What are the vertex and x-intercepts of the graph of the function below y x2 - 2x - 24?

What are the vertex and x-intercepts of the graph of the function below y x2 - 2x - 24?
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The sum of all the integral values of a {where `a in (-10, 10)}` such that the graph of the function `f(x)=||x-2|-a|-3` has exastly three x-intercepts

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Which two points satisfy y -x2 plus 2x plus 4 and x plus y 4?

Description : Which two points satisfy y -x2 plus 2x plus 4 and x plus y 4?

Last Answer : Without any equality signs the given expression can't form anyequations and so therefore determining the values of x and y is notpossible.

Why can a function have multiple x-intercepts but only one y-intercept?

Description : Why can a function have multiple x-intercepts but only one y-intercept?

Last Answer : It can, but only if the line drawn is a curve. ---------------------------------------------------------------------------------- The function is a polynomial of the form: y = f(x) = ... value, eg y = x² has y = 4 for x =  2). Thus there will only be one y value for x = 0, ie only one y-intecept.

Evaluate each of the following using identities: (i) (2x –1x)2 (ii) (2x + y) (2x – y) (iii) (a2b – b2a)2 (iv) (a – 0.1) (a + 0.1) (v) (1.5.x2 – 0.3y2) (1.5x2 + 0.3y2) -Maths 9th

Description : Evaluate each of the following using identities: (i) (2x –1x)2 (ii) (2x + y) (2x – y) (iii) (a2b – b2a)2 (iv) (a – 0.1) (a + 0.1) (v) (1.5.x2 – 0.3y2) (1.5x2 + 0.3y2) -Maths 9th

Last Answer : (i) (2x - 1/x)2 [Use identity: (a - b)2 = a2 + b2 - 2ab ] (2x - 1/x)2 = (2x) 2 + (1/x)2 - 2 (2x)(1/x) = 4x2 + 1/x2 - 4 (ii) (2x + y) (2x - y) [Use identity: (a - b)(a + b) = a2 - b 2 ] (2x + y) (2x - ... ) = a2 - b 2 ](1.5 x 2 - 0.3y2 ) (1.5x2 + 0.3y2 ) = (1.5 x 2 ) 2 - (0.3y2 ) 2 = 2.25 x4 - 0.09y4

What is the point of contact when the line y equals 2x meets the circle x2 plus y2 -8x -y plus 5 equals 0?

Description : What is the point of contact when the line y equals 2x meets the circle x2 plus y2 -8x -y plus 5 equals 0?

Last Answer : If: y = 2xThen: y^2 = 4x^2If: x^2 +y^2 -8x -y +5 = 0Then: x^2 +4x^2 -8x -2x +5 = 0Transposing terms: 5x^2 -10x +5 = 0Dividing all terms by 5: x^2 -2x +1 = 0Factorizing the above: (x-1)(x-1) = 0 meaning x = 1By substitution into original equations point of contact is madeat: (1, 2)

What are the solutions to the simultaneous equations of y equals -2x and x2 plus y2 equals 80?

Description : What are the solutions to the simultaneous equations of y equals -2x and x2 plus y2 equals 80?

Last Answer : If: y = -2x then y ^2 = 4x^2If: x^2 + y^2 = 80 then x^2 +4x^2 = 80So: 5x^2 = 80Divide all terms by 5: x^2 = 16Square root both sides: x = -4 or +4By substitution into the original equation solutions are: (-4,8) and (4, -8)

Check whether the following are quadratic equations: (i) (x+ 1)2=2(x-3) (ii) x – 2x = (- 2) (3-x) (iii) (x – 2) (x + 1) = (x – 1) (x + 3) (iv) (x – 3) (2x + 1) = x (x + 5) (v) (2x – 1) (x – 3) = (x + 5) (x – 1) (vi) x2 + 3x + 1 = (x – 2)2 (vii) (x + 2)3 = 2x(x2 – 1) (viii) x3 -4x2 -x + 1 = (x-2)3 -Maths 10th

Description : Check whether the following are quadratic equations: (i) (x+ 1)2=2(x-3) (ii) x - 2x = (- 2) (3-x) (iii) (x - 2) (x + 1) = (x - 1) (x + 3) (iv) (x - 3) (2x + 1) = x (x + 5) (v) (2x - 1) (x - 3) = (x ... vi) x2 + 3x + 1 = (x - 2)2 (vii) (x + 2)3 = 2x(x2 - 1) (viii) x3 -4x2 -x + 1 = (x-2)3 -Maths 10th

Last Answer : this is the correct answer!

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x3+x2–2x–1, g(x) = x+1 -Maths 9th

Description : Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x3+x2–2x–1, g(x) = x+1 -Maths 9th

Last Answer : Solution: p(x) = 2x3+x2–2x–1, g(x) = x+1 g(x) = 0 ⇒ x+1 = 0 ⇒ x = −1 ∴Zero of g(x) is -1. Now, p(−1) = 2(−1)3+(−1)2–2(−1)–1 = −2+1+2−1 = 0 ∴By factor theorem, g(x) is a factor of p(x

If both (x+1) and (x -1) are factors of ax3 + x2 - 2x + b , find a and b. -Maths 9th

Description : If both (x+1) and (x -1) are factors of ax3 + x2 - 2x + b , find a and b. -Maths 9th

Last Answer : Let p(x) = ax3 + x2 - 2x + b Since (x+1) and (x-1) are the factors of p(x), ∴ p(-1) = 0 and p(1) = 0 ∴ p(-1) = a(-1)3 + (-1)2 - 2 (-1) + b = 0 ⇒ - a + 1 + 2 + b = 0 ⇒ a - b = 3 ---- (i) ... 0 ⇒ a + 1 - 2 + b = 0 ⇒ a + b = 1 ----- (ii) solving equations (i) and (ii) we get a = 2 and b = -1

If x +1 is a factor of ax3 +x2 -2x + 4a - 9, then find the value of a. -Maths 9th

Description : If x +1 is a factor of ax3 +x2 -2x + 4a - 9, then find the value of a. -Maths 9th

Last Answer : The value of a

If both (x+1) and (x -1) are factors of ax3 + x2 - 2x + b , find a and b. -Maths 9th

Description : If both (x+1) and (x -1) are factors of ax3 + x2 - 2x + b , find a and b. -Maths 9th

Last Answer : Let p(x) = ax3 + x2 - 2x + b Since (x+1) and (x-1) are the factors of p(x), ∴ p(-1) = 0 and p(1) = 0 ∴ p(-1) = a(-1)3 + (-1)2 - 2 (-1) + b = 0 ⇒ - a + 1 + 2 + b = 0 ⇒ a - b = 3 ---- (i) ... 0 ⇒ a + 1 - 2 + b = 0 ⇒ a + b = 1 ----- (ii) solving equations (i) and (ii) we get a = 2 and b = -1

If x +1 is a factor of ax3 +x2 -2x + 4a - 9, then find the value of a. -Maths 9th

Description : If x +1 is a factor of ax3 +x2 -2x + 4a - 9, then find the value of a. -Maths 9th

Last Answer : The value of a

If the sum of the zeroes of the polynomial p(x) = (k2 – 14) x2 – 2x – 12 is 1, then find the value of k. -Maths 9th

Description : If the sum of the zeroes of the polynomial p(x) = (k2 – 14) x2 – 2x – 12 is 1, then find the value of k. -Maths 9th

Last Answer : p(x) = (k2 – 14) x2 – 2x – 12 Here a = k2 – 14, b = -2, c = -12 Sum of the zeroes, (α + β) = 1 …[Given] ⇒ − = 1 ⇒ −(−2)2−14 = 1 ⇒ k2 – 14 = 2 ⇒ k2 = 16 ⇒ k = ±4

What is the distance from a point on the x axis to the centre of a circle when a tangent line at the point 3 4 meets the circle of x2 plus y2 -2x -6y plus 5 equals 0?

Description : What is the distance from a point on the x axis to the centre of a circle when a tangent line at the point 3 4 meets the circle of x2 plus y2 -2x -6y plus 5 equals 0?

Last Answer : Circle equation: x^2 +y^2 -2x -6y +5 = 0Completing the squares: (x-1)^2 +(y-3)^2 = 5Centre of circle: (1, 3)Tangent line meets the x-axis at: (0, 5)Distance from (0, 5) to (1, 3) = 5 units using the distanceformula

Let g(x) = 2x and h(x) = x2 + 4. Evaluate (h ∘ g)(−5)?

Description : Let g(x) = 2x and h(x) = x2 + 4. Evaluate (h ∘ g)(−5)?

Last Answer : 104

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A vertex cover of an undirected graph G(V, E) is a subset V1 ⊆ V vertices such that (A) Each pair of vertices in V1 is connected by an edge (B) If (u, v) ∈ E then u ∈ V1 and v ∈ V1 (C) If (u, v) ∈ E then u ∈ V1 or v ∈ V1 (D) All pairs of vertices in V1 are not connected by an edge

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Last Answer : (C) If (u, v) ∈ E then u ∈ V1 or v ∈ V1

A ................. complete subgraph and a ................. subset of vertices of a graph G=(V,E) are a clique and a vertex cover respectively. (A) minimal, maximal (B) minimal, minimal (C) maximal, maximal (D) maximal, minimal

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A certain tree has two vertices of degree 4, one vertex of degree 3 and one vertex of degree 2. If the other vertices have degree 1, how many vertices are there in the graph? (A) 5 (B) n – 3 (C) 20 (D) 11

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Consider a Hamiltonian Graph (G) with no loops and parallel edges. Which of the following is true with respect to this Graph (G) ? (a) deg(v) ≥ n/2 for each vertex of G (b) |E(G)| ≥ 1/2 (n-1)(n-2)+2 edges (c) deg(v) + deg(w) ≥ n for every v and w not connected by an edge (A) (a) and (b) (B) (b) and (c) (C) (a) and (c) (D) (a), (b) and (c)

Description : Consider a Hamiltonian Graph (G) with no loops and parallel edges. Which of the following is true with respect to this Graph (G) ? (a) deg(v) ≥ n/2 for each vertex of G (b) |E(G)| ≥ 1/2 (n-1)(n-2)+2 edges (c) deg(v) + deg( ... edge (A) (a) and (b) (B) (b) and (c) (C) (a) and (c) (D) (a), (b) and (c)

Last Answer : (D) (a), (b) and (c)

Consider an undirected graph G where self-loops are not allowed. The vertex set of G is {(i, j) | 1 ≤ i ≤ 12, 1 ≤ j ≤ 12}. There is an edge between (a, b) and (c, d) if |a – c| ≤ 1 or |b–d| ≤ 1. The number of edges in this graph is (A) 726 (B) 796 (C) 506 (D) 616

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The equation of the line bisecting the join of (3, – 4) and (5, 2) and having its intercepts on the x-axis and y-axis in the ratio 2 : 1 is -Maths 9th

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Last Answer : (d) \(\lambda\) = \(\mu\) Let the equation of the line in the intercept from be\(rac{x}{\lambda}\)+ \(rac{y}{\mu}\) = 1Since it passes through (4, 3) and (2, 5)\(rac{4}{\lambda}\) + \(rac{3}{\mu}\) = 1 ... ) = 1 - \(rac{3}{7}\) = \(rac{4}{7}\) = \(\lambda\) = 7∴ \(\lambda\) = \(\mu\) = 7.

Simplify: (i) (a + b + c)2 + (a – b + c)2 (ii) (a + b + c)2 – (a – b + c)2 (iii) (a + b + c)2 + (a – b + c)2 + (a + b – c)2 (iv) (2x + p – c)2 – (2x – p + c)2 (v) (x2 + y2 – z2)2 – (x2 – y2 + z2)2 -Maths 9th

Description : Simplify: (i) (a + b + c)2 + (a – b + c)2 (ii) (a + b + c)2 – (a – b + c)2 (iii) (a + b + c)2 + (a – b + c)2 + (a + b – c)2 (iv) (2x + p – c)2 – (2x – p + c)2 (v) (x2 + y2 – z2)2 – (x2 – y2 + z2)2 -Maths 9th

Last Answer : answer:

A student wrote the equations of the lines a and b drawn in the following graph as y =1 and 2x + 3y =6. Is he right? -Maths 9th

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Last Answer : (d) Since, the graph of linear equation 2x + 3y = 6 cuts the Y-axis. So, we put x = 0 in the given equation 2x+ 3y = 6, we get 2 x 0+ 3y = 6 ⇒ 3y = 6 y = 2. Hence, at the point (0, 2), the given linear equation cuts the Y-axis.

A student wrote the equations of the lines a and b drawn in the following graph as y =1 and 2x + 3y =6. Is he right? -Maths 9th

Description : A student wrote the equations of the lines a and b drawn in the following graph as y =1 and 2x + 3y =6. Is he right? -Maths 9th

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The graph of the linear equation 2x + 3y = 6 cuts the Y-axis at the point. -Maths 9th

Description : The graph of the linear equation 2x + 3y = 6 cuts the Y-axis at the point. -Maths 9th

Last Answer : (d) Since, the graph of linear equation 2x + 3y = 6 cuts the Y-axis. So, we put x = 0 in the given equation 2x+ 3y = 6, we get 2 x 0+ 3y = 6 ⇒ 3y = 6 y = 2. Hence, at the point (0, 2), the given linear equation cuts the Y-axis.

At what point does the graph of the linear equation 2x + 3y = 9 meet a line which is parallel to the y-axis, at a distance of 4 units from the origin and on the right of the y-axis? -Maths 9th

Description : At what point does the graph of the linear equation 2x + 3y = 9 meet a line which is parallel to the y-axis, at a distance of 4 units from the origin and on the right of the y-axis? -Maths 9th

Last Answer : hope its clear

Draw the graph of the equation y = 2x -Maths 9th

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which graph shows the solution to the system of linear inequalities y>2x+1 y?

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What is the result of isolating x2 in the equation below x2 plus (y - 5)2 30?

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what- use the slopes and y- intercepts of he lines to determine the number of solutions to the system?

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The graph of the linear equation 2x+ 3y = 6 is a line which meets the X-axis at the point. -Maths 9th

Description : The graph of the linear equation 2x+ 3y = 6 is a line which meets the X-axis at the point. -Maths 9th

Last Answer : (c) Since, the graph of linear equation 2x + 3y = 6 meets the X-axis. So, we put y = 0 in 2x + 3y = 6 ⇒ 2x + 3(0) = 6 = 2x + 0 = 6 ⇒ x = 6/2 ⇒ x = 3 Hence, the coordinate on X-axis is (3, 0).

The graph of the linear equation 2x+ 3y = 6 is a line which meets the X-axis at the point. -Maths 9th

Description : The graph of the linear equation 2x+ 3y = 6 is a line which meets the X-axis at the point. -Maths 9th

Last Answer : (c) Since, the graph of linear equation 2x + 3y = 6 meets the X-axis. So, we put y = 0 in 2x + 3y = 6 ⇒ 2x + 3(0) = 6 = 2x + 0 = 6 ⇒ x = 6/2 ⇒ x = 3 Hence, the coordinate on X-axis is (3, 0).

Scaling of a polygon is done by computing a.The product of (x, y) of each vertex b.(x, y) of end points c.Center coordinates d.Only a

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The area of a triangle is 5. Two of its vertices are (2, 1) and (3, –2). The third vertex is (x, y) -Maths 9th

Description : The area of a triangle is 5. Two of its vertices are (2, 1) and (3, –2). The third vertex is (x, y) -Maths 9th

Last Answer : Let A(x1, y1) = (3, 4), B(x2, y2) ≡ (0, 5), C(x3, y3) ≡ (2, -1)and D(x4, y4) ≡ (3, -2) be the vertices of quadrilateral ABCD.Area of quad. ABCD = \(rac{1}{2}\) |{(x1 y2 - x2 y1) + (x2y3 - x3y2) + (x3y4 - x4y3) ... ) + (12 + 6)}|= \(rac{1}{2}\) |{15 - 11 + 0 + 18}| = \(rac{1}{2}\)x 22 = 11 sq. units.

The two vertices of a triangle are (2, –1), (3, 2) and the third vertex lies on the line x + y = 5. The area of the triangle is 4 units. -Maths 9th

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Last Answer : (c) (5, 0) or (1, 4) Let the third vertex of the triangle be P(a, b). Since it lies on the line x + y = 5, a + b = 5 ...(i) Also, given area of triangle formed by the points (2, -1), (3, 2) and (a, b) = 4 ... b) - (-3a + b) = 5 + 15⇒ 4a = 20 ⇒ a = 5 ⇒ b = 0. ∴ The points are (1, 4) and (5, 0).

Find the point on the curve `9y^2=x^3,` where the normal to the curve makes equal intercepts on the axes.

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Find the point on the curve `9y^2=x^3,` where the normal to the curve makes equal intercepts on the axes.

Description : Find the point on the curve `9y^2=x^3,` where the normal to the curve makes equal intercepts on the axes.

Last Answer : Find the point on the curve `9y^2=x^3,` where the normal to the curve makes equal intercepts on the axes.

10) i) \( A=\{a, b, c\} \) and \( B=\{x, 4\} \). Write \( A \times B \)ii) Graph of the function \( f: R \rightarrow R \) is given below.a) Write the value of \( f(x) \)b) Write the range of \( f(x) \)c) Identify The function and choose the correct answer.

Description : 10) i) \( A=\{a, b, c\} \) and \( B=\{x, 4\} \). Write \( A \times B \)ii) Graph of the function \( f: R \rightarrow R \) is given below.a) Write the value of \( f(x) \)b) Write the range of \( f(x) \)c) Identify The function and choose the correct answer.

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What can you say about the graph of the function below Check all that apply. F(x) (0.9)x?

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graph of 2x+9=0 in one variable -Maths 9th

Description : graph of 2x+9=0 in one variable -Maths 9th

Last Answer : 2x+9=0 2x=-9 x=-9/2 x=-4.5

graph of 2x+9=0 in one variable -Maths 9th

Description : graph of 2x+9=0 in one variable -Maths 9th

Last Answer : 2x+9=0 2x=-9 x=-9/2 x=-4.5

If the point (2k – 3, k + 2) lies on the graph of the equation 2x + 3y +15 = 0, find the value of k. -Maths 9th

Description : If the point (2k – 3, k + 2) lies on the graph of the equation 2x + 3y +15 = 0, find the value of k. -Maths 9th

Last Answer : Solution :-