Im trying do it on my own just checking my answer

Answer:

  p(x) = x² +30x -375

Step-by-step explanation:

When a quadratic has real rational coefficients, any irrational or complex roots come in conjugate pairs.

A root of p means (x -p) is a factor of the polynomial. Here, we have roots of -15+10√6 and -15-10√6, so the factored form can be written ...

  p(x) = (x -(-15 +10√6))(x -(-15 -10√6))

Using the factoring of the difference of squares, we can write this as ...

  p(x) = (x +15)² -(10√6)²

Expanding the factored form, we can write the polynomial as ...

  p(x) = x² +30x +225 -600

  p(x) = x² +30x -375

Answer:

put four balls in each been

Step-by-step explanation:

The greatest common factor for the following sets of numbers are as follows,

24, 34, 567 : 1

23, 36, 52, 11 : 1

37, 53, 72, 11², 13 : 1

1, 2, 3, 4, 6, 8, 12, and 24 make up the number 24.

1, 2, 17, and 34 make to the number 34.

1, 3, 7, 9, 21, 27, 63, 81, 189, and 567 make up the number 567.

Because of this, the case's greatest common factor is 1.

The elements of 11 are: 1, 11

The 23 factors are: 1, 23,

1, 2, 3, 4, 6, 9, 12, 18, and 36 make up the number 36.

The sum of 52's factors is: 1, 2, 4, 13, 26, and 52.

Therefore, 1 is the number that these numbers have the most in common, and thus, 1 is the greatest common factor here.

The elements of 13 are: 1, 13, and

These are the 37 factors: 1, 37

These are the components of 53: 1, 53

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72 make up the number 72.

1, 11, and 121 make up the number 121.

Thus, the greatest common factor for 37, 53, 72, 121, 13 is again 1.

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Answer:

y ≤ 2.5x + 5

Step-by-step explanation:

first step is to obtain the equation of the line in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line

m = [tex]\frac{5-0}{0-(-2)}[/tex] = [tex]\frac{5}{0+2}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = 2.5x + 5 ← equation of line

since the line is solid then inequality will be ≤

the solution to the inequality is the blue region below the line , then

y ≤ 2.5x + 5 ← inequality represented by graph

The 8 cm circle radius and the location of the circle X gives the following values;

(a) tan(<XAB) = -(r - 8)/(2•r + 4) = (8 - r)/8

Which gives;

(b) <XAB is approximately 0.644 radians

(c) The area of the shaded region is approximately 3.107 cm²

8 × (8 - r) = 0.5 × 16 × (8 + r) × sin(A)

(8 - r) = (8 + r) × sin(A)

sin(A) = (8 - r)÷(8 + r)

(8 - r)² = 8² + (8 + r)² - 2×8×(8 + r)×cos(A)

16×(8 + r)×cos(A) = (8² + (8 + r)²) - (8 - r)²

Which gives;

cos(A) = ((8² + (8 + r)²) - (8 - r)²) ÷ (16×(8 + r))

cos(A) = (2•r + 4)/(r + 8)

tan(A) = ((8 - r)÷(8 + r))/( (2•r + 4)/(r + 8))

tan(A) = -(r - 8)/(2•r + 4) = (8 - r)/8

(8 - r)/(2•r + 4) = (8 - r)/8

8 = 2•r + 4

2•r + 4 = 8

Therefore;

(b) sin(A) = (8 - r)÷(8 + r)

sin(A) = (8 - 2)÷(8 + 2) = 0.6

Therefore;

<XAB = <A = arcsin(0.6) ≈ 0.644 rad

<XAB in degrees ≈ 36.87°

Angle at sector PXQ = 180° - 2 × (36.87°) ≈ 106.26°

Area of sector PXQ ≈ (106.26°/(360°)) × π × 2²

(106.26°/(360°)) × π × 2² ≈ 3.71

Area of sector APO ≈ (36.87°/(360°)) × π × 8² ≈ 20.59

Area of triangle AXB = 8 × (8-2) = 48

The shaded area is therefore;

48 - (2×20.59 + 3.71) ≈ 3.107

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a) The radius of the small circle is 2 centimeters.

b) The measure of the angle XAB is approximately equal to 51.340°.

c) The area of the shaded region is approximately equal to 2.423 square centimeters.

In this question we must analyze a geometrical system formed by three semicircles and a circle. The small circle touches the two side semicircles tangentially at points P and Q and the uppermost section of it also tangent to the central semicircle (point R).

(a) Therefore, we have to solve the following system of equations:

8² + h² = (8 + r)²      (1)

h + r = 8      (2)

By (2) in (1):

8² + (8 - r)² = (8 + r)²

32 · r = 64

r = 2

The radius of the small circle is 2 centimeters.

(b) The measure of the angle XAB is found by trigonometric functions:

tan m ∠ XAB = OX / AO

tan m ∠ XAB = 10 / 8

m ∠ XAB ≈ 51.340°

The measure of the angle XAB is approximately equal to 51.340°.

(c) The area of the shaded region if the area of the triangle AXB minus the areas of the three circular sections, that is:

A = 0.5 · (16 cm) · (10 cm) · sin 51.340° - (51.340° / 180°) · π · (8 cm)² - 0.5 · (77.320° / 180°) · π · (2 cm)²

A ≈ 2.423 cm²

The area of the shaded region is approximately equal to 2.423 square centimeters.

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The examples of exponential growth include bacteria population growth and compound interest and a real life example of exponential decay is radioactive decay.

Exponential growth is the pattern of data that shows sharper increases over time. Savings accounts with a compounding interest rate can show exponential growth.

There are many real-life examples of exponential decay. An example, is thatsuppose that the population of a city was 100,000 in 1980. Then every year after that, the population has decreased by 3% as a result of heavy pollution. This is an example of exponential decay.

One of the best examples of exponential growth is the observed in bacteria. It takes bacteria roughly an hour to be able to reproduce through prokaryotic fission. In this case, if we placed 100 bacteria in an environment and recorded the population size each hour, we would observe an exponential growth.

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Answer:

question 4:

the smaller building is 262.31 metres tall

Step-by-step explanation:

see the diagram attached:

1. draw a diagram:

2. as you can see in the diagram, a right angled triangle has been created.

3. convert the known angle from degrees and minutes to degrees.

4.  Identify which trigonometry ratio to use:

sin = [tex]\frac{opposite}{hypotenuse}[/tex]

cos = [tex]\frac{adjacent}{hypotenuse}[/tex]

tan = [tex]\frac{opposite}{adjacent}[/tex]

5. insert known values into the equation:

6. Interpreting the question with new knowledge:

the height of building 2 is 262.31 metres.

Answer:

The first option

Kindly award branliest

Answer:8 feet

Step-by-step explanation:

Step-by-step explanation:

1st : Vector translation.

a vector -8j ( 0 , -8 ) helped translate (x , y) => (x , y - 8)

2nd : rotation.

The only rotation that results in (-x , -y) is pi rotation.

formula : (x , y -8) => ( xcos(pi) - ysin(pi) , xsin(pi) + ycos(pi) )

substitute x & y-8 into x & y respectively of the formula above.

The expression to figure out today’s ticket sales is 7x+5y.

Today's ticket sale is less than that of yesterday's.

According to the question,

Adult tickets cost $7 each.

Child tickets cost $5 each.

Let the number of adult and child tickets sold be x and y respectively.

Expression for ticket sales= $(7x+5y)

Dexter has sold 125 kid's tickets and 100 adult tickets today.

Ticket sales = $(7*100+5*125) = $ 1325

He sold 120 adult tickets and 120 kid tickets yesterday.

Ticket sales = $(7*120+5*120) = $ 1440

Thus, from the expression it can be seen that yesterday' s ticket sale is greater than today's ticket sale.

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Answer:

5x^2-x+6

Step-by-step explanation:

That should work

Answer:

d: d [1, infinity) and r (-infinity, 0)

Step-by-step explanation:

right on the test :3 good luck dear!!

Using the binomial distribution, you would expected to draw a face card 8 times.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

For this problem, the parameters are given as follows:

Then the expected value is found as follows:

E(X) = np = 35 x 12/52 = 420/52 = 8.

Thus, you would expected to draw a face card 8 times.

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Ebony’s bank balance is $400 was Day 8 and this can be explained below.

Jade cannot be true because for every transaction made during withdraws, a little amount of money is collected and as such the amount will never remain $400.

Note that the scenario for the above to occur is:

On day 4, her balance = $400

On day 5, her balance = $40

On day 6, her balance = $400

On day 7, her balance = $400

On day 8, her balance = $400

Another fact is that since she deposited 400 at first, on day 8, there will be a 0 increase so the amount will still be 400.

Therefore, if the above is the case, one can deduce the fact that her balance will still be $400.

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Answer:

1/2

Step-by-step explanation:

50% = 50/100 = 1/2

1/2 of the students rode the first bus.

1 - 1/2 = 1/2

1/2 of the students rode the second bus.

Answer:

its log 5 7/8

Step-by-step explanation:

Answer:

See image

Step-by-step explanation:

Using a graphing calculator, first press the Y= button at the top left.

Then enter the equation given in the question.

Next, press 2nd then graph, and you will get the table. Put in whatever values for x to get y.

So your answer is 48, 18, 0, -6, 0, -18, 0, 48

The answers are :

Proof 1

2. Vertically Opposing Angles (V.O.A) (vertically opposite angles are equal)

Proof 2

3. Alternate angles (alternate angles of a transversal are equal)

4. ASA congruence (2 angles and 1 side, where the side is between the angles)

Answer:

Read Explanation

Step-by-step explanation:

The domain is a list of all possible x-values, this graph starts at 0 and proceeds to positive infinity, making the domain:

[0,∞)

The range is a list of all possible y-values, this graph starts at -1 and proceeds to positive infinity, making the range:

[-1,∞)

x-intercepts Are where the line crosses the x-axis, in this graph the line only crosses the x-axis at x of 2. Making its only x-intercept 2.

y-intercepts Are where the line crosses the y-axis, in this graph the line only crosses the y-axis at y of -1. Therefore its y-intercept is -1.

In function notation when a question asks for f(x) its asking for the y values at the given x-values. At x of 3 the y value equals 1.

1. Sea level (0 m) - 100%

2. Mid-level elevation (4,500 m) - 57%

3. Peak (8,850 m) - 33%

Identify the elevation and the percentage of oxygen available at each elevation.

Elevation has a significant impact on the amount of oxygen in the atmosphere. The oxygen level increases with decreasing height and decreases with increasing elevation. Thus, we have a situation where the oxygen concentration is highest at sea level or 0 elevations. The oxygen level drops dramatically when we ascend to greater elevations, say 4,500 m, making breathing difficult. Even at higher altitudes, such as 8,850 m, the oxygen level will drop significantly, making it necessary for a person to undergo extensive training and carry oxygen to survive.

1. Sea level (0 m) - 100%

2. Mid-level elevation (4,500 m) - 57%

3. Peak (8,850 m) - 33%

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The producer surplus at the equilibrium point is 1.0146

An equilibrium (or equilibrium point) of a dynamical machine-generated via an autonomous machine of everyday differential equations (ODEs) is a solution that doesn't change with time.

Equilibrium is the country in which the marketplace delivers and calls for stability each different, and as a result, expenses turn out to be solid. usually, an over-deliver of products or services reasons charges to head down, which leads to higher demand—at the same time as a below-supply or scarcity reasons costs to head up resulting in fewer calls.

The equilibrium equations (balance of linear momentum) are given in index form as(1.4)σji,j+bi=ρu¨i, I,j=1,2,3where σij are additives of (Cauchy) stress, ρ is mass density, and bi is body force additives.

Producer Surplus = area of shadestportion

Area of shaded portion = free of rect minus area of OneD

Aves of OABO=Now serving from

"[3√74-3/5]

= √(x+3)" de

=2 (2√6-√5)

(Jon= √46 = Fure=456-255

(x+3)+1

Area of rectangle OA BC =316

= 3√6

producer surplus = 3√6 - (ure -2√5)

= 2√3-66

= 1.0146

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Answer:

That's a reflection in the x axis.

Step-by-step explanation:

Triangle C is the mirror image  of B with the x axis acting as a mirror.

The function increased at the highest rate in the interval [1/8, 1/2], as can be seen from the function value and its interval values.

A function's maxima and minima are its highest and lowest values, respectively, either on the entire domain or inside a certain range. They are referred to as the function's extrema collectively. The plural forms of maximum and minimum for a function are respectively known as maxima and minima.

The extreme values of a function—their maximum and minimum values—are referred to by the words maxima and minima. Maximum refers to the maximum value or amount that is feasible. A function's biggest value within its range is known as its absolute maximum.

f(x)=6log2x-3

For the interval x ∈[2, 6]

f(x) ∈ [-0.678, 3]

For the interval x ∈ [1/8, 1/2]

f(x) ∈ [ -9.96, -5.32]

For the interval x ∈ [1, 2]

f(x) ∈ [-3, -0.67]

For the interval x∈ [1/2, 1]

f(x) ∈ [-5.32, -3]

The function increased at the highest rate in the interval [1/8, 1/2], as can be seen from the function value and its interval values.

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The simplified fraction expression results into [tex]\frac{1}{9}[/tex].

What is fraction?

A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

A number that represents a rational number is called a common fraction. The three main sorts of fractions are as follows. Proper fractions, incorrect fractions, and mixed fractions are these three types.

Given,

Expression = [tex]\frac{3^{-6}}{3^{-4}}[/tex]

                   = [tex]3^{-6-(-4)}[/tex]

                   = [tex]3^{-6+4}[/tex]

                   = [tex]3^{-2}[/tex]

                   = [tex]\frac{1}{3^2}[/tex]

                   = [tex]\frac{1}{9}[/tex]

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Answer:

2

Step-by-step explanation:

7+2n = 11

2n = 11-7

2n = 4

n = 4/2

therefore n = 2

The domain of f(x) is all set of real values while, the domain of g(x) is x ≤ -1 or x ≥ 2 and both functions have the same range

The functions are given as:

f(x) = x^4 - 2x^3 - 3x^2 + 4x + 4

g(x) = √(x^2 - x - 2)

Domain

The polynomial function f(x) has no restriction on its input.

So, the domain of f(x) is all set of real values

Set the radical of g(x) = √(x^2 - x - 2) greater than 0

x^2 - x - 2 ≥ 0

Factorize

(x + 1)(x - 2) ≥ 0

Solve for x

x ≥ -1 and x ≥ 2

Combine both inequalities

x ≤ -1 and x ≥ 2

So, the domain of g(x) is x ≤ -1 or x ≥ 2

Range

Using a graphical calculator, we have:

Hence, both functions have the same range

We have:

h(x) = (-x^2 + x)/(x^2 - x - 2)

Set the denominator to 0

x^2 - x - 2 = 0

The above represents the radical of the function f(x)

This means that the breaks in the domain of h(x) and the zeros of f(x) are the same

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Complete question

Let f(x) = x^4 - 2x^3 - 3x^2 + 4x + 4, g(x) = √(x^2 - x - 2) and h(x) = (-x^2 + x)/(x^2 - x - 2)

Part A: Use complete sentences to compare the domain and range of the polynomial function f (x) to that of the radical function g(x). (5 points)

Part B: How do the breaks in the domain of h (x) relate to the zeros of f (x)? (5 points)

Answer:

150

Step-by-step explanation:

because full capacity is 3/3, therefore you time 50 by 3, which will be 150 gallons

Answer:

2:3

Step-by-step explanation:

ratio = 4:7

4 parts = 48

1 part = 12

Mary has 48

Anne has 84

Mary will have 56

56:84 = 2:3

Her profit % was increased by 2.77%

Answer:

Solution Given:

discount =10%

profit =25%

S.P with 13% vat = Rs 5,085

S.P+Vat% of S.P= Rs 5,085

S.P(1+13%)=Rs 5,085

S.P=Rs 5,085/1.13

S.P =Rs 4,500

Again

M.P = S.P+discount% of M.P

M.P- discount% of M.P= Rs 4,500

M.P(1-10%)=Rs 4,500

M.P=Rs 4,500/0.9

M.P = Rs 5,000

Now

C.P= (S.P*100)/(1+profit%)

C.P=(4,500*100)/(100+25%)

C.P= Rs 3,600

Again

profit =S.P- C.P= Rs 4,500-Rs 3,600=Rs 900

Again

Due to the excessive demands of her items, she decreased the discount percent by 2%.

So,

New discount = 10%-2%=8%

New S.P= M.P -discount% of M.P

=M.P(1-discount%)

=Rs 5,000(1-8%)

=Rs 4,600

Again

Profit=S.P- C.P

New profit =Rs 4,600 - Rs 3,600=Rs 1,000

Profit% =profit/C.P*100%= 1000/3600*100=27.77%

Profit % increased =New profit%- profit%

=27.77-25

=2.77%