The combination has a refractive power of 0.167 diopters.
The refractive power of a lens is given by the formula P = 1/f, where f is the focal length of the lens in meters. The focal length of a lens in diopters (d) is given by f = 1/d.
To find the refractive power of the combination of a 10 d lens and a 15 d lens, we need to find the equivalent focal length of the combination. The equivalent focal length of two lenses in contact can be found using the formula:
1/f = 1/f1 + 1/f2
where f1 and f2 are the focal lengths of the individual lenses.
Substituting the values for the focal lengths of the two lenses, we get:
1/f = 1/10 + 1/15
Simplifying, we get:
1/f = 1/6
Multiplying both sides by 6, we get:
f = 6 meters
Therefore, the refractive power of the combination of the 10 d and 15 d lenses is:
P = 1/f = 1/6 = 0.167 d^-1.
Thus, the combination has a refractive power of 0.167 diopters.
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A total of 64 musicians entered a music contest, and of these musicians are guitarists. Some of the guitarists play jazz solos, and the rest play classical solos. The ratio of the number of guitarists playing jazz solos to the total number of guitarists in the contest is 1: 4. How many guitarists play classical solos in the contest
The number of guitarist who plays classical solos in the contest is 30.
What is Ratio?Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.
The ratio of a and b is denoted as a : b.
Given that,
Total number of musicians entered in the contest = 64
5/8 of these musicians are guitarists.
Number of guitarists = (5/8) × 64 = 40
Also we have,
Ratio of number of guitarists playing jazz solos to the total number of guitarists = 1 : 4 = 1/4
That is, of the 4 guitarists, 1 is a guitarist playing jazz solos.
Multiplying both numerator and denominator with 10, 1/4 = 10/40
So of the 40 guitarists, 10 number of guitarists play jazz solos.
Number of guitarists who play classical solos = 40 - 10 = 30
Hence 30 guitarists play classical solos.
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What is the solution to the equation 6y –2(y + 1) = 3(y – 2) 6? a. y = –10 b. y = –2 c. y = 2 d. y = 6
The solution to the equation 6y - 2(y + 1) = 3(y - 2) 6 is y = -34. So, the correct answer to the question is a. y = -10.
What is algebraic equation ?
An algebraic equation is a mathematical statement that asserts the equality of two expressions, each of which is made up of numbers and/or variables. The expressions are separated by an equal sign (=). The goal of solving an algebraic equation is to find the value(s) of the variable(s) that make the equation a true statement.
To find the solution to the equation 6y - 2(y + 1) = 3(y - 2) 6, we must first simplify both sides of the equation by following the order of operations (PEMDAS). First, we simplify the right side of the equation: 3(y - 2) 6 = 3y - 6 * 6 = 3y - 36. Next, we simplify the left side of the equation: 6y - 2(y + 1) = 6y - 2y - 2 = 4y - 2.
Now we have the equation: 4y - 2 = 3y - 36
Next, we can add 2 to both sides of the equation and get: 4y = 3y - 34
Finally we subtract 3y from both sides of the equation and get: y = -34
Therefore, the solution to the equation 6y - 2(y + 1) = 3(y - 2) 6 is y = -34. So, the correct answer to the question is a. y = -10.
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-3y = -2x - 1
y = x - 1
i need a solution please help
Answer:
x=4, y=3. (4, 3).
Step-by-step explanation:
-3y=-2x-1
y=x-1
--------------
-3(x-1)=-2x-1
-3x+3=-2x-1
-3x-(-2x)+3=-1
-3x+2x=-1-3
-x=-4
x=4
y=4-1=3
Select all equations that can be used to answer the question: “How many rhombuses are in a trapezoid?”
2/3÷?=1
?⋅2/3=1
1÷2/3=?
1⋅2/3=?
?÷2/3=1
What is the gradient of the line y 6x =- 5?
After solving, the gradient of the line y = 6x - 5 is 6.
We have to find the gradient of the line y = 6x - 5.
The formula known as the slope relates to the method for calculating a line's steepness and inclination. The x and y coordinates of the locations along the line can be used to determine the slope of the lines. It is the ratio of the change in the y-axis to the change in the x-axis, to put it another way.
By utilizing the line equation, the slope of any line may be expressed as
y = mx + b, where m = gradient.
When we compare the given equation y = 6x - 5 by the standard equation, we get m = 6.
So the gradient of the line y = 6x - 5 is 6.
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The write question is:
What is the gradient of the line y = 6x - 5
The graph shows the number of possible passengers for a given number of roller coaster cars that leave the platform. Complete parts a and b.
the slope of the line is 8 and equation line is y = 8x.
What is the slope of line?
Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
We know that formula two find the slope of the line joining two points which is
slope m = 24-16 / 3-2
m = 8/1 = 8
y = 8x
Hence the slope of the line is 8 and equation line is y = 8x.
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A t-shirt company needs to restock their inventory by ordering 562 shirts. The company only has room for 951 shirts in their stock room. Model the number of shirts the company can order, using a compound inequality.
x ≥ 562 and x ≤ 951
x ≤ 562 and x ≥ 951
x ≤ 562 and x ≤ 951
x ≥ 562 and x ≥ 951
H divided by 5 equal 18
Answer: 90
Step-by-step explanation: I multiplied 18 by 5
Answer:
H=90
Step-by-step explanation:
if H÷5=18, then reverse it. so 18×5=90
Which of the following shapes are rectangles?
Which of the following shapes are rectangles?
Which of the following shapes are rectangles?
Which of the following shapes are rectangles?
Which of the following shapes are rectangles?
Which of the following shapes are rectangles?
Which of the following shapes are rectangles?
A rectangle has four sides and angles at 90 degree.
What is a rectangle?A plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square. A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
Given: shape of a rectangle
A rectangle is closed flat shape, having four sides, and each angle equal to 90 degrees. The opposite sides of the rectangle are equal and parallel.
Hence, A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°).
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Mr. Taylor and Mrs. Miller’s classes have been having a fundraising competition. they’ve both kept track of how much money they’ve raised in dollars versus the time in days. while mr. taylor’s class chose to graph their data, mrs. millers class chose to present it in a table. both classes have found that their fundraising over time has been proportional, where the daily increase in money raised is consistent. please explain why you chose this answer i will mark you brainliest
What is the area of the triangle having sides 3 cm 4 cm and 5 cm?
The area of a triangle with sides 3 cm, 4 cm, and 5 cm is 6 cm² using Heron's formula.
Step 1: First, calculate the semi-perimeter of the triangle by adding the three sides of the triangle together and dividing by 2. In this case, the semi-perimeter would be (3 + 4 + 5) / 2 = 6 cm.
Step 2: Next, use the semi-perimeter and the three side lengths of the triangle to calculate the area. The formula for Heron's formula is:
Area = √(s(s-a)(s-b)(s-c))
Where s is the semi-perimeter, and a, b, and c are the three sides of the triangle.
So, plug in the values,
Area = √(6(6-3)(6-4)(6-5))
Area = √(632×1)
Area = √(36)
Area = 6 cm²
Therefore, the area of the triangle is 6 cm²
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Bryson , it has 12 cards each card is a different number from 1 to 12 he chooses a card at random. how likely is it for Bryson to choose an odd number?
Answer:
as likely as not
Step-by-step explanation:
if there are 12 cards then 6 would have even and and 6 would be odd so it is a 50/50 chance so it just as likely as it isn't
The event has an “equal chance” to happen or not, the probability will be 1/2. Therefore, option B is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, Bryson has 12 cards each card is a different number from 1 to 12.
Here, total number of outcomes = 12
Number of favorable outcomes = 6 (odd number of cards)
Now, probability of an event = 6/12
= 0.5
If the event has an “equal chance” to happen or not, the probability will be 1/2.
Therefore, option B is the correct answer.
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What is the slope of =- 10?
The slope of -10 as calculated from the data given is found out to be as 0.
Let's say y = -1= ,
Now, we know that the formula to calculate slope is y = mx+ b y .
This is known as slope-intercept form and can be written as ,
y = m x + b,
m = slope and b b= y-intercept.
y = mx +b y
y = m x + b
Therefore , by looking at this formula we can say that the value of m is 0 .
So , the slope is found out to be 0.
The slope is defined as the change in y coordinate with respect to the change in x coordinate of that line.
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i need help with this
Answer:
lo l oh my gosh hi i havent seen u in so many years
Step-by-step explanation:
what is the answer to two plus two. Please help
Answer:
the answer is 4
2+2=4 bc 1+1 is 2 ×2 and that is 4 your welcome
When you "plug in" a value or idea into the place of something else that has the same value or same idea, what PROPERTY is that called?
When you "plug in" a value or idea into the place of something else that has the same value or same idea, it is called substitution property of equality.
What is Substitution?This is referred to as an operation which means the replacement of the variables (letters) in an algebraic expression with their numerical values.
Substitution property of equality is used for various purposes such as in the substitution of values into expressions, to check solutions for equations, to solve equations that have two variables, and find solutions for systems of equations such as in the case of simultaneous equations thereby making it the correct choice.
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A hot-air balloon ha a 14
14
-foot diameter that i being deflated at a rate of 0. 25
0. 25
feet per minute. How many minute,
x
, will it take before the balloon ha hrunk to a diameter of 8
8
feet?
Total 24 minutes, x, will it take before the balloon has shrunk to a diameter of 8 feet.
In the given question, we have to find how many minute, x, will it take before the balloon has shrunk to a diameter of 8 feet.
From the given question, a hot-air balloon has a 14-foot diameter.
Hot-air balloon is being deflated at a rate of 0.25 feet per minute.
So the slope will be = -0.25, the negative sign is there because hot-air balloon is being deflated.
Let the amount of air left in the hot-air balloon at time n minutes is A(n) feet diameter.
The initial value of A(n) is 14-foot diameter.
Thus when n = 0, the value A(n) will be 14.
So, we can write the relation as
A(n) = -0.25n + 14
We need to find the amount left after x minute. So n = x.
The balloon has shrunk to a diameter of 8 feet. So A(n) = 8 feet
Now the equation is
8 = -0.25x + 14
Subtract 14 on both side, we get
-0.25x = -6
Divide by -0.25 on both side, we get
x = 24
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The complete question is:
A hot-air balloon has a 14-foot diameter that is being deflated at a rate of 0.25 feet per minute. How many minutes, x, will it take before the balloon has shrunk to a diameter of 8 feet?
please solve two answers
The function f(x) is f(x) = -2/3 x -8. The function g(x) is g(x) = -1/6 x - 2
What is a function?
A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.
Given that f(x) is a linear function. The value of f are f(-9) = -2 and f(-3) = -6.
Assume that, f(x) = ax + b
Now putting x = -9 in f(x) = ax + b:
f(-9) = a(-9) + b
Putting f(-9) = -2
-2 = -9a + b ....(i)
Now putting x = -3 in f(x) = ax + b:
f(-3) = a(-3) + b
Putting f(-3) = -6
-6 = -3a + b .....(ii)
By using the elimination method solve equation (i) and (ii).
Subtract equation (ii) from equation (i)
-9a + b = -2
-3b + b = -6
(+) (-) (+)
__________
-6a = 4
Divide both sides by -6:
a = -4/6
a = -2/3
Putting a = -2/3 in equation (i)
-6 = -3(-2/3) + b
-6 = 2 + b
b = -6 - 2
b = -8
Therefore, f(x) = -2/3 x -8
Now compare f(x) = -2/3 x -8 with f(x) = ax + b
a = -2/3 , b = -8
The y-intercept of f(x) is b = -8
The x-intercept of f(x) is b/a = -8/(-2/3) = 12
The y-intercept of g(x) is 6 more than f(x). Thus the y-intercepts of g(x) is 6 + (-8) = -2
The x-intercept of g(x) is 12.
Assume that the linear equation of g(x) is g(x) = hx + k
The y-intercept of g(x) is k = -2
The x-intercept of g(x) is k/h = 12
Putting k = -2:
-2/h = 12
h = -2/12
h = - 1/6
The linear equation of g(x) is g(x) = -1/6 x - 2
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Sophia is going to invest $820 and leave it in an account for 12 years. Assuming the interest is compounded monthly, what interest rate, to the nearest tenth of a percent, would be required in order for Sophia to end up with $1,170?
Answer:2.90%
Step-by-step explanation: good luck!
Due today.. ixl assignments. I have to pick the equation, then solve it.
What is the difference between functions and loops?
In programming, loops are used to keep repeating a block of code until a certain condition is satisfied.
What are functions ?A chunk of code known as a function only executes when it is invoked. Data that you supply to a function are referred to as parameters. In order to reuse code, functions are crucial because they are utilised to carry out specific actions: Use the code several times after just one definition. A variable that saves the memory address of another variable as its value is known as a pointer. The * operator is used to create a pointer variable, which points to a data type of the same type (such as int). In programming, loops are used to keep repeating a block of code until a certain condition is satisfied. Programmers can execute a statement or set of instructions repeatedly without repeating the same code by using a loop statement.To learn more about Loop refer to:
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Solve for r (PLEASE HELP DUE TODAY)
14.3 = pi (r²) (1.4)
In the equation, r will have the value 1.79.
What is an Equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. The sign shows the relationship of equality between the expression written on the left side with the expression written on the right side.
14.3 = pi (r²) (1.4)
(r²) = 14.3/pi(1.4)
where pi = 3.142
(r²) = 14.3/3.142(1.4)
(r²) = 14.3/4.3988
(r²) = 3.212
r = √3.212
r = 1.79
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what are the x-intercepts of this graph?
Please help, i dont really understand this lol
Answer:
A) [tex]x>-2[/tex]
Step-by-step explanation:
[tex]x+4>-x \\ \\ 2x+4>0 \\ \\ 2x>-4 \\ \\ x>-2[/tex]
Why is geometry vocabulary important?
Geometry vocabulary assisted us in continuing to lay the groundwork for thinking critically, clearly, and profoundly. So even if you might not want to or even be able to recall the geometry vocabulary, it nonetheless had a role in your mental growth and helped you become the thoughtful adult you are today.
Who named geometry?The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.
The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.
The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.
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Geometry vocabulary assisted us in continuing to lay the groundwork for thinking critically, clearly, and profoundly. So even if you might not want to or even be able to recall the geometry vocabulary, it nonetheless had a role in your mental growth and helped you become the thoughtful adult you are today.
What is the role of vocabulary development in mathematics?Understanding vocabulary has a significant role in general comprehension in many subject areas, including mathematics. There are several, tried-and-true techniques for teaching vocabulary across all subject areas. The growth of mathematical competency depends on the teaching and learning of the mathematical language.
Our continued development of the foundations required to think critically, clearly, and thoroughly was made possible by our language in geometry. Therefore, even if you might not want to or even be able to recall your geometry vocabulary, it nevertheless had a role in your mental growth and helped you become the thoughtful adult you are today.
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Slope intercept form
The graph of the linear equation y = mx + c is a line with m as slope, m and c as the y-intercept
What is standard form form?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5.
When an equation is given in this format, finding both intercepts is rather simple (x and y). Additionally, when resolving systems of two linear equations, this form is highly helpful.
It is possible to determine the x- and y-intercepts of the corresponding line when we have a linear equation in standard form.
In some circumstances, we might want to convert an equation written in a different form to standard form (for instance, while solving systems of equations).
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Determine if this statement is always, sometimes, or never true.
If a ≥ 0, then |a| = -a
never
sometimes
always
The statement "If a ≥ 0, then |a| = -a" is always false.
What is the absolute value?
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.
The absolute value of a real number, denoted by |a|, is the non-negative value of a without regard to its sign.
Therefore, if a is greater than or equal to zero, the absolute value of a is equal to itself.
On the other hand, -a is the negative of a, which is only the case when a is less than zero.
Hence, |a| can never equal to -a when a ≥ 0, because the absolute value is always non-negative, while -a is always negative.
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The sentence "If a 0, then |a| = -a" is untrue at all times. 4 is equal to 4 in absolute terms. The formal notation for a number's absolute value is |x|.
What is the absolute value?Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line. A number can never have a negative absolute value. The non-negative value of a, indicated by the symbol |a|, is the absolute value of a real number, regardless of its sign. It follows that if an is higher than or equal to zero, its absolute value is also zero.
However, -a is the opposite of a, and is only true when an is less than zero. This means that when an is greater than 0, |a| can never equal -a because the absolute value is always non-negative whereas -a is always negative. Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.
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What is the area? For this Shape.
Please answer this quick!!!
Answer:
19 square meters
Step-by-step explanation:
so split the shape into 2 rectangles (where you drew the line by the number 7)
then 3 times 5 is 15 and for the area of the second triangle it's not 1 times 7 because 7 is the entire side and we just need the smaller part on the right. So we do 7-3 because 3 is the amount of the side we dont need (it says on the bottom) and 1 times 4 is 4 and 4+15 is 19
Need help on question b
The algebraic expression in question b can be simplified to give (x² - 5x)/5.
Simplifying Algebraic expressionSimplification of an algebraic expressions is the process of writing an expression in the most efficient and compact way, that is in their simplest form, without changing the value of the original expression.
2x²(x - 5)/10x = 2x × x(x - 5)/ 2x × 5
2x is a common factor to both the numerator and denominator, hence can cancel out
2x²(x - 5)/10x = x(x - 5)/5
opening bracket we have;
2x²(x - 5)/10x = (x² - 5x)/5
Therefore, (x² - 5x)/5 is the result after simplifying the algebraic expression 2x²(x - 5)/10x
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What is the factoring method of X² 6x 16?
The factoring method for the polynomial x²+6x-16 is to find the values that satisfies the equation.
The given polynomial is x²+6x-16.
Now, in order to factorize the polynomial, we have to think of any two number such that by adding them the sum comes out to be 6 and when we multiply them, there product is -16, this is the factoring method for this polynomial.
So, by hidden trial method, we can analyze that there are two numbers 8 and -2.
By adding them, they becomes 6 and on multiplying they become -16.
So, the factorized form of the polynomial will be,
(x-8)(x+2)
Hence, the polynomial was factorized.
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