Answer:
The translation that maps the vertex of the graph of the function f(x) = x² onto the vertex of the function g(x) = x² - 10x + 2 is 5 units to the right and 23 units down.Explanation:
1) Vertex form of the function that represents a parabola.
The general form of a quadratic equation is Ax² + Bx + C = 0, where A ≠ 0, and B and C may be any real number. And the graph of such equation is a parabola with a minimum or maximum value at its vertex.
The vertex form of the graph of such function is: A(x - h)² + k
Where, A a a stretching factor (in the case |A| > 1) or compression factor (in the case |A| < 1) factor.
2) Find the vertex of the first function, f(x) = x²
This is the parent function, for which, by simple inspection, you can tell h = 0 and k = 0, i.e. the vertex of f(x) = x² is (0,0).
3) Find teh vertex of the second function, g(x) = x² -10x + 2
The method is transforming the form of the function by completing squares:
Subtract 2 from both sides: g(x) - 2 = x² - 10xAdd the square of half of the coefficient of x (5² = 25) to both sides: g(x) - 2 + 25 = x² - 10x + 25Simplify the left side and factor the right side: g(x) + 23 = (x - 5)²Subtract 23 from both sides: g(x) = (x - 5)² - 23That is the searched vertex form: g(x) = (x - 5)² - 23.
From that, using the rules of translation you can conclude immediately that the function f(x) was translated 5 units horizontally to the right and 23 units vertically downward.
Also, by comparison with the verex form A(x - h)² + k, you can conclude that the vertex of g(x) is (5, -23), and that means that the vertex (0,0) was translated 5 units to the right and 23 units downward.
Answer:
Its A
Step-by-step explanation:
edge 2021 :))
A pole is braced with a wire from the top of a pole to the ground. The wire is 100 feet long and makes an angle of 40° with the ground. Find the height of the pole. 64 ft 77 ft 84 ft 156 ft
Answer:
=64 ft
Step-by-step explanation:
The wire, the pole and the flat surface form a right triangle with a base angle of 40°. The pole is the height of the triangle and is opposite the angle 40°.
Therefore we can use the trigonometric ratio -sine of the angle 40° -to find the height.
Sin∅ =opposite/hypotenuse
opposite=hypotenuse × sin∅
=100ft × Sin 40°
=64.28ft
≅64 ft
Given b(x) = X+41, what is b(-10)?
Answer:
your answer would be 6
Step-by-step explanation:
hope this helps
It is 2.3 km from Salma's house to the nearest mailbox. How far is it in meters?
Answer:
2.3km in meters is 2300 Meters
Step-by-step explanation:
Multiply the length value by 1000
Find the value of x round to the nearest tenth
Answer:
Step-by-step explanation:
Note. You should put the item you are trying to solve for in the numerator when using the sine law.
sin(x) / 15 = Sin 27 / 11
sin(x) = 15 * sin(27 / 11
sin(x) = 0.4539
sin(x) = 15 * 0.4539/11
sin(x) = 6.809 / 11
sin(x) = 0.6191
x = sin-1(0.6191)
x = 38.3
Answer: its 38.2 :)
Step-by-step explanation:
what polynomial has roots of -6, 1, and 4
Answer:
C
Step-by-step explanation:
Given the roots of the polynomial are x = - 6, x = 1 and x = 4 the the factors are
(x + 6), (x - 1) and (x - 4)
The polynomial is the product of the factors, that is
f(x) = a(x - 1)(x - 4)(x + 6) ← a is a multiplier
let a = 1 and expand the first pair of factors
f(x) = (x² - 5x + 4)(x + 6)
= x(x² - 5x + 4) + 6(x² - 5x + 4) ← distribute both parenthesis
= x³ - 5x² + 4x + 6x² - 30x + 24 ← collect like terms
f(x) = x³ + x² - 26x + 24 → C
Answer:
x^3 + x^2 - 26x + 24.
Step-by-step explanation:
Knowing the roots we can immediately write it in factor form as follows:
f(x) = (x + 6)(x - 1)(x - 4).
Note that when f(x) = 0 each of the factors can be zero and , for example, when x + 6 = 0 then x = -6.
We now expand the expression:
(x + 6)(x - 1)(x - 4)
= (x + 6)(x^2 - 4x - 1x + 4)
= (x + 6)(x^2 - 5x + 4)
= x(x^2 - 5x + 4) + 6(x^2 - 5x + 4)
= x^3 - 5x^2 + 4x + 6x^2 - 30x + 24 Adding like terms:
= x^3 + x^2 - 26x + 24. (Answer).
Question 7!!!! 12 points
Answer:
[tex]35+50x\le 1325[/tex]
Step-by-step explanation:
So y=mx+b tells us the initial amount is b (also known as the y-intercept).
Anyways you have to pay a one time fee of 35 dollars and then it is 50 dollars per month.
Let x represent the number of months she goes to yoga.
If she goes 1 month it costs her 35+50.
If she goes 2 months it costs her 35+50+50 or just 35+50(2).
If she goes 3 months it costs her 35+50+50+50 or just 35+50(3).
If she goes x months it costs her 35+50x.
Now she only has 1325.
So we want the cost of her x months to be less than or equal to 1325 because she doesn't have more than that.
So we want [tex]35+50x\le 1325[/tex]
Answer:
C
Step-by-step explanation:
Since she want to use her savings of $1325 it means that that is all the money Abbey is going to use so it means that the $1325 is greater or equal to the money she can or is going to spend. There is a one time fee of $35 which is going to be added to it and a monthly fee of $50. Since you don't know how many months, it'll be replaced with an x. so the equation will be 35+50x≤$1325
A man tied a rope to the top of a tree, which is 'x' m tall. The other end of the rope was tied to
the ground, 20 m away from the base of the tree. Given that the length of the rope is 16 m
longer than the height of the tree, find the height of the tree.
(by using pythagoras' theorem)
Answer:
(x+16)^2=20^2+x^2
Step-by-step explanation:
Given there was no bending of the tree, the Pitagorean Theory would help finding the value of the trees hight.
x^2+32x+16^2=400+x^2
32x=(20-16)×(20+16)
x=144/32
x=4m and 50cm
Answer:
Step-by-step explanation:
Please answer. :) ):) ) : ): ): ): ) :)
Answer:
2/5, 8/20, 4/10,16/40
Step-by-step explanation:
40%
Percent means out of 100
40/100 = 4/10 = 2/5
Lets look at the choices
8/100 =4/50 =2/25 not equal
2/5 equal
8/20 = 4/10 =2/5 = equal
4/10 = 2/5 = equal
16/40 = 4/10 = 2/5 equal
Answer:
Second option.
Third option.
Fourth option.
Fifth option.
Step-by-step explanation:
In order to find equivalent fractions to 40%, you can:
- Write 40 as the numerator and 100 as the denominator and then reduce the fraction:
[tex]\frac{40}{100}=\frac{4}{10}=\frac{2}{5}[/tex]
- Multiply the numerator and the denominator of the fraction [tex]\frac{4}{10}[/tex] by 2:
[tex]\frac{4*2}{10*2}=\frac{8}{20}[/tex]
- Multiply the numerator and the denominator of the fraction [tex]\frac{4}{10}[/tex] by 4:
[tex]\frac{4*4}{10*4}=\frac{16}{40}[/tex]
what is the equation of the graphed line in point slope form?
Answer:
y + 3 = 2(x + 3)Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x+x_1)[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have the points (-3, -3) and (0, 3).
Calculate the slope:
[tex]m=\dfrac{3-(-3)}{0-(-3)}=\dfrac{6}{3}=2[/tex]
Put the value of the slope and the coordinates of the point (-3, -3) to the equation of a line:
[tex]y-(-3)=2(x-(-3))\\\\y+3=2(x+3)[/tex]
[tex]y=2x+3[/tex]
Direct the titles to the boxes to form correct pairs not all titles will be used. Match each set of vertices with the type of triangle they form pleaseeeeeeee help .... this is a test
Answer:
The triangle with vertices A (2 , 0) , B (3 , 2) , C (5 , 1) is isosceles right Δ
The triangle with vertices A (-3 , 1) , B (-3 , 4) , C (-1 , 1) is right Δ
The triangle with vertices A (-5 , 2) , B (-4 , 4) , C (-2 , 2) is acute scalene Δ
The triangle with vertices A (-4 , 2) , B (-2 , 4) , C (-1 , 4) is obtuse scalene Δ
Step-by-step explanation:
* Lets explain the relation between the sides and the angles in
a triangle
- The types of the triangles according the length of its sides:
# Equilateral triangle; all its sides are equal in length and all the angles
have measures 60°
# Isosceles triangle; tow sides equal in lengths and the 2 angles not
included between them are equal in measures
# Scalene triangles; all sides are different in lengths and all angles
are different in measures
- The types of the triangles according the measure of its angles:
# Acute triangle; its three angles are acute and the relation between
its sides is the sum of the squares of the two shortest sides is
greater than the square of the longest side
# Obtuse triangle; one angle is obtuse and the other 2 angles are
acute and the relation between its sides is the sum of the squares
of the two shortest sides is smaller than the square of the longest
side
# Right triangle; one angle is right and he other 2 angles are
acute and the relation between its sides is the sum of the squares
of the two shortest sides is equal to the square of the longest side
- The distance between the points 9x1 , y1) and (x2 , y2) is
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
* Lets solve the problem
# The triangle with vertices A (2 , 0) , B (3 , 2) , C (5 , 1)
∵ [tex]AB=\sqrt{(3-2)^{2}+(2-0)^{2}}=\sqrt{1+4}=\sqrt{5}[/tex]
∵ [tex]BC=\sqrt{(5-3)^{2}+(1-2)^{2}}=\sqrt{4+1}=\sqrt{5}[/tex]
∵ [tex]AC=\sqrt{(5-2)^{2}+(1-0)^{2}}=\sqrt{9+1}=\sqrt{10}[/tex]
- Lets check the relation between the sides
∵ AB = BC = √5 ⇒ shortest sides
∵ AC = √10
∵ (AB)² + (BC)² = (√5)² + (√5)² = 5 + 5 = 10
∵ (AC)² = (√10)² = 10
∴ The sum of the squares of the shortest sides is equal to the square
of the longest side
∴ Δ ABC is right triangle
∵ Δ ABC has two equal sides
∴ Δ ABC is isosceles right triangle
# The triangle with vertices A (-3 , 1) , B (-3 , 4) , C (-1 , 1)
∵ [tex]AB=\sqrt{(-3--3)^{2}+(4-1)^{2}}=\sqrt{0+9}=3[/tex]
∵ [tex]BC=\sqrt{(-1--3)^{2}+(1-4)^{2}}=\sqrt{4+9}=\sqrt{13}[/tex]
∵ [tex]AC=\sqrt{(-1--3)^{2}+(1-1)^{2}}=\sqrt{4+0}=2[/tex]
- Lets check the relation between the sides
∵ AB = 3
∵ BC = √13 ⇒ longest sides
∵ AC = 2
∵ (AB)² + (AC)² = (3)² + (2)² = 9 + 4 = 13
∵ (BC)² = (√13)² = 13
∴ The sum of the squares of the shortest sides is equal to the square
of the longest side
∴ Δ ABC is right triangle
∴ Δ ABC is right triangle
# The triangle with vertices A (-5 , 2) , B (-4 , 4) , C (-2 , 2)
∵ [tex]AB=\sqrt{(-4--5)^{2}+(4-2)^{2}}=\sqrt{1+4}=\sqrt{5}[/tex]
∵ [tex]BC=\sqrt{(-2--4)^{2}+(2-4)^{2} }=\sqrt{4+4}=\sqrt{8}[/tex]
∵ [tex]AC=\sqrt{(-2--5)^{2}+(2-2)^{2}}=\sqrt{9+0}=3[/tex]
- Lets check the relation between the sides
∵ AB = √5
∵ BC = √8
∵ AC = 3 ⇒ longest sides
∵ (AB)² + (BC)² = (√5)² + (√8)² = 5 + 8 = 13
∵ (AC)² = (3)² = 9
∴ The sum of the squares of the shortest sides is greater than the
square of the longest side
∴ Δ ABC is acute triangle
∵ Δ ABC has three different sides in lengths
∴ Δ ABC is acute scalene triangle
# The triangle with vertices A (-4 , 2) , B (-2 , 4) , C (-1 , 4)
∵ [tex]AB=\sqrt{(-2--4)^{2}+(4-2)^{2}}=\sqrt{4+4}=\sqrt{8}[/tex]
∵ [tex]BC=\sqrt{(-1--2)^{2}+(4-4)^{2} }=\sqrt{1+0}=1[/tex]
∵ [tex]AC=\sqrt{(-1--4)^{2}+(4-2)^{2}}=\sqrt{9+4}=\sqrt{13}[/tex]
- Lets check the relation between the sides
∵ AB = √8
∵ BC = 1
∵ AC = √13 ⇒ longest sides
∵ (AB)² + (BC)² = (√8)² + (1)² = 8 + 1 = 9
∵ (AC)² = (√13)² = 13
∴ The sum of the squares of the shortest sides is smaller than the
square of the longest side
∴ Δ ABC is obtuse triangle
∵ Δ ABC has three different sides in lengths
∴ Δ ABC is obtuse scalene triangle
Where the above is given,
The triangle with vertices A (2 , 0) , B (3 , 2) , C (5 , 1) is isosceles right Δ
The triangle with vertices A (-3 , 1) , B (-3 , 4) , C (-1 , 1) is right Δ
The triangle with vertices A (-5 , 2) , B (-4 , 4) , C (-2 , 2) is acute scalene Δ
The triangle with vertices A (-4 , 2) , B (-2 , 4) , C (-1 , 4) is obtuse scalene Δ
How to derive the aboveHere is the definition of all the Triangles according to their respective sides:
Equilateral triangle; all of its sides and angles have the same length. They have a 60° angleIsosceles triangle with two equal-length sides and no angles. The measurements are equal between them.Scalene triangles; all sides and angles are different lengths. They are measured differently.Triangle classification based on angle measurement:
Acute triangle; its three acute angles and the relationship between them. The sum of the squares of the two shortest sides of its sides is bigger than the longest side's square.Obtuse triangle; one obtuse angle and two acute angles, and the relationship between its sides is that the total of the squares of the two shortest sides is less than the square of the longest side.The sum of the squares of the two shortest sides is equal to the square of the longest side of a right triangle, which has one right angle and two acute angles.To determined the kind of triangles we are given from the above information, we use the distance formula:
The distance from (x₁, y₁) and (x₂, y₂)
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
The triangle with vertices A (2 , 0) , B (3 , 2) , C (5 , 1)
AB [tex]= \sqrt{(-3- -3)^2 + (4 - 1)^2[/tex]
= √(0+9)
= 3
BC [tex]= \sqrt{(-1- -3)^2 + (1 - 4)^2[/tex]
= √(4+9)
= √13
AC [tex]= \sqrt{(-1- -3)^2 + (1 - 1)^2[/tex]
AC = √(4+0)
= 2
- Lets evaluate the relation between the respective sides
AB = 3
BC = √13 ⇒ longest sides
AC = 2
(AB)² + (AC)² = (3)² + (2)² = 9 + 4 = 13
(BC)² = (√13)² = 13
The sum of the squares of the shortest sides is equal to the square of the longest side
Δ ABC is right triangle
Δ ABC is right triangle
The triangle with vertices A (-5 , 2) , B (-4 , 4) , C (-2 , 2)
AB = √[(-4- -5)² + (4-2)²]
= √(1+4)
= √5
BC = √[(-2- -1)² +(2-4)²
= √(4+4)
= √8
AC = √[(-2- -5)² +(2-2)²
= √(9+0)
= 3
Checking the relation between the sides we know that
AB = √5
BC = √8
AC = 3 ⇒ longest sides
(AB)² + (BC)² = (√5)² + (√8)² = 5 + 8 = 13
(AC)² = (3)² = 9
Hence, the sum of the squares of the shortest sides is greater than the square of the longest side
Δ ABC is acute triangle
Δ ABC has three different sides in lengths
Δ ABC is acute scalene triangle
The triangle with vertices A (-4 , 2) , B (-2 , 4) , C (-1 , 4)
AB = √[(-2- -4)² + (4-2)²]
= √(4+4)
= √8
BC = √[(-1- -2)² + (4-4)²]
= √(1+0)
= 1
AC = √[(-1- -4)² + (4-2)²]
= √(9+4)
= √13
Thus, - checking the relation between the sides
AB = √8
BC = 1
AC = √13 ⇒ longest sides
(AB)² + (BC)² = (√8)² + (1)² = 8 + 1 = 9
(AC)² = (√13)² = 13
The sum of the squares of the shortest sides is smaller than the square of the longest side
Δ ABC is obtuse triangle
Δ ABC has three different sides in lengths
Δ ABC is obtuse scalene triangle
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Consider the two triangles.
To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that....
PLEASE HELP.. extra coins
According to Side Angle Side theorem the correct option is d)
[tex]\rm \dfrac{AC}{GI}=\dfrac{BC}{HI}[/tex]
According to SAS theorem:
If an angle of one triangle is congruent to the corresponding angle of another triangle.And the lengths of the sides including these angles are in proportion, the triangles are similar.From the given triangles we can see that,
[tex]\rm \dfrac{AC}{BC}=\dfrac{GI}{HI}[/tex] ---- (according to SAS theorem)
Therefore, the correct option is D).
For more information, refer the link given below
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Answer:
D !!!!!
Step-by-step explanation:
According to Side Angle Side theorem the correct option is d
AC / GI = BC / HI
-edge did the test
If f(x) = 6x – 4, what is f(x) when x = 8?
Use the substitution method
f(x)= 6x-4
f(8)= 6(8)-4
f(8)= 48-4
f(8)= 44
Answer is f(8)= 44
Answer:
f(8) = 44Step-by-step explanation:
[tex]f(x)=6x-4\\\\\text{Put x = 8 to the equation:}\\\\f(8)=6(8)-4=48-4=44[/tex]
how do u solve two points using the distance formula?
Step-by-step explanation:
For two points (x₁, y₁) and (x₂, y₂), the distance between them is:
d² = (x₁ − x₂)² + (y₁ − y₂)²
The order of points 1 and 2 don't matter. You can switch it:
d² = (x₂ − x₁)² + (y₂ − y₁)²
This is basically the Pythagorean theorem for a coordinate system.
Let's do an example. If you have points (1, 2) and (4, 6), then the distance between them is:
d² = (4 − 1)² + (6 − 2)²
d² = 3² + 4²
d² = 9 + 16
d² = 25
d = 5
If you have points with negative coordinates, remember that subtracting a negative is the same as adding a positive.
For example, the distance between (-1, -2) and (4, 10) is:
d² = (4 − (-1))² + (10 − (-2))²
d² = (4 + 1)² + (10 + 2)²
d² = 5² + 12²
d² = 25 + 144
d² = 169
d = 13
What is the approximate pH of a solution if the concentration of hydrogen ions is 5.0x10^-4 moles per liter
Answer:
it should be 3.3
Step-by-step explanation:
I did it with friend
Answer:
C) 3.3
Step-by-step explanation:
this is the correct answer on ed-genuity, hope this helps! :)
using the discriminant, how many solutions and what type of solution(s) does 12t^2+4t-9=0 have?
a. 2; irrational
b. 2; rational
c. 1; rational
d. no real solutions
The quadratic equation 12t^2 + 4t - 9 = 0 has a discriminant value of 448, which is greater than zero indicating two real solutions. These solutions are irrational given that the square root of the discriminant (448) is not a clean number, hence answer A. 2; irrational, is correct.
Explanation:The quadratic equation in question is 12t² + 4t - 9 = 0. The discriminant (D) of a quadratic equation in the form at² + bt + c = 0 is defined as D = b² - 4ac. Use the values from your equation: a = 12, b = 4, and c = -9. Plugging these values into the formula gives D = 4² - 4*(12)*(-9) = 16 + 432 = 448.
The value of the discriminant determines the solutions of the quadratic equation. If D > 0, then there are two real solutions. If D = 0, then there's one real solution. If D < 0, then there are no real solutions. Here, we have that D = 448 which is greater than 0, hence, the quadratic equation has two real solutions.
The type of solutions depends on whether the square root of D is a rational or irrational number. The square root of 448 is not a clean number, meaning it's an irrational number. Therefore, the solutions are of an irrational type.
So, this quadratic equation has 2 solutions that are irrational meaning the correct answer is A. 2; irrational.
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The equation 12t^2+4t-9=0 has a. two irrational solutions.
Explanation:To determine the number and type of solutions for the equation 12t^2+4t-9=0, we can use the discriminant formula.
The discriminant is found by calculating b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation.
In this case, a = 12, b = 4, and c = -9. Substituting these values into the discriminant formula, we get b^2 - 4ac = (4)^2 - 4(12)(-9) = 16 + 432 = 448.
Since the discriminant (448) is positive, this means that the quadratic equation has two real solutions. The nature of these solutions can be determined by the discriminant as well. If the discriminant is a perfect square, the solutions are rational. If the discriminant is not a perfect square, the solutions are irrational.
In our case, the discriminant (448) is not a perfect square, so the solutions to the equation 12t^2+4t-9=0 are two irrational solutions. Therefore, the correct answer is a. 2; irrational.
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4 more than the quotient of x squared and 3
An expression for the given statement is (x²/3)+4.
The given statement is 4 more than the quotient of x squared and 3.
We need to find an expression for the given statement.
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be addition, subtraction, multiplication, or division.
The terms involved in an expression in math are:
Constant: A constant is a fixed numerical value.
Variable: A variable is a symbol that doesn't have a fixed value.
According to the question, we get (x²/3)+4.
Therefore, an expression for the given statement is (x²/3)+4.
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Valerie is going to use SAS to prove that triangle VWX is congruent to triangle YZX, which of these is a necessary dye in Valerie’s proof
You are correct in selecting choice A as the answer.
You need the middle angles between the two pairs of given congruent sides, so that you can prove the triangles to be congruent through SAS. The vertical angle theorem is used in this case. Alternate interior angles only come from parallel lines, but we dont know if any of the lines are parallel. Even if we did know the lines were paralle, we still wouldn't use the alternate interior angle theorem.
The part that is necessary in Valerie's proof using SAS to prove ΔVWX ≅ ΔYZX is prove that ∠VWX ≅ ∠YXZ by vertical angles.
The SAS(side angle side) theorem for congruent triangle states that If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.
The side WX and XZ are congruent and VX and XZ are congruent . Then the included angles ∠VWX should be congruent to ∠YXZ. The both angles are vertically opposite angles. This can be represented with mathematical symbols below
WX≅XZ
VX ≅XZ
Therefore,
∠VWX ≅ ∠YXZ(vertically opposite angles)
Therefore, the necessary step in Valerie proof is Prove that ∠VWX ≅ ∠YXZ by vertical angles.
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A fence on a hill uses vertical posts L and M to hold parallel rails N and P. If M angle 10=85 then what is the measure of angle 7
Answer:
95 degrees
Step-by-step explanation:
The sum of the two angles 10 and 7 must be 180 degrees, so 180-85 = 95 degrees.
Answer:
m∠7 = 95°
Step-by-step explanation:
From the figure attached,
Rails N and P are parallel and vertical post L works as transverse.
Therefore, by the property of parallel lines, sum of interior angles formed by the transverse are supplementary.
In other words, ∠7 and ∠10 are interior angles and both are supplementary angles.
m∠7 + m∠10 = 180°
Since m∠10 = 85°
m∠7 + 85 = 180
m∠7 = 180 - 85
m∠7 = 95°
Need answer to A and B!
Answer:
P(factor of 56)=5/8
P(multiple of 3)=1/4
Step-by-step explanation:
The positive factors of 56 are 1,2,4,7,8,14,28,56.
The factors of 56 on the spinner are 1,2,4,7, and 8. There are 5 numbers there that are factors of 56.
There are 8 numbers to land on in all.
So the P(factor of 56)=5/8.
Multiples of 3 are 3,6,9,...
The multiples of 3 on the spinner on the board are 3 and 6. There are 2 numbers there that are multiples of 3.
There are 8 numbers to land on in all.
So the P(multiple of 3)=2/8 which reduced to 1/4. I divided top and bottom by 2.
evaluate sin(Tan^-10)
[tex]\tan x=0[/tex] for [tex]x=n\pi[/tex], where [tex]n[/tex] is any integer. The inverse tangent function returns numbers between [tex]-\dfrac\pi2[/tex] and [tex]\dfrac\pi2[/tex]. The only multiple of [tex]\pi[/tex] in this range is 0, so [tex]\tan^{-1}0=0[/tex].
Then
[tex]\sin\left(\tan^{-1}0\right)=\sin0=\boxed0[/tex]
To evaluate sin(Tan^-10), we find that the angle whose tangent is 0 also has a sine of 0, thus the answer is 0.
The question asks to evaluate sin(Tan-10), which is essentially asking for the sine of the angle whose tangent is 0. We know that tangent is the ratio of sine to cosine, and when the tangent is 0, it means that the sine must be 0 as long as the cosine is not 0. Given that the cosine of 0 degrees (or 0 radians) is 1, and the sine of 0 degrees is 0, we can conclude that sin(Tan-10) is 0.
A)55
B)65
C)50
D)60
Answer:
50
Step-by-step explanation:
This is an isosceles triangle which means opposite sides are congruent implies the base opposite angles at the base congruent.
So both of bottom angles are 65 each.
We know the sum of the interior angles of a triangle are 180 degrees.
So we have 65+65+x=180.
Combine like terms:
130+x=180
Subtract 130 on both sides:
x=180-130
x=50
What is the value of tan (B) in the diagram?
Answer:
The correct answer is third option
1/√3
Step-by-step explanation:
From the figure we can see a right angled triangle ABC.
Right angled at C.
AB = 10
AC = 5
BC = 5√3
Points to remember
Tan θ = Opposite side/Adjacent side
To find the value of tan(B)
Tan B = Opposite side/Adjacent side
= AC/BC
= 5/5√3
= 1/√3
Therefore the value of tan(B) = 1/√3
Answer:
Option C is correct.
Step-by-step explanation:
tan (B) = Perpendicular / Base
For angle B:
Perpendicular = 5
Base = 5√3
tan (B) = Perpendicular / Base
tan (B) = 5/5√3
tan (B) = 1/√3
So, Option C is correct.
Drag the tiles to the correct boxes to complete the pairs.
Match each expression to its equivalent form.
Answer:
x² - 16 ⇒ (x + 4)(x - 4)
(2x + 1)³ ⇒ 8x³ + 12x² + 6x + 1
(2x + 3y)² ⇒ 4x² + 12xy + 9y²
x³ + 8y³ ⇒ (x + 2y)(x² - 2xy + 4y²)
Step-by-step explanation:
* Lets explain how to solve the problem
# x² - 16
∵ x² - 16 is a difference of two squares
- Its factorization is two brackets with same terms and different
middle signs
- To factorize it find the square root of each term
∵ √x² = x and √16 = 4
∴ The terms of each brackets are x and 4 and the bracket have
different middle signs
∴ x² - 16 = (x + 4)(x - 4)
* x² - 16 ⇒ (x + 4)(x - 4)
# (2x + 1)³
- To solve the bracket we will separate (2x + 1)³ to (2x + 1)(2x + 1)²
∵ (2x + 1)² = (2x)(2x) + 2(2x)(1) + (1)(1) = 4x² + 4x + 1
∴ (2x + 1)³ = (2x + 1)(4x² + 4x + 1)
∵ (2x + 1)(4x² + 4x + 1) = (2x)(4x²) + (2x)(4x) + (2x)(1) + (1)(4x²) + (1)(4x) + (1)(1)
∴ (2x + 1)(4x² + 4x + 1) = 8x³ + 8x² + 2x + 4x² + 4x + 1 ⇒ add like terms
∴ (2x + 1)(4x² + 4x + 1) = 8x³ + (8x² + 4x²) + (2x + 4x) + 1
∴ (2x + 1)(4x² + 4x + 1) = 8x³ + 12x² + 6x + 1
∴ (2x + 1)³ = 8x³ + 12x² + 6x + 1
* (2x + 1)³ ⇒ 8x³ + 12x² + 6x + 1
# (2x + 3y)²
∵ (2x + 3y)² = (2x)(2x) + 2(2x)(3y) + (3y)(3y)
∴ (2x + 3y)² = 4x² + 12xy + 9y²
* (2x + 3y)² ⇒ 4x² + 12xy + 9y²
# x³ + 8y³
∵ x³ + 8y³ is the sum of two cubes
- Its factorization is binomial and trinomial
- The binomial is cub root the two terms
∵ ∛x³ = x and ∛8y³ = 2y
∴ The binomial is (x + 2y)
- We will make the trinomial from the binomial
- The first term is (x)² = x²
- The second term is (x)(2y) = 2xy with opposite sign of the middle
sign in the binomial
- The third term is (2y)² = 4y²
∴ x³ + 8y³ = (x + 2y)(x² - 2xy + 4y²)
* x³ + 8y³ ⇒ (x + 2y)(x² - 2xy + 4y²)
Solve by substitution. 3x+6y=21 -8x+y=63
What is the solution?
[tex]\bf \begin{cases} 3x+6y=21\\ \cline{1-1} -8x+y=63\\ \boxed{y}=63+8x \end{cases}~\hspace{7em}\stackrel{\textit{substituting on the 1st equation}}{3x+6\left( \boxed{63+8x} \right)}=21[/tex]
[tex]\bf 3x+378+48x=21\implies 51x+378=21\implies 51x=-357 \\\\\\ x=\cfrac{-357}{51}\implies \blacktriangleright x=-7 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{y=63+8x\implies }y=63+8(-7)\implies y=63-56\implies \blacktriangleright y=7 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (-7,7)~\hfill[/tex]
Tasha invests $5000 annually at 6% and an additional $5000 annually at 8%. Thomas invests $10000 annually at 7%. Which statement accurately compares the two investments if interest is compounded annually
Answer:
Answer:
Option B is correct.
Step-by-step explanation:
We will compare the interest earned by both.
Tasha: p = $5000
r = 6% or 0.06
n = 1
So, Amount after a year will be = = $5300
And amount the next year with p = 5300: 5300*1.06= $5618
Additional $5000 at 8%
Here the amount will be = =5400
Next year amount with p = 5400 : 5400*1.08 = $ 5832
Amount in total Tasha will have in 2 years = 5618+5832 = 11450
Thomas:
p = 10000
r = 7% or 0.07
n = 1
After a year the amount will be = =$10700
Amount Next year with p = 10700 : 10700*1.07 = $11449
*****Just after 1 year we can see that Tasha's total amount is high than Thomas. This means at the same consistent rate, each year Tasha's amount will always be higher than Thomas.
So, option B is correct. Tasha’s investment will yield more over many years because the amount invested at 8% causes the overall total to increase faster.
Answer:
B) Tasha’s investment will yield more over many years because the amount invested at 8% causes the overall total to increase faster.
Step-by-step explanation:
I just took the test on edge
Your favorite stock opened the day's trading at $44.17 per share. When trading closed for the day, your stock was priced at $38.41 per share. If you own 145 shares, what was your profit or loss that day?
Answer:
$835.20
Step-by-step explanation:
First you need to find out how many profit you had at first by multiplying 145 and $44.17.
So, 145*$44.17 = 6404.65
Then find out how much profit you had after it decreased by multiplying 145 and $38.41.
So, 145*$38.41 = 5569.45
Now to find how much profit you lost, you have to subtract $6,404.65 and $5,569.45.
$6,404.65 - $5,569.45 = $835.20
In parallelogram math, angle m = (3x+20) and angle T = (5x-4). Find angle A
Answer:
M=T = angle A
try it
then. find angle a the sum of palleogram is .... then 12+A=....
angle A=........
2 cos x +3 sin 2x = 0
answer in degrees
Answer:
If want just the approximated solutions in the interval from 0 to 360:
199.47
340.53
90
270
If you want all the approximated solutions:
199.47+360k
340.53+360k
90+360k
270+360k
Step-by-step explanation:
2 cos(x)+3 sin(2x)=0
First step: Use double angle identity for sin(2x). That is, use, sin(2x)=2sin(x)cos(x).
2 cos(x)+3*2sin(x)cos(x)=0
2 cos(x)+ 6sin(x)cos(x)=0
Factor the 2cos(x) out, like so:
2cos(x)[ 1 + 3 sin(x)]=0
In order for this product to be zero, we must find when both factors are 0.
2cos(x)=0 or 1+3sin(x)=0
Let's do 2cos(x)=0 first.
2cos(x)=0
Divide both sides by 2:
cos(x)=0
So the x-coordinate is 0 on the unit at x=90 deg and x=270 deg (in the first rotation).
Let's do 1+3sin(x)=0.
1+3sin(x)=0
Subtract 1 on both sides:
3sin(x)=-1
Divide both sides by 3:
sin(x)=-1/3
Unfortunately this is not on the unit circle so I'm just going to take sin^-1 or arsin on both sides (this is the same thing sin^-1 or arsin).
x=arcsin(-1/3)=-19.47 degrees
So that means -(-19.47)+180 is also a solution so 19.47+180=199.47 .
And that 360+-19.47 is another so 360+-19.47=340.53 .
So the solutions for [0,360] are
199.47
340.53
90
270
If you want all the solutions just add +360*k to each line where k is an integer.
Find the area of the shaded region.
Answer:
Area = 16
Step-by-step explanation:
The plan is to find the area of the large triangle (blue and white together) and subtract the white triangle's area.
Area of blue + white.
h = 8
b = 5 + 4
b = 9
Area = 1/2 * 8 * 9
Area = 1/2 * 72
Area = 36
===============
Area of white.
h = 8
b = 5
Area = 1/2 * 8 * 5
Area = 20
==============
Area of the shaded region (blue) = Area of both triangles - Area of the white
Shaded = 36 - 20
Shaded = 16
Select the description that is true of the equation 3x + y =9
x-intercept equals
x-intercept equals
y-intercept equals 3
y-intercept equals 9
Answer:
x-intercept equals 3
y-intercept equals 9
Step-by-step explanation:
we have
[tex]3x+y=9[/tex]
step 1
Find the y-intercept
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
substitute in the equation and solve for y
[tex]3(0)+y=9[/tex]
[tex]y=9[/tex]
The y-intercept is the point (0,9)
step 2
Find the x-intercept
The x-intercept is the value of x when the value of y is equal to zero
so
For y=0
substitute in the equation and solve for x
[tex]3x+0=9[/tex]
[tex]x=3[/tex]
The x-intercept is the point (3,0)
therefore
x-intercept equals 3
y-intercept equals 9