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Answer 1



Step-by-step explanation:

If BD is an altitude, it splits triangle ABC into 2 triangles.  It is also a median, so it splits the angle ABC into 2 congruent angles.  Angle ABD and CBD are congruent.  That means that angles A and C are congruent. This is true because the 2 angles at D are both right angles.  Because of this, side AB and side CB are congruent.  That means that this is an isosceles triangle.  

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Manny makes dinner using 1 box of pasta and 1 jar of sauce. if pasta is sold in packages of 6 boxes and sauce is sold in packages of 3 jars, what is the least number of dinners that Manny can make without any supplies leftover?
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A company makes cylindrical crackers that have a cylindrical hole in the middle.

Calculate the slope between the points (2,1) and (-3,4).



To calculate the slope (m) between two points (x₁, y₁) and (x₂, y₂), you can use the formula:

\[ m = \frac{y₂ - y₁}{x₂ - x₁} \]

For the points (2,1) and (-3,4):

\[ m = \frac{4 - 1}{-3 - 2} = \frac{3}{-5} \]

Simplifying the fraction, the slope is:

\[ m = -\frac{3}{5} \]

A bag has 5 red marbles, 6 blue marbles and 4 black marbles. What is the probability of a blue marble, replacing it, and then picking a black marble?





There are 15 total marbles in the bag, of which 6 are blue nd 4 are black.

The probability of pulling a blue marble from the full bag is  6/15 .

The probability of pulling a black marble from the full bag is  4/15 .

The probability of both events happening is

             (6/15) x (4/15)  =  24/225 = 8/75

Determine the most efficient way to use the Binomial Theorem to show the following. (11)^4= 14641A)Write 11=5+6 and expand.
B) Write 11= 10+1 and expand.
C) Write 11= 3+3+2 and expand.
D)Write 11= 4+4+3 and expand.


The formula for binomial theorem is

(a+b)^n=( \left \ {{n} \atop {0}} \right.)a^(n)+( \left \ {{n} \atop {1}} \right.)a^(n-1)b+( \left \ {{n} \atop {0}} \right.)a^(n-2)b^2+...+( \left \ {{n} \atop {n}} \right.)b^n

Now this shall be very easy if the value of a = 1

The formula shall become

(1+b)^n=( \left \ {{n} \atop {0}} \right.)1^(n)+( \left \ {{n} \atop {1}} \right.)1^(n-1)b+( \left \ {{n} \atop {0}} \right.)1^(n-2)b^2+...+( \left \ {{n} \atop {n}} \right.)b^n

Which shall be

(1+b)^n=( \left \ {{n} \atop {0}} \right.)+( \left \ {{n} \atop {1}} \right.)b+( \left \ {{n} \atop {0}} \right.)b^2+...+( \left \ {{n} \atop {n}} \right.)b^n

So to find 11^4

We must break it as 1 + 10.

Option B) is the right answer.

Write (1+10) and expand. As you will have nCr *(10)^(n-r)
Where r index n count ( less terms)

What’s the answer for number 9


The answer is C because complimentary is equal to 90 so 24+66 equals 90 and 34+56 equal 90

Absolute value of 5.23


The absolute value of any positive value is just the value itself so it would still be 5.23

Ngozi earns \$24{,}000$24,000dollar sign, 24, comma, 000 in salary in the first year she works as an interpreter. Each year, she earns a 3.5\%3.5%3, point, 5, percent raise. Write a function that gives Ngozi's salary S(t)S(t)S, (, t, ), in dollars, ttt years after she starts to work as an interpreter.



The function that shows Ngozi's salary after t years is:

S(t) = 24000(1.035)^t

Step-by-step explanation:

Please see the attached file for details