a 10 d lens is placed in contact with a 15 d lens. what is the refractive power of the combination?

The number of guitarist who plays classical solos in the contest is 30.

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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Answer:

A) [tex]x>-2[/tex]

Step-by-step explanation:

[tex]x+4>-x \\ \\ 2x+4>0 \\ \\ 2x>-4 \\ \\ x>-2[/tex]

A rectangle has four sides and angles at 90 degree.

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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In programming, loops are used to keep repeating a block of code until a certain condition is satisfied.

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Answer:

the answer is 4

2+2=4 bc 1+1 is 2 ×2 and that is 4 your welcome

The graph of the linear equation y = mx + c is a line with m as slope, m and c as the y-intercept

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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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

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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Answer:

lo l oh my gosh hi i havent seen u in so many years

Step-by-step explanation:

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

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.

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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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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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|.

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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The algebraic expression in question b can be simplified to give (x² - 5x)/5.

Simplification 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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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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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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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

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.

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.

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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Answer:2.90%

Step-by-step explanation: good luck!

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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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.

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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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

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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In the equation, r will have the value 1.79.

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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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?