Answer:
[tex]x=\sqrt{13}[/tex]
Step-by-step explanation:
[tex]x^{2} - 6 - 7 = 0 \\x^{2} =13\\x=\sqrt{13}[/tex]
How many square feet are there in a rectangular-shaped building that is 34 feet wide and 72 feet long?
The area of the rectangular-shaped building is 2448 square feet.
What is the area of the rectangle?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
Given that a rectangular-shaped building that is 34 feet wide and 72 feet long. The area of the rectangle will be calculated as below:-
Area of rectangle = Length x width
Area of rectangle = 34 x 72
Area of rectangle = 2448 square feet
Therefore, the area of the rectangular-shaped building is 2448 square feet.
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write the non-teerminating decimal as fraction 0.555555555...
Answer:
111111111/200000000
-4 + (3)^2÷ (5 + 4) • 3
Answer: -1
Step-by-step explanation:
We will use the Order of Operations to solve;
Given:
-4 + (3)² ÷ (5 + 4) • 3
Addition in parentheses:
-4 + 9 ÷ (9) • 3
Raise to the power of 2:
-4 + 9 ÷ (5 + 4) • 3
Division:
-4 + 1 • 3
Multiplication:
-4 + 3
Addition:
-1
What is your monthly take home pay if your take home pay is $897.84 every monday
Pls help asap!! due in a hour:( thanks in advance
Answer: 8oz of the 20% and 12oz of the 70%
Step-by-step explanation:
(20*x) + (70*(20-x)) / 20 = 50
(20x +1400-70x) / 20 =50
20x +1400-70x = 1000
50x=400
x=8
20-8=12
A, B and C are coordinates on the line y = x − 7.
Use the table of values to find A, B and C.
1
Y
-8
Coordinates A
notand
X
0
-7
B
1
6
C
The coordinates of A, B and C are (-1, -8), (0, -7) and (1, -6) respectively.
Here, we are given that A, B and C are coordinates on the line y = x − 7.
Also, we are given the following table for x and y values of A, B and C
x -1 0 1
y -8 -7 -6
coordinates A B C
The coordinates of a point are written in (x, y) format where x and y are the values of the x and y axis respectively.
Thus, the coordinates of A are (-1, -8)
the coordinates of B are (0, -7)
and the coordinates of C are (1, -6)
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5 x=10
if u have 5 apple and 10 cakes how many do u come up with
Answer:
x = 2
Step-by-step explanation:
Equation: 5x = 10
--- Divide 5 on both sides
x = 2
This means that each apple can make 2 cakes.
Answer: 2
Step-by-step explanation: because if u divide both sides by 5
Can someone help me with this problem? Thank you!
Please HELP ASAP!!!!
Solve negative a minus five eighths equals three fifths for a.
The solution of the expression for a is a = -1 9/40
How to solve the expression?The expression is given as:
negative a minus five eighths equals three fifths for a.
Rewrite the expression properly as:
-a - 5/8 = 3/5
Collect the like terms in the above expression
So, we have:
a = -5/8 - 3/5
Evaluate the like terms in the above expression
So, we have:
a = -1 9/40
Hence, the solution of the expression for a is a = -1 9/40
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Colton looks around at an assembly. he notices his younger sister to his right and his older brother 7 feet ahead of him. if colton's brother and sister are 8 feet apart, how far apart are colton and his younger sister? if necessary, round to the nearest tenth.
Colton is approximately 3.9 feet apart from his younger sister.
Pythagoras Theorem:
The statement o the Pythagoras theorem is, "if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. "
Then it can be written as,
BC² = AB² + AC².
Where,
AB is the base,
AC is the altitude (height), and
BC is the hypotenuse.
Given,
Colton looks around at an assembly. he notices his younger sister to his right and his older brother 7 feet ahead of him.
And Colton's brother and sister are 8 feet apart.
Now, we need to find the distance between Colton and his younger sister.
Based on the given statement, we can draw their position like the following figure.
Here B represents the position of Colton, A represents the position of his older brother and C represents the position of his younger sister.
Now, we have to use the Pythagoras Theorem in order to solve it,
=> 8² = BC² + 7².
=> 64 = BC² + 49
=> 64 - 49 = BC²
=> BC² = 15
=> BC = √15
Therefore,
=> BC ≈ 3.9 feet
Therefore, the distance between Colden and his younger sister is approximately 3.9 feet.
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Chloe and tino have a combined age of 48. three years ago chloe was double the age tino is now. find tinos age
(solve using simultaneous equations)
As given Chole and Tinos age , the present age of Tino is equal to 15 years.
As given,
Let x and y be the present age of Chole and Tino. respectively.
Combined age = 48
Given condition,
x + y = 48 _______(1)
Three years ago
x - 3 = 2y
⇒x =2y +3 _______(2)
Substitute the value of x in (1),
2y+3 +y =48
⇒ 3y = 45
⇒ y = 15years
Therefore , as given Chole and Tinos age , the present age of Tino is equal to 15 years.
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The number 3465 is divisible by 11 and 5. Given that you change the position of two or more of these four digits, how many of the resulting numbers are divisible by 11 but not by 5?
Answer:
Divisible rule of 11
If the number of digits of a number is even, then add the first digit and subtract the last digit from the rest of the number
Divisible rule of 5
Divisibility by 5 is easily determined by checking the last digit in the number. If the last number is either 0 or 5, the entire number is divisible by 5.
First of all, the number 3456 is not divisible by 11 and 5.
But if we change position of digits then the numbers divisible by 11 are-
3564 / 11= 324
3465 / 11= 315
3465 / 5= 693
4356 / 11 = 396
4653 / 11 = 423
5346 / 11 = 486
5643 / 11 = 513
6534 / 11 = 594
6435 / 11 = 585
6435 / 5=1287
But the numbers 3465 and 6435 are also divisible by 5
So the numbers divisible by 11 but not with 5 are:
3564 , 4356, 4653, 5346, 5643 and 6534
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Group Activity let U= { 2, 4, 6, 8, 10, 12, 14, 16, 18} A = {4, 10, 12, 14,18} B = { 2,4,6,8,10,14,16} Drow the Venn diagram and Find 1.A' 2.B' 3.(AUB)' 4.A'UB'
We get A' as { 2, 6, 8, 16}. B' as {12, 18}, (AUB)' as ∅ and A' U B' as {2, 6, 8, 12, 16, 18}.
We are given the sets as:
U= { 2, 4, 6, 8, 10, 12, 14, 16, 18}
A = {4, 10, 12, 14, 18}
B = { 2, 4, 6, 8, 10, 14, 16}
We first will find out A':
A' = U - A
A' = { 2, 4, 6, 8, 10, 12, 14, 16, 18} - {4, 10, 12, 14, 18}
A' = { 2, 6, 8, 16}
Now, we will find B':
B' = U - B
B' = { 2, 4, 6, 8, 10, 12, 14, 16, 18} - { 2, 4, 6, 8, 10, 14, 16}
B' = { 12, 18}
Now, we have to find:
(AUB)' = U - (AUB)
AUB = {4, 10, 12, 14, 18} U { 2, 4, 6, 8, 10, 14, 16}
AUB = { 2, 4, 6, 8, 10, 12, 14, 16, 18} = U
(AUB)' = U - U = ∅.
Now, we will find A' U B':
A' U B' = { 2, 6, 8, 16} U { 12, 18}
A' U B' = {2, 6, 8, 12, 16, 18}
Therefore, we get A' as { 2, 6, 8, 16}. B' as {12, 18}, (AUB)' as ∅ and A' U B' as {2, 6, 8, 12, 16, 18}.
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Find the functions and their domains. (enter the domains in interval notation.) f(x) = x 1 x , g(x) = x 14 x 2
Functions and their domains of all the subparts are:
(A) (fog)(x) and the domain is [tex](-\infty, \infty)[/tex].(B) (gof)(X) and the domain is [tex](-\infty, \infty)[/tex].(C) (fof)(x) and the domain is [tex](-\infty, \infty)[/tex].(D) (gog)(x) and the domain is [tex](-\infty, \infty)[/tex].What are functions?A function is an expression, rule, or law in mathematics that defines a relationship between a dependent thing (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.So,
(A) (fog)(x) and domain:
[tex](f \circ g)(x)=f(g(x))=(g(x))^2+g(x)=\left(x^2+14 x+2\right)^2+x^2+14 x+2\\=x^4+28 x^3+200 x^2+56 x+4+x^2+14 x+2=x^4+28 x^3+201 x^2+70 x+6[/tex]
The domain of (fog)(x) is the collection of domain values for g(x) with range values in the domain of f(x).
Because both functions are polynomials, the domain is [tex](-\infty, \infty)[/tex].
(b) (gof)(X) and domain:
[tex](g \circ f)(x)=g(f(x))=(f(x))^2+14(f(x))+2=\left(x^2+x\right)^2+14\left(x^2+x\right)+2\\=x^4+2 x^3+x^2+14 x^2+14 x+2=x^4+2 x^3+15 x^2+14 x+2[/tex]
The domain name is [tex](-\infty, \infty)[/tex] because this is a polynomial composition.
(c) (fof)(x) and domain:
[tex]\begin{aligned}&(f \circ f)(x)=f(f(x))=(f(x))^2+f(x)= \\&\left(x^2+x\right)^2+x^2+x=x^4+2 x^3+x^2+x^2+x=x^4+2 x^3+2 x^2+x\end{aligned}[/tex]
Because this is a polynomial composition, the domain is [tex](-\infty, \infty)[/tex].
(d) (gog)(x) and domain:
[tex](g \circ g)(x)=g(g(x))=(g(x))^2+14(g(x))+2=\left(x^2+14 x+2\right)^2+14\left(x^2+14 x+2\right)+2\\=x^4+28 x^3+200 x^2+56 x+4+14 x^2+196 x+28+2=x^4+28 x^3+214 x^2+252 x[/tex]
Because this is a polynomial composition, the domain is [tex](-\infty, \infty)[/tex].
Therefore, functions and their domains of all the subparts are:
(A) (fog)(x) and the domain is [tex](-\infty, \infty)[/tex].(B) (gof)(X) and the domain is [tex](-\infty, \infty)[/tex].(C) (fof)(x) and the domain is [tex](-\infty, \infty)[/tex].(D) (gog)(x) and the domain is [tex](-\infty, \infty)[/tex].Know more about functions here:
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The complete question is given below:
Find the functions and their domains. (enter the domains in interval notation.)
[tex]f(x)=x^2+1 x, g(x)=x^2+14 x+2[/tex]
(a) (fog)(x) and domain
(b) (gof)(X) and domain
(c) (fof)(x) and domain
(d) (gog)(x) and domain
In a shipment of 62 vials, only 14 do not have hairline cracks. if you randomly select 3 vials from the shipment, what is the probability that all 3 of the selected vials have hairline cracks?
The probability that all three of the selected vials have hairline cracks = 0.096
Total number of vials in the shipment = 62
Number of vials with hairline cracks = 14
Number of vials without hairline cracks = 48
Three from 62 vials are selected.
So total outcomes = 62C3
Number of possible outcomes for all 3 of selected vials have hairline cracks = 14C3, which is the number of favorable outcomes
Probability that all three of the selected vials have hairline cracks = Number of favorable outcomes/Total outcomes = 14C3/62C3 = 0.096
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What is 8 and 3/4 into inproper fraction
Answer:
35/4
Step-by-step explanation:
8*4=32
32+3
=35
35/4
The number of digits in the square root of 3686400 is ---------
[one word Q]
Answer:
4
Step-by-step explanation:
[tex]\sqrt{x} 368640 = 1920[/tex]
The number of digits in 1920 is 4
The number of digits in the square root of 3686400 is 4.
What is square root?In mathematics, the square root is a component that, when multiplied by itself, equals the original integer. For instance, the square roots of 9 are both 3 and -3.
The square root of 3686400 is,
√3686400 = ±1920
The number of digits in 1920 is 4.
Only four digits make up 4-digit integers; the first digit must be one or higher, and the other three can be any number between 0 and 9. Examples of four-digit numbers include 5693, 1023, and 9825.
Thus, the number of digits in the square root of 3686400 is 4.
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Graph the equation y= -2x+250
Answer:
Graph in the picture
la suma de los primeros n enteros positivos es un numero de tres digitos iguales. cual es la suma de los digitos de n?
The sum of n natural numbers is three digits number and all digits are the same. The same digits is 6 and the sum is 666.
A three-digit number with the same digits is the sum of n natural numbers.
Let's say the sum of n natural numbers is bbb.
Then,
n( n + 1) / 2 = bbb
n( n + 1) / 2 = b( 111 )
n( n + 1) / 2 = b ( 3 × 37 )
n( n + 1) = 6b × 37
Now, the left-hand side of the equation is the product of two consecutive natural numbers.
Therefore, the right-hand side of the equation is also the product of two consecutive natural numbers.
Hence, 6b = 36
b = 36/ 6
b = 6 and n = 36
As a result, 36 numbers have been added together, and their total is 666.
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What is 8.7x3.9 in a step by step
47=3-6y I can't do it some one helpppppp
Answer: 7.333
Step-by-step explanation:
first move the three over 47-3 = 6y
the divide by - 6 to get y by itself 44/-6 = y
176.912 round off to the closest integer.
help asap!!
Answer:
177
Step-by-step explanation:
In order to round 176.912 to the nearest integer firstly look at the first digit after the decimal point also known as the tenth digit.If the digit in the tenth place is >=5 we will round up and if it is < 5 we will round down keeping the ones place the same and truncating the decimal points.Since the tenth digit 9 is >= 5 we will round up i.e. ( ones place digit + 1 ) and the remaining all digits next to the decimal point are removed.Therefore, the number 176.912 rounded to the nearest integer value is 177 .All Done! Please mark as Brainliest :)
Answer:
177
Step-by-step explanation:
The tenth is 9 which means you round up so the correct answer is 177.
Hope It Helps Sorry If I'm Wrong
Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(3, −6), Q(0, 9), and R(−3, 0). Triangle P′Q′R′ has vertices P′(1, −2), Q′(0, 3), and R′(−1, 0).
Plot triangles PQR and P′Q′R′ on your own coordinate grid.
Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P′Q′R′? Explain your answer. (4 points)
Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis. (4 points)
Part C: Are the two triangles PQR and P′'Q′'R′' congruent? Explain your answer. (2 points)
Answer:
A: sf 2 or 1/2
Step-by-step explanation:
Answer:
Part A: The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/4
Part B:
P''(-1, 0)
Q''(0, -1)
R''(2, -1)
Part C:
The two Triangles PQR and P''Q''R'' are not congruent.
Step-by-step explanation:
Express 405 as product of powers of their prime factors
The factor tree diagram is shown below.
========================================================
Explanation:
The first few primes are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
These numbers have factors of 1 and themself only.
Divide 405 over the smallest prime (2)
405/2 = 202.5
We don't get a whole number result, so 2 is not a factor of 405
Repeat for the prime next prime (3)
405/3 = 135
We get a whole number result. Therefore, 3 is a factor of 405
405 = 3*135
-------------------------
Now focus on 135.
Divide 135 over the smallest prime (2)
135/2 = 67.5
This rules out 2 as a factor of 135
Repeat for the prime number 3
135/3 = 45
So we can see that
135 = 3*45
which shows 3 is a factor of 135.
--------------------------
Now focus on 45. The prime 2 isn't a factor since 45/2 = 22.5 isn't a whole number
But 3 is a prime factor because 45/3 = 15 is a whole number. So 45 = 3*15 is the case.
Furthermore, 15/3 = 5 to show that 15 = 3*5
--------------------------
We can express all of this as a factor tree as shown below. The primes have been circled in red.
We have the primes of: 3, 3, 3, 3, 5
We can shorten the four '3's into 3^4
Therefore, 405 = 3^4 * 5
The product in terms of prime factor is 3*3*3*3*5.
What are prime factors?The factors of a number are numbers that evenly divide into it. A prime factor is a factor that is only divisible by 1 and itself.
Given:
405
On performing prime factorization
405= 3*3*3*3*5
Hence, the prime factors are 3*3*3*3*5.
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Mercury has a freezing point of -38. Water has a freezing point of 32. What is the difference
Three times the greater of two consecutive even integers is 26 less than four times the lesser.
Find the integers.
Answer:
-20, -18
Step-by-step explanation:
let x = the smaller number
Let x + 2 = the larger number
3(x +2) -26 = 4x
3x + 6 -26 = 4x
3x -20 = 4x Subtract 3x from both sides of the equation
-20 = x
x + 2
-20 + 2 = -18
Check:
3(-20 + 2) -26= 4(-20)
3(-18) - 26 = -80
-54 -26 = -80
-80 = -80
Paul started work at company B ten years ago at the salary shown in the table. At the same time Sharla started at company C at the salary shown in the table. Who earned more during the last year? How much more? *picture included*
go ask God bro ain't nobody know that
what is this answer because i have no idea and plus i need the answer ASAP
Step-by-step explanation:
option b is the correct answer
write the value of this expression as a fraction 14/33 x 55/8 x 12/35
Answer: 1
Step-by-step explanation:
[tex]\displaystyle\\\frac{14}{33} *\frac{55}{8} *\frac{12}{35} =\\\\\frac{14*55*12}{33*8*35}=\\\\\frac{2*7*5*11*3*4}{3*11*2*4*5*7}=\\\\\frac{1}{1}=\\\\1[/tex]
slope -1/2, passes through (0, 5)
Our standard linear slope equation is:
mx + b = y
We're told our slope is 1/2, so that's our m value.
When x = 0 our value is 5. If you need this visualized, then:
1/2 * 0 +b = 5
0 + b = 5
b = 5
So our equation looks like:
x/2 + 5 = y