Value rent-a-car rental a luxury car at a daily rate of $43.09 plus 4 cents per mile. a business person is allotted $100 for car rental each day. how many miles can the business person travel on the $100
1. If x-1 is a factor of p(x)=x^3-7x^2+15x-9, which of the following represents the complete factorization for p(x)?
A. (x-3)(x+4)(x+1)
B. (x-3)(x-3)(x-1)
C. (x-3)(x+3)(x-1)
D. (x-3)(x+3)(x+1)
2. The point (1,0) lies on the graph of p(x)=x^4-2x^3-x+2
True or false
Answer:
1. Option B is the correct answer.
2. The point (1,0) lies on the graph of p(x)=x⁴-2x³-x+2.
Step-by-step explanation:
1. Dividing x³-7x²+15x-9 with (x-1).
[tex]\frac{x^3-7x^2+15x-9}{x-1}=x^2-6x+9[/tex]
Factorizing x²-6x+9 we will get
x²-6x+9 = (x - 3)(x-3)
x³-7x²+15x-9 = (x-1)(x - 3)(x-3)
Option B is the correct answer.
2. We have p(x)=x⁴-2x³-x+2
That is y = x⁴-2x³-x+2
We have coordinates (1,0), substituting
y = 1⁴-2 x 1³-1+2 = 0
So when we are substituting x value as 1 we are getting y as zero, so the point lies in curve.
The Ye Ol' Sandwich Shop sells 4 different sandwiches, 6 different drinks, and 3 different desserts. How many different orders could you place if you decided to buy a sandwich and a drink?
If 8 is subtracted from 7 times a number the result is 34
What's the slope of the line ? And explain please
Identify the transformation that maps the figure onto itself.
Answer:
C is the answerStep-by-step explanation:
Rotate 180° about the point (2, -4) -- maps the figure onto itself.
A figure is mapped onto itself when the transformation results in the original pre-image for the image.
Answer: C is the answer
Step-by-step explanation:
Rotate 180° about the point (2, -4) -- maps the figure onto itself. A figure is mapped onto itself when the transformation results in the original pre-image for the image.
What are the SI base units for length and mass?
kilometer and gram
meter and gram
meter and kilogram
kilometer and kilogram
How to calculate percentage increase
A percentage increase can be calculated by first finding the difference between the new and original values, then dividing that difference by the original value. The result is then multiplied by 100 to get the percentage increase. This method can also help calculate inflation rates and various other mathematical problems.
Explanation:To calculate a percentage increase, you need to understand the basic principles of mathematics. Using the context provided, we can define calculating a percentage increase in the following way:
Steps to Calculate Percentage Increase:
For example, suppose the original price for a basket of goods was $20 and the new price is $25. First, find the difference: $25-$20 = $5. This is the increase. Then, divide the increase ($5) by the original price ($20) to get 0.25. Multiply by 100 and you get a 25% increase.
This method can be applied to many scenarios including calculating the rate of inflation. There are also online calculators and computers that can assist in finding these percentages quickly.
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Verify the identity. quantity one minus sine of x divided by cosine of x equals cosine of x divided by quantity one plus sine of x
One angle in a triangle measures twice the smallest angle, whereas the largest angle is nine times the smallest angle. find the measures of all three angles.
The measures of all three angles are 15, 30, and 135 degrees respectively.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
Let the smallest angle be represented as x,
one angle = 2x
largest angle = 9x
Therefore, x + 2x + 9x = 180° (by angles sum in a triangle)
12x = 180°
x = 15°
Then 2x = 15° x 2
= 30°
Also, 9x = 15° x 9
= 135°
Hence, The smallest angle is 15° and the one angle is 30°.
The largest angle is 135°.
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What is the answer to 7x+5-8x
what is the converse of the linear pairs theorem
A three sided regular polygon is called equilateral.
a. True
b. False
1996 gail devers won the 100-meter dash in the olympic games. her times was 10.94 seconds. what was her speed in meters per second?
Solving this problem is just pretty straight forward. We simply have to get the ratio of distance and time to get the speed. that is:
speed = distance / time
speed = 100 m / 10.94 s
speed = 9.14 m/s
Final answer:
Gail Devers' average speed during her Olympic win in the 100-meter dash with a time of 10.94 seconds is calculated to be approximately 9.14 meters per second using the formula speed = distance/time.
Explanation:
In 1996, Gail Devers won the 100-meter dash in the Olympic Games with a time of 10.94 seconds. To find her average speed in meters per second, we use the formula:
s = d / t
where s is speed, d is distance, and t is time. Given that the distance (d) is 100 meters and the time (t) is 10.94 seconds, we can calculate the average speed:
s = 100 m / 10.94 s ≈ 9.14 m/s
Therefore, Gail Devers' average speed during her Olympic 100-meter dash victory was approximately 9.14 meters per second.
Solve the equation n times 50 equals 5000 explain your solution
Point R is at (3, 1.3) and Point T is at (3, 2.4) on a coordinate grid. The distance between the two points is ____. (Input numbers and decimal point only, such as 8.2.)
Answer: The required distance between the two points R and T is 1.1 units.
Step-by-step explanation: Given that point R is at (3, 1.3) and Point T is at (3, 2.4) on a coordinate grid.
We are to find the distance between the two points R and T.
Distance formula :
The distance between the two points A(a, b) and B(c, d) is given by
[tex]d=\sqrt{(c-a)^2+(d-b)^2}.[/tex]
Therefore, the distance between the points R and T is given by
[tex]d=\sqrt{(3-3)^2+(2.4-1.3)^2}=\sqrt{0^2+1.1^2}=\sqrt{1.1^2}=1.1.[/tex]
Thus, the required distance between the two points R and T is 1.1 units.
The distance is 1.1 units, which is the distance between point R is at (3, 1.3) and Point T is at (3, 2.4) on a coordinate grid.
What is a distance formula?It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.
We have two points such that:
R (3, 1.3) and T (3, 2.4)
The distance formula for finding the distance between two points is:
If the points are [tex]\rm (x_1, y_1) \ \ and \ \ (x_2, y_2)[/tex]
[tex]\rm D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Here:
[tex]\rm x_1= 3\\\rm y_1= 1.3\\\rm x_2= 3\\\rm y_2= 2.4\\[/tex]
Then,
[tex]\rm D = \sqrt{(3-3)^2+(2.4-1.3)^2}[/tex]
[tex]\rm D = \sqrt{(1.1)^2}[/tex]
D = √1.21
D = 1.1 units
Thus, the distance is 1.1 units, which is the distance between point R is at (3, 1.3) and Point T is at (3, 2.4) on a coordinate grid.
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Which number produces an irrational number when multiplied by 0.4? A. B. 0.444... C. 3 D.
The number produces an irrational number when multiplied by 0.4 would be C) 3π.
What are irrational numbers?Irrational numbers are those real numbers that are not rational numbers.
Know that all natural numbers are integers, and all integers are rational numbers. That means natural numbers are not irrational.
π is irrational, and so is 3π
The expression 3π +0.4 is an irrational term as well.
If x is irrational and y is rational, then x + y is the irrational term.
Thus, choice C is the answer.
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A golf ball is dropped from a height of 30 ft to the pavement, and the rebound is one fourth the distance it drops. if after each descent it continues to rebound one fourth the distance dropped, what is the distance the ball has traveled when it reaches the pavement on its tenth descent?
The question deals with a sequence of movements of a golf ball falling and rebounding, which forms a geometric series. To find the total distance traveled by the ball on its 10th descent, we calculate the sum of the first 19 terms of this geometric progression.
Explanation:The student is asking about a geometric series problem, which involves a golf ball being dropped from a height and rebounding to a fraction of that height. The sequence of the distances covered by the ball forms a geometric progression.
Let's denote the initial height the ball is dropped from as a, which is 30 ft. The rebound height is one-fourth of the descent, so the rebound ratio, or common ratio r, is 1/4. The ball travels the initial height a plus the rebound distance each time it hits the pavement. This series continues with each rebound being one-fourth of the previous fall. We want to find the total distance traveled by the ball as it hits the pavement on its 10th descent.
The total distance traveled D after the ball hits the pavement for the 10th time is the sum of the first 10 terms of this geometric sequence. Using the formula for the sum of the first n terms of a geometric series, [tex]S_n = a(1-r^n)/(1-r)[/tex], where n is the number of terms, we can calculate the total distance.
For 10 descents, we have n = 19 since each descent and rebound except
the last descent counts as two movements:
[tex]S_{19} = 30(1-(1/4)^{19})/(1-(1/4))[/tex]
[tex]S_{19} = 30(1-(1/4)^{19})/(3/4)[/tex]
By calculating [tex]S_{19[/tex], we find the total distance traveled when the ball hits the pavement on its 10th descent.
For what positive value c does the equation logx = cx^4
Identify the transformation that maps the figure onto itself.
A) Reflect across the line y = -3
B) Reflect across the line x = 3
C) Rotate 180° about the point (3, -3)
D) Rotate 180° about the point (5, -5)
Answer:
The answer is A!!!
Step-by-step explanation:
−65y+19<−2y+41 solve for Y please
what are three ways to name a line with 5 points?
marcella divide 40.8 gallons of paint among 8 containers. how much paint is in each container
round 689002 to the nearest1,000,000
When given a raw score, explain how to use the normal curve to compare to the population
Simplify. −64x6y9−−−−−−−√3 assume all variables are nonnegative.
Answer:
[tex]-4x^2y^3[/tex]
Step-by-step explanation:
We have been given an expression [tex]\sqrt[3]{-64x^6y^9}[/tex]. We are asked to simplify our given expression.
Applying radical rule [tex]\sqrt[n]{-a}=-\sqrt[n]{a}[/tex], when n is odd, we will get:
[tex]-\sqrt[3]{64x^6y^9}[/tex]
We can rewrite terms of our given expression as:
[tex]-\sqrt[3]{(4)^3(x^2)^3(y^3)^3}[/tex]
Using radical rule [tex]\sqrt[n]{a^n}=a[/tex], we will get:
[tex]-4x^2y^3[/tex]
Therefore, simplified form of our given expression is [tex]-4x^2y^3[/tex].
G(a)=2a-1 h(a)=3a-3
Find (g-h)(-4)
Final answer:
To find (g-h)(-4), we calculate g(-4) as -9 and h(-4) as -15. Subtracting the latter from the former results in -9 + 15, which equals 6.
Explanation:
To find (g-h)(-4), we need to calculate the value of g at -4 and the value of h at -4, and then subtract the value of h from g.
The functions are defined as G(a)=2a-1 and h(a)=3a-3. Let's compute these step-by-step:
Calculate g(-4):
G(-4) = 2(-4) - 1
= -8 - 1
= -9
Calculate h(-4):
h(-4) = 3(-4) - 3
= -12 - 3
= -15
Calculate (g-h)(-4):
= g(-4) - h(-4)
= -9 - (-15)
= -9 + 15
= 6
Therefore, (g-h)(-4) equals 6.
Solve each problem and write your answer in scientific notation
A circle has its center at the origin, and (5, -12) is a point on the circle. How long is the radius of the circle?
5
12
13
Answer:
r = 13
Step-by-step explanation:
The radius of a circle that its center at the origin, and passes through point (5, -12) is 13 units
How to determine the length of the radius?The given parameters are:
Center, (a,b) = (0,0)Point, (x,y) = (5,-12)The length of the radius is calculated using:
[tex]r = \sqrt{(x - a)^2 + (y - b)^2}[/tex]
So, we have:
[tex]r = \sqrt{(5 - 0)^2 + (-12 - 0)^2}[/tex]
Evaluate
[tex]r = \sqrt{169}[/tex]
Solve the square root
r = 13
Hence, the radius is 13 units long
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1.What is the value of X? show calculations and formulas
What is the measure of one of the exterior angles of a regular octagon?