Answer:
Here's an example:
convert 2.5 into a mixed number.
Make the denominator less than the original.
The easy way for this is to do 25/10
when you put it through a calculator it ends up being 2.5
(essentially the mixed number and the decimal are the SAME numbers.)
Hope this clarified. :)
To convert a decimal to a mixed number, follow these steps:
Step 1: Identify the whole number part of the decimal. This is the part of the decimal before the decimal point.
Step 2: Identify the decimal part. This is the part of the decimal after the decimal point.
Step 3: Express the decimal part as a fraction by using the place value of the last digit.
Step 4: Simplify the fraction, if possible, by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.
Step 5: Combine the whole number part, the fraction, and simplify if necessary.
Here's an example:
Let's say we have the decimal 2.75.
Step 1: The whole number part is 2.
Step 2: The decimal part is 0.75.
Step 3: To express 0.75 as a fraction, we write it as 75/100. Since 75 and 100 have a common factor of 25, we can simplify it to 3/4.
Step 4: The fraction 3/4 is already in its simplest form.
Step 5: Combining the whole number part and the fraction, we have 2 3/4.
So, the decimal 2.75 can be written as the mixed number 2 3/4.
Remember to always simplify the fraction part if possible.
Ms. Florinda is a kindergarten teacher. She buys 100 pencils and wants to give 2 pencils to each of her students. She has 2 classes, a class with 22 students and a class with 19 students.
Part A
Write an expression for how many pencils she has left after giving them out to her students.
A.
100
−
2
×
(
22
−
19
)
B.
100
−
2
×
22
−
19
C.
100
−
2
×
22
−
2
×
19
D.
100
−
22
−
19
Part B
Does she have enough pencils to give each of her students 2?
Yes or no
, she has
15,18,37,59
More or fewer
than she needs.
Answer:
Part A:
The correct expression for how many pencils Ms. Florinda has left after giving them out to her students is:
A. 100 - 2 × (22 - 19)
Part B:
To determine whether Ms. Florinda has enough pencils to give each of her students 2, we can calculate the total number of pencils needed. The total number of students is the sum of the students in both classes, which is 22 + 19 = 41.
If each student needs 2 pencils, then the total number of pencils needed is 2 × 41 = 82.
Comparing this with the initial number of pencils Ms. Florinda bought (100), we can see that she has more than enough pencils to give each of her students 2.
Yes, she has enough pencils to give each of her students 2.
She has 18 more than she needs.
advanced functions
solve 4(8-2x)=256
Answer:x=-28
Step-by-step explanation:
Distribute the 4 on the left side of the equation:
32 - 8x = 256
Move the constant term to the right side of the equation:
-8x = 256 - 32
-8x = 224
Divide both sides of the equation by -8 to isolate x:
x = 224 / -8
x = -28
A piece of wood is in the shape of a rectangular prism with a length of 10 inches, a width of 4 inches, and a height of 5 inches. You cut the wood in half to form two pieces of wood, each with a length of 5 inches. What is the percent increase in the total surface area? Round your answer to the nearest hundredth, if necessary. %
Answer: 18.18%
Step-by-step explanation:
First, let's calculate the surface area of the original piece of wood. The surface area (SA) of a rectangular prism is given by the formula:
[tex]$$SA = 2lw + 2lh + 2wh$$[/tex]
where [tex]\(l\)[/tex] is the length, [tex]\(l\)[/tex] is the width, and [tex]\(h\)[/tex] is the height. For the original piece of wood, [tex]\(l = 10\) inches[/tex], [tex]\(w = 4\) inches[/tex], and [tex]\(h = 5\) inches[/tex].
After the piece of wood is cut in half, the length becomes 5 inches, but the width and height remain the same. So, for each of the two new pieces of wood, [tex]\(l = 5\) inches[/tex], [tex]\(w = 4\) inches[/tex], and [tex]\(h = 5\) inches[/tex]. The total surface area of the two new pieces of wood is twice the surface area of one of the new pieces.
The percent increase in the total surface area is given by the formula:
[tex]$$\text{Percent Increase} = \frac{\text{New Total SA} - \text{Original SA}}{\text{Original SA}} \times 100\%$$[/tex]
Let's calculate these values.
The percent increase in the total surface area when the piece of wood is cut in half is approximately 18.18%.
pls helpppppppppppppppppp
Answer:
Step-by-step explanation:
Bisector means breaking the segment in half.
answer is A. to have a length exactly half the segment
A boat is traveling in a river that is floating downstream at a speed of 10 km/h. the boat can travel 40 km upstream in the same time it would take to travel 80 km down the stream. what is the speed of the boat in Still water?
The speed of the boat in still water is 3 times the speed of the river current.
To find the speed of the boat in still water, we can use the concept of relative motion and the given information about the boat's speed while traveling upstream and downstream.
Let's assume the speed of the boat in still water is "v" km/h, and the speed of the river current is "c" km/h.
When the boat is traveling upstream, it moves against the current, so its effective speed is reduced.
The boat's speed relative to the ground is given by (v - c) km/h.
Similarly, when the boat is traveling downstream, it moves with the current, so its effective speed is increased.
The boat's speed relative to the ground is given by (v + c) km/h.
According to the problem, the boat can travel 40 km upstream in the same time it would take to travel 80 km downstream.
Since time is constant in both cases, we can set up the following equation:
40/(v - c) = 80/(v + c)
To solve this equation, we can cross-multiply and simplify:
40(v + c) = 80(v - c)
40v + 40c = 80v - 80c
40c + 80c = 80v - 40v
120c = 40v
Dividing both sides by 40, we get:
3c = v.
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A city currently has 2.08 thousand residents. Each year the city's population grows by around 420 persons.
After 14 years what will the approximate population of the city be? Round to three significant digits.
Approximately
thousand residents.
Answer:
the approximate population of the city after 14 years will be 7.96 thousand residents.
Step-by-step explanation:
to calculate the approximate population of the city after 14 years, we need to take into account the annual growth rate.
Given that the city's population grows by around 420 persons each year, we can calculate the total growth over 14 years by multiplying the annual growth rate by the number of years:
14 years × 420 persons/year = 5,880 persons
To find the approximate population after 14 years, we add the total growth to the current population:
2.08 thousand + 5.88 thousand = 7.96 thousand
Triangle ABC with vertices at A(4, 3), B(3, −2), C(−3, 1) is dilated using a scale factor of 1.5 to create triangle A′B′C′. Determine the vertex of point A′.
The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).
1. Start by calculating the distance between the vertices of the original triangle ABC:
- Distance between A(4, 3) and B(3, -2):
Δx = 3 - 4 = -1
Δy = -2 - 3 = -5
Distance = √((-[tex]1)^2[/tex] + (-[tex]5)^2[/tex]) = √26
- Distance between B(3, -2) and C(-3, 1):
Δx = -3 - 3 = -6
Δy = 1 - (-2) = 3
Distance = √((-6)² + 3²) = √45 = 3√5
- Distance between C(-3, 1) and A(4, 3):
Δx = 4 - (-3) = 7
Δy = 3 - 1 = 2
Distance = √(7² + 2²) = √53
2. Apply the scale factor of 1.5 to the distances calculated above:
- Distance between A' and B' = 1.5 * √26
- Distance between B' and C' = 1.5 * 3√5
- Distance between C' and A' = 1.5 * √53
3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):
- A' is located Δx units horizontally and Δy units vertically from A.
- Δx = 1.5 * (-1) = -1.5
- Δy = 1.5 * (-5) = -7.5
- Coordinates of A':
x-coordinate: 4 + (-1.5) = 2.5
y-coordinate: 3 + (-7.5) = -4.5
4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).
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Let (1=1,2,3, 4, 5, 6, 7, 8, 9, 10
The list of elements in the sets are as follows:
A. A ∩ B = {2, 9}
B. B ∩ C = {2, 3}
C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}
D. B ∪ C = {2, 3, 5, 7, 9, 10}
How to find the elements in a set?Set are defined as the collection of objects whose elements are fixed and can not be changed.
Therefore,
universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 7, 8, 9}
B = {2, 3, 5, 9}
C = {2, 3, 7, 10}
Therefore,
A.
A ∩ B = {2, 9}
B.
B ∩ C = {2, 3}
C.
A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}
D.
B ∪ C = {2, 3, 5, 7, 9, 10}
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find the value of x. 142 3x+22
Answer:
x = 40
you can guess and check.
4,5,6,8,9,9,10,12,12,12,17,17,18,18
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
Answer:
x<3
Step-by-step explanation:
[tex] - 2(5 - 4x) < 6x - 4 \\ - 10 + 8x < 6x - 4 \\ 8x - 6x < - 4 + 10 \\ 2x < 6 \\ x < 3[/tex]
Yuri’s sister Karina is 12 years old. In the equation below, y represents Yuri’s age in years.
12 = 3 y minus 2
Which statement accurately relates their ages?
Yuri is 3 years younger than twice Karina’s age.
Yuri is 2 years younger than triple Karina’s age
Karina is 3 years younger than twice Yuri’s age.
Karina is 2 years younger than triple Yuri’s age.
Yuri is 2 years younger than triple Karina’s age
Answer:
yo
Step-by-step explanation:
i think its d
Is f(x)=-x3-x an odd function
The function f(x) = -x³ - x is an odd function.
Is the given function odd, even, or neither?Given the function in the question:
f(x) = -x³ - x
To determine if a function is odd, we need to check if it satisfies the given property:
f(-x) = -f(x)
For all x in the domain of the function.
Given that:
f(x) = -x³ - x
Evaluate f(-x) for the given function f(x) = -x³ - x:
f(x) = -x³ - x
Replace x with -x
f(-x) = -(-x)³ - (-x)
f(-x) = -(-x³) + x
f(-x) = x³ + x
Now, check if -f(x) is equal to x³ + x:
-f(x) = -(-x³ - x)
-f(x) = x³ + x
Since -f(x) = x³ + x, f(x) = -x³ - x is an odd function.
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Because f(x) ___ its inverse is a function.
○ is one to one
X is a function
○ Passes the vertical line test
The inverse of the function f(x) = 2·x - 4, is the option;
g(x) = (1/2)·x + 2
The completed statement is; Because f(x) is one to one, its inverse is a function
What is the inverse of a function?The inverse of a function is one that takes the output of a specified function to produce the input of the function.
The inverse of the function f(x) = 2·x - 4, can be found by making x the subject of the function equation as follows;
f(x) = 2·x - 4
f(x) + 4 = 2·x
2·x = f(x) + 4
x = (f(x) + 4)/2 = f(x)/2 + 2
x = f(x)/2 + 2
Substituting f(x) = x and x = g(x) in the above equation, we get;
g(x) = x/2 + 2
The inverse of the function is therefore, g(x) = (1/2)·x + 2The function f(x) = 2·x - 4 is a one to one function, and the condition of a one to one function guarantees that the inverse of the function is also a function
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Answer:
A
Step-by-step explanation:
is one to one
What else would need to be congruent to show that ABC=AXYZ by SAS?
A
B
OA. ZB=LY
B. BC = YZ
OC. C= LZ
OD. AC = XZ
с
X
Z
Given:
AB XY
BC=YZ
What is needed to be congruent to show that ABC=AXYZ is AC ≅ XZ. option D
How to determine the statementGiven that in ΔABC and ΔXYZ, ∠X ≅ ∠A and ∠Z ≅ ∠C.
We are to select the correct condition that we will need to show that the triangles ABC and XYZ are congruent to each other by ASA rule..
ASA Congruence Theorem: Two triangles are said to be congruent if two angles and the side lying between them of one triangle are congruent to the corresponding two angles and the side between them of the second triangle.
In ΔABC, side between ∠A and ∠C is AC,
in ΔXYZ, side between ∠X and ∠Z is XZ.
Therefore, for the triangles to be congruent by ASA rule, we must have AC ≅ XZ.
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José encontró un álbum de fotos del abuelo cuando tenía nueve años si el álbum tenía 108 páginas cuantas veces se habría es que se habría escrito la cifra nueve para enumerar todo el libro
The total number of times the digit "9" would have been written to number the entire photo album is 12 + 9 = 21 times.
To determine how many times the digit "9" would have been written to number all the pages of the photo album, we need to analyze the numbering pattern.
Since the album has 108 pages, we can observe that the numbers 1 to 9 are repeated 12 times (1-9, 10-19, 20-29, ..., 90-99) to cover the first 99 pages. Each repetition consists of ten numbers, and the digit "9" appears once in each repetition.
So, the digit "9" would have been written 12 times for the numbers 9, 19, 29, ..., 89 and 99.
However, we have an additional 9 pages to consider, which are 100, 101, 102, ..., 108. Each of these pages contains a single "9" in its numbering.
Therefore, the total number of times the digit "9" would have been written to number the entire photo album is 12 + 9 = 21 times.
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The sum of three numbers $x$ ,$y$, $z$ is 165. When the smallest number $x$ is multiplied by 7, the result is $n$. The value $n$ is obtained by subtracting 9 from the largest number $y$. This number $n$ also results by adding 9 to the third number $z$. What is the product of the three numbers?
Answer:
Step-by-step explanation:
Let's break down the given information step by step to solve the problem:
The sum of three numbers x, y, and z is 165: x + y + z = 165.
When the smallest number x is multiplied by 7, the result is n: 7x = n.
The value n is obtained by subtracting 9 from the largest number y: y - 9 = n.
The value n is also obtained by adding 9 to the third number z: z + 9 = n.
We can use this information to form a system of equations:
Equation 1: x + y + z = 165
Equation 2: 7x = n
Equation 3: y - 9 = n
Equation 4: z + 9 = n
To find the product of the three numbers, we need to determine the values of x, y, z, and n.
First, let's solve for n using Equation 2:
7x = n
Now, let's substitute the value of n into Equations 3 and 4:
Equation 3: y - 9 = 7x
Equation 4: z + 9 = 7x
We can rearrange Equation 3 to express y in terms of x:
y = 7x + 9
Now, we can substitute the value of y in Equation 1:
x + (7x + 9) + z = 165
Simplifying:
8x + z = 156
Now, we have two equations:
Equation 4: z + 9 = 7x
8x + z = 156
We can solve this system of equations to find the values of x and z:
From Equation 4, we have z = 7x - 9.
Substituting z in Equation 8x + z = 156:
8x + (7x - 9) = 156
15x - 9 = 156
15x = 165
x = 11
Substituting x = 11 in Equation 4:
z + 9 = 7(11)
z + 9 = 77
z = 68
Now, we have the values of x = 11, y = 7x + 9 = 7(11) + 9 = 86, and z = 68.
The product of the three numbers x, y, and z is:
Product = x * y * z = 11 * 86 * 68 = 64648.
Therefore, the product of the three numbers is 64648.
Amy bought a new car for $21,000
. She paid a 10%
down payment and financed the remaining balance for 36
months with an APR of 3.5%
. Determine the monthly payment that Amy pays. Round your answer to the nearest cent, if necessary.
Answer:
Step-by-step explanation:
To determine the monthly payment Amy pays, we can use the formula for calculating the monthly payment on a loan. The formula is:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal amount (loan amount)
r = Monthly interest rate
n = Number of monthly payments
Given information:
Principal amount (loan amount) = $21,000
Down payment = 10% of $21,000 = $2,100
Remaining balance = $21,000 - $2,100 = $18,900
APR = 3.5%
Number of monthly payments (n) = 36
To calculate the monthly interest rate (r), we divide the annual interest rate by 12 (number of months in a year):
Monthly interest rate (r) = APR / (12 * 100)
Substituting the values into the formula:
r = 3.5 / (12 * 100) = 0.0029167 (rounded to 7 decimal places)
M = (18,900 * 0.0029167 * (1 + 0.0029167)^36) / ((1 + 0.0029167)^36 - 1)
Using a calculator to evaluate the expression within the formula:
M ≈ $539.26
Therefore, the monthly payment that Amy pays is approximately $539.26.
–5 < 2x – 1 < 3 solve?? help aap
Answer:
Step-by-step explanation:
To solve the inequality -5 < 2x - 1 < 3, we will break it down into two separate inequalities and solve each one individually.
First, let's solve the left inequality:
-5 < 2x - 1
Add 1 to both sides:
-5 + 1 < 2x - 1 + 1
-4 < 2x
Divide both sides by 2 (remembering to reverse the inequality when dividing by a negative number):
-4/2 < 2x/2
-2 < x
Now, let's solve the right inequality:
2x - 1 < 3
Add 1 to both sides:
2x - 1 + 1 < 3 + 1
2x < 4
Divide both sides by 2:
2x/2 < 4/2
x < 2
So, the solutions to the inequalities are:
-2 < x < 2
This means that x is greater than -2 and less than 2.
Can someone help me? F(x)+8x-8x^3-x^4+6
Answer:
Step-by-step explanation:
Of course! I'd be happy to help you.
Let's simplify the expression f(x) + 8x - 8x^3 - x^4 + 6 step by step:
The given expression is: f(x) + 8x - 8x^3 - x^4 + 6
Since we don't have any specific information about f(x), we'll assume that f(x) is a constant or a function that doesn't depend on x. In that case, f(x) can be treated as a constant term.
Combining like terms, we have:
f(x) - x^4 - 8x^3 + 8x + 6
There is no further simplification we can do without additional information about the function f(x) or any specific values of x. Therefore, the simplified expression is:
f(x) - x^4 - 8x^3 + 8x + 6
if f(x) = 2x+7 then find f(x+2)
The answer is:
↬ f(x + 2) = 2x + 11
Work/explanation:
To evaluate the function, plug in x + 2 for x:
[tex]\boxed{\large\begin{gathered}\sf{f(x)=2x+7}\\\\\bf{distribute}\\sf{f(x+2)=2(x+2)+7}\\\\\bf{simplify}\\\sf{f(x+2)=2x+4+7}\\\\\sf{f(x+2)=2x+11}\end{gathered}}[/tex]
Hence, f(x +2) = 2x + 11.Let N be the greatest number that will divide 1305,4665 and 6905 leaving the same remainder in each case. What is the sum of the digits in N.
Answer:
4
Step-by-step explanation:
You want the sum of digits of the largest number that divides 1305, 4665, and 6905 with the same remainder.
Largest divisorWe can look at 4665/1305 ≈ 3.57 and 6905/1305 ≈ 5.29 for a clue as to the divisor of interest. These quotients tell us that one possibility is the value that would give quotients of 4 and 6 after the remainder is subtracted from each of the numbers.
For 1305 and 4665, if r is the remainder, we require ...
4(1305 -r) = 4665 -r
5220 -4665 = 4r -r
555/3 = r = 185
If 185 is the remainder in this scenario, then 1305 -185 = 1120 is the divisor. Checking the remainder with 6905, we find ...
6905/1120 = 6 r 185
Sum of digitsThe sum of digits of this divisor is 1 + 1 + 2 + 0 = 4.
The sum of the digits in N is 4.
Rotate the triangle 180 counterclockwise around the origin and enter the coordinates. Enter the number that belongs in the green box A (1,-1) B (4,-2) C (2,-4)
Answer:
A''(-1, 1), B''(-4, 2), C''(-2, 4)
Step-by-step explanation:
When rotated 180°, the symbol of the coordinames change
i.e., if x = 2 it becomes x = -2 and if y = -4, it becomes y = 4
so the coordinates A(1, -1), B(4, -2), C(2, -4)
change to A''(-1, 1), B''(-4, 2), C''(-2, 4)
What transformation is shown below? (Look carefully at the vertices.)
translation
reflection
rotation
can't be determined
The transformation that moves the shape is (a) translation
What transformation moves the shapeFrom the question, we have the following parameters that can be used in our computation:
The figure
Where, we have:
Rectangle ABCD and rectangle ABCD have the same orientationRectangle ABCD and rectangle ABCD have the same sizeThis means that the only transformation is translation
So, the transformation is (a) translation
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Pls geometry work help
Answer:
Step-by-step explanation:
Given:
<RPS = 35
<PAQ = 130
Solution:
If <PAQ = 130 then <QAR =50
because they are a linear pair that add to 180
<QAR = mQR = 50
mRS = 2(<RPS) >inscribed angle
mRS = 2(35)
mRS = 70
<PAQ = 130
<PAQ = mPQ
<PSQ = 1/2 (mPQ) >inscribed angle
<PSQ = 1/2 (130)
<PSQ = 65
<PBS = 180 - <RPQ - PSQ >triangle
<PBS = 180 - 35-65
<PBS = 80
<PBS = <QBR >vertical angles
<QBR = 80
<ABQ = 180- <QBR >linear pair
<ABQ = 180 - 80
<ABQ= 100
<AQB = 180 - <ABQ - <QAR >triangle
<AQB = 180 -100 - 50
<AQB = 30
<AQB = <AQS
<AQS =30
mRS = 70
mPS = 180-mRS 180 for semicircle
mPS = 180 - 70
mPS = 110
A person leaves home and walks 5 miles west, then 6 miles southwest.
How far from home is she?
The person is approximately 7.73 miles from home.
To solve this problem, we can use the Pythagorean theorem and trigonometry. Let us assume that the person starts from the origin (0, 0) and walks 5 miles west, which takes her to the point (-5, 0) on the x-axis.
If we assume that the starting point is (0, 0) and we assign a coordinate system, then the point reached after walking 5 miles west can be represented as (-5, 0). Similarly, the point reached after walking 6 miles southwest can be represented as (-3, -6).Then, she walks 6 miles southwest, which forms a 45-degree angle with the x-axis. We can represent this vector as (6 cos 45°, -6 sin 45°) = (3√2, -3√2).
To find the total distance from home, we need to add the magnitude of these two vectors using the Pythagorean theorem:
d =[tex]\sqrt((-5)^2 + (-3\sqrt2)^2)[/tex]≈ 7.73 miles
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solve the following question
The decay constant for the plutonium is - [ln (0.5 ) / 6300].
option C.
What is the decay constant?The decay constant for the plutonium is calculated by applying the following formula.
The given function for the radioactive decay;
[tex]Q(t) = Q_0e^{-kt}[/tex]
where;
Q(t) is the quantity remaining after a given timeQ₀ is the initial quantityk is the decay constantt is the timeThe decay constant for the plutonium is calculated as;
k = ln(2) / T½
k = ln(2) / 6300
k = ln(0.5⁻¹) / 6300
k = - [ln (0.5 ) / 6300]
Thus, the decay constant for the plutonium is - [ln (0.5 ) / 6300].
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y=1x^2 + 2x - 3 in vertex and intercept form
The vertex and the x-intercepts of the quadratic equation are:
The vertex is (-1, -4)
The x-intercepts are -3 and 1.
To express the quadratic equation [tex]y = x^2 + 2x - 3[/tex]in vertex and intercept form, we need to complete the square to find the vertex and rewrite the equation in terms of the x-intercepts.
First, let's complete the square to find the vertex. We can do this by taking half the coefficient of x, squaring it, and adding/subtracting it to both sides of the equation:
[tex]y = x^2 + 2x - 3\\y = (x^2 + 2x + 1) - 1 - 3\\y = (x + 1)^2 - 4[/tex]
Now we have the equation in the form [tex]y = a(x - h)^2 + k[/tex], where the vertex is at the point (-h, k). The vertex is (-1, -4).
Next, let's find the x-intercepts by setting y = 0:
[tex]0 = x^2 + 2x - 3\\0 = (x + 3)(x - 1)[/tex]
The x-intercepts are -3 and 1.
In vertex and intercept form, the equation is:
[tex]y = (x + 1)^2 - 4[/tex]
The vertex is (-1, -4)
The x-intercepts are -3 and 1.
This form allows us to easily identify the vertex and the x-intercepts of the quadratic equation.
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GEOMETRY 50POINTS
find y to the nearest degree
The value of y in the figure is
35.134 degrees
How to determine the value of yThe value of y is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The figure shows a right angle triangle of
opposite = 19
adjacent = 27
The angle is calculated using tan, TOA let the angle be y
tan y= Opposite / Adjacent
tan y = 19 / 27
y = arc tan (19/27)
y = 35.134 degrees
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[tex]\sqrt{x+7}-1=x[/tex]
Answer:
x = 2
Step-by-step explanation:
Pre-SolvingWe are given the following equation:
[tex]\sqrt{x+7} -1=x[/tex], which we want to solve for x.
To do this, we should isolate the square root on one side, then square both sides. We can then solve the equation as normal, but then we have to check the domain in the end for any extraneous solutions.
SolvingStart by adding 1 to both sides.
[tex]\sqrt{x+7} -1=x[/tex]
+1 +1
________________________
[tex]\sqrt{x+7} = x+1[/tex]
Now, square both sides.
[tex](\sqrt{x+7} )^2= (x+1)^2[/tex]
We get:
x + 7 = x² + 2x + 1
Subtract x + 7 from both sides.
x + 7 = x² + 2x + 1
-(x+7) -(x+7)
________________________
0 = x² + x - 6
This can be factored to become:
0 = (x+3)(x-2)
Solve:
x+3 = 0
x = -3
x-2 = 0
x = 2
We get x = -3 and x = 2. However, we must check the domain.
DomainSubstitute -3 as x and 2 as x into the original equation.
We get:
[tex]\sqrt{-3+7} -1 = -3[/tex]
[tex]\sqrt{4} -1 = -3[/tex]
2 - 1 = -3
-1 = -3
This is an untrue statement, so x = -3 is an extraneous solution.
We also get:
[tex]\sqrt{2+7} -1 = 2[/tex]
[tex]\sqrt{9}-1=2[/tex]
3 - 1 = 2
2 = 2
This is a true statement, so x = 2 is a real solution.
Our only answer is x = 2.
