Step-by-step explanation:
we have to solve 2 right-angled triangles via Pythagoras
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle).
one triangle is 37, 12 and the longer part of the long diagonal.
the second triangle is 13, 12 and the shorter part of the long diagonal.
the whole diagonal is then the sum of both parts.
37² = 12² + longer part²
1369 = 144 + longer part²
longer part² = 1225
longer part = 35
13² = 12² + short part²
169 = 144 + short part²
25 = short part²
short part = 5
so, the total diagonal is 35 + 5 = 40 units.
The length of the longer diagonal obtained using Pythagorean theorem is 40 units
What is the Pythagorean theorem?The Pythagorean theorem is a fundamental geometric relationship that states that the square of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the other two sides (the legs). Mathematically, we get
c² = a² + b²
Where a and b are the lengths of the legs and c is the length of the hypotenuse side of the right triangle.
The diagonals of a kite are perpendicular to each other
The diagonal that is bisected in a kite is the shorter diagonal
The lengths from the left point to the middle and the distance from the right point to the middle are both 12, which indicates that the diagonal from left to right of the kite is bisected, which is the shorter diagonal. Therefore;
The length of the shorter diagonal is; 12 + 12 = 24
Therefore, the longer diagonal forms two right triangles to the left and two right triangles to the right
The hypotenuse length of the right triangles are 37 and 13, while the leg common to both right triangles on each side is half the length of the shorter diagonal, or 12
The Pythagorean theorem indicates that we get;
Length of the longer diagonal = √(13² - 12²) + √(37² - 12²) = 40
The length of the longer diagonal is 40 units
Learn more on Pythagorean theorem here: https://brainly.com/question/30276548
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Natalie has 112 boxes she left 105 five boxes and she found 20 boxes how much dose she have?
Answer:
27 boxes.
Step-by-step explanation:
This situation can be represented by the equation:
(112 - 105) + 20 = ?
First we subtract 105 from 112:
112 - 105= 7
Now add 20.
7 + 20 = 27
Natalie has 27 boxes now.
Help anyonee?? 100 points!!
Answer:
D
Step-by-step explanation:
[tex]4\sqrt{x2[/tex] means [tex](x^{2})^{\frac{1}{4} }[/tex] so then according to indices rule, the powers will be multiplied. Do the same thing for y and z as well, and you will get the answer
if the log↓b(a)=0, what is the value of a?
explain why log↓0 (3) and log↓1 (3) do not exist.
Answer:
1. a = 1
2. See explanation below.
Step-by-step explanation:
First Question
Given:
[tex]\displaystyle \large{\log_b a = 0}[/tex]
Convert to exponential:
[tex]\displaystyle \large{\log_b a = c \to b^c = a}[/tex]
Thus [tex]\displaystyle \large{\log_b a = 0 \to b^0 = a}[/tex]
Evaluate:
[tex]\displaystyle \large{b^0 = a}[/tex]
We know that for every values to power of 0 will always result in 1, excluding 0 to power of 0 itself.
Solution:
[tex]\displaystyle \large{a = 1}[/tex]
__________________________________________________________
Second Question
Given:
[tex]\displaystyle \large{log_0 3}[/tex] and [tex]\displaystyle \large{\log_1 3}[/tex]
Let’s convert to an equation:
[tex]\displaystyle \large{\log_0 3 = x}[/tex] and [tex]\displaystyle \large{\log_1 3 = y}[/tex]
The variables represent unknown values of logarithm.
Convert to exponential:
[tex]\displaystyle \large{0^x = 3}[/tex] and [tex]\displaystyle \large{1^y = 3}[/tex]
Notice that none of x-values and y-values will satisfy the equations. No matter what real numbers you put in, these equations will always be false.
Hence, no solutions for x and y.
How many factors do numbers of the form p^n and q^m have if p and q are two different prime numbers and m and n are natural numbers?
The only common factor between these two numbers will be 1.
How many factors do these numbers share?
Remember that any number can be decomposed as a product of prime numbers. For example for 18 we have:
18 = 2*3*3
There 18 is written as a product of its prime factors.
Now, for our case of p^n and q^m we will have:
p^n = P = p*p*p...*p n times.
q^m = Q = q*q*q*...*q m times.
Now, notice that because q and p are primes, there is no common factor in these two decompositions. (and we can't decompose it furthermore). Then we conclude that the only factor that these numbers share is the trivial one, which is 1.
If you want to learn more about prime numbers, you can read:
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please help me solve for m<C and m<D
Answer:
Step-by-step explanation:
Use law of cosine to calculate the other side.
c² = a² + b² -2ab Cos C
Here, c is the length of the side which is opposite side to ∠E
a = 29 ; b = 25 and C = 109
c² = 29² + 25² - 2*29*25*Cos 107
= 841 + 625 - 1450* (-0.2923)
= 1466 + 423.835
= 1889.835
c =√1889.835
c = 43.47 ≈ 43
No, find ∠D using again use law of cosine
[tex]Cos \ \beta = \dfra{a^{2}+c^{2}}-b^{2}{2ac}\\\\\\ = \dfrac{29^{2}+43^{2}-25^{2}}{2*29*43}\\\\\\Cos \ \beta =\dfrac{841+1849-625}{2494}=\dfrac{2065}{2494}\\\\Cos \ \beta = 0.828\\\\\beta =Cos^{-1} \ 0.828\\\\[/tex]
β = ∠C = 34°
α = 180 - (34 +107)
α = ∠D = 39
Other angles are
∠C = 34° and ∠D°39
for each of the figures, write an absolute value equation that has the following solution set 3 and 7
The solution set 3 and 7 are the true values of the absolute value equation
The absolute value equation that has a solution set of 3 and 7 is [tex]|x - 5| = 2[/tex]
How to determine the absolute value equation?The solution sets of the absolute value equation are given as:
x = {3, 7}
Calculate the mean of the solutions
[tex]x_1 = \frac{7 +3}{2}[/tex]
[tex]x_1 = 5[/tex]
Calculate the difference of the solutions divided by 2
[tex]x_2 = \frac{7 - 3}{2}[/tex]
[tex]x_2 = 2[/tex]
The absolute value equation is the represented as:
[tex]|x - x_1| - x_2 = 0[/tex]
Substitute known values
[tex]|x - 5| - 2 = 0[/tex]
Add 2 to both sides
[tex]|x - 5| = 2[/tex]
Hence, the absolute value equation that has the a solution set of 3 and 7 is [tex]|x - 5| = 2[/tex]
Read more about absolute value equation at:
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Need help, Brainliest if correct only…. dont answer if you don’t know. Thank u!
Answer:
3/1
Step-by-step explanation:
In triangle ABC, the known side is AC, which is equal to 6. The corresponding side to AC from triangle DEF would be FD, which is equal to 2. You divide 6/2 in order to get 3/1.
I need help on this question
Answer:
wow that is a tough one the answer is 438654
Step-by-step explanation:
all that is to it
What is the approximate volume of a cone with a height of 9 ft and radius of 3 ft? Use 3.14 to approximate pi, and express your final answer to the nearest hundredth Enter your answer as a decimal in the box. ft3
Diana can earn money for the tickets she sells. Which of the following statements describes the variables in this situation correctly?
The amount of money earned is the independent variable because it affects the number of tickets sold.
The amount of money earned is the dependent variable because it affects the number of tickets sold.
The number of tickets sold is the independent variable because it affects the amount of money earned.
The number of tickets sold is the dependent variable because it affects the amount of money earned.
Answer:
Option 3 is the correct answer.
Answer: The number of tickets sold is the independent variable because it affects the amount of money earned.
Step-by-step explanation: I just took test got 100%
The number of tickets sold is the independent variable because it affects the amount of money earned.
Please answer this relatively quickly, I'm not in very much of a rush but would like to get this done.
Answer: 6
Step-by-step explanation:
Because you have to multiply then remove the fraction and set equal to 0 and solve for x which I’m pretty sure gives u 6
solve plssss before i dieee i give points
Answer:
should be 66% of children and 1650 children in the town
Step-by-step explanation:
At Daniel's Swimwear, there are 76 bikini styles and 4 other types of swimsuit. What percentage of the swimsuit styles are bikinis?
Total swimwear = 76 bikinis + 4 other types = 80 total
divide number of bikinis by total swimwear then multiply by 100:
76/80 = 0.95
0.95 x 100 = 95%
Answer: 95% are bikinis
After eating a meal at a restaurant, we decided to tip 25%, building a grand total of $87.50. What was the price before the tip?
Answer:
65.62
Step-by-step explanation:
Given:
After eating a meal at a restaurant, we decided to tip 25%, building a grand total of $87.50.
To find:
Price before tip
Solution:
87.50 × 25% = 21.875
~Round~: 21.875 to 21.88
87.50 - 21 .88 = 65.62
Thus the price before the tip is 65.62
Check Answer:
Formula: Higher number - Lower number ÷ original number × 100
Solve:
87.50 - 65.62 = 21.88
21.88 ÷ 87.50=0.25005714285
0.25005714285 × 100 = 25.0057142857
Round - 25%
~lenvy~
if <1 and <2 are vertical angles. If m<1=(5x +12) and m<2=(6x-11), find m<1
Answer:
its 23
Step-by-step explanation:
A missionary used his plane to take an injured girl 855 kilometers to the hospital. If he flew at an average speed of 171 kilometers per hour, how long did it take to reach the hospital?
Step-by-step explanation:
171 km/h
travel distance = 855 km
855 / 171 = 5 hours
it took him 5 hours to fly the 855 km (theoretically to the hospital).
normally, with a plane, you can't land on or at a hospital. you would need a helicopter to be able to do that.
so, he could only fly to a nearby airport, and then travel from there to the hospital. but we have no information about that.
How can i prove this property to be true for all values of n, using mathematical induction.
ps: spam/wrong answers will be reported and blocked.
Proof -
So, in the first part we'll verify by taking n = 1.
[tex] \implies \: 1 = {1}^{2} = \frac{1(1 + 1)(2 + 1)}{6} [/tex]
[tex] \implies{ \frac{1(2)(3)}{6} }[/tex]
[tex]\implies{ 1}[/tex]
Therefore, it is true for the first part.
In the second part we will assume that,
[tex] \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} = \frac{k(k + 1)(2k + 1)}{6} }[/tex]
and we will prove that,
[tex]\sf{ \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 1 + 1) \{2(k + 1) + 1\}}{6}}}[/tex]
[tex] \: {{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 2) (2k + 3)}{6}}[/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k (k + 1) (2k + 1) }{6} + \frac{(k + 1) ^{2} }{6} [/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k(k+1)(2k+1)+6(k+1)^ 2 }{6} [/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)\{k(2k+1)+6(k+1)\} }{6}[/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2 +k+6k+6) }{6} [/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2+7k+6) }{6} [/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(k+2)(2k+3) }{6} [/tex]
Henceforth, by using the principle of mathematical induction 1²+2² +3²+....+n² = n(n+1)(2n+1)/ 6 for all positive integers n.
_______________________________
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If my dot plot is not skewed or symmetrical which measure of variability should I use? (15 data points) PLEASE HELP THE ASSIGNMENT IS DUE TONIGHT!
these are the data points: 5,6,7,7,7,8,8,9,9,9,9,9,10,10,11
I also need the best measure of center!
If the data is not skewed, then the mean is the best measure of center.
This then also includes the standard deviation because the standard deviation relies on the mean.
To get the mean, add up the data values:
5+6+7+7+7+8+8+9+9+9+9+9+10+10+11 = 124
Then divide by the sample size n = 15
124/n = 124/15 = 8.267 approximately
Once you determine the mean, you can then determine the standard deviation which involves a bit more complicated steps. The rough outline is:
Subtract each data value from the mean. So right off the bat, we can see how important the mean is when it comes to calculating the standard deviation.Square those differences from step one.Add up the squares to get the Sum of the Squared Errors (SSE)Divide the SSE by n-1 to get the sample variance, or divide by n to get the population variance. It will depend on context which version you go for.Apply the square root to the variance to get the standard deviation.Once again, step 1 shows how critical the mean is to finding the standard deviation. The standard deviation measures how far each value is from the mean on average. In other words, it's like a measure of the average distance from the mean.
Use of spreadsheet software is strongly recommended to keep track of everything. You can also use a standard calculator to compute the standard deviation. There are also tons of free online calculators that can help out with that as well.
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If the data was skewed to one side, then the median is the better measure of center because it is not affected by outliers. The IQR (interquartile range) is used instead of the standard deviation for skewed distributions.
I need help with this question 80 pts
Answer:
65
Step-by-step explanation:
angle 2 is equal to angle 4, so that means angle 4 is also 130⁰.
130=2y
130/2=2y/2
65=y
Answer:
y = 65°
Step-by-step explanation:
Vertical Angle Theorem: When two straight lines intersect, the opposite vertical angles are always equal (congruent) to each other.
⇒ m∠2 = m∠4
⇒ 130° = 2y
⇒ y = 130° ÷ 2
⇒ y = 65°
what is 0.0981 rounded to the nearest tenth of a percent
Answer:
0.1 percent
Step-by-step explanation:
sorry I don't have an explanation. sorry if it's wrong, at least I tried
Answer:
0.1
Explanation:
It's right
How far could the Apostle Paul walk in 4.5 hours if he walked an average of 4.3 kilometers per hour?
Answer 19.35 km
Step-by-step explanation:
We are looking for the Distance that Apostle Paul walked in 4.5 Hours!
I will be using the formula Distance=rate*time 1)
We DONT know the distance so I'll leave it as variable "D".
We know his rate of walking is 4.3 km/h, and we know he walked for a total of 4.5 hours.
Set up the following equation. D=4.3*4.5 2)
Simplify the equation above: D=19.35
please answer the following questions
Answer:
False
Step-by-step explanation:
There are some quadratic equations that cannot be solved using the factoring technique. That is why the quadratic formula exists, to solve equations that cannot be factored.
A sample of radium has a weight of 1.5 mg and a half-life of approximately 6 years.
a. How much of the sample will remain after 6 years?
Answer:
0.75mg
Step-by-step explanation:
6 years is its half life, meaning that half of it will have iradiated by that point. 1.5 / 2 = 0.75
spherical water tank of radius R = 5m is emptied through a small circular hole of radius r = 0.03 m at the bottom. The top of the tank is open to the atmosphere. The instantaneous water level h in the tank (measured from the bottom of the tank, at the drain) can be determined from the solution of the following ODE:
dh /dt =r²(2gh)^0.5/ 2hR-h²
where g = 9.81 m/s². If the initial (t = 0) water level is h=6.5 m, compute the time required to drain the tank to a level of h= 0.5m. Use the fourth-order Runge-Kutta method.
Answer:
water level is h=6.5 m, compute the time required to drain the tank to a level of h= 0.5m. Use the fourth-order Runge-Kutta method.
Step-by-step explanation:
water level is h=6.5 m, compute the time required to drain the tank to a level of h= 0.5m. Use the fourth-order Runge-Kutta method.
The price of a used car that Billy is buying is $5,000. If he has to pay 8% in taxes, how much will be have to pay for the car including taxes?
Answer:
5400
Step-by-step explanation:
8% of 5000 is 400. 5000 + 400 - 5400.
Answer:
$5400
Step-by-step explanation:
We need to find the amount of tax in $
So, if 100% = $5000
8% = ?
cross multiply to be : 8 × 5000
100
to get $400
Add it to the $5000 to get $5400
What is the value of n in the equation below?
Answer:
9
Step-by-step explanation:
12ⁿ⁻⁵ = 12⁴
n - 5 = 4
n = 9
what is 3.1 converted into a simplified fraction?
Answer:
31/10
Step-by-step explanation:
Choose the multiplication problem that correctly shows partial products.
A) A
B) B
C) C
Answer:
B) B
Step-by-step explanation:
2 times 4 is 8, so in this case the option is option b as none of the other options show this.
In total,
2 * 4 = 8
60 * 4 = 240
240 + 8 = 248
What is the value of a,c ?
Answer:
Step-by-step explanation:
Inscribed angle of diameter is 90°
⇒ ∠ACB = 90°
In ΔACB,
∠A + ∠ B + ∠ACB = 180° {Angle sum property of triangle}
a + 4a + 90 = 180
5a + 90 = 180
5a = 180 - 90
5a = 90
a = 90 ÷ 5
a = 19 -----------(I)
In ΔCOB,
OC = OB {Radius}
⇒ΔCOB is an isosceles triangle.
c = 4a {angles opposite to equal angles are conguent}
c = 4*19 {From (I)}
c= 76
3/9 and 1/2 common denominator
Given:
[tex]\frac{3}{9}[/tex] and [tex]\frac{1}{2}[/tex]
Finding a common denominator:
9 * 2 = 18
-> If you need to stop here, a common denominator is 18.
Converting [tex]\frac{3}{9}[/tex]:
[tex]\frac{3}{9}[/tex] = [tex]\frac{3*2}{9*2}[/tex] = [tex]\frac{6}{18}[/tex]
Converting [tex]\frac{1}{2}[/tex]:
[tex]\frac{1}{2}[/tex] = [tex]\frac{1*9}{2*9}[/tex] = [tex]\frac{9}{18}[/tex]
-> [tex]\frac{6}{18}[/tex] and [tex]\frac{9}{18}[/tex]