How are the triangles congruent?

Solutions of given exponents are :

1.  [tex]9^{18}[/tex]   2. [tex]16x^4[/tex]   3.  [tex]\frac{6561}{y^2}[/tex]

In, mathematics a exponent or exponential equation or exponential function is inverse of a logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The shows the behavior of something to the power of something. The basic form of the exponential can be written as [tex]a^x[/tex]

where, a = the base of function

            x = exponential

Important properties of exponential :

According to the question,

1. given, [tex](9^{3})^6[/tex]

  use the property, [tex](a^n)^m = a^{nm}[/tex]

   [tex](9^{3})^6[/tex] = [tex]9^{3.6} = 9^{18}[/tex]

2. Given, [tex](2x)^4[/tex]

   use the property, [tex](ab)^n = a^n.b^n[/tex]

    [tex](2x)^4[/tex] = [tex]2^4.x^4 = 16x^4[/tex]

3. Given , [tex](\frac{3^4}{y}) ^{2}[/tex]

    use the property, [tex](\frac{a}{b})^n = \frac{a^n}{b^n}[/tex]

     [tex](\frac{3^4}{y}) ^{2}[/tex] = [tex]\frac{(3^4)^2}{y^2}[/tex]

    now use ,  [tex](a^n)^m = a^{nm}[/tex]

     = [tex]\frac{3^8}{y^2} = \frac{6561}{y^2}[/tex]

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The technique researchers use to reduce the impact of confounding variables is randomization.

Confounding variables are variables that affects or influences both the dependent and independent variable.

Some techniques used to reduce this influence are;

The most effective way of reducing the impact of confounding variables is the conduction of random trials.

Thus, the technique researchers use to reduce the impact of confounding variables is randomization.

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To spray on 2 lawns is required [tex]3\frac{1}{9}[/tex]  gallons.

Mixed fraction A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Given ;

  A container with [tex]3\frac{1}{2}[/tex] gallons of weed killer can spray =  [tex]2\frac{1}{4}[/tex] lawans

∵ in [tex]\frac{9}{4}[/tex] lawn the week killer can spray =  [tex]\frac{7}{2}[/tex]gallons

∴ in 1 lawn the weed killer is  used = [tex]\frac{7}{2}[/tex] × [tex]\frac{4}{9}[/tex] gallon

∴ in 2 lawns the weed killer can spray =[tex]\frac{7}{2}[/tex]  ×  [tex]\frac{4}{9}[/tex]× 2 =[tex]\frac{28}{9}[/tex]  gallon =[tex]3\frac{1}{9}[/tex]gallons

  [tex]3\frac{1}{9}[/tex] gallons require to spray 2 lawns.

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Answer: 6 hours

Step-by-step explanation: 6 apartments divided by 2 is 3 apartments and 4 hours divided by 2 is 2 hours. 3 apartments per 2 hours. So, 3/2 x 3/3 is 9/6 which is 9 apartments for 6 hours.

Answer: 20 cm

Step-by-step explanation: if the length of R-N= 5cm therefore you multiply 5 by each dot so H-O is 5 cm, H-R is 10 cm, H-N is 15 cm, and H-S is 20 cm.

1. The value of x is 14°

2. The value of x is 23°

3. The value of x is 22.5°

From the question, we are to determine the value of x in the given diagrams.

1.

∠ CBA = 180° - 6x (Linear pair theorem)

and

m ∠BAC + m ∠CBA = m ∠FCB (Exterior angle theorem)

Thus,

2x + 180° - 6x = 124°

180° - 4x = 124°

180° - 124° = 4x

56° = 4x

x = 56/4

x = 14°

Hence, the value of x is 14°

2.

m ∠ABE = 4x (Alternate angles theorem)

m ∠ABD + m ∠ABE + m ∠EBF = 180° (Sum of angles on a straight line)

x + 4x + 65° = 180°

x + 4x = 180° - 65°

5x = 115°

x = 115°/5

x = 23°

Hence, the value of x is 23°

3.

m ∠EAB = 2x (Vertical angles theorem)

m ∠AEB = 180° - 4x (Linear pair theorem)

m ∠ABE = 180° - 6x (Linear pair theorem)

m ∠EAB + m ∠AEB + m ∠ABE = 180° (Sum of angles in a triangle)

Thus,

2x + 180° - 4x + 180° - 6x = 180°

180° + 180° - 180° = 6x + 4x -2x

180° = 8x

x = 180°/8

x = 22.5°

Hence, the value of x is 22.5°

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Probability is nothing but the ratio of favorable cases to all possible cases or in simple terms it is the ratio of sample set to all set

We are required to find all the cases in which sum of any two bills is 20$ or more

The total number of bills are two $ 1 bills, two $ 5 bills, two $ 10 bills, and two $ 20 bills.

The total case of drawing any two bills will be =

2 for $ 1 bill x two for 5$ bill x two for 10$ bill x two 20$ bills

=2 x 2x2x2 =16

Hence 16 ways in which two bills can be drawn at random

Cases in which bill can be greater than 20$= (1,20)(20,1)(5,20)(20,5)(10,10)(20,10)(10,20) (20,20)= 8 cases

Hence, total number of possible outcomes = 8

Hence the probability of bill to be 20$ or more= favorable outcome/total outcome

=8/16 =1/2

Hence the probability is 1/2

Disclaimer: the fraction sign is missing in question options

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The factors of the equation is  (x - 5)  (x + 2).

Given the equation is x²-3x-10

we are asked to factorize the equation.

Factorization is the process of identifying two or more expressions whose product is an algebraic expression. It is often referred to as finding the factors of an expression. Finding two or more expressions whose product is the given expression—known as factorization—is the process of breaking down algebraic expressions. A factor is any number that divides the given number by itself without leaving any remainder. It simply implies representing a number as the product of two other integers.

x²-3x-10

x² - 5x + 2x - 10

x(x - 5) + 2(x - 5)

(x - 5)  (x + 2)

Thus, the factorization of the given expression  x²-3x-10

= (x - 5)  (x + 2)

Hence we get the factors as (x - 5)  (x + 2)

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Answer:

To factor the quadratic expression a2 - 3x - 10, we need to find two numbers that multiply to give -10 and add to give -3. These numbers are -5 and 2. Therefore, we can write:

a2 - 3x - 10 = (a - 5)(a + 2)

So the factors of the quadratic expression a2 - 3x - 10 are (a - 5) and (a + 2).

The formula for calculating Alex's earnings from his employment at the theme park is 8(40 x 9 + 100) = 8(360 + 100) = 8(460) = $3,680.

Given: that the plane ticket costs $2,200 and that y = 11.5x gives the function that represents the potential earnings Alex may make from the tech internship, the inequality that reflects the maximum number of hours Alex can work at the internship follows.

He puts in 20 hours every week at the internship, which translates to 160 hours of work over the course of 8 weeks.

Given that the internship pays $11.5 an hour for 160 hours, her earnings of 11.5 x 160 = $1,840 will not be sufficient to cover the cost of the plane ticket.

A few of the theme park employment that are available in this sector include costume character work, ride technician, admissions attendant, lifeguard, and gaming attendant. Workers at concession stands must be swift to prevent long queues and receive cash for food and drinks.

Hence, Alex's employment at the internship will not generate enough income to pay for the ticket.

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The range of the function is {-11, -9, -7, -5}.

The given function is g(x)=x−13.

We need to find the range of g(x).

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

Now, put x=2,4,6,8 in the given function and find the range of function.

So, g(2)=2−13=-11

g(4)=4−13=-9

g(6)=6−13=-7

g(8)=8−13=-5

Therefore, the range of the function is {-11, -9, -7, -5}.

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The equation which describe the relationship between the profit, y, and the number of candles sold, x is x - y = 3.

Given that:-

When 10 candles are sold, the store makes a profit of $7.

When 15 candles are sold, the store makes a profit of $12.

When 20 candles are sold, the store makes a profit of $17.

We have to write an equation which describe the relationship between the profit, y, and the number of candles sold, x.

As we can observe from the given data,

number of candles sold - 3 = profit (in $)

Hence, we can write,

x - 3 = y

x - y = 3.

Where,

x represents the number of candles sold and,

y represents the profit

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The statement that is true about the segment connecting points B and C is D. The segment has a finite length that can be measured.

It should be noted that ieometry, a line segment is the part of a straight line bounded by two distinct end points, and contains every point on the line that is between its endpoints.

It should be noted that the length of a line segment is given by the Euclidean distance between its endpoints.

Therefore, in this case, the statement that is true about the segment connecting points B and C is that the segment has a finite length that can be measured.

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Answer:

Median

Step-by-step explanation:

Median: (16+17)/2= 16.5

Mean: 11+13+15+15+16+17+18+19+19+20= 163

163/10= 16.3

Median is greater.

hi

A = 6x^(2)+4x+3*y + 6y + y^(2)

A= 6x²+y²+4x+9y

Answer:

3x - 8y = -12

Step-by-step explanation:

Standard form is:

[tex]Ax + By = C[/tex]

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[tex]8y - 12 = 3x\\\rule{150}{0.5}\\8y - 8y -12 =3x - 8y\\\\-12 = 3x-8y\\\\\boxed{3x - 8y = -12}[/tex]

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A graph is attached. Hope this helps!

Answer:

1. A, 450 = 2(p+w); 450 = 3(p-w)

2. A, 2 units

3. D, Between step 6 and step 7

Step-by-step explanation:

1. This one is confusing on first glance.

[tex]450 = 2(p+w); 450 = 3(p-w)[/tex] Lets break down this equation.

[tex]2(p+w)[/tex] means, the plane speed, plus the windspeed, will take 2 hours to travel 450 KM. The reason we add the plane speed and the windspeed is because we have a tailwind instead of a headwind, the wind is pushing us forward, adding to the planes speed.

[tex]3(p-w)[/tex] means, the plane speed, minus the windspeed, will take 3 hours to travel 450 KM. We subtract the wind speed from the plan speed because the wind is a headwind, it's pushing us backwards, taking away from the planes speed.

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2. Let set these up as two-sided equations.

[tex](6x+3) + (4x) + (2x + 1) = (5x) + (5x) + (3x+2)[/tex]

Combine like terms

[tex]12x + 4 = 13x + 2[/tex]

Subtract 12x from both sides

[tex]4 = 1x + 2[/tex]

Subtract 2 from both sides

2 = 1x, or x = 2.

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3. Take a look at step 6. You want to get x by itself, to do that, and get rid of the 8, you'd divide both sides by 8 to get [tex]x = -\frac{15}{4}[/tex]

Answer:

51/8

Step-by-step explanation:

each bracelet length as a fraction will be 51/8 inches if the artist uses the 51 inches of the string to make 8 bracelets

The scale of the drawing is 6 feet = 17 inches

Scaling is the process of increasing or reducing the size of a figure by a factor k.

In the given statement is:

Shane made a scale drawing of a hotel. a room in the hotel, which is 18 feet wide in real life, is 51 inches wide in the drawing.

A figure which is 18 feet wide in real life, is 51 inches wide in the drawing, hence the scale is:

Now, According to the question is

18 feet = 51 inches

Divide both sides by 3:

6 feet = 17 inches

Therefore, the scale of the drawing is 6 feet = 17 inches

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The area of the base is 216 cm².

The volume of a cuboid is 1296 cm³.

The breadth of the cuboid is double the height of the cuboid and the length of the cuboid is triple the height of the cuboid.

Let the length, breadth, and height of the cuboid be l, b, and h respectively.

Then,

l = 3(h)

b = 2(h)

The volume of a cuboid is given as:

V = l × b × h

1296 = 3(h) × 2(h) × h

1296 = 6 × h³

h³ = 1296 / 6

h³ = 216

h = ∛216

h = ∛(6)³

h = 6 cm

Therefore, the length of the b is l = 3(h) = 3 × 6 = 18 cm

The breadth of the cuboid will be:

b = 2(h)

b = 2 × 6

b = 18 cm

Now the volume of the cuboid is also given as:

Volume = base area of  cuboid × height

1296 = base area × 6

base area = 216 cm²

The base area is 216 cm².

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Answer:

72

Step-by-step explanation:

Step-by-step explanation:

QC = Qu + UC

Qu= 22

Uc= 70

QC= 22 + 70

QC = 92

There are total 35 such ways in which a person can adopt rules.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

According to the question, we are Given,

Total rules = 7

No of rules a person can adopt = 5

using combinations,

= ⁷C₅

= 7! / 5! (7 - 5)!

= 7! / 5! 2!

= 35

So a person can choose it in 35 possible ways.

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Answer:

1) [tex]\frac{51}{2}[/tex]    2) [tex]\frac{55}{12}[/tex]

Step-by-step explanation:

Answer:  I simplify the answer for u my friened 25.5

The number 78.263 using ones, tenths, and thousandths means

This is the value of each digits based on its position in a number.

It is divided into whole number part and fractional part.

Whole number part:

Fractional part:

78.263

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Answer:

f(x) = 12x+35

f(5) = 95 pages written at 5 months

Step-by-step explanation:

Step 1: write the slope intercept equation

f(x) = mx+b

f(x) = the value of the equation at month x

m = slope of the linear equation (pages written PER month)

x = the month

b = intercept of the equation (pages already written)

Step 2: relate given information to the variables

m = 12 pages per month

b = 35 pages already written

Step 3: update equation

f(x) = 12x+35

Step 4: solve for x = 5 months

f(5) = 12(5) + 35 = 60 + 35 = 95

Answer:

0.4

Step-b0.y-step explanation:

Pat and John will meet in 3 hours.

It should be noted that speed = Distance / Time

The appropriate equation will be:

80t + 24t = 312

104t = 312

t = 312/104

t = 3. hours

Therefore, it will take them 3 hours to meet.

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Answer:

2.1 cm (nearest tenth)

Step-by-step explanation:

The radius (r) of a circle is the distance between its center and its circumference.  Therefore, from inspection of the given circle:

⇒ r = OX = OY = OA

Given:

⇒ AB = OA + OB

⇒ 3.5 = r + OB

⇒ OB = 3.5 - r

As OX = OY and AB is perpendicular to XY then XB = BY.

As XY = 3 cm:

⇒ XB = BY = 1.5 cm

Therefore, for ΔOBX:

Pythagoras Theorem

[tex]a^2+b^2=c^2[/tex]

where:

Use Pythagoras Theorem and the defined sides of ΔOBX to find r:

[tex]\implies OB^2+XB^2=OX^2[/tex]

[tex]\implies (3.5-r)^2+1.5^2=r^2[/tex]

[tex]\implies 12.25-7r+r^2+2.25=r^2[/tex]

[tex]\implies 14.5-7r+r^2=r^2[/tex]

[tex]\implies 14.5-7r+r^2-r^2=r^2-r^2[/tex]

[tex]\implies 14.5-7r=0[/tex]

[tex]\implies 14.5=7r[/tex]

[tex]\implies 7r=14.5[/tex]

[tex]\implies \dfrac{7r}{7}=\dfrac{14.5}{7}[/tex]

[tex]\implies r=2.07142857...\: \sf cm[/tex]

Therefore, the radius of the circle is 2.1 cm (nearest tenth).

Hence she got 90 correct answer.

Ratio of the number of problems she got incorrect to the number of problems she got correct = 2:9

Number of incorrect answers = 8

Let the number of incorrect answers be 2x

Let the number of correct answers be 9x.

So, According to question, we get that

[tex]2x = 20\\ x =\frac{20}{2} \\ x = 10[/tex]

So, the number of correct answers would be

  [tex]9x = 9\times 10\\\\ =90[/tex]

Hence she got 90 correct answer.

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