What is the length of the hypotenuse of the triangle 8cm 15cm?

Answer:

a>63

Step-by-step explanation:

You treat the inequality sign just as you would an equal sign.

Isolate a to find the solutions.

Therefore, you need to multiply 21 on both sides:

a > 21 × 3

Which comes out to:

a > 63

On solving the provided question, we can say that  triangles BCD and CFE are similar by AAA property. so , angle BDC = angle CFE, therefore t = 39

An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.

here,

triangles BCD and CFE are similar by AAA property.

so , angle BDC = angle CFE,

therefore t = 39 ( sides to correspondence angles are equal )

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The required value of the x for the given right angle triangle is x = 4.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

here,
For the given right-angle triangle,
cosФ = base/hypoentuse
cos60 = 2/x
1 / 2 = 2/x
x = 4

Thus, the required value of the x for the given right angle triangle is x = 4.

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For every quart, there are 4 cups. In two quarts, there are eight cups. In four quarts, there are sixteen cups. A 5 quart container holds 20 cups.

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Answer:

you get a negative answer.

The equation of a line which passes through (5, 6) and (-3, 4) is 4y=x+19.

In the given question, we have to find the equation of a line which passes through (5, 6) and (-3, 4).

The point-slope approach is typically used when two points that sit on a specific line are specified.

A line's equation is written as y - y(1) = m(x - x(1)), where y(1) is the Y-axis coordinate, m is the slope, and x(1) is the X-axis coordinate.

Firstly we find the value of m using the formula

m = [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]

From the given points x(1) = 5, y(1) = 6, x(2) = -3, y(2) = 4.

Now putting the value

m = [tex]\frac{4-6}{-3-5}[/tex]

Now solving

m = [tex]\frac{-2}{-8}[/tex]

m = [tex]\frac{1}{4}[/tex]

Now we finding the equation of line. We can use any one point in the given points.

Now taking the points (5, 6), x(1) = 5 and y(1) = 6

Now putting the value in equation y - y(1) = m(x - x(1)).

y - 6 = [tex]\frac{1}{4}[/tex](x - 5)

Multiply by 4 on both side, we get

4(y - 6) = x - 5

4y - 24 = x - 5

Add 24 on both side, we get

4y = x + 19

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Answer:y=2x-3 and x=7

Step-by-step explanation: x + y = 18

"The second is 3 less than twice the first."

SO that looks like:  

the second ("Y")  "is" always means "equals" and then 3 less - means we subtract 3, and then twice the first means 2 times the "x"

So we end up with:

y = 2x - 3

Now we also know that we can only solve an equation with ONE variable in it, BUT we have an "x" and a "y!"  But the good thing is that if we have an equation with an equals sign in the middle, we can substitute either side of the equation in for that variable in another equation. So....

we have now:

x + y = 18, and

y = 2x - 3

so taking what comes after the "y =" part above, we can substitute that into the first equation to get this:

x + (2x - 3) = 18  

Now we have only one variable - X, and we can solve for x! Rearranging our parentheses from the above equation, we can get:

(x + 2x) - 3  = 18, or 3x - 3 = 18.

Then we can get:

3x = 21

then we divide BOTH sides by 3 to get:

3x  =   21, or 7!  So X = 7!

Answer: ??

Step-by-step explanation:

Answer:

Step-by-step explanation:

huh

The range of a logarithmic function is dependent on the base of the logarithm.

The set of all real numbers constitutes the range of a logarithmic function.

As a result, x > 0 (or) (0, ∞) is the domain of the log function y = log x. The set of all real numbers is the range of any log function (R)

A logarithm is a measurement of the amount that a fixed number (the base) must be increased in order to create a particular number.

Basically,

if y=ax

So, logₐ(y) = x

The base of the logarithm in this instance is a. The following two bases are frequently employed: base-10 and Base-e

'e' is a mathematical constant having a value of around 2.718.

If the base is "e," we use a specific expression: ln(x)

Fundamentally,

ln(x)=loge(x)  

Here, e is the base.

Base-10 will be used if no base is provided, as in the formula

log(x)=log10(x)

Here 10 is the base

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).

A function's range is the collection of values it may take as input. After we enter an x value, the function outputs this sequence of values. The y values are those.

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When 8.0 X 10 is rewritten to the -2nd in standard form, 800 is obtained by comprehending negative exponents.

The amount of times a number has been multiplied by itself is referred to as an exponent. For instance, 2 to the third (written as 23) equals 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Keep in mind that a number raised to the power of one equals itself. Exponent is the process of expressing huge numbers in terms of powers. In other words, exponent refers to the number of times a number has been multiplied by itself. For instance, 6 is multiplied by itself four times, yielding 6 6 6 6. This can be expressed as 64.

given

This number is 10 to the power of 2, as the exponent is 2.

Due to the positive exponent, the answer is a number higher than the origin or base number.

We shift the decimal to the right twice to arrive at our conclusion:

8.0.0 -> 800

When 8.0 X 10 is rewritten to the -2nd in standard form, 800 is obtained by comprehending negative exponents.

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The expected value of the number of points she scores on a toss of the 2 dice is 7.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, Greta rolls a pair of 6- sided dice.

If she gets two of a kind she scores the sum of the 2 dice.

The number of sample space N(S) of rolling two dice is 36.

The number of events for getting same number on both dice are,

(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) = 6.

Therefore, The probability of getting the same numbers on both dice is,

= 6/36.

= 1/6.

The total score is,

= 2 + 4 + 6 + 8 + 10 + 12.

= 42.

We know The expected value, also known as the expectation, average, is a generalization of the weighted average in the field of probability theory. Informally, the anticipated value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.

Therefore, The expected value of the number of points she scores on a toss of the 2 dice is,

= (1/6)×42.

= 7.

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After taking the common, the factored form of [tex]27x^3+64[/tex] is [tex](3x+4)(9x^2-12x+16)[/tex].

In the given question, we have to find the factored form of [tex]27x^3+64[/tex].

The following is how we factor the GCF out of a polynomial:

(1) Find the expression's numbers' greatest common factor before analyzing each variable or expression separately to identify the GCF. Factor out the least power that arises if the variable or expression appears in every term.

(2) Write the GCF outside the parentheses and divide each term by the GCF inside the parentheses to factor out a GCF.

To solve this question we use the formula [tex](a^3+b^3) = (a+b)(a^2-ab+b^2)[/tex]

We can write [tex]27x^3+64[/tex] as

[tex]27x^3+64[/tex] = [tex](3x)^3-(4)^3[/tex]

[tex]27x^3+64[/tex] = [tex](3x+4)((3x)^2-3x\cdot4+(4)^2)[/tex]

[tex]27x^3+64[/tex] = [tex](3x+4)(9x^2-12x+16)[/tex]

Hence, the factor form of [tex]27x^3+64[/tex] is [tex](3x+4)(9x^2-12x+16)[/tex].

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The complete question is:

What is the factored form of [tex]27x^3-64[/tex]?

By calculating , with the subject of x  we get x = 4 + 5y / y + 3  as a final resultant .

What is subject of a formula?

Making x the subject of a formula means rearranging the formula so that we have a single x variable equal to the rest of it.

Making x subject of the formula is as follows:

x = 4 + 5y / y + 3

y = 4 - 3x ÷ x - 5

cross multiply

y(x - 5) = 4 - 3x

distribute the values on the left side

yx - 5y = 4 - 3x

add 3x to both sides of the equation

yx + 3x - 5y = 4 - 3x + 3x

yx + 3x - 5y = 4

add 5y to both sides

yx + 3x - 5y + 5y = 4 + 5y

yx + 3x  = 4 + 5y

factorise the left hand side

x(y + 3) = 4 + 5y

divide both sides by (y + 3)

Therefore,

x = 4 + 5y / y + 3

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Answer:

C

Step-by-step explanation:

The answer is C. The total amount spent on car insurance didn't increase by a constant amount each month.

A linear relationship means that the relationship between two variables can be described by a straight line, with the rate of change being constant. In this case, the relationship between the number of months since Adele got her car and the total amount of money she had spent on car insurance is not linear. If the relationship was linear, we would expect the rate of increase to be constant, but in this case, the rate of increase is not constant. The car insurance cost 183 in the first month, 732 in 4 months, and 2196 in a year. That means 183 in 1 month, 549 in 4 months, and 1464 in a year. As we see, the rate of increase is not constant.

To solve a quotient problem, you can use the following steps of understanding the problem, dividing the quotient by divisor, finding the remainder, checking the solution.

Understand the problem: Read the problem carefully and make sure you understand what is being asked. Identify the dividend, divisor, and the quotient.

Set up the problem: Write the problem using the standard division format: dividend ÷ divisor = quotient.

Divide: Begin by dividing the leftmost digit of the dividend by the divisor. Write the quotient above the dividend, to the left of the dividend, and above the divisor.

Multiply and Subtract: Multiply the divisor by the quotient digit and write the product under the corresponding digit of the dividend. Then subtract this product from the corresponding digits of the dividend.

Bring down the next digit: Bring down the next digit of the dividend to the right of the remainder. Repeat steps 3 and 4 until the remainder is zero or until you have reached the desired level of accuracy.

Check the work: Verify that the quotient is correct by multiplying the divisor and quotient, and adding the remainder (if any) to the product. The result should be equal to the dividend.

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Step-by-step explanation:

The solution to the system can be found by graphing the equations and finding the point of intersection of the two lines. The point of intersection is the point (x,y) that satisfies both equations. In this case, the point of intersection is (2,15) which means that at x=2 and y=15 the system of equations is satisfied.

The possible values of x are;  8 > x

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

The given diagram is a triangle. From the diagram we can see that;

2x + 8 > 3x (according to the length)

Solve the resulting inequality;

2x + 8 > 3x

8 > 3x - 2x

8 > x

x> 0.5

Hence the possible values of x are  8 > x

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Answer:

I believe that it is 14° but I would double check

The Addition Method for Solving Systems of Equations in Two Variables. The addition technique, sometimes known as the elimination method, is a third approach for solving systems of linear equations. In this procedure, we sum two terms with the same variable but opposing coefficients.

The addition property of equality is used in the elimination approach for solving systems of linear equations. Each side of an equation can have the same value. So, if you have a system where x - 6 = 6 and x + y = 8, you may add x + y to the left side of the first equation and 8 to the right.

Gaussian elimination, often known as row reduction in mathematics, is a method for solving systems of linear equations. It is made up of a series of operations performed on the matching coefficient matrix.

To set up your elimination, multiply terms in one or both equations by a constant. Then you may remove or add terms from one equation and delete a variable.

The Gaussian elimination rules are the same as the rules for the three basic row operations; in other words, you can algebraically act on a matrix's rows in the following three ways (or combinations of them): Two rows are swapped. dividing a row by a constant (any constant which is not zero)

In normal Gaussian elimination, you can only perform two things: swap two rows and add (or remove) a multiple of one row to a row below it.

Gaussian elimination, often known as row reduction in mathematics, is a method for solving systems of linear equations. It is made up of a series of operations performed on the matching coefficient matrix.

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If Rodrigo randomly selects one of his CDs, then the probability that it will be a pop CD is 1/18.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that Rodrigo is organizing his CD collection.

The number of pop CDs are 5

The number of other CDs are 85.

If Rodrigo randomly selects one of his CDs we have to find the probability that it will be a pop CD

The total number of cd are 90.

The the probability that it will be a pop CD is 5/90 which is 1/18.

Hence, If Rodrigo randomly selects one of his CDs, then the probability that it will be a pop CD is 1/18.

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A straight-line graph is a visual depiction of a linear function. The general equation of straight-line graph is: y = mx+c

where m is the gradient. y and c are intercept.

example=y=4x+1

In order to plot straight line graphs, we need to replace values for x into the equation for the graph and work out the equivalent values for y.

We frequently put these values in a table to make our work clearer. Once we have calculated the coordinates, we can action these as a graph.

occasionally, we only need a sketch of a straight-line graph – we do not need it to be plotted with the same correctness as we would get by calculating coordinates.

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The total number of numbers among the second one thousand natural numbers that are not multiples of any of the first three odd prime number is 1 + 1 + 1 - 1 - 1 + 1 = 2.

A natural number is not a multiple of the first three odd prime numbers (3, 5, 7) if and only if it is not divisible by any of them. There are 1000-999=1 number among the second one thousand natural numbers that is not divisible by 3. There are 1000-999=1 number among the second one thousand natural numbers that is not divisible by 5. There are 1000-999=1 number among the second one thousand natural numbers that is not divisible by 7. However, if a number is divisible by 3 and 5, it is also divisible by 15 and we have counted it twice. Similarly, if a number is divisible by 3 and 7, or 5 and 7, or all three, we have counted it thrice, twice and thrice respectively. Hence, the total number of numbers among the second one thousand natural numbers that are not multiples of any of the first three odd prime number is 1 + 1 + 1 - 1 - 1 + 1 = 2.

Therefore, The total number of numbers among the second one thousand natural numbers that are not multiples of any of the first three odd prime number is 1 + 1 + 1 - 1 - 1 + 1 = 2.

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The total number of numbers among the second one thousand natural numbers that are not multiples of any of the first three odd prime number is 1 + 1 + 1 - 1 - 1 + 1 = 2.

A natural number is not a multiple of the first three odd prime numbers (3, 5, 7) if and only if it is not divisible by any of them. There are 1000-999=1 number among the second one thousand natural numbers that is not divisible by 3. There are 1000-999=1 number among the second one thousand natural numbers that is not divisible by 5. There are 1000-999=1 number among the second one thousand natural numbers that is not divisible by 7. However, if a number is divisible by 3 and 5, it is also divisible by 15 and we have counted it twice. Similarly, if a number is divisible by 3 and 7, or 5 and 7, or all three, we have counted it thrice, twice and thrice respectively. Hence, the total number of numbers among the second one thousand natural numbers that are not multiples of any of the first three odd prime number is 1 + 1 + 1 - 1 - 1 + 1 = 2.

Therefore, The total number of numbers among the second one thousand natural numbers that are not multiples of any of the first three odd prime number is 1 + 1 + 1 - 1 - 1 + 1 = 2.

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Answer:

3 times

Step-by-step explanation:

-6 + 3 = -3

-3 + 3= 0

0 + 3 = 3

Answer:  it can go in 2 times

Step-by-step explanation:

i'm not 100% sure if this is correct I hope it helps sorry if I got it wrong

The person can see far upto 53.08 miles.

The Pythagorean Theorem states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

In other words, for the triangle shown below, a² + b² = c².

The legs, a and b, are the perpendicular sides of the right triangle and the hypotenuse, c, is the side opposite the right angle.

This application is frequently used in construction projects and basically anything that involves right triangles life roofs to a house and so on

The length of the hypotenuse (4960 miles + 1500 feet) and you know the length of the base (4960 miles), you can readily find the height using the Pythagorean theorem (c² = a² + b²).

I converted the distances from miles to feet. The numbers are large but manageable.

Earth's radius = 4960 miles = 26,188,800 feet.

Earth's radius plus height of the skyscraper = 26,9188,800 + 1500 ft

= 26,190,300 feet.

c² = a² + b²

(26,190,300)² = (26,188,800)² + h²

Solve for h

h² = 6.85931814X10^14 - 6.85853245X10^14

h^2 = 78,569,000,000

h = 280,301.623 feet = 53.08 miles

Thus, the person can see far upto 53.08 miles.

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The person can see far upto 53.08 miles.

The Pythagorean Theorem states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

In other words, for the triangle shown below, a² + b² = c².

The legs, a and b, are the perpendicular sides of the right triangle and the hypotenuse, c, is the side opposite the right angle.

This application is frequently used in construction projects and basically anything that involves right triangles life roofs to a house and so on

The length of the hypotenuse (4960 miles + 1500 feet) and you know the length of the base (4960 miles), you can readily find the height using the Pythagorean theorem (c² = a² + b²).

I converted the distances from miles to feet. The numbers are large but manageable.

Earth's radius = 4960 miles = 26,188,800 feet.

Earth's radius plus height of the skyscraper = 26,9188,800 + 1500 ft

= 26,190,300 feet.

c² = a² + b²

(26,190,300)² = (26,188,800)² + h²

Solve for h

h² = 6.85931814X10^14 - 6.85853245X10^14

h² = 78,569,000,000

h = 280,301.623 feet = 53.08 miles

Thus, the person can see far upto 53.08 miles.

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The value of f(-2) is -1.

Now, According to the question:

Properties of functions:

By the property of function,

f(-x) = -f(x)

Hence if the value of f(x) is given then we can find the value of f(-x) by using the above mentioned property.

Here f(2) = 1

Hence by using the above mentioned property , we get

f(-2) = -f(2)

Substituting f(2) equal to 1 , we get

f(-2) = -1

Hence, the value of f(-2) is -1.

The given question is incomplete, complete question is:

If f(2) = 1, what is the value of f(-2)?

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Answer: Velocity describes motion by indicating how fast an object moves and in what direction. Speed is a magnitude of velocity, which indicates only how fast an object moves. Speed shows how much distance is traversed in a given interval of time:

Step-by-step explanation:

The probability that one card drawn is 6 = 1/13.

How likely something is to happen is determined by its probability. The probability is calculated by dividing the total number of outcomes by the total number of potential events.

The likelihood is based on the range of potential outcomes. the total number of possible outcomes. As an illustration, since there is only one way to get a head and a total of two possible results, the likelihood of flipping a coin and getting heads is one in two. a tail or a head. We write P(heads) = 12 here.

Given,

the deck of 52 cards,

There are 4 sixes in total of hearts, clubs, diamonds and spades suits.

the probability that one card drawn is 6 = 4 /52 = 1/13

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In triangle ACB, the measure of ∠ACD is 67.5 degrees. Hence, option B is the correct option for this question.

A, B, C, and D lie on circle M, Line segment BD is a diameter.

We know that the measure of an inscribed angle CDA = 1/2(arc AC).

And arc AC = 90 degrees.

Hence, we get,  

∠CDA = 90 / 2

∠CDA = 45 degrees

We know that triangle ACD is isosceles, also the sum of all the angles in a triangle is 180 degrees.

∠ACD + ∠CAD + ∠CDA = 180 degrees

Also, we have ∠ACD = ∠CAD

∠ACD + ∠ACD + ∠CDA = 180 degrees

∠ACD  = 180-45 / 2

∠ACD   = 67.5 degrees

So the measure of ∠ACD is 67.5 degrees.

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The complete question is -

Points A, B, C, and D lie on circle M. Line segment BD is a diameter. Triangle A C D is inscribed within circle M. Point B is on the circle between points C and B. A line is drawn to connect points D and B. Lines are drawn from points C and A to point M to form a right triangle. Arcs C D and A D are congruent. What is the measure of angle ACD?

a) 45.0°

b) 67.5°

c) 112.5°

d) 135.0°

The equation that describes the hanger is y = x + 1.b-This line will represent the equation y = x + 1.c. The equation for the first hanger is y = x + 1.

Equation is a mathematical statement that expresses the equality of two expressions by using symbols. It typically consists of an equals sign (=) and two expressions that are related by the equals sign. Equations are used to describe the relationship between different variables, such as the area of a circle or the speed of a moving object. Equations are also used to solve problems, to make predictions, or to reveal patterns or trends.

a. The equation that describes the hanger is y = x + 1. This equation states that the y-coordinate (height of the hanger) is always 1 unit greater than the x-coordinate (width of the hanger).

b. To find x, I will draw more hangers to represent each step of the process. For the first hanger, I will draw a line with a y-intercept of 1 and a slope of 1. This line will represent the equation y = x + 1.

For the second hanger, I will draw a line with a y-intercept of 1 and a slope of 2. This line will represent the equation y = 2x + 1.

For the third hanger, I will draw a line with a y-intercept of 1 and a slope of 3. This line will represent the equation y = 3x + 1.

The reason I chose to draw each hanger with a y-intercept of 1 is to represent the constant value of 1 in each equation. The slope of each hanger is increased by 1 from the previous hanger to represent the coefficient of x in each equation.

c. The equation for the first hanger is y = x + 1. This equation matches the hanger because the y-intercept is 1 and the slope is 1.

The equation for the second hanger is y = 2x + 1. This equation matches the hanger because the y-intercept is 1 and the slope is 2.

The equation for the third hanger is y = 3x + 1. This equation matches the hanger because the y-intercept is 1 and the slope is 3.

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Therefore, the system of equations with the elimination approach has a solution of (5, -2) for the equations 6x + 10y = 10 and -6x - 24y = 18.

An equation is a mathematical formula that joins two statements and uses the equal symbol (=) to indicate equivalence. For instance, in the equation 3x + 5 = 14, the equal sign divides the variables 3x + 5 and 14. The relationship between the two sentences on either side of a letter is explained by a mathematical formula. There is frequently only one variable, which also serves as the symbol. for instance, 2x - 4 = 2.

given

6x + 10y = 10

-6x - 24y = 18

-14y = 28

y = -2

so x = 6x -20 = 10

= 6x= 30

x = 5

Therefore, the system of equations with the elimination approach has a solution of (5, -2) for the equations 6x + 10y = 10 and -6x - 24y = 18.

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