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3 years ago

What is the solution to the system of equations below?

Mathematics

1 answer:

kifflom [539]3 years ago

4 0

Answer:

(-5,-14)

Step-by-step explanation:

To find the solution of the system of two equations

$\left\{\begin{array}{l}y=4x+6\\y=2x-4\end{array}\right.$

equate right sides of these two equations:

$4x+6=2x-4$

Rewrite terms with x into the left side and without x into the right side:

$4x-2x=-4-6\\ \\2x=-10\ [\text{divide by 2}]\\ \\x=-5$

Substitute x=-5 into the first equation:

$y=4\cdot (-5)+6=-20+6=-14$

The solution is (-5,-14)

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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

Amiraneli [1.4K]

The correct representations of the given inequality are

–6x + 15 < 10 – 5x

and

A number line with an open circle at 5 and a bold line that starts at 5 and is pointing to the right. The correct options are the third and fourth options

<h3>Solving inequality</h3>

From the question, we are to solve the inequality

The given inequality is

–3(2x – 5) < 5(2 – x)

First, clear the brackets

–6x + 15 < 10 – 5x

NOTE: This is one of the correct representations of the inequality

Collect like terms

-6x + 5x < 10 - 15

-x < -5

Divide both sides by -1 and flip the sign

x > 5

Representing this on a number line, we get a number line with an open circle at 5 and a bold line that starts at 5 and is pointing to the right.

Hence, the correct representations of the given inequality are

–6x + 15 < 10 – 5x

and

A number line with an open circle at 5 and a bold line that starts at 5 and is pointing to the right. The correct options are the third and fourth options

Learn more on Inequalities here: brainly.com/question/246993

#SPJ1

6 0

2 years ago

What is the value of y in the parallelogram below?

vredina [299]

In a parallelogram, consecutive angles are supplementary.

3y + 78 = 180

3y = 102

y = 34

4 0

3 years ago

Read 2 more answers

Which equation is not equivalent to the other equations?

Colt1911 [192]

I think the answer is C. X*4=-12+3

8 0

3 years ago

Find the area and perimeter

Ivenika [448]

Answer: area = 379.7 mm²

Perimeter = 95.84 mm

Step-by-step explanation:

The composite shape contains a semi circle and a trapezoid.

The area of a semi circle is

1/2 × πr²

Radius = diameter/2

Radius = 20/2 = 10 mm

Area = 1/2 × 3.14 × 10 = 15.7 mm²

Area of trapezoid is expressed as

1/2(a + b)h

Area = 1/2 × (20 + 32)14

Area = 1/2 × 52 × 14) = 364mm²

Area of the composite shape is

15.7 + 364 = 379.7 mm²

Formula for determining the perimeter of the semicircle is

1/2 × πd

Perimeter = 1/2 × 3.14 × 20 = 31.4mm

Looking at the attached photo, we would determine the slant height,h, by applying Pythagorean theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

h² = 12² + 14² = 340

h = √340/= 18.44

Perimeter of the composite shape is

31.4 + 14 + 32 + 18.44 =95.84 mm

7 0

3 years ago

Help me with this question please

ivolga24 [154]

Answer:

D. 2019

Step-by-step explanation:

So I started by rewriting the function f(x)

1000 = 10^3 so

f(x)=10^3 times 1.03^x

1.03 = 103/100 so

f(x)= 10^3 times (103/100)^x

to raise a fraction to a power you just raise the numerator and denominator to that power so

f(x)= 10^3 times 103^x/100^x

change it to exponential form with a base of 10

f(x)=10^3 times 103^x/10^2x

then you can reduce it with the 10^3

f(x)=103^x/10^2x-3

so now that thats in more of a standard form you can find the intersection of the two functions

which is at (9.012,1305.244)

x is the number of years after 2010, so they will be equal ~9 years after 2010, which is 2019.

7 0

2 years ago