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3 years ago

Solve: c-10+3c<2 step by step

Mathematics

1 answer:

Veronika [31]3 years ago

8 0

Answer:

c < 3

Step-by-step explanation:

We can first add 10 to both sides to remove the -10.

This is additive property of equality, where both sides must stay the same ratio, so we always use the same property on both sides unless simplifying what is already there.

So we now have c + 3c < 12.

As I mentioned less than 2 full sentences above, we can simplify without doing the same thing to both sides if it is already there, so we can add the c + 3c since it is already there.

We now have 4c < 12.

Then, we divide both sides by 4 to get c, and again mentioned about 4 sentences above, we need to divide both sides.

So we now should have c < 3.

NOTE: IF YOU HAVE A SIMILAR PROBLEM WHERE THE VARIABLE IS NEGATIVE LIKE -4a FOR EXAMPLE, THE INEQUALITY SIGN CHANGES DIRECTION. IN THIS PROBLEM, THAT IS NOT THE CASE, BUT FOR FUTURE PROBLEMS, THAT IS A <u>MUST</u>.

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A rectangle has perimeter 28cm. Its area is 42sq.cm. Determine the dimensions of the rectangle. Include a diagram in your soluti

yawa3891 [41]

The dimensions of the rectangle are: b=9.65 cm and h=4.35 cm or b=4.35 cm and h= 9.65 cm.

<h3>Quadrilaterals</h3>

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle is equal to base x height (A=bh). The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2b+2h.

<h3>System of Linear Equations</h3>

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

The question gives:

Perimeter=28cm

Area= 42 cm²

If the perimeter is the sum of all sides of the rectangle, you have:

Perimeter= 2b+2h=28

If the area of the rectangle is 42cm², you have:

Area=bh=42 cm²

You can write a system of linear equations.

2b+2h=28 (1)

bh=42 (2)

From equation 2, you have $b=\frac{42}{h}$ . Then, you can replace it in equation 1.

$2*\frac{42}{h}+2h=28 \\ \\ 84+2h^2=28h\\ \\ 2h^2-28h+84=0 \; dividing\; by\; 2\\ \\ h^2-14h+42=0$

Now, you should solve the quadratic equation.

$h_{1,\:2}=\frac{-\left(-14\right)\pm \sqrt{\left(-14\right)^2-4\cdot \:1\cdot \:42}}{2\cdot \:1}$

$h_{1,\:2}=\frac{-\left(-14\right)\pm \:2\sqrt{7}}{2\cdot \:1}$

$h_1=\frac{-\left(-14\right)+2\sqrt{7}}{2\cdot \:1}=7+\sqrt{7}=9.65 cm$

$h_2=\frac{-\left(-14\right)-2\sqrt{7}}{2\cdot \:1}=7-\sqrt{7}=4.35cm$

If h1=9.65 cm, then $b_1=\frac{42}{9.65} =4.35 cm$ , and if h2=4.35 cm, then $b_1=\frac{42}{4.35} =9.65 cm$ .

Read more about the quadratic function here:

brainly.com/question/1497716

#SPJ1

8 0

1 year ago

What is the value of 4p-2 when p=8

3241004551 [841]

Answer: Hence, the value of expression is 30 when p = 8.

Step-by-step explanation:

Since we have given that

$4p-2$

and we have p = 8.

So, we substitute the value of p in the above expression.

so, it becomes,

$4(8)-2\\\\4\times 8-2\\\\=32-2\\\\=30$

Hence, the value of expression is 30 when p = 8.

3 0

3 years ago

A pizza place offers 3 different cheeses and 12 different toppings. In how many ways can a pizza be made with 1 cheese and 3 top

svetlana [45]

You have to choose 1 sort of cheese from 3 ( 3 ways ). Also you have to choose 3 toppings from 12 different toppings:
12 * 11 * 10 = 1,320 ways.
In total: 3 * 1,320 = 3,960
Answer:
In 3,690 ways can pizza be made with 1 cheese and 3 toppings.

3 0

3 years ago

Number 2 please thanks

Alex

Answer:

c) 2x+1

Step-by-step explanation:

Let's x be number of Nick's goals.

Emma has scored 1 more than twice the number of Nicks.

1 more is +1, of twices the number is 2x.

so 2x+1=15

6 0