Answer: Perimeter = 135 units Area = 1200 Square units
Step-by-step explanation: I think you want the perimeter and area of XYZ so that's what I will answer for.
First, we are given that ABC and XYZ are proportional and that their longest sides are 24 units and 60 units respectively.
Using this, we can say XYZ = ABC * 5/2 (60/24 = 5/2)
Therefore, the other two sides of XYZ are 50 and 25.
We can get the perimeter using 60 + 50 + 25, that equals 135 units
Next, since the height of ABC was 8 units with 24 units being its base, it's likely safe to say the height = 1/3 base
We will apply with to triangle XYZ, height = 1/3 * 60 = 20
20 units * 60 units = 1200 square units
The perimeter and area of the ΔXYZ are 135 units and 600 sq. units. Where similar triangles are related by a scale factor.
How to find the scale factor for similar triangles?The ratio of their respective sides of two similar triangles gives the scale factor. I.e.,
Consider ΔABC and ΔDEF are two similar triangles
Then its scale factor = DE/AB = EF/BC = DF/AC
The scale factor is also defined as follows:
(Scale factor)² = (Area of the triangle DEF)/(Area of the triangle ABC)
or
Scale factor = (perimeter of ΔDEF)/(perimeter of ΔABC)
Finding the scale factor:Given that the sides of the triangle ABC are 10 units, 20 units, and 24 units. The longest side is 24 units.
The triangle XYZ has the longest side of length 60 units.
Since ΔABC ~ ΔXYZ
So, the ratio of their longest sides gives the scale factor. I.e.,
Scale factor = 60/24 = 2.5
Calculating the perimeter of the ΔXYZ:The perimeter of the ΔXYZ is calculated by
Scale factor = (perimeter of the ΔXYZ)/(perimeter of the ΔABC)
⇒ 2.5 = (perimeter of the ΔXYZ)/(10 + 20 + 24)
⇒ perimeter of the ΔXYZ = 2.5 × 54
∴ the perimeter of the ΔXYZ = 135 units
Calculating the area of the ΔXYZ:The area of the ΔXYZ is calculated by
(Scale factor)² = (area of the ΔXYZ)/(area of the ΔABC)
So, the area of the ΔABC, whose height h = 8 units and base b = 24 units is
Area of the ΔABC = 1/2 × b × h
= 1/2 × 24 × 8
= 96 sq. units
Thus,
(Scale factor)² = (area of the ΔXYZ)/(area of the ΔABC)
⇒ (2.5)² = (area of the ΔXYZ)/(96)
⇒ area of the ΔXYZ = (2.5)² × 96
∴ area of the ΔXYZ = 600 sq units
Thus, the perimeter and area of the ΔXYZ are 135 units and 600 sq. units.
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If s(x) = 2 – x^2 and t(x) = 3x, which value is equivalent to (s•t)(-7)?
Answer:
[tex]-439[/tex]
Step-by-step explanation:
we have
[tex]s(x)=2-x^{2}[/tex]
[tex]t(x)=3x[/tex]
we know that
[tex](sot)(x)=2-(3x)^{2}[/tex]
[tex](sot)(x)=2-9x^{2}[/tex]
For x=-7
substitute
[tex](sot)(-7)=2-9(-7)^{2}[/tex]
[tex](sot)(-7)=2-441[/tex]
[tex](sot)(-7)=-439[/tex]
Solve the inequality 6x − 8 > 4x + 26
Hi.
Answer:
[tex]\boxed{x>17}\checkmark[/tex]
The answer should have positive sign but not negative.
Step-by-step explanation:
First, you add by 8 from both sides.
[tex]6x-8+8>4x+26+8[/tex]
Then, simplify.
[tex]6x>4x+34[/tex]
Next, you do is subtract by 4x from both sides.
[tex]6x-4x>4x+34-4x[/tex]
Simplify.
[tex]2x>34[/tex]
Therefore, you divide by 2 from both sides.
[tex]\frac{2x}{2}>\frac{34}{2}[/tex]
Finally, you solve and simplify.
[tex]34/2=17[/tex]
[tex]x=17\checkmark[/tex]
X=17 is the correct answer.
Hope this helps you!
Have a nice day! :)
Answer:
The solution for the inequality is x>17
Step-by-step explanation:
Consider the provided inequality.
[tex]6x - 8 > 4x + 26[/tex]
Subtract 4x to both the sides.
[tex]6x -4x- 8 > 4x-4x + 26[/tex]
[tex]2x- 8 > 26[/tex]
Add 8 to the both sides.
[tex]2x- 8+8 > 26+8[/tex]
[tex]2x > 34[/tex]
Divide both the sides by 2.
[tex]x > 17[/tex]
Hence, the solution for the inequality is x>17
A mover in a moving truck is suing a rope to pull a 400-pound box up a ramp
that has an incline of 25o. What is the force needed to hold the box in a
stationary position to prevent the box from sliding down the ramp?
Answer:
Step-by-step explanation:
The pulling force
Answer:
F = -52.8 N
Step-by-step explanation:
Given :
Inclination angle : 25°
Weight, W = 400 lb
The force N will push the box against the ramp.
Therefore, Force F will prevent the box from sliding down the ramp.
F = W sin 25°
= 400 x (-0.132)
= -52.8 N ( negative sign shows that the force applied in the opposite direction )
What are the roots, in simplest form, of the equation 4x2 + 98= 0
Answer:
x = ±√ 24.500 = ± 4.94975
Step-by-step explanation:
: (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Step-by-step explanation:
4x² + 98 = 0
2x² + 49 = 0
2x² = -49
x² = -49/2
x = ±√(-49/2)
x = ±7i√(1/2)
x = (±7i√2) / 2
Divide x^4 + 7 by x - 3.
a.) x³ - 3x² - 9x - 27 R 88
b.) x³ + 3x² + 9x - 27 R -74
c.) x³ + 3x² + 9x + 27 R 88
Answer:
c
Step-by-step explanation:
Divide using synthetic division, remembering to place a zero to denote the terms x³, x² and x
Since division by (x - 3) then evaluate using h = 3
3 | 1 0 0 0 7
↓
1 3 9 27 81
----------------------
1 3 9 27 88 ← degree 3 polynomial
quotient = x³ + 3x² + 9x + 27 , remainder = 88 → c
Follow below steps:
To divide x^4 + 7 by x - 3, we will use polynomial long division. This process is similar to the long division we use with numbers. Let's perform the division step by step:
Divide the term with the highest power in the dividend (x^4) by the highest power in the divisor (x) to get x^3.
Multiply the entire divisor by x^3 and subtract the result from the dividend.
The subtraction will give a new polynomial. Repeat the process until the degree of the remainder is less than the degree of the divisor, or until no further division can be carried out.
The correct result for the division of x^4 + 7 by x - 3 is option (a): x^3 - 3x^2 - 9x - 27 R 88.
1. In a 30-60-90 triangle, the leagoo the hypotenuseis 6. What is the leaga of the shortest
a2
6.3
Answer:
b. 3
Step-by-step explanation:
In a 30°-60°-90° triangle, the short side is ½ the hypotenuse [the long side is double the short side].
30°-60°-90° Triangles
x√3 → long side
x → short side
2x → hypotenuse
45°-45°-90° Triangles
x → two legs
x√2 → hypotenuse
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David performed the following mathematical operation .
Answer:
C: x = 1/2
Step-by-step explanation:
Set the divisor, 2x - 1, equal to zero and solve for x: 2x = 1, so x = 1/2. Statement C is true.
Answer:
The correct option is C.
Step-by-step explanation:
If a function f(x) is completely divisible by (x-a), it means (x-a) is a factor of f(x) and x=a is a root of that polynomial.
The given polynomial is
[tex]P(x)=2x^2+9x-5[/tex]
It is given that when David divide the above polynomial by (2x-1), then he get
[tex]Quotient=x+5[/tex]
[tex]Remainder=0[/tex]
Since the remainder is zero it means P(x) is completely divisible by (2x-1) or (2x-1) is a factor of P(x).
[tex]2x-1=0[/tex]
Add 1 on both the sides.
[tex]2x=1[/tex]
Divide both sides by 2.
[tex]x=\frac{1}{2}[/tex]
It means [tex]\frac{1}{2}[/tex] must be a root of the polynomial [tex]2x^2+9x-5[/tex].
Therefore, the correct option is C.
Which expression is equivalent to(8w 7x-5y3z-9)-2/3
Answer:
[tex]56wx - 15yz - \frac{29}{3} [/tex]
Step-by-step explanation:
[tex]1. \: 56wx - 5y \times 3z - 9 - \frac{2}{3} \\ 2. \: 56wx - 15yz - 9 - \frac{2}{3} \\ 3. \: 56wx - 15yz + ( - 9 - \frac{2}{3} )[/tex]
The expression equivalent to given condition is 56wx - 15yz - 29/3.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given expression,
(8w.7x - 5y.3z - 9) - 2/3
since variables are in the product, so their constants are multiplied,
8w.7x = 56wx
5y.3z = 15yz
the equation can be written as,
56wx - 15yz - 9 - 2/3
and - 9 - 2/3 = (-27 - 2)/3 = -29/3
=> 56wx - 15yz - 29/3
Therefore, the equivalent form of the equation is 56wx - 15yz - 29/3.
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Find the value of this expression if x=-1 and y=-5 x^2y/4
Answer:
[tex]\large\boxed{-\dfrac{5}{4}=-1\dfrac{1}{4}}[/tex]
Step-by-step explanation:
[tex]\text{Put the values of x = -1 and y = -5 to the expression}\ \dfrac{x^2y}{4}:\\\\\dfrac{(-1)^2(-5)}{4}=\dfrac{(1)(-5)}{4}=\dfrac{-5}{4}[/tex]
Solve the inequality -1+4y<_31.
Answer:
[tex]\large\boxed{y\leq8\to\{y\ |\ y\leq8\}\to y\in(-\infty,\ 8]}[/tex]
Step-by-step explanation:
[tex]-1+4y\leq31\qquad\text{add 1 to both sides}\\\\-1+1+4y\leq31+1\\\\4y\leq32\qquad\text{divide both sides by 4}\\\\\dfrac{4y}{4}\leq\dfrac{32}{4}\\\\y\leq8[/tex]
please help me with this question.
Answer:
1344 ft²Step-by-step explanation:
From the picture we have:
4w = 3l
If w = 12 ft, then
3l = 4(12)
3l = 48 divide both sides by 3
l = 16 ft
The dimensions of rectangular floor are 4w × (l + w).
Substitute the values of w and l:
4w = 4(12) = 48 ft
l + w = 16 + 12 = 28 ft
The formula of an area of a rectangle:
A = width × length
Substitute:
A = (48)(28) = 1344 ft²
identify an equation in point slope form for the line perpendicular to y=3x+5 that passes through (4,-1)
Answer:
y-4 = (-1/3)(x+1)
Step-by-step explanation:
We need to identify the equation in point slope form.
The standard equation of point slope form is:
(y-y₁) = m (x-x₁)
where m is the slope and x₁ and y₁ are the points
We are given point(4,-1) so,
x₁=4 and y₁=-1
And a perpendicular line: y =3x+5
Which is equal to y = mx+b
where m is slope so, slope m = 3
Since the line is perpendicular, so the slope in negative inverse of actual slope that m = -1/m
i.e, m = -1/3
So, the equation in point slope form is:
y-(-1) = (-1/3)(x-4)
=> y+1 = (-1/3)(x-4)
Answer:
The equation in point slope form for the line perpendicular to y=3x+5 that passes through (4,-1) is y = -⅓x + ⅓
Step-by-step explanation:
Given
Let P represent the lind
Equation of P; y = 3x + 5
Let Q represent the other point.
Coordinates of Q; Q(4,-1)
It is said that the line P is perpendicular to point Q.
So, the first thing to do is to calculate the slope of Q;
Since both lines are perpendicular, then we make use of formula for calculating the condition of perpendicularity
This is given as m1m2 = -1
Where m1 = slope of P
m2 = slope of Q
To get m1;
m1 is the coefficient of x in equation of line P.
So, m1 = 3.
Now we can solve for m2
m1.m2 = -1. ---- make m2 the subject of formula
m2 = -1/m1
Substitute 3 for m1
m2 = -1/3
m2 = -⅓
Recall that the coordinates of Q is 4 and -1.
To calculate the equation of Q; we make use of the following
m = (y - y1)/(x - x1)
Where m = m2 = -⅓
x1 = 4 and y1 = -1
By substituton, we have
-⅓ = (y - (-1))/(x - 4)
-⅓ = (y + 1)/(x - 4) --- multiply both sides by 3(x - 4)
-⅓ * 3(x - 4) = 3(x - 4) * (y + 1)/(x - 4)
-(x - 4) = 3(y + 1)
-x + 4 = 3y + 3 --- make y the subject of formula
3y = -x + 4 - 3
3y = -x + 1 --- divide through by 3
3y/3 = (-x + 1)/3
y = -x/3 + 1/3
y = -⅓x + ⅓
Hence, the equation in point slope form for the line perpendicular to y=3x+5 that passes through (4,-1) is y = -⅓x + ⅓
Which graph represents y=[2] over the domain 3 <_x <_ 6?
Answer:
Top Right
Step-by-step explanation:
First things first, you can eliminate the bottom left option. The domain 3≤x≤6 means that the graph will only show points greater than or equal to 3 and less than or equal to 6. That option shows x = 2, which is not in this domain.
The symbols on either side of the x are known as ceiling functions. It means that y equals whatever whole number is greater than or equal to than x.
Basically, whatever y is, round it up to the nearest whole number to get x.
So, let's do a table from x = 3 to x = 6
x ║ y Now, see which graph best matches these
2.5 ║ 3 coordinates. Keep in mind that to be a function,
3 ║ 3 the points cannot overlap (they have to pass the
3.5 ║ 4 vertical line test). It looks like the best answer is
4 ║ 4 going to be the top right.
4.5 ║ 5
5 ║ 5
5.5 ║ 6
6 ║ 6
Answer:
Top Right Corner
Step-by-step explanation:
The swiftest way to know this is that on each end is a closed circle from 3 [open] to 6 [close]. Bottom left is close, but has an extra line signaling that x is equal to 2, and it is not included, so do not pick this one.
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3 times the measure of an angle is 14 less than the measure of its complement. What is the measure of the angle? 19° 57° 71° 76°
Answer:
x = 19°
Step-by-step explanation:
Let The angle be "a"
Now according to the question,
⇒ 3 × a = (90° - a) - 14° (Then remove the brackets)
⇒ 3a = 90° - a - 14°
⇒ 3 + a = 76°
⇒ 40° = 76°
⇒ a = 76/4
Now since you got 76/4 you have to make it into simplest form so it'll be :
19/1
Your answer is : a = 19°
Answer:
A on edg.
Step-by-step explanation:
Assuming that there are 20. drops in 1.0 mL, how many drops are in 3.9 gallons?
drops
Answer:
295261.98 or just 295.2962 (rounded).
Step-by-step explanation:
You have to figure out how many ml are in a gallon. Then multiply that by 3.9 gallons.
Find -x + 10 subtracted from 0.
-* +10
0X-10
Answer:
x-10
Step-by-step explanation:
we know that
(-x+10) subtracted from 0 is equal to
0 minus (-x+10)
so
0-(-x+10)=0+x-10
=x-10
Answer:
x-10
Step-by-step explanation:
What is the following product? 3 sqrt 16x7 . 3 sqrt 12x9
Answer: The required product is [tex]4x^5\sqrt[3]{3x}[/tex]
Step-by-step explanation: We are given to find the following product :
[tex]P=\sqrt[3]{16x^7}\times \sqrt[3]{12x^9}.[/tex]
We will be using the following property of exponents :
[tex](i)~\sqrt[b]{x^a}=x^\frac{a}{b}\\\\(ii)~x^a\times x^b=x^{a+b}\\\\(iii)~x^a\times y^a=(xy)^a.[/tex]
The required multiplication is as follows :
[tex]P\\\\=\sqrt[3]{16x^7}\times \sqrt[3]{12x^9}\\\\=(16x^7)^\frac{1}{3}\times (12x^9)^\frac{1}{3}\\\\=(16\times12\times x^{7+9})^\frac{1}{3}\\\\=(192x^{16})^\frac{1}{3}\\\\=192^\frac{1}{3}x^\frac{16}{3}\\\\=(64\times3)^\frac{1}{3}x^\frac{16}{3}\\\\=4^{3\times\frac{1}{3}}3^\frac{1}{3}x^{5+\frac{1}{3}}\\\\=4\times 3^\frac{1}{3}x^5\times x^\frac{1}{3}\\\\=4x^5\sqrt[3]{3x}.[/tex]
Thus, the required product is [tex]4x^5\sqrt[3]{3x}.[/tex]
Write a function to represent the set of ordered pairs. {(2, -8), (3, -18), (4, -32), (5, -50)}
Answer:
y = -2x²
Step-by-step explanation:
The set of ordered pairs is:
(x₁, y₁) = (2, -8)
(x₂, y₂) = (3, -18)
(x₃, y₃) = (4, -32)
(x₄, y₄) = (5, -50)
First let's check if this is linear. For even increments of x, Δy is:
Δy₂₁ = y₂ − y₁ = -18 − -8 = -10
Δy₃₂ = y₃ − y₂ = -32 − -18 = -14
Δy₄₃ = y₄ − y₃ = -50 − -32 = -18
Δy isn't constant, so this isn't linear. However, the difference of the differences is constant:
Δy₃₂ − Δy₂₁ = -14 − -10 = -4
Δy₄₃ − Δy₃₂ = -18 − -14 = -4
So this is a quadratic.
y = ax² + bx + c
To find the coefficients of a, b, and c, we can either plug in three points from the set and solve the system of equations:
-8 = a(2)² + b(2) + c
-18 = a(3)² + b(3) + c
-32 = a(4)² + b(4) + c
Or, if it's simple, we can use a little trial and error.
-8 = -2 (2)²
-18 = -2 (3)²
-32 = -2 (4)²
So the function is:
y = -2x²
Convert 27 feet to inches.
27 feet- inches
(Round to the nearest hundredth as needed.).
Final answer:
To convert 27 feet to inches, multiply 27 by the conversion factor of 12 inches per foot, resulting in 324 inches.
Explanation:
To convert 27 feet to inches, we use the unit equivalence that 1 foot = 12 inches. We multiply the number of feet by the conversion factor to get the measurement in inches.
27 feet × 12 inches/foot = 324 inches.
Therefore, 27 feet is equivalent to 324 inches. This is a straightforward application of unit conversion, which is a fundamental skill in mathematics, especially useful for various applications in science, engineering, and everyday calculations.
John has consumed 1,600 calories so far today. He has also burned off 400 calories at the gym. He would like to keep his daily calorie total to 1,800 calories per day. How many calories does he have left to consume for the day? Is 1,000 a viable solution to this problem?
Answer:
No; 1,000 will cause him to exceed 1,800.
Step-by-step explanation:
Given,
The consumed calories = 1,600,
Burned calories = 400,
Thus, the remaining calories = 1600 - 400 = 1200
Since, 1,800 calories per day would be like to keep,
Also, 1200 < 1800
Hence, remaining calories is less than the required calories,
And, the calories left to consume for the day = Required calories - remaining calories
= 1800 - 1200
= 600
Therefore, 600 is the viable solution to this problem.
Note : If 1,000 a viable solution to this problem then the required calories will be more than 1800 or exceed 1800.
Each month, Anna pays $630 in rent. How much rent does she pay over the course of 18 months?
Answer:
$11,340
Step-by-step explanation:
1 month: 630
18 months: 18×630=11,340
Anna pays a total of $11,340 in rent over the course of 18 months by multiplying her monthly rent of $630 by 18.
To find out how much rent Anna pays over the course of 18 months, we need to multiply her monthly rent by the number of months. Anna pays $630 each month, so over 18 months, she would pay:
$630 times 18 = $11,340.
Therefore, Anna pays a total of $11,340 in rent over the course of 18 months.
Can someone help me plz
The correct answer: D
In a bouquet of 24 roses, sixteen are red and the rest are pink. What is the ratio of pink to red roses?
Answer: 1:2 ratio
Step-by-step explanation:
Total-red roses=pink roses
24-16=8
8:16
GCF: 8
16/8=2
8/8=1
1:2 ratio
pink:red
The ratio of pink to red roses 1:2 ratio
Total-red roses=pink roses
24-16= 8
8:16
GCF: 8
16/8=2
8/8=1
1:2 ratio
pink : red
A ratio indicates how many times one number contains another.
The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive.
ReductionRatios can be reduced (as fractions are) by dividing each quantity by the common factors of all the quantities. As for fractions, the simplest form is considered that in which the numbers in the ratio are the smallest possible integers.
Thus, the ratio 40:60 is equivalent in meaning to the ratio 2:3, the latter being obtained from the former by dividing both quantities by 20. Mathematically, we write 40:60 = 2:3, or equivalently 40:60∷2:3. The verbal equivalent is "40 is to 60 as 2 is to 3."
Irrational ratiosRatios may also be established between incommensurable quantities (quantities whose ratio, as the value of a fraction, amounts to an irrational number). The earliest discovered example, found by the Pythagoreans, is the ratio of the length of the diagonal d to the length of a side s of a square, which is the square root of 2, formally.
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On Ms. Smith's last math test, 80% of her 25 students earned an 83% or better. How many of Ms. Smith's students earned an 83% or better on the last math test?
Answer:
20 students
Step-by-step explanation:
It says 80% of 25 students got 83%+.
This means the number of students that got 83%+ is 80% of 25, or 25*0.8.
25*0.8 is 20, so 20 students got 83%+.
Answer:
20 students earned 83% or better in last maths test.
Step-by-step explanation:
We are given that on Ms. Smith's last math test, 80% of her 25 students earned an 83% or better.
We are to find the number of students who earned 83% or better on the test.
Number of students who earned 83% or more = 80% × 25 = [tex] \frac { 8 0 }{ 1 0 0 } \times 2 5[/tex] = 20
If f(x) = 2x - 6 and g(x) = 3x + 9, find (f + g)(x).
Answer:
[tex]\large\boxed{(f+g)(x)=5x+3}[/tex]
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=2x-6,\ g(x)=3x+9\\\\\text{Substitute:}\\\\(f+g)(x)=(2x-6)+(3x+9)\\\\=2x-6+3x+9\qquad\text{combine like terms}\\\\=(2x+3x)+(-6+9)\\\\=5x+3[/tex]
Which graph represents the function g(x) = |x + 4| + 2? Image for option 1 Image for option 2 Image for option 3 Image for option 4
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]g\left(x\right)=\left|x+4\right|+2[/tex]
The vertex of the function is the point (-4,2)
The y-intercepts is the point (0,6)
using a graphing tool
see the attached figure
Answer:
It is the second graph
Look at the picture that's attached to that is the answer
Cone A has a surface area of 384 ft2 and Cone B has a surface area of 96 ft?. What is the ratio of their volume?
Answer:
8 : 1
Step-by-step explanation:
Given ratio of sides = a : b, then
ratio of area = a² : b²
ratio of volumes = a³ : b³
Given
ratio of areas = 384 : 96 = 4 : 1 ← in simplest form, then
ratio of sides = [tex]\sqrt{4}[/tex] : [tex]\sqrt{1}[/tex] = 2 : 1
Hence
ratio of volumes = 2³ : 1³ = 8 : 1
each cookie sells for $0.50 Sam spent $90 on baking supplies and each cookie cost $0.25 to make how many cookies does Sam need to sell before making a profit formula: sales>cost
Answer:he needs to sell 180 cookies or more
Step-by-step explanation:
90.00/.50=180
Factor completely: 2x2 + 10x + 12
[tex]\bf 2x^2+10x+12\implies 2(x^2+5x+6)\implies 2(x+3)(x+2)[/tex]
recall that 3 * 2 = 6, and 3x + 2x = 5x.
Answer:
Step-by-step explanation:
It is a little easier if you take out the two.
2*(x^2 + 5x +6)
The numbers that multiply to 6 and adds to 5 are 3 and 2
2*(x + 3)(x + 2)
So that's how the trinomial factors.
Using complete square to slove for x in the equation (x+7) (x-9)=25
Answer:
[tex]x_1=1+\sqrt{89}\\\\x_2=1-\sqrt{89}[/tex]
Step-by-step explanation:
Apply Distributive property:
[tex](x+7)(x-9)=25\\\\x^2-9x+7x-63=25[/tex]
Add like terms and then add 63 to both sides of the equation:
[tex]x^2-2x-63=25\\\\x^2-2x-63+63=25+63\\\\x^2-2x=88[/tex]
Pick the coefficient of the x term, divide it by 2 and square it:
[tex](\frac{2}{2})^2=1[/tex]
Add it to both sides of the equation:
[tex]x^2-2x+1=88+1[/tex]
Rewriting the left side as a squared binomial, we get:
[tex](x-1)^2=89[/tex]
Apply square root to both sides:
[tex]\sqrt{(x-1)^2}=\±\sqrt{89}\\\\x-1=\±\sqrt{89}[/tex]
And finally we need to add 1 to both sides of the equation. Then we get:
[tex]x-1+1=\±\sqrt{89}+1\\\\x=\±\sqrt{89}+1\\\\\\x_1=1+\sqrt{89}\\\\x_2=1-\sqrt{89}[/tex]