Answers
[tex]y=\dfrac{1}{2}x+2\\\\for\ x=0\to y=\dfrac{1}{2}(0)+2=0+2=2\to(0;\ 2)\\\\for\ x=2\to y=\dfrac{1}{2}(2)+2=1+2=3\to(2;\ 3)\\\\y=2x-1\\\\for\ x=0\to y=2(0)-1=0-1=-1\to(0;\ -1)\\\\for\ x=2\to y=2(2)-1=4-1=3\to(2;\ 3)\\\\Look\ at\ the\ picture.\\\\Answer:\ (2;\ 3)\to x=2;\ y=3.[/tex]
Related Questions
What is the answer to: (51 + 11.22 + 35.92)?
Answers
Answer:
It would equal 98.14
Step-by-step explanation:
A satellite travels about 2272 miles in 8 minutes about how many miles does a satellite travel in 3 minutes
Answers
Answer:
852 miles
Step-by-step explanation:
We presume the speed is constant, so the satellite will travel 3/8 the distance in 3/8 the time.
... d = (3/8)·(2272 miles) = 852 miles
_____
1 minute is 1/8 of 8 minutes, so 3 minutes is 3/8 of 8 minutes.
River rambler charges $25 per day to rent a kayak. How much will it cost to rent a kayak for 5 days? Write and solve an equation to solve this problem.
Answers
Answer:
C=25d
Step-by-step explanation:
We write an equation where C or cost is my output and d or days is my input. I should be able to put in any number of days and find the cost. Let's gather some data:
River Ramble
Day 1 $25(1)=25 cost
Day 2 $25(2)=50 cost
Day 3 $25(3)=75 cost
Day d $25(d)=C.
Our equation is C=25d.
How do you recognize if a binomial is a difference of perfect squares and how is the pattern used to factor the binomial?
Answers
Answer:
A difference of squares has the following form [tex]a^2-b^2[/tex]. Any two perfect squares connected by subtraction can be factored.
It factors to (a+b)(a-b).
Step-by-step explanation:
A binomial is an expression with only terms where at least one is a term with a variable. When we can factor for difference of squares, we can have two variable terms or just one with a constant.
A difference of squares has the following form [tex]a^2-b^2[/tex]. Any two perfect squares connected by subtraction can be factored.
It factors to (a+b)(a-b).
You are going to flip a coin 8 times. The first 3 times you flip the coin you get tails. What is the probability that all the remaining flips will also be tails?
Answers
Answer:
So when you flip the coin 8 times and you get tails 3 of the times then you should do 3 plus 5 and you will get 8 as your total again so then the answer is 5 out of 8 total.
Step-by-step explanation:
The probability that all the remaining flips will be tails is 1/32, or approximately 0.03125.
Explanation:The probability of getting tails on each coin flip is 50 percent since a fair coin has two equally likely outcomes: heads or tails.
If the first three coin flips resulted in tails, the remaining five coin flips are independent events. The probability of getting tails on each of the remaining flips is still 50 percent.
The probability of getting all the remaining flips to be tails is calculated by multiplying the probabilities of each individual flip. Since there are five remaining flips, the probability is 0.5 raised to the power of 5, or 1/32 (approximately 0.03125).
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The expression 1/2bh gives the area of a triangle where b is the base of the triangle and h is the height of the triangle. What is the area of a triangle with the base of 7cm and a height of 4 cm?
Answers
[tex]A_{\triangle}=\dfrac{1}{2}bh\\\\\text{We have}\ b=7cm,\ h=4cm\\\\\text{Substitute:}\\\\A_{\triangle}=\dfrac{1}{2}(7)(4)=\dfrac{28}{2}=\boxed{14\ cm^2}[/tex]
The starting salary for a delivery driver is $35,000 per year with a yearly increase of 3%. Which type of function best models this situation?
A) exponential
B) linear
C) quadratic
D) radical
Answers
Answer: Exponential
$35,000(1.03)^x
Step-by-step explanation:
Answer:
The answer is exponential hope this helps mark me brainliest.
A formula for electrical circuits states that E=P/\I where E represents the force in volts, P represents power in watts, and I represents current in amps. Solve this formula for I. Then find I when the force E = 3.6 volts and the power P = 45 watts.
Answers
Answer:
[tex]I=12.5[/tex] amp
Step-by-step explanation:
The formula is,
[tex]E=\dfrac{P}{I}[/tex]
where,
E = Electromotive force in volts,
P = Power in watts,
I = Current in amps.
Given values are,
E = 3.6 volts,
P = 45 watts,
I = ??
Putting the values,
[tex]\Rightarrow 3.6=\dfrac{45}{I}[/tex]
[tex]\Rightarrow I=\dfrac{45}{3.6}=12.5[/tex] amp
Simplify: (3–a)·2+a =
Answers
Answer:
The simplified form of the given expression is 6-a.
Step-by-step explanation:
The given expression is
[tex](3-a)\cdot 2+a[/tex]
According to distributive property.
[tex]a\cdot (b+c)=ab+ac[/tex]
Use distributive property.
[tex]3(2)-a(2)+a[/tex]
[tex]6-2a+a[/tex]
Combine like terms.
[tex]6+(-2a+a)[/tex]
[tex]6-a[/tex]
Therefore the simplified form of the given expression is 6-a.
There are 70 students in the school band. 40% of them are sixth graders, 20% are seventh graders, and the rest are eighth graders. How many band members are sixth graders? How many band members are seventh graders? What percentage of the band members are eighth graders?
Answers
Answer:
The band members of sixth graders are 28.
The band members of seventh graders are 14.
The percentage of the band members eighth graders are 40% .
Step-by-step explanation
Formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
As given
There are 70 students in the school band.
40% of them are sixth graders, 20% are seventh graders, and the rest are eighth graders.
Now first find out the band members are sixth graders .
Percentage = 40%
Total value = 70
Put in the formula
[tex]40 = \frac{Number\ of\ band\ members\ are\ sixth\ graders\times 100}{70}[/tex]
[tex]Number\ of\ band\ members\ are\ sixth\ graders = \frac{40\times 70}{100}[/tex]
[tex]Number\ of\ band\ members\ are\ sixth\ graders = \frac{2800}{100}[/tex]
[tex]Number\ of\ band\ members\ are\ sixth\ graders = 28[/tex]
Therefore the number of band members are from sixth graders are 28 .
Now first find out the band members are seventh graders .
Percentage = 20%
Total value = 70
[tex]20 = \frac{Number\ of\ band\ members\ are\ seventh\ graders\times 100}{70}[/tex]
[tex]Number\ of\ band\ members\ are\ seventh\ graders = \frac{20\times 70}{100}[/tex]
[tex]Number\ of\ band\ members\ are\ seventh\ graders = \frac{1400}{100}[/tex]
[tex]Number\ of\ band\ members\ are\ seventh\ graders = 14[/tex]
Therefore the number of band members are from seventh graders are 14.
Now find out the percentage of the eighth graders of the band members.
Total number of band members = sixth graders members + seventh grade members + eighth graders members
As sixth graders members = 28
seventh grade members = 14
Total number of band members = 70
Put in the above
70 = 28 + 14 + eighth graders members
70 - 42 = eighth graders members
28 = eighth graders members
Put in the percentage formula
[tex]Percentage = \frac{28\times 100}{70}[/tex]
[tex]Percentage = \frac{2800}{70}[/tex]
Percentage = 40%
Therefore the percentage of the band members are eighth graders is 40 %.
Answer:
The band members of sixth graders are 28.
The band members of seventh graders are 14.
The percentage of the band members eighth graders are 40% .
Step-by-step explanation
Formula
As given
There are 70 students in the school band.
40% of them are sixth graders, 20% are seventh graders, and the rest are eighth graders.
Now first find out the band members are sixth graders .
Percentage = 40%
Total value = 70
Put in the formula
Therefore the number of band members are from sixth graders are 28 .
Now first find out the band members are seventh graders .
Percentage = 20%
Total value = 70
Step-by-step explanation:
Therefore the number of band members are from seventh graders are 14.
Now find out the percentage of the eighth graders of the band members.
Total number of band members = sixth graders members + seventh grade members + eighth graders members
As sixth graders members = 28
seventh grade members = 14
Total number of band members = 70
Put in the above
70 = 28 + 14 + eighth graders members
70 - 42 = eighth graders members
28 = eighth graders members
Put in the percentage formula
Percentage = 40%
Therefore the percentage of the band members are eighth graders is 40 %.
Help plz 30 points!!
Answers
900 workers : 3.2×10⁵
Dividing by 9×10² becomes
1 worker :[tex]\frac{3.2}{9}[/tex] ×10³
3.2/9 is just 0.36 rounded so it is
1 worker : 0.36×10³
or A
Answer:
the answer is a
Step-by-step explanation:
if m ║ n and m ∠5 = 65°, what is m ∠1?
Answers
Answer:
65
Step-by-step explanation:
Since <5 and <1 are corresponding angles and m is parallel to n
<5 = <1
<5 =65
so <1 = 65
Eileen collected 98 empty cans to recycle and Carl 82 cans. They packed a equal number of cans into each of three boxes. How many cans were in each box?
Answers
Answer: 60 cans in each box
Step-by-step explanation:
98+82=180
180/3=60
Jupiter has 11 more than 4 times as many moons has Neptune. Neptune has 14 moons. Let j equal the number of moons Jupiter has.
Answers
Final answer:
Jupiter has 67 moons.
Explanation:
To solve this problem, let's define j as the number of moons Jupiter has. According to the given information, Jupiter has 11 more than 4 times as many moons as Neptune, which has 14 moons. So, we can set up an equation: j = 4n + 11, where n is the number of moons Neptune has. Since Neptune has 14 moons, we can substitute that value into the equation: j = 4(14) + 11. Simplifying further, we get j = 56 + 11 = 67. Therefore, Jupiter has 67 moons.
solve 14^x+1=36
Round to the nearest ten-thousandth.
Answers
Answer:
x = 1.3472 to the nearest ten thousandth.
Step-by-step explanation:
14^x + 1 = 36
14^x = 35
Taking logarithms:-
x ln 14 = ln 35
x = ln 35 / ln 14
= 1.3472.
The solution, rounded to the nearest ten-thousandth, is x = 1.5404.
To solve the equation [tex]14^x + 1 = 36[/tex], we first isolate the exponential term by subtracting 1 from both sides of the equation, which gives us [tex]14^x = 35.[/tex]
The next step is to take the logarithm of both sides of the equation.
We could use any base for the logarithm, but it's common to use base 10 or the natural logarithm base (e). In this case, let's use the natural logarithm:
[tex]ln(14^x) = ln(35)[/tex]
We can then use the property of logarithms which allows us to bring the exponent down as a multiplier:
[tex]x * times ln(14) = ln(35)[/tex]
Now, you can solve for x by dividing both sides by ln(14):
[tex]x = ln(35) / ln(14)[/tex]
Using a calculator, we find the quotient and then round to the nearest ten-thousandth:
x = 1.5404
This value is the solution to the original equation.
If a right triangle has sides of length a, b and c and if c is the largest, then it is called the "hypotenuse" and its length is the square root of the sum of the squares of the lengths of the shorter sides (a and b). assume that variables a and b have been declared as doubles and that a and bcontain the lengths of the shorter sides of a right triangle: write an expression for the length of the hypotenuse.
Answers
Assuming this is for a programming language like c++, then the expression might look like
c = sqrt(a*a + b*b)
or you can use the pow function (short for power function)
c = sqrt( pow(a,2) + pow(b,2) )
writing "pow(a,2)" means "a^2"; similarly for b as well.
the length of hypotenuse can be found using the formula [tex]c = \sqrt{a^2+b^2}[/tex]
The pytharogas theorem states that:
[tex]hypotenuse^2 = perpendicular^2+ base^2[/tex]
The Pythagorean Theorem relates the length of the legs of a right triangle, labeled a and b, with the hypotenuse, labeled c. The relationship is given by:
[tex]a^2 + b^2 = c^2[/tex]
This can be rewritten, solving for c:
[tex]c = \sqrt{a^2+b^2}\\\\[/tex]
Thus, the length of hypotenuse can be found using the formula [tex]c = \sqrt{a^2+b^2}[/tex]
When 4 is subtracted from the square of a number, the result is 3 times the number. Find the negative solution.
Answers
Answer:
-1
Step-by-step explanation:
because if you put it in a equation for you get x^2-4=3x therefore you use the quadratic formula and solve the two answers you get are 4 and -1 so since its negative solution it must be -1 must be the square
The negative solution for a quadratic equation, set up to represent the expression 'When 4 is subtracted from the square of a number, the result is 3 times the number', is -1.
Explanation:The subject of this question is a quadratic equation. If we let n be the number, the provided question can be rewritten as:
n² - 4 = 3n
To solve this equation for n, we rearrange terms to get a standard quadratic equation:
n² - 3n - 4 = 0
We can solve this equation using the quadratic formula:
n = [-b ± sqrt(b² - 4ac)] / (2a)
Substituting the values a = 1, b = -3, c = -4 into the formula, we obtain:
n = [3 ± sqrt((-3)² - 4 × 1 × -4)] / (2 × 1)
which simplifies to:
n = [3 ± sqrt(9 + 16)] / 2 = [3 ± sqrt(25)] / 2 = [3 ± 5] / 2
Thus we have two solutions:
n = 8/2 = 4 and n = -2/2 = -1
Since we are looking for the negative solution, the number we are looking for is -1.
Learn more about Quadratic Equations here:https://brainly.com/question/30098550
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Help me please!!! 30 points! :)
Answers
[tex] \frac{625 {(5xy)}^{ - 3} }{ {(5x)}^{2} {y}^{7} } \: = \: 625 \times \frac{1}{ {(5xy)}^{3} } \times \frac{1}{ {(5x)}^{2} {y}^{7} } \: = \: 625 \times \frac{1}{125 {x}^{3} {y}^{3} } \times \frac{1}{25 {x}^{2} {y}^{7} } \: = \: \frac{1}{5 {x}^{5} {y}^{10} } [/tex]
Ryan will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $59 and costs an additional $0.08 per mile driven. The second plan has an initial fee of $46 and costs an additional $0.10 per mile driven.A) for what amount of driving do the two plans cost the same? B) What is the cost when the two plans cost the same
Answers
1st's plan total cost = 0,08x + 59
2nd's = 0,10x + 46
(x stands for the total of miles)
a) For you two know when the costs will be the same, you set one equation equal to the other and you find out that if you drive 650 miles, you'd pay the same amount of money. It doesn't matter which plan you pick.
b) Knowing this, just place 650 into the equation and solve.
The height, h(t), in feet of an object thrown into the air with an initial upward velocity of 63 feet per second is given by the formula h(t) = -16t2 + 63t, where t is the time in seconds. What is the height, in feet, of the object after 3 seconds?
Answers
Answer:
The height of the object after 3 seconds is 45 feets.
Step-by-step explanation:
The height of an object thrown into the air with an initial upward velocity of 63 feet per second is given as
[tex]h(t)=-16t^2+63t[/tex]
Where, h(t) is height of the object in feet and t is the time in seconds.
We have to find the height of the object after 3 seconds. So, substitute t=3.
[tex]h(3)=-16(3)^2+63(3)[/tex]
[tex]h(3)=-16(9)+189[/tex]
[tex]h(3)=-144+189[/tex]
[tex]h(3)=45[/tex]
Therefore height of the object after 3 seconds is 45 feets.
To calculate the height of an object after 3 seconds using the equation h(t) = -16t^2 + 63t, substitute t with 3 and solve. This results in a height of 45 feet.
To find the height after 3 seconds, we substitute t with 3 into the equation, getting h(3) = -16(3)2 + 63(3). Calculating this step-by-step, we first find the square of 3, which is 9, and then multiply it by -16 to get -144. Next, we multiply 63 by 3 to get 189. Adding these two results together, we end up with 45 feet. Therefore, the height of the object after 3 seconds is 45 feet.
Sketch the plane curve represented by the given parametric equations. Then use interval notation to give the relation's domain and range. X = 2t, y = t2 + t + 3
Answers
Answer:
Domain: [tex]( -\infty,\infty )[/tex] and Range: [tex][ -1,\infty )[/tex]
Step-by-step explanation:
We have the parametric equations [tex]x= 2t[/tex] and [tex]y=t^{2}+t+3[/tex].
Now, we will find the values of 'x' and 'y' for different values of 't'.
t : -3 -2.5 -2 -1.5 -1 0 1 1.5 2
[tex]x= 2t[/tex] : -6 -5 -4 -3 -2 0 2 3 4
[tex]y=t^{2}+t+3[/tex] : 9 6.75 5 3.75 3 3 5 6.75 9
Now, we can see that these parametric equations represents a parabola.
The general form of the parabola is [tex]y=ax^{2}+bx+c[/tex].
Now, we have the point ( x,y ) = ( 0,3 ). This gives that c = 3.
Also, we have the points ( x,y ) = ( -2,3 ) and ( 2,5 ). Substituting these in the general form gives us,
4a - 2b + 3 = 3 → 4a - 2b = 0 → b = 2a.
4a + 2b + 3 = 5 → 4a + 2b = 2 → 2a + b = 1 → 2a + 2a = 1 ( As, b = 2a ) → 4a = 1 → [tex]a=\frac{1}{4}[/tex].
So, [tex]b=\frac{1}{2}[/tex].
Therefore, the equation of the parabola obtained is [tex]y=\frac{x^{2}}{4}+\frac{x}{2}+3[/tex].
The graph of this function is given below and we can see from the graph that domain contains all real numbers and the range is [tex]y\geq -1[/tex].
Hence, in the interval form we get,
Domain is [tex]( -\infty,\infty )[/tex] and Range is [tex][ -1,\infty )[/tex]
Answer:
Domain:
[tex](-\infty,\infty)[/tex]
Range:
[tex][2.75,\infty)[/tex]
Step-by-step explanation:
we are given parametric equation as
[tex]x=2t[/tex]
[tex]y=t^2+t+3[/tex]
We can change into rectangular equation
we can eliminate t from first equation and plug into second equation
[tex]x=2t[/tex]
[tex]t=\frac{x}{2}[/tex]
now, we can plug that into second equation
[tex]y=(\frac{x}{2})^2+\frac{x}{2}+3[/tex]
now, we can draw graph
Domain:
we know that
domain is all possible values of x for which any function is defined
we can see that our equation is parabolic
and it is defined for all values of x
so, domain will be
[tex](-\infty,\infty)[/tex]
Range:
we know that
range is all possible values of y
we can see that
smallest y-value is 2.75
so, range will be
[tex][2.75,\infty)[/tex]
To take a taxi, it costs \$3.00$3.00 plus an additional \$2.00$2.00 per mile traveled. You spent exactly \$20$20 on a taxi, which includes the \$1$1 tip you left. How many miles did you travel?
Answers
Answer:
8 miles
Step-by-step explanation:
Given:
To take a taxi initial cost = $ 3.00
Per mile cost = $ 2.00
Total spent = $20
Tip Given = $ 1
To find:
Total miles traveled=?
Solution:
Now the total cost f the ride was $ 20
As we see that initial cost for all the trips would stay the same
Let someone travels x miles
then according to the given
Initial cost + 2 * miles traveled + tip = total cost
Putting from the given values it becomes
3 + 2 * x + 1 = 20
Now we have to find x here which is the total miles traveled
solving the above equation
3+1+2x=20
4+2x=20
2x=20-4
2x=16
dividing both sides by 2
x =8 miles
so total miles travelled by the person is 8 miles
Answer: 8 miles you traveled.
Step-by-step explanation:
What is an equation of the line, in point-slope form, that passes through the given point and has the given slope?
Answers
Answer: [tex]y -3 = \frac{4}{11} (x - 11)[/tex]
Step-by-step explanation:
We can use the point-slope formula to write the equation of a line given a point on the line and the slope of the line:
Slope = m
Given point (x₁,y₁)
Formula = (y-y₁) = m(x-x₁)
Given point: (11,3); slope: 4/11
Answer : [tex]y - 3 = \frac{4}{11} (x - 11)[/tex]
[tex]\textit{\textbf{Spymore}}[/tex]
If two angles are supplementary, which is the sum of their measurements? A. 45o B. 90o C. 120o D. 180o
Answers
Two supplementary angle when added together need to equal 180 degrees.
Answer:
Two supplementary angle when added together need to equal 180 degrees.
Step-by-step explanation:
Drag and drop numbers into the boxes so that the paired values are in a proportional relationship.
x 1 3 _____ 5 8
y 4 12 16 20 _____
4
12
32
8
36
Answers
Answer:
4 and 32
Step-by-step explanation:
We are given paired values for two variables x and y and we are to fill in the missing values such that they are in a proportional relationship.
For x, we have the following paired values:
[tex]1, 3, ___, 5, 8[/tex]
So from the given options, 4 fits the best here which is greater than 3 and lesser than 5.
And for y, we have:
[tex]4, 12, 16, 20, ___[/tex]
Here, 32 fits the best from all the options as it is the next (available) number after 20.
6y + 2x - 2y - 3x
PLEASE HELP ASAP THANK YOU
Answers
Answer:
4y-x
Step-by-step explanation:
Combine like-terms.
6y-2y and -3x+2x
Do the Math
4y and -x
4y-x
The measure of an angle is 78 less than the measure or its complement.What is the measure of the angle
Answers
Answer:
84°
Step-by-step explanation:
2 complementary angles sum to 90°
let x be the angle then complement = x - 78, hence
x + x - 78 = 90 ( add 78 to both sides )
2x = 168 ( divide both sides by 2 )
x = 84
hence the angle is 84°
Please help! Write the slope-intercept form of the equation for the line.
a. y=-8/7x-3/2
b. y=-3/2x+7/8
c. y=-7/8x-3/2
d. y=7/8x-3/2
Answers
Answer:
C
Step-by-step explanation:
The slope intercept of a line is y=mx +b where
m is the slope which is calculated as the vertical distance divided by the horizontal distance between two points.b is the y-intercept for value on the y-axis for which the line crosses it.This graph crosses the y-axis (the vertical line) halfway between -1 and -2. This is -3/2. This means only answers a, c, and d are options.
The graph moves up from -3/2 to its next point at (-4,0). We calculate the slope using:
Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We substitute [tex]x_1=0\\y_1=-1.5[/tex] and [tex]x_2=-4\\y_2=2[/tex]
[tex]m=\frac{2-(-1.5)}{-4-0}[/tex]
[tex]m=\frac{2+1.5}{-4}=\frac{3.5}{-4} =-0.875[/tex]
This decimal is equivalent to -7/8. This means C is the answer.
This equation represents a line with a slope of [tex]\( -\frac{7}{8} \)[/tex](meaning the line slopes downward from left to right) and a y-intercept of [tex]\( -\frac{3}{2} \)[/tex](where the line crosses the y-axis). The correct answer is option c
The slope-intercept form of the equation of a line is [tex]\( y = mx + b \),[/tex] where m represents the slope of the line, and b represents the y-intercept (where the line crosses the y-axis).
Let's analyze each option:
a.[tex]\( y = -\frac{8}{7}x - \frac{3}{2} \):[/tex]
- Slope [tex]\( m = -\frac{8}{7} \)[/tex]
- y-intercept [tex]\( b = -\frac{3}{2} \)[/tex]
b. [tex]\( y = -\frac{3}{2}x + \frac{7}{8} \):[/tex]
- Slope [tex]\( m = -\frac{3}{2} \)[/tex]
- y-intercept[tex]\( b = \frac{7}{8} \)[/tex]
c.[tex]\( y = -\frac{7}{8}x - \frac{3}{2} \):[/tex]
- Slope [tex]\( m = -\frac{7}{8} \)[/tex]
- y-intercept [tex]\( b = -\frac{3}{2} \)[/tex]
d.[tex]\( y = \frac{7}{8}x - \frac{3}{2} \):[/tex]
- Slope[tex]\( m = \frac{7}{8} \)[/tex]
- y-intercept[tex]\( b = -\frac{3}{2} \)[/tex]
Among the given options, the correct slope-intercept form is option c:
[tex]\[ \boxed{y = -\frac{7}{8}x - \frac{3}{2}} \][/tex]
Order the numbers from least to greatest. A) 1.5, 1.66, 2.4, 3.25, 3.33 B) 1.5, 1.66, 2.4, 3.33, 3.25 C) 1.66, 1.5, 2.4, 3.25, 3.33 D) 3.25, 3.33, 2.4, 1.66, 1.5
Answers
What is the fourth term of the expansion of the binomial (2x + 5)5? A. 10x2 B. 5,000x2 C. 1,250x3 D. 2,000x3
Answers
Answer:
B would be the answer for this question.
Step-by-step explanation:
Answer: The fourth term is [tex]5000x^2.[/tex]
Step-by-step explanation: We are given to find the fourth term in the expansion of the following binomial :
[tex]B=(2x+5)^5.[/tex]
We know that
the r-th term in the expansion of the binomial [tex](a+x)^n[/tex] is given by
[tex]T_r=^nC_ra^{n-(r-1)}b^{r-1}.[/tex]
For the given term, we have
n = 5 and r = 4.
Therefore, fourth term is given by
[tex]T_4\\\\=^5C_{4-1}(2x)^{5-(4-1)}5^{4-1}\\\\=^5C_3(2x)^25^3\\\\=\dfrac{5!}{3!(5-3)!}\times4x^2\times125\\\\\\=\dfrac{5\times4}{2\times1}\times 500x^2\\\\=5000x^2.[/tex]
Thus, the fourth term is [tex]5000x^2.[/tex]