Anna has leaned a ladder against the side of her house. The ladder forms a 72º angle with the ground and rests against the house at a spot that is 6 meters high. What length is the best approximation for the distance along the ground from the bottom of the ladder to the wall?

4x^2+25y^2=100

[tex]4x^2+25y^2=100 \\\\ Dividing \;both \;sides \;by \;100 \\\\ \frac{4x^2}{100}+ \frac{25y^2}{100}= \frac{100}{100} \\\\ \frac{x^2}{25}+ \frac{y^2}{4}= 1 \\\\ \frac{x^2}{5^2}+ \frac{y^2}{2^2}= 1 \\\\ This \;is \;an \;ellipse. \\\\

\frac{x^2}{a^2}+ \frac{y^2}{b^2}= 1 [/tex]

Domain of an ellipse is x ∈ [-a,a] and Range of an ellipse is y ∈ [-b,b].

So, given equation is an Ellipse where Domain is x ∈ [-5,5] and Range is y ∈ [-2,2].

No, there is not enough information given to prove that ΔVZX and ΔWXZ are congruent by SAS.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

The given information only provides the lengths of two sides and the measures of two angles in the triangles, but we do not know if the third side is congruent, and we cannot assume that it is by the given information.

Additionally, the given information does not specify that one of the congruent sides is included between the congruent angles, which is necessary for the SAS postulate to be used to prove congruence.

Therefore, there is not enough information given to prove that ΔVZX and ΔWXZ are congruent by SAS.

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Answer:

mos def 15

Step-by-step explanation:

Answer: 20 units

Step-by-step explanation:

We know that the area of a circle is given by :-

[tex]\text{Area}=\pi r^2[/tex], where r is the radius of the circle.

We are given that the area of the circle = [tex]100\pi[/tex] square units.

[tex]\Rightarrow\ 100\pi=\pi r^2\\\\\Rightarrow\ r^2 =100[/tex]

Taking square root on both the sides , we get

[tex]\\\\\Rightarrow\ r=10[/tex]

The diameter of the circle is given by :-

[tex]d=2r=2(10)=20\text{ units}[/tex]

Answer:

D) y2 = -5x - 8

Step-by-step explanation:

A function is a rule between two sets A and B so that each element of set A (Domain) corresponds to a single element of set B (Range). Mathematically they can be expressed as:

[tex]f: A\rightarrow B\\\\a\rightarrow b =f(a)[/tex]

So:

[tex]y^2=-5x-8\\\\y=\pm \sqrt{-5x-8}[/tex]

Isn't a function because the elements of the domain don't corresponds to a single element of the range.

We can see this in an easier way using the vertical line test, which is a visual way to determine if a curve is a graph of a function or not. If a vertical line intersects a curve in an xy plane more than once, then for a value of x the curve has more than one value of y, and then the curve does not represent a function.    

I attached you the graphs, so you can corroborate the results visually.

The number of cakes she can make is 9.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Stella has 6 pounds of chocolate. She will use 2/3 pounds of the chocolate to make one cake.

The number of cakes will be calculated as,

Number = 6 / ( 2 / 3 )

Number = ( 6 x 3 ) / 2

Number = 9

Therefore, the number of cakes will be 9.

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The actual measurement of angle H is thus 110 degrees.

To find the actual measurement of angle H in triangle GHI, we can use the fact that the sum of the interior angles in any triangle is always 180 degrees. Given the expressions for angles G, H, and I as G = (2x + 5)", H = (6x − 10)", and I = (x + 5)", we can set up the equation (2x + 5) + (6x - 10) + (x + 5) = 180 to find the value of x. After determining x, we substitute it back into the expression for angle H to get the desired measurement.

Setting up the equation we have:
(2x + 5) + (6x - 10) + (x + 5) = 180

Combine like terms to get 9x = 180

Divide both sides by 9 to find x: x = 20 degrees

Now plug this value into the expression for angle H: H = 6(20) - 10

We find that H = 120 - 10 degrees, so H = 110 degrees

To find the measurement of angle H in triangle GHI, we apply the fact that the sum of angles in a triangle is always 180 degrees. By solving the equation that sets this sum, we find the value of x, and then use it to determine that angle H measures 110 degrees.

The annual interest rate of the CD was 3.75 %

Explanation

Simple Interest formula is : [tex] I =P*r*t [/tex] , where [tex] I= [/tex] Amount of interest, [tex] P= [/tex] Principal/Initial amount, [tex] r= [/tex] rate of interest in decimal form and [tex] t= [/tex] time in years

Here Abner earned $1575 in simple interest and he initially deposited $6000. So, [tex] I=1575 [/tex] dollar and [tex] P= 6000 [/tex] dollar

Also given that, [tex] t = 7 [/tex] years

Now according to the formula...

[tex] I= P* r*t\\ \\ 1575= 6000*r*7\\ \\ 1575= 42000*r\\ \\ r= \frac{1575}{42000}= 0.0375 [/tex]

For getting the interest rate in percentage, we will multiply it by 100%. So... (0.0375 × 100) % = 3.75 %

So, the annual interest rate of the CD was 3.75 %

The probability that a college basketball player makes exactly three of his next four free throws is calculated using binomial probability, resulting in approximately 38.58%.

The probability that a college basketball player makes exactly three of his next four free throws, given that he makes 5/6 of his free throws, involves calculating a binomial probability. We have four independent events (four free throws), and we want exactly three successes (made throws) and one failure (missed throw). We use the following formula for the binomial probability:

P(X=k) = C(n, k) × p^k × (1-p)^(n-k)

where:

In this problem:

Plugging in the values:

P(X=3) = C(4, 3) × (5/6)^3 × (1/6)^1

C(4, 3) is 4, since there are four different ways to make three throws and miss one (MMM-M, MM-MM, M-MMM, MMMM-). So the calculation gives:

P(X=3) = 4 × (5/6)^3 × (1/6) = 4 × (125/216) × (1/6) = 500/1296, which simplifies to about 0.3858 or 38.58%.

Therefore, the probability that he makes exactly three of his next four free throws is 0.3858 or 38.58%.

A number that divides evenly into another number is known as factor.

The correct answer is

B.) factor.

A factor is a number that divides evenly into another number. To find the factors of a number, you can perform a process of division or use other mathematical methods.

Let's take an example to illustrate:

If we consider the number 12, its factors are the numbers that divide it evenly without leaving a remainder. We can start by dividing 12 by 1:

12 ÷ 1 = 12

Since there's no remainder, 1 is a factor of 12. Now, let's try dividing 12 by 2:

12 ÷ 2 = 6

Again, there's no remainder, so 2 is also a factor of 12. Continuing this process, we find that 3 is also a factor of 12:

12 ÷ 3 = 4

And finally, 12 ÷ 4 = 3

So, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Each of these numbers divides evenly into 12, making them factors. Therefore, the correct answer is B.) factor.

Factors are essential in various mathematical concepts, including prime factorization, finding greatest common divisors, and simplifying fractions. Understanding factors helps in solving problems related to divisibility and multiplication. By identifying factors, we can break down complex numbers into simpler components, aiding in various mathematical computations and analyses. Hence, recognizing factors is fundamental in mathematics.

Complete question:

A number that divides evenly into another number is known as which of the following?

A.) prime number

B.)factor

C.) multiple

D.) Integer

The rate of crickets chirping is linearly dependent on the temperature and can be represented by the equation y = 4x -100, whereby y is the number of chirps per minute, and x is the temperature in °F.

This is essentially a linear equation problem where the rate of cricket chirps is related to the temperature.

Firstly, we list our two points: (59, 76) and (65, 100).

We can then calculate the slope (m). m = (y2-y1) / (x2-x1) = (100-76)/(65-59) = 24/6 = 4.

We have the rate of cricket chirps increasing by 4 chirps per increase in 1°F. Our equation is now of the form y= 4x + b.

Finally, we'll calculate the y-intercept (b) by plugging one of our points into the equation. If we choose the point (59, 76), we get 76 = 4*59 + b. Solving for b, we get b = -100.

So, the equation is y = 4x -100, where y is the number of chirps per minute, and x is the temperature in °F.

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The only point outside of the line is (2, 0)

In order to find if a point is outside, inside or on the line, you simply have to put the number into the equation. If the result is both sides are equal, then it is on the line. If the left side is bigger than the right side, then it is outside of the line. If the right side is bigger than the left, then it is inside of the line. So lets plug in and see where (2, 0) falls.

(x - 2)^2 + (y + 3)^2 = 4

(2 - 2)^2 + (0 + 3)^2 = 4

0^2 + 3^2 = 4

0 + 9 = 4

9 = 4

Since the left side is bigger than the right, we know it is outside of the line

Answer:

reflection over the y-axis

Step-by-step explanation:

The range of f(x) is a single value which is the y-coordinate of any point on the horizontal line representing f(x).

The range of a function is the set of possible values its output can have. In this case, the function f(x) is a horizontal line. Since f(x) is restricted to the portion between x = 0 and x = 20, inclusive, the range of f(x) is the set of all y-values within that range. Since the graph of f(x) is a horizontal line, the range of f(x) is a single value, which is the y-coordinate of any point on the line.

Based on the graph shown below, the range of f(x) include the following: B. { f(x)| –∞ < f(x) ≤ 4}

In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following range:

Range = (-∞, 4] or {f(x)| –∞ < f(x) ≤ 4}

Complete Question;

What is the range of f(x)?

{ f(x)| –∞ < f(x) < ∞}

{ f(x)| –∞ < f(x) ≤ 4}

{ f(x)| 4 < f(x) < ∞}

{ f(x)| 0 ≤ f(x) < ∞}