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6801.

Solve:⅓(7x - 1) = 1/4

Answer» The value of x is 1/4.

An equation is a mathematical statement with an 'equal to' symbol between two algebraic expressions that have equal values.

6802.

Choose the correct slope of the line that passes through the points (1, −3) and (3, −5).

Answer» The slope(m) of the line that passes through the points (1, −3) and (3, −5) is m = -1.

The slope of a line determines the inclination of the line with the positive x-axis.

6803.

Which of the following describes the translation of y = |x| to y = |x + 7| - 2 y = |x| translated 2 units to the left and 7 units down y = |x| translated 7 units to the right and 7 units down y = |x| translated 2 units to the right and 7 units up y = |x| translated 7 units to the left and 2 units down

Answer» Which of the following describes the translation of y = |x| to y = |x + 7|-2

Solution:

6804.

One exterior angle of a regular pentagon has a measure of (2x)°. What is the value of x?

Answer» One exterior angle of a regular pentagon has a measure of (2x)°. What is the value of x?

Solution:

6805.

Identify the 27th term of an arithmetic sequence where a1 = 38 and a17 = -74.

Answer» Identify the 27thterm of an arithmetic sequence where a1= 38 and a17= -74.

Solution:

6806.

How Do You Find the Next Three Terms in 2, 5, 10, 17, 26,....?

Answer» The next three terms of the series 2, 5, 10, 17, 26,... are37, 50, and 65

We will try to find out the logic behind the given series of numbers and with the help of that logic, we can find the next three numbers.

6807.

What are the Solutions of the Equation 4x2+ 3x = 24 – x?

Answer» The solutions of the equation 4x2+ 3x = 24 – x are -3, and 2.

We will be simplifying the equation to solve it.

6808.

What is the 32nd term of the arithmetic sequence where a1 = -33 and a9 = -121?

Answer» What is the 32nd term of the arithmetic sequence where a1 = -33 and a9 = -121?

Solution:

6809.

Find all the local maxima, local minima, and saddle points of f(x, y) = x3 − 3y2 + 3xy − 3y.

Answer» The function f(x, y) has local maxima at (-1, -1) and saddle pointat (1/2, -1/4).

Maxima and minima are very important topics in mathematics in which we can find the maximum or minimum value of a function using its derivatives.

6810.

The measure of angle θ is 600°. the point (x, y) corresponding to θ on the unit circle is

Answer» The measure of angle θ is 600°. the point (x, y) corresponding to θ on the unit circle is

Solution:

6811.

Find a unit vector in the direction of the given vector v = (1, 3).

Answer» The unit vector for v = (1, 3) will be (1/√10, 3/√10).

Vectors are quantities with both magnitude and direction.Vectors are used to represent quantities in physics, such as velocity, acceleration, force, or torque.

6812.

What are the possible rational zeros of f(x) = 3x4 + x3 - 13x2 - 2x + 9?

Answer» What are the possible rational zeros of f(x) = 3x4+ x3- 13x2- 2x + 9?

Solution:

6813.

What is a possible value for the missing term of the geometric sequence 50, ___, 450

Answer» What is a possible value for the missing term of the geometric sequence 50, ___, 450

Solution:

6814.

What is the fully factored form of 32a³ + 12a²? 4a² (8a + 3), 4a (8a² + 3a), 12a² (3a + 1), 12a (3a² + a)

Answer» What is the fully factored form of 32a³ + 12a²?
4a² (8a + 3), 4a (8a² + 3a), 12a² (3a + 1), 12a (3a² + a))

Solution:

6815.

If the polynomial ax3+ bx- c is divisible by x2+ bx + c then what is the value of 'ab'?

Answer» If the polynomial ax3+ bx- c is divisible by x2+ bx + c then value of ab is 1.

Apolynomialis a type of expression in which the exponentsof allvariablesshould be awhole number.

6816.

Find the 270 degrees value for all the trigonometric angles.

Answer» The value of 270º for all the six trigonometric ratios are: sin 270° = – 1, cos 270°= 0, tan 270° = Not defined, cosec 270° = – 1, sec 270° = Not defined, cot 270°= 0

We can proceed by using trigonometric ratios of different angles.

6817.

How to find the magnitude of a vector with 3 components

Answer» The magnitude of a 3-dimensional vector with 3 components V = (a, b, c) is given as√(a2 + b2 + c2).

The magnitude of a vector signifies the positive length of that particular vector.

6818.

Find the surface area of a sphere with radius 10 in. Leave your answer in terms of pi.

Answer» Find the surface area of a sphere with radius 10 in. Leave your answer in terms of pi.

Solution:

6819.

What is 8 inches in centimeters?

Answer» 8 inches is 20.32 centimeters.

Inches and centimeters are different measuring units used to measure length or height.

6820.

The cubic centimeter (cm3 or cc) has the same volume as a

Answer» The cubic centimeter (cm3 or cc) has the same volume asthe milliliter

A centimeter is aunit of themetric systemthat is used to measure length.

6821.

What is the equation, in standard form, of a parabola that contains the following points? (-2, 18), (0, 4), (4, 24) y = 2x2 - 3x + 4 y = -3x2+ 2x + 4 y = -4x2- 3x - 2 y = -2x2+ 3x - 4

Answer» What is the equation, in standard form, of a parabola that contains the following points? (-2, 18), (0, 4), (4, 24)

Solution:

6822.

What is the next number? 1, 1, 2, 4, 3, 9, 4

Answer» What is the next number? 1, 1, 2, 4, 3, 9, 4

Solution:

6823.

25 Bags of wheat weighing 40 kg costs Rs.2750. Find the cost of 35 bags, if each bag weighs 50 kg?

Answer» If 25 bags of wheat weighing 40 kg costs Rs.2750, the cost of 35 bags, if each bag weighs 50 kgis Rs.4812.50.

We'll use the Unitary method to find the cost.

6824.

Where are the asymptotes of f(x) = tan (2x) from x = 0 to x = π?

Answer» Where are the asymptotes of f(x) = tan (2x) from x = 0 to x = π?

Solution:

6825.

What is the sin-1x + sin-1y formula?

Answer» The formula forsin-1x + sin-1y issin-1[x√ (1 - y2) + y√ (1 - x2)]

Trigonometry is the branch of mathematics that deals with the relationships of angles and sides of a triangle.Inverse trigonometric functions are the inverse ratio of the basic trigonometric ratios. Let's look into a concept related toinverse trigonometric functions.

6826.

How do you write a rule for the nth term of the arithmetic sequence given a20= 240, a15= 170?

Answer» How do you write a rule for the nth term of the arithmetic sequence given a20 = 240, a15 = 170?

Solution:

6827.

Simplify to get a complex number 1/(3 + 4i)in standard a + bi form.

Answer» The simplified form of the complex number1/(3 + 4i) is 3/25 - 4/25i in the standard a + bi form.

Complex numbers are interesting types of numbers that can't be represented on the number line. A complex number has two parts: one is imaginary and the other one is real. These numbers are represented in the complex plane. They find their applications in various fields related to engineering and science.

6828.

What is the equation of the line shown in this graph?

Answer» The equation of the line shown in this graph is y = (-1/2)x - 3

Graph of a line

6829.

Given: -3x + y = 1. Write the equation in general form ax + by + c = 0.

Answer» Given: -3x + y = 1. Write the equation in general form ax + by + c = 0.

Solution:

6830.

What is the value of 1/4 times 1/4?

Answer» The value of 1/4 times 1/4 is 1/16.

The multiplication of fractions starts with the multiplication of the given numerators, followed by the multiplication of the denominators.

6831.

The side length of an equilateral triangle is 6 cm. What is the height of the triangle?

Answer» The height of the given equilateral triangle is 3√3 cm.

An equilateral triangle is a regular polygon with 3 equal sides.

6832.

How to find the lateral area of a rectangular prism?

Answer» The lateral surface area of a rectangular prism can be found using the formula 2 ( l + b ) h.

A rectangular prism is a three-dimensional solid that has all its lateral faces in a rectangleshape.

6833.

Explainthe elimination method of linear equation in 2 variables with an example.

Answer» The elimination method is one of the most widely used methods to solve a system of linear equations, where we eliminate any one of the variables and then find the value of the other variable.

The linear equations in two variables are of the highest exponent order of 1 and have one, none, or infinitely many solutions. Thestandard form of linear equation is ax + by + c = 0, where x and y are the two variables.

6834.

How do you find the exact values of sin 22.5° using the half-angle formula?

Answer» The exact value of sin 22.5° using the half-angle formula is√(2 -√2) / 2 or0.38

We can find the exact value by using thehalf-angle formula.

6835.

What is the axis of symmetry of the function f(x) = -(x + 9)(x - 21)?

Answer» What is the axis of symmetry of the function f(x) = -(x + 9)(x - 21)?

Solution:

6836.

Solve the quadratic equation x2 + 5x + 6 = 0

Answer» The roots of the quadratic equation x2 + 5x + 6 = 0 are -2 and -3

We will split the middle term to solve this quadratic equation.

6837.

If f(x) = |x| and g(x) = |x| - 4, which transformation is applied to f(x) to get g(x)?

Answer» If f(x) = |x| and g(x) = |x| - 4, which transformation is applied to f(x) to get g(x)?

Solution:

6838.

Two positive integers are 3 units apart on a number line. Their product is 108. Which equation can be used to solve for m, the greater integer? m(m - 3) = 108 m(m + 3) = 108 (m + 3)(m - 3) = 108 (m - 12)(m - 9) = 108

Answer» Two positive integers are 3 units apart on a number line. Their product is 108. Which equation can be used to solve for m, the greater integer?

Solution:

6839.

The sum of 2 digit number and the number obtained by reversing the order of the digit is 165. If the digit differ by 3, find the number, when ten's digit is bigger than the unit 's digit.

Answer» The number whosesum with the number obtained by reversing the order of the digits is 165 and the difference between the digits is 3 is 96.

A two-digit number 'ab' can be represented as a sum of its respective place valuesi.e., ab = 10a + b

6840.

Identify and calculate the area and perimeter for each quadrilateral.

Answer» (a)Perimeter = 20 units and Area = 25sq. units, (b)Perimeter = 28units and Area =15/2 sq. units

the area and perimeter for each quadrilateral

6841.

Find the area of the part of the plane 4x + 3y + z = 12 that lies in the first octant.

Answer» Find the area of the part of the plane 4x + 3y + z = 12 that lies in the first octant.

Solution:

6842.

Fill in the blanks. (1) Zero has ________ reciprocal. (2) The numbers ________ and ________ are their own reciprocals. (3) The reciprocal of 5 is ________. (4) Reciprocal of 1/x, where x≠0 is ________. (5) The product of two rational numbers is always a _______. (6) The reciprocal of a positive rational number is ________

Answer» (1) no (2) 1, -1 (3) 1/5 (4) x (5) rational number (6) positive rational number

We will use the definition of reciprocal to answer this question.

6843.

Write the equation of the circle with center (2,4) and containing the point (-2,1)?

Answer» Write the equation of the circle with center (2,4) and containing the point (-2,1)?

Solution:

6844.

Differentiate the function. v = x + 13 x2

Answer» On differentiating the function v = x + 13 x2, we get dv / dx = 1 + 26x

We will use the concept of differentiation in order to find the value of derivatives.

6845.

What is a line segment that passes through the center of the circle?

Answer» Diameter is a line segment that passes through the center of a circle.

A line segment is the part of the line having two endpoints.

6846.

What is 10to the 6th power?

Answer» The value of 10raised to 6thpower i.e., 106is 1000000.

The exponentor power of a number shows how many times the number is multiplied by itself.

6847.

With an interest rate of 6 percent, the present value of $100 next year is approximately?

Answer» With an interest rate of 6 percent, the present value of $100 next year is approximately?

Solution:

6848.

Explain the intersection of two events, Aand B.

Answer» Intersection of two events, A and B, is a set that contains all the elements of A that also belong to B and vice-versa.

Sets are very useful for representing one or more objects in the form of a venn diagram. They are also used to represent the common items in different sets and how they relate to each other.

6849.

Find the value or values of y in the quadratic equation y2 + 4y + 4 = 7.

Answer» Find the value or values of y in the quadratic equation y2 + 4y + 4 = 7.

Solution:

6850.

What is equivalent to 3/5?

Answer» The fractions equivalent to 3/5are 6/10, 9/15, 12/20, etc.

To find the equivalent fractions for any given fraction, we divideor multiplythe numerator and thedenominatorby the same number.