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3 years ago

Solve and graph the following compounf inequalities 7<5x+2<22

Mathematics

2 answers:

Digiron [165]3 years ago

7 0

1<x<4 is the answer for the question

nevsk [136]3 years ago

3 0

Hey there!

7 < 5x + 2 < 22
Let's start by adding -2 to both sides
7 - 2 < 5x + 2 - 2 < 22 - 2
5 < 5x < 20
Then divide each part by 5 :)
5/5 < 5x < 20/5
1 < x < 4

I hope this helps. Please let me know if you have questions about the answer.
Down bellow is the graph.

Best of luck with your studies!

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WILL REWARD BRAINIEST! What is the volume of the composite figure if both the height and the diameter of the cylinder are 10.5 f

Mashutka [201]

Answer:

908.74

Step-by-step explanation:

The formula for the volume of a cylinder is V = h * pi * r^2

h is height, r is radius, and pi is 3.14. The radius is half of the diameter, so that would make the radius 5.25.

So now plug it into the formula:

V = 10.5 * pi * (5.25)^2

= 908.74

Hope this helped! :)

7 0

3 years ago

A restaurant serves custom-made omelets, where guests select meat, cheese, and vegetables to be added to their omelet. There are

FrozenT [24]

Answer:

15 possible combinations

Step-by-step explanation:

Given

$Vegetables = 6$

$Selection = 2$

Required

Determine the possible number of combinations

The question emphasizes on "selection" which means "combination".

So; To answer this question, we apply the following combination formula:

$^nC_r = \frac{n!}{(n-r)r!}$

In this case:

$n = 6$

$r = 2$

The formula becomes:

$^6C_2 = \frac{6!}{(6-2)!2!}$

$^6C_2 = \frac{6!}{4!2!}$

$^6C_2 = \frac{6*5*4!}{4!2*1}$

$^6C_2 = \frac{6*5}{2}$

$^6C_2 = \frac{30}{2}$

$^6C_2 = 15$

Hence, there are 15 possible combinations

7 0

3 years ago

Select the correct answer.

lesya692 [45]

Answer:

The Answer is A. slope = 1.5 and y-intercept = -2

Step-by-step explanation:

In y=mx+b form b represents your y-intercept and m (or the number next to the x) is your slope

6 0

3 years ago

An electronics company produces transistors, resistors, and computer chips. Each transistor requires 3 units of copper, 1 unit

padilas [110]

Answer:

An electronics company can be produce 350 transistors and 340 computer chips, they can´t produce resistors.

Step-by-step explanation:

1. We will name the variables for transistors, resistors and the computer chips.

a = Transistors

b= Resistors

c = Computer chips

2. We propose three linear equations, one for the copper, one for the zinc and one for the glass.

$\left \{ {{3a+3b+2c=1730} \atop {a+2b+c=690}}\atop {2a+b+2c=1380}} \right.$

3. We write the matrix form as Ax=d

$A=\left(\begin{array}{ccc}3&3&2\\1&2&1\\2&1&2\end{array}\right)$

$x=\left(\begin{array}{ccc}a\\b\\c\end{array}\right)$

$A=\left(\begin{array}{ccc}1730\\690\\1380\end{array}\right)$

With this formula the solution of x is $x=\frac{d}{A}$ or $x=A^{-1}d$

4. We will find the inverse matrix $A^{-1}$ using the formula:

$A^{-1} = \frac{1}{detA} (C_{A})^{T}$

a. det A

$det A=\left[\begin{array}{ccc}3&3&2\\1&2&1\\2&1&2\end{array}\right] =3*(4-1)-3*(2-2)+2*(1-4)=9-0-6=3$

b. $(C_{A})^{T}$

$C_{A}=\left(\begin{array}{ccc}4-1&.(2-2)&1-4\\-(6-2)&6-4&-(3-6)\\3-4&-(3-2)&6-3\end{array}\right)$

$C_{A}=\left(\begin{array}{ccc}3&.0&-3\\-4&2&3\\-1&-1&3\end{array}\right)$

$(C_{A}) ^T=\left(\begin{array}{ccc}3&0&-3\\-4&2&3\\-1&-1&3\end{array}\right)^T$

$(C_{A}) ^T=\left(\begin{array}{ccc}3&-4&-1\\0&2&-1\\-3&3&3\end{array}\right)$

c. $A^{-1}$

$A^{-1}=\frac{1}{3} \left(\begin{array}{ccc}3&-4&-1\\0&2&-1\\-3&3&3\end{array}\right)$

5. As $x=\frac{d}{A}$ or $x=A^{-1}d$ , the solution of x is:

$x=\frac{1}{3}\left(\begin{array}{ccc}3&-4&-1\\0&2&-1\\-3&3&3\end{array}\right)\left(\begin{array}{ccc}1730\\690\\1380\end{array}\right)$

$x=\frac{1}{3}\left(\begin{array}{ccc}(3*1730)+(-4*690)+(-1*1380)\\(0*1730)+(2*690)+(-1*1380)\\(-3*1730)+(3*690)+(3*1380)\end{array}\right)$

$x=\frac{1}{3}\left(\begin{array}{ccc}1050\\0\\1020)\end{array}\right)$

$X=\left[\begin{array}{ccc}350\\0\\340\end{array}\right]$

Therefore:

a= 350 Transistors

b=0 Resistors

c=340 Computer chips

4 0

3 years ago

Malcolm ran the 440-yard and the 220-yard dash at a track meet.There are 3 in one yard. How many total feet did Malcolm run?Esti

Tresset [83]

For this case we have the following conversions:

1 yard = 3 feet

The estimate distance Is:

400yd = 1200feet

200yd=600 feet

Ten, the estimate Is:

1200 + 600 = 1800 feet

The real distance Is:

The total distance in yards is given by:

440 + 220 = 660 yd

Then, let's transform this distance to feet, with the given conversion:

660 * 3 = 1980 feet

The distance traveled is reasonable for a person

Comparing the estimate and the actual answer, the distance malcom Ran Is reasonable.

Answer:

Malcolm ran 1980 feet.

The distance is reasonable.

5 0

3 years ago

Read 2 more answers