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3 years ago

1/3 of a number decreased by 13 equals 45

Mathematics

1 answer:

mezya [45]3 years ago

6 0

Answer:

174

Step-by-step explanation:

45+13=58

58*3

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Solve for x and y matrix

charle [14.2K]

Answer:

$x=-1$

$y=5$

Step-by-step explanation:

$\begin{pmatrix}x&y\\ \:-1&4\end{pmatrix}\begin{pmatrix}2&5\\ \:4&1\end{pmatrix}=\begin{pmatrix}18&0\\ \:14&-1\end{pmatrix}$

$\begin{pmatrix}x&y\\ -1&4\end{pmatrix}\begin{pmatrix}2&5\\ 4&1\end{pmatrix}$

$=\begin{pmatrix}x\times \:2+y\times \:4&5x+y\\ 14&-1\end{pmatrix}$

$=\begin{pmatrix}18&0\\ 14&-1\end{pmatrix}$

$\begin{bmatrix}x\times \:2+y\times \:4=18\\ 5x+y=0\end{bmatrix}$

$x=-1$

$y=5$

<u>OAmalOHopeO</u>

8 0

2 years ago

Find the values of x and y leave answers in simplest radical form. *The altitude is:

jok3333 [9.3K]

$x = \sqrt{ { \sqrt{18} }^{2} + {2}^{2} } = \sqrt{18 + 4} = \sqrt{22} \\ y = \sqrt{ { \sqrt{18} }^{2} + {9}^{2} } = \sqrt{18 + 81} = \sqrt{99} = 3\sqrt{11}$

5 0

3 years ago

What is 4 to the power of x minus 3 =18

mote1985 [20]

3 to the power of 4:

=34
x
n
=
3
4

=3⋅3⋅3⋅3
=
3
⋅
3
⋅
3
⋅
3

=81
=
81

For example, 3 to the power of -4:

=3−4
x
n
=
3
−
4

=134
=
1
3
4

=13⋅3⋅3⋅3
=
1
3
⋅
3
⋅
3
⋅
3

=181
=
1
81

=0.012346

7 0

2 years ago

Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour. She also does yard work for $12 per hour. Li

Fittoniya [83]

Answer:

(a)

$r\geq 5$

$r+y\leq 15$

$8r+12y\geq 120$

$y\geq 0$

(c)Maximum number of hours Lia can work at the restaurant and still meet her earnings goal = 15 hours

(d)Maximum Earning = $160

Step-by-step explanation:

Let r be the number of hours worked at the restaurant.

Let y be the number of hours of yard work,

Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour.

$r\geq 5$

Since she does yard work, $y\geq 0$

Lia’s parents allow her to work a maximum of 15 hours per week overall.

$r+y\leq 15$

Lia’s goal is to earn at least $120 per week.

The restaurant, r pays $8 per hour

Yard work, y pays $12 per hour.

Therefore:

$8r+12y\geq 120$

The system of inequalities that represent this problem is therefore:

$r\geq 5$

$r+y\leq 15$

$8r+12y\geq 120$

$y\geq 0$

(b)The graph of the inequality is attached below

(c)When the graph is plotted, the vertices of the feasible region are:

(5,10)
(5, 6.7)
(15,0)

Where the first term is for the number of hours worked in the restaurant.

The maximum value of r possible is 15 from the three points.

Therefore, she can work at the restaurant for 15 hours and still meet her earning goal.

(d)Maximum Amount Lia can earn in 1 Week

At (5,10), Earning=(5X8)+(10X12)=40+120=$160

At (5, 6.7), Earning=(5X8)+(6.7X12)=40+80.4=$120.4
At (15,0) Earning=(15X8)+(0X12)=$120

Since she has to work at least 5 hours at the restaurant, the maximum amount possible is $160.

8 0

3 years ago

Rearrange x = 3g + 2 to make g the subject.

Kisachek [45]

Answer:

g = $\frac{x-2}{3}$

Step-by-step explanation:

x = 3g + 2 ( subtract 2 from both sides )

x - 2 = 3g ( divide both sides by 3 )

$\frac{x-2}{3}$ = g

5 0

1 year ago

Read 2 more answers