Given the mapping diagram, DAYS (month), below, DAYS (July) = _____

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.

-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:

4/15

Step-by-step explanation:

To find the probability we use the mutually exclusive probability formula P(A) + P(B). The probability of picking a E tile is

1

5

and the probability of picking a Y tile is

1

15

. The sum is

4

15

.

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

19

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:

[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:

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:

Step-by-step explanation:

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

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]

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°

Answer:

The anser is D. I just had this question