Answer:
- 5 < x < 10
Step-by-step explanation:
Given
- 6 < x - 1 < 9 ( add 1 to each of the 3 intervals )
- 5 < x < 10
The value of x ranges from -5 to 10 as this inequality - 5 < x < 10.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given inequality is -6 < x-1 < 9. The value of x will be calculated as,
x- 1 < 9
x < 10
x- 1 > -6
x > 1 - 6
x > -5
Therefore, the value of x ranges from -5 to 10 as this inequality - 5 < x < 10.
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Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why DEF= KLM?
Check all that apply.
The congruence theorems that will be used to prove that both triangles are congruent are: C. LL E. SAS.
What is the LL Theorem?The LL theorem is a triangle congruence theorem that states that if the two pairs of legs of two right triangles are congruent, then the triangles are congruent.
What is the SAS Theorem?The SAS theorem is a triangle congruence theorem that states that if the two pairs of sides and a pair of included angles of two triangles are congruent, then the triangles are congruent.
Based on the information given, the theorem that can be used to show both triangles are congruent are: C. LL E. SAS
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Triangle DEF can be proven congruent to triangle KLM using the Leg-Leg (LL) Theorem, Side-Angle-Side (SAS) Theorem, and Hypotenuse-Leg (HL) criterion .
The correct answer is option B, C and E.
In geometry, a congruence theorem is a statement that two geometric figures are congruent, meaning that they have the same size and shape. There are many different congruence theorems, but the most common ones are the Side-Angle-Side (SAS) Theorem, the Angle-Side-Angle (ASA) Theorem, and the Leg-Leg (LL) Theorem.
The LL Theorem is a special congruence theorem that applies to right triangles. It states that if two right triangles have two congruent legs, then the triangles are congruent. This means that all of their corresponding sides and angles are congruent.
In the diagram provided, we have two right triangles, DEF and KLM. We are given that DE = KL and DF = LM. Since these are the legs of the two triangles, we can use the LL Theorem to conclude that DEF = KLM.
Hypotenuse-Leg (HL): This criterion applies specifically to right-angled triangles. If the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. Here, the right angles at D and K establish the triangles as right triangles, and the equal side lengths ED = KL and DF = KM complete the congruence conditions.
We cannot use the HL Theorem because the diagram does not explicitly show that the two triangles are right triangles.
Therefore, from the given options the correct one is B , C and E.
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Fine the value of k for which the pair of linear equation kx+3y=k+2 and 12x+ ky has no solution
Answer:
Step-by-step explanation:
it will have no sol. when a1/a2=b1/b2!=c1/c2
!= means not equal to
kx+3y=k+2
kx+3y-(k+2)=0 equation 1
12x+ky=0
taking a1/a2=c1/c2
k/12=3/k
k^2=36
k=6
when k= 6 it will have no sol
How do I add -6 and positive 13
Answer:
7
Step-by-step explanation:
This operation is identical to subtracting 6 from 13. The correct result is 7.
i need help on this question, someone please help!!
show your work too!
i even looked up the answer to this, and it doesn't even match my choices.
thank you!:)
Answer:
y=−x−1/3x−8
Step-by-step explanation:
y=8x−1/3x+1
To find the inverse function, swap x and y, and solve the resulting equation for x.
If the initial function is not one-to-one, then there will be more than one inverse.
So, swap the variables: y=8x−1/3x+1 becomes x=8y−1/3y+1.
Now, solve the equation x=8y−1/3y+1 for y.
y=−x−1/3x−8
Sorry I was in a rush and couldn't do the fractions as formulae. Hope it helped anyways.
Can someone tell me the answers
1.
Evaluate u + xy , for u = 2, x = 9, and y = 6.
56
24
66
17
Answer:
Your answer is 56.
Step-by-step explanation:
To solve this problem, we simply need to plug in the given numbers into the expression.
If we do this, we get the following:
u + xy
2 + (9*6)
Using PEMDAS, we know that we have to perform the multiplication in this problem before the addition. Thus the first step in simplification is multiplying 9 and 6 together. If we do this, we get:
2 + 54
Next, we simply add together the two remaining terms.
54 + 2 = 56
Therefore, your answer is 56, the first option.
Hope this helps!
Which expression is a difference of cubes?
Answer:
Option 4 is correct.
Step-by-step explanation:
Given the following options
we have to choose the difference of cubes.
Option 1:
[tex]9w^{33}-y^{12}[/tex]
[tex]9(w^{11})^{3}-(y^4)^3[/tex]
which is not the difference of cubes
Option 2:
[tex]18p^{15}-q^{21}[/tex]
[tex]18(p^5)^3-(q^7)^3[/tex]
which is not the difference of cubes
Option 3:
[tex]36a^{22}-b^{16}[/tex]
[tex](6a^{11})^2-(b^8)^2[/tex]
which is the difference of square
Option 4:
[tex]64c^{15}-a^{27}[/tex]
[tex](4c^5)^3-(a^9)^3[/tex]
which is the difference of cubes.
Can someone answer C. Please it’s my last try I got it wrong 2 times so please explain!
Answer:
5.
Step-by-step explanation:
What you require is the area of the rectangle whose base is between 210 and 215.
The number having levels between 210 and 214
= 20 * the relative frequency
= 20 * 0.25
= 5 (answer).
r(x) = -0.21x^3 + x^2 - 8.1x - 3 for x= -1 and x = 2
Answer:
r(-1) = 6.31 and r(2) = -16.88
Step-by-step explanation:
* Lets read the problem and solve it
- Evaluate means find the value, so evaluate r(x) means find the value
of it at the given values of x
∵ r(x) = -0.21x³ + x² - 8.1x - 3
∵ x = -1 and x = 2
- Then find r(-1) by substitute x by -1 and find r(2) by substitute x by 2
# At x = -1
∴ r(-1) = -0.21(-1)³ + (-1)² - 8.1(-1) - 3
∴ r(-1) = -0.21(-1) + (1) - 8.1(-1) - 3
∴ r(-1) = 0.21 + 1 + 8.1 - 3
∴ r(-1) = 6.31
# At x = 2
∴ r(2) = -0.21(2)³ + (2)² - 8.1(2) - 3
∴ r(2) = -0.21(8) + (4) - 8.1(2) - 3
∴ r(2) = -1.68 + 4 - 16.2 - 3
∴ r(2) = -16.88
* r(-1) = 6.31 and r(2) = -16.88
HELP Geometry, can someone please answer this
Check the picture below.
What is p(-2)?
Rounded to the nearest tenth please:)
Answer:
0.2
Step-by-step explanation:
[tex]\text{f(x) = }\dfrac{90}{9+\frac{50}{e^x}}[/tex]
[tex]\text{f(-2) = }\dfrac{90}{9+\frac{50}{e^{-2}}}[/tex]
[tex]\text{f(-2) =} \dfrac{ 90 }{9 + 50*e^2}[/tex]
Now we can work out the denominator separately.
9 + 50*e^2
9 + 50*7.389
9 + 369.45
378.45
Now use this number to get the final answer.
f(-2) = 90 / 378.45
f(-2) = 0.237 To the nearest tenth
f(-2) = 0.2
There was a lot of movement for that e^x factor make sure you study carefully how that moved around and why. It's a good question. Get what you can from it.
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
In thinking about what number each term may be multiplied by to eliminate the fractions, we can take one of two courses:
1) Find the lowest common multiple, ie. the lowest value that each of the fraction denominators have in common as a multiple.
Now a multiple is basically that number multiplied by an integer - for example, multiples of 2 are 2, 4, 6, 8, 10, etc.
So, let us write out the first few multiples for each of the denominator values:
4 (from 3/4): 4, 8, 12, 16, 20
3 (from 1/3): 3, 6, 9, 12, 15, 18
2 (from 1/2): 2, 4, 6, 8, 10, 12, 14, 16
Looking at the values above, we can see that the lowest value that occurs in all three sets of numbers is 12, thus 12 is the lowest common multiple.
Therefor, in order to eliminate the fractions before solving, each term must be multiplied by 12.
2) You could alternatively try multiplying the equation (or simply each fraction) by each of the possible answers and seeing if that will eliminate all of the fractions - this may seem quicker at first but it is always worthwhile understanding how to calculate this question without having possible answers, and as you complete more questions, the process of finding the lowest common multiple will become more natural and even quicker in the end. Nonetheless, let us try this method:
a) Multiplying each fraction by 2
(3/4)*2 = 3/2
This does not eliminate the fraction, therefor 2 is not the answer.
b) Multiplying each fraction by 3
(3/4)*3 = 9/4
This does not eliminate the fraction, thus 3 is not the answer.
c) Multiplying each fraction by 6
(3/4)*6 = 9/2
This does not eliminate the fraction, therefor 6 is not the answer.
d) Multiplying each fraction by 12
(3/4)*12 = 9 (this works so far)
(1/3)*12 = 4 (this also works so far)
(1/2)*12 = 6 (this also works)
Since multiplying each fraction by 12 will eliminate the fractions, 12 is the answer.
Answer:
D is the answer
Step-by-step explanation:
If f(x) = 5x3 – 2 and g(x) = x+1, find (f - g)(x).
Answer:
10
Step-by-step explanation:
x=2
f(2)=5x3-2=15-2=13/2=6.5=f
g(2)=2+1=3/2=1.5=g
(6.5-1.5)(2)=(13-3)=10
Answer:
5x³ - x - 3
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x)
= 5x³ - 2 -(x + 1) = 5x³ - 2 - x - 1 = 5x³ - x - 3
Annmarie can plow a field in 240 minutes. Gladys can plow a field 80 minutes faster. If they work together, how many minutes does it take them to plow the field?
A)96 min
B)160
C)400
D)480
Thanks for the help!
Answer:
Option A is the correct answer.
Step-by-step explanation:
Let the work plow a field be x.
Annmarie can plow a field in 240 minutes.
Rate at which Annmarie can plow[tex]=\frac{x}{240}[/tex]
Gladys can plow a field 80 minutes faster
Time taken by Gladys = 240 - 80 = 160 minutes.
Rate at which Gladys can plow[tex]=\frac{x}{160}[/tex]
If they combine time taken to plow [tex]=\frac{x}{\frac{x}{240}+\frac{x}{160}}=\frac{240\times 160}{240+160}=96\texttt{ minutes}[/tex]
Option A is the correct answer.
the time taken for Annmarie and Gladys to plow the field together is 96 minutes. The correct answer is A) 96 min.
Annmarie can plow a field in 240 minutes, and Gladys can do it in 160 minutes (since she is 80 minutes faster). To find out how long it would take for them to plow the field together, we can use the formula for combined work rates:
Let A be Annmarie's work rate and G be Gladys's work rate. Annmarie's work rate is 1 field per 240 minutes, or 1/240 fields per minute. Gladys's work rate is 1 field per (240 - 80) minutes, or 1/160 fields per minute.
Combined work rate of Annmarie and Gladys: A + G = 1/240 + 1/160.
Now, to find the time it would take them working together, we take the reciprocal of the combined work rate.
The combined work rate is:
1/240 + 1/160 = 1/240 + 1/160 = (1x160 + 1x240) / (240x160) = (160 + 240) / (240x160) = 400 / (240x160)
The time it takes for them to work together is the reciprocal of 400 / (240x160), which is (240x160) / 400.
Calculate: (240x160) / 400 = 38400 / 400 = 96
Therefore, the time taken for Annmarie and Gladys to plow the field together is 96 minutes. The correct answer is A) 96 min.
the area of a rectangular wall of a barn is 252 square ft. its length is 10 ft longer than twice its width. find the lenght and width of the barn
Answer:
L=9 ft
W=28 ft
Step-by-step explanation:
LW=252
L=10+2W
Plug 2nd into 1st
(10+2W)W=252
Distribute
10W+2W^2=252
Divide both sides by 2
5W + W^2=126
Reorder using commutative property
W^2+5W =126
Subtract 126 on both sides
W^2+5W-126=0
What are two numbers multiply to be -126 and add to be 5?
My scratch paper:
-126=-2(63)
-126=-2(7)(9)
-126=-14(9)
So 14(-9) is -126 and 14+(-9)=5 so these are our magic numbers
(W+14)(W-9)=0
W=-14 or W=9
So W=9 is what makes sense here sense length can't be negative
Now let's go back and find L...
L=10+2W=10+2(9)=10+18=28
The problem can be solved by setting up a quadratic equation based on the given information. By solving the equation, we find that the width is 7 feet, and the length is 24 feet.
Explanation:In this problem, we are given that the area (A) of the rectangular wall is 252 square feet, and the length (L) of the wall is 10 feet longer than twice its width (W). We need to find both the length and width of the barn. The formula for the area of a rectangle is A = L × W.
From the problem, we know that L = 2W + 10. Substituting this into the formula gives us A = W × (2W + 10). Set this equal to 252 to get 252 = W × (2W + 10). Solving this quadratic equation, we find that the width of the barn is 7 feet. Substituting this value into L = 2W + 10, the length of the barn is 24 feet.
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Evaluate 4k2 + 3 when k = 5
Answer:
103
Step-by-step explanation:
Evaluate 4k2 + 3
To evaluate 4k² + 3, when k = 5, which means when you sees k, put 5 in replacement
4k² + 3 = 4(5)² + 3
4(5×5) + 3
4(25) + 3
open the bracket
4 × 25 = 100
∴ 100 + 3 = 103
Please mark me brainliest
[tex]\text{Hey there!}[/tex]
[tex]\text{If k = 5 the replace the 'k' value with 5}[/tex]
[tex]\text{4(5)}^2+3[/tex]
[tex]\text{(5)}^2=5\times5=25[/tex]
[tex]\text{4 (25)+ 3 = ?}[/tex]
[tex]\text{4 (25) = 25 + 25 + 25 + 25 = 100}[/tex]
[tex]\text{100 + 3 = 103}[/tex]
[tex]\boxed{\boxed{\bf{Your\ answer: 103}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
The endpoints of a diameter of a circle are A(2,1) and B(5,5). Find the area of the circle in terms of pi.
Answer:
The area of the circle is [tex]A=6.25\pi\ units^{2}[/tex]
Step-by-step explanation:
step 1
Find the diameter of circle
we know that
The diameter of the circle is equal to the distance AB
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute the values
[tex]AB=\sqrt{(5-1)^{2}+(5-2)^{2}}[/tex]
[tex]AB=\sqrt{(4)^{2}+(3)^{2}}[/tex]
[tex]AB=\sqrt{25}[/tex]
[tex]AB=5\ units[/tex]
therefore
the diameter of the circle is
[tex]D=5\ units[/tex]
step 2
Find the area of the circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
[tex]r=5/2=2.5\ units[/tex] ----> the radius is half the diameter
substitute
[tex]A=\pi (2.5)^{2}[/tex]
[tex]A=6.25\pi\ units^{2}[/tex]
20000000000000x 3065
Answer:
61300000000000000
Step-by-step explanation:
Multiplying 20,000,000,000,000 by 3,065 results in 61,300,000,000,000,000.
Write down the numbers in standard form:
2 x[tex]10^{13}[/tex] for 20,000,000,000,000 and
3.065 x 10³ for 3,065.
Multiply the two standard forms:
(2 x [tex]10^{13}[/tex]) * (3.065 x 10³).
Combine the powers of 10:
2 * 3.065 = 6.13 and
[tex]10^{13}[/tex] * 10³ = [tex]10^{16}[/tex]
The result is 6.13 x [tex]10^{16}[/tex]
In standard numerical form, this is 61,300,000,000,000,000.
So, 20,000,000,000,000 x 3,065 equals 61,300,000,000,000,000.
Complete Question:
Multiply 20000000000000 x 3065.
A restaurant owner needs to order at least 176 filet mignon steaks to be stocked for a busy Friday night. He only has room to store 321 steaks in his refrigerator. Model the number of steaks the restaurant owner can order, using a compound inequality.
x ≥ 176 and x ≤ 321
x ≤ 176 and x ≥ 321
x ≤ 176 and x ≤ 321
x ≥ 176 and x ≥ 321
Answer:
x ≥ 176 and x ≤ 321
Step-by-step explanation:
Let
x -----> the number of steaks the restaurant owner can order
we know that
[tex]x\geq 176[/tex] ----> inequality A
[tex]x\leq 321[/tex] ----> inequality B
so
the compounded inequality is equal to
[tex]176 \leq x \leq 321[/tex]
Explanation of modeling the number of steaks a restaurant owner can order using a compound inequality.
Explanation:To model the number of steaks the restaurant owner can order using a compound inequality, we represent the situation with x ≥ 176 and x ≤ 321. This means the owner can order any amount of steaks from 176 to 321. So, the correct compound inequality is x ≥ 176 and x ≤ 321.
What set of transformations could be applied to rectangle ABCD to create A'B'C'D'?
Answer:
rotate 180 degrees ccw from (0,0)
Answer:
We get Rectangle A'B'C'D' by rotating the Rectangle ABCD by 180° about origin.
Step-by-step explanation:
We are given a graph which Rectangle ABCD and A'B'C'D'
To find : Set of transformation
From the graph,
Vertex of the Rectangle ABCD,
A( -4 , 2 ) , B ( -4 , 1 ) , C ( -1 , 1 ) and D ( -1 , 2 )
Vertices of Rectangle A'B'C'D'
A( 4 , -2 ) , B ( 4 , -1 ) , C ( 1 , -1 ) and D ( 1 , -2 )
Clearly from above,
we get that coordinates of the vertices of Rectangle A'B'C'D' is negative of the coordinates of the vertices of Rectangle ABCD .
That is if Coordinates of A( x , y ) then A'( -x , -y )
This transformation is done when we rotate the given figure by 180° about origin.
Therefore, We get Rectangle A'B'C'D' by rotating the Rectangle ABCD by 180° about origin.
The slope of the line whose equation is x-3y= 1 is
0-3
-1/3
0
0
1/3
x-3y= 1
The equation needs to be rewritten in proper Slope intercept form ( y = mx+b) where m is the slope and b is the y-intercept.
x-3y = 1
Subtract x from each side:
-3y = 1-x
Divide both sides by -3:
y = 1/-3 - x/-3
Simplify:
y = 1/3x - 1/3
The slope is 1/3
Factor the expression below.
x^2 – 6x + 9
A.
(x - 3)(x - 3)
B.
3(x2 - 2x + 3)
C.
(x - 3)(x + 3)
D. (x + 3)(x + 3)
Answer:
A.
(x - 3)(x - 3)
Step-by-step explanation:
x^2 – 6x + 9
What 2 numbers multiply to 9 and add to -6
-3*-3 =9
-3+-3 = -6
(x-3) (x-3)
The perimeter of the rectangle below is 184 m .What is the value of y
Step-by-step explanation:
2x + 2y = 184 ---- eqn 1
y = 184 - 2x / 2
y = 92 - x ---- eqn 2
Annabelle's total pay varies directly with the number of hours she works. If she works 4 hours, she earns $100. How much does Annabelle earn if she works 6 hours? Plz show work:)
A.$90.
B. $120.
C. $150.
D. $300
Answer:
C. $150 :)
Step-by-step explanation:
If Annabell works 4 hours and earns $100 that means for every hour she earns $25 so 25×4=100 so then multiply 25×6=15]
Answer: C. $150.
Step-by-step explanation:
When two quantities x and y are directly proportional ,then the equation of direct proportion is given by :-
[tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]
Given : Annabelle's total pay varies directly with the number of hours she works. If she works 4 hours, she earns $100.
Let [tex]x_1=100\ ;\ y_1=4 \ :\ x_2=x,\ y_2=6[/tex], then we ahve
[tex]\dfrac{100}{4}=\dfrac{x}{6}\\\\\Rightarrow\ x=\dfrac{100\times6}{4}=150[/tex]
Hence, Annabelle earns $150 if she works 6 hours.
Find the area of an equilateral triangle with a side of 6 inches
Answer:
9√3in^2 hope this helps. found an answer...
Answer:
9 sqrt 3
Step-by-step explanation:
It was correct on my quiz
1/4 x 6 squared x sqrt 3
A carnival game has the possibility of scoring 50 points, 75 points, or 150 points per turn. The probability of scoring 50 points is 60%, 75 points is 30%, and 150 points is 10%. The game operator designed a simulation using a random number generator to predict how many points would be earned for a turn.
Integer Value Points Frequency
0 - 5 50 55
6 - 8 75 32
9 150 13
10. What is game’s expected value of points earned for a turn?
(SHOW WORK)
Answer:
The game’s expected value of points earned for a turn is 71.
Step-by-step explanation:
Here we know that:
Points Frequency
50 55
75 32
150 13
Here points earned is a random variable.
We need to find its expected value,
Finding Expected value:
Expected value of a random variable is its mean value. So we will first find the mean value of points earned per turn from the table we are given.
Total number of turns = sum of frequencies
= 55 + 32 + 14 = 100
Total points earned = 50(55) + 75(32) + 150(13)
= 7100
Expected value of points earned for a turn = Mean value of points
= Total points/no. of turns
= 7100/100
= 71
Identify any extraneous solution. See above pic
Answer:
There are no extraneous solutions
Reasoning:
An extraneous solution is a solution that isn't valid, it might be imaginary like the square root of a negative number.
first we want to isolate z:
1+sqrt(z)=sqrt(z+5)
^2 all ^2 all
(1+sqrt(z))(1+sqrt(z))=z+5
expand
1+2sqrt(z)+z=z+5
-1 -z -z -1
2sqrt(z)=4
/2 /2
sqrt(z)=2
^2 all ^2 all
z=4
Since there is one solution and it is a real number, there are no extraneous solutions.
[tex]D:z\geq 0\wedge z+5\geq 0\\D:z\geq 0\wedge z\geq -5\\D:z\geq0\\\\1+\sqrt z=\sqrt{z+5}\\1+2\sqrt z+z=z+5\\2\sqrt z=4\\\sqrt z=2\\z=4[/tex]
[tex]4\in D[/tex] so there are no extraneous solutions.
A line has a slope of -4/5. Which ordered pairs could be points on a line that is perpendicular to this line? Select two options.
A - (–2, 0) and (2, 5)
B - (–4, 5) and (4, –5)
C - (–3, 4) and (2, 0)
D - (1, –1) and (6, –5)
E - (2, –1) and (10, 9)
Answer:
A and E
Step-by-step explanation:
A line has a slope of -4/5, then a perpendicular line has a slope 5/4, because
[tex]-\dfrac{4}{5}\cdot \dfrac{5}{4}=-1[/tex]
Find the slopes of the lines in all options:
A. True
[tex]\dfrac{5-0}{2-(-2)}=\dfrac{5}{4}[/tex]
B. False
[tex]\dfrac{-5-5}{4-(-4)}=-\dfrac{5}{4}[/tex]
C. False
[tex]\dfrac{0-4}{2-(-3)}=-\dfrac{4}{5}[/tex]
D. False
[tex]\dfrac{-5-(-1)}{6-1}=-\dfrac{4}{5}[/tex]
E. True
[tex]\dfrac{9-(-1)}{10-2}=\dfrac{5}{4}[/tex]
Answer:
C
Step-by-step explanation:
=(0-4)/(2+3)
=-4/5
Can someone please help me!!
Answer:
x = 6Step-by-step explanation:
Use Angle Bisector theorem (look at the picture).
We have the equation:
[tex]\dfrac{3}{x}=\dfrac{x-4}{4}[/tex] cross multiply
[tex]x(x-4)=(3)(4)[/tex] use the distributive property
[tex]x^2-4x=12[/tex] subtract 12 from both sides
[tex]x^2-4x-12=0\\\\x^2+2x-6x-12=0\\\\x(x+2)-6(x+2)=0\\\\(x+2)(x-6)=0\iff x+2=0\ \vee\ x-6=0[/tex]
[tex]x+2=0[/tex] subtract 2 from both sides
[tex]x=-2<0[/tex]
[tex]x-6=0[/tex] add 6 to both sides
[tex]x=6[/tex]
Factor completely, then place the answer in the proper location on the grid. 49x 2 + 42xy + 9y 2
Answer:
(7x + 3y)(7x + 3y) or we could write it as (7x + 3y)^2.
Step-by-step explanation:
49x 2 + 42xy + 9y 2
The square root of 49xy^2 = 7x and the square root of 9y^2 = 3y.
Now 7x *3y = 21xy and 2 * 21xy = 42xy so the factors are:
(7x + 3y)(7x + 3y).
49x 2 + 42xy + 9y 2 is a perfect square trinomial.
Answer:
[tex](7x+3y)(7x+3y)[/tex]
Step-by-step explanation:
We are given that an expression
[tex]49x^2+42xy+9y^2[/tex]
We have to find the factor of given expression
[tex](7x)^2+2\times (7x)\times 3+(3y)^2[/tex]
Identity:[tex](a+b)^2=a^2+2ab+b^2[/tex]
Using the identity,then we get
[tex](7x+3y)^2[/tex]
[tex](7x+3y)(7x+3y)[/tex]
Hence, the factor of given expression is given by
[tex](7x+3y)(7x+3y)[/tex]