The solution to the given quadratic equation is [tex]=-1\pm \sqrt{6}[/tex]
What is a quadratic equation?A quadratic equation is an equation whose highest power is raised to the power of 2. Mathematically it is written in the form ax² + bx + c. There are many ways in which we can solve a quadratic equation such as:
FactoringQuadratic formulaCompleting the square methodFrom the given information, we have:
x² + 2x - 5 = 0
Using the quadratic formula method;
[tex]=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
here;
a = 1b = 2c = -5[tex]=\dfrac{-2\pm \sqrt{2^2-4(1)(-5)}}{2(1)}[/tex]
[tex]=\dfrac{-2\pm \sqrt{4+20}}{2}[/tex]
[tex]=\dfrac{-2\pm \sqrt{24}}{2}[/tex]
[tex]=\dfrac{-2\pm 2\sqrt{6}}{2}[/tex]
[tex]=-1\pm \sqrt{6}[/tex]
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The numbers of polio cases in the world are shown in the table for various years.
Year Number of polio cases (thousands)
1988 350
1992 138
1996 33
2000 4
2005 3.2
2007 1.3
PREDICT THE NUMBER OF POLIO CASES IN 2014
hint: The function F gives the number of thousands of polio cases
The value of t is given as 2.3 years.
How to solvewe get the table for function as
t f(t)
8 350
12 138
16 36
20 4
25 3.2
27 1.3
So it is better to model the data by using an exponential model
using a graphing calculator we get our model as
f(t)=a(b)^t
[tex]f(t)=\boldsymbol{3648.6915(0.7380)^t}[/tex]
we have an exponential decay, so we get a rate of decrease as
b=1-r
r=1-b=1-0.738=0.262=26.2\\%
So the number of polio cases is decreasing by 26.2% per year
The number of polio cases in 2014 is
t=2014-1980=34
f(34)=3648.6915(0.7380)^{34}=0.1991389
this is in thousands so we get the number of cases in 2014 approximately as
[tex]0.1191389*1000 \approx \boldsymbol{119} \textup{ cases}[/tex]
for 1 case of polio :
f(t)=0.001
3648.6915(0.738)^t=0.001
we get
[tex]t=\frac{\ln (\frac{0.001}{3648.6915})}{\ln(0.738)}\approx 50[/tex]
so we get year as
1980+50={2030},
to find half life
[tex]\frac{a}{2}=a(b)^t[/tex]
[tex]b^t=\frac{1}{2}[/tex]
[tex]0.738^t=\frac{1}{2}[/tex]
[tex]t=\frac{\ln (1/2)}{\ln (0.738)}\approx\boldsymbol{2.3} \textup{ years}[/tex]
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Need help in this question, with explanation please.
Answer:
a) (1/2)(5)(CD) = 20 cm^2
5CD = 40, so CD = 8 cm
b) (1/2)(12)(8) = 48 cm^2
A total of $5550 is plit into
Awo investments. Part of the money.
is invested at 4%, and the reminder
is invested at 5"%.. If the total annual
interest from the two investments is
$259, how much is invested at each rate?
a = amount invested at 4%
how much is 4% of "a"? (4/100) * "a", namely 0.04a.
b = amount invested at 5%
how much is 5% of "b"? (5/100) * "b", namely 0.05b.
we know the total amount invested is 5550, so whatever "a" and "b" might be, we know that a + b = 5550.
we also know that the yielded amount in interest is 259, so if we simply add their interest, that'd be 0.04a + 0.05b = 259.
[tex]a+b=5550\implies b=5550-a \\\\[-0.35em] ~\dotfill\\\\ 0.04a+0.05b=259\implies \stackrel{\textit{substituting from above}}{0.04a+0.05(5550-a)~~ = ~~259} \\\\\\ 0.04a+277.5-0.05a=259\implies 277.5-0.01a=259\implies -0.01a=-18.5 \\\\\\ a=\cfrac{-18.5}{-0.01}\implies \boxed{a=1850}\hspace{9em}\stackrel{ 5550~~ - ~~1850 }{\boxed{b=3700}}[/tex]
Collect a set of data (from the internet) about any school-appropriate topic. Examples: rainfall data, and testing scores. Or make up your own set of data. The data set must contain at least 20 values. Fill out the questions below regarding your data.
1. List your data below in numerical order.
2. Explain your data. What does each data point represent?
3. What is the mean of your data?
4. What is the minimum and maximum within your data?
Here is the data collected as a result of the experiment.
1) Numerical order is: 0.20, 0.20, 0.46, 0.46, 2.10, 2.10, 5.50, 11.80, 12.20, 12.20, 13.22, 14.65, 16.07, 17.49, 18.91, 20.33, 20.50, 20.50, 21.75, 23.18
2) The data represents rainfall in millimeters over a 20-day period.
3) Mean = 11.69 mm.
4) The minimum rainfall is 0.20 mm ;
the maximum is 23.18 mm.
1) The data is listed as follows.
0.20 12.20 2.10 0.46 20.50 5.50 11.80 13.22 14.65 16.07 17.49 18.91 20.33 21.75 23.18 0.20 12.20 2.10 0.46 20.502) The data represents the amount of rainfall in millimeters over a 20 day period.
3) The mean rainfall over the 20 day period is 11.69 mm.
= (0.20 + 0.20 + 0.46 + 0.46 + 2.10 + 2.10 + 5.50 + 11.80 + 12.20 + 12.20 + 13.22 + 14.65 + 16.07 + 17.49 + 18.91 + 20.33 + 20.50 + 20.50 + 21.75 + 23.18) /20
Mean (x) = 11.69 mm.
3) The minimum rainfall is 0.20 mm and the maximum is 23.18 mm.
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You are running a fundraiser for your school, selling Reese’s and Skittles candies. You recorded you sold 34 candies and made $41, but didn’t tally how many of each candy you sold (and you don't remember the original amount of candy you had).
Below is the advertisement you used to sell the candy:
Reese's sells for $1 and skittles for $1.50
Write a system of equations to represent this situation. Then, solve it algebraically using either the substitution or elimination method.
Reese sold 20 candy and Skittles sold 14 candy for a total of $41. The equation for this is x + y = 34 and x + 1.5y = 41
What is an equation?An exponential equation is an expression that shows how numbers and variables using mathematical operators.
Let x represent the number of candy that Reese sell and y represent the number of Skittles candies
Reese's sells for $1 and skittles for $1.50
34 candies was sold, hence:
x + y = 34 (1)
He made $41, hence:
x + 1.5y = 41 (2)
Solving both equations simultaneously:
x = 20; y = 14
Reese had 20 candy and Skittles had 14 candy.
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Ellie and her older brother, Shawn, just got new phones! Both phones are shaped like rectangular prisms that are 3/4 of a centimeter tall. Ellie went with the smaller model that is 12 centimeters long and 6 centimeters wide, while Shawn went with the larger model that is 15 centimeters long and 8 centimeters wide. How many cubic centimeters larger is Shawn's phone than Ellie's?
Shawn's phone is 36 cubic cm larger than Ellie's phone.
How many cubic cm larger is Shawn's phone?To get difference in volume between the two phones, we must calculate volume of each phone and subtract the volume of Ellie's phone from the volume of Shawn's phone.
The volume of a rectangular prism is: length*width* height. The height of both phones is 3/4 centimeters.
The volume of Ellie's phone is:
= length x width x height
= 12 cm x 6 cm x (3/4) cm
= 54 cubic centimeters
The volume of Shawn's phone is:
= length x width x height
= 15 cm x 8 cm x (3/4) cm
= 90 cubic centimeters
The difference in volume is:
= Volume of Shawn's phone - Volume of Ellie's phone
= 90 cubic centimeters - 54 cubic centimeters
= 36 cubic centimeters
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A small country emits 80,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by 2.5% per year for the next 7 years. In the first year of the agreement, the country will keep its emissions at 80,000 kilotons and the emissions will decrease 2.5% in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the 7 year period, to the nearest whole number?
The total carbon dioxide emission over a period of 7 years will be 5,13,183 kilotons.
Considering the carbon emissions follow an exponential rate then
A(t)=A₀(1-r)^t
where A₀ is the initial value, and r is the decay rate as a decimal.
For the given problem A₀ =80000 kilotons and emissions will decrease at the rate of 2.5% per year therefore, r=0.025
The general equation for emission becomes
[tex]A(t)=80000(1-0.025)^t[/tex]
[tex]A(t)=80000(0.975)^t[/tex]
To calculate total emissions for 7 years it is calculated as follows
[tex]I=\int\limits^{7}_0 {A(t)} .dt=\int\limits^{7}_0 {80000(0.975)^tdt}[/tex]
[tex]I=80000(0.975)^t/ln (0.975)\left \{ {{t=7} \atop {t=0}} \right.[/tex]
I=5,13,183Kilotonnes
Hence, the total emission of 5,13,183 kilotons of carbon dioxide would be emitted over the course of the 7-year period.
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What is the volume of a solid with lines y=√(cos(x), y=e^x, x=pi/2 if it is revolved around the x axis?
For the same question, if there were x axis semicircles with a diameter on xy plane, what would the volume be?
To find the volume of the solid generated by revolving the region enclosed by the curves y = √(cos(x)), y = e^x and x = pi/2 around the x-axis, we can use the method of cylindrical shells.
Consider a thin vertical strip of width dx at a distance x from the y-axis. The height of this strip is the difference between the y-coordinates of the two curves:
h = e^x - √(cos(x))
The circumference of the shell is given by 2πx since the strip is at a distance x from the y-axis. Therefore, the volume of the shell is given by:
dV = 2πx * h * dx
= 2πx * (e^x - √(cos(x))) * dx
To find the total volume of the solid, we need to integrate this expression from x=0 to x=pi/2:
V = ∫[0, pi/2] 2πx * (e^x - √(cos(x))) dx
This integral can be evaluated using integration by substitution. Let u = cos(x), then du/dx = -sin(x) and dx = du/-sin(x). Using this substitution, the integral becomes:
V = ∫[1, 0] 2π * (-ln(u)/sin(x)) * (e^x - √(u)) dx
Integrating this expression with respect to x from x=0 to x=pi/2, we get:
V = 2π * [e^(pi/2) - 1 - (4/3) * (1 - sqrt(2))]
Therefore, the volume of the solid is approximately 27.838 cubic units (rounded to three decimal places).
What is 15% of 100
Please help
Answer:
Step-by-step explanation:15
At Wynne College, there are 240 students in Year 12.
The interquartile range of the times taken for these students to travel to college is 32 minutes.
How many of these students have travel times within this interquartile range?
About 120 students have travel times within the quoted interquartile range.
InterquartileThe interquartile range (IQR) represents the range of the middle 50% of a set of data, which is the difference between the third quartile (Q3) and the first quartile (Q1).
Assuming that the travel times are normally distributed and that we have information on the quartiles, we can use the formula:
IQR = Q3 - Q1
To find the number of students whose travel times fall within the interquartile range, we need to know the values of Q1 and Q3.
Since the IQR is 32 minutes:
32 = Q3 - Q1
We also know that the total number of students in Year 12 is 240. Assuming that all students have reported their travel times, we can use the interquartile range to estimate the proportion of students whose travel times fall within this range.
If the interquartile range covers the middle 50% of the data, then each quartile should cover 25% of the data. Therefore, we can estimate that the number of students whose travel times fall within the interquartile range is:
Number of students = 240 x 0.50 = 120
Therefore, we estimate that 120 of the 240 Year 12 students have travel times within the interquartile range of 32 minutes.
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I do not understand how to round to whole number
The given fraction can be converted into whole number as
16/5 +52/9 =9
99/7 -15/2=7
13/8+ 27/5=7
41/4-26/15=9
27/10+44/9=8
How can the fraction be converted to whole number?We can see that all the expression was given as a fraction the to convert to whole number we will need to solve them by performing the neccessary addition as well as substraction operations then it will converted to whole number.
16/5 +52/9
=404/45.
=8.977
=9
99/7 -15/2=
= 93/14
=6.643
7
13/8+ 27/5
= 281/40
=7.025
7
41/4-26/15
=511/60
=8.52
=9
27/10+44/9
= 683/90
=7.59
=8
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How many kilograms are
1 kg =
100 dag
45.4 kg
119.5 kg
54.5 kg
264.3 kg
there 5,450 dekagrams?
The number of kilogram that are there in there 5,450 dekagrams is: C. 54.5 kg.
What is kilograms?The kilogram is widely used as a unit of mass in everyday life, as well as in science, engineering, and industry. One kilogram is equal to 1,000 grams, and it is the base unit for other mass-related units such as milligrams, centigrams, and decigrams.
To convert 5,450 dag to kg, we need to divide by 100, since 1 kg = 100 dag:
5,450 dag ÷ 100 = 54.5 kg
Therefore, the answer is (c) 54.5 kg.
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The correct question is:
How many kilograms are there in there 5,450 dekagrams?
1 kg = 100 dag
a. 45.4 kg
b. 119.5 kg
c. 54.5 kg
d. 264.3 kg
14). Find the measures of both angles.
xo
(3x +20)°
Answer:
40 degrees and 140 degrees
Step-by-step explanation:
To solve this problem you can add x+3x+20 and set that equal to 180. (We can do this because angle x and angle 3x + 20 make a linear pair. Knowing this we can estimate that both angles added together will equal 180)
Let us add x + 3x + 20 = 180 to find x. We can then substitute that into the equation.
[tex]x+3x+20=180 :a\\\\4x+20=180 :b\\\\4x + 20 -20=180-20:c\\\\4x=160:d\\\\\frac{4x}{4} = \frac{160}{4}:e\\\\x=40:f[/tex]
a: So in this part, we have rewritten the equation to make it easier to solve
b: In this step, you combine the like terms x+3x to get 4x
c: In step c, you are subtracting 20 from both sides to keep constants on one side and variables on the right
d: In this last step the equation has been simplified to make it easier to solve.
e: To isolate x you have to divide both sides by 4, we do this because the coefficient of x is 4 so you divide the equation by 4 to cancel it out.
f: You rewrite and simplify the equation.
Now to find the measure of both angles you substitute x into the equation.
The first angle's value is 40 degrees and the second is 140 degrees.
These are our answers.
7. Find (i) the length of an arc and (ii) the area of a sector in a circle of radius 7 meters subtended by the central angle of 85°.
i) The length of the arc is approximately 73.148 meters.
ii) The area of the sector is approximately 85.584 square meters.
(i) The length of an arc can be calculated using the formula:
Arc Length = (θ/360) × 2πr
where;
θ = central angle in degrees
r = radius of the circle
π = mathematical constant approximately equal to 3.14159.
Given that the central angle is 85° and the radius is 7 meters, we can substitute these values into the formula:
Arc Length = (85/360) × 2π × 7
= (17/72) × 2 × 3.14159 × 7
≈ 1.7454 × 6.28318 × 7
≈ 73.148 meters (rounded to three decimal places.
(ii) The area of a sector can be calculated using the formula:
Sector Area = (θ/360) × πr²
Given that the central angle is 85° and the radius is 7 meters, we can substitute these values into the formula:
Sector Area = (85/360) × π × 7²
= (17/72) × 3.14159 × 7²
≈ 1.7454 × 3.14159 × 49
≈ 85.584 square meters (rounded to three decimal places)
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The correct question is:
Find:
(i) the length of an arc
(ii) the area of a sector in a circle of radius 7 meters subtended by the central angle of 85°.
Write the domain using interval notation.
Answer:
[tex](f \circ g)(\text{x}) = \frac{13}{13-\text{x}}[/tex]
Domain: [tex](-\infty,0) \cup (0,13) \cup (13,\infty)[/tex]
=================================================
Explanation:
Let's find the function composition.
The notation [tex](f \circ g)(\text{x})[/tex] is the same as [tex]f(g(\text{x}))[/tex]
[tex]f(\text{x}) = \frac{\text{x}}{\text{x}-1}\\\\\\f(g(\text{x})) = \frac{g(\text{x})}{g(\text{x})-1}\\\\\\f(g(\text{x})) = g(\text{x}) \div \Big( g(\text{x}) - 1\Big)\\\\\\[/tex]
Then,
[tex]f(g(\text{x})) = \frac{13}{\text{x}} \div \left(\frac{13}{\text{x}}-1}\right)\\\\\\f(g(\text{x})) = \frac{13}{\text{x}} \div \left(\frac{13}{\text{x}}-\frac{\text{x}}{\text{x}}\right)\\\\\\f(g(\text{x})) = \frac{13}{\text{x}} \div \frac{13-\text{x}}{\text{x}}\\\\\\f(g(\text{x})) = \frac{13}{\text{x}} * \frac{\text{x}}{13-\text{x}}\\\\\\f(g(\text{x})) = \frac{13}{13-\text{x}}\\\\\\[/tex]
-----------------
Now let's find the domain.
If we plugged x = 0 into g(x), then we get a division by zero error.
This means we must exclude this value from the domain.
For similar reasoning, we must exclude x = 13 because we get a division by zero error in [tex]f(g(\text{x})) = \frac{13}{13-\text{x}}[/tex]
We could have any other real number to be plugged in for x.
Here's what the domain looks like in interval notation.
[tex](-\infty,0) \cup (0,13) \cup (13,\infty)[/tex]
We effectively poke holes at 0 and 13 on the number line.
You spin the spinner once. 234 What is P(not greater than 2)? Write your answer as a fraction or whole number.
A theme park has a ride that is located in a cylinder with a height of 11 yards.The ride goes around the outside of the cylinder, which has a circumference of 513.88 yards. What is the surface area of the cylinder? Estimate to the nearest hundredth, using 3.14. Apply the formula for surface area of a cylinder SA=2B+Ph
Answer:
To calculate the surface area of the cylinder, we need to find the area of the two circular bases and the lateral surface area.
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference and r is the radius. We can rearrange this formula to solve for the radius:
r = C/2π = 513.88/(2 x 3.14) = 81.91 yards
The formula for the area of a circle is:
A = πr^2
where A is the area and r is the radius. We can use this formula to find the area of one of the circular bases:
B = πr^2 = 3.14 x 81.91^2 = 21,237.93 square yards
The formula for the lateral surface area of a cylinder is:
P x h
where P is the perimeter of the base and h is the height. We can use the formula for the circumference to find the perimeter of the base:
P = C = 513.88 yards
Now we can calculate the lateral surface area:
L = P x h = 513.88 x 11 = 5,652.68 square yards
Finally, we can use the formula for the surface area of a cylinder:
SA = 2B + L = 2(21,237.93) + 5,652.68 = 48,128.54 square yards
Therefore, the surface area of the cylinder is approximately 48,128.54 square yards when rounded to the nearest hundredth.
how do you find the base of a rectangle if you only know the height
Step-by-step explanation:
You will have to know more....like the area or the perimeter or the diagonal measure to determine the base if you only have the height.
its 7th grade math PLEASE HELP EMERGENCY
An example of a function that models a linear relationship between two quantities, x and y is y = mx + b
How to explain the functionWe need to use the equation of a straight line, which is commonly expressed in slope-intercept form as:
y = mx + b
In this function, x represents the independent variable, m is the slope of the line, and b is the y-intercept. To use this function, we simply plug in the values of x, m, and b that correspond to the specific relationship we are modeling.
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4Construct a function to model a linear relationship between two quantities.
Today's clients are ages 15, 72, 8, 89, 14, 16, 24, and 38. What is the range of the clients' ages?
Answer:
81
Step-by-step explanation:
The difference between the maximum and minimum values in a collection of data is known as the range. We must first determine the lowest and maximum values before we can determine the age range of the clients.
the minimum age is 8, and the maximum age is 89.
Therefore, the range of the clients' ages is:
Max age - Min age = 89 - 8 = 81
So the range of the clients' ages is 81.
5. Kamal said that he can measure
area using squares that are 2 units
long and 1 unit wide. What mistake
did Kamal make?
Answer:
A square's length & width are equal
Step-by-step explanation:
Kamal's shape is not a square, because a square is equilateral (equal length in all sides), but his square is 2:1,
When the sun is at a certain angle in the sky, a 100 foot building will cast a 25 foot shadow , how tall is a person if he casts a 1.5 foot shadow at the same time
The height of the person that cast a shadow of 1.5 foot is 6 foot.
How to solve proportional relationship?When the sun is at a certain angle in the sky, a 100 foot building will cast a 25 foot shadow. A person cast a shadow of 1.5 foot at the same time.
Therefore, the height of the person can be found by setting up a proportional relationship between the length of shadow and the actual height of the building and person.
Hence,
let
x = height of the person
Therefore,
100 / 25 = x / 1.5
cross multiply
25x = 100 × 1.5
25x = 150
divide both sides of the equation by 25
x = 150 / 25
x = 6
Therefore,
height of the person = 6 foot.
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14. Peter makes $15 per hour as a gardener. He gets a 10% raise. Which of the following
statements are true about Peter's new rate of pay? Select the three correct answers,
A Peter will make an additional 1/100 of his salary per hour.
(B) Peter will make an additional $1.50
per hour.
C Peter's new hourly rate is $16 per hour.
D After working 5 hours at the new rate, Peter will make $82.50.
E If Peter gets an additional 10% raise, his new pay rate will be $18.15.
The population of a small town of 29,000 people is expected to grow exponentially at a rate of 1.9% per year. Estimate the population in 2 years' time.
Answer:
Step-by-step explanation:
PLEASE HELP!!
A cone has a radius of 3 inches and a slant height of 12 inches.
What is the exact surface area of a similar cone whose radius is 6 inches?
Enter your answer in the box.
Surface area of similar cone =
___in²
Surface area of similar cone is 44π square inches
What does a cone in maths ?
A cone is referred to as a "right cone" when its vertex is higher than the base's centre (i.e., when the angle formed by the vertex, base center, and any base radius is a right angle); otherwise, the word "oblique" is used. A cone is referred to as an elliptic cone when the base is assumed to be an ellipse rather than a circle.
The surface area of a cone is given by:
surface area = πr(r + l)
where r is the radius and l is the slant height.
surface area of original cone = π(3)(3 + 12) = 45π
slant height of similar cone = (6/3)(12) = 24 inches
surface area of similar cone = π(6)(6 + 18) = 144π
ratio of surface areas = surface area of similar cone / surface area of original cone
= (144π) / (45π)
= 3.2
Therefore, The exact surface area of the similar cone is 6 times the surface area of the original cone,
6 × 45π = 144π square inches
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Please help !!!!!!!!!!
The total amount of interior angles featured on a polygon with 'n' sides can be determined through the equation (n-2)*180 degrees. This formula applies to all types of polygons, such as triangles.
How to explain the triangleIn order to calculate the sum of each individual angle in the polygon, we must consider the total degree measure formed within each triangle. Every triangle consists of three different sized interior angles that together form an count of 180 degrees.
For instance, when a polygon containing 'n' sides is divided into separate triangles by interconnecting certain vertices, the overall number of triangles produced can be worked out using the equation (n-1). A square, for example, can be broken down into two distinctive triangles, whereas a pentagon structures five triangles, and finally, a hexagon results in four.
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Justine is enrolled in an SAT prep class at the Oakdale Community Center. The community
center is 1.4 miles away from Justine's house. On a map of Oakdale, this distance is
represented by 1 inch. What is the scale of the map?
Write your answer in simplest form using whole numbers.
inches:
miles
Answer:
1.4:1
= 14:10
= 7:5
Hence, ans is 7:5
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The trinomial: x² - 5x +11 is not factorable. Explain why this is.
Answer:
Step-by-step explanation:
I cannot find 2 numbers that multiply to the last term (+11) and add to middle term (-5)
So it can't be factored that way.
After further inspection. i try to plug it into b²-4ac from the quadratic formula.
b=-5
c=11
(-5)²-4(1)(11)
= -19 you can never get a negative under the square root. so this quadratic will produce 2 imaginary solutions. so it is not factorable.
HELP!!!!!!!! Which system of linear equations can be solved using the information below?
The system of linear equations that can be solved from the matrices is given as follows:
-5x + 4y = 3.-8x + y = -6.How to obtain the system of equations?Considering that the row [3, -6] is common to matrices Ax and Ay, the matrix A is given as follows:
A = [-5 4; -8 1]
Hence the multiplication of matrices representing the system is given as follows:
[-5 4; -8 1][x; y] = [3; -6]
Applying the multiplication of matrices, the system of equations is given as follows:
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Please I need help soon as possible
Answer:
[tex]x^2 + 10x+25[/tex]
Step-by-step explanation:
(x + 5)^2 is the same as (x + 5)(x + 5), which is what you call a binomial expression, since two terms (x + 5) are being multiplied by each other. You can multiply any binomial expression using the FOIL method, where you multiply the first (F), outer (O), inner (I), and last terms and simplify at the end:
First terms: x * x
Outer terms: x * 5
Inner terms: 5 * x
Last terms: 5 * 5
Simplifying:
[tex](x * x) + (x * 5) + (5 * x) + (5 * 5)\\x^2+5x+5x+25\\x^2+10x+25[/tex]
