Answer:
c = 17
Step-by-step explanation:
Use the Pythagorean Theorem to solve this problem.
The equation is a² + b² = c².
"a" and "b" are the length of the two shorter sides or values.
"c" is the length of the longest side or value, also the hypotenuse.
Since we know the two smaller values, we can replace "a" and "b" with 8 and 15. It does not matter which letter you decide to replace with which number.
Then simplify and isolate "c" to find the largest value.
a² + b² = c²
8² + 15² = c² Substitute "a" and "b". Square the numbers to simplify
64 + 225 = c² Add to simplify
289 = c²
√289 = √c² Square root both sides
√289 = c "c" will be isolated because √ and ² are reverse operations
c = √289 Put 'c' on the left side for standard formatting.
c = 17 Answer
Therefore the largest value, c, is 17 in the triple.
Final answer:
Using the Pythagorean theorem, a² + b² = c², we find that the largest value in the Pythagorean triple with the smallest values 8 and 15 is 17.
Explanation:
If 8 and 15 are the two smallest values in a Pythagorean triple, we can use the Pythagorean theorem to find the largest value, often denoted as c, in the triple. The formula for the Pythagorean theorem is a² + b² = c². Solving for c gives us c = √(a² + b²).
Using 8 as a and 15 as b, we can substitute these values into the equation:
c = √(8² + 15²)
c = √(64 + 225)
c = √289
c = 17
Therefore, the largest value in the Pythagorean triple is 17.
a food truck sells salad for $6.50 each and drinks for $2.00 each. The food truck's revenue from selling a total of 209 salads ans drinks in one day was $836.50. How many salads were sold that day?
Answer:
93
Step-by-step explanation:
s= salads d= drinks
$6.5s + $2d = $836.5
s + d =209
s = 209-d
6.5 (209-d) + 2d = 836.5
1358.5 - 6.5d + 2d = 836.5
-4.5d = -522
d = 116
s = 209 - 116 = 93
The graph for the equation y=-2x+1 is shown below. If another equation is graphed so that the system has no solution, which equation could that be
Answer:
B. y = -1/2 (4x + 2)
Step-by-step explanation:
your welcome :) and sorry that I'm a bit late
The interior angles formed by the sides of a hexagon have measures that sum to 720°. What is the measure of angle F? Enter your answer in the box. m∠F= ° An irregular hexagon labeled ABCDEF with angle A parenthesis x minus sixty parenthesis degrees, angle B parenthesis X minus forty parenthesis degrees, angle C one hundred thirty degrees, D one hundred twenty degrees, E one hundred ten degrees, F parenthesis x minus twenty parenthesis degrees
Answer: [tex]m\angle F=140\°[/tex]
Step-by-step explanation:
The missing figure is attached.You know that the sum of the interior angles of an hexagon is 720 degrees.
Based on that and given the figure attached, you can set up the following equation:
[tex](x-60)+(x-40)+130+120+110+(x-20)=720[/tex]
The next step is to solve for "x" in order to find its value. This is:
[tex]x-60+x-40+130+120+110+x-20=720\\\\3x=720-240\\\\3x=480\\\\x=\frac{480}{3}\\\\x=160[/tex]
Now you must substitute the valUe of "x" calculated above, into [tex]m\angle F=(x-20)\°[/tex]:
[tex]m\angle F=(160-20)\°[/tex]
Finally, evaluating, you get that the measure of the angle F is:
[tex]m\angle F=140\°[/tex]
Answer:
114 is the real correct answer
Step-by-step explanation:
May God Bless
Suppose a population has a doubling time of 25 years. By what factor will it grow in 25 years? 50 years? In 100 years?
A population with a doubling time of 25 years will grow by a factor of 2 in 25 years, by a factor of 4 in 50 years, and by a factor of 16 in 100 years, based on the exponential growth rule.
Explanation:If a population has a doubling time of 25 years, by what factor will it grow in various timeframes? Let's calculate this using the rule of exponential growth.
In 25 years, the factor by which the population will grow is 2, because the definition of doubling time implies that the population doubles every 25 years.
In 50 years, which is two doubling periods, the population will grow by a factor of 2^2 (2 raised to the power of 2), which is 4.
In 100 years, which is four doubling periods, the population growth factor will be 2^4 (2 raised to the power of 4), which equals 16.
Thus:
After 25 years, growth factor = 2After 50 years, growth factor = 4After 100 years, growth factor = 16Find two consecutive even integers such that the sun of the larger and twice the smaller is 62.
Answer:
20 and 22.
Step-by-step explanation:
Let the consecutive integers be a and b
Then b = a + 2
a is the smaller integer.
[tex]\begin{array}{rcl}2a + b & = & 62\\2a + a + 2& = & 62\\3a + 2 & = & 62\\3a & = & 60\\a & = & \dfrac{60}{3}\\\\& = & \mathbf{20}\\\end{array}[/tex]
a = 20
b = 20 + 2 = 22
The two integers, in ascending order, are 20 and 22.
Check:
2(20) + 22 = 62
40 + 22 = 62
62 = 62
OK.
The Indian Ocean is 2/10 of the area of the world’s oceans. What fraction represents the area of the remaining oceans that make up the world’s ocean? Wrote in simplest form
Answer I believe it would just be 8/10
Step-by-step explanation:
You have 2/10 of the worlds ocean which = Indian Ocean
So Your remaining ocean (10-2 = 8)
Also known as 8/10
The remaining oceans make up 4/5 of the world's oceans after subtracting the 1/5 that represents the Indian Ocean.
If the Indian Ocean covers 2/10 (or 1/5 when simplified) of the world's oceans, then the fraction representing the remaining oceans is found by subtracting this fraction from the whole (1, as the whole represents all of the world's oceans).
So, the calculation to find the fraction of the area of the remaining oceans would be:
1 - 2/10 = 1 - 1/5 = 5/5 - 1/5 = 4/5
Therefore, the remaining oceans make up 4/5 of the area of the world's oceans.
Evaluate the expression when x=3 and y= -2
Answer:
-11
Step-by-step explanation:
To evaluate an expression with variables, replace the variables with what the question tells you to.
Replace "x" with 3. Replace "y" with -2.
-x + 4y
= -(3) + 4(-2) Multiply 4 and -2 first to get -8
= (-3) + (-8) Add normally. -3 + (-8) is the same as (-3) - 8.
= -11 Answer
Therefore the solution is -11.
which inequality is equivalent to -m>_15
Answer:
m<=-15
Step-by-step explanation:
GIVING BRAINLIEST Consider these proportions: 3:7.5 4:10 5:12.5 6:15 Which of the following proportions belongs to the above set? A 1:2.5 B 2:4.5 C 7:12.5 D 8:20 a. A and B c. C and D b. B and C d. D and A
Answer:
3:7.5 = 1:2.5 = 2:5
4:10 = 2:5
5:12.5 = 10:25 = 2:5
6:15 = 2:5
A and D belong to this set:
A: 1:2.5 = 2:5
D: 8:20 = 2:5
The first mechanic charged $95 per hours, and the second mechanic charged $70 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $2,000. How long did each mechanic work?
Answer:
Step-by-step explanation:
Let a represent the hours put in my mechanic 1 and b represent that of mechanic 2.
a + b = 25, i.e. a = 25 - b
95a + 70b = 2000
Let's substitute the value of a in the second equation
95(25 - b) + 70b = 2000
2375 - 95b + 70b = 2000
2375 - 25b = 2000
-25b = 2000 - 2375
-25b = -375
b = 375/25
b = 15hrs
If b = 15hrs,
a + 15 = 25
a = 10hrs
Write a multiplication equation and a subtraction equation that both involve a fraction and have the same solution. Solve your equation to show that the solution are the same.
Answer:
[tex]x = \frac{3}{5} \times \frac{5}{7}[/tex] and [tex]y = \frac{16}{21} - \frac{1}{3}[/tex]
Step-by-step explanation:
We have to write a multiplication equation and a subtraction equation that both involve a fraction and have the same solution.
Let the multiplication equation be, [tex]x = \frac{3}{5} \times \frac{5}{7}[/tex].
And the subtraction equation is, [tex]y = \frac{16}{21} - \frac{1}{3}[/tex]
Now, [tex]x = \frac{3}{5} \times \frac{5}{7} = \frac{3}{7}[/tex] and [tex]y = \frac{16}{21} - \frac{1}{3} = \frac{16 - 7}{21} = \frac{9}{21} = \frac{3}{7}[/tex]
Therefore, in both the equations the solution is [tex]\frac{3}{7}[/tex]. (Answer)
Final answer:
Both a multiplication equation (½ * 2 = 1) and a subtraction equation (1 - ½ = ½) can be constructed to have the same solution, where the multiplication involves doubling the fraction and the subtraction involves a whole number minus the fraction.
Explanation:
Creating a multiplication equation and a subtraction equation with the same solution involves finding a common value that the operations can share. Here's a simple example:
Let's say we have the fraction ½. If we want a multiplication equation, we could multiply this fraction by 2 to get 1 (since ½ * 2 = 1).
Multiplication equation: ½ * x = 1, where x = 2.
For the subtraction equation, we consider the fact that subtracting 0 from any number leaves it unchanged. We can use this to our advantage by creating an equation where we subtract a fraction from itself:
Subtraction equation: y - ½ = ½, where y = 1.
By solving these equations, we can see they have the same solution:
½ * 2 = 11 - ½ = ½Both equations simplify to the same value, demonstrating that multiplication and subtraction can indeed share the same result when formulated correctly.
Is 0,3 a solution to 2x-y=-3
Answer:
Yes, (x, y) = (0, 3) is a solution
Step-by-step explanation:
You can determine whether a given ordered pair is a solution by substituting those values into the equation, then checking to see if the resulting statement is true.
For x=0 and y=3, the equation becomes ...
2·0 -3 = -3 . . . . . a true statement
(0, 3) is a solution to the equation
sixteen and two-tenth subtracted from two times a number
Step-by-step explanation:
Let the required number = x
To find, the required number = ?
According to question,
∴ 2x - 16 - 2 × 10 = 0
⇒ 2x - 16 - 20 = 0
⇒ 2x - 36 = 0
⇒ 2x = 36
⇒ x = 18
∴ The required number = 18
Thus, the required number is 18.
Answer: x=18
Explanation:
The sale price of a sweater is $48. The price is 20% less than the original price. What was the original price.
The original price of the sweater, before a 20% discount, was found to be $60. This was calculated by dividing the sale price of $48 by 0.80, as the sale price represents 80% of the original price.
Explanation:The student is asking how to find the original price of a sweater given that the sale price is $48 and this sale price represents a 20% discount from the original price.
To find the original price, we need to understand that the sale price is 80% of the original price (100% - 20% discount). Let's denote the original price as P. We can set up the equation P * 0.80 = $48. Solving for P, we get P = $48 / 0.80
The calculation will give us the original price which is $60. The original price of the sweater was $60 before the 20% discount was applied.
Final answer:
The original price of the sweater was $60.
Explanation:
Let x be the original price of the sweater.
According to the given information, the sale price of the sweater is $48, which is 20% less than the original price.
So, we can set up the equation as follows-
Original Price - Discount = Sales Price
x - 0.2x = $48
Simplifying:
0.8x = $48
Dividing both sides by 0.8, we get:
x = $60
Therefore, the original price of the sweater was $60.
Kendra is three times her daughter's age plus seven years Kendra is 49 years old write an equation to find her daughter's age
Answer: [tex]49 = 3x + 7[/tex]
Step-by-step explanation:
Let the daughter's age be x and Kendra's age be y , then from the first statement;
[tex]y = 3x + 7[/tex]
Since Kendra's age is 49 , substitute it into the equation , we have
[tex]49 = 3x + 7[/tex]
subtract t from both sides
[tex]49 - 7 = 3x[/tex]
[tex]42 = 3x[/tex]
divide through by 3
[tex]x = 14[/tex]
Therefore : the daughter's age is 14
Answer:
3x+7=49
Step-by-step explanation:
Widget Wonders produces widgets. They
have found that the cost, o(x), of making x
widgets is a quadratic function in terms of x.
The company also discovered that it costs
$20.50 to produce 3 widgets. $60.50 to
produce 7 widgets, and $133 to produce 12
widgets.
What is the total cost of producing nine widgets
Shawn's father gave him $168. Shawn bought 10 books, each of which cost $10. How much money does Shawn have left?
will make brainliest
Answer:
68$
Step-by-step explanation:
cost of 10 book= 10$ * 10= 100$
now,
Remaining money= 168$-100$
=68$
Answer:
$68
Step-by-step explanation:
If each of the 10 books costs $10, you must multiply $10 x 10 to get $100. Then, you do $168 - $100 and get $68.
Please Help !
TRYING TO MAKE HONOR ROLL
Which point represents the solution to the system of equations below ?
Answer:
I think its c. but i could be wrong
If 2y + 6 = 1 −3y, then y = −−−−−−
Answer:
y = -1
Step-by-step explanation:
Add 3y to both sides:
2y + 3y + 6 = 1 - 3y + 3y
Simplify:
5y + 6 = 1
Subtract 6 from both sides to isolate the y value:
5y + 6 - 6 = 1 - 6
Simplify:
5y = -5
Divide by 5 on both sides to solve:
5y/5 = -5/5
Simplify:
y = -1
The school that Julia goes to is selling tickets to the annual dance competition. On the first day
of ticket sales the school sold 5 adult tickets and 13 child tickets for a total of $159. The school
took in $51 on the second day by selling 1 adult ticket and 5 child tickets. What is the price each
of one adult ticket and one child ticket?!
We have a system of equations in two variables, namely, a and c. Use the substitution to find a and c.
Answer:
The price of 1 adult ticket is $11, while the price of one child ticket is $8.
Step-by-step explanation:
Let's identify what we already know:
1) On the first day of ticket sales, the school sold $159 worth of tickets.
2) On the first day, they sold 5 adults tickets, and 13 adult tickets.
3) The school sold $51 worth of tickets on the second day.
4) The school sold 1 adult ticket, and 5 child tickets.
Let's create two formulas:
(5 times x) + (13 times y) = $159
(1 times x) + (5 times y) = $51
You invested into a content management company that specializes in peer to peer networks four years ago with a stock value
of $56.30 a share. Today, a single share of the company is worth $32.21. Given this information, determine the decay factor
for the four year period and round your answer to the hundredth place.
a 57.0
C. 570
b. 0.57
d. 1.57
Answer:
0.57
Step-by-step explanation:
56.30 divided by 1.57=32.21
start time 1:20 pm end time 2:00pm elapsed time
Answer:
40 minutes
Step-by-step explanation:
Elapsed time = end time - start time
Elapsed time = 2:00 - 1: 20
Elapsed time = 40 minutes
3x^+7x-6 factor completely
The factor for given equation [tex]3x^2+7x-6[/tex] is (3x-2) and (x+3).
Step-by-step explanation:
To find the factors of the equation,
1) Multiply the coefficient of the [tex]x^2[/tex] and the constant value.
⇒3×(-6)= -18.
2) Now find two numbers that can result is in -18 while multiplying and 7 (middle term or coefficient of x) while adding.
⇒9 × (-2) = -18.
9+(-2)= 7.
Now spit the equation as[tex]3x^2+9x-2x-6[/tex].
=[tex](3x^2+9x)-(2x-6)[/tex].
=3x(x+3) - 2(x+3).
=(x+3)(3x-2). (by taking out the common term x+3)
∴ The factor for given equation [tex]3x^2+7x-6[/tex] is (3x-2) and (x+3).
f(x) is a quadratic function with x-intercepts at (−1, 0) and (−3, 0). If the range of f(x) is [−4, ∞) and g(x) = 2x2 + 8x + 6, compare f(x) and g(x). Select the statement that is not correct?
A) Both functions have the same vertex.
B) Both functions have the same domain.
C) Both functions have the same x-intercepts.
D) Both functions are decreasing on the interval (−∞, −2).
Answer:
B) Both functions have the same domain.
C) Both functions have the same x-intercepts.
D) Both functions are decreasing on the interval (−∞, −2).
Step-by-step explanation:
step 1
Find the vertex of f(x)
we know that
The x-coordinate of the vertex is the midpoint of the roots
we have
x=-1 and x=-3
so
the midpoint is
(-1-3)/2=-2
The y-coordinate of the vertex is -4 (because the range is [−4, ∞))
therefore
The vertex of f(x) is the point (-2,-4)
Is a vertical parabola open upward
The vertex is a minimum
The domain is all real numbers
step 2
we have
[tex]g(x)=2x^2+8x+6[/tex]
Find the vertex
Factor the leading coefficient
[tex]g(x)=2(x^2+4x)+6[/tex]
Complete the square
[tex]g(x)=2(x^2+4x+4)+6-8[/tex]
[tex]g(x)=2(x^2+4x+4)-2[/tex]
Rewrite as perfect squares
[tex]g(x)=2(x+2)^2-2[/tex]
Is a vertical parabola open upward
The vertex is the point (-2,-2)
The domain is all real numbers
The range is the interval [−2, ∞)
Find the x-intercepts
For g(x)=0
[tex]0=2(x+2)^2-2[/tex]
[tex]2(x+2)^2=2[/tex]
[tex](x+2)^2=1\\x+2=\pm1\\x=-2\pm1[/tex]
so
The roots or x-intercepts are
x=-1 and x=-3
Verify each statement
A) Both functions have the same vertex
The statement is false
The vertex of f(x) is (-2,-4) and the vertex of g(x) is (-2,-2)
B) Both functions have the same domain.
The statement is true
The domain is all real numbers
C) Both functions have the same x-intercepts
The statement is true (see the explanation)
D) Both functions are decreasing on the interval (−∞, −2)
The statement is true
Because the x-coordinate of the vertex is the same in both functions, and both functions open upward
Answer:
The answer is A
Step-by-step explanation:
Help help help help
Answer:
b=[tex]\frac{t-5}{4}[/tex]Step-by-step explanation:
4b+5=t
First, you must get the variable alone! Substract 5 from both sides!
4b+5=t
-5 -5
The 5 cancels out because 5-5=0
The new equation is 4b=t-5
You must divide by 4 to get the variable alone since your solving for b!
4b=t-5
4 4
b= [tex]\frac{t-5}{4} \\[/tex]
This is your answer!
T=42-0.7t how fast did the temperature drop?
The given equation describes a linear relationship between temperature and time. The slope, -0.7, indicates that the temperature is dropping at a rate of 0.7 degrees per unit of time.
Explanation:The equation given, T=42-0.7t, is in the form of a linear equation, y=mx+b, where T is the temperature in degrees Celsius, t is the time, 42 represents an initial temperature, and -0.7 is the slope representing the rate of temperature change over time.
In this equation, the slope, -0.7, tells us that the temperature is decreasing or dropping at a rate of 0.7 degrees per unit of time. This could be per minute, per hour, etc., depending on the context given.
Note that because the '-0.7' is negative, we know that the temperature is decreasing, or dropping, rather than increasing. If it were positive, it would mean the temperature is rising. Thus, when you're asked how fast the temperature is dropping, the answer based on this equation is that it's dropping at a rate of 0.7 degrees per unit of time.
Learn more about Rate of Temperature Change here:https://brainly.com/question/11482539
#SPJ12
The temperature drops at a rate of 0.7 degrees per time unit, as indicated by the coefficient of t in the equation T = 42 - 0.7t.
The equation given, T = 42 - 0.7t, suggests a relationship between temperature (T) and time (t), where the temperature drops over time due to some cooling process, such as a cold front arriving. To determine how fast the temperature is dropping, we look at the coefficient of t in the equation, which is -0.7. This means that for every unit of time that passes, the temperature drops by 0.7 units. Thus, the rate of temperature drop is 0.7 degrees per time unit, assuming the temperature is measured in degrees and time in matching time units (likely minutes or seconds).
In a class room of 30 students, 18 are female and 12 are male. If you randomly select one person, what is the probability you will select a female
Select all that apply.
What did scribes in medieval Europe do?
became nomadic preachers
copied books and other religious material
kept records and wrote about current events
preserved learning and libraries
developed a way to treat eyestrain
Final answer:
Scribes in medieval Europe had several important roles:
including copying books and religious material, keeping records and writing about current events,preserving learning and libraries.Explanation:
Scribes in medieval Europe had several important roles:
They copied books and other religious material: Scribes were responsible for hand-copying books, particularly ones related to Christian theology, such as the Bible. They also copied classical Greek or Roman writings that would have otherwise been lost. These hand-copied books, known as illuminated manuscripts, were often beautifully illustrated.They kept records and wrote about current events: Scribes also played a crucial role in keeping records and documenting current events. They wrote about important historical and political events, as well as religious and civil information.They preserved learning and libraries: Monasteries, where many scribes worked, became major centers of learning in medieval Europe. Scribes helped preserve knowledge from the ancient world by copying and preserving books. They also contributed to the development of libraries.Ben works in a sandwich shop. On average, he makes 3 sandwiches every 10 minutes. If Ben works 6 hours how many sandwiches will he make?
Answer: 108
Step-by-step explanation:
18 sandwiches are mad every hour then multiply it by 6 .
Find the 20th term of the arithmetic sequence 15, 9, 3, -3, ...
The 20th term is -106
15,9,3,-3,-9,-15,-21,-28,-35,-41,-46 (10) -6 x 10 = -60
-60 + -46
-106
You're just subtracting by 6.
Answer:
-99
Step-by-step explanation:
you subtract by 6 every number.....
-3-6=-9
-9-6=-15
so on and so on until you get to the 20th term.....