Answers
Answer:
A, C
Step-by-step explanation:
x² + 3x - 5 = 0
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-3 \pm \sqrt{3^2 - 4(1)(-5)}}{2(1)} [/tex]
[tex] x = \dfrac{-3 \pm \sqrt{29}}{2} [/tex]
Related Questions
1. A student determines that one solution to a system of quadratic-quadratic equations is (2.1).
Determine the value of n if the equations are:
4x² - my=10
mx² + ny=20
Answer: -4
Answers
The value of n is approximately -0.327.
To determine the value of n, we can substitute the given solution (x = 2.1) into the system of equations:
4x² - my = 10 ...(1)
mx² + ny = 20 ...(2)
Substituting x = 2.1 into equation (1), we get:
4(2.1)² - my = 10
8.4 - my = 10
-my = 10 - 8.4
-my = 1.6
Now, substituting x = 2.1 into equation (2), we get:
m(2.1)² + ny = 20
4.41m + ny = 20
Since we already have an expression for -my from equation (1), we can substitute it into equation (2):
4.41m + (-1.6) = 20
4.41m - 1.6 = 20
4.41m = 20 + 1.6
4.41m = 21.6
To solve for m, we divide both sides by 4.41:
m = 21.6 / 4.41
m ≈ 4.9
Now that we have the value of m, we can substitute it back into equation (1) to solve for n:
4(2.1)² - 4.9y = 10
8.4 - 4.9y = 10
-4.9y = 10 - 8.4
-4.9y = 1.6
Finally, to solve for y, we divide both sides by -4.9:
y = 1.6 / -4.9
y ≈ -0.327
Consequently, n has a value of roughly -0.327.
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Which equation represents the hyperbola shown in the
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(x - 2)² (v+3)² = 1
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(x + 2)²
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(y - 3)²
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Answers
The equation that represents the hyperbola shown in the graph is (y - 3)²/4 - (x + 2)²/25 = 1.
From the given options, the equation that represents the hyperbola shown in the graph is (y - 3)²/4 - (x + 2)²/25 = 1.
To determine the equation of a hyperbola, we examine the standard form:
For a hyperbola centered at (h, k), with vertical transverse axis, the standard form is:
(y - k)²/a² - (x - h)²/b² = 1
From the given graph, we can observe that the center of the hyperbola is (-2, 3). This corresponds to the values of (h, k) in the standard form.
Next, we need to determine the values of a and b, which are the lengths of the transverse and conjugate axes, respectively. Looking at the graph, we see that the transverse axis has a length of 2a = 4, so a = 2. The conjugate axis has a length of 2b = 10, so b = 5.
Plugging these values into the standard form, we obtain:
(y - 3)²/4 - (x + 2)²/25 = 1
The equation that represents the hyperbola shown in the graph is (y - 3)²/4 - (x + 2)²/25 = 1.
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The correct equation representing the hyperbola shown in the graph is:
(x + 2)²/25 - (y - 3)²/4 = 1.
The equation that represents the hyperbola shown in the graph is:
(x + 2)²/25 - (y - 3)²/4 = 1
Let's analyze the options provided:
(x - 2)²(v + 3)² = 1:
This equation is not a valid representation of a hyperbola because it contains a term (v + 3)², which is not consistent with the variable used in the graph.
(x + 2)²/25:
This equation represents a horizontal parabola, not a hyperbola.
(x - 2)²/25:
This equation represents a horizontal parabola, not a hyperbola.
(y - 3)²/1:
This equation represents a vertical line, not a hyperbola.
(y - 3)²/4:
This equation represents a hyperbola with a vertical transverse axis and a conjugate axis length of 2b = 4 (b = 2).
The equation is in the standard form for a hyperbola with a vertical transverse axis.
The equation is provided as a standard form assuming the given coordinates and graph match the standard form representation of a hyperbola.
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If the mass of a proton is 1.67 × 10-24 gram, what is the mass of 2,000 protons?
Answers
Answer:
3.34 * 10^-21 g
Step-by-step explanation:
1.67*10^-24 * 2000 = 1.67 * 10^-24 * 2 *10^3 = 3.34 * 10^-21 g
-5 -4 -3 -2 -1 4 3 C -1 O 10 -2- -4 -3- -5- 1 2010. © 2023 Edmentum. All rights reserved. 2 3 4 5 If function f is the parent exponential function f(x) Replace the value of a to complete the equation. = TO X e, what is the equation of transformed function g in terms of function f R S 9 sin cos tan sin cos tan-¹ /A
Answers
Given the equation f(x) = a · bx where a and b are constants. So, the answer to the given problem is g(x) = a · bx + h, and the explanation of the trigonometric function.
To find the equation of transformed function g in terms of function f is explained below: If f(x) = a · bx, then the transformed function g(x) can be represented by g(x) = a · bx + h, where h is the vertical shift (if h > 0, the graph shifts upward, and if h < 0, the graph shifts downward).
Now, we have to replace the value of 'a' to complete the equation of g(x). But, we don't have any value of 'a' provided in the question. Hence, we can't determine the equation of transformed function g in terms of function f for the given information.
Next, let's move to the trigonometric function. It is given that: R S 9 sin cos tan sin cos tan-¹ /ASin, Cos, Tan, Cosec, Sec, and Cot are six trigonometric functions. Let's see their definitions and their corresponding inverse functions:
1. Sine: It is defined as the ratio of the length of the side opposite the given angle to the length of the hypotenuse in a right-angled triangle. Its corresponding inverse function is sin⁻¹.
2. Cosine: It is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle. Its corresponding inverse function is cos⁻¹.
3. Tangent: It is defined as the ratio of the length of the side opposite the given angle to the length of the adjacent side in a right-angled triangle. Its corresponding inverse function is tan⁻¹.
4. Cosecant: It is defined as the ratio of the length of the hypotenuse to the length of the side opposite the given angle in a right-angled triangle. Its corresponding inverse function is cosec⁻¹.
5. Secant: It is defined as the ratio of the length of the hypotenuse to the length of the adjacent side in a right-angled triangle. Its corresponding inverse function is sec⁻¹.
6. Cotangent: It is defined as the ratio of the length of the adjacent side to the length of the side opposite the given angle in a right-angled triangle. Its corresponding inverse function is cot⁻¹.
Hence, the answer to the given problem is g(x) = a · bx + h, and the explanation of the trigonometric function.
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What is the percent of 1 - 3√(5/35) ?
Answers
Answer:
1 - 3√(5/35) = 1 - 3√(1/7) = 1 - 3*(1/sqrt(7)) ≈ 0.0755
0.0755 * 100 = 7.55%
Step-by-step explanation:
To find the percentage of 1 - 3√(5/35), we need to first evaluate the expression.
1 - 3√(5/35) = 1 - 3√(1/7) = 1 - 3*(1/sqrt(7)) ≈ 0.0755
To convert this decimal to a percentage, we simply multiply by 100:
0.0755 * 100 = 7.55%
what is the value of x in the triangle
Answers
Answer:
7
Step-by-step explanation:
In an 30-60-90 right triangle, the longer leg is the shorter leg multiplied by [tex]\sqrt{3}[/tex]
So [tex]7\sqrt{3} =x*\sqrt{3[/tex]
[tex]7=x[/tex]
x=7
Answer:
A. 21
Step-by-step explanation:
This is a 30-60-90 triangle, where you have one 30° angle, one 60°, and one 90° (aka right) angle.
The sides of a 30-60-90 triangle adhere to the following rules:
The side opposite the 30° angle is the shortest side and we can call its length "x".The side opposite the 60° angle is the medium length side and its length is given by x * √3. This means its length is the product of the length of the side opposite the 30° angle and √3.The side opposite the 90° (right) angle is the longest side (aka the hypotenuse) and its length is given by 2x. This means its length is twice the length of the side opposite the 30° angle.Since 7√3 is the length of the side opposite the 30° angle, the entire expression represents x.
Since the length of the side opposite the 60° angle is given by x * √3, the length of this side is (7√3)(√3).
Simplifying gives us 7*3, which is 21.
Thus, the value of x in the triangle is 21 (answer choice A.)
On a coordinate plane, a triangle has points F (3, 4), D (5, negative 3), and E (1, negative 2).
What are the coordinates of the image of vertex D after a reflection across the x-axis?
(5, 3)
(–5, –3)
(–3, 5)
(3, –5)
Answers
Answer:
(5, 3 )
Step-by-step explanation:
under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
D (5, - 3 ) → (5, - (- 3) ) → (5, 3 )
Answer:
(5,3)
Step-by-step explanation:
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