the side lengths of a cube are doubled, the volume of the cube will also double. Is she correct? Explain.
Answer:
no, it's not correct
Step-by-step explanation:
volume or the cube = L³
so if we doubled the side lengths
They would be 2L
then the volume= (2L)³ = 8L³
so that would make the volume 8 times the first value not double
How is the number of Electoral College seats per state determined? A. by the number of party delegates assigned to the state B. by the total number of
Each state is given a specific amount of "votes" under the "Electoral College" system. The amount of "votes" each state receives is proportionate to its size.
What is the makeup of the Electoral College? There are 538 electors in all. The number of electors allotted to each state is equal to the sum of its two Senate seats plus the number of representatives in the House of Representatives.Three electoral votes are granted to the District of Columbia under the 23rd Amendment. According to the amount of each State's population as established by the Census, each State is given a certain number of electors equal to the sum of its U.S. Senators (which are always two) and U.S. Representatives.There are two steps involved in selecting each State's electors. The political parties in each State first select elector candidate slates before the general election. Second, during the general election, each State's voters choose its electors by voting ballots.To learn more about Electoral College refer to :
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Please Help! You Dont Have To do the Bottom Questions Just The Top!
Complete the inequality below to describe the
domain of the graph shown.
Domain:
DONE
completo the inequality holow to dogorike the
On solving the provided inequality equation we cans ay that therefore, 60x + 45 <250 is the necessary inequality for the given situation.
Describe inequality.An inequality in mathematics shows how two values are related in an imbalanced algebraic expression. According to inequality signals, one of the two variables on either side of the inequality may be larger than, greater than or equal to, less than, or less than or equal to another value.
If the daily cost for each crew member is $60, the daily wage for crew members is $60, and the daily cost of operations is $45; the amount paid equals the total of the wages for each crew member plus the cost of operations. In this case, let x indicate the size of the crew.
= 60x + 45
Since the maximum daily payment is $250,
In other words, the total payment cannot be more than $250.
60x + 45 ≤ 250
Therefore , the required inequality for given problem is 60x + 45 ≤ 250.
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What is 5 in the expression 5x called?
The term 5 in 5x is known as the coefficient of the expression.
A coefficient is defined as a term or a number which is multiplied by a variable. This constant terms generally precedes the variable term.
A coefficient is a generally a multiplicative factor in a polynomial series, or in an equation.
Expressions are mathematical statements which are composed of two terms in which at least one contain variables, numbers, or both. These terms are either numbers or variables or numbers and variables multiplying each other. These expressions are a combination of numbers with mathematical ,operators are used to separate them.
Eg, 2x - 90 =45
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Solve for x in this triangle. Round your answer to the nearest tenth. 18 Xº 23
Answer:
51.50004959055205
Step-by-step explanation:
[tex]sin (x) = \frac{18}{23}[/tex]
47.3 , 48.1 ,47.4 ,47.16 , 47.07 least to greatest,please help(,:
Answer:
47.07, 47.16, 47.3, 47.4, 48.1
Step-by-step explanation:
lol
Find the total surface area of a cone with a base diameter of 7cm and height of 8cm
Answer: The formula for the surface area of a cone is S = π * r * s + π * r², where r is the radius of the base and s is the slant height of the cone.
To find the surface area of a cone, you first need to find the radius of the base. Since the base diameter is given as 7cm, you can divide this by 2 to find the radius of the base:
r = 7cm / 2 = 3.5cm
Next, you need to find the slant height of the cone. You can use the Pythagorean theorem to do this.
slant height = sqrt(r^2 + h^2) = sqrt(3.5² + 8²) = sqrt(12.25 + 64) = sqrt(76.25) = 8.766cm
Now you can substitute these values into the formula for the surface area of a cone and find the surface area of the cone.
S = π * r * s + π * r² = π * 3.5cm * 8.766cm + π * 3.5² cm² = 12.571 cm² + 38.485 cm² = 51.056 cm²
So the surface area of a cone with a base diameter of 7cm and height of 8cm is 51.056 cm²
Step-by-step explanation:
Solve for x in this triangle. Round your answer to the nearest tenth. 13 35⁰ X
Answer:
x ≈ 10.6
Step-by-step explanation:
using the cosine ratio in the right triangle
cos35°= [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{13}[/tex] ( multiply both sides by 13 )
13 × cos35° = x , then
x ≈ 10.6 ( to the nearest tenth )
!PLEASE HELP ASAP!
These two figures are similar. Find the length of side x.
the length of side x = 12.5.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Here, we have,
From the given figure, we get.
These two figures are similar.
so, we have,
8/x=y/5 ............(1)
10/15=4/z ......(2)
8/15=y/z .....(3)
Solving we get,
x=12.5
Hence, the length of side x = 12.5.
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