Answers
The area of the figure is 112 square inches.
Step-by-step explanation:
Step 1:
To calculate the value of the composite shape we first divide it into shapes that we know.
In this case, the composite shape consists of a triangle and a square attached below it.
If we can calculate the individual areas of the two shapes we should be able to calculate the area of the composite shape.
Step 2:
The triangle has a base length [tex]=10-6=4[/tex] inches and the height is [tex]16-10=6[/tex] inches.
The area of the triangle [tex]= \frac{1}{2} (b)(h) = \frac{1}{2} (4)(6) = 12.[/tex]
The area of the triangle is 12 square inches.
Step 3:
The area of a square is the square of its side length. The given square has a side length of 10 inches.
The area of the square [tex]= a^{2} = 10^{2} = 100.[/tex]
The area of the square is 100 square inches.
Step 4:
Now we calculate the area of the entire figure by adding the areas of the triangle and the square.
Area of the figure [tex]= 100 + 12 = 112.[/tex]
So the area of the figure is 112 square inches.
Related Questions
What is the first operation to use to simplify the expression?
3,500÷(34+8×2)−4
Answers
Final answer:
To simplify the expression 3,500÷(34+8×2)−4, first simplify the expression inside the parentheses, then divide and subtract to get the final answer of 66.
Explanation:
To simplify the expression 3,500÷(34+8×2)−4, we need to follow the order of operations which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In this case, we first simplify the expression inside the parentheses, which is (34+8×2). We perform the multiplication first, then the addition, resulting in 34+16. Next, we divide 3,500 by the sum of 34 and 16. Finally, we subtract 4 from the quotient.
Step-by-step:
1. Simplify (34+8×2) = 34+16 = 50
2. Divide 3,500 by 50 = 70
3. Subtract 4 from 70 = 66
Which two of the following numbers are irrational?
16
6π
6√
36−−√
0.3636
Answers
Answer:
6π,0.3636
Step-by-step explanation:
An irrational number is a number that cannot be expressed as a fraction for any integers.
So 6π and 0.3636 are irrational numbers
Without counting them one-by-one, how many orange
tiles should you buy for the border of the Nguyens' 3 x 3
swimming pool?
Answers
To find out how many tiles they would need for the border of a 3 x 3 swimming pool, you would need to add 3 tiles on the top, 3 tiles on the bottom, and 2 tiles on the left and right sides, resulting in a total of 10 tiles.
Explanation:The student wants to find out how many orange tiles they will need for the border of the Nguyens' 3 x 3 swimming pool. To do this, we can visualize the 3 x 3 square and count the tiles around the border, but we want to find a way to do it without counting them one-by-one.
The pool is 3 tiles by 3 tiles, which is a total of 9 tiles. However, the border tiles are only the tiles around the edges. Moreover, corners are shared by two sides. So, for a 3 x 3 square, there are 3 tiles on the top, 3 tiles on the bottom, 2 tiles on the left, and 2 tiles on the right. So, in total, we would need 3 + 3 + 2 + 2 = 10 tiles for the border of the pool.
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Final answer:
To find the number of orange tiles needed for the border of the Nguyens' 3 x 3 swimming pool, we need to calculate the perimeter of the pool and divide by the length covered by each tile.
Explanation:
To find the number of orange tiles needed for the border of the Nguyens' 3 x 3 swimming pool, we need to calculate the perimeter of the pool. The perimeter is the sum of all the sides of the pool.
In a 3 x 3 pool, each side has a length of 3 units. Since there are 4 sides, the total perimeter is 4 x 3 = 12 units.
Each tile covers a length of 1 unit, so to find the number of tiles needed, we divide the perimeter by the length covered by each tile: 12 ÷ 1 = 12 tiles.
ce
Which rigid transformation(s) can map AABC onto a
FED?
O
reflection, then dilation
reflection, then translation
rotation, then translation
rotation, then reflection
O
Answers
Answer:
B. reflection, then translation
Step-by-step explanation:
Hope this helps :)
Triangle ABC can be mapped onto triangle FED through reflection, then translation
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Triangle ABC can be mapped onto triangle FED through reflection, then translation
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which of The following numbers is largest Try This question out and I’ll give you brainliest
Answers
Answer: 0.153 is the largest
Step-by-step explanation:
1/7=0.14, 1/12=0.08, and 15%= 0.150
Sienna earns $9.36 for each hour she works. This week she worked 15.67 hours. How much did Sienna earn this week?
Answers
Answer:
146.67 dollars
Step-by-step explanation:
9.36*15.67
Answer:
$146.67
Step-by-step explanation:
$9.36 per hour
15.67 hours
Multiply
$146.67
Hope this helps :)
Solve for y.
-3=7(y-9/7)
Answers
Answer: Y= 6/7 or Y=0.86
Step-by-step explanation:
-3=7(y-9/7)
-3=7y-9
+9 +9
6=7y
divide both sides to get y by it self
6/7=y
Answer:
Y=6/7
Step-by-step explanation:
You have to isolate the variable by doing the opposite of PEMDAS to both sides of the equation.
What is 12% on $3,200 in sales?
Answers
Answer:
The easiest way of calculating discount is, in this case, to multiply the normal price $3200 by 12 then divide it by one hundred. So, the discount is equal to $384. To calculate the sales price, simply deduct the discount of $384 from the original price $3200 then get $2816 as the sales price.
WhT is the answer to -8(-4f-9)
Answers
Answer:
32f+72
Step-by-step explanation:
Distribute the -8
Answer:
32f + 72
Step-by-step explanation:
-8(-4f-9)
Distribute
(-8)(-4f) + (-8)(-9)
Multiply
32f + 72
Hope this helps :)
Find the area of the figure.
If you really know, you don't need the answer choices
Good Luck :)
Answers
The answer is B.)
1. Find the area of the rectangle = L x W
- 5 x 6 = 30
2. Find the area of the triangle = bh/2
- 4*3/2 = 6
3. Add the areas of the figures.
- 30 + 6 = 36 cm^2
If the rate 130 miles per 2 hours is reduced to a unit rate, the result is
miles per hour.
Answer here
Answers
Answer:
65 miles every 1 hour
Step-by-step explanation:
Unit rate is found once one of the units is 1. In this case we need to reduce the ratio so that it is 1 hour and we get a unit rate. We can do this by dividing both sided by 2 so that the hours are reduced to 1.
130=2
130/2=65 2/2=1
65=1
65 miles every hour
The unit rate of 130 miles per 2 hours is 65 miles per hour. This is calculated by dividing the number of miles (130) by the number of hours (2).
Explanation:In Mathematics, the term unit rate refers to the ratio of two measurements, in which the denominator is 1. In this situation, you are given the rate of 130 miles per 2 hours and need to reduce it to a unit rate. To do this, you divide the number of miles (130) by the number of hours (2).
The calculation would be 130 miles ÷ 2 hours = 65 miles per hour. Hence, the unit rate of 130 miles per 2 hours is 65 miles per hour. This means that if you travel at this rate, you would cover 65 miles in one hour.
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I need the answers for these pls help
Answers
Answer:
1)
A. m arc QRS = 100°
B. m arc QRT = 255°
C. m arc UTS = 180°
D. m arc UTR = 205°
2)
1] The major arc CA = 255°
2] The minor arc AB = 90°
Step-by-step explanation:
In a circle:
The measure of an central angle is equal to the measure of its subtended arcThe measure of a circle is 360°Any chord divides a circle into two arcs, a minor arc its measure is < 180° and a major arc its measure is > 180°, the sum of the measures of the minor and major arcs is 360°If the measures of the minor and major arcs are equal, then each arc represents a semi-circle1)
In circle O
A.
∵ m∠QOR = 75°
∵ ∠QOR subtended by arc QR
- By using the 1st note above
∴ m of arc QR = m∠QOR
∴ m of arc QR = 75°
∵ m∠ROS = 25°
∵ ∠ROS subtended by arc RS
∴ m of arc RS = m∠ROS
∴ m of arc RS = 25°
The measure of arc QRS is the sum of the measures of arcs QR and RS
∴ m arc QRS = 75° + 25° = 100°
B.
∵ m∠SOT = 155°
∵ ∠SOT subtended by arc ST
∴ m of arc ST = m∠SOT
∴ m of arc ST = 155°
The measure of arc QRT is the sum of the measures of arcs QR, RS and ST
∴ m arc QRT = 75° + 25° + 155 °= 255°
C.
∵ m∠UOT = 25°
∵ ∠UOT subtended by arc UT
∴ m of arc UT = m∠UOT
∴ m of arc RUT = 25°
The measure of arc UTS is the sum of the measures of arcs UT and TS
∴ m arc UTS = 25° + 155° = 180°
D.
The measure of arc UTR is the sum of the measures of arcs UT, TS and SR
∴ m arc UTR = 25° + 155° + 25 = 205°
2)
1]
∵ The sum of the measures of the minor and major arcs is 360°
∵ m of minor arc AC = 105°
- Subtract 105 from 360° to find the measure of the major arc CA
∴ m of major arc CA = 360° - 105°
∴ m of major arc CA = 255°
2]
∵ m of major arc AB = 270°
- Subtract 270° from 360° to find the measure of the minor arc AB
∴ m of minor arc AB = 360° - 270°
∴ m of minor arc AB = 90°
prove that :
1/sin^2A -1/tan^2A =1
Answers
To prove that:
[tex]$\frac{1}{\sin ^{2}A}-\frac{1}{\tan ^{2}A}=1[/tex]
LHS = [tex]\frac{1}{\sin ^{2}A}-\frac{1}{\tan ^{2}A}[/tex]
Using basic trigonometric identity, [tex]\tan (x)=\frac{\sin (x)}{\cos (x)}[/tex]
[tex]$=\frac{1}{\sin ^{2}A}-\frac{1}{\left(\frac{\sin A}{\cos A}\right)^{2}}[/tex]
[tex]$=\frac{1}{\sin ^{2}A}-\frac{1}{\frac{\sin^2A}{\cos^2 A}}[/tex]
[tex]$=\frac{1}{\sin ^{2}A}-\frac{\cos^2 A}{\sin^2A}[/tex]
[tex]$=\frac{1-{\cos^2 A}}{\sin ^{2}A}[/tex]
Using trigonometric identity: [tex]1-\cos ^{2}(x)=\sin ^{2}(x)[/tex]
[tex]$=\frac{\sin ^{2}A}{\sin ^{2}A}[/tex]
= 1
= RHS
LHS = RHS
[tex]$\frac{1}{\sin ^{2}A}-\frac{1}{\tan ^{2}A}=1[/tex]
Hence proved.
Carlos purchased a leather sofa four years ago for $1,500.00. Since he purchased it, its value has been decreasing by 30% per
year.
A. Find the missing values for the table shown.
B. Explain how you found each of the missing values in the table.
Carlos purchased it. Then
C Write an expression in the form a(b) that represents the value of the sofa in dollars t years
est your expression for t=0,1,2,3, and 4. Show your work.
Answers
Answer:
A) Table:
Value of the sofa in dollars:
Year Value
0 $1,500
1 $1,050
2 $735
3 $514.50
4 $360.15
B) Multiply successively by 0.70
C) [tex]1,500(0.7)^t[/tex]: see the tests below
Explanation:
A) Find the missing values for the table shown
Although the table was not provided with the question, you can create a complete table from the supplied information.
Table: value of the sofa
Year Value
0 $1,500
1 A
2 B
3 C
4 D
Then, determine the missing values, i.e. A, B, C, and D
Notice that 30% is 0.30 and a reduction in the value is determined by mutiplying the starting value by 1 - 0.3 = 0.7.
A = $1,500 × 0.7 = $1,050.00B = $1,050 × 0.7 = $735.00C = $735 × 0.7 = $514.50D = $514.50 × 0.7 = $360.15Thus, once completed the table would be:
Year Value
0 $1,500
1 $1,050
2 $735
3 $514.50
4 $360.15
B. Explain how you found each of the missing values in the table.
I multiplied successively by 0.70 which is the constant decaying rate of the function.
C. Write an expression in the form [tex]a(b)^t[/tex] that represents the value of the sofa in dollars t years after Carlos purchased it. Then test your expression for t = 0, 1, 2, 3, and 4.
a is the purchasing value of the sofa or the value when t = 0: 1,500b is the decaying rate: 1 - 30% = 1 - 0.3 = 0.7Thus, the expression is:
[tex]1,500(0.7)^t[/tex]Test it for t = 0, 1, 2, 3, and 4:
1,500(0.7)⁰ = 1,500(1) = 1,500 [tex]\checkmark[/tex]1,500(0.7)¹ = 1500(0.7) = 1,050 [tex]\checkmark[/tex]1,500(0.7)² = 1,500(0.49) = 735 [tex]\checkmark[/tex]1,500(0.7)³ = 1500(0.343) = 514.5 [tex]\checkmark[/tex]1,500(0.7)⁴ = 1,500(0.2401) = 360.15 [tex]\checkmark[/tex]“I think I can make it. I’ll just jump.” says Denis, flashing a grin as he looks to the neighboring rooftop.
“Wait!” Vera exclaims. “First let's find the distance! Here, take a look at this diagram.”
“I’ve never much cared for math,” Denis frowns.
Vera rolls her eyes. “We know the distance between us, and we know the angles between ourselves and your target landing point. All we need to do is...”
Denis jumps.
“...apply the law of sines.” Vera gasps.
According to Vera's diagram, how far did Denis need to jump to reach the neighboring rooftop?
Answers
9514 1404 393
Answer:
5.3 m
Step-by-step explanation:
The angle opposite the given side is ...
180° -105° -40° = 35°
Then the law of sines tells us the unknown distance (d) is ...
d/sin(40°) = 4.7 m/sin(35°)
d = (4.7 m)sin(40°)/sin(35°) ≈ 5.267 m
Denis will need to jump about 5.3 m to reach the neighboring roof.
_____
Additional comment
Denis will need a running start. The world record for a standing broad jump is less than 4 m.
please answer and explanation
Answers
61.23 square inches of metal is needed to create a cylindrical can.
Solution:
Diameter of the base = 3 in
Radius of the base = 3 ÷ 2 = 1.5 in
Height of the cylinder = 5 in
The value of π = 3.14
To find the surface area of the cylinder:
Surface area of the cylinder = [tex]2 \pi r^{2}+2 \pi r h[/tex]
= 2 × 3.14 × (1.5)² + 2 × 3.14 × 1.5 × 5
= 14.13 + 47.1
Surface area of the cylinder = 61.23 sq. in
Hence 61.23 square inches of metal is needed to create a cylindrical can.
If MP = 6x – 5, QR = 3x + 1, and RN = 6, what is QN?
Answers
Answer:
19 units.
Step-by-step explanation:
Consider the below figure attached with this question.
From the below figure it is given that MN=PQ.
It is given that MP = 6x – 5, QR = 3x + 1, and RN = 6.
Since non parallel sides are equal, therefore it is an isosceles trapezoid.
The diagonals of an isosceles trapezoid are equal.
[tex]MP=QN[/tex]
[tex]MP=QR+RN[/tex]
Substitute the given values.
[tex]6x-5=3x+1+6[/tex]
[tex]6x-5=3x+7[/tex]
[tex]6x-3x=5+7[/tex]
[tex]3x=12[/tex]
[tex]x=4[/tex]
The value of x is 4.
[tex]QN=MP=6x-5=6(4)-5=24-5=19[/tex]
Hence, the measure of QN is 19 units.
To find QN, RN from the value of QR which is 3x - 5
Explanation:The value can be found using Algebraic expressions.
To find QN, we need to find the value of QR and subtract RN from it.
Given that QR = 3x + 1 and RN = 6, we can substitute these values into the equation.
So, QN = (3x + 1) - 6.
Simplifying further, QN
= 3x + 1 - 6
= 3x - 5.
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6 Write an equation in point-slope form given the points (-1,-7) and (2, 5). a. y - 5 = 4 (x - 2) b. y + 5 = 4 (x + 2) c. y - 2 = 4 (x - 5) d. y + 2 = 4 (x + 5)
Answers
Answer:
A - y - 5= 4(x - 2)
Step-by-step explanation:
First find slope with the two points given
( -1 , -7) and ( 2 , 5)
Using
m = y_2 - y_1 / x_2 - x_1
m - slope
x_1 = -1
y_1 = -7
x_2 = 2
ÿ_2 = 5
Inserting the values
m = 5 - (-7) / 2 - (-1)
= 5 + 7 / 2 + 1
= 12 / 3
= 4
Slope is 4
Then let's proceed
y - y_1 = m ( x - x_1)
using ( 2 , 5) as x_1 and y_1 respectively
x_1 = 2
y_1 = 5
m = 4
y - 5 = m ( x - 2)
m = 4
y - 5 = 4 ( x - 2)
We are asked to give the answer in point slope form
Yepa is solving 1.6 ÷ 6.4.
She uses an equivalent expression to do the division problem.
Which choice shows how Yepa could have found the correct solution to 1.6 ÷ 6.4?
Answers
Answer:
1/4=0.25
Step-by-step explanation:
The required answer is 0.25.
Given that, 1.6 ÷ 6.4.
How to divide decimals?To divide a decimal by another decimal:
Move the decimal point in the divisor to the right until it is a whole number.Move the decimal point in the dividend to the right by the same number of places as the decimal point was moved to make the divisor a whole number.Then divide the new dividend by the new divisor.Now, 1.6/6.4=0.25
Therefore, the required answer is 0.25.
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Max and some friends shared the cost of a meal. The meal cast $51 and each person contributed $17 how many people share the cost of the meal
Answers
Answer:
3
Step-by-step explanation:
51 divided by 17 equals 3
What is the value of the expression? 32+[4×(15÷3)]−5
Answers
Answer:
47
Step-by-step explanation:
32+[4×(15÷3)]−5
At first we have to apply "BODMAS" rule. According to the rule, we will work 1st bracket.
Hence,
32+[4×5]−5
Then, we will take 3rd bracket into consideration,
32+20−5
Then, we will use addition from the BODMAS rule-
52 - 5
Finally, subtracting 5 from 52, we can get
= 47
The value of the expression is 47.
Final answer:
The value of the expression 32+[4×(15÷3)]−5 is calculated using the order of operations to be 47.
Explanation:
The value of the expression 32+[4×(15÷3)]−5 can be calculated by following the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). Let's solve it step by step:
Solve the expression inside the parentheses: (15÷3) = 5.
Multiply this result by 4: 4×5 = 20.
Add this result to 32: 32 + 20 = 52.
Finally, subtract 5 from this sum: 52 − 5 = 47.
Therefore, the value of the expression is 47.
how to find critical points
Answers
Answer:
look for places where the derivative is zero or undefined
Step-by-step explanation:
Find the derivative. Critical points are where the derivative is zero, and where it is undefined.
__
A polynomial function may or may not have points where the derivative is zero. It will never have points where the derivative is undefined (tangent lines are vertical).
A rational function, or one involving fractional exponents may have critical points where the derivative is undefined.
__
For example, the function ...
y = √(1 -x^2)
has the derivative ...
y' = -x/√(1 -x^2)
This has a zero at x=0 (tangent is horizontal). It is undefined at x = ±1, where the denominator is zero (tangent is vertical). Those values of x tell you the critical points are (-1, 0), (0, 1), (1, 0).
Critical points in a mathematical function are found by deriving the function, setting the derivative equal to zero, and solving for x. The x-values obtained are the x-coordinates of the critical points. An example is provided for the function f(x) = x3 - 3x2.
Explanation:To find the critical points in a function, you first need to identify the derivative of the function. Once you have obtained the derivative, you set it equal to zero and solve for x. The x-values you get are the x-coordinates of your critical points.
Let's illustrate with an example, using the function f(x) = x3 - 3x2.
First, let's find the derivative, f'(x) = 3x2 - 6x. Then set f'(x) = 0 and solve for x. This gives us x = 0 and x = 2. Therefore, (0, f(0)) and (2, f(2)) are the critical points of the function.
Please note, critical points are also the points where the derivative is undefined. However, in this case the derivative exists for all real numbers, so we do not have any such critical points here.
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1) 1336 = 8(-14x - 29)
Answers
Answer:
x = -14
Step-by-step explanation:
Step 1: Distribute
1336 = 8(-14x - 29)
1336 = -112x - 232
Step 2: Add 232 to both sides
1336 + 232 = -112x - 232 + 232
1568 = -112x
Step 3: Divide both sides by -112
1568 / -112 = -112x / -112
-14 = x
Answer: x = -14
Answer:
The solution is x = -14
Step-by-step explanation:
To solve for x, first perform the indicated multiplication. We get:
1336 = 8(-14x - 29) => 1336 = -112x - 232
Adding 232 to both sides isolates -112x:
1336 + 232 = -112x, or
1568 = -112x
Next, x = -1568/112 = -14
The solution is x = -14.
Find a positive angle less than 360° that is coterminal with the given angle.
525°
Answers
Answer:
165
Step-by-step explanation:
525-360=165
Type the Integer that makes the following addition sentence true.
Answers
Answer:
11
Step-by-step explanation:
3 + 38 - 63 + 33 = 11
Answer:
11
Step-by-step explanation:
I found the answer simply by doing trial-and-error, but here are the steps:
11 - 33 = -22
-22 + 63 = 41
41 + (-38) = 3
3/4 of m into an algebraic expression
Answers
The word OF means to multiply in math.
So, 3/4 of m becomes (3/4)m, which means 3/4 TIMES m.
We can also write the expression
this way: (3m)/4.
They both mean the same thing.
The requried 3/4 of m is represented by the algebraic expression (3/4)m, and its value depends on the specific value assigned to m.
To express 3/4 of a quantity, m, as an algebraic expression, we can multiply 3/4 by m.
The algebraic expression for 3/4 of m is (3/4)m.
To evaluate this expression, we simply multiply 3/4 by the value of m.
For example, if m = 10, we substitute m = 10 into the expression to find (3/4)(10) = (3/4) * 10 = 30/4 = 7.5.
Therefore, 3/4 of m is represented by the algebraic expression (3/4)m, and its value depends on the specific value assigned to m.
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Can someone answer this question please answer it correctly if it’s corect I will mark you brainliest
Answers
Answer:
$38.4
Step-by-step explanation:
20% discount means he has to pay:
100 - 20 = 80% of the marked price.
80/100 × 48 = 38.4
Answer:
$38.4
Step-by-step explanation:
To find the discounted price of a item, you need to apply the regular price and its sale percentage.
To find the "20% off sale" do this:
100% - 20% = 80%
Then multiply the regular price to the "80%".
Regular price of the watch: $48
Discounted price: $48 x 80% = $38.4
Hope this helps!!!:)A cone has a radius of 11 inches and a height of 15 inches. What is the volumes of the cone rounded to the nearest cubic inch
Answers
[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h }{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r = 11\\ h = 15 \end{cases}\implies V=\cfrac{\pi (11)^2(15)}{3} \\\\\\ V=605\pi \implies V \approx 1900.664\implies \stackrel{\textit{rounded up}}{V = 1901}[/tex]
The distance from Jason's house to school is 0.6 kilometer. What is this distance in meters?
Answers
Answer:
600 meters
Step-by-step explanation:
1 kilometer= 1000 meters
0.6/1=x/100
Which makes x=600
A system of equations that ended with the statement 5=5 has no solution? False or true
Answers
Answer: no solution
Step-by-step explanation:
In a system of equations, if the final equation simplifies to a statement that is always true, like 5=5, this indicates the system has in fact an infinity of solutions, not no solutions.
Explanation:The question given pertains to the solution of a system of equations. In a system of equations, if you simplify to a point where you end up with a statement that is always true, such as 5=5, this indicates that the system has an infinite number of solutions, not no solutions as suggested.
Let's imagine we have a system of two linear equations representing two lines on a graph. If the lines overlap perfectly (one is exactly the same as the other), every point on the line is a point of intersection, meaning it is a solution to the system. When we simplify such a system algebraically, we get an identity like 5=5 which is true no matter what values the variables may take, directly indicating that there are an infinite number of solutions.
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