Answer:
x = arccos(3/4) + 2πn where n = 0,1,2,3,4, ....
Step-by-step explanation:
We can solve the equation 4cos(x) + 3 = 6 by isolating the cos(x) term on one side of the equation.
4cos(x) + 3 - 3 = 6 - 3
4cos(x) = 3
cos(x) = 3/4
Now we can find the solutions of the equation by finding the values of x that make cos(x) equal to 3/4. Since -π < x < π, we can find the solutions in the range of -π < x < π.
x = cos^-1(3/4) + 2πn, where n is an integer
x = cos^-1(3/4) + 2πn, where n = 0, 1, 2, ...
The solutions are x= cos^-1(3/4) and x = cos^-1(3/4) + 2π, x = cos^-1(3/4) + 4π
Keep in mind that cos^-1(3/4) is the inverse cosine function or arccos(3/4) so the final solution is x = arccos(3/4) + 2πn where n = 0,1,2,3,4, ....
Find the number of ways of choosing three points from the grid below, so that they form an isosceles right triangle.
There are 28 ways of choosing three points from the grid below, so that they form an isosceles right triangle.
What is an isosceles triangle?A triangle that has two equal lengths of sides and two equal measures of angles is called an isosceles triangle.
The grid figure is given in the attached image.
The given image displays seven triangles (counting the original 2).
There can be 7 x 4 = 28 isosceles right triangles,
since each has degree 4 rotational symmetry around the figure's center.
The complete figure is given in the image.
Therefore, there are 28 ways of choosing three points from the grid below.
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Please look at the picture and answer the question thank you
Answer:
[ 5, ∞ )
Step-by-step explanation:
brackets on the ends of the interval indicate x can equal the value inside the bracket
parenthesis on the ends of the interval indicate x cannot equal the value inside the parenthesis.
x ≥ 5
expressed in interval notation as
[ 5, ∞ )
What is the answer of this triangle congruence question.
The value of x in the triangles are 9.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
The triangles are congruent.
That means, their corresponding angles are also congruent.
In ΔJKL,
the sum of all the angles of the triangle is 180°.
So,
x²-2x + x + 29 + 3x + 52 = 180
x² + 2x - 99 = 0
Solving the quadratic equation,
x² +11x - 9x - 99 = 0.
x (x + 11) -9 (x + 11) = 0
x = 9 and x = -11
Here, we take x = 9.
Therefore, the value of x is 9.
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Samantha received a $100 gift card to an online store. She wants to purchase some bracelets that cost $15 each. There will be a $25 overnight shipping fee. How many bracelets can she buy?
Let u and v be two vectors in space with u =2i-j-2k and |v|| = 12. If u and v are parallel, then find the vector v.
Therefore , the solution of the given problem of vectors comes out to
be -25.
Why do they have the name "vectors"?An object with both magnitude and direction is referred to as a vector. A vector can be visualised geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.
Here,
Given:
lul=3,|v|=4 and |w|=5
Also, u+v+w=0
On squaring both sides, we get
=> u2+v2+w2+2(u.v+v.w+w.u) = 0
=> 32+42+52 +2(u.v+v.w+w.u) = 0
=> 9+16+25+2(u.v+v.w+w.u) = 0
=> u.vv.w+w.u
=> -50 = -25
Therefore , the solution of the given problem of vector comes out to
be -25.
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Use the circle Q shown below to answer the following questions:
4. Measure of arc AB = ______ 10. Measure of arc BAD = _____
5. Measure of arc DC = ______ 11. Measure of arc ADC = _____
6. Measure of arc BC = ______ 12. Measure of arc ACB = _____
7. Measure of arc AED =______ 13. Measure of arc ABD = _____
8. Measure of arc BD = ______ 14. Measure of arc CED = _____
9. Measure of arc AC =______ 15. Measure of arc BAC=_____
The measure of the arcs in relationship to the central angles measures are:
4. 40°
5. 50°
6. 90°
7. 180°
8. 140°
9. 130°
10. 220°
11. 230°
12. 320°
13. 180°
14. 310°
15. 270°
What is the Relationship between the Measure of the Central Angle and the Subtended Arc of a Circle?The relationship is that the measure of the central angle is the same as the measure of the arc it subtends in a circle.
4. Measure of arc AB = measure of central angle AOB
Substitute
Measure of arc AB = 40°
5. Measure of arc DC = measure of central angle DOC
Substitute
Measure of arc DC = 50°
6. Measure of arc BC = 180 - 40 - 50 = 90°
7. Measure of arc AED = 180°
8. Measure of arc BD = 90 + 50 = 140°
9. Measure of arc AC = 40 + 90 = 130°
10. Measure of arc BAD = 180 + 40 = 220°
11. Measure of arc ADC = 180 + 50 = 230°
12. Measure of arc ACB = 360 - 40 = 320°
13. Measure of arc ABD = 180°
14. Measure of arc CED = 360 - 50 = 310°
15. Measure of arc BAC = 40 + 180 + 50 = 270°
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Finding the Reflection Line On a coordinate plane, triangle 1 is reflected across the x-axis to form triangle 4, is reflected across a diagonal to form triangle 3, is reflected across the y-axis to form triangle 2. Use the figure to complete the statements. Triangle 1 is the image of triangle 2 reflected over the . Triangle 2 is the image of triangle 3 reflected over the . Reflecting triangle 4 over the y-axis results in triangle .
The statements are Triangle 1 is the image of triangle 2 reflected over the Y axis, Triangle 2 is the image of triangle 3 reflected over the X axis and Reflecting triangle 4 over the y-axis results in triangle 3.
What is Reflection?Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.
We have four triangles in the figure given.
So reflection of a figure results in the mirror image of the figure.
Line of reflection is the line through which a figure is reflected.
Line of reflection of the triangles 1 and 2 is the Y axis.
So Triangle 1 is the image of triangle 2 reflected over the Y axis.
Line of reflection of triangles 2 and 3 is X axis.
So Triangle 2 is the image of triangle 3 reflected over the X axis.
Also line of reflection is y axis for triangles 4 and 3.
So Reflecting triangle 4 over the y-axis results in triangle 3.
Hence using the concept of line of reflections, Triangle 1 is the image of triangle 2 reflected over the Y axis, Triangle 2 is the image of triangle 3 reflected over the X axis and Reflecting triangle 4 over the y-axis results in triangle 3.
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Write 8,400,000 m3 as a fraction of 0.012 km3. Give your answer in its simplest form.
what is the fraction of 0.3
Answer:
3/10
This is to reach the character limit
Answer:
3/10
Step-by-step explanation:
0.3 =
3/10 ==> since there is a non-zero number before the decimal, the
number is being divided by 10. If there was an extra 0, add a 0 to 10 and divide the number by 100. (0.3 = 3/10. 0.03 = 3/100)
Add another 0 to make 0.003, which is 3/1000 (add an extra 0 to 100 to make 1000, 10->100->1000).
Find The Missing Number
1. 1:2=4N
2: 3:8=N:16
3.15:20=30:N
4.N:25=2:5
5.10:N=40:80
The missing number of all the ratios are given below.
What is ratio?The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
The ratios are given.
1. 1:2=4:N
2: 3:8=N:16
3.15:20=30:N
4.N:25=2:5
5.10:N=40:80
p:q can be written as p/q.
To find the missing number:
1. 1:2=4:N
1/2 = 4/N
So, N = 8
2: 3:8=N:16
So, N = 6
3.15:20=30:N
So, N = 40
4.N:25=2:5
So, N = 10
5.10:N=40:80
N = 20
Therefore, all the missing numbers are given above.
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Consider the quadratic equation x squared minus 7 x minus 18 equals 0
Find the solutions by factoring.
x = -9, x = 2
x = -2, x = 9
x = -6, x = 3
x = -3, x = 6
Answer:
x = -2, x = 9
Step-by-step explanation:
Given quadratic equation:
[tex]x^2-7x-18=0[/tex]
To factor a quadratic in the form ax²+bx+c, first find two numbers that multiply to ac and sum to b.
[tex]\implies ac=1 \cdot -18=-18[/tex]
[tex]\implies b=-7[/tex]
Therefore, the two numbers are: -9 and 2.
Rewrite b as the sum of these two numbers:
[tex]\implies x^2-9x+2x-18=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-9)+2(x-9)=0[/tex]
Factor out the common term (x - 9):
[tex]\implies (x+2)(x-9)=0[/tex]
Apply the zero-product property:
[tex]\implies x+2=0 \implies x=-2[/tex]
[tex]\implies x-9=0 \implies x=9[/tex]
Therefore, the solutions to the given quadratic equation are:
x = -2, x = 9ayo earns 50,000 monthly and he spends 35,000 altogether. if he saves the rest, find the percentage of his savings
Answer:
30%.
Step-by-step explanation:
Ayo earns 50,000 monthly and he spends 35,000 altogether, so he saves the rest of his income. To find the percentage of his savings, we can divide his savings by his total income and multiply by 100.
His total income is 50,000
His total expenditure is 35,000
His savings = total income - total expenditure = 50,000-35,000 = 15,000
So the percentage of his savings = (savings / total income) x 100 = (15,000 / 50,000) x 100 = 0.3 x 100 = 30%
Therefore, Ayo's savings percentage is 30%.
NO LINKS!!! NOT MULTIPLE CHOICE!!!
Find a counterexample to show that the following conjectures are false:
a. The sum of two numbers is always greater than zero.
b. The sum of a positive number and a negative number is always positive.
c. If a figure has four sides, then it is a rectangle.
Answer: a. The sum of two numbers is always greater than zero.
Step-by-step explanation:
A counterexample to this conjecture would be when the two numbers are both negative. For example, the sum of -5 and -3 is -8, which is less than zero.
b. The sum of a positive number and a negative number is always positive.
A counterexample to this conjecture would be when the negative number is greater than the positive number. For example, the sum of 5 and -6 is -1, which is less than zero.
c. If a figure has four sides, then it is a rectangle.
A counterexample to this conjecture would be a square. A square has four sides, but it is not a rectangle because all of its angles are 90 degrees while a rectangle has four right angles.
It's good to keep in mind that a conjecture is a statement that is made based on observations and that it hasn't been proven yet, therefore a counterexample can be used to show that the conjecture is false.
Answer:
a) -5 + 1 = -4
b) 2 + (-10) = -8
c) A scalene trapezium.
Step-by-step explanation:
A counterexample is proof that a conjecture is false.
Part aGiven conjecture:
The sum of two numbers is always greater than zero.If one of the numbers is negative, and its absolute value is equal to or greater than the value of the positive number, the result will always be equal to or less than zero.
Counterexample:
-5 + 1 = -4As -4 is less than zero, this proves that the conjecture is false.
Part bGiven conjecture:
The sum of a positive number and a negative number is always positive.If the absolute value of the negative number is greater than the value of the positive number, the result will always be negative.
Counterexample:
2 + (-10) = -8As -8 is negative, this proves that the conjecture is false.
Part cGiven conjecture:
If a figure has four sides, then it is a rectangle.Counterexample:
A scalene trapezium.The interior angles of a rectangle are congruent (90°).
A scalene trapezium has four sides, but as its interior angles are all different, it is not a rectangle. This proves that the conjecture is false.
How many square feet of outdoor carpet will we need for this hole?
The area of carpet that will be needed for the hole is 6 square feet
What is area off a rectangle?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
The hole has a rectangular shape.
Therefore the area of the hole =l×w
length = 3ft
width = 2ft
area of the hole = 3×2 = 6 squared feet
therefore the area of the carpet that will be needed for the hole is 6 square feet
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Assume you are given the set B where B = {2,4,6,8,10}. Consider this statement.
Answer:false
Step-by-step explanation:
1.5 (-2)^(n-1) > -6000
Find n (n is integer)
Answer:
что там а? я даже не знаю hehe
In △ABC, the length of median BM is half the length of side AB and ∠ABM measures 40°. Find m∠ABC.
Answer:
m∠ABC = 180.
Step-by-step explanation:
In a triangle, the median to the side opposite the largest angle bisects that angle.
Since BM is a median, it bisects ∠C, the angle opposite side AB.
Let's call the angle opposite side AB angle x, so x/2 = 40.
Therefore, x = 80
Since a triangle has 180 degree, then if we add all the angles in the triangle we get:
m∠ABC = m∠BAC + m∠BCA + m∠CAB = x + (180-x) + (180-x) =180
So m∠ABC = 180
In an elastic collision, momentum and kinetic energy are conserved.T or F?
Answer: True. In an elastic collision, both momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy of the system before the collision is equal to the total momentum and total kinetic energy of the system after the collision.
Step-by-step explanation:
Andrew is conducting a survey to determine the most common eye color. Why doesn't he use mode, not the mean or the median, to analyze his results
The mode is the most common value in a set of data and is typically used for categorical data such as eye color.
Why is the Mode used and not the Mean or Median?The mean and median, on the other hand, are measures of central tendency used for numerical data.
Since eye color is a categorical variable, the mode would be the appropriate measure to use to determine the most common eye color in Andrew's survey.
It can be seen that the mean, median, and mode are the most common measures of central tendency for a set of data, and typically, you use the mode with categorical, ordinal, and discrete data and this is the appropriate data collection that Andrew should use to find the most common eye color and not mean or median.
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Find the domain of fg f(x) = x + 2 g(x) =1/x + 2
Answer:
x+2 domain: (-infiniy, +infinity) or -infinity<x<infinity
1/x +2 domain: (-infinity, 0) and (0, infinity) or 0<x<0
8 minus the product of 9 and r in algebraic expression
The algebraic expression of 8 minus the product of 9 and r is 8 - 9r
How to determine the algebraic expressionFrom the question, we have the following parameters that can be used in our computation:
8 minus the product of 9 and r
The product of 9 and r can be represented as 9r
So, we have the following representation
8 minus 9r
Minus means -
So, we have
8 - 9r
Hence, the expression is 8 - 9r
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What is the value of X
Answer:
x = 17
Step-by-step explanation:
The sum of the interior angles of a triangle is 180
x + 17 + 4x - 34 + 6x + 10 = 180 Combine like terms
11x -7 = 180 Add 7 to both sides
11x - 7 + 7 = 180 + 7
11x = 187 Divide both sides by 11
[tex]\frac{11x}{11}[/tex] = [tex]\frac{187}{11}[/tex]
x = 17
Answer:
the answer is x=17 because the triangle is isosceles
The expression 3 1/2x + 18 represents the perimeter of the rectangle shown. Write an expression that represents the length of the strangle
Answer:
L = 1/2x
Step-by-step explanation:
The perimeter of a rectangle is the sum of all four sides. In this case, the perimeter is represented by the expression 3 1/2x + 18.
Since the perimeter of a rectangle is the sum of the lengths of all four sides, so, if we know the perimeter and one side's length, we can find the length of the other side.
We can use the expression 3 1/2x + 18 to find the length of the rectangle.
Let's assume that the length of the rectangle is represented by the variable L and the width is represented by the variable W.
So we know that the perimeter of the rectangle is represented by the expression 3 1/2x + 18 and the perimeter of a rectangle is 2(L + W)
So we can write the equation
2(L + W) = 3 1/2x + 18
Expanding the left side of the equation:
2L + 2W = 3 1/2x + 18
Now we know that one of the sides of the rectangle is 1/2x so
L = 1/2x
Therefore, the expression that represents the length of the rectangle is 1/2x
The following are the ratings of males by females in an experiment involving speed dating. Use the given data to construct a boxplot and identify the 5-number summary. 1.0 1.5 2.5 3.0 4.0 4.0 4.5 4.5 4.5 4.5 4.5 5.0 5.0 5.5 5.5 5.5 6.0 6.0 6.5 6.5
I question below and select the best answer choice. *
What property was used to simplify the expression?
12 × 47 = 12 × (40 + 7)
= 12 X 40 + 12 × 7
= 480 + 84
= 564
The property used to simplify the expression is 12 × 47 = 12 × (40 + 7) is distributive property.
What is distributive property?The distributive property states that an expression which is given in form of x (y + z) can be solved as x × (y + z) = xy + xz.
In other words, distributive property is a rule that states that you can distribute the terms of an expression.
Therefore, let's check the property used on the expression as follows:
12 × 47 = 12 × (40 + 7)
12 × 40 + 12 × 7
480 + 84
564
Hence, the property used on the expression is distributive property.
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NASA’s research center has seven crates of hard-shell space suits. Each crate has two suits. If three suits crack during pressure testing, how many suits are left that are NOT cracked?
A man jogs from P to Q to M to R to Q back to P at an average speed of 150 yards per minute. To the nearest tenth of a minute, about how long does it take him to travel the entire distance
The time needed to travel the entire distance is given as follows:
1.27 minutes.
How to obtain the time it took to travel the entire distance?Before obtaining the time, we need to obtain the entire distance.
The distance is the perimeter of the rectangle, which is the sum of all the outer side lengths of the right triangle.
The sides of the right triangle are given as follows:
40 yards and 70 yards.
Applying the Pythagorean Theorem, the length of the hypotenuse is given as follows:
h² = 40² + 70²
[tex]\sqrt{40^2 + 70^2}[/tex]
h = 80.6 yards.
Then the total distance is given as follows:
40 + 70 + 80.6 = 190.6 yards.
The time is given by the division of the distance by the velocity of 150 yards per minute, hence:
t = 190.6/150
t = 1.27 minutes.
Missing InformationThe problem is given by the image presented at the end of the answer.
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I need help with these questions
In mathematics, the value for x is 9.38 in Example 1 and 11.40 in Example 2.
What are the value signifies?
The value in mathematics refers to the numerical representation of a quantity or concept. It represents the numerical magnitude of a mathematical expression, equation, or quantity.
For example, in the expression 2 + 3 = 5, the value of 2, 3, and 5 all represent specific numerical magnitudes. The value of a variable, such as x or y, can change depending on the context or equation it is used in, but it still represents a specific numerical value.
Values can be represented in different forms, such as integers, fractions, decimals, or real numbers, and they are used to perform mathematical operations and solve mathematical problems.
a) Example 1
AB is a diameter
PQ is a chord
AO = 13
AO is perpendicular to PQ (2AP=AQ)
In Δ APO
[tex](AO)^2 =(AP)^2+ (PO)^2[/tex]
[tex](13)^2 = (9)^2 + X^2[/tex]
[tex]169 = 81 +X^2[/tex]
X^2 = 169-81
X^2 = 88
X = √88
X = 9.38
As a consequence, 9.38 is equal to x.
b) Example 2
LM = 18
KN = 7
LK = ?
LN = 9
In Δ LKN:
[tex]X^2 = (KN)^2 + (LN)^2[/tex]
[tex]X^2 = (7)^2 + (9)^2[/tex]
X^2 = 49 + 81
X^2 = 130
X =√ 130
X = 11.40
As a consequence, 11.40 is equal to x.
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Tell whether (2, 23) is solution of y = 9x + 5.
Answer:
Yes.
(2, 23) is a solution for the equation y = 9x + 5
Step-by-step explanation:
(2, 23) means that for an x value of 2, the y value should be 23
The equation is y = 9x + 5
Substitute x = 2 on the right side
y = 9(2) + 5 = 18 + 5 = 23
Since this matches the given value of y =23, we can conclude that
(2, 23) is a solution for y = 9x + 5
Anyone please help me asap???!!((:
Answer:
B
Step-by-step explanation:
They put the decimal point in the wrong place.
Answer:
the answer is that 2.5 - 0.8 = 1.7
