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2 years ago

11

Explain or show how to determine if the following coordinates are a solution to the following system of linear inequalities. y&l

t;4x+8 y>x-6

1 answer:

Leni [432]2 years ago

5 0

The inequalities y < 4x + 8 and y > x - 6, the solution to the inequalities is the darker region shown in the graph.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the inequalities y < 4x + 8 and y > x - 6, the solution to the inequalities is the darker region shown in the graph.

Find out more on equation at: brainly.com/question/2972832

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Ben has 4 unit cubes. how many different rectangular prisms can he make using all 4 unit cubes

miskamm [114]

2 rectangular prisms.

4 0

4 years ago

Read 2 more answers

Find a point on the line y = 4 that is equidistant from the two points (0,1) and (5,6)

butalik [34]

Answer:

The point on the line $y=4$ that is equidistant from points (0,1) and (5,6) is (2, 4).

Step-by-step explanation:

Let be $y = 4$ , $A = (0,1)$ and $B = (5,6)$ . As we know that given function is a horizontal line, the condition of equidistance between that a point within that line and both points must be:

$r_{A/P} = r_{B/P}$

Where:

$r_{A/P}$ - Distance of point A with respect to P.

$r_{B/P}$ - Distance of point B with respect to P.

We expand this equivalence by Pythagorean Theorem:

$\sqrt{(x_{A}-x_{P})^{2}+(y_{A}-y_{P})^{2}} = \sqrt{(x_{B}-x_{P})^{2}+(y_{B}-y_{P})^{2}}$

$(x_{A}-x_{P})^{2} + (y_{A}-y_{P})^{2} = (x_{B}-x_{P})^{2}+(y_{B}-y_{P})^{2}$

$x_{A}^{2}-2\cdot x_{A}\cdot x_{P}+x_{P}^{2} + y_{A}^{2}-2\cdot y_{A}\cdot y_{P}+y_{P}^{2} = x_{B}^{2}-2\cdot x_{B}\cdot x_{P}+x_{P}^{2} + y_{B}^{2}-2\cdot y_{B}\cdot y_{P}+y_{P}^{2}$

$x_{A}^{2}-2\cdot x_{A}\cdot x_{P} + y_{A}^{2}-2\cdot y_{A}\cdot y_{P} = x_{B}^{2}-2\cdot x_{B}\cdot x_{P} + y_{B}^{2}-2\cdot y_{B}\cdot y_{P}$

And we get this expression:

$x_{A}^{2}+y_{A}^{2}-x_{B}^{2}-y_{B}^{2} - 2\cdot (x_{A}-x_{B})\cdot x_{P}-2\cdot (y_{A}-y_{B})\cdot y_{P} = 0$

If we know that $x_{A} = 0$ , $y_{A} = 1$ , $y_{P} = 4$ , $x_{B} = 5$ and $y_{B} = 6$ , the expression is reduced to this:

$0^{2}+1^{2}-5^{2}-6^{2}-2\cdot (0-5)\cdot x_{P} -2\cdot (1-6)\cdot (4) =0$

$10\cdot x_{P}-20=0$

The remaining component of the point within the line is:

$x_{P} = 2$

The point on the line $y=4$ that is equidistant from points (0,1) and (5,6) is (2, 4).

6 0

3 years ago

The product of the ages of three children is 1872. The age of the middle child is the average of the ages of the other two child

sergejj [24]

The total age of the three children are = 37years

<h3>Calculation of the total age of children</h3>

The product of the ages of three children is = 1872.

Let take child 1 = x

child 2 = x

child. 3 = x

Therefore, the age of three children = x³= 1872

Therefore;

$x = \sqrt[3]{1872}$

X = 12.32448

The age of the middle child = 12.32448 + 12.32448

= 24.64896/2

= 12.32448

Therefore the sum of their ages = 12.32448 + 12.32448 + 12.32448 = 37years.

Learn more about age calculation here:

brainly.com/question/2744275

7 0

3 years ago

Y=x^2-2x-19 <br> y+4x=5<br><br> solution set system of equation is (-6,29) and ______.

Blababa [14]

Hello :
<span>Y=x²-2x-19 ...(1)
y+4x=5.....(2)
by (2) : y = 5-4x ....(*)
subsct in (1) : 5-4x</span>=x²-2x-19
x²+2x-24 =0
<span>Δ = 2²-4(1)(-24) = 100=10²
x1 = (-2-10)/2 =-6
x2= (-2+10)/2=4
if : x =-6 by(*) : y= 5-4(-6)=29
if x= 4 y = 5-4(4)=-11
</span><span>solution set system of equation is (-6,29) and (4,-11)______.</span>

6 0

3 years ago

A line passes through the points (5, –8) and (6, 2). What is the slope?

Andreyy89

Answer:

use cymath it really helps with finding slopes

Step-by-step explanation:

6 0

3 years ago