In 1980, the United States' national debt exceeded $9 billion dollars. Express the exact dollar amount in scientific notation.
How many lines of symmetry does a regular octagon have?
I don't understand how we do this PLEASE help me!!!
28 = (45 + KL)/2
56 = 45+ KL
KL = 56-45
KL = 11
What is the quotient (x3 – 3x2 + 3x – 2) ÷ (x2 – x + 1)?
-2/x+1
the / is a fraction symbol xxx
the sum of 3 numbers is 26. the second number is twice the first and the third number is 6 more than the second. find the number
Answer:
the numbers are 4, 8, 14
Step-by-step explanation:
If we subtract 6 from the third number and from the total, we find that we now have 5 times the first number for a total of 20.
The first number is 4.
The second number is 2×4 = 8.
The third number is 8 + 6 = 14.
One side of triangle is half the longest side. the third side is 7 feet less than the longest side. the perimeter is 43. find all three sides.
How much dirt is there in a hole 3 feet deep, 6 ft long and 4 ft wide?
the volume of the hole would be 3 * 6 * 4 =72 cubic feet.
However, since it is a hole, there would be no dirt in it.
A baseball pitcher pitches a ball at the speed of 83 mph what conversion factors can be used to find the speed of the ball in feet per second
Answer: [tex]121.73\text{ feet per second}[/tex]
Step-by-step explanation:
Given : The speed of a baseball pitcher = 83 mph
or 83 miles per hour
Since , we know that
1 mile= 5280 feet
1 hour = 3600 seconds
Then, 83 miles per hour = [tex]\dfrac{\text{83 mile}}{\text{1 second}}=\dfrac{83\times5280\text{ feet}}{1\times3600\text{ seconds}}[/tex]
[tex]\approx121.73\text{ feet per second}[/tex]
Hence, the speed of the ball in feet per second = [tex]121.73\text{ feet per second}[/tex]
How would you represent 3 quarter notes as a fraction?
12 sixteen notes have a nice day
The average wind speeds for one year at 44 climatic data centers around the United States are as follows:
9.0, 6.9, 9.1, 9.2, 10.2, 12.5, 12.0, 11.2, 12.9, 10.3, 10.6, 10.9, 8.7, 10.3, 10.6, 10.9, 8.7, 10.3, 11.0, 7.7, 11.4, 7.9, 9.6, 8.0, 10.7, 9.3, 7.9, 6.2, 8.3, 8.9, 9.3, 11.6, 10.6, 9.0, 8.2, 9.4, 10.6, 9.5, 6.3, 9.1, 7.9, 9.7, 8.8, 6.9, 8.7, 9.0, 8.9, 9.3
a) Make a stem plot of the average wind speeds data. The frequency in the stem for 9 to 9.9 is?
b) The first quartile for the wind speed data set is?
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. x2 + 4x + 3 = 0
HELP ME PLEASE!
Peter walks 30 feet away from his house and places a mirror on the ground. He backs 6 feet away from the mirror so that he can see the tip of the roof. Peter's eyes are 5 feet above the ground. Peter and the house are both perpendicular to the ground. The angles between the top of the house, the mirror, and the ground and between Peter's eyes, the mirror, and the ground are congruent as shown in the image below:
Image depicts a mirror on the ground between a person and a house. The mirror is 6 feet away from the person and 30 feet away from the house.
What is the height of the house?
By setting up a proportion based on the similar triangles formed by Peter's line of sight and the analogous line from the top of the house to the mirror, we find that the house is 25 feet tall.
According to the Law of Reflection and the information provided, we have two similar triangles: one formed by Peter's eyes, the mirror, and the point on the ground directly below his eyes, and the other formed by the top of the house, the mirror, and the point on the ground directly below the top of the house.
The first triangle has a height of 5 feet (Peter's eye level) and a base of 6 feet (the distance from Peter to the mirror). The second triangle's height is what we are trying to find (height of the house), and its base is 30 feet (distance from the house to the mirror).
Because the triangles are similar, the ratios of their corresponding sides are equal. So, we can set up the following proportion:
Height of Peter's eyes / Distance to mirror = Height of the house / Distance to mirror from house
5 feet / 6 feet = Height of the house / 30 feet
Now, cross-multiply to solve for the height of the house:
5 feet * 30 feet = Height of the house * 6 feet
Height of the house = (5 * 30) / 6
Height of the house = 150 / 6
Height of the house = 25 feet
Therefore, the height of the house is 25 feet.
Simplify.
Square root of 121m^8n^4
A. 11mn
B. 11m^2n^2
C. 11m^4n^2
Answer:
B
Step-by-step explanation:
no
Quadrilateral ABCD is a parallelogram with diagonals that intersect at point E. If /,/, /, and /, solve for x.
A.
x = 2
B.
x = 4
C.
x = 6
D.
x = 8
Need help with math problem
Multiply
(3x – 7)(3x – 5)
A.
9x 2 + 6x + 35
B.
9x 2 + 36x + 35
C.
9x 2 – 36x – 35
D.
9x 2 – 36x + 35
What are the solutions of the equation x6 + 6x3 + 5 = 0? Use factoring to solve.
Consider the equation [tex] x^6+6x^3+5=0 [/tex].
First, you can use the substitution [tex] t=x^3 [/tex], then [tex] x^6=(x^3)^2=t^2 [/tex] and equation becomes [tex] t^2+6t+5=0 [/tex]. This equation is quadratic, so
[tex] D=6^2-4\cdot 5\cdot 1=36-20=16=4^2,\ \sqrt{D}=4,\\ \\ t_{1,2}=\dfrac{-6\pm 4}{2} =-5,-1 [/tex].
Then you can factor this equation:
[tex] (t+5)(t+1)=0 [/tex].
Use the made substitution again:
[tex] (x^3+5)(x^3+1)=0 [/tex].
You have in each brackets the expression like [tex] a^3+b^3 [/tex] that is equal to [tex] (a+b)(a^2-ab+b^2) [/tex]. Thus,
[tex] x^3+5=(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25}) ,\\x^3+1=(x+1)(x^2-x+1) [/tex]
and the equation is
[tex] (x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25})(x+1)(x^2-x+1)=0 [/tex].
Here [tex] x_1=-\sqrt[3]{5} , x_2=-1 [/tex] and you can sheck whether quadratic trinomials have real roots:
1. [tex] D_1=(-\sqrt[3]{5}) ^2-4\cdot \sqrt[3]{25}=\sqrt[3]{25} -4\sqrt[3]{25} =-3\sqrt[3]{25} <0 [/tex].
2. [tex] D_2=(-1)^2-4\cdot 1=1-4=-3<0 [/tex].
This means that quadratic trinomials don't have real roots.
Answer: [tex] x_1=-\sqrt[3]{5} , x_2=-1 [/tex]
If you need complex roots, then
[tex] x_{3,4}=\dfrac{\sqrt[3]{5}\pm i\sqrt{3\sqrt[3]{25}}}{2} ,\\ \\x_{5,6}=\dfrac{1\pm i\sqrt{3}}{2} [/tex].
Write a conditional that multiplies the value of the variable pay by one-and-a-half
The student came to the conclusion that the system has infinitely many solutions, which is not correct. Describe the error was the student work being shown.
In a survey, the planning value for the population proportion is p*=.35. how large a sample should be taken to provide a 95% confidence interval with a margin of error of .05 (to the nearest whole number)?
WILL GIVE A BRAINLIEST PLEASE HELP!!!
Use the formula below to find the 6th term in the geometric sequence.
a(n)=(5)x(3/2)n-1
A.
5
B.
15/2
C.
1,215/32
D.
3,645/64
Need help geometry ^^^
What is i^16 simplified
On his birthday newton was 14 years old and his father was 41 newton noticed that his age was his fathers age with the digits reversed how many years later with their ages next have their digits reversed
When the age of Newton will be 25 years , the age of his father will be reversed i.e., 52 yrs.
It is given that when Newton was 14 years old , his fathers age was 41 yrs.
We have to find out that at what age of Newton his fathers age will be reversed again ?
Solve for the value of x ; 10 x - 14 = 12x - 28 ?
The value of x will be 7.
Let's assume the tens place as x and one's place as y.
The actual number will be ; 10 x + y.
Reverse numbers pairs can be written as (10x+y) and (10y+x).
As the age of Newton's father is 41 yrs when he is 14 yrs old , so we have ;
(10x+y) - (10y+x) = 41–14 = 27
Hence , we can say that the age difference between Newton and his father is 27 years. This age difference will be same forever.
So ;
(10x+y) - (10y+x) = 27
and we have to find all values of x and y that will satisfy this equation.
⇒ (10x+y) - (10y+x) = 27
⇒ 9x - 9y = 27
⇒ x - y = 3
For all x’s and y’s who have their difference as 3 will answer the question. For example , (4,1) (5,2) (6,3) (7,4) (8,5) …. and so on.
Since Newton's father age today is 41 yrs.
The next age to satisfy the condition is 52 yrs.
This makes Newton’s age to be 52 - 27 = 25 which is the reverse of 52.
So , the answer of the question is that Newton should be of 25yrs , for his age to be the reverse of his father’s age.
Thus , when the age of Newton will be 25 years , the age of his father will be reversed i.e., 52 yrs.
To learn more about algebra click here ;
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A model rocket is launched with an initial upward velocity of 32 m/s. The rocket's height h (in meters) after t seconds is given by the following.
h=32t-5t^2
Find all values of t for which the rocket's height is 10 meters.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Answer:
0.33 and 6.07
Step-by-step explanation:
What is 51/4 ÷ 22/7 ? A. 1219/64 B. 219/64 C. 2 D. 12
B is correct :
5 1/4 = 21/4
2 2/7=16/7
21/4x7/16=147/64=2 19/64
Find the surface area of the sphere.
Round to the nearest hundredth.
The equation of the straight line of slope 3 passing through the point (2, 5) may be written as
HELP might fail class
One key advantage for including multiple predictor variables in the equation of a regression line is that it allows you to
Lola takes the train from Paris to Nice. The distance between the two cities is about 921,000 meters. If the train travels at a speed of 307 kilometers per hour, how long will it take Lola to travel from Paris to Nice
Answer:
First,you need to convert 307km/hr into 85.2 meter per second.The formula for finding time is the distance divided by the speed.So,the answer is 10809 second,about 3 hours.