Answer:
Area of rectangular land = 1,440 cm².
Perimeter of rectangular land = 152 cm
Step-by-step explanation:
Given:
Length of rectangular land = 36 cm
Width of rectangular land = 40 cm
Find:
Area of rectangular land
Perimeter of rectangular land
Computation:
Area of rectangle = length x width
Area of rectangular land = 36 x 40
Area of rectangular land = 1,440 cm²
Perimeter of rectangle = 2[l + b]
Perimeter of rectangular land = 2[36 + 40]
Perimeter of rectangular land = 2[76]
Perimeter of rectangular land = 152 cm
In a geometric sequence, the term a(n+1) can be smaller than the term a(n-)
Answer:
the answer is true
Step-by-step explanation:
the ratio is less than 1
Match each percent with the fraction or decimal equivalent. 5% 0.25 15% 0.07 6.5% 1 20 25% 0.065 7% 3/20
Answer:
5% = 1/20
15% = 3/20
6.5% = 0.065
25% = 0.25
7% = 0.07
Step-by-step explanation:
I hope this helps! Just ask me if you have any questions.
Have a nice dayy! :)
Answer:
.05 25% .15 7% .065 100% 2000% .25
Step-by-step explanation:
Percentages to decimals :
example
5% = .05
First remove the % sign: 5
Where is the decimal? Here : 5.00
Now move the decimal to the left two places. Fill the gaps with zeros : .05
Another way to do it is by divide the number by 100. Use a calculator if necessary.
Example 2: 6.5%
Move decimal two places to left: .065
Example 3: .56%
Move decimal to places to the left: .0056
Decimals to percentages. Do the exact opposite. Move decimal to places to the right then add the % sign.
Example: .25 becomes 25%
.07 becomes 07% or just 7%
Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.
Passing through (-3, -6) and (2,9)
What is the equation of the line in point-slope form?
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
What is the equation of the line in slope-intercept form?
Answer:
slope-inercept form: y = 3x + 3 point-slope form: y - 9 = 3(x - 2)
Step-by-step explanation:
slope-intercept form:
y2 - y1 / x2 - x1
9 - (-6)/ 2 - (-3)
= 3
y = 3x + b
9 = 3(2) + b
9 = 6 + b
3 = b
y = 3x + 3
point-slope form:
y - 9 = 3(x - 2)
4x⁴+3x²y²+9y⁴
solve by step by step
Answer:
4x^4+3x^2y^2+9y^2
(2x^2)^2 + 2×2x^2×3y^2 + (3y^2)^2 - 9
(2x^2 + 3y^2)^2 - (3)^2
(2x^2 +3y^2+3)(2x^2+3y^3-3)
Work out the area of the shaded
Hi there!
[tex]\large\boxed{73m^2}}[/tex]
Once again, divide the figure into 3 rectangles:
Top rectangle:
3m × 5m = 15m²
Long rectangle (subtract 5m from 9m to get the width):
12m × 4m = 48m²
Bottom rectangle:
2m × 5m = 10m²
Add up areas:
15m² + 48m² + 10m² = 73m²
the diagram on the right shows a circle.given that the length of arcs RS=2QR , angle QPR=35° and anglePSQ=45°,determine the value of
(a) angle SPR
(b) angle SRP
9514 1404 393
Answer:
(a) ∠SPR = 70°
(b) ∠SRP = 30°
Step-by-step explanation:
The applicable relationships are ...
the measure of an arc is twice the measure of the inscribed angle it subtendsthe sum of measures of the arcs of a circle is 360°the sum of measures of the angles of a triangle is 180°__
QR is subtended by 35° inscribed angle QPR, so is 2×35° = 70°.
PQ is subtended by 45° inscribed angle PSQ, so is 2×45° = 90°.
RS is 2×QR, so is 2×70° = 140°.
(a) Inscribed angle SPR is half the measure of arc RS, so is 140°/2 = 70°.
__
(b) Arc SP is the remaining arc in the circle, so is ...
arc SP = 360° -arc PQ -arc QR -arc RS = 360° -90° -70° -140° = 60°.
Inscribed angle SRP is half the measure of arc SP, so is 60°/2 = 30°
Select the correct answer.
A distribution center is redesigning two of its shipping boxes. The volume of these two boxes needs to be the same, and their dimensions are shown.
Write a system of equations to represent the volume of each box, y. Which statement describes the number and viability of the systems solutions?
Answer:
The system has two solutions, but only one is viable because the other results in negative side lengths.
Step-by-step explanation:
correct on edmentum or plato
Please helpppp
Find l.
Answer:
Step-by-step explanation:
radius of base=8/2=4 ft
l²=4²+9²=16+81=97
l=√97 ft
One number is 6 times a second number. The sum of the two numbers is 56. Find the numbersOne number is 6 times a second number.
The sum of the two numbers is 56. Find the numbers
Answer:
I think its 56 = 56
Step-by-step explanation:
Answer:
8 and 48
Step-by-step explanation:
This can be written as a system of equations. X will be the smaller number and y will be the larger:
6x = y
x + y = 56
Then substitute y in the second equation for 6x(seen in first equation) and solve.
x + 6x = 56
7x = 56
x = 8
So one number is 8. To find the other plug in 8 for x in either of the original equations (both get the same answer for y).
6x = y
6 * 8 = y
48 = y
Then double check by seeing if they fit the requirements of the problem.
Hope this helps!
cual es el 75% de 160¿
What is 75% of 160¿
Answer:
120
Step-by-step explanation:
calculator
5
Mark is investing $8,000 in an account paying 5.5% interest compounded weekly.
What will Mark's account balance be in 6 years?
Answer:
you divide a 8000÷ 5.5 yor answer is it
Consider the following equations and name the property of equality used to solve for the variable.
A. x + 3.75 = 7
B. –3b = 18
C. StartFraction m Over 5 EndFraction = negative 25
D. m – 4 = 9
9514 1404 393
Answer:
A. subtraction
B. division
C. multiplication
D. addition
Step-by-step explanation:
Observe what is done to the variable. Choose the operation that turns the unwanted value into the appropriate identity element.
A. 3.75 is added. To make that value be 0, we subtract 3.75.
B. -3 is multiplied. To make that value be 1, we divide by -3.
C. m is divided by 5. To make that 1/5 multiplier be 1, we multiply by 5.
D. 4 is subtracted. To make that value be zero, we add 4.
_____
Additional comment
Since subtraction is the same as addition of the opposite, and division is the same as multiplication by the reciprocal, the only two properties we really need are the addition property and multiplication property. Your grader may disagree.
Answer:
Other dude is right.
Step-by-step explanation:
Be safe, have an amazing day. :)
Let N be the smallest positive integer whose sum of its digits is 2021. What is the sum of the digits of N + 2021?
Answer:
[tex]10[/tex].
Step-by-step explanation:
See below for a proof of why all but the first digit of this [tex]N[/tex] must be "[tex]9[/tex]".
Taking that lemma as a fact, assume that there are [tex]x[/tex] digits in [tex]N[/tex] after the first digit, [tex]\text{A}[/tex]:
[tex]N = \overline{\text{A} \, \underbrace{9 \cdots 9}_{\text{$x$ digits}}}[/tex], where [tex]x[/tex] is a positive integer.
Sum of these digits:
[tex]\text{A} + 9\, x= 2021[/tex].
Since [tex]\text{A}[/tex] is a digit, it must be an integer between [tex]0[/tex] and [tex]9[/tex]. The only possible value that would ensure [tex]\text{A} + 9\, x= 2021[/tex] is [tex]\text{A} = 5[/tex] and [tex]x = 224[/tex].
Therefore:
[tex]N = \overline{5 \, \underbrace{9 \cdots 9}_{\text{$224$ digits}}}[/tex].
[tex]N + 1 = \overline{6 \, \underbrace{000 \cdots 000000}_{\text{$224$ digits}}}[/tex].
[tex]N + 2021 = 2020 + (N + 1) = \overline{6 \, \underbrace{000 \cdots 002020}_{\text{$224$ digits}}}[/tex].
Hence, the sum of the digits of [tex](N + 2021)[/tex] would be [tex]6 + 2 + 2 = 10[/tex].
Lemma: all digits of this [tex]N[/tex] other than the first digit must be "[tex]9[/tex]".
Proof:
The question assumes that [tex]N\![/tex] is the smallest positive integer whose sum of digits is [tex]2021[/tex]. Assume by contradiction that the claim is not true, such that at least one of the non-leading digits of [tex]N[/tex] is not "[tex]9[/tex]".
For example: [tex]N = \overline{(\text{A})\cdots (\text{P})(\text{B}) \cdots (\text{C})}[/tex], where [tex]\text{A}[/tex], [tex]\text{P}[/tex], [tex]\text{B}[/tex], and [tex]\text{C}[/tex] are digits. (It is easy to show that [tex]N[/tex] contains at least [tex]5[/tex] digits.) Assume that [tex]\text{B} \![/tex] is one of the non-leading non-"[tex]9[/tex]" digits.
Either of the following must be true:
[tex]\text{P}[/tex], the digit in front of [tex]\text{B}[/tex] is a "[tex]0[/tex]", or[tex]\text{P}[/tex], the digit in front of [tex]\text{B}[/tex] is not a "[tex]0[/tex]".If [tex]\text{P}[/tex], the digit in front of [tex]\text{B}[/tex], is a "[tex]0[/tex]", then let [tex]N^{\prime}[/tex] be [tex]N[/tex] with that "[tex]0\![/tex]" digit deleted: [tex]N^{\prime} :=\overline{(\text{A})\cdots (\text{B}) \cdots (\text{C})}[/tex].
The digits of [tex]N^{\prime}[/tex] would still add up to [tex]2021[/tex]:
[tex]\begin{aligned}& \text{A} + \cdots + \text{B} + \cdots + \text{C} \\ &= \text{A} + \cdots + 0 + \text{B} + \cdots + \text{C} \\ &= \text{A} + \cdots + \text{P} + \text{B} + \cdots + \text{C} \\ &= 2021\end{aligned}[/tex].
However, with one fewer digit, [tex]N^{\prime} < N[/tex]. This observation would contradict the assumption that [tex]N\![/tex] is the smallest positive integer whose digits add up to [tex]2021\![/tex].
On the other hand, if [tex]\text{P}[/tex], the digit in front of [tex]\text{B}[/tex], is not "[tex]0[/tex]", then [tex](\text{P} - 1)[/tex] would still be a digit.
Since [tex]\text{B}[/tex] is not the digit [tex]9[/tex], [tex](\text{B} + 1)[/tex] would also be a digit.
let [tex]N^{\prime}[/tex] be [tex]N[/tex] with digit [tex]\text{P}[/tex] replaced with [tex](\text{P} - 1)[/tex], and [tex]\text{B}[/tex] replaced with [tex](\text{B} + 1)[/tex]: [tex]N^{\prime} :=\overline{(\text{A})\cdots (\text{P}-1) \, (\text{B} + 1) \cdots (\text{C})}[/tex].
The digits of [tex]N^{\prime}[/tex] would still add up to [tex]2021[/tex]:
[tex]\begin{aligned}& \text{A} + \cdots + (\text{P} - 1) + (\text{B} + 1) + \cdots + \text{C} \\ &= \text{A} + \cdots + \text{P} + \text{B} + \cdots + \text{C} \\ &= 2021\end{aligned}[/tex].
However, with a smaller digit in place of [tex]\text{P}[/tex], [tex]N^{\prime} < N[/tex]. This observation would also contradict the assumption that [tex]N\![/tex] is the smallest positive integer whose digits add up to [tex]2021\![/tex].
Either way, there would be a contradiction. Hence, the claim is verified: all digits of this [tex]N[/tex] other than the first digit must be "[tex]9[/tex]".
Therefore, [tex]N[/tex] would be in the form: [tex]N = \overline{\text{A} \, \underbrace{9 \cdots 9}_{\text{many digits}}}[/tex], where [tex]\text{A}[/tex], the leading digit, could also be [tex]9[/tex].
Can someone help me solving this problem? I'm confuse so I want help..
question :
a) The length and breadth of a rectangular room are 10m and 8m respectively. How many pieces of carpet 5m long and 2m wide are required to cover it's floor?
Please help me solving this problem !
Answer: 8
Step-by-step explanation:
this is my last set of questions if anyone could get them all completed I have 15 points on it If you could add a small explanation so I can learn from it really appreciate it :) brainliest for anyone who does all 3 questions
Answer:
832.5
A unit rate is a rate with 1 in the denominator.
A tailor had 5000 buttons.He sawed 9 buttons on each shirt and had 2048 buttons left.Then,he sold all shirts at $36 each.find the total amount collected by the tailor?
Answer: $11,808
Step-by-step explanation:
5000 - 2048 = 2952
By subtracting the total number of buttons by the number of buttons left, it can be calculated that the tailor used a total of 2952 buttons.
Each shirt has 9 buttons, therefore the number of shirts can be calculated as:
2952 ÷ 9 = 328.
Since the shirts sold at $36 each and there are 328 shirts made, the total amount can be calculated as $36 · 328 = $11,808
(I hope this is right :\)
The total amount collected by the tailor $11,808.
What is division?Division is the process of splitting a number or an amount into equal parts.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
A tailor had 5000 buttons.
He sawed 9 buttons on each shirt and had 2048 buttons left.
Then, he sold all shirts at $36 each.
now,
5000 - 2048 = 2952
By subtracting the total number of buttons by the number of buttons left, it can be calculated that the tailor used a total of 2952 buttons.
Each shirt has 9 buttons, therefore the number of shirts can be calculated as:
2952 ÷ 9 = 328.
Since the shirts sold at $36 each and there are 328 shirts made,
the total amount can be calculated as $36 · 328
= $11,808
Hence, the total amount collected by the tailor $11,808.
To learn more on division click:
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Suzi is 1.7 meters tall. At 2:00 pm, Suzi measures her shadow to be 0.3 meters long. At the same time, a near by tree casts a shadow that is 2.4 meters long. How tall is the tree? (Give your answer in tenths.)
Please help, im confused ;w;
Answer:
[tex]x=7\text{ and } m\angle KLM = 34^\circ[/tex]
Step-by-step explanation:
We are given ethat KM and JN are parallel.
And we want to find the value of x.
Notice that ∠JKM and ∠LKM form a linear pair. Linear pairs total 180°. Therefore:
[tex]m\angle JKM + m\angle LKM = 180[/tex]
We know that ∠JKM measures (14x + 8). Substitute:
[tex](14x+8)+m\angle LKM =180[/tex]
Solve for ∠LKM:
[tex]m\angle LKM = 172-14x[/tex]
Next, since KM and JN are parallel, by the Corresponding Angles Theorem:
[tex]\angle JNM \cong \angle KML[/tex]
Since we know that ∠JNM measure (10x + 2), we can conclude that:
[tex]m\angle KML = 10x+2[/tex]
Next, recall that the three interior angles of a triangle must total 180°. Therefore:
[tex]m\angle KLM + m\angle LKM + m\angle KML = 180[/tex]
Substitute:
[tex](5x-1)+(172-14x)+(10x+2)=180[/tex]
Solve for x. Rewrite:
[tex](5x-14x+10x)+(-1+172+2)=180[/tex]
Combine like terms:
[tex](1x)+(173)=180[/tex]
Therefore:
[tex]x=7[/tex]
To find ∠KLM, substitute in 7 for x and evaluate. So:
[tex]m\angle KLM = 5(7) - 1 =34^\circ[/tex]
Which of the following numbers does not have
factors that include the smallest factor (other
than 1) of 119 ?
A. 28
B. 35
C. 40
D. 63
Answer:
C. 40
Step-by-step explanation:
The smallest factor of 119 (other than 1) is 7.
28/7 = 4,
35/7 = 5,
40/7 = 5 5/7
63/7 = 9
So it is 40
Someone please help me ASAP!!! Worth 11 points
Answer:
A' = (-3, 0)
Step-by-step explanation:
The coordinates of point A are (-6, 2).
The translation adds 3 to x and subtracts 2 from y.
A'(-6 + 3, 2 - 2) = A'(-3, 0)
Answer: A' = (-3, 0)
if a real estate company gives 3% commission on to it's agents. if an agent sold a piece of land for 12,50,000, how much cccommision did the agent get ?
Answer:
37500
Step-by-step explanation:
3% of 1250000
That is (3/100)*1250000
The answer is 37500
Tariq wants to make some purple paint.
He mixes blue, red and white paint in the ratio 5:3:2
Tariq needs 60 litres of purple paint.
He gets a discounted price of 60% on the red paint.
Calculate how many litres of red paint he buys at the discounted price.
Answer:
18 liters
Step-by-step explanation:
Blue : red : White = 5 : 3 : 2
Quantity of Blue paint = 5x
Quantity of Red paint = 3x
Quantity of White paint = 2x
Total paint = 5x + 3x + 2x = 10x
10x = 60 liters
x = 60/10
x = 6
Quantity of red paint = 3x = 3*6 = 18
Which graph represents the function?
g(x) = {x if x < 2
{-3 if x >= 2
Step-by-step explanation:We have to graph the function g(x) which is given as:
g(x)= x when x<2
and -3 when x ≥2.
Clearly after looking at the function we see that the function is not continuous since we find the continuity at x=2 as follows.
Left hand limitat 2:
g(2-h)=lim h→0 2-h
=2-0=2
Also right hand limit at x=2 is:
g(2+h)=lim h→0 (2+h)
= 2+0=2
Also g(2)= -3.
As:
Left hand limit= Right hand limit but is not equal to function's value at that point.
Hence, the function is discontinuous at x=2.
so for x<2 we will get a graph of a line y=x.
and for x≥2 we will get a straight line y=-3 parallel to the domain.
Solve the attachment...
Answer:
Step-by-step explanation:
= [tex]\int\limits^1_0 {5x\sqrt{x} } \, dx[/tex]
= [tex]\int\limits^1_0 {5xx^{1/2} } \, dx[/tex]
= [tex]\int\limits^1_0 {5x^{3/2} } \, dx[/tex]
= 5 [tex]\int\limits^1_0 {x^{3/2} } \, dx[/tex]
= 5*[tex]\frac{2}{5}[/tex]*[tex]x^{5/2}[/tex] |[tex]\left[\begin{array}{ccc}1\\0\\\end{array}\right] \left[/tex]
= 5*[tex]\frac{2}{5}[/tex]*[tex]1^{5/2}[/tex]
= 2
Answer:
2 ( Option A )
Step-by-step explanation:
The given integral to us is ,
[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]
Here 5 is a constant so it can come out . So that,
[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]
Now we can write √x as ,
[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]
Simplify ,
[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]
By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,
[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]
On simplifying we will get ,
[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]
the sum of three consecutive terms of an arithmetic progression is 24, find the middle term?
Answer:
Therefore,
Middle term = 8
Sequence,
a-d, a, a+d = 8-6, 8, 8+6
= 2,8,14
Step-by-step explanation:
Answer:
The middle term is 8
Step-by-step explanation:
The middle term is 8.
solve for x
[tex] \sqrt{x^2-4x+8} +x=2 - x[/tex]
please show all workings
Answer:
[tex]\displaystyle x=-\frac{2}{3}[/tex]
Step-by-step explanation:
We want to solve the equation:
[tex]\displaystyle \sqrt{x^2-4x+8}+x=2-x[/tex]
We can isolate the square root. Subtract x from both sides:
[tex]\sqrt{x^2-4x+8}=2-2x[/tex]
And square both sides:
[tex](\sqrt{x^2-4x+8})^2=(2-2x)^2[/tex]
Expand:
[tex]x^2-4x+8=4-8x+4x^2[/tex]
Isolate the equation:
[tex]3x^2-4x-4=0[/tex]
Factor:
[tex]\displaystyle (3x+2)(x-2)=0[/tex]
Zero Product Property:
[tex]3x+2=0\text{ or } x-2=0[/tex]
Solve for each case. Hence:
[tex]\displaystyle x=-\frac{2}{3}\text{ or } x=2[/tex]
Now, we need to check for extraneous solutions. To do so, we can substitute each value back into the original equation and check whether or not the resulting statement is true.
Testing x = -2/3:
[tex]\displaystyle \begin{aligned} \sqrt{\left(-\frac{2}{3}\right)^2-4\left(-\frac{2}{3}\right)+8}+\left(-\frac{2}{3}\right)&\stackrel{?}{=}2-\left(-\frac{2}{3}\right)\\ \\ \sqrt{\frac{4}{9}+\frac{8}{3}+8}-\frac{2}{3}&\stackrel{?}{=}2+\frac{2}{3} \\ \\ \sqrt{\frac{100}{9}}-\frac{2}{3}& \stackrel{?}{=} \frac{8}{3}\\ \\ \frac{10}{3}-\frac{2}{3} =\frac{8}{3}& \stackrel{\checkmark}{=}\frac{8}{3}\end{aligned}[/tex]
Since the resulting statement is true, x = -2/3 is indeed a solution.
Testing x = 2:
[tex]\displaystyle \begin{aligned}\sqrt{(2)^2-4(2)+8}+(2) &\stackrel{?}{=}2-(2) \\ \\ \sqrt{4-8+8}+2&\stackrel{?}{=}0 \\ \\ \sqrt{4}+2&\stackrel{?}{=}0 \\ \\ 2+2=4&\neq 0\end{aligned}[/tex]
Since the resulting statement is not true, x = 2 is not a solution.
Therefore, our only solution to the equation is x = -2/3.
Step-by-step explanation:
Hey there!
Given;
[tex] \sqrt{ {x}^{2} - 4x + 8} + x = 2 - x[/tex]
Take "X" in right side.
[tex] \sqrt{ {x - 4 + 8}^{2} } = 2 - 2x[/tex]
Squaring on both sides;
[tex] {( \sqrt{ {x}^{2} - 4x + 8 } )}^{2} = {(2 - 2x)}^{2} [/tex]
Simplify;
[tex] {x}^{2} - 4x + 8 = {(2)}^{2} - 2.2.2x + {(2x)}^{2} [/tex]
[tex] {x }^{2} - 4x + 8 = 4 - 8x + 4 {x}^{2} [/tex]
[tex]3 {x}^{2} - 4x - 4 = 0[/tex]
[tex]3 {x}^{2} - (6 - 2)x - 4 = 0[/tex]
[tex] 3 {x}^{2} - 6x + 2x - 4 = 0[/tex]
[tex]3x(x - 2) + 2(x - 2) = 0[/tex]
[tex](3x + 2)(x - 2) = 0[/tex]
Either;
3x+2 = 0
x= -2/3
Or;
x-2 = 0
x= 2
Check:
Keeping X= -2/3,
√(x²-4x+8 ) +X = 2-x
√{(-2/3)²-4*-2/3+8}+(-2/3) = 2+2/3
8/3 = 8/3 (True)
Now; Keeping X= 2
√{(2)²-4*2+8}+2 = 2-2
8 ≠0 (False)
Therefore, the value of X is -2/3.
Hope it helps!
Can someone help me with this math homework please!
Answer:
1/2
8
Step-by-step explanation:
When its talking about the result or output, look at the range, and then follow the line(s) back to the number(s) in the domain. Do the opposite when it's talking about the function of a certain number, e.g. f(4).
Is it possible for an angle in a triangle to be opposite both the longest side of the triangle and the shortest side of the triangle? Explain.
Answer: No, it's not possible.
Explanation: An angle must only be opposite exactly one side.
The town of Lakehorn is built on a grid system. Town hall is located downtown at point (0,0). A new school is located 3 miles north and 2 miles east of town hall. Only students who live outside a 5-mile radius from the school are eligible to ride the school bus. Which of the following students are eligible to ride the bus? Select all that apply.
The students eligible to ride the bus are: Marinna, Kaleb and Thomas
What is the distance between two points?The distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex] is,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
What is an equation of circle with center at (h, k)?An equation of circle with center at (h, k) and radius 'r' is,
[tex](x-h)^2 + (y-k)^2=r^2[/tex]
For given example,
Town hall is located downtown at point (0,0). A new school is located 3 miles north and 2 miles east of town hall.
Considering positive x-axis = East
negative x-axis = West
positive y-axis = North
negative y-axis =South
Also, locate the position of each student on the graph.
Then the given situation would as shown in following diagram.
We have been given, only students who live outside a 5-mile radius from the school are eligible to ride the school bus.
Using the equation of the circle,
the equation for the area within a circle of 5-mile radius from the school would be,
[tex](x-2)^2+(y-3)^2=5^2[/tex]
From the graph we can observe that, Marinna, Kaleb and Thomas live outside a 5-mile radius from the school.
Therefore, the students eligible to ride the bus are: Marinna, Kaleb and Thomas
Learn more about the equation of circle here:
https://brainly.com/question/10618691
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x+3/2 + (x-1) = 4/5
Answer:
x = [tex]\frac{3}{20}[/tex]
Step-by-step explanation:
Given
x + [tex]\frac{3}{2}[/tex] + (x - 1) = [tex]\frac{4}{5}[/tex]
Multiply through by 10 ( the LCM of 2 and 5 ) to clear the fractions
10x + 15 + 10(x - 1) = 8
10x + 15 + 10x - 10 = 8
20x + 5 = 8 ( subtract 5 from both sides )
20x = 3 ( divide both sides by 20 )
x = [tex]\frac{3}{20}[/tex]
x + 3/2 + x - 1 = 4/5
Collect the same terms
x + x + 3/2 - 1 = 4/5
2x + 3/2 - 2/2 = 4/5
2x + (3 - 2)/2 = 4/5
2x + 1/2 = 4/5
2x + 0.5 = 0.8
Subtract both sides 0.5
2x + 0.5 - 0.5 = 0.8 - 0.5
2x + 0 = 0.3
2x = 3/10
Divide both sides by 2
2x ÷ 2 = ( 3/10 ) ÷ 2
x = 3/10 × 1/2
x = 3/20
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Check :3/20 + 3/2 + ( 3/20 - 1 ) = 4/5
3/20 + 30/20 + ( 3/20 - 20/20 ) = 4/5
(3 + 30)/20 + (3 - 20)/20 = 4/5
33/20 - 17/20 = 4/5
(33 - 17)/20 = 4/5
16/20 = 4/5
4 × 4 / 4 × 5 = 4/5
4/5 = 4/5
Thus we found the correct value of x .
And we're done...
