Given that and are supplementary angles and that , explain how to find the measure of the complement of .

Answer:

1. Given.

2. <5 is supplementary to <4.

2. Angles 5 and 4 are consecutive angles, and by the consecutive angles theorem, the two are supplementary.

3. m<4 + m<5 = 180

3. By the definition of supplementary angles, m<4 + m<5 = 180.

4. m<2 = m<4

4. Angles 2 and 4 are corresponding angles, and by the corresponding angles postulate, the two are congruent. By the definition of congruent angles, m<2 = m<4.

5. m<5 + m<2 = 180

5. Substitution property of equality.

The perpendicular bisector of a chord passes through the center of a circle.

In geometry, a chord is a straight line segment that connects two points on the circumference of a circle. It is the longest possible segment within the circle.

The perpendicular bisector of a chord is a line that passes through the midpoint of the chord, creating two equal halves, and is perpendicular to the chord.

Notably, for any chord in a circle, its perpendicular bisector always intersects at the center of the circle, making it a significant geometric property.

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The length of edge FC in the triangular prism is: 12 cm.

Volume of a right triangular prism = 1/2(Length of triangular base × height of triangular base × height of the prism).

Considering the image given showing a right triangular prism, we have the following:

Volume of triangular prism = 900 cubic centimeters

Length of triangular base = FC = ?

Height of triangular base = 10 centimeters

Height of the prism = 15 centimeters

Plugin the values

900 = 1/2(FC × 10 × 15)

900 = 1/2(FC × 150)

Multiply both sides by 2

2(900) = 2(1/2(FC × 150))

1,800 = FC × 150

Divide both sides by 150

1,800/150 = FC × 150/150

12 = FC

FC = 12 cm

The length of edge FC is: 12 cm.

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Answer: 12

Step-by-step explanation:

Answer:

Graph b.

Step-by-step explanation:

B is not a function because it fails the vertical line test.
To be a function any vertical line drawn must pass through the graph at one point only. That is not true for graph B - a line can pass through 2 points on this graph.

The real statement is that the closer you get to the center of the vortex, the closer the current speed approaches infinity. option C is correct.

Given the speed s of the flow in a given vortex is modeled by x=300/d, where d is the distance to the center of the vortex.

speed is defined as the rate of change of an object's position in any direction. Speed ​​is measured as the ratio of distance traveled to time traveled.

As d approaches 0, you are approaching the center of the vortex.

[tex]\begin{aligned}S&=\lim_{d\rightarrow 0}\frac{300}{d}\\ &=\frac{300}{0}\\ &=\infty\end[/tex]

Thus, if the flow in a given vortex is modeled by x = 300/d, as one approaches the center of the vortex, the speed of the flow tends to infinity.

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Answer: C- As you move closer to the center of the whirlpool, the speed of the current approaches infinity.

The number of boys wear glasses are 156 boys.

In this question,

Total number of pupils in the school = 910

Ratio of boys = 3/7

Then, number of boys = 910 × 3/7

⇒ 130 × 3

⇒ 390

Ratio of boys wear glasses = 2/5

Then, number of boys wear glasses = 390 × 2/5

⇒ 78 × 2

⇒ 156

Hence we can conclude that the number of boys wear glasses are 156 boys.

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68 is the wrong number in the sequence 808, 408, 208,108, 68

A number system is defined as a system of writing to express numbers.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The given sequence is 808, 408, 208,108, 68

Eight hundred eight, Four hundred and eight, two hundred and eight, one hundred eight and sixty eight.

808, 408, 208,108, 68

Let us find the difference between the consecutive numbers

400, 200, 100, 40

As we observe the first three terms having the common ratio where as 40 and 100 has different ratio.

Hence, 68 is the wrong number in the sequence 808, 408, 208,108, 68

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The element value c₂₄ = -12 and d₁₃ = 14 if C = 2A + 3B and A and B are the matrix.

To find the element:

As we have given two matrices A and B:

Therefore, the element value c₂₄ = -12 and d₁₃ = 14 if C = 2A + 3B and A and B are the matrix.

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By adding fractions, we conclude that the correct option is the third one:

"one and two sevenths tubes"

We know that:

The total amount of paint will be given by the direct addition of these two fractions, notice that the denominator is the same in both cases, so we can just add the numerators.

5/7 + 4/7 = (5 + 4)/7 = 9/7

We can rewrite this as:

9/7 = 7/7 + 2/7 = 1 + 2/7

Thus, the correct option is the third one

"one and two sevenths tubes"

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The answer is C. 3√5.

[tex]g(x)=5cos((\pi )/(2)x-(3\pi )/(2))-2[/tex]

generate by:  Amplitude:5    Period:4

                      Phase shift:(3 to the right)    Vertical shift:-2

x=3,g(x)= 3

x=4,g(x)= -2

x=5,g(x)= -5

x=6,g(x)= -2

x=7,g(x)= 3

the graph is like cos(x)

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The first five terms of the sequence with the given nth term are 1, 3/2, 3/2, 9/8, 27/40.

In this question,

The nth term of the sequence is [tex]a_n=\frac{3^{(n-1)} }{n!}[/tex]

Now substitute the values of n = 1,2,3,4,5

For n = 1,

⇒ [tex]a_1=\frac{3^{(1-1)} }{1!}[/tex]

⇒ [tex]a_1=\frac{3^{0} }{1}[/tex]

⇒ a₁ = 1

For n = 2,

⇒ [tex]a_2=\frac{3^{(2-1)} }{2!}[/tex]

⇒ [tex]a_2=\frac{3^{(1)} }{(1)(2)}[/tex]

⇒ [tex]a_2=\frac{3}{2}[/tex]

For n = 3,

⇒ [tex]a_3=\frac{3^{(3-1)} }{3!}[/tex]

⇒ [tex]a_3=\frac{3^{(2)} }{(1)(2)(3)}[/tex]

⇒ [tex]a_3=\frac{9}{6}[/tex]

⇒ [tex]a_3=\frac{3}{2}[/tex]

For n = 4,

⇒ [tex]a_4=\frac{3^{(4-1)} }{4!}[/tex]

⇒ [tex]a_4=\frac{3^{(3)} }{(1)(2)(3)(4)}[/tex]

⇒ [tex]a_4=\frac{27}{24}[/tex]

⇒ [tex]a_4=\frac{9}{8}[/tex]

For n = 5,

⇒ [tex]a_5=\frac{3^{(5-1)} }{5!}[/tex]

⇒ [tex]a_5=\frac{3^{(4)} }{(1)(2)(3)(4)(5)}[/tex]

⇒ [tex]a_5=\frac{81}{120}[/tex]

⇒ [tex]a_5=\frac{27}{40}[/tex]

Hence we can conclude that the first five terms of the sequence with the given nth term are 1, 3/2, 3/2, 9/8, 27/40.

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Answer:

no solution

Step-by-step explanation: because if it has no variables that are the same it has no solution.

Answer: 2

Step-by-step explanation:

Each of the two sides of the equation is set equal to y

Answer:

7/10

Step-by-step explanation:

take 3, 2, 1 from the equation and your left with 7 numbers. Add those together you get 10. 7/10 is the probability that you will draw a number greater than 3

Answer:

[tex]y = \sqrt{x+25} + 5[/tex]

Step-by-step explanation:

Swap x and y

x = y² – 10y

Add 25 to each side to complete the square

x + 25 = y² – 10y + 25

Factor

x + 25 = (y – 5)²

Take the square root of each side

[tex]\sqrt{x+25}[/tex] = y – 5

Add 5 to both sides

[tex]\sqrt{x+25}[/tex] + 5 = y

Answer:

Wayne used 2/5 more flour than sugar

Step-by-step explanation:

If you add 2/5 to 2/5 you get 4/5

Pick 2 coordinates:

I choose first & last one (0,15) & (8-9)

Change in y is 24

(15--9 = 24)

Change in x is 8

(0 - 8) = - 8

24/-8 = - 3

So, slope = - 3

Hope this helps!

Answer:

-3

Step-by-step explanation:

The formula to find the slope is (change in y)/(change in x). In other words, rise over run.

If we look at the data, we can see that the x and y value changes.

x value: 0 --> 2 --> 4 --> 6 --> 8

y value: 15 --> 9 --> 3 --> -3 --> -9

When y changed from 15 to 9, the x changed from 0 to 2.

y: 15 --> 9

x: 0 --> 2

There was a difference of -6 in the y and a difference of 2 in the x.

At the top, I wrote that the slope was (change in y)/(change in x)

With -6 and 2 we found, we can say that the slope is -6/2.

If we simplify this answer, we end up with -3.

So -3 is the slope of the data.

Answer:

-7624928000 is the right answer.

Step-by-step explanation:

(-7624928) × 997 + 7624928 × (-3)

= -7602053216 + (-22874784)

= -7624928000        Ans..

Hope its helpful :-)

If so, please mark me as brainlist :-)

Answer:

Step-by-step explanation:

=(-7624928) * 997 + 7624928 * (-3)

=-7602053216+(-22874784)

=-7624928000

Answer:

[tex] - 0.2026[/tex]

Step-by-step explanation:

I hope it is the right answer

1

Anything raised to the power of zero is 1, other than zero itself.

However, as it is given that x is not equal to zero, the answer must be 1.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation: }[/tex]

[tex]\mathsf{(4x^2)^0}[/tex]

[tex]\huge\textbf{Simplifying:}[/tex]

[tex]\mathsf{(4x^2)^0}\\\\\mathsf{= (4 \timesx^2)^0}\\\\\mathsf{= 4(x \times x)^0}\\\\\mathsf{= (4x^2)^0}\\\\\mathsf{= 1}[/tex]

[tex]\huge\textbf{Therefore, your answer should:}[/tex]

[tex]\huge\boxed{\frak{1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The equation 23 · y + 50 + 27 · y = 50 · y + 50 has infinite solutions.

In this question we have an equation in implicit form: 23 · y + 50 + 27 · y = 50 · y + 50, we need to transform its expression into explicit form by using algebra properties:

23 · y + 50 + 27 · y = 50 · y + 50         Given

50 · y + 50 = 50 · y + 50                      Commutative, associative and distributive properties / Definition of addition

0 = 0 Compatibility with addition / Existence of additive inverse / Modulative property / Result

The equivalence indicates that the equation 23 · y + 50 + 27 · y = 50 · y + 50 has infinite solutions.

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Answer:

  Order of exponentiation can be swapped here, and the fractional power written as a root.

Step-by-step explanation:

The commutative property of multiplication and the rules of exponents apply.

The rule is ...

  (a^b)^c = a^(bc)

The given expression can be rearranged to ...

  [tex]\left(3^\frac{1}{5}\right)^2=3^{\frac{1}{5}\cdot2}=3^{2\cdot\frac{1}{5}}=\left(3^2\right)^\frac{1}{5}\\\\=9^\frac{1}{5}=\boxed{\sqrt[5]{9}}[/tex]

An inequality greater than (-3) but less than or equal to 3 is as follows:

- 3 < x ≤ 3

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.

An inequality have the following signs:

Therefore, an inequality greater than (-3) but less than or equal to 3 can be represented as follows:

Note the value we are comparing is x.

Hence,

- 3 < x ≤ 3

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Answer: C, 93m^2

Step-by-step explanation:

first step is to find the surface area of the base. it's 3x3, so that would be 9m^2. the sides of the rectangular prism are 5x3, so one side is 15m^2. there are 4, so 15x4=60m^2. now for the top, which is a triangular prism. each side has a height of 4 and a base of 3. the area of a triangle is 1/2bh, so 1/2(3)(4), which is 6. 4 of these makes 24 m^2. add up all of final numbers to get 9+60+24. this comes to 93m^2, or C.

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {a}^{2} - 64 }{ {a}^{2} - 10a + 24} \sdot \cfrac{ {a}^{2} - 12a + 36 }{ {a}^{2} + 4a - 32} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{( {a}^{} + 8)(a - 8) }{ {a}^{2} - 6a - 4a+ 24} \sdot \cfrac{ {a}^{2} - 6a - 6a + 36 }{ {a}^{2} + 8a - 4a- 32} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{( {a}^{} + 8)(a - 8) }{ {a}^{} (a - 6) - 4(a - 6)} \sdot \cfrac{ {a}^{} (a - 6) - 6(a - 6) }{ {a}^{}(a + 8) - 4(a + 8)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{( {a}^{} + 8)(a - 8) }{(a - 6) (a -4)} \sdot \cfrac{ (a - 6) (a - 6) }{ {}^{}(a - 4)(a + 8)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{(a - 8) }{(a -4)} \sdot \cfrac{ (a - 6) }{ {}^{}(a - 4)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{(a - 8)(a - 6) }{(a -4) {}^{2} } [/tex]

Or [ in expanded form ]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {a}^{2} - 8a - 6a + 48 }{ {a}^{2} - 8a + 16 } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {a}^{2} -14a + 48 }{ {a}^{2} - 8a + 16 } [/tex]

Answer:

[tex]\dfrac{(a-8)(a-6)}{(a-4)^2}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{a^2-64}{a^2-10a+24} \cdot \dfrac{a^2-12a+36}{a^2+4a-32}[/tex]

Factor the numerator and denominator of both fractions:

[tex]\textsf{Apply the Difference of Two Squares formula} \:\:\:x^2-y^2=(x-y)(x+y):[/tex]

[tex]\begin{aligned} a^2-64 & =a^2+8^2 \\ & =(a-8)(a+8)\end{aligned}[/tex]

[tex]\begin{aligned}a^2-10a+24 & =a^2-4a-6a+24\\& = a(a-4)-6(a-4)\\ & = (a-6)(a-4) \end{aligned}[/tex]

[tex]\begin{aligned}a^2-12a+36 & =a^2-6a-6a+36\\& = a(a-6)-6(a-6)\\ & = (a-6)(a-6) \end{aligned}[/tex]

[tex]\begin{aligned}a^2+4a-32 & =a^2+8a-4a-32\\& = a(a+8)-4(a+8)\\ & = (a-4)(a+8) \end{aligned}[/tex]

Therefore:

[tex]\dfrac{(a-8)(a+8)}{(a-6)(a-4)} \cdot \dfrac{(a-6)(a-6)}{(a-4)(a+8)}[/tex]

[tex]\textsf{Apply the fraction rule}: \quad \dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{ac}{bd}[/tex]

[tex]\dfrac{(a-8)(a+8)(a-6)(a-6)}{(a-6)(a-4)(a-4)(a+8)}[/tex]

Cancel the common factors (a + 8) and (a - 6):

[tex]\dfrac{(a-8)(a-6)}{(a-4)(a-4)}[/tex]

Simplify the numerator:

[tex]\dfrac{(a-8)(a-6)}{(a-4)^2}[/tex]

By the use of the completing the square method, the maximum height is 3 ±√29/4 + 9 m.

The maximum height has been modeled by the use of the equation f(x)= -4x^2 +24x -29. Now we know that f(x)= h so we can write;

h = -4x^2 +24x -29

Now we have;

0 = -4x^2 +24x -29

-4x^2 +24x -29= 0

x^2 - 6x = -29/4

(x - 3)^2 = -29/4 + 3^2

(x - 3)^2 =  -29/4 + 9

x = 3 ±√29/4 + 9 m

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Answer:  25 pounds

Step-by-step explanation: 100% - 20% = 80%

20 divided by 80% = 25