cosαcotβ+sinα is equivalent to cos(α+β)/cosβ for all values of α and β for which cos(α+β)/cosβ is defined. Therefore, the correct option 1.
Using the sum of angles formula for cosine and the definition of cotangent, we can derive the equivalent expression.
cos(α+β) = cosαcosβ - sinαsinβ (sum of angles formula for cosine)
cotβ = cosβ/sinβ (definition of cotangent)
Now, divide cos(α+β) by cosβ:
cos(α+β)/cosβ = (cosαcosβ - sinαsinβ)/cosβ
To simplify, we can separate the terms:
= (cosαcosβ)/cosβ - (sinαsinβ)/cosβ
= cosα(cotβ) - sinα(sinβ/cosβ)
Now, since tanβ = sinβ/cosβ, we can rewrite the expression as:
= cosαcotβ + sinα
Hence, the equivalent expression is cosαcotβ+sinα which corresponds to option 1.
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How do you factor polynomials with roots?
By setting y = 0 and factoring, we can determine the roots of other polynomial functions. Because there is only one value of x for which x - 3 = 0 and no values of x for which x2 + 3x + 9 = 0.
what are polynomials?A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.
By setting y = 0 and factoring, we can determine the roots of other polynomial functions. Because there is only one value of x for which x - 3 = 0 and no values of x for which x2 + 3x + 9 = 0, the equation y = x3 -27 = (x - 3)(x2 +3x2 + 9) has only one root (x = 3). (the discriminant is negative).
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What is the quotient StartFraction 15 p Superscript negative 4 Baseline q Superscript negative 6 Baseline Over negative 20 p Superscript negative 12 Baseline q Superscript negative 3 Baseline EndFraction in simplified form? Assume p not-equals 0, q not-equals 0.
Negative StartFraction 3 p Superscript 8 Baseline Over 4 q cubed EndFraction
Negative StartFraction 3 Over 4 p Superscript 16 Baseline q Superscript 9 Baseline EndFraction
Negative StartFraction p Superscript 8 Baseline Over 5 q cubed EndFraction
Negative StartFraction 1 Over 5 p Superscript 16 Baseline q Superscript 9 Baseline EndFraction
The quotient of the fraction is -3/4 * p²/q²
What is quotient?We should know that when a number is divided by another number, the result is the quotient of the number
We have to find the quotient of the following division, -3/4 * p²/q²
This implies that (15p⁻⁴q⁻⁶)/(-20p⁻¹²q⁻³)
Now, (15p⁻⁴q⁻⁶)/(-20p⁻¹²q⁻³) will give
3/4p[(⁻⁴(⁻¹²)]q²(⁻⁶-(⁻³)]
We know that all the terms in the expression are in product form, so we can treat them separately}
Hence we know the property of exponent as aˣ/aᵇ=a(ᵇ⁻ˣ]
Hence this implies that -3/4 * p⁶/q²
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how to solve 3x+5<14
Answer:
x<3
Step-by-step explanation:
3x+5<14
Your first step is to simplify the inequality.
To do this, always look to see if you can subtract any numbers from both sides to isolate a variable.
You can subtract 5 from both sides to isolate the 3x on one side.
After that, you will get 3x<9
Next, you must divide both sides by 3 to try and get x by itself, completing the inequality.
9/3 = 3
Your are left with: x<3
Done!
Answer:
x < 3
Step-by-step explanation:
3x + 5 < 14 subtract 5 from both sides
3x + 5 - 5 < 14 - 5
3x < 9 Divide both sides by 3
[tex]\frac{3x}{3}[/tex] < [tex]\frac{9}{3}[/tex]
x < 3
Use the origin as the center of dilation and the given scale factor to find the coordinates of the vertices of the image of the polygon.
K = 1/2
The vertices of the polygon in the graph have co-ordinates as J(6,3) K(2,3) L(2,-3) M(6,-3)
What are polygons?In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
Given here: A polygon JKLM
From the graph we can observe the co-ordinates as J(6,3) K(2,3) L(2,-3) M(6,-3)
Hence, the vertices of the polygon in the graph have co-ordinates as J(6,3) K(2,3) L(2,-3) M(6,-3)
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At noon, a tank contains 5 in of water. After several hours, it contained 3 in of water. What is the percent decrease of water in the tank?
Answer: To calculate the percent decrease of water in the tank, we can use the following formula:
Percent decrease = (Initial value - Final value) / Initial value x 100%
In this case, the initial value of water in the tank is 5 inches and the final value is 3 inches. So, the percent decrease is:
(5 - 3) / 5 x 100% = 2 / 5 x 100% = 40%
So, the percent decrease of water in the tank is 40%.
Step-by-step explanation:
Rachna ha nickel, dime, and quarter in her piggy bank. She ha $4. 65 altogether. She ha three more quarter han dime and twice a mahy nickel a quarter. How many quarter doe Rachna have?
Rachel has 0.41 quarters that can be obtained using the equation Q + D + N = T.
We can start by using the following equation to find the number of quarters Rachel has: Q + D + N = T
Where Q is the number of quarters, D is the number of dimes, N is the number of nickels, and T is the total amount of money in dollars. We know that T is $4.65, and we know that Rachel has twice as many nickels as quarters, and three more quarters than dimes.
Let's assume that Rachel has x number of quarters
So we can write the above equation as:
x + (x+3) + 2x = 4.65
4x+3 = 4.65
4x = 1.65
x = 0.4125
Rachel has 0.4125 quarters, Which is not possible as it is a decimal. So we need to round it off to the nearest whole number.
Rachel has 0.4125 quarters which is equivalent to o.41 quarters.
Therefore, Rachel has 0.41 quarters that can be obtained using the equation Q + D + N = T.
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A^15 • a^4 is equal to a^n. What is n
Therefore , the solution of the given problem of expressions comes out to be n= 19.
Definition of expressionsAddition, subtraction, division, and the term multiply are examples of numerical computations that are possible. The words are arranged as follows: An equation, a calculator, and an integer or variable A mathematical expression is mainly composed of constants, numbers, and processes (such as additions, subtraction, multiplying, or dividing, etc.). Contradictory claims or expressions and variable are possible.
Here,
Given : a^15.a^4
to find a^n
thus,
=>a^15.a^4 = a^n
=> a^(15+4) = a^n
=> a^19 = a^n
So, on comparing above expression
We get ,
n= 19
thus , n=19 is the solution for this problem
Therefore , the solution of the given problem of expressions comes out to be n= 19.
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PLEASE HELP! Matthew uses this scale model of a design he plans to paint on a wall. He uses the key 1 cm = 2.5 ft. One gallon of paint will cover 400 square feet of wall.
How many gallons of paint will Matthew use?
Enter your answer as decimal in the box.
Answer: Matthew will use 12.25 Gallons of Paint. (I'm not sure if I have the correct amount of cm so if you think/know it's a different amount, use the step by step explanation to figure it out. Good luck :D)
Step-by-step explanation: 28x2.5 = 70. 70 Feet to Square Feet = 4900 square feet. 4900 divided by 400 = 12.25.
On a negatively skewed curve, which of the following statements is true?
a. The mean, median, and mode is the same.
b. The mode is lower than the mean which is lower than the median.
c. The median is lower than the mode which is lower than the mean.
d. The mean is lower than the mode which is lower than the median.
e. The mean is lower than the median which is lower than the mode.
Answer:
The mean is lower than the median which is lower than the mode.
Step-by-step explanation:
Solve for X. X can be positive, negative, whole number or decimal.
The value of x in the angle is -6
What is the value of x?Here, m ∠A = 86°m ∠B = (x +53)°
m ∠C = (x +53)°
An isosceles triangle always has three angles that add up to 180° degrees.2 (x + 53) + 86 = 180
2x + 106 + 86 = 180
2 x + 192 = 180
2x = 180- 192
2x = -12
x = -6
What is an isosceles triangle?An isosceles triangle always has three angles that add up to 180 degrees.Triangles that have at least two sides of equal length are said to be isosceles. Triangles are three-sided enclosed polygons, and depending on how long their sides are, they can be categorized as equilateral, isosceles, or scalene.The base and the apex angle are divided by the perpendicular from the apex angle.The isosceles triangle is divided into two congruent triangles by the perpendicular, which is sometimes referred to as its line of symmetry.An isosceles triangle has two equal sides, known as the legs, and an angle between them, known as the vertex angle or apex angle.The base is the side directly across from the vertex angle, and base angles are equal.To learn more about isosceles triangle, refer:
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Five times the difference of twice a number and three is twenty-five. What is the number?
The value of the number in the statement is 8
How to determine the value of the numberFrom the question, we have the following parameters that can be used in our computation:
A mathematical statement represented as
Five times the difference of twice a number and three is twenty-five
Represent the number with x
So, we have
Five times the difference of twice x and three is twenty-five
When represented as an equation, we have
5(x - 3) = 25
Divide both sides by 5
This gives
x - 3 = 5
Add 3 to both sides
x = 8
Hence, the number is 8
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A cookie recipe states for every 3 cups of flour, 1 1/2 teaspoon of vanilla are needed how many teaspoons are needed for 5 cups of flour
Answer:
Step-by-step explanation:
2
How do you find the height of an obtuse angle?
To find the height of an obtuse angle in a triangle, you can use the following steps:
Identify the obtuse angle in the triangle.Draw the altitude from the vertex of the obtuse angle to the hypotenuse.The altitude forms a right triangle with the hypotenuse as the base and the altitude as the height of the obtuse angle.Use the Pythagorean theorem to find the length of the altitude. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.It is important to note that the hypotenuse of the right triangle (the base) must be the side opposite to the obtuse angle, and the other two sides should be the legs of the triangle. Also, the altitude can fall inside or outside of the triangle, it does not affect the calculation of the height.
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Select all the group of number that are ordered correctly from leat to greatet. 2,−4,6,−8
−13,−16,12,1
−110,0. 2,310,14
−112,−0. 75,−0. 25,112
−8,−34,−3,14
The correct group is 3rd. (Option C)
The groups of numbers that are ordered correctly from least to greatest are :
-13,−16,12,1
-110,0.2,310,14
-112,−0.75,−0.25,112
The first group has -13, -16, 12 and 1. -13 and -16 are the smallest numbers and 1 is the largest, so it is ordered incorrectly from least to greatest.
The second group has -110,0.2,310,14 and -110 is the smallest number and 310 is the largest, so it is ordered incorrectly from least to greatest.
The third group has -112, -0.75, -0.25 and 112. -112 is the smallest number and 112 is the largest, so it is ordered correctly from least to greatest.
The last group has -8,-34,-3,14 and -34 is the smallest number and 14 is the largest, so it is not ordered incorrectly from least to greatest.
Therefore, the correct group is 3rd. (Option C)
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Giselle spent $18.72 on supplies to make friendship bracelets. She plans to sell the bracelets, b, for $1 each. Write an algebraic expression to show Giselle's profit.
The algebraic formula to represent Giselle's profit is $b*1 - $18.72, or $b - $18.72, where $18.72 is spent on supplies.
what is expressions ?A statement that contains at least two numbers or variables, along with at least one mathematical operation, is referred to as a mathematical expression. Any one of the following mathematical operations could be used: addition, subtraction, multiplication, or division. The following are an expression's fundamental parts: : (Number/Variable, Math Operator, Number/Variable). A statement that includes at least two numbers or variables, at least one mathematical operation, and the word "expression" is referred to as a mathematical expression. Let's review expressive writing. The alternative number, which is known as x, is 6 more than half of the given number. This sentence is denoted by the phrase x/2 + 6 in mathematics.
given
number of bracelets = b
profit = $b*1 - $18.72
The algebraic formula to represent Giselle's profit is $b*1 - $18.72, or $b - $18.72, where $18.72 is spent on supplies.
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What are the 4 method of quadratic equation?
The four methods to solve quadratic equations are factorising, quadratic formula, graphing and completing the square.
Factorising is nothing but the method of equating the given equation to zero.
Quadratic formula method is by placing the coefficients of the given quadratic equation into the formula and obtaining the solutions.
Completing the square method is when a quadratic equation has a square term. We would once more have a linear equation if we could place two square terms on either side of the quality sign.
We can find the solution of a quadratic equation using a graph. Rearrange the equation so that one side corresponds to the graphed function. Plot this function and write y = the other side of the equation. To obtain the answers, draw vertical lines from the intersection spots down to the x-axis.
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a Ferris wheel has a radius of 65 ft what is the circumference of the circle ( this would be the distance traveled by a passenger in one full rotation of the Ferris wheel use pi equals 3
never mind it equals 390 ft because C= 2 x 3 x 65 witch equals 390 ft
The circumference of the Ferris is 408.2 ft.
What is the circumference?We know that the circumference can be described as the distance round the circle. We have to note that the radius of the feriis would be very important as we try to obtain the circumference of the ferris.
We can see that the radius of the Ferris as is clear from the question that we have here is 65 ft. When the circumference can be gotten from the use of;
C = 2πr
Where r = radius and C = circumference
Thus;
C = 2 * 3.14 * 65
C = 408.2 ft
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2. The rectangle below has a perimeter (distance around the rectangle) of 88 feet. How long are the sides? Show your work.
The length and width of the rectangle with 88 feet perimeter are 33 feet and 11 feet respectively
What is an equation?An equation is used to show the relationship between numbers and variables.
The perimeter of a shape is the sum of the distance along its sides. For a rectangle:
Perimeter = 2(length + width)
Let L represent the length and W represent the width of a rectangle with a perimeter of 88 feet
If the length of the rectangle is 3 times its width, hence:
L = 3W
Perimeter = 2(L + W)
88 = 2(L + W)
But L = 3W:
88 = 2(3W + W)
44 = 3W + W
4W = 44
W = 11 feet
L = 3W = 3(11) = 33 feet
The length and width are 33 feet and 11 feet respectively
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The radio of ducks to swans is 4:5 there are
45. Animals in all how many ducks are there.
Answer:
20 ducks
Step-by-step explanation:
4+5=9
4/9:x/45
9*5=45
4*5=20ducks
Describe the following transformation. Select all that apply
g(x) = -2(x + 5)
The transformation g(x) = -2(x + 5) is described as follows
vertical shift up 5 unitshorizontal shift left 5 unitsreflection over the y axisvertical stretch by a factor of 2What is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Translation refers to a type of transformation that involve a linear movement.
The following movements are involved in translation
leftrightupdownhe left and right movements are on the horizontal direction controlled by the x coordinate. (x + 5) = horizontal shift left 5 units
While the up and down movements are on the vertical direction controlled by the y coordinate. k(x + 5) vertical shift up 5 units
multiplying the equation by a number greater than one leads to vertical stretch since it is a negative number this will be a reflection over the y axis
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4x - 6y = 14
3x + y = 27
find x and y
Answer:
Step-by-step explanation:
Alicia had $375 in her savings account. She withdraws $12 a week to buy lunch. Assuming she does not deposit any more money. Write a linear function to represent how much money (y) Alicia will have after x weeks. A y = 375 + 12x B y = 375 − 12x C x = 375 + 12y D x = 375 − 12y
please help with the question above.
Answer: D
Step-by-step explanation:
Determine the t critical value for a two-sided confidence interval in each of the following situations:
a. Confidence level = 95%, df = 10
b. Confidence level = 95%, df = 15
c. Confidence level = 99%, df = 15
d. Confidence level = 99%, n = 5
e. Confidence level =98%, df = 24
f. Confidence level = 99%, n = 38
The t critical value for a two-sided confidence interval in each of the following situations:
a. Confidence level = 95%, df = 10, t critical value = 1.812
b. Confidence level = 95%, df = 15, t critical value = 1.753
c. Confidence level = 99%, df = 15, t critical value = 2.602
d. Confidence level = 99%, n = 5, t critical value = 3.365
e. Confidence level = 98%, df = 24, t critical value = 2.306
f. Confidence level = 99%, n = 38, t critical value = 2.821
The t-critical value is a value that is used to determine the margin of error in a two-sided t-test with a given level of confidence and degrees of freedom. The t-critical value can be looked up in a t-table, or calculated using a t-distribution calculator.
It is important to note that for a small sample size (n<30) t-distribution is used instead of the normal distribution, in that case, the degrees of freedom is n-1 and the t-critical value is different than the one calculated with degrees of freedom.
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8. The new United States needed a way to
borrow money for its government, its industrial
and its commercial activity.
development,
O True
O False
Answer:
Step-by-step explanation:
true
Answer: True.
Step-by-step explanation: The new United States needed a way to borrow money for its government, its industrial development, and its commercial activity.
What is the center of the following hyperbola?
(x-3)² (y + 2)²
49
A (2,7)
B (-3,2)
C
c (7,2)
D (3,-2)
Answer:
Step-by-step explanation:
The center of a hyperbola is located at the point where the two foci (focii) are located. In this case, the center of the hyperbola is located at point (3,-2), which is option D.
"Write an equation in slope-intercept form for the trend line that is drawn."
Answer:
y = - 3x--------------------------------
The line passes through the origin, therefore one point on the line is sufficient to determine the equation:
y = kx, is the form of this equationThe point on the line is (1, - 3), so the line is:
y = - 3xAnswer:
[tex]y=-3x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
From inspection of the given graph, two points on the line are:
(1, -3)(2, -6)Substitute the two points into the slope formula to calculate the slope of the line:
[tex]\implies m=\dfrac{-6-(-3)}{2-1}=\dfrac{-3}{1}=-3[/tex]
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and one of the points on the line into the point-slope formula:
[tex]\implies y-(-3)=-3(x-1)[/tex]
[tex]\implies y+3=-3x+3[/tex]
[tex]\implies y=-3x[/tex]
In Ms. Rickets’ math class, students made a “polygon path” that consists of regular polygons of 3, 4, 5, and 6 sides joined together as shown.
All the angles from the polygon path made by the students are;
∠1 = 96°
∠2 = 90°
∠3 = 162°
∠4 = 132°
∠5 = 60°
How up illustrate the polygon?The images of the polygon are missing and so i have attached them. From the attached image, we can see we have;
Triangle (3-sided polygon)
Square (4-sided polygon)
Pentagon (5-sided polygon)
Hexagon (6 sided polygon)
Now, we know that formula for external angle of a polygon with n sides is 360/n.
Thus, for the 6-sided polygon, the ∠5 = 360/6
∠5 = 60°
Since ∠4 is shared by the pentagon and hexagon, then;
∠4 = (360/5) + 60
∠4 = 72° + 60°
∠4 = 132°
Since ∠3 is shared by the square and pentagon, then;
∠3 = 90 + 72
∠3 = 162°
∠2 = 90° because external angles of a square = 360/4 = 90°
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If sarah can blow up three balloons in one minute , how long will it take her to blow up 21 balloons?
Sarah can blow 7 minutes to blow 21 balloons
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: Sarah can blow 3 balloons in 1 minute
Then unit rate of sarah is 3 balloons per minute
Thus the time she would take to blow 21 balloons is 21/3=7 minutes
Hence, Sarah can blow 7 minutes to blow 21 balloons
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What are the determinants for solving this linear system?
5x + 3y = 17
−8x − 3y = 9
The determinants for solving the linear system is given as follows:
|A| = 9.|Ax| = -78.|Ay| = 91.How to obtain the determinant of the matrices?The system of equations for this problem is defined as follows:
5x + 3y = 17−8x − 3y = 9The matrix A is composed by the coefficients of x and y, hence:
A = [5 3]
= [-8 -3]
The determinant of a 2 x 2 matrix is the multiplication of the principal diagonal subtracted by the multiplication of the secondary diagonal, hence:
|A| = 5 x (-3) - 3 x (-8)
|A| = -15 + 24
|A| = 9.
For the matrix Ax, the coefficients of x are replaced by the results of the equalities, hence:
Ax = [17 3]
= [9 - 3]
|Ax| = 17 x (-3) - 3 x 9
|Ax| = -51 - 27
|Ax| = -78.
For the matrix Ay, the coefficients of y are replaced by the results of the equalities, hence:
Ax = [5 17]
= [-8 -9]
|Ay| = 5 x (-9) + 17 x 8
|Ay| = 91.
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Please help I will give brainliest
Answer:
Rectangular
Step-by-step explanation:
I would be rectangular if you listened in class you would know.