p² +6r - 27
factoring quadratics

See the graphs below

FOR GRAPH 1:

Let's take:

[tex]f(x)=sin(x)[/tex]

Let's transform this function as follows:

Step 1. Horizontal compression by 1/2:

[tex]f(x)=sin(2x)[/tex]

Step 2. Vertical stretch:

[tex]f_{1}(x)=2sin(2x)[/tex]

Step 3. Vertical shifting 3 units down

[tex]f_{2}(x)=2sin(2x)-3[/tex]

Finally:

[tex]h(x)=f_{2}(x)=2sin(2x)−3[/tex]

The graph is shown in the First Figure below.

FOR GRAPH 2:

Applying a similar method we get:

The graph is shown in the Second Figure below.

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To graph h(x) = 2sin(2x) - 3 and g(x) = 4cos(2x) - 2, multiply the sine and cosine functions by 2 and 4 for amplitude, adjust the period by halving it due to the 2x factor, and shift vertically by -3 and -2 respectively.

To graph h(x) = 2sin(2x) - 3 and g(x) = 4cos(2x) - 2, you can follow these steps:

The resulting graphs will show sine and cosine waves with adjusted amplitudes, periods, and vertical shifts. Remember to use 3.14 as an approximation for π to determine the x-values where key points like maxima, minima, and intercepts occur.

Answer:

7 and 1/4 or 7.25

Step-by-step explanation:

28/4 = 7

1/4 = 0.25

7 + 0.25 = 7.25

Answer:

[tex]\frac{29}{4}[/tex] or [tex]7\frac{1}{4}[/tex]

Step-by-step explanation:

29/4 is the most simplified it can get, if you want it as a mixed fraction then it is 7 1/4.

Answer:

24 dollars

Step-by-step explanation:

6$for each one if u multiply then you'll get the number

Answer:

$24.00

Step-by-step explanation:

hope i helped

Answer:

Step-by-step explanation:

B 4C and log 625

Final answer:

The average speed of the second car is calculated by subtracting the distance traveled by the first car from the total distance apart, and then dividing by the time elapsed. The second car has an average speed of 50 mph.

Explanation:

The student is asking for help to find the average speed of the second car when two cars, starting at the same point and traveling in opposite directions, end up being 520 miles apart after 4 hours. The first car travels at an average speed of 80 mph.

To solve this, we need to calculate the total distance covered by both cars in the time frame given. We already know the total distance apart is 520 miles.

The first car travels at 80 mph for 4 hours, covering 80 mph * 4 h = 320 miles. To find out how far the second car traveled, subtract the distance covered by the first car from the total distance apart: 520 miles - 320 miles = 200 miles.

Finally, to find the average speed of the second car, divide the distance traveled by the time. Thus, the second car's average speed is 200 miles / 4 h = 50 mph.

Final answer:

To find the average speed in mph of the other car, divide the total distance traveled by the time. Subtract the first car's average speed from the total speed to find the other car's average speed.

Explanation:

To find the average speed in mph of the other car, we need to determine the total distance traveled. Since the two cars are 520 miles apart at the end of 4 hours, we can divide the total distance by the time to find the average speed.

The first car has an average speed of 80 mph, so the total distance traveled by both cars is 80 mph * 4 hours = 320 miles.

The other car's average speed can be found by subtracting the first car's average speed from the total speed: 320 miles - 80 mph = 240 mph.

Answer:

[tex]P(Blue)=0.60[/tex]

Step-by-step explanation:

Probability: [tex]Probability\ of\ an\ event=\frac{favourable\ outcome}{total\ outcome}[/tex]

[tex]Total\ marbles=20\\\\Hence\ total\ outcomes=20\\\\Blue\ marbles=12\\\\Hence\ favourable\ outcomes=12\\\\P(Blue)=\frac{12}{20}\\\\P(Blue)=\frac{2\times 6}{2\times 10}\\\\P(Blue)=\frac{6}{10}\\\\P(Blue)=0.60[/tex]

Answer:

Approximately there are 3,785.6 milliliters in one gallon

Step-by-step explanation:

Let's find out how many milliliters are there in one gallon.

1 US Cup = 236.6 ml (actual equivalence)

Let's recall that:

16 US Cups = 1 US Gallon

Therefore,

1 US Gallon = 16 * 236.6 ml

1 US Gallon = 3,785.6 ml

Approximately there are 3,785.6 milliliters in one gallon

Answer:

You have a full amount of chocolate cake and you eat [tex]\frac{1}{3}[/tex] part of the cake and left the remaining amount for the next day. So, what amount of cake that you left for the next day?

Step-by-step explanation:

We have to make a subtraction problem so, that the answer to the problem is [tex]\frac{2}{3}[/tex].

Now, the problem may be described as follows :

You have a full amount of chocolate cake and you eat [tex]\frac{1}{3}[/tex] part of the cake and left the remaining amount for the next day. So, what amount of cake that you left for the next day?

So, the solution is [tex](1 - \frac{1}{3}) = \frac{2}{3}[/tex] amount of the cake. (Answer)

Answer:

d. 5

Step-by-step explanation:

Answer: 48

Step-by-step explanation:

You can either add 8 six times or get a calculator and solve.

Answer:Perimeter is the limit of any given geometric figure. Circumference is just the name given to a circle’s perimeter, in other words, the circle’s limit, its edge.

The reason for this is because the perimeter is, by definition, the sum of the lenghth of every side of any given geometric figure. A circle has either no sides, or number of sides, so its perimeter has to be treated differently.

Remember that π (Pi) equals 3.141592 approximately. This is a constant, meaning that no matter what circle you are studying, Pi will always have the same value. It is the relation between the diameter and the lenght of its circumference. A circle with diameter xwill travel 3.141592x before it completes a revolution. This is where Pi comes from.

So the difference would be that a “normal” perimeter is only the sum of the sides. A circumference is the perimeter of a circle, given a diameter and the constant value of Pi, that derives from other properties of the circle, and not by its sides (remember a circle has either none or nnumber of sides).

Answer:

[tex]12+c-2d[/tex]

Step-by-step explanation:

The correct expression of the problem is

[tex]4\left(3 + \dfrac14c - \dfrac12d\right)[/tex]

Applying the distributive property

[tex]4\left(3 + \dfrac14c - \dfrac12d\right)=(4*3)+(4*\dfrac{1}{4} c)-(4*\dfrac{1}{2} d)=(12)+(c)-(2d)[/tex]

therefore

The equivalent expression is equal to

[tex]12+c-2d[/tex]

Answer:

option 2: (-1,170, -23,400) and (170, 3,400)

Step-by-step explanation:

correct answer for e2020

Answer:

B. (-1,170, -23,400) and (170, 3,400)

Step-by-step explanation:

Answer:

yessssssssssssssssssssssssss

Answer:

PRIME

Step-by-step explanation:

the GCF of 64 and 27 is 1

>therefore the polynomial is already factored and can’t be factored further.

Sophia's expression is incorrect because she did not multiply 2 by -1 correctly.

Ursula's expression is incorrect because she cannot simplify 2-4x.

A correct equivalent expression is 6-2+4x.

What can I say? I got this correct on ttm.

Hope you have a great day~

Answer:

x-int: (2, 0)

y-int: (0,8)

(8-0)/(0-2)= 8/-2=  -4

y - 0 = -4(x - 2)

y = -4x + 8

Step-by-step explanation:

Answer: 200+7 * X=

Step-by-step explanation:

Answer:

sum = addition, times = multiplication, a number = a variable (let's say n)

Use this written out problem to write the algebraic expression?

200 + 7n    or   7n +200   (both are the same)

Step-by-step explanation:

Answer:

Step-by-step explanation:

C! hopes this helps

Answer:

0.25

Step-by-step explanation:

Scale factor = ratio of the sides

Assuming the first rectangle is with shorter side 6,

Scale factor = 1.5/6 = 15/60 = 1/4 = 0.25

Divide the new length by the original length:

The arrow points from 6 to 1.5, so the new length is 1.5 and the original length was 6.

1.5 / 6 = 0.25. The scale factor was 0.25

Answer:

x = 5

Step-by-step explanation:

Start by distributing the 5 to remove parentheses.  To do this multiply the numbers and variable in the parentheses by 5.

10x - 20 - 11 = 4 + 3x

Next. you want to get the variables to one side.  This is done by subtracting 3x from both sides.

7x - 20 - 11 = 4

Now solve the -20 - 11.

7x - 31 = 4

You need to have the variable all by itself.  To do this, first add -31 to both sides.

7x = 35

Finally divide by 7.

x = 5

Hope this helped.  

Eileen was 600 feet away from the finish line before the race began.

Step-by-step explanation:

Step 1; Eileen rode at a speed of 20 feet per second whereas Andrew rode at a speed of 15 feet per second. So for every second that passes the distance in between decreases by 5 seconds. Assume x is the number of seconds at which the distance in between is 0. The distance in between at the beginning of the race is 150 feet due to the headstart.

Distance between them = Decreasing distance every second × x

150 feet = 5 feet/ second × x

x = 150 feet / 5 feet/second = 30 seconds.

So it takes Eileen 30 seconds to cover the distance between her and Andrew and cross the finishing line at the same time.

Step 2; The race lasted for 30 seconds so we can find the distance Andrew and Eileen traveled by multiplying their speed per second with the total number of seconds.

Distance Andrew traveled = speed per second × total number of seconds

= 15 feet per second × 30 seconds = 450 feet

Distance Eileen traveled = speed per second × total number of seconds

= 20 feet per second × 30 seconds = 600 feet

Graph plot;

The X-axis is time with 5 seconds for each cm

the y-axis is distance with 100 feet for each cm.

Eileen's plot (0,0), (5,100), (10,200), (15,300), (20,400), (25,500), (30,600).

Andrew's plot (0,150), (5,225), (10,300), (15,375), (20,450), (25,525), (30,600).

Supplementary angles add up to 180 degrees. If one angle measures 56 degrees, the other supplementary angle equals 180-56 which equals 124 degrees. So, the second angle measures 124 degrees.

Supplementary angles are two angles that add up to 180 degrees. Therefore, if one of these angles measures 56 degrees, the other one must be the value that when added to 56 completes 180. We can find it by using the formula for supplementary angles: angle B = 180 - angle A.

So, to find the measure of the second angle, we subtract the measure of the first angle (56 degrees) from 180 degrees.

Angle B = 180° - 56° = 124°.

Therefore, the second angle measures 124 degrees (Choice D).

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Answer:

17.78 meters

Step-by-step explanation:

Let

x ----> the horizontal distance, in meters, to home plate

[tex]\theta[/tex] ----> the angle of vision

we know that

[tex]tan(\theta)=\frac{40}{x}[/tex] ----> by TOA (opposite side divided by the adjacent side)

we have

[tex]tan(\theta)=\frac{9}{4}[/tex]

substitute

[tex]\frac{9}{4}=\frac{40}{x}[/tex]

solve for x

[tex]x=40(4)/9\\x=17.78\ m[/tex]

Number of pounds of macadamia nuts is 8 pounds and number of pounds of almonds is 4 pounds.

Step-by-step explanation:

Step 1:

Given total pounds of mixture = 12 pounds, cost of macadamia nuts per pound = $9, cost of almonds per pound = $5.25, total cost of mixture per pound = $7.75.

Let number of pounds of macadamia nuts be x and number of pounds of almonds be 12-x.

Step 2:

Form an equation using the above information.

⇒ 9x + 5.25 (12-x) = 12 × 7.75

⇒ 9x + 63 - 5.25x = 93

⇒ 9x - 5.25x = 30

⇒ 3.75x = 30

⇒ x = 8

Number of macadamia nuts is 8 pounds.

Step 3:

Calculate number pounds of almonds

⇒ Number of pounds of almonds = 12 - x = 4 pounds.

Answer:

-9 is correct

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

<3

Answer:

4 years

Step-by-step explanation:

9% of the population is 1800. subtract that to get 18200. thats 1 year. subtract again to get 16400. thats 2 years. again to get 14600. 3 years. and then again to get 12800 which is less than 13000. so its 4 years.

Final answer:

Using the exponential decay formula, it takes approximately 8 years for a town's population of 20,000 to decrease to fewer than 13,000 at a yearly decrease rate of 9%.

Explanation:

The question involves calculating the number of years it takes for a town's population to decrease to fewer than 13,000 given an initial population of 20,000 and a yearly decrease rate of 9%. To solve this, we use the formula for exponential decay, which is P(t) = P₀[tex]e^{rt}[/tex], where P(t) is the population at time t, P0 is the initial population, r is the rate of decrease, and t is the time in years.

Substituting the given values, we have 13,000 = 20,000[tex]e^{-0.09t}[/tex]. Solving for t, we take natural logarithms on both sides, which gives ln(13,000/20,000) = -0.09t, leading to t = ln(13,000/20,000) / -0.09. This calculation yields t ≈ 8.04 years, meaning the population will be fewer than 13,000 in about 8 years.

This is a practical application of exponential decay in analyzing population dynamics, highlighting how populations decrease over time under consistent negative growth rates.

Answer:

15 units²

Step-by-step explanation:

The figure is composed of 2 rectangles.

The rectangle on the left has

A = 4 × 3 = 12 units²

The rectangle on the right has

A = (3 - 2) × (7 - 4) = 1 × 3 = 3 units²

Thus area of figure = 12 + 3 = 15 units²

To find the area of an irregular polygon, divide it into regular shapes and sum their areas. The area of a square is simple: side length squared. When scaling, areas of similar shapes increase by the square of the scaling factor.

To calculate the area of an irregular polygon, we often need to divide it into regular shapes such as triangles, rectangles, or squares. Once we do that, we can calculate the area of each shape and then sum all the areas to find the total area of the irregular polygon. For instance, if an irregular shape fits within a square of side a, its area is less than a² based on the premise that the area of a circle inscribed in a square is smaller than the square's area yet larger than half. For a square, the calculation is relatively straightforward with the formula for area being side length squared (a²).

Calculating the area becomes even more important when applied to real-life examples, such as surveying land parcels which can have highly irregular outlines. The concept is similar to understanding the relationship between the area of a square and its side length when measuring larger plots of land like a state or a carpet on a house's blueprint. We use scales or conversion factors to translate a drawn measurement to actual size.

The comparison of areas can also be seen in the example where Marta's larger square's area is four times that of the smaller one because areas of similar shapes scale by the square of the scaling factor (in this case, 2).

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Answer:

20-2x=16

Divide all by 2

10-x=8

x=2,

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

y = kx

2⅔ = k(¼)

8/3 = k/4

k = 4×8/3 = 32/3

y = (32/3)x

y = (32/3)(1⅛)

y = (32/3)(9/8)

y = 3×4 = 12