The Scottish mathematician John Napier reported his findings on logarithms in 1614.
The comparison of arithmetic and geometric series predicted the development of logarithms. He was there to aid with the multiplication of quantities known as sines at the time.
The value of the entire sine was equal to the length of the hypotenuse in a right-angled triangle with a hypotenuse of, say, 107 units. He provided a definition in terms of relative rates.
Because both motions are equally spaced apart in time and have an equal shift at the beginning, the logarithm of any sine is a number that comes very close to expressing the line that increased equally over the course of time while the line of the entire sine decreased proportionately into that sine.
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A package of 85 paper plates costs $8. 08, while a package with 55 paper plates costs $4. 40. Which is the better
buy? Round your answer to the nearest cent if necessary.
Algebra
The pack with 55 paper plates that costs $4.40 is a better buy that the pack with 85 paper plates which costs $8.08.
We must utilize the unitary method in this elementary algebra issue, which is nothing more than figuring out the price per plate in both of the cases. The cost per plate for the $8.08 box of 85 paper plates must now be determined. As a result, since 85 plates cost $8.08, 1 plate must cost $8.08/85, or around 9.5 cents per plate. When we repeat the job for the second scenario, we see that 55 plates cost $4.40, making 1 plate cost $4.40/55, or 8 cents per plate. Now that each plate costs less in the second scenario, it turns out to be a superior purchase.
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which does not describe the same situation.
On solving the provided question, we can say that from the graphs we have the following equation - [tex]6x^2 = y +7[/tex] => x = +6, -6
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
here,
from the graphs we have the following equation -
[tex]6x^2 = y +7[/tex]
y = -1
x^2 = 36
x = +6, -6
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Describe a situation that can be represented by the table.
X
2
4
6
8
10
12
y
22.50
20
17.50
15
12.50
10
This table could represent the prices of a certain item in a store.
Describe a situation that can be represented by the table?The x-values are the quantities of the item the customer is purchasing, and the y-values are the corresponding prices for those quantities.For example, if a customer buys 10 of the item, they would pay $12.50.This table could represent the cost of an item in a store for each number of items purchased. As the number of items purchased increases, the cost per item decreases.This is an example of the theory of economies of scale, which states that as the production of a good or service increases, the average cost of producing each unit decreases.This is often due to increased efficiency, specialization of labor, and technological advances. In this example, the store has decided to offer volume discounts to customers as an incentive for them to purchase more items.This allows the store to move more stock and potentially increase their profits.To learn more about the prices of a certain item in a store refer to:
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A fashion designer makes cashmere scarves and wool sweaters to sell at a kiosk in the mall for $35 each. The function f(x)=35(x+16) represents the total amount, in dollars, the designer earns by selling x cashmere scarves and 16 wool sweaters at the kiosk. What is the value of f(11) ?
Answer: 945
Step-by-step explanation: f(x)=35(x+16)
f(11)=(11+16)
=35 * 27
=945
PLEASE HELP ME ASAP SOLVE WITH EXPLANATION3
The circumference of the circle is 22 cm. The correct option is D.
What is a circumference?The circumference, also known as the length of a circle, is its circumference. By using the radius or diameter, we can calculate the circumference of a circle.
The circumference of the circle is calculated by the formula written below:-
C = 2 x π x r
Given that the radius of the circle is 3.5 cm. The circumference of the circle is calculated as:-
C = 2 x π x r
C = 2 x π x 3.5
C = 22 cm
Hence, the circumference of the circle is 22 cm.
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temperature on a summer afternoon is 76°F. Define a variable and write an expression to find the temperature after it changes. Then evaluate your expression for a decrease of 8 degrees Fahrenheit.
8+ c; 8 + (-76) = 84 F
On solving the provided question, we can say that the required expression is " 76 + c; 76 + (–8) = 68; 68°F ".
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
the required expression is
C. " 76 + c; 76 + (–8) = 68; 68°F ".
If 76 is the starting point or current temperature, then c would be the temperature change that occurred. The negative symbol on 8 indicates that there will be a decrease of 8 degrees, which will be experienced.
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Find the value of y. Round to the nearest hundredth, if necessary.
Y
8 cm
13 cm
A 14.42 cm
B15.26 cm
C21 cm
D25 cm
Answer:
15.26 cm
Step-by-step explanation:
The given triangle is a right angled triangle, with perpendicular and base as 13cm and 8cm respectively, we need to find out y which is hypotenuse.
From Pythagoras theorem,
[tex]\implies \rm h^2=p^2+b^2\\ [/tex]
[tex]\implies \rm h =\sqrt{(13cm)^2+(8cm)^2}\\ [/tex]
[tex]\implies \rm h =\sqrt{169cm^2+64cm^2}\\[/tex]
[tex]\implies \rm h = \sqrt{ 233}=\boxed{15.26\ cm } [/tex]
and we are done!
-Rishabh
PLS DO NUMBER 1 WILL MARK BRAINLIEST AND ADD 100 MORE PIOINTS HURRY PLEASE! THANK YOU
The line y = mx + 4 has a slope of 2 and it is y = 2x + 4.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know lines parallel to each other have the same slope.
We also know, slope(m) = (y₂ - y₁)/(x₂ - x₁).
Slope(m) = (6 + 2)/(5 - 1).
slope(m) = 8/4.
slope(m) = 2.
So, The line y = mx + 4 is, y = 2x + 4.
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There are 15 children in Lola's preschool class. During free time yesterday, 1 of them chose to play at the water table. What is the probability that a randomly selected child chose to play at the water table yesterday? Write your answer as a fraction or whole number.
Answer:
Step-by-step explanation:
6 or 7
I think the screenshot explains it
Using exponent properties, we can simplify the given expression as:
4ⁿ⁺⁴ = 256*4ⁿ
How to simplify the given expression?
Remember the exponent property for the product:
xᵃ*xᵇ = xᵃ*ᵇ
Then our expression can be rewritten as:
4ⁿ⁺⁴
We can expand that as
4ⁿ⁺⁴ = 4ⁿ*4⁴
And the second factor can be simplified to:
4⁴ = 16*16 = 256
Then the simplified expression will be:
256*4ⁿ
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if answered quick AND CORRECT. you will be given brainliest
Answer: $1,312.5 difference
Step-by-step explanation:
1050 x 1.5 = 1575
1575 x 1.5 = 2,362.5
2,362.5 - 1050 = 1,312.5
pallavi wants to study the relationship between wearing a seat belt and the extent of injuries in automotive accidents. when should she generate the hypothesis she will be typing to prove?
Pallavi should generate her hypothesis before conducting her study.
A hypothesis is a statement that predicts the relationship between two or more variables. It serves as a guide for the research and allows Pallavi to focus her study on a specific question or problem. In this case, her hypothesis should state her prediction about the relationship between wearing a seat belt and the extent of injuries in automotive accidents.
For example, her hypothesis could be "Wearing a seat belt will significantly reduce the extent of injuries in automotive accidents." This hypothesis can then be tested and supported or disproved through her research. It's important for Pallavi to generate a clear and testable hypothesis so that she can conduct a valid study with accurate results.
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If the angles of a triangle with measures in the ratio of 4 : 7 : 7, then find the measure of the
smallest angle.
40°
50°
60°
70°
angle in triangle= 180
4 + 7+7= 18
180/18 = 10
10 = 1 part
smallest = 4 parts
10x4= 40
so answer is 40
Answer:
(a) 40°
Step-by-step explanation:
You want the measure of the smallest angle in a triangle whose angle measures have the ratios 4 : 7 : 7.
RatiosWe notice that the sum of the numbers in the ratios is 4+7+7 = 18, so multiplying by 10 will make the sum equal to 180, the number of degrees in a triangle.
4 : 7 : 7 = 40 : 70 : 70
The smallest angle is 40°.
__
Additional comment
The other two angle measures are 70°.
Please answer and explain how to solve with quadratic formula:
What are the solutions to x^2 + 8x + 20 = 0?
Answer:
x = -4 + 2 i or x = -4 - 2 i
Step-by-step explanation:
Solve for x:
x^2 + 8 x + 20 = 0
Subtract 20 from both sides:
x^2 + 8 x = -20
Add 16 to both sides:
x^2 + 8 x + 16 = -4
Write the left hand side as a square:
(x + 4)^2 = -4
Take the square root of both sides:
x + 4 = 2 i or x + 4 = -2 i
Subtract 4 from both sides:
x = -4 + 2 i or x + 4 = -2 i
Subtract 4 from both sides:
Answer: x = -4 + 2 i or x = -4 - 2 i
in a circle with radius 7.3, an angle intercepts an arc of length 26.2. find the angle in radians to the nearest 10th.
The angle subtended by the arc rounded off to the nearest 10th is 3.6 radians.
We have been given that the length of the arc subtended by the angle at the center is 26.2 units.
The radius of the said circle is 7.3 units.
Now the relation between the length of the arc, the angle subtended by it on the center of the circle, and the radius of the circle is given by
l = rθ
where,
l s the length of the arc in radians
r is the radius of the circle in radians
θ is the angle subtended by the arc
Here l = 26.2 units
r = 7.3 units
Hence we get
θ = l/r
θ = 26.2/7.3
= 3.589 radians
= 3.6 radians
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Which combination of measurements could form a triangle?
A) 16m, 55m, 72m
B) 5m, 12m, 18m
C) 18m, 22m, 36m
D) 12m, 32m, 45m
Answer:
B) 5m, 12m, 18m
evaluate: 5.7 + f = 7 (PLEASE HURRY ILL GIVE BRAINLIEST HOW EVER GETS IT RIGHT!!!!)
A.f = 2.7
B.f = 1.7
C.f = 1.3
D.f = 12.7
I NEED HELP STAT THIS IS DUE IN 1 HOUR AND IM ONLY STARTING-
Answer: 2.6
Step-by-step explanation:
1.25 + 1.35 = 2.6
Answer:
1.25+1.35=2.6
Step-by-step explanation:
Hanna works at an aquarium and needs to drain the seahorse tank for cleaning. the gallons of water in the tank based on the number of minutes it has been draining is shown in the table below.
The statement that are true for the table are :
The aquarium initially contained 60 gallons .
The aquarium drains at the rate of 2.5 gallon per minutes.
The statement/equation that is false for the table is y = 2.5x + 60.
How to represent a situation with an equation?Hanna works at an aquarium and needs to drain the seahorse tank for cleaning.
The gallons of water in the tank based on the number of minutes it has be draining is shown in the table.
Therefore, let's represent it in slope intercept form.
y = mx + b
where
m = slopeb = y-interceptHence, using (0, 60) and (4, 50)
m = 50 - 60 / 4 - 0 = - 10 / 4 = -2.5
Therefore,
y = -2.5x + b
y = -2.5x + 60
Therefore, y = 2.5x + 60 is not the true equation.
The aquarium initially contained 60 gallons is a true statement.
The aquarium drains at the rate of 2.5 gallon per minute is true.
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Which of the following describes an altitude of a triangle?
Pilihan jawaban
A segment that passes through the middle of the triangle.
A segment with endpoints at the vertex and midpoint of the opposite side.
A segment that connects two midpoints of two sides.
A segment that connects the vertex and the opposite side at 90 degrees
The correct answer is: A segment that connects the vertex and the opposite side at 90 degrees.
An altitude of a triangle is a line segment that connects a vertex of the triangle to the opposite side, and is perpendicular to that side. This is also called a "perpendicular bisector" of the side. It forms a right angle with the base at the point of intersection. The length of the altitude represents the height of the triangle, and it is used in finding the area of the triangle.
A perpendicular bisector is a line that bisects another line segment at a right angle, through the intersection point. Thus, we can say, a perpendicular bisector always divides a line segment through its midpoint. The term bisect itself means dividing equally or uniformly.
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x/7 ≥ − 6=============
The range of value of x in the inequality x/7 ≥ -6 is x≥ -42
What is inequality?Inequality, is a statement of an order relationship. Some terms used in inequality are ,greater than, greater than or equal to, less than, or less than or equal to. They are used between two numbers or algebraic expressions.
greater than has the sign >
greater than or equal to has the sign ≥
less than has the sign < and
less than or equal to has ≤
solving the range of value of x in the inequality x/7 ≥- 6
multiply both sides by 7
x ≥ -42
Therefore the range of value of x is x ≥ -42
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 Solve each system of inequalities by graphing.
inequalities by graphing. is x≥0,y≥0
What is inequalities by graphing.?To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid lineA system of inequalities is two or more inequalities that pertain to the same problem. In order to solve the system, we will need to graph two inequalities on the same graph and then be able to identify the areas of intersection on the graph.A system of inequalities is a set of two or more inequalities in one or more variables. Systems of inequalities are used when a problem requires a range of solutions, and there is more than one constraint on those solutions.To learn more about inequalities by graphing refers to:
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Lorraine prepared a 1.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.5 quarts of tomatoes. If 1 gallon equals 4 quarts, how many jars can Lorraine fill? PLEASE HELP
4 jars Lorraine can fill with tomatoes as in step with the given unit conversion.
What is unit conversion?The same attribute is expressed using a unit conversion but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other measurement unit instead of miles.
Given this, Lorraine prepared a 1.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.5 quarts of tomatoes
Since 1 gallon is equal to 4 quarts.
Total tomatoes Lorrain has = 1.5 gallons = 1.5 * 4 quarts
Total tomatoes Lorrain has = 6 quarts
Since one jar can only fit 1.5 quarts of tomatoes
Thus,
the number of jars that can be filled = 6/1.5 = 4
Therefore, 4 jars Lorraine can fill with tomatoes as per the given unit conversion.
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Line m is represented by the equation y+2=32(x+4) . Select all equations that represent lines perpendicular to line m .
The equation of the perpendicular line will be y = -(2/3)x + c and y = -(4/6)x + c. Then the correct options are A and E.
What is the equation of a perpendicular line?Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation is given below.
y + 2 = (3/2)(x + 4)
The equation of the perpendicular line is given as,
y = -(2/3)x + c
y = -(4/6)x + c
The equation of the perpendicular line will be y = -(2/3)x + c and y = -(4/6)x + c. Then the correct options are A and E.
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The complete question is given below.
Which of the following is equivalent to (g+h)(p+a-r) ?
Answer:
A) gp+gq−gr+hp+hq−hr
Step-by-step explanation:
Original: (g+h)(p+q−r)
Multiply: (g)(p)+(g)(q)+(g)(−r)+(h)(p)+(h)(q)+(h)(−r)
Simplify: gp+gq−gr+hp+hq−hr
Hope this helped! :)
Verview
Question Progress
Homework Progress
15/50 Maris
The lengths of the rectangle have been measured to the
nearest tenth of a metre.
Work out the following, writing down all the figures on your calculator display:
a) The upper bound for the perimeter of the rectangle.
b) The lower bound for the area of the rectangle.
15. 8 m
5. 2 m
a) The upper bound for the perimeter of the rectangle is 42.4 m.
b)The lower bound for the area of the rectangle is 83.21 cm².
We have, The lengths of the rectangle have been measured to the nearest tenth of a metre. So, degree of accuracy of measurements = 1/10 m = 0.1 m
We need to work out the upper and lower bounds for each side, when side length = 15.8 m and width = 5.2 m
Upper bound of length = 15.8 + 0.1
= 15.9 m
Lower bound of length = 15.8 - 0.1 = 15.7
Upper bound of width = 5.2 + 0.1 = 5.3
Lower bound of width = 5.2 - 0.1 = 5.1
For lower bound of Area :
We know the area of a rectangle is equals to product of width and length, so for the upper bound for the area we multiply the lower bound fo width and the lower bound of length together:
So lower bound of Area of rectangle
= 15.7× 5.1 = 83.21 cm²
For upper bound of Perimeter :
We know that the perimeter of rectangle is equals to two times of sum of each side of the rectangle, so for the upper bound for the perimeter we use the upper bound of each side:
2( 15.9 + 5.3) = 2× 21.2 = 42.4 m
Hence, the required area is 83.21 cm² and perimeter 42.4 m .
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square tuvw is dilated by a scale factor of 6 6 to form square t'u'v'w'. side u'v' measures 18 18. what is the measure of side uv?
A square tuvw is dilated by a scale factor of 6. The measure of side uv is 3 units.
Dilation is a transformation that makes items smaller or larger by using a scale factor.
Scale factor is the ratio of the size of the resulted dilated shape to the size of original shape.
Scale factor = size of dilated figure / size of original figure.
In the problem, the scale factor = 6.
The dilated square has side length of 18.
Hence,
Scale factor = side of t'u'v'w' / side of tuvw
6 = 18 / side of tuvw
side of tuvw = 18/6 = 3
There were typos in your question, most likely it was:
square tuvw is dilated by a scale factor of 6 to form square t'u'v'w'. side u'v' measures 18. what is the measure of side uv?
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Classify the equation as an identity, contradiction, or conditional equation.
-6(k+10)-27=14(k+6)
= -6K-60-27 = 14 (k+6)
= -6k -87=14 (k+6)
= -6k-87= 14(K+6)
= -6K-87=14K+84
Add 87 to both the sides
= -6K-87=14K+84
= -6k-87+87 =14k+84+87
Add the numbers
-6 k=14k+171
Subtract 14k from both sides
-6 k=14k+171
-6k-14k=14k+171-14k
∴-20k=171
Divide both sides by the same factor
-20k=171
-20k/-20 = 171/-20
∴ k =-171/20
What is contradiction?Generally, we use direct arguments to prove the truth of the statement. Sometimes, we use indirect arguments to prove the statement using a powerful tool in Mathematics called the “Proof by Contradiction”. In this article, we will discuss how to prove the statement using the proof by contradiction method with the help of an example.In Mathematics, a contradiction occurs when we get a statement p, such that p is true and its negation ~p is also true.Now, let us understand the concept of contradiction with the help of an example.Consider two statements p and q.Statement p: x = a/b, where a and b are co-prime numbers.Statement q: 2 divides both “a” and “b”.Here, in this case, we have to assume that the statement “p” is true” and also manage to show that the statement “q” is true. Hence, we have arrived at a contradiction, because the statement “q’ implies the negation of statement “p” is true.
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How do you draw a vertical line?
Answer:You draw from top to bottom
What is the equation of the line that passes through the point 3 7 and has a slope of?
The equation of the line that passes through the point (3,-7) and has a slope of -4/3 is 4x + 3y + 9 = 0.
In the given question, we have to find the equation of the line that passes through the point (3,-7) and has a slope of -4/3.
A point on the line and the slope of the line are required in the point-slope version of the equation of a line. (X(1), Y(1)) serves as the line's reference point, and its slope is m. Consequently, the line equation is as follows.
(y - y(1)) = m(x - x(1))
From the given question, the value of m = -4/3 and x(1) = 3, y(1) = -7
Now putting the value in the formula
(y - (-7)) = -4/3(x - 3)
(y + 7) = -4/3(x - 3)
Multiply by 3 on both side, we get
3(y + 7) = -4(x - 3)
Now simplifying using the distributive property
3y + 21 = -4x + 12
Subtract 21 on both side, we get
3y = -4x - 9
Add 4x + 9 on both side, we get
4x + 3y + 9 = 0
Hence, the equation of the line that passes through the point (3,-7) and has a slope of -4/3 is 4x + 3y + 9 = 0.
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The complete question is:
What is the equation of the line that passes through the point (3,-7) and has a slope of -4/3?