Answer:
D
Step-by-step explanation:
If those two functions are the factors of a quadratic, then each of them can be equated to 0 to find the roots. Sometimes the roots are called the zeros.
2x - 5 = 0 Add 5 to both sides
2x - 5 + 5 = 0 + 5 Combine
2x = 5 Divide both sides by 2
2x/2 = 5/2
x = 5/2
You don't really have to find the other factor's 0 point. There is only 1 option that makes x = 5/2. On a test, it is important to take short cuts and save time. I'll find the other root anyway because this is not a test.
3x + 4 = 0 Subtract 4 from both sides
3x + 4-4 = 0 - 4 Combine
3x = - 4 Divide both sides by 3
3x/3 = - 4/3
x = - 4/3
f(x)= x³ lf x=-2₁ y =?
If x=-1, y =?
If x= 0, y =?
Answer:
Step-by-step explanation:
if x= -2, f(x)= -8
x= -1, y= -1
x=0, y=0
Kelley writes the expression n 2 to model the phrase "xander studied two more hours than nandini." which best explains the accuracy of kelley’s expression? it is accurate. in the phrase "two more hours than nandini," "two" is "2," "more" is " ," and nandini’s study time is unknown or "n," so 2 n or n 2 are correct translations. it is inaccurate. in the phrase "two more hours than nandini," "two" is "2," "more" is " ," and nandini’s study time is unknown or "n," so 2 n is the correct translation. it is inaccurate. in the phrase "two more hours than nandini," "two" is "2," "more than" is ">," and nandini’s study time is unknown or "n," so 2 greater-than n is the correct translation. it is inaccurate. in the phrase "two more hours than nandini," "two" is "2," "more than" is "<," and nandini’s study time is unknown or "n," so 2 less-than n is the correct translation.
It is accurate. In the phrase “two more hours than Nandini,” n + 2 are correct translations. Then the correct option is A.
What is Algebra?Algebra is used to analyze mathematical symbols, and logic is used to manipulate those symbols.
As an example, Kelley models the sentence "Xander studied two more hours than Nandini" using the equation n + 2.
Consequently, the following will describe Kelley's expression's accuracy the best:
It is precise. Since "two" is translated as "2," "more" as "+," and "Nandini's study time is unknown or "n," 2 + n or n + 2 are the appropriate translations for the sentence "two more hours than Nandini."
So, option A is the best choice.
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I understand that the question you are looking for is :
Kelley writes the expression n + 2 to model the phrase “Xander studied two more hours than Nandini.” Which best explains the accuracy of Kelley’s expression?
It is accurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more” is “+,” and Nandini’s study time is unknown or “n,” so 2 + n or n + 2 are correct translations.
It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more” is “+,” and Nandini’s study time is unknown or “n,” so 2 + n is the correct translation.
It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more than” is “>,” and Nandini’s study time is unknown or “n,” so 2 greater-than n is the correct translation.
It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more than” is “<,” and Nandini’s study time is unknown or “n,” so 2 less-than n is the correct translation.
Show your work and hurry please
Answer:
15
Step-by-step explanation:
Note: Take note , absolute value will give the magnitude of the value. (Which means ignoring the + / - signs.)
Eg. | - 19 | = 19
Therefore,
[tex] \frac{12(30 - (9 + {4}^{2})) }{10 - | - 6| } \\ = \frac{12(30 - (9 + 16))}{10 - 6} \\ = \frac{12(30 - 25)}{4} \\ = \frac{12(5)}{4} \\ = \frac{60}{4} \\ = 15[/tex]
Geometry: fill in the blanks, ASAP! It’s urgent
Answer:
3. 125
4. 115
5. m<1 = 70, m<2 = 55, m<3 = 55
6. m<2 = 50, m<3 = 50, m<4 = 80, m<6 = 130
The functions f(x) and g(x) are graphed.
f(x)
324
2
-6-5-4-3-2-1₁.
297 49
-2+
-3
-4
g(x)
1 2 3 4 5 6 x
Which represents where f(x) = g(x)?
Of(0) = g(0) and f(2)= g(2)
Of(2)= g(0) and f(0) = g(4)
Of(2)= g(0) and f(4) = g(2)
Of(2)= g(4) and f(1) = g(1)
Answer: Option 1
Step-by-step explanation:
The graphs intersect at x=0 and x=2.
The answer that represents the point where f(x) = g(x) is; A: f(2) = g(2) and f(0) = g(0)
What are functions?A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math.
Given is a graph we need to find the point of intersection where f(x) = g(x)
How to find the coordinates of Intersection :-
From the attached graph, we see that is represents the relationship between the functions f(x) and g(x).
Now, the coordinates of the points where f(x) = g(x) will be the coordinates of the points where both graphs intersect.
The first point of intersection, we see that;
f(0) = g(0) = 4
Second point shows;
f(2) = g(2) = 0
Thus, we can conclude that;
f(2) = g(2) and f(0) = g(0)
Hence, the answer that represents the point where f(x) = g(x) is; A: f(2) = g(2) and f(0) = g(0)
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A shop is having a 10% off sale. Find the sale price of a cap which normally costs $12?
Answer: $10.8
Step-by-step explanation: To do this, we need to find 90% of $12 because the cap is 10% off. We can do this by multiplying 12 by 0.9. 12 x0.9 = 10.8.
(06.01) evaluate the expression 34 ÷ (14 − 5) × 2. numerical answers expected! answer for blank 1:
Answer:
1.89
Step-by-step explanation:
34 ÷ (14 − 5) × 2
34 ÷ (9) × 2
34 ÷ 18
1.89
Numerical expression:
numerical expression is a phrase involving numbers.
In mathematics, a numerical expression is a set of numbers that have been written together by utilizing arithmetic operators addition, subtraction, multiplication, and division.
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By evaluating the expression 34 ÷ (14 − 5) × 2 we get = 1.89
What is BODMAS ?Children can use the acronym BODMAS to help them remember the proper sequence to carry out mathematical operations when solving problems. The abbreviation BODMAS stands for B-Brackets, O-Orders (powers/indices or roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction.
What is numerical expression?A numerical expression is a sentence that uses numbers. A numerical expression in mathematics is a group of integers that have been combined using the addition, subtraction, multiplication, and division arithmetic operators.
According to the given Information :Appling the BODMAS
= 34 ÷ (14 − 5) × 2
= 34 ÷ (9) × 2
= 34 ÷ 18
= 1.89
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Consider two forces of 17 and 42 pounds both acting in the horizontal direction on a single object. find the resultant force acting on the object. magnitude = direction angle =
The forces have a magnitude of 59 pounds, and their direction angles are zero.
What is the magnitude of force?The total amount of forces exerted on an object is referred to as the magnitude of force. The strength of the force increases when all the forces are pulling in the same direction. The force's strength reduces when forces are exerted on an item from different angles.When two forces operating on a body in opposite directions along the same line of action are equal in magnitude, they cancel one another out. When two forces operating on a body in opposite directions along the same line of action are equal in magnitude, they cancel one another out.According to this formula, the amount of net force acting on an item is equal to the mass times the acceleration of the object.Magnitude is a term that refers to size or importance. The depth of the Grand Canyon serves as an illustration of magnitude. The scope of the hunger crisis in the world serves as an illustration of magnitude. A measurement of the energy released by an earthquake, as shown on the Richter scale (geology).Two forces of 17 and 42 pounds act horizontally on an object.
i.e
F1 = 17 pounds
F2 = 42 pounds
As the magnitude of the force represents the sum of all the forces
The direction is the same
Magnitude : 17 + 42 = 59 pounds
The Direction angles : 0
As they have the same direction so angle will be 0.
The forces have a magnitude of 59 pounds, and their direction angles are zero.
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Answer:59 and 0
Step-by-step explanation:
EDGE
a.) 6(x+2) = 5(x-y)
b.) 5(a-2x) = 9(x+1)
make x the subject
a) 6x + 12 = 5x - 5y
6x-5x = -5y-12
x = -5y-12
b) 5a-10x = 9x+9
-10x-9x = 9-5a
-19x = 9-5a
x = 9-5a/-19
Show that the curve x = 7 cos(t), y = 4 sin(t) cos(t) has two tangents at (0, 0) and find their equations
The equations with tangents at (0,0) are [tex]y = \frac{4}{7} x[/tex] and
[tex]y = -\frac{4}{7} x[/tex].
In this question,
The curves are x = 7 cos(t), y = 4 sin(t) cos(t)
Two tangents at (0, 0)
In this case, the parametric derivative of x and y are expressed in terms of t.
The first derivative dy/dx can be expressed as
[tex]\frac{dy}{dx}=\frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]
Now, dy/dt is obtained by differentiate y with respect to t,
[tex]\frac{dy}{dt}= 4[cos(t)(cos(t))+sin(t)(-sin(t))][/tex]
⇒ [tex]\frac{dy}{dt}= 4[cos^{2} (t)-sin^{2} (t)][/tex]
Now, dx/dt is obtained by differentiate x with respect to t,
[tex]\frac{dx}{dt} =7(-sin(t))[/tex]
⇒ [tex]\frac{dx}{dt} =-7sin(t)[/tex]
Thus, [tex]\frac{dy}{dx}=\frac{4[cos^{2}(t)-sin^{2}(t ) ]}{-7sin(t)}[/tex]
At (0,0) x = 0 and y = 0, Then
0 = 7 cos(t)
0 = 4 sin(t) cos(t)
and
cos(t) = 0
sin(t) cos(t) = 0
There are two values between -π and π which satisfy these equations simultaneously are
t = π/2
t = -π/2
The equation of a straight line given a point and its slope is
y-y₀ = m(x-x₀)
The two tangents lies at (0,0), so the equation becomes
y = mx
Then the two straight lines will be
y = m₁x and
y = m₂x
For t = π/2,
[tex]m_1=\frac{dy}{dx}=\frac{4[cos^{2}(\frac{\pi }{2} )-sin^{2}(\frac{\pi }{2} ) ]}{-7sin(\frac{\pi }{2} )}[/tex]
⇒ [tex]m_1=-\frac{4[0-1]}{7(1)}[/tex]
⇒ [tex]m_1=\frac{4}{7}[/tex]
For t = -π/2,
[tex]m_2=\frac{dy}{dx}=\frac{4[cos^{2}(-\frac{\pi }{2} )-sin^{2}(-\frac{\pi }{2} ) ]}{-7sin(-\frac{\pi }{2} )}[/tex]
⇒ [tex]m_2=-\frac{4[0-1]}{-7(1)}[/tex]
⇒ [tex]m_2=-\frac{4}{7}[/tex]
Thus the equations with tangents at (0,0) are [tex]y = \frac{4}{7} x[/tex] and
[tex]y = -\frac{4}{7} x[/tex].
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Select the correct answer from each drop-down menu.
-60
8-
6-
4
2-
-4-2 O
-2-
-4-
-6-
-8-
-N
4
2
-6
Quadrilateral 1 and quadrilateral 2 are polygons that can be mapped onto each other using similarity transformations. The
transformation that maps quadrilateral 1 onto quadrilateral 2 is a
followed by a dilation with a scale factor of
Reset
Nexts
The transformation that maps quadrilateral 1 onto quadrilateral 2 is a translation followed by a dilation with a scale factor of 2.
What is a transformation?A transformation can be defined as the movement of a point on a cartesian coordinate from its original (initial) position to a new location.
The types of transformation.In Geometry, there are different types of transformation and these include the following:
DilationReflectionRotationTranslationBased on similarity transformation of both quadrilateral 1 and quadrilateral 2, we can infer and logically deduce that the transformation which directly maps quadrilateral 1 onto quadrilateral 2 is a translation followed by a dilation with a scale factor of 2, as shown in the image attached below.
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how many ounces of water must be added 100 oz. of 60% iodine to produce a 55% solution ? round your answer to the nearest hundreth.
Answer:
10 ounces
Step-by-step explanation:
Answer:
9.09 ounces
Step-by-step explanation:
The added water can be calculated by writing an equation for the amount of iodine in the diluted solution.
SetupLet x represent the number of ounces of water added to the 60% solution. The total amount of iodine in the mixture is ...
0.60(100) +0(x) = 0.55(100+x) . . . . . ounces of iodine in the mix
SolutionSimplify the equation:
60 = 55 +0.55x
5 = 0.55x . . . . . . . subtract 55
x = 5/0.55 ≈ 9.09
9.09 ounces of pure water must be added to produce a 55% solution.
Which of the following fractions has the largest value 11/20 10/21 9/19 8/17 or 6/13
Answer:
11/20
Step-by-step explanation:
You could turn them all into equivalent fractions, but the common denominator would be 1,763,580. Yuck.
Look at the relationship for the numerators to the denominators. The only numerator that is more than half of its denominator is 11/20. Half of 20 would be 10 and 11 has a larger value than 10, so as a decimal, it would be more than .5. All of the other numerators are less than half, so that they have to less than .5.
If you changed all of the numbers to decimals, you would see that 11/20 has the largest value.
At time t, the position of a body moving along the s-axis is s=t^3 -18t^2+60t m. Find the displacement of the body from t=0 to t=3.
a. 56 m
b. 67 m
c. 105 m
d. 45 m
The displacement between t = 0 and t = 3 is 45 meters, so the correct option is d.
How to find the displacement?The displacement is defined as the difference between the final position and the initial position.
The initial position is what we get when we evaluate in t = 0.
s = 0^3 -18*0^2+60*0 = 0
The initial position is 0 meters.
The initial position is what we get when we evaluate in t = 3.
s = 3^3 -18*3^2+60*3 = 45
The final position is 45 meters.
Then the displacement is:
D = 45m - 0m = 45m
The correct option is d.
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A plane intersects one cone of a double-napped cone such that the plane is neither parallel to the generating line nor perpendicular to the axis. what conic section is formed?
The conic section will form an Ellipse.
What is Circle?The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape. The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is symmetrical in rotation around the center at all angles.
What is conic section?A conic section is a curve formed when the surface of a cone and a plane connect. The hyperbola, parabola, and ellipse are the three forms of conic sections; the circle is a special case of the ellipse, though historically it was occasionally referred to as a fourth type.
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radians and degrees
180° irc =
[tex]\Large\texttt{Answer}[/tex]
[tex]180^\circ=\pi\:radians}[/tex]
[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]
[tex]\Large\texttt{Process}[/tex]
⇨ For converting from degrees to radians, use this conversion factor:
[tex]\bf{\cfrac{\pi}{180}}[/tex]
⇨ Convert
[tex]\bf{\cfrac{180}{1}\times\cfrac{\pi}{180}}[/tex]
⇨ The 180s cancel out, and we have:
[tex]\pi[/tex]
Hence
[tex]\bf{180^\circ=\pi\:radians}[/tex]
Hope that helped
Find the coordinates of the vertices of the figure after the given transformation: T<−5,−2>
The vertices of the figure after the transformation: T<−5, −2>; 5 units left and 2 units down is X'(-3, -3), V'(-4, 0), E'(-1, -1), K'(0, -5)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformations are transformation that preserve the shape and size of a figure such are reflection, rotation and translation.
The vertices of the figure after the transformation: T<−5, −2>; 5 units left and 2 units down is X'(-3, -3), V'(-4, 0), E'(-1, -1), K'(0, -5)
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y=4x−5 y=2x+3 Is (4,11)(4,11)left parenthesis, 4, comma, 11, right parenthesis a solution of the system?
The solution to the systems if equation y = 4x - 5, y = 2x + 3 is (x, y) = (4, 11)
Equationy = 4x - 5
y = 2x + 3
Equation both equations4x - 5 = 2x + 3
collect like terms4x - 2x = 3 + 5
2x = 8
divide both sides by 2x = 8/2
x = 4
Substitute x = 4 intoy = 4x - 5
= 4(4) - 5
= 16 - 5
y = 11
Therefore, the solution to the system of be equation is x = 4 and y = 11
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what book has the solution in it?
Answer:
Book 3
Step-by-step explanation:
So we have four statements:
1: Book 1 or Book 2
2: Book 3 or Book 4
3: Book 4
4: Not Book 3
We also have the condition that only 1 of the statements are correct, and more important, the other 3 are incorrect.
So it may be a bit difficult to see at first, but the solution, has to be book 3. The reason for this is if we assume statement 1, statement 2, or statement 3 is true, that would imply that the statement 4 is false, meaning the solution is in book 3.
If we assume that statement 2 is true, then statement 4 is false, meaning that book 3 has the solution, which aligns statement 2. It also aligns with statement 1 being false, because it's not book 1 or 2, and it also aligns with statement 3 being false, because the solution is not in book 4.
Let's look at why assuming any other statement to be true, leads to contradictions.
So let's assume the first statement is true, this means the solution is book 1 or 2. But this means the statement 4 is false, meaning book 3 has the solution. This contradicts the first statement which we assume is true, thus the first statement is not true.
Let's now assume the third statement is true, this means statement four is false meaning it's book 3, but this contradicts the third statement which says it's book 4. Thus this statement cannot be true
Let's assume the last option is true, this means book 3 has no solution, and since all the other are false, book 4 has no solution, book 3 or 4 has no solution, book 1 or 2 has no solution either. This means that none of the books have solutions, and assuming one of the books does have a solution, this statement cannot be true.
X
-3
-1
1
3
f(x) = -x + 7
f(x)
8
2323
20
6
Determine the input that would give an output value of
W/N!
2
X=
=-3x+7
Answer: 19
Step-by-step explanation:
Multiplying both sides of the equation by [tex]-3[/tex] gives that [tex]x=19[/tex].
.
y = x2 + 3
y = x + 5
A rope that is 245cm long is cut into three pieces. The ratio of the lengths of the first piece to the second piece is 2/3, and the ratio of the lenghts of the second piece to the third piece is 4/5. What is the length of the longest of the the three pieces?
The length of the longest piece of the cut rope is; 105 cm
How to work with ratios?We are given that;
Length of rope = 245 cm
We need to make the ratio of second piece equal in both the ratio to find the ratio of all three pieces.
2:3
4:5
Multiply 1st ratio by 4 and 2nd ratio by 3:
Now, the ratio becomes: 8:12 and 12:15
And the ratio of three pieces can be represented as:
8: 12: 15, this ratio is the first piece: second piece: third piece
Thus;
8x + 12x + 15x = 245
35x = 245
x = 245/35
So, the pieces lengths will be;
First piece = 8 * 7 = 56 cm
Second piece = 12 * 7 = 84 cm
Third piece = 15 * 7 = 105 cm
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Can someone please help me with these problems and show work, if the answer isn’t with work I will remove your comment and you won’t get the points, please help
m∠B = 57.52°, m∠B = 70.8°, AB = 46.03 km and AC = 39.08 ft. This can be obtained using the Laws of cosine formula and Laws of sine formula.
Find the required angles and sides:Laws of cosine formula,In a triangle ABC,
⇒ a² = b² + c² - 2bc cos A
⇒ b² = a² + c² - 2ac cos B
⇒ c² = a² + b² - 2ab cos C
where a, b and c are sides of a triangle and A, B and C are the angles of a triangle.
Laws of sine formula,In a triangle ABC,
⇒ [tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]
where a, b and c are sides of a triangle and A, B and C are the angles of a triangle.
In the question we can use the laws of cosine formula and laws of sine formula,
5) Given that,
AB = c = 13 km
AC = b = 21 km
m∠A = 91°
By using Laws of cosine formula,
⇒ a² = b² + c² - 2bc cos A
a² = 21² + 13² - 2(21)(13) cos 91°
a² = 441 + 169 - 546 (-0.0174524064)
a² = 610 + 9.52901391 = 619.529014
⇒ a = 24.89 km
By using Laws of sine formula,
⇒ [tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]
sin 91°/24.89 = sin B/21
sin B = 0.999847695×21/24.89 = 0.843583833
⇒ m∠B = 57.52°
6) Given that,
AB = c = 11 cm
BC = a = 13 cm
AC = b = 14 cm
By using Laws of cosine formula,
⇒ b² = a² + c² - 2ac cos B
14² = 13² + 11² - 2(13)(11) cos B
196 = 169 + 121 - 286 cos B
196 = 290 - 286 cos B
cos B = 94/286
cos B = 0.328671329
⇒ m∠B = 70.8°
7) Given that,
AC = b = 24 km
BC = a = 26 km
m∠C = 134°
By using Laws of cosine formula,
⇒ c² = a² + b² - 2ab cos C
c² = 26² + 24² - 2(26)(24) cos 134°
c² = 676 + 576 - 1248 (-0.69465837)
c² = 1252 + 866.933646 = 2118.93365
⇒ AB = c = 46.03 km
8) Given that,
AB = c = 26 ft
BC = a = 21 ft
m∠B = 112°
By using Laws of cosine formula,
⇒ b² = a² + c² - 2ac cos B
b² = 21² + 26² - 2(21)(26) cos 112°
b² = 441 + 676 - 1096 (-0.374606593)
b² = 1117 + 410.568826 = 1527.56883
⇒ AC = b = 39.08 ft
Hence m∠B = 57.52°, m∠B = 70.8°, AB = 46.03 km and AC = 39.08 ft.
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After a rotation of 90° about the origin, the coordinates of the vertices of the image of a triangle are A'(5, 3), B'(–2, 1), and C'(1, 7). What are the coordinates of the vertices of the pre-image?
A -
B -
C -
The coordinates of the vertices of the preimages are A ( 3, 5) , B ( 1, 2) and C ( 7, -1)
How to determine the coordinatesIt is important to note the following about the 90 degrees rotation about the origin
A( x ,y ) becomes A' ( -y, x ) switch x and y and make y negativeNote that
A ( x, y) is the coordinates of the preimage
A' ( -y , x) is the coordinates after the said rotation about the origin
Converting the transformed coordinates to the preimage coordinates
For vertex A
A' ( 5, 3)
Compare with A' ( -y, x)
x = 3
y = -5
Substitute the values
A ( 3, 5 )
For vertex B
B' ( -2, 1)
Compare with B' ( -y, x)
x = 1
y = 2
Substitute the values
B ( 1, 2)
For vertex C
C' ( 1, 7)
Compare with C' ( -y, x)
x = 7
y = -1
Substitute the values
C ( 7, -1)
Thus, the coordinates of the vertices of the preimages are A ( 3, 5) , B ( 1, 2) and C ( 7, -1)
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A vector in the xy plane has a magnitude of 25 and an x component of 12. The angle it makes with the positive x axis is?
The angle it makes with the positive x axis in the xy plane is 61.3145 degrees.
In this question,
A normal vector to the plane is any vector that starts at a point in the plane and has a direction that is orthogonal (perpendicular) to the surface of the xy plane .
The magnitude of the xy plane, hypotenuse = 25 units
The x component of the xy plane, base = 12 units
Let θ be an angle, then the angle it makes with the positive x axis is
[tex]\theta = cos^{-1}(\frac{base}{hypotenuse} )[/tex]
⇒ [tex]\theta = cos^{-1}(\frac{12}{25} )[/tex]
⇒ [tex]\theta = cos^{-1}(0.48)[/tex]
⇒ [tex]\theta = 61.3145[/tex]
Hence we can conclude that the angle it makes with the positive x axis in the xy plane is 61.3145 degrees.
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Solve the equation by first using a sum-to-product formula. (enter your answers as a comma-separated list. let k be any integer. round terms to three
Solutions of the equation are 22.5°, 30°.
The given equation is sin(5θ) - sin(3θ) = cos(4θ)
We take left side of the equation
sin(5θ) - sin(3θ) = 2cos ((5θ+3θ)/2) (sin(5θ-3θ)/2)
=2cos4θsinθ [From sum-product identity]
Now we can write the equation as
2cos(4θ)sin(θ) = cos(4θ)
2cos(4θ)sinθ - cos(4θ) = 0
cos(4θ)[2sinθ - 1] = 0
cos(4θ) = 0
4θ = 90°
θ = 90/4
θ = 22.5°
and (2sinθ - 1) = 0
sinθ = 1/2
θ = 30°
Therefore, solutions of the equation are 22.5°, 30°
For more information about trigonometric identities, visit
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x =
30°
xo
90°
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Answer:
here is the answer
hope it helps u
happy to help
stay safe and healthy
step by step explanation :x=90(being adjacent angle)
now ,
x+30=180(being alternate angle)
x=180-30
x=150#
i think my answer ia wrong sorry -_-
Answer:
x=90
Step-by-step explanation:
x is on a straight line with 90 degrees (given angle measure angle)
you should do 180-90=90 to find that angle x is 90 degrees.
36) The ratio of Slade's stickers to Corbett's stickers is 5: 2. If Corbett
has 27 fewer stickers than Slade, how many stickers do they have
in all?
Answer: 63 Stickers
Step-by-step explanation:
Given information:
Ratio = Slade : Corbett = 5 : 2
Corbett has 27 fewer stickers
Set variables:
Let x be the number of stickers Corbett has
Let x + 27 be the number of stickers Slade has
Set proportional equation:
[tex]\frac{2}{5}~ =~\frac{x}{x~+~27}[/tex]
Cross multiply the system
[tex]2~(x~+~27)~=~5~*~x[/tex]
Simplify by distributive property
[tex]2~*~x~+~2~*~27~=~5x[/tex]
[tex]2x~+~54~=~5x[/tex]
Subtract 2x on both sides
[tex]2x~+~54~-~2x~=~5x~-~2x[/tex]
[tex]54~=~3x[/tex]
Divide 3 on both sides
[tex]54~/~3~=~3x~/~3[/tex]
[tex]{x=18}[/tex]
Add Corbett's and Slade's amounts together
Corbett = x = 18 stickers
Slade = x + 27 = 18 + 27 = 45 stickers
Total = 18 + 45 = [tex]\Large\boxed{63~Stickers}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
63 stickers
Step-by-step explanation:
Define the variables:
Let x be the number of stickers Slade had.If Corbett has 27 fewer stickers than Slade:Given ratio:
Slade : Corbett = 5 : 2
Substitute the defined variables:
[tex]\implies \sf x : x - 27 = 5 : 2[/tex]
[tex]\implies \sf \dfrac{x}{x-27}=\dfrac{5}{2}[/tex]
Cross multiply:
[tex]\implies \sf 2x=5(x-27)[/tex]
Expand:
[tex]\implies \sf 2x=5x-135[/tex]
Subtract 5x from both sides:
[tex]\implies \sf -3x=-135[/tex]
Multiply both sides by -1:
[tex]\implies \sf 3x=135[/tex]
Divide both sides by 3:
[tex]\implies \sf x=45[/tex]
Therefore, Slade had 45 stickers.
Substitute the found value of x into the expression for the number of stickers Corbett had:
[tex]\implies \sf 45-27=18[/tex]
Therefore, Corbett had 18 stickers.
Total number of stickers = 45 + 18 = 63
find unknown angles, value of 'x' and unknown sides:
HELP!!! MATH!!! 100 PTS !!!
Suppose f is a one-to-one, differentiable function and its inverse function f−1 is also differentiable. One can show, using implicit differentiation (do it!), that
(f^−1)′(x)=1/(f′(f^−1(x)))
Find (f^−1)′(6) if f(−1)=6 and f′(−1)=3/7.
Answer:
(f^−1)′(6)=1/(f'(f^-1(6)))
(f^−1)′(6)=1/(f'(f^-6)))
I hope this helps.