Find m∠1 in each figure

Answer:

[tex]AB_{3}[/tex]

Step-by-step explanation:

Given : [tex]A_{3}B_{9}[/tex]

To Find : Which represents the empirical formula for[tex]A_{3}B_{9}[/tex]?

Solution:

Definition of Empirical Formula - A formula that gives the simplest whole-number ratio of atoms in a compound.

[tex]A_{3}B_{9}[/tex]

To reduce it in simplest form

Divide the subscript numbers by 3

So, the resultant : [tex]AB_{3}[/tex]

Thus the empirical formula for [tex]A_{3}B_{9}[/tex] :

[tex]AB_{3}[/tex]

Answer:

[tex]f(x) = 2x+3[/tex]

Step-by-step explanation:

The function f(x) is the another way of representing the y-values in the function

i.e

[tex]y=f(x)[/tex]

Then y-axis be labeled with f(x)  

Also; the ordered pair is written as: (x, f(x)) instead of (x, y)

Given the equation:

[tex]y = 2x+3[/tex]

replace y = f(x)

then;

[tex]f(x) = 2x+3[/tex]

therefore, the equation  y=2x+3 using function notation is, [tex]f(x) = 2x+3[/tex]

Differential equation: In solving equations involving x, y, and z, taking steps with various values of h optimizes the process.

Step size h: When h=0.5 over the interval 0 to 2, solutions can be calculated by incrementing x from 1 to 1+h.

Optimizing procedures: By choosing appropriate values for h, the iterative process can be streamlined for better efficiency.

Break apart the factor 8 into 5 and 3, and then use the distributive property to calculate 7x5 and 7x3. Add the two products together to find that the product of 7 and 8 is 56.

To find the product of 7 and 8, you can break apart the array into more manageable pieces. One way to do this is by using the distributive property, which in this case lets you split one of the factors and multiply each part separately before adding the results. For example, you can break the number 8 into 5 and 3 because 5 + 3 equals 8. Then you multiply 7 by each part:

After calculating these two products, you add them together to find the final product:

35 + 21 = 56

Therefore, the product of 7 and 8 is 56. This approach can make multiplication easier, especially when dealing with larger numbers or when trying to calculate in your head.

A triangle inscribed in a semicircle can be identified as a right triangle.

A triangle inscribed in a semicircle can be identified as a right triangle.

To see why, consider that when a triangle is inscribed in a semicircle, one of its sides will coincide with the diameter of the circle. Since the diameter of a circle is always a straight line, it forms a right angle (90 degrees) with the semicircle's arc. Therefore, the triangle that is inscribed in the semicircle has a right angle as one of its angles, making it a right triangle.

Answer:

Step-by-step explanation:

Given  : slope=.25, x-intercept=24 ...?

Answer:

The orthocenter of the triangle is [tex](\frac{5}{4},1)[/tex] and option b is correct.

Step-by-step explanation:

The ends of the base of an isosceles triangle are at (2,0) & (0,1).

Orthocentre of the triangle is the intersection point of all three altitudes from its vertices.

First find any two altitudes, then find intersection point of altitudes.

The equation of a side is x=2, which is an vertical line. The opposite vertices of this side is (0,1), so the perpendicular line is a horizontal line. The equation of first altitude is

[tex]y=1[/tex]                              .... (1)

In an isosceles triangle, then attitude is the median of non-equal side. It means the altitude is passing through the midpoint of base side.

[tex]Midpoint=(\frac{2+0}{2},\frac{0+1}{2})=(1,0.5)[/tex]

Slope of base side is

[tex]m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{1-0}{0-2}=-0.5[/tex]

The product of slopes of two perpendicular lines is -1.

[tex]m_1\times m_2=-1[/tex]

[tex]-0.5\times m_2=-1[/tex]

[tex]m_2=2[/tex]

The point slope form of a line is

[tex]y-y_1=m(x-x_1)[/tex]

Where, m is slope.

The slope of second altitude is 2 and it passing through the pint (1,0.5), therefore the equation of second altitude is

[tex]y-0.5=2(x-1)[/tex]

[tex]y=2x-1.5[/tex]                ..... (2)

From equation (1) and (2), we get

[tex]x=\frac{5}{4}[/tex]

[tex]y=1[/tex]

Therefore the orthocenter of the triangle is [tex](\frac{5}{4},1)[/tex] and option b is correct.

Keywords:

Functions, subtraction, operation of functions

For this case, we are given two functions of the form [tex]y_ {1} = f (x)[/tex], where [tex]f (x) = 4x + 1[/tex] and[tex]y_ {2} = g (x)[/tex], where [tex]g (x) = x ^ 2-5[/tex]. We must find the subtraction (f-g) (x). So, by definition of operation of functions we have to:

[tex](f-g) (x) = f (x) -g (x)[/tex]

So, we have:

[tex](f-g) (x) = 4x + 1- (x ^ 2-5)[/tex]

Knowing that: [tex]- * + = -\ and\ - * - = +[/tex]

[tex](f-g) (x) = 4x + 1-x ^ 2 + 5\\(f-g) (x) = - x ^ 2 + 4x + 6[/tex]

Answer:

[tex](f-g) (x)[/tex]is given by[tex]-x ^ 2 + 4x + 6[/tex]

The construction method for creating a perpendicular line through a point not on a line is indeed useful for constructing a perpendicular bisector, based on the principle that all right angles are equal to one another. Therefore given statement is true.

The construction method used to construct a perpendicular through a point not on a line can indeed be used to construct a perpendicular bisector. This is true because both constructions rely on the same geometric principles. E4, which states that all right angles are equal to one another, supports this fact. In constructing a perpendicular line through a point not on the line, one essentially finds the point on the existing line that is closest to the external point and constructs a right angle there. This same method can be adapted for a segment to create a perpendicular bisector. By selecting the midpoint of the segment and then constructing a right angle using the segment as one side, this similarly results in a perpendicular bisector.

Final answer:

The construction method used to construct a perpendicular through a point not on a line being also applicable for constructing a perpendicular bisector is True. Both involve similar steps of drawing arcs with a compass that intersect and then drawing a line through those intersections, leveraging the properties of equidistant points and perpendicular bisectors.

Explanation:

The statement that the construction method used to construct a perpendicular through a point not on a line could also be used to construct a perpendicular bisector is True. The basic geometrical constructions used for both are quite similar. To construct a perpendicular through a point not on a line, one would typically use the following process:

Place the compass at the given point and draw an arc that crosses the line twice.

Without changing the compass width, move the compass to each intersection point and draw two arcs that intersect above and below the line.

Draw a line connecting the intersection points of these arcs. This is the perpendicular line through the point.

To construct a perpendicular bisector, one would:

Place the compass at one end of the line segment and draw an arc above and below the line.

Without changing the compass width, repeat from the other end of the line segment so that the arcs cross.

Connect the intersection points of the arcs to form the perpendicular bisector.

In both cases, we utilize the property that the perpendicular bisector of a line segment is the set of all points equidistant from the segment's endpoints, and similarly, through a point not on a line, we can construct two such points that are equidistant from it on the line, therefore satisfying Corollary regarding points equidistant from the extremities of a straight line determining a perpendicular to the line at its middle point.

So if we add 9 slices to pizza, and 10 more...We get...0 because I ate them all

19

Answer:

A. {2,3,5,7,11,13}

Step-by-step explanation:

Since, prime numbers are the whole numbers which have only two multiple which are 1 and itself.

Thus, the prime numbers are,

2, 3, 5, 7, 11, 13, 17, 19, 23, ..................

Note : 1 is not a prime number because it has only one multiple i.e. 1.

or it does not satisfy the definition of prime number.

Thus, the prime numbers that are less than 15,

2, 3, 5, 7, 11, 13

Which are the elements of the set S,

Hence, S = { 2, 3, 5, 7, 11, 13 }

OPTION A is correct.

Answer: The answer is (c) 7 and 42.

Step-by-step explanation: We are given that one number is six times another number and their difference is 35. We are to find the two numbers.

Let 'x' and 'y' be the two numbers. Then, we have

[tex]y=6x,\\\\y-x=35.[/tex]

Substituting the value of 'y' from first equation in the second, we have

[tex]6x-x=35\\\\\Rightarrow 5x=35\\\\\Rightarrow x=7,[/tex]

and

[tex]y=6\times 7=42.[/tex]

Therefore, the numbers are 7 and 42.

Thus, the answer is (c) 7 and 42.

Answer:

68.5°

Step-by-step explanation:

Here is the solution:

m<FDE = 1/2( Arc BC + Arc 76)
m<FDE = 1/2 (61° + 76°)
m<FDE = 137/2 = 68.5°

So the answer is 68.5°

To find the standardized version of x in a given city's annual precipitation data, use Z = (x - mean) / standard deviation.

The standardized version of x (annual precipitation in a city) can be calculated using the formula: Z = (x - mean) / standard deviation. Substituting the given values, Z = (x - 15.3) / 4.2. This helps in determining how many standard deviations a particular precipitation amount is from the mean.

-Add 2 quarts. Michael incorrectly used gallons instead of quarts for his recipe. Since 1 gallon equals 4 quarts, he simply needs to add 2 more quarts to the existing gallon to meet the recipe's requirement of 6 quarts.

The question involves unit conversion between gallons and quarts. Since the recipe calls for 6 quarts of water and Michael has already put 1 gallon (which is 4 quarts) into the bowl, he needs to add more water to reach the required amount.

A gallon is equivalent to 4 quarts, so Michael should add 2 quarts more to the 4 quarts he already has, totaling the 6 quarts needed for the recipe.

Answer:

The anser is D. I just had this question