In the figure below, segment HK and segment IJ intersect at P, and segment HI is parallel to segment Jk. Which of the following angles must be congruent to angle PKJ?

Here's your answer down here↓:

Step-by-step explanation:

x^3 - y^3 = (x - y)(x^2 + xy + y^2)

(x^4 - y^4) = (x^2 - y^2)(x^2 + y^2) = (x - y)(x + y)(x^2 + y^2)

Ok. So the factor (x-y) appears once in the top line and once in the second line. So we are going to take it the least amount of times.

So, the factor (x + y) appears in the top line zero times and in the second line one time so we will take it where it appears the least which is zero times so we are still at (x - y)

And it Same goes for the factors of (x^2 + y^2) and (x^2 + xy + y^2)

53) Vertical angles are congruent, so [tex]m\angle IDA=121^{\circ}[/tex]

54) [tex]\angle YDA[/tex] and [tex]\angle YDF[/tex] are supplementary, so [tex]m\angle YDA=180^{\circ}-121^{\circ}=59^{\circ}[/tex]

55) Because vertical angles are congruent, [tex]m\angle FDI=59^{\circ}[/tex]. Now, because DR bisects [tex]\angle FDI[/tex], this means [tex]m\angle RDI=\frac{59}{2}=29.5^{\circ}[/tex]

56) This is a geometric sequence where the next term is obtained by multiplying the previous term by -2, so the next two numbers are 16, -32

The measure of the other side of a quadrilateral is [tex]3\sqrt{13}[/tex] cm.

In the given quadrilateral one side is unknown we need to find the unknown side.

By dividing the given quadrilateral into a rectangle and a triangle we can find the other side.

The Pythagoras theorem states that if a triangle is right-angled, then the square of the hypotenuse is equal to the sum of the squares of the other two sides. That is, [tex]c^{2}=a^{2}+b^{2}[/tex].

Now, [tex]x^{2} =9^{2}+6^{2}=81+36=17[/tex]

⇒[tex]x=\sqrt{13 \times 9} =3\sqrt{13}[/tex]

Therefore, the measure of the other side of a quadrilateral is [tex]3\sqrt{13}[/tex] cm.

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Answer:

this is step by step explenation

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Answer:

0.7855 square feet

Step-by-step explanation:

90/360×3.142×1 squared

=0.7855

The area of a regular octagon with an apothem of 2 cm is 3cm ^2.

The area of a regular octagon with an apothem of 2 cm.

Given the apothem length,

the area of a regular polygon becomes,

[tex]A=\frac{1}{2}\times P\times A[/tex]

P=  the perimeter of the regular polygon

A is the apothem of the regular polygon

Here, we get

p=2=2cm, a=3cm.

So, plugging in the given values, we get

[tex]A=\frac{1}{2} \times 2cm\times 3cm[/tex]

A=1cm⋅3cm

A=3cm^2

Therefore the area of a regular octagon with an apothem of 2 cm is 3cm ^2.

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Answer:

20 can be the answer of it

For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The correct option is A.

Inconsistent System

For a system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

If the two of the given system of equations are plotted on the graph, then it can be observed that the two lines have different slopes. Therefore, the correct option is A.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:Angle \:\: of \:\: elevation= 30° [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Let the angle of elevation be " x "

[tex]\qquad \tt \rightarrow \: \cos(x) = \dfrac{9 \sqrt{3} }{18} [/tex]

[tex]\qquad \tt \rightarrow \: \cos(x) = \dfrac{ \sqrt{3} }{2} [/tex]

[tex]\qquad \tt \rightarrow \: x = \cos {}^{ - 1} \bigg( \cfrac{ \sqrt{3} }{2} \bigg ) [/tex]

[tex]\qquad \tt \rightarrow \: x = 30 \degree \: \: or \: \: \cfrac{ \pi}{6} \: \: rad[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

The angle is 60 degree.

Step-by-step explanation:

First of all, we will find the height if the tree by using Pythagorean theorm.

Let, height of tree be x.

18^2=(9(3^1/2))^2+x^2

324=243+x^2

x^2=324-243

x^2=81

x=9

Now, let the angle be y.

tan y= x/base

tan y=9/9×(3^1/2)

tan y=1.73

y=cot 1.73

y= 60

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:Domain : \fbox{-3}\leqslant x \leqslant \fbox{-1}[/tex]

[tex]\qquad \tt \rightarrow \:Range :\:\:\fbox{-4}\leqslant x \leqslant \fbox{-3}[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Domain = All possible values of x for which f(x) is defined

[ generally the extension of function in x - direction ]

Range = All possible values of f(x)

[ generally the extension of function in y - direction ]

[tex] \large\textsf{For the given graph : } [/tex]

[tex]\qquad \tt \rightarrow \: domain : \fbox{-3}\leqslant x \leqslant \fbox{-1}[/tex]

[tex]\qquad \tt \rightarrow \: range : \:\:\fbox{-4}\leqslant x \leqslant \fbox{-3}[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

option 2

Step-by-step explanation:

the chord- chord angle BFE is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is

∠ BFE = [tex]\frac{1}{2}[/tex] ( BE + DC) = [tex]\frac{1}{2}[/tex] (72 + 152)° = [tex]\frac{1}{2}[/tex] × 224° = 112°

Answer:

The smallest number all three numbers can be divided by is 4.

Step-by-step explanation:

12/4=3

16/4=4

24/4=6

Hope this helps!

If not, I am sorry.

Kat should tell Kim that It's too late to change the area of this kite because the length of the diagonals of a kite determines its area.

In Mathematics, the area of a kite is equal to one-half the product of the length of its diagonals. Mathematically, the area of a kite can be calculated by using this formula:

A = ½ × d₁ × d₂

Where:

Since Kit has already cut his sticks for the diagonals, Kat should tell him that it's too late to change the area of this kite because the length of the diagonals of a kite determines its area.

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Answer:

1/11

Step-by-step explanation:

probability =total number of items ÷ 1

=11÷1

=1/11

Answer:

  yes

Step-by-step explanation:

The commutative property of addition applies to let you swap the order of the summands.

__

Here is how the commutative property can be applied.

  5x = 3 -x . . . . . given

  5x = (3) +(-x) . . . . shown as a sum

  5x = (-x) +(3) . . . . order swapped using commutative property of addition

  5x = -x +3 . . . . . . equivalent equation

Answer:

2ab(a2b−2)

Step-by-step explanation:

Answer:

A. is correct answer

Step-by-step explanation:

full explanation

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: x² + y² = 64[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Standard equation of circle is :

[tex]\qquad \tt \rightarrow \: (x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]

Since the circle is centered at origin, h = k = 0

[tex]\qquad \tt \rightarrow \: (x - 0) {}^{2} + (y - 0) {}^{2} = {8}^{2} [/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + {y}^{2} = 64 [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Let x= cost of 20 pepsi

so 1 Pepsi = 20 naira

20 = x

x= 20*20

x= 400 naira

Therefore the cost of 20 pepsi is 400 naira

Research study measuring relationship suggests that video games may have a detrimental effect on an individual's grades.

This study analyzes the correlation between video game usage and academic performance. Scholastic Aptitude Test (SAT) and grade-point average (GPA) scores were used to gauge academic performance. The amount of time a student spends playing video games has a negative correlation with students' GPA and SAT scores. As video game usage increases, GPA and SAT scores decrease.

A chi-squared analysis found a p value for video game usage and GPA was greater than a 95% confidence level (0.005 < p < 0.01). This finding suggests that dependence exists. SAT score and video game usage also returned a p value that was significant (0.01 < p < 0.05). Chi-squared results were not significant when comparing time spent studying and an individual's SAT score. This research suggests that video games may have a detrimental effect on an individual's GPA and possibly on SAT scores. Although these results show statistical dependence, proving cause and effect remains difficult, since SAT scores represent a single test on a given day. The effects of video games maybe be cumulative; however, drawing a conclusion is difficult because SAT scores represent a measure of general knowledge. GPA versus video games is more reliable because both involve a continuous measurement of engaged activity and performance. The connection remains difficult because of the complex nature of student life and academic performance. Also, video game usage may simply be a function of specific personality types and characteristics.

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Answer:

the first one listed (y = -[tex]2^{x}[/tex] + 4)

Step-by-step explanation:

a 0 at an x-intercept means that when plugging in that number, you get a 0 as a y-value.

So, the easiest method to use is to plug x=2 into each equation listed, because we can see that (2,0) is a point on this graph

if y= -[tex]2^x\\[/tex] + 4

y = -2² + 4

y = -4 + 4

y = 0

This means that this graph has corresponding real zero(s) to the function    y= [tex]-2^x[/tex] + 4

(I chose which graph to test by looking to see which option seemed right)

The amount paid by sam will be 11526.75k for the meal.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

Sam pays 512 .75k less than the amount rob pays for his meal .ridwan pays three times the amount rob pays for his meal. if the total amount paid by them is 47,645.25k.

We will form an expression from the data given above in the question.

Amount paid by Sam  = ( r - 512.75 )

Amount paid by rob = r

( r - 512.75 ) + 3r = 47645.25

( r + 3r ) = 47645.25 + 512.75

4r = 48158

r = 12039.5

The amount paid by sam will be calculated as:-

S = r - 512.75

S = 12039.5 - 512.75

S = 11526.75

Therefore the amount paid by sam will be 11526.75k for the meal.

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Answer:

13x = 39

x=3

y=10

ANSWER :

The pH level of a swimming pool indicates the level of acidity or alkalinity

of the swimming pool.

Correct Responses;

First Part:  Please find attached the required graph of the pH function created with MS Excel.

The pH value is 0 when x = 1

The pH value is 1 when x = 0.1

The pH level if the hydronium ions is raised to 0.50 is approximately 0.301029996.

Second Part: The transformation that results in a y-intercept is f(x + 1), because f(0 + 1) exists and is equal to 0.

STEPS

Method by which the above responses are obtained

First part

The given pH function is f(x) = -㏒₁₀x

Where;

x = The amount of hydronium ions

A substance with a pH < 7 is acidic

A substance with a pH > 7 is alkaline

A neutral solution has pH = 7

Water is a neutral solution

The graph of the pH function created with MS Excel is attached

The table of values of the graph is as follows;

From the graph, we have;

When the pH value is 0, the hydronium ion concentration is 1

The pH value is 1 when x = 1 × 10⁻¹ = 0.1

The pH level if the hydronium ions, x = 0.5 is given from the graph as follows;

pH = f(0.5) = -㏒₁₀(0.5) ≈ 0.301029996

The pH value when the hydronium ions is 0.5 is pH ≈ 0.301029996

Second Part

Using f(x) = -㏒₁₀x as the parent function, the graph of f(x) + 1, and f(x + 1) are plotted

From the graph, we have;

The graph of f(x) + 1 = -㏒₁₀x + 1

The graph of f(x + 1) = The graph of -㏒₁₀(x + 1)

At the y-intercept, x = 0, therefore;

f(x) + 1 = f(0) + 1 = -㏒₁₀0 + 1 = Undefined

f(x + 1) = f(0 + 1) = -㏒₁₀(0 + 1) = 0

Therefore;

The transformation that results in a y-intercept is f(x + 1) because f(0 + 1) is 0, which is defined.

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Answer:

10x + 332

when, x=0

Step-by-step explanation:

Please give me brainlist.

The probability of an investor choosing both stocks AND bonds from portfolio B is 0.25 or 25%.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

A financial planner has three portfolios: A, B, and C.

Each portfolio has stocks and Bond

P(stock) = 0.5

P(bond) = 0.5

Customers are equally likely to choose stocks.

P(stock and bond from B) = P(stock, B) + P(bond, B)

= 0.25×0.5 + 0.25×0.5

= 0.25 or

= 25%

Thus, the probability of an investor choosing both stocks AND bonds from portfolio B is 0.25 or 25%.

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Answer:

1 = 120

2 = 120

Step-by-step explanation:

Answer:

8 units

Step-by-step explanation:

ratios  

(x-3) /( x+1)  = (x-2)/(x+3)     cross multiply

x^2 -x -2 = x^2 - 9

  -x - 2 + 9 = 0

    x = 7          

           so TS = x + 1 = 8 units