Answer:
f(x)=-3(x+1)^2+27
Step-by-step explanation:
Forst, simplify the expression by pulling out -3, but leave 24 out.
=-3(x^2+2x)+24
Then complete the square of the equatio inside the parenthesis (remember to subtract from the outside what you add to the inside times -3).
=-3(x^2+2x+1)+24+3
=-3(x+1)^2+27
The equation is now in vertex form.
from that, we now know that the vertex is (-1,27).
Set this equation equal to 0 to find the x intercepts:
0=-3(x+1)^2+27
-27=-3(x+1)^2
9=(x+1)^2
3 and -3=x+1
x=2 and -4
what is the parent function of
f(x)=2/5(-x-5)^5 +2
Answer:
Parent function: [tex]x^{5}[/tex]
Step-by-step explanation:
Parent function is the simplest form of the type of function given
for equation: [tex]\frac{2}{5} (-x -5)^{5} +2[/tex]
the simplest form is: [tex]x^{5}[/tex]
The diagram represents three statements: p, q, and r. For what value is both p ∧ r true and q false? 2 4 5 9
Answer:
the answer is C.5
Step-by-step explanation:
finding x :8x + 10 - 5x = 15.
Answer:
Here you go! 8x+10-5x!
Just kidding. here you go. x=1.66
Step-by-step explanation:
you can simplifiy the x´s by making it 3x by subtracting. You can also subract 10 from both sides. That leaves you with 3x=5.
x=1.66
Answer:
[tex]\large\boxed{x=\dfrac{5}{3}=1\dfrac{2}{3}}[/tex]
Step-by-step explanation:
[tex]8x+10-5x=15\qquad\text{subtract 10 from both sides}\\\\8x+10-10-5x=15-10\qquad\text{combine like terms}\\\\3x=5\qquad\text{divide both sides by 3}\\\\x=\dfrac{5}{3}[/tex]
Which of the following points lies on the graph of f(x) = -x 2?
(-4, 2)
(-2, -4)
(-2, 4)
(4, -2)
Answer:
(-2, -4)
Step-by-step explanation:
we have
[tex]f(x)=-x^{2}[/tex]
we know that
If a ordered pair lies on the graph, then the ordered pair must satisfy the equation of f(x)
Verify each ordered pair
case A) (-4, 2)
Substitute the value ox x and the value of y in the equation and then compare the results
[tex]2=-(-4)^{2}[/tex]
[tex]2=-16[/tex] ------> is not true
therefore
The point not lies on the graph
case B) (-2, -4)
Substitute the value ox x and the value of y in the equation and then compare the results
[tex]-4=-(-2)^{2}[/tex]
[tex]-4=-4[/tex] ------> is true
therefore
The point lies on the graph
case C) (-2, 4)
Substitute the value ox x and the value of y in the equation and then compare the results
[tex]4=-(-2)^{2}[/tex]
[tex]4=-4[/tex] ------> is not true
therefore
The point not lies on the graph
case D) (4, -2)
Substitute the value ox x and the value of y in the equation and then compare the results
[tex]-2=-(4)^{2}[/tex]
[tex]-2=-16[/tex] ------> is not true
therefore
The point not lies on the graph
Solve for b
-11b + 7 = 40
b =
Answer:
b = - 3
Step-by-step explanation:
Given
- 11b + 7 = 40 ( subtract 7 from both sides )
- 11b = 33 ( divide both sides by - 11 )
b = - 3
Answer:
-3
Step-by-step explanation:
-11b + 7 = 40
-11b = 40 - 7
-11b = 33
b = 33/-11
b = -1
Happy to help
Pls mark as Brainliest
During the trip, the Morales family drove on several different highways. Gabriela and Luis noticed that sometimes the mile markers were increasing, and other times the mile markers were decreasing.
On one highway, Gabriela noticed that they passed mile marker 123 at 1:00. She then saw that they reached mile marker 277at 3:00. Since Mr. Morales was driving at a constant speed, their mile-marker location over time can be represented by a line where the time in hours is the independent variable and the mile marker is the dependent variable. The points (1,123) and (3,277) are two points on this line.
What is the value of the slope of this line?
Enter your answer as the correct value, like this: 42
If your answer is a fraction, use the / symbol. For example, if your answer is 314, enter your answer like this: 3/14
Answer:
The slope of the line is 77
Explanation:
We know the speed is constant and that the mile-marker location over time can be represented by a line. This means that the equation is linear.
The slope can, therefore, be calculated as follows:
[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex]
where (x₁ , y₁) and (x₂ , y₂) are two points on the line
We are given that the two points (1, 123) and (3, 277) are two points in the line
Substitute with them in the above equation to get the slope as follows:
[tex]slope = \frac{277-123}{3-2}=77[/tex]
Hope this helps :)
The slope of a line represents the rate of change between two variables. The value of the slope in this scenario is 77/2.
The slope of a line represents the rate of change between two variables. In this case, the slope can be calculated using the formula:
slope = (change in y) / (change in x).
Given the points (1,123) and (3,277), the slope can be calculated as follows:
slope = (277 - 123) / (3 - 1).
Therefore, the value of the slope of the line representing the Morales family's mile-marker locations over time is 77/2.
A function g(x) has x-intercepts at (1/2,0) and (6,0) which could be g(x)?
g(x)=2(x+1)(x+6)
g(x) =(x-6)(2x-1)
g(x)=2(x-2)(x-6)
g(x) = (x+6)(x+2)
The answer is g(x)=(x-6)(2x-1).hope this helps please add brainlist
Answer:
[tex]\boxed{g(x) = (x - 6)(2x - 1)}[/tex]
Step-by-step explanation:
An x-intercept is the value of x when g(x) = 0. So, for each function, we must set g(x) = 0 and solve for x.
(a) g(x) = 2(x + 1)(x + 6) = 0
x + 1 = 0 x + 6 = 0
x = -1 x = -6
Wrong.
(b) g(x) = (x - 6)(2x - 1)
x - 6 = 0 2x – 1 = 0
x = 6 2x = 1
x = ½
Right.
(c) g(x) = 2(x - 2)(x - 6)
x - 2 = 0 x - 6 = 0
x = 2 x = 6
Wrong.
(d) g(x) = (x + 6)(x + 2)
x + 6 = 0 x +2 = 0
x = -6 x = -2
Wrong.
The only function that has x-intercepts at (½, 0) and (6, 0) is
[tex]\boxed{g(x) = (x - 6)(2x - 1)}[/tex]
Gold has a density of 19.32 grams per cubic centimeters and is worth $40.26 per gram. The figure shows the dimensions of a particular bar of gold. What is this bar of gold worth?
Do 19.32 x 40.26 which should equal $777.82
Find two additional polar representations of the point. Write each coordinate in simplest form with the angle in
Answer:
The other two other representation are (6 , -4π/3) and (-6 , -π/3)
Step-by-step explanation:
* Lets revise some important facts about the polar form of a point
- In polar coordinates there is an infinite number of coordinates for a
given point
- The point (r , θ) can be represented by any of the following coordinate
pairs (r , θ+2πn) , (-r , θ + [2n+1]π) , where n is any integer
* Now lets solve the problem
∵ A point has polar coordinates (6 , 2π/3)
- We can find many points as the same with this point
- The point (r , θ) can be represented by any of the following coordinate
pairs(r , θ + 2πn) and (-r , θ + (2n + 1)π), where n is any integer.
∵ The angle in [-2π , 2π]
∵ r = 6 and Ф = 2π/3
- Let n = -1
∴ (r , Ф + 2πn) = (6 , 2π/3 + 2π(-1)) = (6 , 2π/3 - 2π) = (6 , -4π/3)
* One point is (6 , -4π/3)
∴ (-r , θ + (2n + 1)π) = (-6 , 2π/3 + (2(-1) + 1)π) = (-6 , 2π/3 + (-2 + 1)π)
∴ (-r , θ + (2n + 1)π) = (-6 , 2π/3 + (-1)π) = (-6 , 2π/3 - π)
∴ (-r , θ + (2n + 1)π) = (-6 , -π/3)
* One point is (-6 , -π/3)
Final answer:
To find two additional polar representations of a point, you can add or subtract 2π radians (or 360° if using degrees) from the original angle, while keeping the radius the same.
Explanation:
A student has asked for two additional polar representations of a point. Polar coordinates specify the location of a point in a plane by a distance from the origin (r) and an angle (φ) with respect to the positive x-axis. To find additional representations, we can add 2π radians to the angle for each full rotation around the circle, keeping the same distance 'r'. For example, if a point has polar coordinates (r, φ), two other representations could be (r, φ + 2π) and (r, φ - 2π), or if in degrees, (r, φ + 360°) and (r, φ - 360°).
Hank's pickup can travel 68 miles on 4 gallons of gas. How many gallons will Hank's pickup need to travel 51 miles?
Answer:
3
Step-by-step explanation:
68/4 to get how many miles per gallon
17
51/17 to see how many gallons of gas
3 gallons of gas
Based on the information given, Hank's pickup has a fuel efficiency of 17 miles per gallon. Therefore, it will require approximately 3 gallons of gas to travel 51 miles.
Explanation:To determine how many gallons of gas Hank's pickup will need to travel 51 miles, we first establish the rate of gas consumption for the vehicle. As per the given data, Hank's pickup can travel 68 miles on 4 gallons. This gives us a rate of 68 miles/4 gallons = 17 miles per gallon.
Now, to find out how many gallons are required to travel 51 miles, we divide 51 miles by the rate of 17 miles per gallon. So, the calculation is as follows:
51 miles ÷ 17 miles/gallon = 3 gallons.
Therefore, Hank's pickup will require approximately 3 gallons to travel 51 miles.
Learn more about Fuel Efficiency here:https://brainly.com/question/13347135
#SPJ3
Andre has enough to fill 3500 in.3.. he decides to change the length of the step so that he will use all of the cement. What will be the new length of the step?
Answer:
43.75 inches or 43 and 3/4 inches.
Step-by-step explanation:
Ok, thanks for the complement of information.
So, to find the volume of that step, which is a rectangular prism, we would use the simple formula:
V = length * width * height
In this case, we have the total volume (3,500 cu in), we have the width (10 inches) and we have the height (8 inches). But we need to find out the new length in order for him to use all 3,500 cu in of cement.
So, we transform the formula above into:
length = V / (width * height)
then we plug-in the numbers:
length = 3,500 / (8 x 10) = 3,500 / 80 = 43.75
So, the new length of the step would be 43.75 inches or 43 and 3/4 inches.
An angle measures 41 degrees. What is its supplement?
An angle measures 31 degrees. What is its compliment?
Answer:
139 and 59, respectively
Step-by-step explanation:
By definition, supplementary means that the angles all add up to equal 180 degrees. Therefore, 180 - 41 = 139.
By definition, complementary means that the angles all add up to equal 90 degrees. Therefore, 90 - 31 = 59.
-y-2=3y+5 what is the answer
Answer:
y= -7/4
Step-by-step explanation:
-2-y=3y+5 (subtract 5 from both sides)
-7-y=3y (add 1y to both sides)
-7=4y (divide by 4)
y= -7/4
Answer:
y = -7/4
Step-by-step explanation:
Step 1: Isolate x by combining like terms
4y = -7
Step 2: Simplify
y = -7/4
If the equation below is solved by graphing, which statement is true?
log(6x+10) = log 1/2 x
a. the curves intersect at approx. x=0.46
b. the curves intersect at approx. x=0.75
c. the curves intersect at approx. x=1.11
d. the curves intersect at approx. x=3.07
Step-by-step explanation:
the curves intersect at approcx=0.46
Answer:
a. the curves intersect at approx. x=0.46Step-by-step explanation:
The given function is
[tex]log(6x+10)=log_{\frac{1}{2} }x[/tex]
If we graph this function, the result is like the image attached. There you can observe that the intersection point is at (0.464, 1.107).
If we round this points to the nearest hundred, they would be
x = 0.46 and y = 1.11.
Therefore, the right answer is
a. the curves intersect at approx. x=0.46
Need help with these questions please help!!
Answer:
C) 8+x > 10
Step-by-step explanation:
I think C is the correct answer because it's an open circle, it can't equal to 2 and it must be higher than 2.
Answer:-
Q no.8 :
9, 13, 17 can merely be the correct option.
Explanation:-
• The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third.
For instance:-
1) Calculation: 9 + 13 = 22 which is greater than the third side (the hypotenuse) that was 17. And hence is correct.
2) Calculation: 10 + 10 = 20 which is equal to the third/hypotenuse side that was also 20. Therefore it doesn’t fit the theorem and is unable to form a triangle.
3)Calculation: 6+8 = 14 which is less than the greatest/hypotenuse/third side or the side of measure 15. Thence, it isn’t the correct also. No accurate triangle can be formed from all these(6, 8, 15) measurements.
4) Calculation: 2+3 = 6 which is equal to the third /hypotenuse side of measure 6 also. And therefrom no triangle can be constructed from the given sides(2, 3, 6).
• The third important property of triangles is the triangle inequality rule, which states:
“The length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides”.
(Note: I honestly prefer you to understand from the first point which is far much clearer than the second one).
the set of all points in a plane that are equidistant from two points is an
A midpoint.
It is a set of points (single point) that is equidistant from point A and point B.
In other words the distance between point A and midpoint M is equal to the distance between point M and point B.
Answer:
The set of all points in a plane that are equidistant from two points is a Perpendicular Bisector.
Step-by-step explanation:
Given: Two points on the plane.
We need to find what has set of all such point which is equidistant from two given fixed point.
Point which is equidistant from two fixed point is known as mid point of the line segment formed by joining the fixed points.
So, all the point which is equidistant from fixed points form a perpendicular bisector.
Therefore, The set of all points in a plane that are equidistant from two points is a Perpendicular Bisector.
The general form of the equation of a circle is x2+y2−4x−8y−5=0.
What are the coordinates of the center of the circle?
Enter your answer in the boxes.
Answer:
centre = (2, 4)
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² - 4x - 8y - 5 = 0
Rearrange the x/y terms together and add 5 to both sides
x² - 4x + y² - 8y = 5
Use the method of completing the square on both the x/y terms
add ( half the coefficient of the x/y terms )² to both sides
x² + 2(- 2)x + 4 + y² + 2(- 4)y + 16 = 5 + 4 + 16
(x - 2)² + (y - 4)² = 25 ← in standard form
with centre (2, 4) and r = [tex]\sqrt{25}[/tex] = 5
What is the exponential form of 3*3*3*3*x*x*x*z*z?
3*3*3*3 = 3^4 = 81
x*x*x = x^3
z*z = z^2
3*3*3*3*x*x*x*z*z =
3^4x^3z^2 =
81x^3z^2
Answer:
9xz√x
Step-by-step explanation:
you take two 3's you pair them up you do the two time witch gives you three times three or nine you then pair up the x's giving you 9x and that leaves one x to go on the inside of the sq root symbol then you pair up the z's and because there are only two z's put them together on the outside equaling 9xz√x
please answer me x and y
Answer: x=5√3(you've got it correct!)
y=15
In∆ADC,
Cos 60°=DC/10
DC=5
y=20-5
y=15
Answer:
x = 5√3y = 15Step-by-step explanation:
Look at the picture.
ΔABC, ΔDBA and ΔDAC are the triangles 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.
Therefore
in ΔDAC:DC : AD : AC = 1 : √3 : 2
If AC = 10, then DC = 10 : 2 = 5 and AD = x = 5√3
in ΔDBA:AD : BD : AB = 1 : √3 : 2
If AD = 5√3, then AB = 2 · 5√3 = 10√3 and BD = y = 5√3 · √3 = 5 · 3 = 15
during the baseball season, the white sox won 15 games out of 20. what percentage of the game did they win?
Answer:
75%
Step-by-step explanation:
15 divided by 20 = .75 then convert to a percentage is 75%
3 out of every 5 picks are orange. If 12 picks are orange,how many picks are they in all
Answer: The answer to your question is 20
Step-by-step explanation: We know that 3 out of every 5 picks are oranges. And if the next 12 picks are orange, what is the total number of oranges in all?
So first, you would set up a proportion, which would look like this:
3 oranges/ 5 picks = 12 oranges/ x picks
Let the number of picks be known as x, our variable, since we don't know how many oranges are there total.
Next, when you have a proportion that you are trying to solve, the best thing to do is cross multiply, which will look this:
3x = 12(5)
3x = 60
3x/3 = 60/3
x=20 picks
Therefore, the answer is 20 picks
The mean of a set of normally distributed data is 600 with a standard devastation of 20. What percent of data is between 580 and 620
Answer: 68%
Step-by-step explanation:
Match the polynomials with their factors. 2a2 + 5a − 3 (a + 1)(2a − 3) 2a2 − a − 3 (a − 1)(2a + 3) 2a2 − 5a − 3 (2a − 1)(a + 3) 2a2 + a − 3 (2a + 1)(a − 3)
Answer:
2a² + 5a - 3 = (2a - 1)(a + 3)
2a² - a - 3 = (2a - 3)(a + 1)
2a² - 5a - 3 = (2a + 1)(a - 3)
2a² + a - 3 = (2a + 3)(a - 1)
Step-by-step explanation:
* To factor a trinomial in the form ax² ± bx ± c:
- Look at the c term
# If the c term is positive
∵ c = r × s ⇒ r and s are the factors of c
∴ r and s will have the same sign (sign of b)
∵ a = h × k ⇒ h , k are the factors of a
∴ rk + hs = b
∴ (hx + r)(kx + s) ⇒ if b +ve OR (hx - r)(kx - s) ⇒ if b -ve
# If the c term is negative
∵ c = r × s ⇒ r and s are the factors of c
∴ r and s will not have the same sign
∵ a = h × k ⇒ h and k are the factors of a
∴ rk - hs = b OR hs - rk = b
(hx + r)(kx - s) OR (hx - r)(kx + s)
* Now lets solve the problem
∵ 2a² + 5a - 3
∴ c = -3 ⇒ -ve term
∴ r , s have different sign
∵ 3 = 1 × 3 then r = 1 , s = 3
∵ a = 2
∵ a = h × k
∵ 2 = 2 × 1 then h = 2 , k = 1
∵ rk = 1
∵ sh = 6
∴ sh - rk = 5 ⇒ same value of b
∵ (hx - r)(kx + s)
∴ 2a² + 5a - 3 = (2a - 1)(a + 3)
∵ 2a² - a - 3
∴ c = -3 ⇒ -ve term
∴ r , s have different sign
∵ 3 = 3 × 1 then r = 3 , s = 1
∵ a = 2
∵ a = h × k
∵ 2 = 2 × 1 then h = 2 , k = 1
∵ rk = 3
∵ sh = 2
∴ sh - rk = -1 ⇒ same value of b
∵ (hx - r)(kx + s)
∴ 2a² - a - 3 = (2a - 3)(a + 1)
∵ 2a² - 5a - 3
∴ c = -3 ⇒ -ve term
∴ r , s have different sign
∵ 3 = 1 × 3 then r = 1 , s = 3
∵ a = 2
∵ a = h × k
∵ 2 = 2 × 1 then h = 2 , k = 1
∵ rk = 1
∵ sh = 6
∴ rk - hs = -5 ⇒ same value of b
∵ (hx + r)(kx - s)
∴ 2a² - 5a - 3 = (2a + 1)(a - 3)
∵ 2a² + a - 3
∴ c = -3 ⇒ -ve term
∴ r , s have different sign
∵ 3 = 3 × 1 then r = 3 , s = 1
∵ a = 2
∵ a = h × k
∵ 2 = 2 × 1 then h = 2 , k = 1
∵ rk = 3
∵ sh = 2
∴ rk - sh = 1 ⇒ same value of b
∵ (hx + r)(kx - s)
∴ 2a² + a - 3 = (2a + 3)(a - 1)
i dont know whats the answer can someone help me ?
Answer: 1206.37
Step-by-step explanation:
Multiply the pie times the radius and height
3.14 * 8^2 * 6
Answer:
V =384 pi units ^3
or
V =1205.76 units ^3
Step-by-step explanation:
Volume of a cylinder is given by
V = pi r^2 h
where r is the radius and h is the height
V = pi (8)^2 *6
V = pi (64)*6
V =384 pi units ^3 (exact answer)
or is we used 3.14 for pi
V = (3.14) * 384
V =1205.76 units ^3
In March, volunteers for a charity walkathon in Toronto raised $89,351. Volunteers in Montreal raised $102,459. Volunteers in Edmonton raised $78,505.
a. Round each amount to the nearest thousand dollars.
b. Add the rounded amounts to estimate the total amount of money raised.
c. Use the estimate to choose the exact total from among the following.
(1) $250,615 (2) $350,615 (3) $270,315 (4) $170,015
In your question, we are trying to find the total amount of money raised when the money is rounded to the nearest thousands.
Answer: (3) 270,315In order to solve the problem, we would need to round the money raised to the thousands place.
The thousands place would be the number before the comma. (_),000.
Lets round for Part A:
89,351. The thousands place would be 9 in this case, when you look at the number to the right of it (3), it's not big enough to make 9 bigger, so we would keep the thousands place the same. It would end up as 89,000.
102,459. The thousands place would be 2, the number to the right of it is not big enough to be rounded up, so we would keep it the same. It would end up as 102,000.
78,505. The thousands place would be 8. The number to the right of it is a big enough number to let the number 8 be rounded, therefore we would round the 8 up to 9. It would end up as 79,000.
Part B
Our current values would be 89,000, 102,000, and 79,000.
Now, for part B, we would add the rounded values to get an estimate of the money saved:
[tex]89,000+102,000+79,000 =270,000[/tex]
You should get 270,000. Remember, that's just an estimate number.
Part C:
The answer choice that's close to that number is answer choice (3), $270,315.
Your FINAL answer should be (3) $270,315.
What is the volume of this cylinder? (Round to the nearest inch ) 7( radius)
14( height)
Please help me
Answer:
The formula for the volume of a cylinder is:
V= pi * radius^2 * height
When the values are plugged in, you would have:
V= pi * 7^2 * 14
Then simplified....
V= pi * 49 * 14
V= pi * 686
V= 2155.13256036
and when rounded to the nearest inch...
the volume would be approximately 2155 inches.
An annular solar eclipse occurs when the moon is at its farthest point from the earth during a total eclipse. True False
-Hello There-
The Answer To This Question Would Be "TRUE"
Have A Great Day!
PLEASE HELP! 8 points!! Find the first 5 terms.
Answer:
2, 6, 12, 20, 30
Step-by-step explanation:
To find the first 5 terms, substitute n = 1, 2, 3, 4, 5 into the rule
a₁ = 1² + 1 = 1 + 1 = 2
a₂ = 2² + 2 = 4 + 2 = 6
a₃ = 3² + 3 = 9 + 3 = 12
a₄ = 4² + 4 = 16 + 4 = 20
a₅ = 5² + 5 = 25 + 5 = 30
Solve the following equation for x
Answer:
C
Step-by-step explanation:
Using the laws of logarithms
• log x + log y ⇔ log(xy)
• log x = log y ⇒ x = y
Given
logx + log(x - 3) = log 3x
log x(x - 3) = log 3x, hence
x(x - 3) = 3x
x² - 3x = 3x ( subtract 3x from both sides )
x² - 6x = 0 ← factor out x from each term
x(x - 6) = 0
Equate each factor to zero and solve for x
x = 0
x - 6 = 0 ⇒ x = 6
Solutions are x = 0, x = 6 → C
Answer: OPTION A
Step-by-step explanation:
You need to remember the logarithms properties:
[tex]log(a)+log(b)=log(ab)\\\\log(a)-log(b)=log(\frac{a}{b})\\\\log(a)^b=b*log(a)[/tex]
Rewrite the equation:
[tex]log(x(x-3))=log(3)+log(x)[/tex]
Like this logarithm has base 10, you can make this procedure:
[tex]log(x(x-3))-log(x)=log(3)[/tex]
[tex]log\frac{(x(x-3))}{(x)}=log(3)[/tex]
[tex]log(x-3)=log(3)[/tex]
[tex]10^{log((x-3))}=10^{log(3)}[/tex]
Then:
[tex](x-3)=3[/tex]
Now you need to solve for the variable "x":
[tex]x=3+3\\x=6[/tex]
Use completing the square to solve for x in the equation x^2-10x+25=35.
It actually has 2 answers
x =(10+√140)/2=5+√ 35 = 10.916
or:
x =(10-√140)/2=5-√ 35 = -0.916
ANSWER
[tex]x =5 \pm \sqrt{35} [/tex]
EXPLANATION
The given quadratic equation is:
[tex] {x}^{2} - 10x + 25 = 35[/tex]
Group the constants on the RHS,
[tex] {x}^{2} - 10x= 35 - 25[/tex]
[tex] {x}^{2} - 10x= 10[/tex]
Add the square of half the coefficient of x to both sides of the equation,
[tex]{x}^{2} - 10x + ( - {5)}^{2} = 10 + ( - {5)}^{2} [/tex]
[tex]{x}^{2} - 10x + 25= 10 + 25[/tex]
We factor the perfect square to get:
[tex]{(x - 5)}^{2} =35[/tex]
[tex]x - 5 = \pm \sqrt{35} [/tex]
[tex]x =5 \pm \sqrt{35} [/tex]