A rectangular pool is 6 meters wide and 8 meters long. If you swim diagonally across the pool, how many meters would you be swimming?
If you swim diagonally across the rectangular pool, the distance you swim is 10 meters.
Given the following data:
Width of rectangle = 6 metersLength of rectangle = 8 metersTo determine the distance you swim in meters, we would apply Pythagorean's theorem since the width is along the x-axis while the length is along the y-axis.
Note: The diagonal side of the rectangular pool represents the hypotenuse.
Mathematically, Pythagorean's theorem is given by the formula:
[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex]
Substituting the given parameters into the formula, we have;
[tex]Hypotenuse^2 = 6^2 + 8^2\\\\Hypotenuse^2 = 36+64\\\\Hypotenuse^2 = 100\\\\Hypotenuse = \sqrt{100}[/tex]
Hypotenuse = 10 meters.
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I have invested for a loan of Php 5,000, and I need to repay in one lump sum at the end of one year. What annual interest rate corresponds to a lump-sum payment of Php 5,425?
Based on the information given, it can be deduced that the annual interest rate will be 8.5%.
Principal = 5000
Interest = 5425 - 5000 = 425
Time = 1 year
Rate = Unknown.
Simple Interest = PRT / 100
425 = (5000 × R × 1)/100
42500 = 5000R.
R = 42500/5000
R = 8.5%
In conclusion, the correct option is 8.5%.
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which car can travel furthur on one gallon of gas/ green car 18.4 miles on 0.8 gallons or black car 17.4 miles on 0.75 gallons
Answer:
The black car
Step-by-step explanation:
First, we need to fin the mile to gallon ratio.
To get this we would divide the number of miles by the gallon for each car
Green Car:
18.4/0.8
23 miles per gallon
Black car:
17.4/0.75
23.2 miles per gallon
In conclusion, The black car would travel further on one gallon of gas than the green car would.
Hope this helps!!
Please tell me if I have messed up!!
I enjoy learning from my mistakes:)
Jake has two dogs, Euclid and Pythagoras. Euclid is a smaller dog and Pythagoras is larger. Jake found that
Pythagoras lost 13 pounds from January to June. If Pythagoras gains 1.2 times Euclid's weight, Pythagoras's
weight would still be á pound less than he did in January. What is Euclid's weight?
4
(a) Write an equation that represents the scenario. Begin by defining your variable.
(b) Solve the equation. Show your work.
(c) What is Euclid's weight?
(d) Jake adopts a third dog, Riemann. Riemann weighs exactly twice what Euclid weighs. The combined
weight of the three dogs is 603 pounds. What is Riemann's weight, and what is Pythagoras's
2
weight? Show your work.
We want to answer different things about the weight of the dogs, with simple algebra we will find that the answers are:
a) P - 13lb + 1.2*E = P - 1lbb) E = 10lbc) Euclid's weight is 10 pounds.d) Pythagora's weight is 33 pounds and Riemann's weight is 20 pounds.We start by defining the two variables we will be using:
E = Euclid's weightP = Pythagoras's weightFirst, Pythagoras loses 13 lb, then his new weight is:
P' = P - 13lb
We know that if he wins 1.2 Euclid's weight, he will still have a pound less than before.
A) using the above information we can rewrite:
P - 13lb + 1.2*E = P - 1lb
This is the equation we need to solve.
b) So we want to solve this for E, then we move all the other terms to the right side:
1.2E = P - 1lb - P + 13lb
1.2E = 12lb
E = (12lb)/1.2 = 10lb
c) The solution of the above equation tells us that the weight of the dog is 10lb.
d) Let's define R as the weight of the third dog.
We know that:
R = 2*E = 2*10lb = 20lb
We also know that the combined weight of the 3 dogs is 63 lb, then we have:
E + R + P = 63lb
10lb + 20lb + P = 63lb
P = 63lb - 10lb -20lb = 33lb
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Evaluate each expression
Answer:
4 * 4 ÷ 4 = 4
8 ÷ (2*2) = 2
Step-by-step explanation:
[tex]4 * 4 \div4\\\rule{150}{0.5}\\\text{Use PEMDAS}\\\\4 * 4 \div4\\\\4 * 1\\\\\boxed{4}[/tex]
==============================
[tex]8 \div (2*2)\\\rule{150}{0.5}\\\text{Use PEMDAS}\\\\8 \div (2*2)\\\\8 \div 4\\\\\boxed{2}[/tex]
I hope this helps.
Please help with Exponential Problem !!!
Answer:
D) f(3) = 54
Step-by-step explanation:
f(3) = 2 x 3^3
f(3) = 2 x 27
f(3) = 54
Hope this helps! Pls give brainliest!
Answer:
D
Step-by-step explanation:
first you need to do the exponent and you substitute the 3 in for ex
so 3^3=27
then you multiply it by 2 to get 54
Translate and simplify: the product of –12 and the difference of p and q.
Hey there!
“Product” is multiplication so let’s say it means “multiply” & “difference” is subtraction so let’s say it means “subtract”
p & q is/are the variables, whereas -12 is a coefficient
“The [PRODUCT of -12] and the [DIFFERENCE of p & q]”
Product = multiply/multiplication
“-12 ×”
DIFFERENCE
“p - q”
So, based on that information we have your answer: “-12 × p - q”
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Ashton is 3 times the age of Jason. Ashton is 6 years older
than Nolan. Jason is 7 years old. How old is Nolan? Explain
Answer:
nolan is 15,
Step-by-step explanation:
3*7=21-6=15
solution:
age of Jason is 7
and Ashton is 3 times age of Jason=7*3=21
Nolan age=21-6=15
therefore the age of Nolan is 15 years
√((2+√3)÷(2-√3))
what is the answer?
20 POINTS AND BRAINLIST! WILL BE GIVEN!!
complete the following statements.
<1 and <5 are remote interior angles of <4.
_ and _ and are remote interior angles of <6.
_ and _ are remove interior angles of <2.
The sum of the remote interior angles are equal to the exterior angles.
The completed statements are;
∠1 and ∠3 are remote interior angles of ∠6
∠3 and ∠5 are remote interior angles of ∠2
Reasons:
Remote interior angles are the angles that are not on the same vertex as an exterior angle
The remote interior angles of ∠4 are ∠1 and ∠5
Similarly, we have;
∠1 and ∠3 are remote interior angles of ∠6
∠3 and ∠5 are remote interior angles of ∠2
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Please help me as soon as possible.
[tex]\begin{array}{llll} x~-2y=-13\\ 5x+2y=-17\\ \cline{1-1} 6x+0y=-30 \end{array}\qquad \implies 6x=-30\implies x=\cfrac{-30}{6}\implies x=-5 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 1st equation}}{(-5)-2y=-13\implies }-2y=-8\implies y = \cfrac{-8}{-2}\implies y = 4 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (-5~~,~~4)~\hfill[/tex]
The national debt of a county is the total amount of money the government of that country owes. Imagine everyone in the United States was asked to help pay off the national debt. How much would each person have to pay?
(*Hint: Use the numbers below in your calculations.*)
According to npr.org, as of Feb. 2019, the US national debt was $22 trillion.
According to the United States Census Bureau, as of 2018, the US population was 327.2 million people.
PLEASE ANSWER
Answer:
Each person have to pay $67,237
Step-by-step explanation:
Amount each person would pay = Total amount of debt/ Size of Population
= 22000000000000/327200000
= 67237. 164
Approximately $67,237
Answer: 46572
Step-by-step explanation:
It is how you do the math look over your answers you got this
(a) $21,000.00 is to be divided in the ratio 5:7:9 respectively for three siblings Antony, Terry
and Jack. Calculate how much money each sibling will get.
Answer:
See below for answer
Step-by-step explanation:
Set up the equation 5x+7x+9x=2100 and solve for x:
5x+7x+9x=2100
21x=2100
x=100
Now multiply the proportion by 100:
5:7:9 * 100 = 500:700:900
This means that Antony will get $500, Terry will get $700, and Jack will get $900.
A farm lets you pick 3 pints of raspberries for $12.00
do you want me to find the answer or something because ur just doing something and not saying what to do with it
The mean temperature for the first 7 days in January was 4 °C.
The temperature on the 8th day was 6 °C.
What is the mean temperature for the first 8 days in January?
PLEASE HELP!!
what is the intermediate step in the form (x+a)^2=b as a result of completeting the square for the following equation?
x^2-34=16x
Answer:
1: x =(16-√392)/2=8-7√ 2 = -1.899
2: x =(16+√392)/2=8+7√ 2 = 17.899
Step-by-step explanation: I found two solutions it’s either one or two.
I hope this helped :) I tried my best.
A baseball player on a professional baseball team has 207 hits in 575 at-bats. What
is the ratio of hits to at-bats? Choose the correct answer in the most simplified
form:
Answer:
9/25
Step-by-step explanation:
find a number that both the top and bottom are divisible by,
23 is the greatest common division we can make such that the top and bottom remain whole numbers
so,
[tex]\frac{207 }{575}[/tex] ÷23
=(207/23)÷(575/23)
=[tex]\frac{9}{25}[/tex]
help help help help math math
Answer:
[tex]2916^3\\[/tex]
Step-by-step explanation:
As the formula is [tex]\frac{4}{3}\pi \cdot r^3[/tex]
But we take [tex]\pi[/tex] as 3 so it would be [tex]\frac{4}{3}3\cdot r^3[/tex]
And the radius is 9 half of Diameter
We would write it like this
= [tex]\frac{4}{3}3\cdot 9^3[/tex]
Then when we solve it would become [tex]2916^3\\[/tex]
I hope this helps :)
A. Encode the following decimal fractional value to binary floating point notation using the 8-bit floating-point format.
• -3.5
Answer:
Solution:
o -3.5
As number is negative so sign bit notation is 1.
o First convert 3.5 into binary Binary of 3.5 is 011.1
Mantissa field:
0111
radix in .0111 must be moved 3 bit to the right to obtain
011.1
So exponent is positive 3…
Final 8 bit floating point notation is
1
1
1
1
0
1
1
1
Step-by-step explanation:
h(r) = r^2 + 11r - 26
1) What are the zeros of the function?
Write the smaller r first, and the larger r second.
smaller s =
larger r =
2) What is the vertex of the parabola?
The zeros of the function h(r) = r² + 11r - 26 are r = -13, r = 2 and the vertex is (-11/2, -225/4).
What are the zeros and vertex of the function?Given the function in the question:
h(r) = r² + 11r - 26
To find the zeros of the function h(r) = r² + 11r - 26, we need to solve the equation h(r) = 0.
Using factoring:
r² + 11r - 26 = 0
Find two numbers whose sum is 11 and whose product is -26.
The numbers are -2 and 13.
Factor the equation:
(r - 2)(r + 13) = 0
Hence:
r - 2 = 0 and r + 13 = 0
Therefore, smaller r = -13, larger r = 2.
Next, we determine the vertex of the function:
Using the formula for the x-coordinate of the vertex, which is given -b/2a.
Here, the coefficient of r² is 1 (a = 1),
The coefficient of r is 11 (b = 11).
Substituting these values into the formula, we get:
r = -b/2a
= -11/( 2×1 )
= -11/2
The x-coordinate of the vertex is -11/2.
To find the y-coordinate, we can substitute r = -11/2 value back into the function:
h(r) = r² + 11r - 26
h(-11/2) = (-11/2)² + 11(-11/2) - 26
= 121/4 - 121/2 - 26
= 121/4 - 242/4 - 104/4
= (121 - 242 - 104)/4
= -225/4
Therefore, the vertex is (-11/2, -225/4).
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Sean has three dollars more than twice as much money as Peter if Sean has $10 how much money does Peter have
Answer:
peter has $3.50
Step-by-step explanation:
3.50 times 2 is 7 plus 3 is 10
Evaluate the difference quotient for the given function.
f(t) = g(t) h(t) , where g(t) = cos(t) and h(t) =sin(t)
Assuming you mean f(t) = g(t) × h(t), notice that
f(t) = g(t) × h(t) = cos(t) sin(t) = 1/2 sin(2t)
Then the difference quotient of f is
[tex]\dfrac{\frac12 \sin(2(t+h)) - \frac12 \sin(2t)}h = \dfrac{\sin(2t+2h) - \sin(2t)}{2h}[/tex]
Recall the angle sum identity for sine:
sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
Then we can write the difference quotient as
[tex]\dfrac{\sin(2t)\cos(2h) + \cos(2t)\sin(2h) - \sin(2t)}{2h}[/tex]
or
[tex]\boxed{\sin(2t)\dfrac{\cos(2h)-1}{2h} + \cos(2t)\dfrac{\sin(2h)}{2h}}[/tex]
(As a bonus, notice that as h approaches 0, we have (cos(2h) - 1)/(2h) → 0 and sin(2h)/(2h) → 1, so we recover the derivative of f(t) as cos(2t).)
Drag and drop the fractions to order them from least to greatest. 2/3 -4/5 1/4 -3/7
Step-by-step explanation:
I hope this helps out bye.
A six-sided number cube is rolled 500 times. The results are 280 even numbers and 220 odd numbers. How does the relative frequency of rolling an even number compare to the theoretical probability? Select from the drop-down menus to correctly complete the statements. The relative frequency of rolling an even number is Choose... the theoretical probability. The theoretical probability is Choose... and the relative frequency is Choose... .
Answer:
Choice B) experimental probability is larger
Step-by-step explanation:
There are 3 odd numbers (1,3,5) out of 6 total (1,2,3,4,5,6) on the number cube. So theoretically, the chances of rolling an odd number are 3/6 = 1/2 = 0.5
When we do the experiment, we roll an odd number 325 times out of 500 trials total. So the experimental probability is 325/500 = 0.65
Comparing the results of 0.5 and 0.65, we see that 0.65 is larger. So the experimental probability is larger.
Note: with a large number of trials, the experimental probability should get closer and closer to the theoretical probability. This is assuming that all trials are independent of one another and the number cube is properly weighted.
Answer:
1: greater than
2: 0.5
3: 59%
Step-by-step explanation:
I took the test and here is da proof:
{I left it blank on purpose so other can see the right answer (: }
Which is NOT true?
7 + 7 = 19 - 5
9 + 9 = 11 + 7
19 = 13 + 5
20 - 12 = 4 + 4
Answer:
c.19 = 13 + 5
Step-by-step explanation:
Yoni has a ribbon that measures 5/3 yards. She wants to cut it into 3 equal pieces. What is the length of each piece of ribbon? 5\8 yards 5/6 yards 5/9 yards 5/3 yards
Answer:
5/9 yards
Step-by-step explanation:
[tex] \frac{5}{3} \div \frac{3}{1} \\ = \frac{5}{3} \times \frac{1}{3} \\ = \frac{5}{9} [/tex]
Jacob put hummingbird feeders in his garden. To make the food for his small feeder, he mixed sugar with warm water. He used the same amount of sugar for his large feeder, but he added more water to completely fill it. Which mixture was sweeter?
Answer:
Step-by-step explanation:
The smaller feeder is sweeter as it has more sugar molecules per unit of water than the larger feeder.
Jack’s school bag contains 8 books each of weight 3/8 pounds, and 6 folders of weight 1/2 pound. b) What fraction of the total weight is folders?
Answer:
3/6
Step-by-step explanation:
Answer:
3/6 é a resposta tabom me de coraçãozinho
find the perimeter of the triangle A(4,-2) B(9,-2) C(9,10)
Answer:
30 units
Step-by-step explanation:
A graph can help you see the lengths of the sides. This is a right triangle, so the length of the hypotenuse is found using the Pythagorean theorem:
5² +12² = b² = 169
b = √169 = 13
The perimeter is 5+12+13 = 30 units.
(15,9) and (x,-3), find all x such that the distance between 2 points is 15
Answer:
See image
Step-by-step explanation:
I used distance formula to calculate. But if you haven't learned distance formula or solving radical equations, or solving equations by taking sq roots then maybe you were just supposed to graph it and look for the points. The answers came out to be nice neat numbers, so that is possible. x = 6 and x = 24
