If p(x) = b² - 16b +32 and q(x) = -32b-32 what values of x does p(x)=q(x)?

Answer:

7

Step-by-step explanation:

As we want to find the whole number, and to do so we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.

21/3 = 7

The population of a city is increasing at a rate of 4% each year. In 2020, there were. 236,000 people in the city.

Given, In 2015, the population of the town decreased by 10%, so [tex]8250 x 10/100 = 825[/tex]  people left the town, bringing the population down to [tex]8250 - 825 = 7425.[/tex]

From 2015 to 2020, the population increased by 15% so [tex]7425 x 15/100 = 1113.75[/tex] people came back to the town, bringing the population to [tex]7425+1113.75 = 8538.75[/tex]

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Answer: k = 11

Step-by-step explanation:

[tex]\frac{11}{3k} = \frac{1}{3} \\\\[/tex]

Cross multiply:

[tex]11 * 3 = 1*3k[/tex]

[tex]33 = 3k[/tex]

[tex]k = 11[/tex]

Answer:

Surface Area = 2(22 x 15) + 2(12 x 15) + 2(22 x 12)

Surface Area = 660 + 360 + 528

Surface Area = 1,548 inches²

Step-by-step explanation:

∠1 and ∠3 are vertical angles and congruent.

What is congruence?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

What are vertical angles?

The opposing angles form when two lines cross. They are constantly on par. In this illustration, the angles a° and b° are vertical. The term "vertical" refers to the vertex, not up or down, where they cross.

Here,

we have given a diagram and we have to determine which statement is true that satisfies the true conditions.

By applying congruent property. we get

∠1 = ∠3 are vertivally opposite angle.

This is the only condition that satisfy the true condition from given statement.

Hence, ∠1 and ∠3 are vertical angles and congruent.

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Answer:

x=7/2

x=3/2

Step-by-step explanation:

Answer: ax^2+bx+c=0

(4x^2+20x+20=0)

Step-by-step explanation:

It may not make sense but...

Add -20 to both sides of the equation.

4x-20x=-20

Add -20 to both sides of the equation.

4x^2-20x+20=-20+20

Simplify the expression.

4x^2+20x+20=0

I hope this was what you were looking for. :) If not I'm still glad to help.

The best estimate for 225% of 50 is (a) greater than O but less than 1. 50

The maximum likelihood method will be used to calculate the point estimate as follows:

T, note the total number of trials.

List the number of accomplishments, S.

MLE = S / T should be used. Your point estimate is the outcome. Prior to explaining a "formal" method of approximation by rounding each number in the calculation to one significant figure, students must first estimate the result of a computation, use a calculator to determine the precise result, then compare the two results. The most accurate estimate is a definite estimate, as it is created by estimating the individual expenses for the various aspects of the project and then combining them into one estimate. Typically, bottom-up estimates are classified under this heading.

The best estimate for 225% of 50 is

= (225*50)/100

= 11250/100

= 112.5

So that, The best estimate for 225% of 50 is (a) greater than O but less than 1. 50

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The equivalent trigonometric identity to cot²θ + 1 is cot²θsec²θ

Trigonometric identities are equations which contain the trigonometric ratios.

Since we have the trigonometric identity cot²θ + 1,we need to find its equivalent expression.

So, we proceed as follows

Since cot²θ + 1 = 1/tan²θ + 1     (since cot²θ = 1/tan²θ)

Now taking the L.C.M, we have that

1/tan²θ + 1 = (1 + tan²θ)/tan²θ

We know that the trigonometric identity 1 + tan²θ = sec²θ

So, substituting this into the equation, we have that

(1 + tan²θ)/tan²θ =  sec²θ/tan²θ

Since cot²θ = 1/tan²θ, substituting the values of the variables into the equation, we have that

sec²θ/tan²θ = cot²θsec²θ

So, cot²θ + 1 = cot²θsec²θ

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Answer:

The (1/4) slope is the prive per ticket.  The y intercept is the money in the cash box before any tickets were sold.

Step-by-step explanation:

Let y be the money and x the numbers of tickets sold, as requested.  We are told that the equation for this situation is:

   y = (1/4)x + 8

Let's assume the money is in units of dollars.  The slope of (1/4) would mean that each carnival game ticket cost $(1/4), or 25 cents.  The y-intercept is the value of y when x=0, which means zero tickets have been sold.  That means that the cash box had $8 before any sales were made.  [perhaps to use for making change].

Answer:

35 dimes and 65 nickels

Step-by-step explanation:

We will need use a system of equations to find the total number of nickels and dimes.

Because there are 100 dimes and there are only nickels and dimes, one equation is N + D = 100, where N is the total number of nickels and D is the total number of dimes.

Because a dime is worth $0.10, a nickel is worth $0.05, and the total change in the jar is worth $6.75, the second equation is 0.05N + 0.1D = 6.75

Substitution will be the easiest method to solve:

[tex]0.05N+0.1D=6.75\\N+D=100\\\\N=-D+100\\\\0.05(-D+100)+0.1D=6.75\\-0.05D+5+0.1D=6.75\\0.05D+5=6.75\\0.05D=1.75\\D=35\\\\N+35=100\\N=65[/tex]

Answer:

its 6.11

6.11 ÷ 1 = 6.11

Calculated to 2 decimal places.

6. 1 1

1 6. 1 1

− 6

0 1

− 1

0 1

− 1

0

Answer:

1) 39

2) 13

3) 2

Step-by-step explanation:

1) She had 22 books, she now has 61 books, so she bought 61-22 = 39 books at the yard sale.

2) 143/11 = 13

3) 6-4 = 2

Scores earns an intelligence score of 130

According to the 68-95-99.7 rule, 68% of persons have WAIS scores ranging from 100-15 to 100+15. WAIS scores between 85 and 115 are obtained by 99.7% of the population. As a result, 32% of adults have WAIS scores of 85 or above. Factor Analysis is a statistical process used to discover clusters of similar questions (called factors) on a test; it is used to identify multiple levels of performance that underpin one’s overall score.

The WAIS categories are shown below and are based on a mean of 100: Scores of 130 and higher are deemed talented. Scores between 120 and 129 are regarded extremely intelligent. Normal intellect is defined as a score between 110 and 119.

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Complete question is: A performance score on the WAIS that is higher than all but 2 percent of all scores earns an intelligence score of:

The outcome for the event "at least two tails" is HTT. Option B

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.

HHH → All heads

HHT → Two heads + one tail

HTH → Two heads + one tail

HTT → Two tails + one head

THH → One tail + two heads

THT → Two tails + one head

TTH → Two tails + one head

TTT → All tails

Therefore, At least two tails means → Sample space outcome with two tails Or all tails

Therefore, from the given options HTT is having two tails. Option B is the correct option.

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The time duration for the population to exceed 10,000 is approximately 6.6 hours

What is time ?

In mathematics, time is described as a continuing and continuous series of events that take place in chronological order from the past through the present and into the future. The duration of events, the gaps between them, or even the sequencing of occurrences can all be quantified, measured, or compared using time.

the time frame that an activity, process, or state lasts or continues to exist: duration is a non-spatial continuum that is measured in terms of subsequent occurrences from the past, present, and future.

The mathematical symbol used to represent the multiplication process and its subsequent product is the multiplication sign, sometimes referred to as the times sign or the dimension sign.

t = The time duration in hours

The initial population of the cells = 1,000

Therefore, at t = 0, P(0) = 1,000 = P₀ × 1.42^0

∴  P(0) = 1,000 = P₀ × 1 = P₀

P₀ = 1,000

When the population is 10,000, we have;

P(t) = 10,000 = 1,000 × 1.42^t

∴ 1.42^t = 10,000/1,000 = 10

㏒(1.42^t) = ㏒(10) = 1

∴ t × ㏒(1.42) = 1

t = 1/㏒(1.42) = 6.56649071898

∴ The time duration for the population to exceed 10,000, t ≈ 6.6 hours.

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Answer: x<-2 or -2>x<1 or x>1

(-infinity,-2) U (-2,1) U (1,infinity)

Step-by-step explanation:

5. The width of the house. = 30 feet

6. The height of the house. = 22.5 feet

7. The height of the first floor. = 12.5 feet

8. The height of the roof. = 10 feet

9. The width of the door. = 5 feet

10. The height of the door. = 7.5 feet

The actual length of each segment is calculated by counting the units in the scale drawing and multiplying by the scale factor

In the problem, the scale factor is  two and a half feet = 2.5 feet

5. The width of the house

number of units from the drawing = 12 units

actual length = number of units from the drawing * scale factor

actual length = 12 * 2.5 = 30 feet

6. The height of the house

number of units from the drawing = 9 units

actual length = 9 * 2.5 = 22.5 feet

7. The height of the first floor

number of units from the drawing = 5 units

actual length = 5 * 2.5 = 12.5 feet

8. The height of the roof

number of units from the drawing = 4 units

actual length = 4 * 2.5 = 10 feet

9. The width of the door.

number of units from the drawing = 2 units

actual length = 2 * 2.5 = 5 feet

10. The height of the door.

number of units from the drawing = 3 units

actual length = 3 * 2.5 = 7.5 feet

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Answer:

Depending of the figure that you are trying to find perimeter on, you just add up all the sides of that figure.

Answer:

The perimeter is the distance around a figure.

Step-by-step explanation:

For example, if I have a square where each side is 5 inches.  The perimeter would be 20 inches.  5 + 5+ 5 + 5, a square has four sides and each side length is 5 inches.

The factors for the Polynomial are (x+1) and (x+2).

According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0.

Given:

f(x) = 2x³ + 9x² + 13x + 6

Now, first (x+1) =0

x= -1

put x= -1 in f(x) as

f(-1) = 2(-1) + 9(1) + 13(-1) + 6

      = -2 + 9 - 13 + 6

      = 0

So, (x+1) is factor of f(x).

Now, second (x-1)= 0

x= 1

put x= 1 in f(x) as

f(1) = 2(1) + 9(1) + 13(1) + 6

      = 2 + 9 + 13 + 6

      = 31

So, (x-1) is not a factor of f(x).

Now, second (x+2)= 0

x= -2

put x= -2 in f(x) as

f(1) = 2(-2)³ + 9(-2)² + 13(-2) + 6

      = -16 + 36 - 26 + 6

      = 0

So, (x+2) is factor of f(x).

Now, second (x-2)= 0

x= 2

put x= 2 in f(x) as

f(1) = 2(2)³ + 9(2)² + 13(2) + 6

      = 16 + 36 + 26 + 6

      = 84

So, (x-2) is not a factor of f(x).

Now, second (x+3)= 0

x= -3

put x= -3 in f(x) as

f(1) = 2(-3)³ + 9(-3)² + 13(-3) + 6

      = -54 + 81 - 39 + 6

      = -6

So, (x+3) is not a factor of f(x).

Now, second (x-3)= 0

x= 3

put x= 3 in f(x) as

f(1) = 2(3)³ + 9(3)² + 13(3) + 6

      = 54 + 81 + 39 + 6

      = 180

So, (x-3) is not a factor of f(x).

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The sum of the greatest common factor (HCF) and least common multiple (LCM) of 3 and 6 is 9.

The H.C.F. defines the highest common factor present in between given two or more numbers, while L.C.M. defines the least common multiple number which is exactly divisible by two or more numbers.

factors of 3 are 1 and 3

factors of 6 are 1, 2, 3, and 6

3 = 1 × 3

6 = 2 × 3

LCM = 2 × 3

LCM = 6

HCF = 3

sum of HCF and LCM of 3 and 6 = 3 + 6

sum of HCF and LCM of 3 and 6 = 9

Therefore, 9 is the sum of the greatest common factor HCF least common multiple LCM of 3 and 6.

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The solving in the below shows similarity in triangles ΔAED ≈ΔBEC By SSS criteria.

The sizes of similar triangles vary while having the same shape. The comparable angles in identical triangles are equal. The ratio of the corresponding sides of comparable triangles is the same. The ratio of any pair of corresponding sides' squares to any similar triangle's area is the same.

Two triangles are comparable if they fall under one of the headings below: Angles in two comparable pairs are equal. Three pairs of corresponding sides make up the ratio. The comparable angles amongst two pairs of adjacent sides are proportional and equal.

Given that ΔAED ≈ΔBEC & AC = BD.

as  ΔAED ≈ΔBEC, AD = BC     .................(1)

Now in  ΔABD and ΔBAC,

     AD = BC        

(corresponding sides of similar triangles) [from (1)]

     AB = AB        

(common side)

     AC = BD      

   (given)

∴     ΔABD ≈ΔBAC  (By SSS criteria)    

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Answer:

Step-by-step explanation:

(f.g)(x)=[tex]-3*(-3x)^{2}+3=-27x^{2}+3[/tex]

On solving the provided question, we can say that number 12 is the smallest natural number is abundant

Natural numbers are those employed in mathematics for counting and ranking. Cardinal numbers are the ones used for counting, and ordinal numbers are the ones used for organizing. The natural numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11... are the ones to use while counting or sorting them. Integer a sum that consists of integers and zero. not using decimals or fractions. Integers are not fractions or decimals. Although all integers are integers (as are all natural numbers), not all integers are also integers or natural numbers. For instance, the integer -5 is both an integer and a natural number, but it is neither.

number 12 is the smallest natural number is abundant

factor of 12 = 1,2,3,4,6,12,

1~1

2>1

3>1

4>2+1

.............

10> 1+2+5

11>1

therefore, number 12 is the smallest natural number is abundant

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Complete question: A natural number is abundant if it is less than the sum of its proper divisors. What is the smallest abundant number?

Answer:

-5 = |5|

Step-by-step explanation:

Absolute value is the number of distance from zero. Therefore, it doesn't matter if the number is positive or negative in absolute value it is always positive.

Answer:

45 degree

Step-by-step explanation:

45+45 90 +90 180

All triangles will have 180 degrees angle

The value of P(X<Y) could be p(1−q) / p+q−pq if  X ∼ Geom(p) and Y ∼ Geom(r) are independent

What is probability ?

Probability could be defined as the ratio of number of favourable outcomes and total number of outcomes.

Given ,

X ∼ Geom(p) and Y ∼ Geom(r) are independent.

P(X<Y)=P(⋃1≤k<n,n∈N{X=k,Y=n})

=∑1≤k<n,n∈NP(X=k,Y=n)

=∑n=1∞∑k=1n−1P(X=k)P(Y=n)

=∑n=1∞∑k=1n−1p(1−p)k−1q(1−q)n−1

=pq∑n=1∞(1−q)n−11−(1−p)n−1p

=q∑n=1∞(1−q)n−1(1−(1−p)n−1)

=1−q / ∑n=1∞[(1−q)(1−p)]n−1

=1−q / 1−(1−p)(1−q)

=1−(1−p)(1−q)−q / 1−(1−p)(1−q)

=p(1−q) / p+q−pq.

Hence, The value of P(X<Y) could be p(1−q) / p+q−pq if  X ∼ Geom(p) and Y ∼ Geom(r) are independent.

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There are several types of angles, including: acute angles, right angles, obtuse angles, straight angles, reflex angles, complementary angles, supplementary angles, adjacent angles, linear pair, vertically opposite angles, alternate interior angles, alternate exterior angles, and corresponding angles.

Acute angles: angles measuring less than 90 degrees.

Right angles: angles measuring exactly 90 degrees.

Obtuse angles: angles measuring greater than 90 degrees but less than 180 degrees.

Straight angles: angles measuring exactly 180 degrees.

Reflex angles: angles measuring greater than 180 degrees but less than 360 degrees.

Complementary angles: two angles that add up to 90 degrees.

Supplementary angles: two angles that add up to 180 degrees.

Adjacent angles: two angles that share a common vertex and a common side but no common interior points.

Linear pair: two angles that add up to 180 degrees and share a common side.

Vertically opposite angles: two angles formed by two intersecting lines that are opposite to each other.

Alternate interior angles: two angles formed by two intersecting lines that are on opposite sides of the transversal and inside the parallel lines.

Alternate exterior angles: two angles formed by two intersecting lines that are on opposite sides of the transversal and outside the parallel lines.

Corresponding angles: two angles formed by two intersecting lines that are in the same relative position.

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The proportion equation for c in terms of j is written as c = 0.9j

In order to find the proportional equation for c in terms of j that matches the context, what you would have to do would be to divide 9.90 dollars by 11 bottles of pineapple juice.

This would tell us the price that one of the bottles of juice is been sold for.

Hence we would have

9.90 / 11

= 0.9

Hence the equation would be: c = 0.9j

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