find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval.
Answers
Remember that
If f is continuous over [a,b] and differentiable over (a,b), then there exists c∈(a,b) such that
[tex]f^{\prime}(c)=\frac{f(b)-f(a)}{b-a}[/tex]In this problem, we have the function
[tex]f(x)=\frac{9}{x^3}[/tex]over the interval [1,3]
so
f(a)=f(1)=9/(1)^3=9
f(b)=f(3)=9/(3)^3=1/3
substitute
[tex]f^{\prime}(c)=\frac{\frac{1}{3}-9}{3-1}=\frac{-\frac{26}{3}}{2}=-\frac{26}{6}=-\frac{13}{3}[/tex]Find out the first derivative f'(x)
[tex]f^{\prime}(x)=-\frac{27}{x^4}[/tex]Equate the first derivative to -13/3
[tex]\begin{gathered} -\frac{27}{x^4}=-\frac{13}{3} \\ \\ x^4=\frac{27*3}{13} \\ \\ x=1.58 \end{gathered}[/tex]therefore
The value of c is 1.58 (rounded to two decimal places)Related Questions
Which equation represents the same line as the points in the table?
Input (x) Output (y)
−5 5
0 0
7 −7
x=−yx is equal to negative y
y=−x+5y is equal to negative x plus 5
y=−x−7y is equal to negative x minus 7
y=−x
Answers
Answer: (c) y = −1/3x −2
Step-by-step explanation:
I know it because I looked on brainly .
[tex]3/7*14/15*10/18\\[/tex]
Answers
The value of the fraction 3/7 × 14/15 × 10/18 is 2/9.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.
The value of the fraction will be:
= 3/7 × 14/15 × 10/18
= 3/7 × 14/15 × 5/9
= 3/1 × 2/3 × 1/9
= 1 × 2 × 1/9
= 2/9
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Two friends drive off in different directions from the same place. One heads North at 40 miles per hour, while the other heads East at 25 miles per hour.
Complete an equation for the distance between the friends after t hours.
Answers
The equation for the distance between the friends after t hours is 47.17t.
What is the distance between two points?Let one point be (x, y) and another point be (h, k). Then the distance between the points will be
D² = (x - h)² + (y - k)²
Two companions drive off this way and from a similar spot. One travels North at 40 miles each hour, while different travels East at 25 miles each hour.
The equation for the distance between the friends after t hours is given as,
Let the x-axis as east and the y-axis as north. Then the coordinate after t hours will be (25t, 0) and (0, 40t). Then the distance between them is given as,
D² = (25t - 0)² + (0 - 40t)²
D² = 625t² + 1600t²
D² = 2,225t²
D = 47.17 t
The equation for the distance between the friends after t hours is 47.17t.
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please help asap please please i’ll give brainliest
Answers
Answer:
[tex] C = \dfrac{5}{9}(F - 32) [/tex]
Step-by-step explanation:
[tex] F = \dfrac{9}{5}C + 32 [/tex]
Switch sides to have C on the left side.
[tex] \dfrac{9}{5}C + 32 = F [/tex]
Subtract 32 from both sides.
[tex] \dfrac{9}{5}C = F - 32 [/tex]
Multiply both sides by 5/9.
[tex] \dfrac{5}{9} \times \dfrac{9}{5}C = \dfrac{5}{9} \times (F - 32) [/tex]
[tex] C = \dfrac{5}{9}(F - 32) [/tex]
HURRY ASAP!
What is four-twelfths times seven?
Your answer should be in whole or mixed number form.
A. two and four-twelfths
B. 3
C. six and six-sevenths
D. 21
Answers
Answer:
A
Step-by-step explanation:
(7 / 12) × 4 = 28 / 12 = 2 and 4 twelfths
the image of the point (-9, 9)under a translation is (-5, 13). find the coordinates of the image of the point (-6, "-7)" under the same translation.
Answers
The coordinates of the image of the point (-6, -7) after translation is (-20,-3).
What are coordinates?a pair of figures used to specify a point's location on a coordinate plane using the horizontal and vertical separations from the two reference axes. They are typically expressed by the x-value and y-value pair (x,y). Always, the x-coordinate comes before the y-coordinate.
An ordered group of numbers known as coordinates is used to specify a point's location. In the event that the point is on a plane, two numbers are used.
The horizontal and vertical addresses of a point in any two-dimensional (2D) space, such as a sheet of paper or a computer display screen, are called the X and Y coordinates, respectively. These coordinates work as a pair to pinpoint a point's precise location.
A point located at (x,y), translated by (a,b) maps to the point (x+a,y+b).
If we know the location of the point (x,y) and the location of its image (x',y'), we can know the values of (a,b) by subtracting:
(a,b) = (x',y') - (x,y)
We know the coordinates of the point (9,9) and the coordinates of its image (-5,13). Calculate the translation:
(a,b) = (-5,13) - (9,9) = (-14,4)
If the point (-6,-7) is translated under the same conditions, then it will map to the point (-6,-7) + (-14,4) = (-20,-3).
The coordinates of the image are (-20,-3)
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Help me in these equation9^2 + b^2 = 15.81^2
Answers
ANSWER
b = 13
EXPLANATION
We want to solve the equation:
[tex]9^2+b^2=15.81^2[/tex]To do this, simplify the equation:
[tex]81+b^2=249.96[/tex]Isolate b:
[tex]\begin{gathered} b^2=249.96-81 \\ b^2=168.96 \\ Find\text{ the square root of boths side:} \\ b=\sqrt[]{168.96} \\ b=13 \end{gathered}[/tex]That is the answer.
The weight M of an object on the moon varies directly as its weight E on earth. A person whoweighs 156.71 lb on earth weighs 26.64 lb on the moon. How much would a 213.53-lb personweigh on the moon?A 213.53-1b person would weigh___ lb on the moon. (Round to the nearest tenth.)
Answers
Since the weight varies directly, we have that
[tex]156.71=k\times26.64[/tex]where k is the constant of proportinality.
In order to find k, we can divide both sides by 26.64 and get
[tex]\begin{gathered} \frac{156.71}{26.64}=k \\ or\text{ equivalently, } \\ k=\frac{156.71}{26.64} \end{gathered}[/tex]which gives
[tex]k=5.8825[/tex]Once we know the constant of proportionallity, we can write
[tex]213.53=k\times x[/tex]where x denotes the unknown weight on the Moon. Since k is 5.8825, we get
[tex]213.53=5.8825\times x[/tex]Then, by dividing both sides by 5.8825, we obtain
[tex]\begin{gathered} \frac{213.53}{5.8825}=x \\ or\text{ equivalently,} \\ x=\frac{213.53}{5.8825} \end{gathered}[/tex]Therefore, we have
[tex]x=36.299\text{ lb}[/tex]Finally, by rounding to the nearest tenth, the answer is: 36.3 lb
(G.5d, 1 pt) Determine the range for the measure of AC. А 10 m B 13 m O A. 10
Answers
The length of a side must be less than the sum of the other two sides. Here, that means x < 10+13, or x < 23.
In addition, remember that the length of a side must be greater than the difference of the other two sides. That means x > 13 - 10, or x > 3.
Therefore we have two limits for the value of x: 3 and 23.
3 < x < 23
i need to know how to solve this question please
Answers
ANSWER
w = 6.71 or -6.71
EXPLANATION
PLEASE HELP ME WITH THE QUESTION IN THE PIC BELOW
Answers
Let's calculate the distance between F and G:
F=(-4,-2)
G=(2,-2)
[tex]d=\sqrt[]{(2-(-4))^2+(-2-(-2))^2}=\sqrt[]{36}=6[/tex]The distance between M and P is half the distance between F and G, so:
[tex]\frac{d}{2}=3[/tex]The coordinates of P are:
P=(2,-8)
and
M=(x,-8)
So:
[tex]\begin{gathered} 3=\sqrt[]{(x-2)^2+\mleft(-8-\mleft(-8\mright)\mright)^2} \\ 3=x-2 \\ \text{solving for x:} \\ 3+2=x \\ 5=x \\ x=\pm5 \\ \end{gathered}[/tex]Since M is in the 3rd quadrant:
M= (-5,-8)
----------------------------------------------
Let:
(x1,y1)=(-2,1)
(x2,y2)=(-5,4)
[tex]\begin{gathered} d=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ d=\sqrt[]{(-5-(-2))^2+(4-1)^2} \\ d=\sqrt[]{9+9}=\sqrt[]{18} \end{gathered}[/tex]In the diagram,ABCD is a rectangular wall that casts a shadow CDEF, on the ground. The wall has a height of 4 feet. The shadow is a parallelogram that has a height, FG, that is twice the height of the wall. If the area of the wall is 29.2 square feet, find the area of the shadow.
Answers
We know that the height of the rectangular shape is BC=AD= 4 feet and the the area is A=29.2 ft^2. Since the area of our rectangle is given by
[tex]A=(DC)\times(BC)[/tex]we get
[tex]29.2=DC\times4[/tex]By moving the number 4 to the left hand side, we have
[tex]\begin{gathered} \frac{29.2}{4}=DC \\ \text{then} \\ DC=7.3 \end{gathered}[/tex]which also is the lenght of one side of our parallelogram.
Now, the area of our parallelogram is given by
[tex]A_P=\text{base}\times height[/tex]where the base is given by segment DC=7.3 ft and the height FG=2 BC. Then, we get
[tex]\begin{gathered} A_P=DC\times FG \\ A_P=DC\times2BC \end{gathered}[/tex]by substituting our previous result and BC=4 ft, we obtain
[tex]\begin{gathered} A_P=7.3\times2(4) \\ A_P=7.3\times8 \\ A_P=58.4ft^2 \end{gathered}[/tex]Then, the answer is 58.4 ft^2
List from greatest to least:5.1 , 5 1/5, 5.5 and 5 1/4
Answers
Answer:
5.5, 5¼, 5 1/5 and 5.1.
Explanation:
To list the height from greatest to least, we convert each of them to a decimal.
[tex]\text{Suki}=5\frac{1}{5}=5+\frac{1}{5}=5+0.2=5.2[/tex][tex]\text{Also, Amir=5}\frac{1}{4}=5+\frac{1}{4}=5+0.25=5.25[/tex]Therefore, the weights are: 5.1, 5.2, 5.5 and 5.25
Arranging them from greatest to least gives:
5.5, 5.25, 5.2 and 5.1 which is equivalent to: 5.5, 5¼, 5 1/5 and 5.1.
State the postulate or theorem, if any, that could be used to prove two triangles
Answers
The angle sum property of a triangle the and in isosceles triangle base angles are equal theorem are used.
In the given triangle, the measure of two angles are 67° and 35°.
What is angle sum property of a triangle?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
7a) Using angle sum property of triangle, we get
Now, 67°+35°+x=180°
⇒ 102°+x=180°
⇒ x=180°-102°
⇒ x=78°
7b)
67°+78°+y=180°
⇒ 145°+y=180°
⇒ y=180°-145°
⇒ y=35°
8a) In isosceles triangle base angles are equal.
Here, p=q
50°+p+q=180°
⇒ 50°+p+p=180°
⇒ 2p=130°
⇒ p=65°
So, p=q=65°
8a) Here, c+115°=180°
⇒ c=180°-115°
⇒ c=65°
So, b=c=65°
Now, a+b+c=180°
⇒ a+65°+65°=180°
⇒ a+130°=180°
⇒ a=50°
Hence, the angle sum property of a triangle the and in isosceles triangle base angles are equal theorem are used.
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In the given figure, mBJ = 106 and FHJH. Which statement is true?
F
H
G
Figure not drawn to scale
K
106°
OA.
The measure of ZG is 21", and triangle FGH is isosceles.
OB.
The measure of ZG is 56", and triangle FGH is isosceles.
O.C.
The measure of ZG is 21", and triangle FGH is not isosceles.
The measure of ZG is 56", and triangle FGH is not isosceles.
D.
Answers
The 106° measure of arc [tex]m\widehat{HJ}[/tex] and the length of the chords [tex]\widehat{FH}[/tex] and [tex]\widehat{JH}[/tex], which are the same, indicates that m∠G = 21° and ΔFGH is not isosceles. The correct option is option C;
C. The measure of ∠G is 21°, and triangle FGH is not isosceles
What is an isosceles triangle?An isosceles triangle is a triangle that have two sides of the same length and two angles of the same measure.
According to the outside angle to a circle theorem, the measure of the outside angle ∠G formed by the secant GJ and the tangent GF is equal to the difference of the measures of the arcs [tex]m\widehat{F'KJ}[/tex], and arc [tex]m\widehat{FH}[/tex] divided by 2.
[tex]m\widehat{F'KJ}[/tex] = 360° - [tex]m\widehat{FH}[/tex] - [tex]m\widehat{HJ}[/tex]
[tex]\widehat{FH}[/tex] = [tex]\widehat{JH}[/tex]
[tex]\widehat{FH}[/tex] ≅ [tex]\widehat{JH}[/tex]
The lengths of the chord intercepted by congruent arcs are congruent.
Therefore; [tex]\widehat{JH}[/tex] ≅ [tex]\widehat{FH}[/tex]
Which indicates;
[tex]m\widehat{JH}[/tex] = 106° = [tex]m\widehat{FH}[/tex]
[tex]m\widehat{F'KJ}[/tex] = 360° - 106° - 106° = 148°
m∠G = ([tex]m\widehat{F'KJ}[/tex] - [tex]m\widehat{FH}[/tex]) ÷ 2
m∠G = (148° - 106°) ÷ 2 = 21°
m∠G = 21°[tex]m\widehat{F'KJ}[/tex] = 148°
m∠FHJ = 148° ÷ 2 = 74° (Angle at the center is twice angle formed at the circumference)
∠FHJ = ∠HFG + ∠G (exterior angle to triangle ΔFGH)
∠HFG = ∠FHJ - ∠G
Therefore; m∠HFG = 74° - 21° = 53°
m∠HFG = 53°
m∠FHG = 180° - 74° = 106° (linear pair angles property)
m∠G ≠ m∠FHG ≠ m∠HFG, therefore, ΔFGH is not isoscelesThe correct option is option C.
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A smaller number and a larger number add up to 8 and have a difference of 6. (Let X be the larger number and Y be the smaller number)
Answers
If the larger number is x, and the smaller one is y, then what we have is;
[tex]\begin{gathered} x+y=8---(1)\text{ both add up to 8} \\ x-y=6---(2)\text{ both have a difference of 6} \\ \text{From equation (1), make x the subject,} \\ x=8-y \\ \text{Substitute for the value of x into equation (2)} \\ x-y=6 \\ (8-y)-y=6 \\ 8-y-y=6 \\ 8-2y=6 \\ 8-6=2y \\ 2=2y \\ \text{Divide both sides by 2} \\ y=1 \\ \text{If x+y=8, then when y=1} \\ x+1=8 \\ x=8-1 \\ x=7 \end{gathered}[/tex]Therefore, the numbers are 7 and 1
What are the coordinates of J A G when reflected over the line y=2?
Answers
We can start by plotting the triangle JAG and the line y = 2 to see how we can solve it:
We can see the line y = 2 (red line) over which we have to reflect the point J, A and G.
To do that we have to look at the distance of each point to the line.
This distance will be the distance at which the image point will be located, opposite to the the original point.
As y = 2 is an horizontal line, the distance is vertical and the x-coordinate of the original points and the images will remain equal. Only the y-coordinate will change.
We can sketch the procedure as:
Then, for example, poing G is 1 unit below y = 2, so its image G' will be one unit over the line y = 2, locating at (2,3).
Point J is 2 units above y = 2, so J' will be 2 units below y = 2.
Point A is 3 units above y = 2, so A' will be 3 untis below y = 2
We can plot the remaining points as:
The red triangle is the original triangle and the blue triangle is the image.
Answer:
The coordinates are J'=(1,0), A'=(3,-1) and G'=(2,3).
How would I find the length of the highlighted arc in the circle? Also I need to know how I would right the answer using pi as the symbol
Answers
The rule of the length of the arc of a circle is
[tex]L=\frac{x^{\circ}}{360^{\circ}}\times2\pi r[/tex]Where
x is the central angle subtended by the arc
r is the radius of the circle
From the given figure
The radius is 3 units, then
r = 3
The central angle of the highlight arc is a right angle, then
x = 90 degrees
Substitute them in the rule above
[tex]\begin{gathered} L=\frac{90}{360}\times2\times\pi\times3 \\ \\ L=\frac{1}{4}\times6\pi \\ \\ L=\frac{6}{4}\pi \\ \\ L=\frac{3}{2}\pi \\ \\ L=1.5\pi\text{ unit} \end{gathered}[/tex]The length of the highlight arc is 1.5pi units
Help me please (question in photo)
Answers
To graph the ellipse, connect (-2, -3), (6, 2), (14, -3), and (6, -8) with a smooth curve
How to graph an ellipse?The standard form of the equation of an ellipse with center (h, k) and major axis parallel to the x-axis is:
(x-h)²/a² + (y-k)²/b² = 1
When a>b
Major axis length = 2a
Coordinates of the vertices are (h±a, k)
Minor axis length is 2b
Coordinates of covertices are (h, k±b)
Coordinates of foci are (h±c, k). Also c²= a²-b²
Given: the equation (x-6)²/64 + (y+3)²/25 = 1
Comparing the given equation with (x-h)²/a² + (y-k)²/b² = 1:
h = 6, k = -3 => (h, k ) = (6, -3)
Thus, the center of the ellipse is (6, -3)
Coordinates of the vertices are (h±a, k)
Since a² = 64, a = √64 = 8
Thus, the endpoints of the major axis are 8 units from the center
(h±a, k) implies (h-a, k) or (h+a, k). Thus:
(h±a, k) = (6-8, -3) = (-2, -3) or (6+8, -3) = (14, -3)
Coordinates of covertices are (h, k±b)
Since b² = 25, a = √25 = 5
Thus, the endpoints of the minor axis are 5 units from the center
(h, k±b) implies (h, k-b) or (h, k+b). Thus:
(h, k±b) = (6, -3-5) = (6, -8) or (6, -3+5) = (6, 2)
Therefore:
The center of the ellipse is (6, -3). The endpoints of the major axis are 8 units from the center. The endpoints of the minor axis 5 are units from the center.
To graph the ellipse, connect (-2, -3), (6, 2), (14, -3), and (6, -8) with a smooth curve.
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What is the average rate of change of f over the interval [-3, 9]? Give an exact number.
Answers
Answer: the answer is -5/6
Step-by-step explanation:
which of the following correctly explains why-14 is an acceptable answer to the equation x2=196?(-14x14=19614*14=196(-14)=196142=196
Answers
Daley, this is the solution:
We have: x² = 196
√x² = √196
x = +/- 14
Thus,
• 14 * 14 = 196
,• -14 * -14 = 196
,• 14² = 196
,• -14² = 196
Any of these options could be taken to explain why +/- 14 is an acceptable value for x.
Upload your work at the end email to your teacher for full credit. Do not enter any words/spaces. Your answer should be a whole number. Answer:
Answers
x = 4
The area of the figure can be found below.
The size of the farm is a rectangle therefore, we use the area of a rectangle to find the area of the farm.
[tex]\begin{gathered} \text{area of the farm=lw} \\ \text{where} \\ l=\text{length} \\ w=\text{width} \\ l=3x+1+2x+4+5x-2=10x+3=10\times4+3=43 \\ w=2x+1+3x=5x+1=5\times4+1=21 \\ \text{area}=43\times21=903unit^2 \end{gathered}[/tex]Combine like terms. -3 + 7x^2- 4x – 5 + 3x^2 – 2x
Answers
The expression is given as,
[tex]-3+7x^2-4x-5+3x^2-2x[/tex]Rearranging the like terms,
[tex]7x^2+3x^2-4x-2x-5-3[/tex]Like terms : Terms that have same power of variable.
Simplifying further,
[tex]10x^2-6x-8[/tex]Thus the result of the given expression is,
[tex]10x^2-6x-8[/tex]Answer:
-8 + 10x^2 - 6x
Step-by-step explanation:
(doesn’t have to be in this order)
1. Combine numbers with the x^2
-3 + 10x^2 - 4x - 5 - 2x
2. Combine regular numbers
-8 + 10x^2 - 4x - 2x
3. Combine numbers with the plain x
-8 + 10x^2 - 6x
A, B, and C are collinear, and point B lies in between point A and point C. Point D is a point not on the line. Given thatmZABD = (x - 2)° and mZCBD = (5x), find mZCBD.
Answers
Answer:
70degrees
Explanation:
The diagrammatical representation of the statement is as shown;
Since the sum of angles on a straight line is 180degrees, then;
m8x+2 + 5x = 180
13x + 2 = 180
13x = 180 + 2
13x = 182
x = 182/13
x = 14
Get mmmmHence the measure of m
X^3+3x^2+kx-10 and x-1 is a factor what is k
Answers
Answer:
6
Step-by-step explanation:
Using the factor theorem, the expression evaluated at [tex]x=1[/tex] will equal [tex]0[/tex].
[tex]1^3+3(1^2)+k(1)-10=0 \\ \\ 1+3+k-10=0 \\ \\ k=6[/tex]
a car can travel 476 miles on 14 gallons of gas write an equation relating to the distance D to the number of gallons G. how many gallons of gas does this car need to travel 578 MI
Answers
step 1
Find the unit rate
divide the total miles by the total gallons of gas
so
476/14=34 miles/gal
Let
y ------> the distance in miles
x -----> the number of gal
we have that
the linear equation is equal to
y=34x
part 2
If y=578 miles
Find the value of x
substitute in the equation
578=34x
solve for x
x=578/34
x=17 gallons
How many miles did a plane travel if it flew 455 miles per hour in 3 hours?
Answers
The distance travelled by the plane is 1365 miles.
Given,
Speed of the pane =455 miles per hour
Time taken =3 hours
To find distance covered by the plane use formula,
[tex]speed =\frac{Distance}{Time taken}\\ \\Distance=Speed * time taken\\\\Distance=455*3\\\\Distance=1365 miles[/tex]
Thus, the distance travelled by the plane is 1365 miles.
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It is stretched horizontally by a factor of 2 and translated up 3 units.
It is compressed horizontally by a factor of 2 and translated up 3 units.
It is stretched vertically by a factor of 2 and translated up 3 units.
It is compressed vertically by a factor of 2 and translated up 3 units.
Answers
The correct option B. It is compressed horizontally by a factor of 2 and translated up 3 units.
What is meant by the term translation?The translated shapes appear to be the same size as that of the original shape, and thus the shapes are congruent. They were simply shifted in one or even more directions. There isn't any change in the form because it is simply moved from one location to another.For the given question;
The image function is defined as ; y = ㏒(2x) + 3
The parent function is; y = ㏒(x).
The first graph, X, is multiplied by 2 (2x), compressing it horizontally by a factor of 2.The number 3 is then added, which moves the graph up three units.Thus, the image function y = ㏒(2x) + 3 is obtained by the process as,compressed horizontally by a factor of 2 and translated up 3 units.
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The complete question is-
How is the graph of y = ㏒(2x) + 3 related to the graph of y = ㏒(x).
Options are-
A. It is stretched horizontally by a factor of 2 and translated up 3 units.
B. It is compressed horizontally by a factor of 2 and translated up 3 units.
C. It is stretched vertically by a factor of 2 and translated up 3 units.
D. It is compressed vertically by a factor of 2 and translated up 3 units.
11. Drew and Nick are selling two different types of raffle tickets for their math club. One
raffle ticket is for a computer and the other is for a gift card. The tickets are different
prices. Drew sells 8 tickets for the computer and 5 tickets for the gift card and receives
$50. Nick sells 8 tickets for the computer and 11 tickets for the gift card and receives
$62. How much does each type of ticket cost?
Answers
Gift card tickets = 2$ each
This is the process I used! You could’ve totally solved any variabel first but this was how I chose to do it! You could’ve also substituted into ANY of the two equations but I went with switching back and forth!
Select the correct answer.
Which equation combines with the given equation to form a system of equations with the solution x = 3 and y = 9?
x + 2y = 21
A.
OB.
O C.
O D.
OE.
4x+6y=64
2x+y = 36
4x + y = 21
-3x + 4y = 33
3x + 2y = 28
Answers
The correct option C; 4x + y = 21 is the equation combines with the x + 2y = 21 equation to form a system of equations with the solution x = 3 and y = 9.
What is meany by the term system of equations?simultaneous equations, system of equations Two or more equations must be solved together in algebra, and the solution should first satisfy all of the equations with in system. The number of parameters must equal the amount of unknowns for a system to produce a unique solution.x + 2y = 21 eq .....(i)
The solutions are x = 3 and y = 9.
Put the values of x and y in equation (i),
3 + 2 × 9 = 21
3 + 18 = 21
21 = 21
Now, evaluate every option by substituting the values.
A. 4x + 6y = 64
Put the values of x and y in equation,
4 × 3 + 6 × 9 ≠ 64
48 ≠ 64
In correct option.
B. 2x + y = 36
Put the values of x and y in equation,
2 × 3 + 9 ≠ 36
15 ≠ 36
Incorrect option
C. 4x + y = 21
Put the values of x and y in equation,
4 × 3 + 9 = 21
12 + 9 = 21
21 = 21
Correct option.
Thus, equation combines with the x + 2y = 21 equation to form a system of equations with the solution x = 3 and y = 9 is 4x + y = 21.
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