Answers
thus
[tex]\bf \stackrel{0}{h}=-16t^2+64\implies 0=-16t^2+64\implies 16t^2=64\implies t^2=\cfrac{64}{16} \\\\\\ t^2=4\implies t=\sqrt{4}\implies t=\stackrel{seconds}{2}[/tex]
as far as 5, is correct, however
[tex]\bf \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{15^2+8^2}\implies c=\sqrt{289}\implies c=17[/tex]
Related Questions
y=1x-4 in standard form
Answers
ay+bx=c
so, we can write:
y-x=-4
That's it....
y=x-4
Bess practices trumpet 1/2 hr on Monday and 1 3/5 hr on Wednesday.
How many hours does Bess practice trumpet?
Answers
IF b= -8 and a= 3 what are the steps to solve the following:
b -a - 3 =
Answers
(-8) - 3 - 3 is the same as saying -8 + -3 + -3
So, -8 + -3 + -3 or (-8) - 3 - 3 = -14
Thus the answer is: 14
Besides the 90° angle measure, what are the other two angle measures of a right triangle with side lengths 5, 12, and 13? Round to the nearest degree.
Answers
Let α be the angle opposite to the side with a length of 12 units, then according to the Law of sines:
[tex] \frac{13}{sin90^o}= \frac{12}{sin \alpha } \ \ \to \ \ sin \alpha = \frac{12 \cdot sin90^o}{13}= \frac{12*1}{13} \approx 0.923 \ \ \to \ m\angle \alpha \approx 67^o[/tex]
In a triangle, the three interior angles always add to 180° ⇒
third angle = 180 - 90 - 67 = 23°
Answer:
67° and 23° (to the nearest degree).
The other two angles are 23 degrees and 67 degrees.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
Given a right angled triangle with one angle 90 degrees.
We need to find the other two angle measures of a right triangle with side lengths 5, 12, and 13
The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.
The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.
The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.
In this problem, the hypotenuse is the largest size of 13.
The angle opposite to the side of length 5 is found as follows:
sinθ=5/13
θ=sin⁻¹5/13
θ=23
By angle sum of 3 angles is of 180º, the other angle is of 67º.
Hence, the other two angles are 23 degrees and 67 degrees.
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On a Venn diagram, a value that represents what two circles have in common is written outside of both circles. True or false
Answers
Values that are in common with both circles will be inside both circles. These values will be in the overlapping region of the two circles.
How do write 21,070 in standard form
Answers
Final answer:
The number 21,070 is already in standard form. Standard form is a straightforward expression of a number as commonly written, without the need for scientific notation for simple numbers like this one.
Explanation:
The number 21,070 written in standard form is simply 21,070 itself. In mathematics, standard form refers to the way a number is commonly written. This number is already in standard form because it is expressed in a direct and straightforward manner. There is no need for further simplification or conversion. When numbers are very large or very small, they can be cumbersome to write out in full, which is why scientists and mathematicians may use scientific notation to express them.
For instance, if we had a larger number like 77,123,450, we could write it in scientific notation as 7.712345 × 10⁷, emphasizing that it is 7.712345 times ten to the seventh power.
For the provided number 21,070, no such conversion is necessary, and it remains 21,070 in standard notation.
A survey asked a group of people the size of their households. The results are shown in the frequency distribution.
What is the mean of the frequency distribution? Round your answer to the nearest tenth.
Household size 1 2 3 4 5
f 2 4 6 5 2
3
3.1
3.8
11.6
Answers
Answer: 3.1
Step-by-step explanation:
The mean of the frequency distribution is 3.1. Which is the correct answer would be an option (B)
What is arithmetic mean?
Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean. One of the basic methods used to acquire a result, the term "Mean" is commonly used in the field of statistics.
The formula for the mean of a given set of data is as follows:
Mean = Sum of Observations/Total number of observations
Given the frequency distribution as :
Household size (x) Frequency (f) fx
1 2 1 × 2 = 2
2 4 2 × 4 = 8
3 6 3 × 6 = 18
4 5 4 × 5 = 20
5 2 5 × 2 = 10
Summation of fx = (Σfx) = 2 + 8 + 18 + 20 + 10 = 58
Total frequency = (Σf) = 2 + 4 + 6 + 5 + 2 = 19
⇒ Mean = Σfx/Σf
⇒ 58/ 19
⇒ 3.1
Thus, the mean of the frequency distribution is 3.1.
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If 4 bushels of rye weigh 76 lb, how much do 8.5 bushels of rye weigh?
Answers
19 x 8.5 = 161.5 lbs for 8.5 bushels
8.5 bushels of rye weigh 161.5 lbs
Answer: 161.5 lbs
Step-by-step explanation:
Given : The weight of 4 bushes of rye = 76 lb
By applying UNITARY METHOD, the weight of 1 bush will be :-
[tex]\text{ Weight of 1 bush}=\dfrac{76}{4}\\\\\Rightarrow\ \text{ Weight of 1 bush}=19\text{lb}[/tex]
Now, the weight of 8.5 bushes = [tex]8.5\times19[/tex]
The weight of 8.5 bushes = 161.5 lbs
Therefore, the weight of 8.5 bushels of rye= 161.5 lbs
Hence, the required answer is "161.5 lbs".
McDonald's is the king of the burger world, as it has more hamburger joints than any other restaurant chain. In 2013, McDonald's had 1427 locations in Canada. If the population of Canada was approximately 35.16 million citizens in 2013, what was the number of McDonald's restaurants per capita in Canada in 2013? Express your answer in scientific notation rounded correctly to three decimal places.
Answers
In 2013, there were approximately 4.509 McDonald's restaurants per 100,000 people in the US.
To calculate the number of McDonald's restaurants per capita in the US in 2013, we divide the total number of McDonald's locations (14267) by the population of the US (316,500,000).
[tex]\[ \text{McDonald's per capita} = \frac{14267}{316500000} \][/tex]
Performing the division, we get [tex]\( 4.509 \times 10^{-5} \)[/tex].
This means there were approximately 4.509 McDonald's restaurants per 100,000 people in the US in 2013.
So, the number of McDonald's restaurants per capita in the US in 2013 is [tex]\( 4.509 \times 10^{-5} \) or \( 4.509 \times 10^{-5} \)[/tex] McDonald's per person.
Find the scale factor if an airplane is 87 feet long; 2 inches = 15 feet.
Answers
two inches to15ft is to x inches to 87ft
A boat traveled downstream a distance of 80 mi and then came right back. If the speed of the current was 7 mph and the total trip took 3 hours and 20 minutes, find the average speed of the boat relative to the water.
Answers
going forth and back is 80 miles, thus upstream as well as downstream is just 80 miles.
now, bear in mind that say, the boat has a "still water" of "b", when going downstream, is not going "b" fast is going "b+7" because the current's is adding to it, likewise when is going upstream is going "b-7" because is going against the current and thus the current is eroding speed from it.
now, the whole trip took 3 hours and 20 minutes, bearing in mind that 20 minutes is 1/3 of an hour, so is 3 and 1/3 hours, or 10/3 of hours.
if say it took "t" hours going down, then going up it took the slack from 10/3 and "t", that is, it took "10/3 - t".
[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ Downstream&80&b+7&t\\ Upstream&80&b-7&\frac{10}{3}-t \end{array} \\\\\\ \begin{cases} 80=t(b+7)\implies \frac{80}{b+7}=\boxed{t}\\\\ 80=(b-7)\left(\frac{10}{3}-t \right)\\ ----------\\ 80=(b-7)\left(\cfrac{10}{3}- \boxed{\frac{80}{b+7}} \right) \end{cases}[/tex]
[tex]\bf \cfrac{80}{b-7}=\cfrac{10}{3}-\cfrac{80}{b+7}\implies \cfrac{80}{b-7}=\cfrac{10(b+7)-80(3)}{3(b+7)} \\\\\\ \cfrac{80}{b-7}=\cfrac{10b+70-240}{3(b+7)}\implies \cfrac{80}{b-7}=\cfrac{10b-170}{3(b+7)} \\\\\\ 3(b+7)80=(b-7)(10b-170)\\\\\\ 240(b+7)=(b-7)(10b-170) \\\\\\ 240b+1680=10b^2-240b+1190\implies 0=10b^2-480b-490 \\\\\\ 0=b^2-480b-49\implies 0=(b-49)(b+1)\implies b= \begin{cases} \boxed{49}\\ -1 \end{cases}[/tex]
By converting the total trip time to minutes, using the formula for speed (distance/time), and using a system of equations representing the total trip speed when the boat is moving downstream and upstream, we can find the average speed of the boat relative to the water.
Explanation:To solve this problem, we first need to convert the total trip time to minutes to make calculations easier. Given in the problem, 3 hours 20 minutes equates to 200 minutes. Next, we should use the formula for speed, which is distance divided by time. We know that the total distance traveled by the boat is 80 miles downstream and 80 miles back, totaling 160 miles.
When moving downstream, the speed of the boat and the speed of the current both aid in the boat’s motion. Thus we have speed of the boat = speed of the boat in still water + speed of the current. However, when the boat is moving upstream, the speed of the current works against the boat's motion. Thus we have speed of the boat = speed of the boat in still water - speed of the current.
By using the system of these equations and the fact that total time equals total distance divided by the speed of the boat, we can find the speed of the boat in still water, which represents the average speed of the boat relative to the water.
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Let's say the debt in the United States is now near 1.8 × 10^13 dollars and that there are about 300,000,000 people in the United States. If every person paid their fair share of the debt, approximately how much would that be per person?
Answers
If the total debt is near $1.8 × 10¹³, then every person has to pay $60,000.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the mentioned data in the question,
Total debt in the United States = $1.8 × 10¹³
Total number of people in the United States = 3 × 10⁸
If every person paid their share, then each person has to pay,
= ($1.8 × 10¹³)/(3 × 10⁸)
= $6 × 10⁴ or,
It can be written as $60,000.
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what percent of 18 is 63
Answers
63/18=x/100
63(100)=18(x)
6300=18x
350=x
Check Your Math
3.5*18=63
63=63
Does this set of ordered pairs represent a function?
{(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)}
Answers
a function will not have any repeating x values...it can have repeating y values, just not the x ones. So if all the x values are different, then it is a function
Answer:
Option C is correct
Yes, the set of ordered pairs {(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)} represents the function.
because every x-value corresponds to exactly one y-value.
Step-by-step explanation:
A function states that it is a relation in which every domain value is paired with exactly one element of range.
Given the set of ordered pair:
{(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)}
Domain is all the x-values, and range is all the y-values.
Domain: {-5, -1, 0, 3, 8}
Range: {-5, -2, -2, 7, 9}
By definition:
each input value (i.e x values) is paired with exactly one element of y-value.
therefore,the set of ordered pairs {(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)} represents the function.
Given line L = ax + by + c = 0, b 0 What is the x-intercept? y-intercept?
Answers
Answer:
On Odyssey ware it is -c/a
Step-by-step explanation:
The x-intercept and the y-intercept of a line can be found by setting y and x to zero in the line equation respectively. The x-intercept is -c/a and the y-intercept is -c/b.
Explanation:To find the x and y-intercepts of the given line equation L = ax + by + c = 0, we must set one variable to zero and solve for the other.
To find the x-intercept of a line, we can set y to zero (as this is the case when the line crosses the x-axis), we get:
L = ax + b(0) + c = 0 or x = -c/a
Therefore the getX-intercept of the line is -c/a.
Similarly to find the y-intercept of the line equation, we can set x to zero (as this is the case when the line crosses the y-axis), we get:
L = a(0) + by + c = 0 or y = -c/b
Hence, the y-intercept of the line is -c/b.
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Joe has 310 baseball cards. He writes the number of cards in expanded form. How many ones will he write?
Answers
Answer:
The expanded form of 310 is:
310 = 300 + 10.
Joe will write two numbers to form 310.
Step-by-step explanation:
The expanded form is used to write numbers and see the math value of individual digits. So, the numbers are separated into individual place values and decimal places and form a mathematical expression.
310 in expanded form is 300 + 10 = 310.
Shawn downloads movies at a base price of $2 per movie. If he downloads 5 movies, he will get a 25% discount. How much will Shawn save on the base price if he downloads 5 movies?
Answers
First, you will need to multiply the amount of movies times the base price.
5 * 2 = 10
Now, 25% is a quarter and we know a quarter of 10 is 2.5.
This means that the normal price with no deal will be $10.
Subtract $2.50 and you have your answer!
10 - 2.5 = 7.5
He only has to pay $7.50 and saves $2.50!
:)
Answer:
$2.50
Step-by-step explanation
"find the third length of the right triangle. give an exact answer and an approximation" HELP PLS
Answers
then, check the picture below.
Which of the following functions has the greatest y-intercept?
f(x) x y
−3 −14
−2 −6
−1 −2
0 3
1 5
2 6
or g(x) = 3 cos(2x) + 1
please include explanation
Answers
g(x) = 3 cos 2x + 1
when x = 0 g(x) = 3 cos 0 + 1 = 3*1 + 1 = 4
so the answer is g(x)
Answer:
g(x) has greatest y-intercept.
Step-by-step explanation:
We are given a table of values for function f(x) as:
x y=f(x)
−3 −14
−2 −6
−1 −2
0 3
1 5
2 6
We know that the y-intercept of a function is a point where the x-value is zero.
i.e. the input value is zero.
Hence, after looking at the table of values of the function f(x) we have the y-intercept of the function f(x) is:
y=3
Also we are given function g(x) as:
g(x) = 3 cos(2x) + 1
Hence, we calculate the y-intercept of the function g(x) by taking x=0
on taking x=0 we have:
g(0)=3 cos(0)+1
g(0)=3+1=4
Hence, the y-intercept of function g(x) is 4.
Hence, g(x) has the greatest y-intercept.
List of fractions and decimals in order from least to greatest 1.45 1 1/2 1 1/3 and 1.2
Answers
Thanks (;
What is 630 rounded to the nearest ten?
Answers
In an attempt to reduce the growth of its population, China instituted a policy limiting a family to one child. Rural Chinese suggested revising the policy to limit families to one son. Assuming the suggested policy is adopted and that any birth is as likely to produce a boy as a girl, and the successive births are independent, explain the following:
A) What would be the average family size?
B) What would be the ratio of newborn boys to newborn girls?
Answers
find the Factor of
48m - 80n.
Answers
80n = 16(5n)
so
48m - 80n = 16(3m - 5n)
Store A advertises a sale for 3 loaves of bread for $5.94. Explain how to use an equivalent rate to find the unit price of the bread at Store A.
Answers
Answer: I wrote the rate, with $5.95 in the numerator and 3 loaves in the denominator. I needed to find an equivalent rate expressed as a fraction with the denominator of 1. I noticed 3 loaves divided by 3 gave a denominator of 1, so I divided $5.94 by 3 to find that each loaf costs $1.98.
Just did it on Edge 2021
Btw Can you mark me brainlest pls
The equivalent rate of the bread is $1.98.
Since the store advertises a sale for 3 loaves of bread for $5.94, in order to find the equivalent rate, the person has to divide $5.94 by 3. This will be:
= $5.94/3
= $1.98
Therefore, the equivalent rate of the loaves of bread will be $1.98
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42in to 9 feet insimplest form
Answers
In the numer 6,666.666 how does the 6 in the hundredths place compare to 6 in the place to its left
Answers
the six to the left is worth more than the six in the hundredths
hope
i helped
the 6 in the hundreths place is 1/10 the value of the 6 in the place to the left
Tom ate 1/2 of the 1/2 leftovers. How much pie in all did he eat?
Answers
hope it helps?!
What is the midpoint of the x-intercepts of
f(x) = (x – 4)(x + 4)?
Answers
Answer:
midpoint is (0,0)
Step-by-step explanation:
the midpoint of the x-intercepts of
[tex]f(x) = (x - 4)(x + 4)[/tex]
To find the midpoint of x intercepts, we need to find the x intercepts first
we find x intercepts by replacing f(x) with 0
[tex]0 = (x - 4)(x + 4)[/tex]
Set each factor =0 and solve for x
[tex]x-4=0 , x=4[/tex]
[tex]x+4=0, x=-4[/tex]
X intercepts are -4 and 4
Midpoint of -4 and 4 is [tex]\frac{-4+4}{2} =0[/tex]
X intercepts lies on x axis . So midpoint is (0,0)
If 5 sandwhich rolls cost 1.10 how much will 14 rolls cost
Answers
Solve the system using the elimination method.
2x + y − z =9
−x + 6y + 2z =−17
5x + 7y + z =4
Whats x, y, and z???
Answers
Using the elimination method, the given system of equations leads to a solution of x = -1, y = 1, and z = -2.
Explanation:Solving the SystemThe first step in solving this system of equations using the elimination method is to try and eliminate one of the variables. Let's start with eliminating 'z' by adding the first and the third equation: [tex](2x + y - z) + (5x + 7y + z) = 7x + 8y = 13.[/tex]Now we can eliminate 'z' from the second equation as well by subtracting from it twice the first one:[tex]-(-x + 6y + 2z) - 2(2x + y - z) = -3x + 4y = -5.[/tex]Then we solve the new system of two equations: 7x + 8y = 13 and -3x + 4y = -5. Using substitution or elimination on this will give y = 1Substituting y = 1 into the equation -3x + 4y = -5 gives x = -1.Finally, substituting x = -1 and y = 1 into the first original equation 2x + y - z = 9 gives z = -2. So, the solution is x = -1, y = 1, z = -2.Learn more about Elimination Method here:https://brainly.com/question/13877817
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