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enot [183]
4 years ago
14

Translate this phrase into an algebraic expression. 62 less than twice a number Use the variable n to represent the unknown numb

er. ​
Mathematics
1 answer:
Vikentia [17]4 years ago
4 0

Answer:

62<2x

Step-by-step explanation:

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The first two steps in determining the solution set of the system of equations, y = x2 – 6x + 12 and y = 2x – 4, algebraically a
Vadim26 [7]
Y = 2x - 4....so sub in 2x - 4 for x in the other equation

y = x^2 - 6x + 12
2x - 4 = x^2 - 6x + 12
x^2 - 6x - 2x + 12 + 4 = 0
x^2 - 8x + 16 = 0
(x - 4)(x - 4) = 0

x - 4 = 0
x = 4

x - 4 = 0
x = 4

solution is (4,4)
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3 years ago
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A chemist needs to create a 50% HCl solution. (HCl is hydrochloric acid. A "50% HCl solution" contains 50% HCl and the other 50%
lorasvet [3.4K]

25/100=30/x x=120 (30+70y)/(120+100y)=50/100 100y=?

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3 years ago
For the soccer banquet, the players and their family members selected their favorite main dish and side dish. Of the 39 people w
Oduvanchick [21]

Question:

For the soccer banquet, the players and their family members selected their favorite main dish and side dish. Of the 39 people who chose chicken as the main dish, 18 wanted potatoes. Of the 32 people who chose rice as a side dish, 6 chose fish as a main dish. A total of 8 people chose a vegetarian meal with potatoes, and a total of 10 people chose fish as their main dish.

Which two-way table correctly displays this data?

a. A 5-column table has 3 rows. The first column has entries Rice, Potatoes, Total. The second column is labeled Chicken with entries 18, 21, 39. The third column is labeled Fish with entries 4, 6, 10. The fourth column is labeled Vegetarian with entries 8, 5, 13. The fifth column is labeled total with entries 30, 32, 62.

b. A 5-column table has 3 rows. The first column has entries Rice, Potatoes, Total. The second column is labeled Chicken with entries 21, 18, 39. The third column is labeled Fish with entries 6, 4, 10. The fourth column is labeled Vegetarian with entries 5, 8, 13. The fifth column is labeled total with entries 32, 30, 62.

c. A 5-column table has 3 rows. The first column has entries Rice, Potatoes, Total. The second column is labeled Chicken with entries 14, 18, 32. The third column is labeled Fish with entries 6, 4, 10. The fourth column is labeled Vegetarian with entries 19, 8, 27. The fifth column is labeled total with entries 39, 30, 69.

d. A 5-column table has 3 rows. The first column has entries Rice, Potatoes, Total. The second column is labeled Chicken with entries 18, 14, 32. The third column is labeled Fish with entries 4, 6, 10. The fourth column is labeled Vegetarian with entries 8, 19, 27. The fifth column is labeled total with entries 30, 39, 69.

Answer:

b. A 5-column table has 3 rows. The first column has entries Rice, Potatoes, Total. The second column is labeled Chicken with entries 21, 18, 39. The third column is labeled Fish with entries 6, 4, 10. The fourth column is labeled Vegetarian with entries 5, 8, 13. The fifth column is labeled total with entries 32, 30, 62.

Step-by-step explanation:

The question above is a two way table because it consists of two tables that are arranged in a column and row format or design.

A two way table is a table that up of values or numbers or frequencies for two variables. One of the variables is placed in a column while the other is placed in a row.

In the question above, we where given two variables, variable one is the main dish while variable two is the side dish. The proper way to display the data correctly is to

Create a 5-column table has 3 rows. The first column has entries Rice, Potatoes, Total. The second column is labeled Chicken with entries 21, 18, 39. The third column is labeled Fish with entries 6, 4, 10. The fourth column is labeled Vegetarian with entries 5, 8, 13. The fifth column is labeled total with entries 32, 30, 62.

Therefore, Option b. is the correct option.

5 0
4 years ago
Read 2 more answers
Student pick 144 oz of strawberry to make strawberry jam how many ounce pounds of strawberry did they pick
zhuklara [117]

Answer:

9 pounds

Step-by-step explanation:

1 lb = 16 ounces

144/16 = 9 pounds

8 0
3 years ago
Suppose that A and B are nonsingular matrices. Then AB is also nonsingular. Furthermore, a theorem from linear algebra then stat
kherson [118]

Answer:

A) Verified

B) Proved

Step-by-step explanation:

a) Let's verify it for 2 x 2 matrix,

A=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] and B=\left[\begin{array}{ccc}e&f\\g&h\end{array}\right]

AB=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]\left[\begin{array}{ccc}e&f\\g&h\end{array}\right]=\left[\begin{array}{ccc}a.e+b.g&a.f+b.h\\c.e+d.g&c.f+d.h\end{array}\right]

(AB)^{-1}=\frac{1}{(a.e+b.g)(c.f+d.h)-(a.f+b.h)(c.e+d.g)}\left[\begin{array}{ccc}c.f+d.h&-(a.f+b.h)\\-(c.e+d.g)&a.e+b.g\end{array}\right]

A^{-1}=\frac{1}{a.d-b.c} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right]

B^{-1}=\frac{1}{e.h-f.g} \left[\begin{array}{ccc}h&-f\\-g&e\end{array}\right]

B^{-1}A^{-1}=\frac{1}{(a.e+b.g)(c.f+d.h)-(a.f+b.h)(c.e+d.g)}\left[\begin{array}{ccc}c.f+d.h&-(a.f+b.h)\\-(c.e+d.g)&a.e+b.g\end{array}\right]

So it is proved that the results are same.

b) Now, let's prove it for any n x n matrix.

(AB)(AB)^{-1}=I\\\\A^{-1}(AB)(AB)^{-1}=A^{-1}I\\\\IB(AB)^{=1}=A^{-1}I\\\\B(AB)^{=1}=A^{-1}\\\\B^{-1}B(AB)^{=1}=B^{-1}A^{-1}\\\\I(AB)^{=1}=B^{-1}A^{-1}\\\\(AB)^{=1}=B^{-1}A^{-1}

8 0
3 years ago
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