एक आयत मॉडल में भुजाएं (2x+3) और (x+4) हैं। कुल क्षेत्रफल क्या होगा?
A rectangle model has sides (2x+3) and (x+4). What will be the total area?
#rectangle grid
#area model
#algebra tiles
A \(2x^2+11x+12\) / correct total
B \(2x^2+7x+12\) / one strip missed
C \(2x^2+8x+3\) / wrong corner
D \(2x^2+12x+7\) / swapped parts
Explanation opens after your attempt
Correct Answer
A. \(2x^2+11x+12\) / correct total
Step 1
Concept
The cells are \(2x^2\), (8x), (3x), and (12), whose sum is \(2x^2+11x+12\). In exams add all four cells.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+11x+12\) / correct total. The cells are \(2x^2\), (8x), (3x), and (12), whose sum is \(2x^2+11x+12\). In exams add all four cells.
Step 3
Exam Tip
खाने \(2x^2\), (8x), (3x), और (12) हैं जिनका योग \(2x^2+11x+12\) है। परीक्षा में चारों खाने जोड़ें।
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एक टाइल मॉडल में \(x^2\), दो (3x) आयत और (9) का छोटा वर्ग है। पूरा वर्ग किस भुजा का है?
A tile model has \(x^2\), two (3x) rectangles, and a small square (9). What is the side of the complete square?
#algebra tiles
#perfect square
#side
A (x+9)
B (x+3)
C (x-3)
D (3x+1)
Explanation opens after your attempt
Step 1
Concept
Two (3x) rectangles and \(9=3^2\) form ((x+3)2 ). Exam tip: the small square tells the side part.
Step 2
Why this answer is correct
The correct answer is B. (x+3). Two (3x) rectangles and \(9=3^2\) form ((x+3)2 ). Exam tip: the small square tells the side part.
Step 3
Exam Tip
दो (3x) आयत और \(9=3^2\) मिलकर ((x+3)2 ) बनाते हैं। परीक्षा में छोटा वर्ग भुजा बताता है।
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यदि किसी वर्ग मॉडल में \(x^2\), दो (6x) आयत और (36) छोटा वर्ग हैं, तो बाहरी भुजा क्या होगी?
If a square model has \(x^2\), two (6x) rectangles, and a small square (36), what is the outer side?
#algebra-tiles
#outer-side
#complete-square
A (x+6)
B (x+12)
C (x-6)
D (6x+6)
Explanation opens after your attempt
Step 1
Concept
The small square has side (6), and the large part is (x). Exam tip: take the sum of the side parts.
Step 2
Why this answer is correct
The correct answer is A. (x+6). The small square has side (6), and the large part is (x). Exam tip: take the sum of the side parts.
Step 3
Exam Tip
छोटे वर्ग की भुजा (6) है और बड़ा भाग (x) है। परीक्षा में बाहरी भुजा भागों का योग लें।
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यदि ((x+a)2 ) के वर्ग मॉडल में प्रत्येक आयत का क्षेत्रफल (11x) है, तो अंतिम छोटा वर्ग क्या होगा?
If in the square model of ((x+a)2 ), each rectangle has area (11x), what will the final small square be?
#unknown constant
#algebra tiles
#perfect square
A (22)
B (121)
C \(11x^2\)
D (22x)
Explanation opens after your attempt
Step 1
Concept
Each rectangle is (ax=11x), so (a=11) and the small square is (121). Exam tip: identify the constant side from one rectangle.
Step 2
Why this answer is correct
The correct answer is B. (121). Each rectangle is (ax=11x), so (a=11) and the small square is (121). Exam tip: identify the constant side from one rectangle.
Step 3
Exam Tip
प्रत्येक आयत (ax=11x) है इसलिए (a=11) और छोटा वर्ग (121) है। परीक्षा में एक आयत से स्थिर भुजा पहचानें।
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टाइल मॉडल में \(p^2+18p+81\) एक पूर्ण वर्ग बनाता है। यदि बीच का भाग दो बराबर आयतों से बना है, तो प्रत्येक आयत का क्षेत्रफल क्या होगा?
A tile model \(p^2+18p+81\) forms a perfect square. If the middle part is made of two equal rectangles, what is the area of each rectangle?
#algebra tiles
#middle rectangles
#perfect square
A (9p)
B (18p)
C (81p)
D (p+9)
Explanation opens after your attempt
Step 1
Concept
The total middle term is (18p), so each equal rectangle is (9p). Exam tip: split (2ab) into two equal rectangles.
Step 2
Why this answer is correct
The correct answer is A. (9p). The total middle term is (18p), so each equal rectangle is (9p). Exam tip: split (2ab) into two equal rectangles.
Step 3
Exam Tip
बीच का कुल पद (18p) है इसलिए प्रत्येक बराबर आयत (9p) होगा। परीक्षा में (2ab) को दो समान आयतों में बाँटें।
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यदि \(x^2+10x+25\) को टाइलों से पूर्ण वर्ग बनाया गया है, तो दो समान आयतों में से प्रत्येक का क्षेत्र कितना होगा?
If \(x^2+10x+25\) is made as a complete square using tiles, what is the area of each of the two equal rectangles?
#complete-square
#algebra-tiles
#middle-term
A (10x)
B (25x)
C (2x)
D (5x)
Explanation opens after your attempt
Step 1
Concept
The total middle term is (10x), so each equal rectangle has area (5x). Exam tip: split the middle term into two equal parts.
Step 2
Why this answer is correct
The correct answer is D. (5x). The total middle term is (10x), so each equal rectangle has area (5x). Exam tip: split the middle term into two equal parts.
Step 3
Exam Tip
बीच का कुल पद (10x) है इसलिए प्रत्येक समान आयत (5x) का होगा। परीक्षा में बीच के पद को दो बराबर भागों में बांटें।
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एक ग्रिड मॉडल में पंक्ति विभाजन (x), (4) और स्तंभ विभाजन (x), (-7) है। कुल क्षेत्रफल क्या होगा?
In a grid model, the row divisions are (x), (4) and the column divisions are (x), (-7). What will be the total area?
#signed grid
#rectangle area
#algebra tiles
A \(x^2-3x-28\)
B \(x^2+11x-28\)
C \(x^2-11x+28\)
D \(x^2+3x-28\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-3x-28\)
Step 1
Concept
The parts are \(x^2\), (-7x), (4x), and (-28). The total is \(x^2-3x-28\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-3x-28\). The parts are \(x^2\), (-7x), (4x), and (-28). The total is \(x^2-3x-28\).
Step 3
Exam Tip
भाग \(x^2\), (-7x), (4x), और (-28) हैं। कुल \(x^2-3x-28\) है।
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एक आयत टाइल मॉडल में भुजाएं (t+3) और (t-4) हैं। क्षेत्रफल का सरलीकृत रूप क्या होगा?
In a rectangular tile model the sides are (t+3) and (t-4). What is the simplified area?
#rectangle model
#product identity
#algebra tiles
A \(t^2+7t-12\)
B \(t^2-t-12\)
C \(t^2-7t+12\)
D \(t^2+t+12\)
Explanation opens after your attempt
Correct Answer
B. \(t^2-t-12\)
Step 1
Concept
The area is ((t+3)(t-4)=t-2 -4t+3t-12=t-2 -t-12). Exam tip: keep signs carefully.
Step 2
Why this answer is correct
The correct answer is B. \(t^2-t-12\). The area is ((t+3)(t-4)=t-2 -4t+3t-12=t-2 -t-12). Exam tip: keep signs carefully.
Step 3
Exam Tip
क्षेत्रफल ((t+3)(t-4)=t-2 -4t+3t-12=t-2 -t-12) है। परीक्षा में चिह्नों को सावधानी से रखें।
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टाइल मॉडल में \(x^2\) टाइल और (1) टाइल के बीच दो (x) टाइलें लगाकर कौन सा पूर्ण वर्ग बनता है?
In a tile model, placing two (x) tiles between an \(x^2\) tile and a unit tile forms which perfect square?
#algebra tiles
#complete square
#visual identity
A ((x+2)2 )
B \(x^2+1\)
C ((x+1)2 )
D \(x^2+2\)
Explanation opens after your attempt
Correct Answer
C. ((x+1)2 )
Step 1
Concept
The total tiles give \(x^2+2x+1\). Exam tip: two (x) tiles form ((x+1)2 ).
Step 2
Why this answer is correct
The correct answer is C. ((x+1)2 ). The total tiles give \(x^2+2x+1\). Exam tip: two (x) tiles form ((x+1)2 ).
Step 3
Exam Tip
कुल टाइलें \(x^2+2x+1\) देती हैं। परीक्षा में दो (x) टाइलें ((x+1)2 ) बनाती हैं।
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(x+1) भुजा वाले वर्ग में कितनी (x) वाली आयत टाइलें आती हैं?
How many (x)-rectangle tiles appear in a square with side (x+1)?
#algebra tiles
#x tiles
#visual square
A (2)
B (1)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
In ((x+1)2 =x-2 +2x+1), there are two (x)-rectangle tiles. Exam tip: count rectangles in both directions.
Step 2
Why this answer is correct
The correct answer is A. (2). In ((x+1)2 =x-2 +2x+1), there are two (x)-rectangle tiles. Exam tip: count rectangles in both directions.
Step 3
Exam Tip
((x+1)2 =x-2 +2x+1) में (x) वाली दो आयतें होती हैं। परीक्षा में दोनों दिशाओं की आयतें गिनें।
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टाइल मॉडल में \(x^2\) की एक टाइल, (x) की चार टाइलें और (1) की चार टाइलें मिलकर कौन सा वर्ग बनाते हैं?
In a tile model, one \(x^2\) tile, four (x) tiles, and four unit tiles form which square?
#algebra tiles
#perfect square
#visual model
A ((x+2)2 )
B ((x+4)2 )
C \(x^2+2x+4\)
D ((x-2)2 )
Explanation opens after your attempt
Correct Answer
A. ((x+2)2 )
Step 1
Concept
The total area is \(x^2+4x+4\), which is ((x+2)2 ). Exam tip: identify the number from unit tiles.
Step 2
Why this answer is correct
The correct answer is A. ((x+2)2 ). The total area is \(x^2+4x+4\), which is ((x+2)2 ). Exam tip: identify the number from unit tiles.
Step 3
Exam Tip
कुल क्षेत्रफल \(x^2+4x+4\) है जो ((x+2)2 ) है। परीक्षा में इकाई टाइलों से संख्या पहचानें।
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यदि \(x^2+2xy+y^2\) को टाइलों से बनाया गया है, तो बाहरी भुजा क्या होगी?
If \(x^2+2xy+y^2\) is made with tiles, what will be the outer side?
#algebra tiles
#outer side
#perfect square
A \(x-y\)
B \(xy\)
C \(2x+y\)
D \(x+y\)
Explanation opens after your attempt
Correct Answer
D. \(x+y\)
Step 1
Concept
These tiles form a square of side \(x+y\). Exam tip: identify the outer side of a perfect square.
Step 2
Why this answer is correct
The correct answer is D. \(x+y\). These tiles form a square of side \(x+y\). Exam tip: identify the outer side of a perfect square.
Step 3
Exam Tip
ये टाइलें मिलकर भुजा \(x+y\) का वर्ग बनाती हैं। परीक्षा में पूर्ण वर्ग की बाहरी भुजा पहचानें।
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एक आयत के भाग \(x^2\), \(5x\), \(x\) और \(5\) हैं। यह किस गुणन को दिखाता है?
A rectangle has parts \(x^2\), \(5x\), \(x\), and \(5\). Which multiplication does it show?
#rectangle multiplication
#algebra tiles
#factors
A \((x+5)(x+5)\)
B \((x+5)(x+1)\)
C \((x-5)(x-1)\)
D \((x+6)(x+5)\)
Explanation opens after your attempt
Correct Answer
B. \((x+5)(x+1)\)
Step 1
Concept
The sum of parts is \(x^2+6x+5\), which matches \((x+5)(x+1)\). Exam tip: read the outside dimensions.
Step 2
Why this answer is correct
The correct answer is B. \((x+5)(x+1)\). The sum of parts is \(x^2+6x+5\), which matches \((x+5)(x+1)\). Exam tip: read the outside dimensions.
Step 3
Exam Tip
भागों का योग \(x^2+6x+5\) है जो \((x+5)(x+1)\) से मिलता है। परीक्षा में बाहरी आयाम पढ़ें।
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अलजेब्रा टाइल में \(x^2\) टाइल, \(7x\) टाइल और \(12\) इकाई टाइलें मिलकर कौन सा क्षेत्र दिखा सकती हैं?
In algebra tiles, \(x^2\) tile, \(7x\) tiles, and \(12\) unit tiles can show which area?
#algebra tiles
#area expression
#visual model
A \(x^2+12x+7\)
B \(x^2+7x+12\)
C \(x^2-7x+12\)
D \(7x^2+12\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+7x+12\)
Step 1
Concept
The tile areas add directly to make \(x^2+7x+12\). Exam tip: count like tiles.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+7x+12\). The tile areas add directly to make \(x^2+7x+12\). Exam tip: count like tiles.
Step 3
Exam Tip
टाइलों के क्षेत्र सीधे जुड़कर \(x^2+7x+12\) बनाते हैं। परीक्षा में समान टाइलों की संख्या गिनें।
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एक \(x\) बाय \(x\) वर्ग और दो \(x\) बाय \(5\) आयतों के साथ \(5\) बाय \(5\) वर्ग जोड़ा गया है। यह किसका मॉडल है?
An \(x\) by \(x\) square, two \(x\) by \(5\) rectangles, and one \(5\) by \(5\) square are combined. This is a model of what?
#algebra tiles
#square expansion
#visual model
A \((x-5)^2\)
B \(x^2-25\)
C \(x^2+5x+25\)
D \((x+5)^2\)
Explanation opens after your attempt
Correct Answer
D. \((x+5)^2\)
Step 1
Concept
The total area is \(x^2+10x+25\). Exam tip: write two \(5x\) rectangles as \(10x\).
Step 2
Why this answer is correct
The correct answer is D. \((x+5)^2\). The total area is \(x^2+10x+25\). Exam tip: write two \(5x\) rectangles as \(10x\).
Step 3
Exam Tip
दिए गए भागों का कुल क्षेत्र \(x^2+10x+25\) है। परीक्षा में दो \(5x\) आयतों को \(10x\) लिखें।
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दृश्य मॉडल में \(x^2+12x+36\) को किस पूर्ण वर्ग के रूप में देखा जा सकता है?
In a visual model, \(x^2+12x+36\) can be seen as which perfect square?
#perfect square
#algebra tiles
#visual identity
A \((x+12)^2\)
B \((x+6)^2\)
C \((x-6)^2\)
D \((x+3)^2\)
Explanation opens after your attempt
Correct Answer
B. \((x+6)^2\)
Step 1
Concept
Here \(36=6^2\) and \(12x=2 \times 6x\). So it is \((x+6)^2\).
Step 2
Why this answer is correct
The correct answer is B. \((x+6)^2\). Here \(36=6^2\) and \(12x=2 \times 6x\). So it is \((x+6)^2\).
Step 3
Exam Tip
\(36=6^2\) और \(12x=2 \times 6x\) है। इसलिए यह \((x+6)^2\) है।
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टाइल मॉडल में \(x^2\) टाइल एक है और \(x\) टाइल \(8\) हैं। यदि स्थिर टाइल \(16\) हैं तो पूरा वर्ग किसका मॉडल है?
In a tile model there is one \(x^2\) tile and \(8\) \(x\)-tiles. If there are \(16\) constant tiles then the complete square models what?
#algebra tiles
#complete square
#visual model
A \((x+4)^2\)
B \((x+8)^2\)
C \((x-4)^2\)
D \(x^2+16\)
Explanation opens after your attempt
Correct Answer
A. \((x+4)^2\)
Step 1
Concept
\(x^2+8x+16\) is written as \((x+4)^2\). Exam tip: identify it using \(2 \times 4=8\).
Step 2
Why this answer is correct
The correct answer is A. \((x+4)^2\). \(x^2+8x+16\) is written as \((x+4)^2\). Exam tip: identify it using \(2 \times 4=8\).
Step 3
Exam Tip
\(x^2+8x+16\) को \((x+4)^2\) लिखा जाता है। परीक्षा में \(2 \times 4=8\) देखकर पहचानें।
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