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1 year ago

Is the ordered pair (0, 4) a solution of the inequality y≤x−3? Explain.

Mathematics

2 answers:

matrenka [14]1 year ago

8 0

The given ordered pair is not the solution for y ≤ x − 3.

<h3>What is linear inequality?</h3>

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

The inequality is given as y ≤ x - 3.

The x coordinate for the ordered pair (0,4) is 0.

And, the y coordinate is 4.

Substitute the value of x and y in the given inequality as follows,

y ≤ x - 3

=> 4 ≤ 0 - 3

=> 4 ≤ -3

Which is not true.

Hence, the ordered pair (0, 4) is not solution of the inequality y ≤x − 3.

To know more about linear inequality click on,

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Andrew [12]1 year ago

4 0

The ordered pair (0,4) does not satisfy the inequality thus, it will be not the solution to the given inequality.

<h3>What is inequality?</h3>

A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

As per the given inequality,

y ≤ x - 3

Put x = 0

y ≤ 0 - 3

y ≤ -3

Since 4 ≤ -3 is the wrong statement thus it will not satisfy the inequality.

Hence "The ordered pair (0,4) does not satisfy the inequality thus, it will be not the solution to the given inequality".

For more about inequality,

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slava [35]

Answer:

<h3><u>Question 7</u></h3>

<u>Lateral Surface Area</u>

The bases of a triangular prism are the triangles.

Therefore, the Lateral Surface Area (L.A.) is the total surface area excluding the areas of the triangles (bases).

$\implies \sf L.A.=2(10 \times 6)+(3 \times 6)=138\:\:m^2$

<u>Total Surface Area</u>

Area of the isosceles triangle:

$\implies \sf A=\dfrac{1}{2}\times base \times height=\dfrac{1}{2}\cdot3 \cdot \sqrt{10^2-1.5^2}=\dfrac{3\sqrt{391}}{4}\:m^2$

Total surface area:

$\implies \sf T.A.=2\:bases+L.A.=2\left(\dfrac{3\sqrt{391}}{4}\right)+138=167.66\:\:m^2\:(2\:d.p.)$

<u>Volume</u>

$\sf \implies Vol.=area\:of\:base \times height=\left(\dfrac{3\sqrt{391}}{4}\right) \times 6=88.98\:\:m^3\:(2\:d.p.)$

<h3><u>Question 8</u></h3>

<u>Lateral Surface Area</u>

The bases of a hexagonal prism are the pentagons.

Therefore, the Lateral Surface Area (L.A.) is the total surface area excluding the areas of the pentagons (bases).

$\implies \sf L.A.=5(5 \times 6)=150\:\:cm^2$

<u>Total Surface Area</u>

Area of a pentagon:

$\sf A=\dfrac{1}{4}\sqrt{5(5+2\sqrt{5})}a^2$

where a is the side length.

Therefore:

$\implies \sf A=\dfrac{1}{4}\sqrt{5(5+2\sqrt{5})}\cdot 5^2=43.01\:\:cm^2\:(2\:d.p.)$

Total surface area:

$\sf \implies T.A.=2\:bases+L.A.=2(43.01)+150=236.02\:\:cm^2\:(2\:d.p.)$

<u>Volume</u>

$\sf \implies Vol.=area\:of\:base \times height=43.011193... \times 6=258.07\:\:cm^3\:(2\:d.p.)$

8 0

1 year ago

An architect is sketching a blueprint of a patio for a new fence. On the blueprint, C is the midpoint of segment AD. Point B is

Slav-nsk [51]

The length of AD is 32 feet

Step-by-step explanation:

An architect is sketching a blueprint of a patio for a new fence

On the blueprint, C is the midpoint of segment AD
Point B is the midpoint of segment AC
BC = 8 feet

We need to find the length of AD

A mid-point divides a line segments into two equal parts in length

∵ C is the mid-point of AD

- The mid-point C divides the line segments AD into two equal parts

∴ AC = CD

∵ B is the mid point of AC

∴ AB = BC

∵ BC = 8 feet

∴ AB = 8 feet

- AC contains AB and BC

∵ AC = AB + BC

∴ AC = 8 + 8 = 16

∵ AC = CD

∵ AC = 16

∴ CD = 16

- AD contains AC and CD

∵ AD = AC + CD

∴ AD = 16 + 16 = 32

The length of AD is 32 feet

Learn more:

You can learn more about the mid-point in brainly.com/question/3269852

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3 years ago

A piece of string measures 2 16/20. Which of the following is equivalent to the length of the string in meters?

Ivenika [448]

Answer:

H: 2.8

Step-by-step explanation:

first divide 16 by 20 then you get a decimal.

then you add the decimal answer to the whole number (2)

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3 years ago

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Nastasia [14]

Answer:

Step-by-step explanation:

square root of 73 is about 8.5

square root of 10 is about 3. multiply by 3, you get 9.

square root of 7 is about 2.6. multiply by 5, you get 13.

when determining if you can make a triangle, if all variants of two sides can add up to be greater than the third side, you can make the triangle. so 8.5+9 > 13; 13+9 > 8.5; 13+8.5 > 9. this means it can make a triangle and all you have to do is order the sides.

8.5 is smallest which corresponds to angle c because it's opposite. 9 goes to angle a, then finally 13 goes to angle b. thus, angles c, a, b is the order.

side note: the smallest side length will always correspond with the smallest angle.

hope this helps :)

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3 years ago

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miss Akunina [59]

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2 years ago

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