QUICKLY!! We know that a triangle with side lengths x^2-1,2x and x^2+1 is a right triangle. Using those side lengths, find the missing triples and x-values.
Write the triples in parentheses, without spaces between the numbers, and with a comma between numbers. Write the triples in order from least to greatest.
Type the correct answer in each box.
x value--------------------pythagorean triple
3 ____________
________ (8,15,17)
5 ______________
__________ (12,35,37)
Answer:
[tex]\begin{array}{ccl}x \ value&&Pythagorean \ triple\\3&&(6, 8, 10)\\4&&(8, 15, 17)\\5&&(10, 24, 26)\\6&&(12, 35, 37)\end{array}[/tex]
Step-by-step explanation:
The given side lengths of the right triangle are;
x² - 1, 2·x and x² + 1
A Pythagorean triple are three numbers, a, b, and c, such that, we have;
a² + b² = c²
From the given side lengths, we have;
We note that (x² + 1) > (x² - 1)
(x² + 1) > 2·x for x > 1
Therefore, with (x² + 1) as the hypotenuse side, we have;
(x² - 1)² + (2·x)² = (x² + 1)²
Therefore, when the x-value is 3, we have;
(3² - 1)² + (2 × 3)² = (3² + 1)²
8² + 6² = 10²
The least is 6² = (2 × 3)², from (2·x)²
Therefore;
The Pythagorean triple is 6, 8, 10
The order of the triple is (2·x), (x² - 1), (x² + 1)
2) The x-value for the triple, (8, 15, 17), is obtained as follows;
The least, 8 = 2·x
∴ x = 8/2 = 4
The x-value = 4
3) The Pythagorean triple where the x-value = 5 is therefore;
(2·x), (x² - 1), (x² + 1), where x = 5 gives; (2×5 = 10), (5² - 1 = 24), (5² + 1 = 26)
Therefore, the Pythagorean triple where x = 5 is 10, 24, and 26
4) The x-value for the Pythagorean triple (12, 35, 37) is given by 12 = 2·x
Therefore, x = 12/2 = 6
Therefore, we get;
[tex]\begin{array}{ccl}x \ value&&Pythagorean \ triple\\3&&(6, 8, 10)\\4&&(8, 15, 17)\\5&&(10, 24, 26)\\6&&(12, 35, 37)\end{array}[/tex]
Toby's little brother used his set of wooden blocks to build a giant tower. He stacked up 30 blocks to make a tower that was 64 inches tall.
How tall is each block?
Write your answer as a proper fraction or mixed number.
Solution to the question:
Number of blocks stacked: 30
Height of tower: 64 inches
Height of each block: ?
To find the height of each block, we divide the total height of the tower with the number of blocks stacked
Therefore,
Height of each block: 64/30 = 2.13 inches
So, the height of each block is 2.13 inches.
Which of the following values is closest to the standard deviation for the set
of data shown below?
23, 64, 73, 47, 22, 46, 34, 48, 67, 89, 83, 12, 23, 44, 16
I don't have a question
Answer:
then why are you asking?
Step-by-step explanation:
okay
How would the domain and range of the function y = one-fourth x minus 6 be determined? Explain.
Answer:
Domain = ( -∞ , ∞ )
Range = ( ∞ , ∞ )
Step-by-step explanation:
A function is given to us and we need to find the domain and range of the given function .
The function :-
[tex]\rm \implies y = \dfrac{1}{4}x - 6 [/tex]
Definitions :-
Range :- The range is the set of all valid y values .Domain :- All real numbers except where the expression is undefined.In this case, there is no real number that makes the expression undefined. Therefore the domain will be :-
Domain :-
[tex]\rm Domain = ( -\infty , \infty ) [/tex]
or
[tex]\rm Domain = \{ x | x \in \mathbb{R} \}[/tex]
Range :-
[tex]\rm Range = ( -\infty , \infty ) [/tex]
or
[tex]\rm Range = \{ y | y \in \mathbb{R}\} [/tex]
Answer:
Create a table or a graph of the function. The domain represents all input values and the range represents all output values. The domain and range contain all real numbers.
Step-by-step explanation:
what are the x-coordinates of the solutions? Choose all that apply.
a. -2
b. 1
c. -1
d. 0
Answer:
a. -2
c. -1
Step-by-step explanation:
these are the only values for x, where the 2 equations deliver the same y value.
in case of a. y = -2×-2 - 1 = 4 - 1 = 3
and y = 3¹ = 3
c. y = -2×-1 - 1 = 2 - 1 = 1
y = 3⁰ = 1
If you know the answer to any of these please Ill mark brainliest.
Answer:
Step-by-step explanation:
1) 2/9 = 185/x
2x = 1665
x = 832.5 or 8.325 meters
2) unit rate is the cost of one unit
i.e a dozen eggs cost $1.20 that
would be 10 cents each
3) 300 tissues for $3.75 vs. 250 for $2.99
one is 1.24 cents per tissue
the other 1.19 ... the 250 package is a better buy
Somebody please help me!!!
Find the value of t for a t-distribution with 12 degrees of freedom such that the area to the left of t equals 0.025. Round your answer to three decimal places, if necessary.
Answer:
-2.179
Step-by-step explanation:
Given :
Degree of freedom, df = 12
Area to the left = 0.025
The value of T can be obtained using either a t distribution table or a T value calculator :
t0.025, 12 (to the left) = t(1-0.025), 12 = t0.975,12 = - 2.1788
Therefor le, t value with 12 degree of freedom, with area to the left being 0.025 is - 2.179
You have 3 pounds of egg whites. You need 8 oz to make one serving of consommé.How many servings can you make?
The number of servings you can make is 6
How to determine the number of servings?The given parameters are:
Available = 3 poundsContent per serving = 8 ozNext, we convert oz to pounds
Content per serving = 8 * 0.0625 pound
This gives
Content per serving = 0.5 pound
The number of serving is then calculated as:
Number = Available/Content per serving
This gives
Number = 3/0.5
Evaluate
Number = 6
Hence, the number of servings is 6
Read more about proportions at:
https://brainly.com/question/1781657
#SPJ9
Solve the system of equations.
−5x−3y−9=0
4x−18y−54=0
y=? x=?
Answer:
Step-by-step explanation:
Eq. 1 ) −5x−3y−9=0
Eq. 2) 4x−18y−54=0
there are two routes to solve this, Substitution or elimination, I'll go for the 2nd one because I can see that the y values are a multiple of each other :)
6 *( −5x−3y−9=0 )
Eq. 3) -30x -18y =54
subtract Eq. 2 from Eq. 3 :)
-30x -18y =54
-( 4x−18y=54)
-34x = 0
so according to the equations then x =0 but, that's not really a full answer, so now we should go back and try the other method, substitution,
then:
-5x = 9 +3y
x = - 9/5 + (-3/5)y
now plug that into Eq. 2
4( - 9/5 + (-3/5)y ) - 18y = 54
-36/5 + (-12/5)y -18y = 54
(-12/5)y - (90/5)y = 54+36/5
-(102/5)*y =270/5+36/5
-(102/5)y = 306/5
y = (-5/102)*(306/5)
y = -306/102
y = -3
then plug in for either equation
-5x-3( -3) = 9
-5x + 9 = 9
-5x = 0
x = 0
now we have the full answer
check it by plugging in both x and y into the 2nd equation
4(0) - 18(-3) = 54
54= 54
this seems good
A farmer in China discovers a mammal
hide that contains 71% of its original
amount of C-14.
N = Noekt
No = inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
Answer:
Step-by-step explanation:
I'm assuming you're looking for the age of the mammal hide, since there's no question here, but there's also nothing else to solve for. Remember a few things before we move on. First, if we are not told the initial amount with which we start, we have to assume that it's 100%. Second, remember that natural log and e are inverses of each other so they eliminate each other in application. Now to set up the problem. It looks like this:
[tex]71=100e^{-.0001t}[/tex] and begin by dividing both sides by 100 to get
[tex].71=e^{-.0001t}[/tex] and take the natural log of both sides. The other important thing to remember about the rules for logs and natural logs is that when you take the natural log of something, you are "allowed" to move the exponent down out front, which is why we do this. We cannot currently solve for t when it's stuck up there where it is right now. Taking the natural log allows us to bring that exponent down AND eliminate both the natural log and the e at the same time:
ln(.71) = -.0001t and we divide to solve for t:
[tex]\frac{ln(.71)}{-.0001}=t[/tex] and
[tex]\frac{-.3424903089}{-.0001}=t[/tex] so
t = 3424.9 years, or rounded, 3425 years.
Every floor of a 20 storey building is 5m in high. If a lift moves 2m every second, how long will it take to move from 3rd floor to 15th floor?
Answer:
30 seconds
Step-by-step explanation:
→ Work out how many floors it's going to travel
15 - 3 = 12 floors
→ Work out how many meters 12 floors is
12 × 5 = 60 meters
→ Work out how long that will take
60 ÷ 2 = 30 seconds
(Ignore)-Character fill- jsysbssmhzbsskkdhsbsnsdjsvsvsbsjhs
Step-by-step explanation:
[tex]x = kh \\ x = 33 \\ hj = 4x + 9 \\ x = 9 - 4 \\ x = 5 \\ jk = 3x + 3 \\ x = 3 - 3 \\ x = 0[/tex]
Sabe-se que EF = xcm , GH = (x + 6) cm , RS = 16 cm e NP = 28 cm . Sabendo que EF ,GH , RS ,e NP São, nessa ordem, segmentos proporcionais, determine o valor de x .
Answer:
The value of x is 8 .
Step-by-step explanation:
It is known that EF = x cm , GH = (x + 6) cm , RS = 16 cm and NP = 28 cm . Knowing that EF ,GH , RS , and NP are, in that order, proportional segments, determine the value of x .
As EF, GH, RS and NP are in proportion
So,
EF : GH = RS : NP
[tex]\frac{x}{x+6}=\frac{16}{28}\\\\7 x = 4 (x + 6)\\\\7 x = 4 x + 24 \\\\3 x = 24 \\\\x = 8[/tex]
Latoya created a factor tree and wrote the prime factorization of 90 shown below.
A factor tree of 90. 90 branches to 9 and 10. 9 branches to 3 and 3. 10 branches to 2 and 5. The equation is 90 = 2 times 3 times 5.
What is Latoya’s error?
She should not have found the factors of 9.
She should have included an exponent of 2 on the 3.
She should have included 9 and 10 in the prime factorization.
She should have started the tree with 2 times 45.
Answer:
She should have included an exponent of 2 on the 3
Step-by-step explanation:
The factor tree can be presented as follows;
[tex]{}[/tex] 90
[tex]{}[/tex] ↓
[tex]{}[/tex] 9 ↔ 10
[tex]{}[/tex] ↓ ↓
[tex]{}[/tex] 3 ↔ 3 2 ↔ 5
Therefore, the prime factorization of 90 is equal to 90 = 3 × 3 × 2 × 5
She should have wrote, 90 = 3² × 2 × 5
Therefore, the error is that she should have included an exponent of 2 on the 3.
Answer:
B
✔ She should have included an exponent of 2 on the 3.
Step-by-step explanation:
E2021
How to solve ,step by step
Answer:
gradient = slope = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{rise}{run}[/tex]
Slope intercept Form equation : y = mx + b
m = slope or gradient
b = y - intercept ( where the line crosses the y = axis)
x and y = are place holders for a coordinate pair that makes the equation true
c) y = -6x + 8
The -6 is the m. It's the slope or gradient.
the + 8 is the b. It's the y- intercept.
d) y = 4
This is a horizontal line. It intercepts the y-axis at 4.
That means the 4 is the y-intercept.
There is no x. That means the slope is 0. The line rises 0 as it runs left to right.
e) y -4x= 0
equation needs to be is standard form y = mx + b.
add 4x to both sides in order to isolate the y variable.
y = 4x + 0.
The slope or gradient is 4. The y - intercept is 0. The line crosses through the origin.
f) y -x = -8
Add x to both sides.
y = x - 8
There is one x. That means the gradient is 1. The y-intercept is the -8
g) y + 3x = 7
Subtract 3x from both sides.
y = -3x + 7
-3 = gradient. 7 = y-intercept.
h) y + [tex]\frac{1}{2}[/tex]x = -4
Subtract [tex]\frac{1}{2}[/tex]x from each side.
y = -[tex]\frac{1}{2}[/tex]x - 4
One last thing. If you are presented with an equation without a y, the gradient is 'undefined'.
example : x = 4
This a vertical line passing through 4 on the x-axis. There is no 'b' because its not crossing the y-axis.
Why is it 'undefined' ?
As the line rises it, it does not 'run' left or right. [tex]\frac{rise}{0}[/tex] . Zero can never, ever be in the denominator. Denominators can't be zero. That is why we say it's 'undefined'.
Hope this helps.
Evalute f (3) if(x) = -4x+5
Answer: f(3)=-7
Step-by-step explanation:
To evaluate f(3), we want to plug in x=3 into f(x)=-4x+5.
f(3)=-4(3)+5 [multiply]
f(3)=-12+5 [add]
f(3)=-7
Now, we know that f(3)=-7.
Find the measure of the indicated angle
Answer:
76°
Step-by-step explanation:
180-(2*52)
= 180-104
= 76
Answered by GAUTHMATH
if f(x) = 2x² +1 and g(x) = x² - 7 find (f+g) (x)
Help me find (f+g)(x) please!
Answer:
[tex](f+g)(x) = 3x^2 - 6[/tex]
Step-by-step explanation:
[tex]f(x) = 2x^2 + 1, \ g(x) = x^2 - 7\\\\(f +g)(x) = f(x) + g(x) \\\\(f+g)(x) = 2x^2 + 1 + x^2 - 7 \\\\(f+ g)(x) = 3x^2 - 6[/tex]
The sum of four consecutive numbers is two more than three times the greatest of these numbers. Find the numbers.
Answer:
9, 10, 11, 12
Step-by-step explanation:
Let the consecutive numbers be:
x, x+1, x+2, x+3
Greatest of the numbers will be: x + 3
x+x+1+x+2+x+3 = 3(x+3) + 2
4x + 6 = 3(x+4) + 2
4x + 6 = 3x + 12 + 2
4x + 6 = 3x + 14
Collect like terms
4x - 3x = 14 - 6
x = 8
x +1 = 8+ 1 = 9
x + 2 = 8 + 2 = 10
x + 3 = 8 + 3 = 11
x + 4 = 8 + 4 = 12
Choose the correct answer from the given four options:In an AP if a = –7.2, d = 3.6, an = 7.2, then n
2
4
3
5
Answer:
n=5
Step-by-step explanation:
by using
n=(an-a)/a+1
substituting values
n= 7.2-(-7.2)/3.6 +1
n=5
find the value of the given equation (-155)+(-20) + (-14) + (-133) + (190) + (170) +(-73)
Answer:
-37
Step-by-step explanation:
-155-20-14-133-73=-395
190+170=360
-395+360=-37
square root of 10 using graph.
please help
Step-by-step explanation:
final answer is 4 91 1 6 this is square root of 10
If m2BGF = 152° what is mLAGF?
Answer:
152-88 = 64
Step-by-step explanation:
my friend took time to round once around a circular field is 30seconds. Calculate the area of field of the school of his speed is 90 meter/sec
Answer:
im bad at math but i think its 120
Sierra king is a nail technician she allows 20 minutes for a manicure and 45 for a pedicure in her 7 hour work day no more than 5 pedicures can be scheduled each day the prices are $18 for a Medicare and $45 for a pedicure how many manicures and pedicures should ms.king schedule to maximize her daily income? what is her maximum daily income?
Answer: the income is 369$
Step-by-step explanation:
please I need answer right now pleasssseee
only C
C. -3×(-2/3)²
Answer:
-4/3
Step-by-step explanation:
-3 x (-2/3)²
= -3 x (4/9)
= -4/3
FOR EASY BRAINLIEST ANSWER QUESTION BELOW!
1. Solve each word problem .twice a number added three times the sum of the number and 2 is more than 17. Find the numbers that satisfy condition
Answer:
x > 23/5
Step-by-step explanation:
2x+ 3(x+2)>17
2x + 3x + 6 >17
5x >23
x > 23/5
PLZ Find a ratio equivalent to 9/10. Then use the ratios to write a proportion.
a 70/63 9/10=70/63
b 19/70 9/10=19/70
c 19/20 9/10=19/20
d 63/70 9/10=63/70
Answer:
63/70 = 9 : 10
Step-by-step explanation:
Given ratio:
9/10
a 70/63
= 10/9
= 10 : 9
b 19/70
= 19:70
c 19/20
= 19 : 20
d 63/70
= 9/10
= 9 : 10
The equivalent ratio to 9/10 = 63/70
= 9 : 10