WHAT IS THE EQUATION OF POINT SLOPE FORM

For anyone who needs the measure itself, it's 70.

Peter needs 33 whole days to be able to speak 75 words.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Peter begins his kindergarten year able to spell 10 words.

He is going to learn to spell 2 new words every day.

Assuming no. of days it will take him to be able to spell at least 75 words

is d.

∴ The inequality that represents this scenario is 2d + 10 ≥ 75.

2d ≥ 65.

d ≥ 32.5 but it will take him 33 whole days to learn 75 words.'

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The proof was completed by assuming that two supplementary angles could both be obtuse, which would mean that their sum is more than 180°. This contradicts the definition of supplementary angles, where their sum should always be exactly 180°, and hence proves that two supplementary angles cannot both be obtuse.

To complete the indirect proof, we start by assuming that two supplementary angles, let's call them angle1 and angle2, can indeed both be obtuse angles. An obtuse angle is defined as an angle which measures more than 90°. Therefore, if both angle1 and angle2 are obtuse, they would each measure more than 90°, meaning that their sum (angle1 + angle2) would measure more than 180°.

However, the definition of supplementary angles is such that their sum should always be exactly 180°. Therefore, we reach a contradiction in our assumed scenario: the sum of angle1 and angle2 cannot be both more than 180° (by our assumption that they are both obtuse) and exactly 180° (by the known definition of supplementary angles).

This contradiction means that our initial assumption was incorrect, thus completing the proof. In other words, two supplementary angles cannot both be obtuse, as it would contradict the definition of supplementary angles.

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Answer:

69 and 11,  took me 1 hour to slove this

Step-by-step explanation:

Answer:

- m∠ABC = m∠ACB = 25° (as triangle ABC is isosceles).

- m∠BAC = 130°.

- m∠BDC = m∠DCB = 30° (as triangle DBC is isosceles).

Explanation:

We can solve this problem by using the properties of isosceles triangles and the fact that the sum of angles in a triangle is 180 degrees.

1. Since triangle DBC is isosceles, m∠DBC = m∠DCB.

Therefore, m∠DCB = 30°.

2. In triangle ABC, since it's isosceles, m∠ABC = m∠ACB.

3. We know that m∠ABD = 155°. Since triangle ABD is a triangle, the sum of its angles is 180 degrees. So, m∠ABD + m∠BAD + m∠ADB = 180°. Therefore, m∠BAD + m∠ADB = 180° - 155° = 25°.

4. Since triangle ABC is isosceles, m∠ABC = m∠ACB = 25°.

5. In triangle ABC, the sum of its angles is 180 degrees. So, m∠ABC + m∠BAC + m∠ACB = 180°. Substituting the known values, we get 25° + m∠BAC + 25° = 180°. Solving for m∠BAC,

we find m∠BAC = 180° - 25° - 25° = 130°.

Answer:

Commutative additive property.

Step-by-step explanation:

Given  : 3z+4=4+3z

To find : which property is illustrated the following statement.

Solution : We have given  

3z + 4 = 4 + 3z.

Commutative additive property : a + b = b + a .

Example :  2 + 3 = 3 +2 = 5.

Hence  this the commutative additive property 3z + 4 = 4 + 3z.

Therefore, Commutative additive property.

The probability of heads on the fifth trial is still 0.5, just like any other coin flip.

The probability of heads on the fifth trial is still 0.5, just like any other coin flip. The outcome of each coin flip is independent of the previous flips, so each trial has the same probability of resulting in heads or tails.

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Answer:

[tex](x+5\sqrt{2}i)(x-5\sqrt{2}i)[/tex]

Step-by-step explanation:

The factorization is in the form (x-a)(x-b) where a,b are zeros of the equation [tex]x^{2} +50=0[/tex].

[tex]x^{2} =-50[/tex]

[tex]x =\sqrt{-50}[/tex]

[tex]x =\sqrt{50}i = 5\sqrt{2}i[/tex] and [tex]x =-\sqrt{50}i = -5\sqrt{2}i[/tex]

So, the factorization is [tex](x+5\sqrt{2}i)(x-5\sqrt{2}i)[/tex]

Complex numbers are numbers with real and imaginary part.

The factorized expression is [tex]\mathbf{x^2 + 50 = (x^2 +5i\sqrt 2)(x^2 -5i\sqrt 2) }[/tex]

The expression is given as:

[tex]\mathbf{x^2 + 50}[/tex]

Set to 0

[tex]\mathbf{x^2 + 50 = 0}[/tex]

Subtract 50 from both sides

[tex]\mathbf{x^2 = -50}[/tex]

Take square roots

[tex]\mathbf{x = \sqrt{-50}}[/tex]

Expand

[tex]\mathbf{x = \sqrt{25 \times -2}}[/tex]

Take square roots of 25

[tex]\mathbf{x =\pm 5\sqrt{-2}}[/tex]

Expand

[tex]\mathbf{x = \pm5\sqrt{2 \times -1}}[/tex]

Split

[tex]\mathbf{x =\pm 5\sqrt{2} \times \sqrt{-1}}[/tex]

In complex numbers,

[tex]\mathbf{\sqrt{-1} = i}[/tex]

So, we have:

[tex]\mathbf{x = \pm5i\sqrt{2}}[/tex]

So, we have:

[tex]\mathbf{x^2 + 50 = (x^2 +5i\sqrt 2)(x^2 -5i\sqrt 2) }[/tex]

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Answer:

I hope this helps

Step-by-step explanation:

Answer:

slope = -3

Step-by-step explanation:

To find the slope of the graphed line, we can use the slope formula:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Slope formula}}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\textsf{where:}\\\phantom{w}\bullet\;\;m\; \textsf{is the slope.}\\\phantom{w}\bullet\;\;(x_1,y_1)\;\textsf{and}\;(x_2,y_2)\;\textsf{are two points on the line.}\end{array}}[/tex]

First, identify two points on the line:

Substitute the coordinates into the slope formula:

[tex]m=\dfrac{0-3}{1-0}=\dfrac{-3}{1}=-3[/tex]

Therefore, the slope of the graphed line is:

[tex]\Large\boxed{\boxed{\textsf{slope}=-3}}[/tex]