Answer: False.
Step-by-step explanation: The two equations are not equivalent because the constant terms on the right side of each equation are different. The first equation has -20 on the right side, while the second equation has 0 on the right side. The equations cannot be manipulated into each other because the constant terms are different.
Evaluate: f(g(0))
Pre cal test question
Our succinct response is therefore 8 . Functions are typically denoted by the letter f. (x).
what is functions ?Mathematics deals with numbers and their variants, equations and related structures, shapes and their locations, and locations where they might be found. The term "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is an association between inputs and outputs where each input results in a single, unique output. Functions are typically denoted by the letter f. (x). The input is an x. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four main categories of functions that are available.
given
To locate f(h(7)), two functions are presented to us.
Finding h(7) h(x)=x3343
h(7)=73343=343343=0 would be my first step.
Knowing h(7) now allows us to enter it into f. (x).
f(x)=5x2−13x+8
f(0)=5⋅02−13⋅0+8=8
Our succinct response is therefore 8 . Functions are typically denoted by the letter f. (x).
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Consider the graph of the function f(x) = log x
select all the correct answers
which are features of function g if g(x) = 4 log(x) +4?
∆ x-intercept of (0.1, 0)
∆ y-intercept of (0, 4)
∆ range of (-∞, ∞)
∆ domain of (4, ∞)
All the correct options are:
The x-intercept of g(x) is (0.1, 0).
And the range is (-∞, ∞).
What is Logarithmic?The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.
Given:
The functions,
f(x) = log x
And g(x) = 4logx + 4
The graph of g(x) is given in the attached image.
The x-intercept of g(x) is (0.1, 0).
And the domain is (0, ∞)
And the range is (-∞, ∞).
Therefore, all the features of function g(x) are given above.
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What are trigonometric ratios Class 10?
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.
Trigonometry is a discipline of mathematics that deals with the sides and angles of a right-angled triangle in geometry. As a result, trig ratios are evaluated in terms of sides and angles.
Thus, The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
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Greg took a job through an employment agency. The job offers an annual salary of $28,600, which is paid weekly. Greg will have to pay the agency a fee of 23% of his first four weeks' pay. Calculate the fee. Show all working.
Answer: To calculate the fee, we need to know the annual salary, the percentage fee and the number of weeks that the fee will be applied. In this case, the annual salary is $28,600, the fee is 23% and the number of weeks is 4.
First, we need to calculate the weekly pay by dividing the annual salary by 52 weeks in a year:
Weekly Pay = $28,600 / 52
Weekly Pay = $550
Then we can calculate the amount of money that the agency will charge for the first four weeks by multiplying the weekly pay by the number of weeks:
4 Weeks Pay = 4 x $550
4 Weeks Pay = $2200
Now, we can calculate the fee by multiplying the 4 weeks pay by 23%:
Fee = $2200 x (23 / 100)
Fee = $506
So, the agency will charge Greg a fee of $506 for the first four weeks of his job.
Step-by-step explanation:
PLEASE HELP A 25,000-mile steel band is placed around the earth, snugly fit at the equator. The band is cut, and 36 inches of string is spliced into the steel band. This new, larger circular band is placed around the earth, so its center coincides with the center of the earth, and a gap is created. How wide is this gap?
When you have finished, post your work showing the formula used for calculating the gap (g), show all calculations solving for g (gap), and a statement interpreting the results of your work.
The distance is roughly 6 inches wide, The gap is actually the same width as the one made by adding 36 inches of thread to a band that is wrapped around a nickel.
Circumference of circle,
C=2лr
The radius must rise if the circumference grows by 36 inches. Call the increase in radius g "gap," please.
Therefore, r+g is the new, greater radius. Based on the formula, we may construct an equation for the larger circle.
C+36=2π(r+g)
C+36=2x+2лg
We may take these equal amounts off of both sides of the equation because C = 2r.
36=2πg
To find g, divide both sides by 2л. The spacing is just under 6 inches because 2n is roughly 6. The equation explains why the starting circumference has no bearing on the result; as a result, the earth and the nickel produce the identical gaps.
Drawing a graph demonstrates the logic behind this response. C = 2r enables us to write the following:
r = c/2π
This equation has a graph on the r, C axes that is a straight line with a slope of 1/(2л) and a zero y-intercept. The graph demonstrates that regardless of the initial circumference, any 36-inch increase in circumference results in the same (roughly 6-inch) rise in radius.
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What is the multiplicative inverse of 4 /- 9?
The multiplicative inverse is explained as the reciprocal of a specified number. It is used to clarify mathematical expressions.
The word 'inverse' implies something contrary/ opposite in effect, order, position, or direction. Any number when it is multiplied by its multiplicative inverse results in always one.
Find the multiplicative inverse of positive integers is similar to natural numbers (explained above).
Just like positive integers, the multiplication of a negative number and its reciprocal must be equal to one. hence, the multiplicative inverse of any negative number is it is reciprocal.
The multiplication inverse of 4/-9 is:
So, the inverse of 4/-9 is = -9/4.
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Do you think you can determine the imaginary solutions by examining the graph? Explain your reasoning.
The answer to whether or not it is possible to determine imaginary solutions by examining the graph of p(x)=x^2+1 is no.
What is function?Function is a block of code that performs a specific task. It is a reusable code that can be called multiple times with different parameters. Functions are an important part of programming because they allow you to reuse code and make your code more organized and efficient. Functions also make it easier to debug code, as errors can be contained to a single function instead of spreading throughout the entire program.
The graph of this function does not contain any imaginary solutions, instead it is a parabola with its vertex at the origin and its axis of symmetry being the y-axis. This can be seen from the graph, as the graph is symmetrical about the y-axis and does not contain any points in the fourth quadrant, meaning that any solutions that would fall in this quadrant would be imaginary.
In addition, imaginary solutions cannot be determined from this graph, as the imaginary solutions would not be visible on the graph. Imaginary solutions are solutions that are not real, meaning they are not visible on the graph, as they do not exist in the real number system. This is because the graph only displays real number solutions, not imaginary ones.
Therefore, it is not possible to determine imaginary solutions by examining the graph of p(x)=x^2+1, as the graph only displays real number solutions, and imaginary solutions cannot be seen on the graph.
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Mr. Bajada paid 200000 as down payment for a farm. The remaining amount is to be settled by paying 16 200 at the end of each month for 5 years. If interest is 5 % compounded semi annually what is the cash price of his farm
If interest is 5% compounded semi-annually, the cash price of his farm is P 915625.
Compound interest is the interest you gain on interest. This can be illustrated by using basic math: if you have P 100 and it earns 5% interest each year, you'll have P 105 at the end of the first year. At the end of the second year, you'll have P 110.25.
Down payment = P 200000
Amount paid in monthly instalments = 60 × 16200 = P 972000
Total amount paid = P 200000 + P 972000 = P 1172000
A = P(1+r/100)¹⁰
11,72,000 = P (1+5/200)¹⁰
11,72,000 = P(1.025)¹⁰
P = 11,72,000/(1.025)¹⁰
= 11,72,000/1.28
= 915625 P
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What is 73 rounded to the nearest 10?
The Round-off of 73 nearest to the 10th is 70. This process is called rounding off the numbers.
The process is used to simplify the numbers so that the number can easily be calculated, he Round-off process can take place to the nearest 10, 100,1000, and so on, this is called round-off. T It can also be used for numbers as well as decimal numbers so that we can write the decimal number in simplified form.
For example: if the distance between the USA and Mexico is 1190 mi, what is the round-off distance? = 1200 mi.
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How many solutions you can obtain for a system of linear equations in 2 variables?
Answer: The slopes of the two equations are the same but the intercepts are different; therefore the lines are parallel and the system has no solutions. This is an inconsistent system.
Question 2 Assuming you know the coordinates of the key points (vertex, foci, directrix), explain how to graph the functions of a parabola
A parabola's vertex, which is its maximum or minimum, and focus, which is a fixed point inside the parabola, are both mathematical terms. The parabola's axis is parallel to the directrix, which lies outside the parabola.
How to Find the Focus, Vertex, and Directrix of a Parabola?Vertex, Focus, and Directrix are the three elements that make up a parabola. A parabola's vertex, which is its maximum or minimum, and focus, which is a fixed point inside the parabola, are both mathematical terms. The parabola's axis is parallel to the directrix, which lies outside the parabola.When a parabola opens upwards or downwards, the typical form is (xh)2=4p(yk), where the directrix is y=kp and the focus is h,k+p.When a parabola opens to the right or left, the typical form is (y+k)2=4p(xh), with h+p,k as the focus and x=hp as the directrix.Y=ax2+bx+c is a parabola; hence,
Focus: (b2a,4ac,b2+14a), Directrix: y=c(b2+1)4a, Vertex: (b2a,4ac,b24a).To Learn more About parabola's vertex Refer To:
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What is a vertical line example?
Vertical Line is a line that runs perpendicular to the Y-axis. It runs in a straight line from top to bottom and vice versa. Any point along this line will have the same x-coordinate value.
No slope exists along the vertical lines. Since it follows the y-axis parallel, the slope cannot be determined. As a result, x = an is the equation for the vertical line that, at any point, say "a," crosses the x-axis.
Since a vertical line has no y-intercept and 0 for the slope denominator, its slope is infinity or undefined.
In mathematics, we use a vertical line to determine whether the relationship is a function. If all vertical lines crossed it no less than once, it would be a function. Another name for this is the vertical line test. If a graph only has one output (y) for each input (x), it will be regarded as a function. A vertical line is therefore not a function.
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keith tabulated the values for the average speeds on each day of his road trip as 61.5, 62.2, 55.7, 50.6, 71.3, 70.8, and 66.8 mph. he wishes to construct a 90% confidence interval. what value of t* should keith use to construct the confidence interval? answer choices are rounded to the thousandths place.
To create the 90% confidence interval for the average speeds on his road journey, Keith should utilise t* 1.943.
To construct a confidence interval for the mean of a sample, Keith needs to use the t-distribution with a degree of freedom equal to one less than the sample size.
Since Keith has seven days of data, the degrees of freedom (df) is
= 7 - 1
= 6.
A 90% confidence interval corresponds to a 95% confidence level, as the remaining 5% is divided evenly between the two tails of the t-distribution.
The value of t* for a 90% confidence level and 6 degrees of freedom is 1.943.
So, Keith should use t* ≈ 1.943.
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What are two ways to represent 4/5? Move numbers to the boxes two equation.
Answer:
are you allowed to repeat numbers?
if so, the first one will be 2/5 + 2/5
if not, the first one will be 1/5 + 3/5
for the second one, the only possible combination would be 1/5 + 2/5 + 1/5
Step-by-step explanation:
Find the area of the shaded regions below. Give your answer as a completely simplified exact value in term of pie.
1) The area of the shaded portion is; 63π
2) The area of the shaded portion is; 4π - 8√2
How to find the area of the shaded region?1) The formula for area of a circle is;
A = πr²
where r is radius
The radius here is 9cm and so;
A = π * 9²
A = 81π
The area of a sector is given by the formula;
(θ/360) * πr²
Thus;
A_sect = (80/360) * π * 9²
A_sect = 18π
Area of shaded region = 81π - 18π
Area of shaded region = 63π
2) Using trigonometric ratio, we can find the diameter LN as;
4/LN = cos 45
4/LN = 1/√2
LN = 4√2
Formula for area of semi circle is;
A = ¹/₂πr²
A = ¹/₂ * π * (¹/₂ * 4√2)²
A = ¹/₂ * π * 8
A = 4π
Area of triangle = ¹/₂ * 4 * 4√2
= 8√2
Area of shaded portion = 4π - 8√2
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I could pay more if wanted
The ink will diffuse one micrometer in 5 x 10⁻⁴ seconds
How to find the time to diffuse the inkFrom the problem it can be deduced that
time, t in seconds it takes t diffuse 1 centimeters
t = x² / 2D
The diffusion coefficient for a drop of ink in water is about 10⁻⁵ square centimeters per second
D = 10⁻⁵ cm²/s
time to for the ink to diffuse 1 micrometer
1 micrometer = 10⁻⁴ centimeter = x
t = x² / 2D
t = (10⁻⁴)² / 2 * 10⁻⁵
t = 5 x 10⁻⁴ seconds
In 5 x 10⁻⁴ seconds the ink will diffuse 1 micrometer
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Reflect ABC across the y-axis.
A (0,2) B (3, -2) C(-3,-2)
Answer: just graph it on the y-axis
Step-by-step explanation:
convert 60ft to mi. (5280 ft= 1mi and 3600 sec
The distance 60ft when converted to miles is 1/88 mi or 0.0114 mi
How to convert 60ft to mi?Distance can be measured in various units such as miles, kilometers, feet, meters, etc.
To convert a distance from one unit to another, you need to know the conversion factor between the units.
In this case, the conversion factor is 5280. Therefore, to convert 60 feet to miles, divide it by 5280 (since 5280 ft = 1 mi). Therefore, based on the information given above, the calculation will be done thus:
60ft = 60/5280 mi
= 1/88 mi = 0.0114 mi
Therefore, the calculation shows that the conversion will be 0.0114 miles.
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I need help plsssssssssss
Answer:I think its multiply
Step-by-step explanation: 90 x 2 = 180
Betsy is ordering prizes for a school fair. She must order two helium balloons for every five people and three stuffed animals for every eight people organizers expect 120 people to attend. The fair decided each statement about Betsy‘s order is true or false.
The options that are true or false as regards the ratios are;
Options A & D are true
Options B & C are false
How to solve ratio problems?We are given;
Number of helium balloons ordered for every 5 people = 2
Number of stuffed animals for every eight people = 3
Total number of people to attend = 120
A) The ratio of helium balloons to stuffed animals;
Number of helium balloons = 2/5 * 120 = 48
Number of stuffed animals = 3/8 * 120 = 45
Ratio = 48:45 = 16:15
This is true according to the option
B) The ratio of stuffed animals to helium balloons;
Number of helium balloons = 2/5 * 120 = 48
Number of stuffed animals = 3/8 * 120 = 45
Ratio = 45:48 = 15:16
This is false according to the option
C) This is false according to the calculations above
D) This is true according to the calculations above
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What kind of triangle has 2 equal sides *?
An isosceles triangle is a triangle with two equal sides.
An isosceles triangle is one with two sides that are the same length. An isosceles triangle's two angles, opposite to equal sides, are equal in size.
Also, the two angles opposite the two equal sides are equal. In other words, we can say that “An isosceles triangle is a triangle which has two congruent sides".
Triangles are three-sided polygons that are categorized into three types based on their sides, such as:
Scalene triangle (All three sides are unequal)
Isosceles triangle (Only two sides are equal)
Equilateral triangle (All three sides are equal)
Thus, An isosceles triangle is a triangle with two equal sides.
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23.f(s) = Vs - 1 ÷Vs + 1 .Find the derivatives.
Answer:The derivative of f(s)
Step-by-step explanation:
The derivative of f(s) = (Vs - 1)/(Vs + 1) with respect to s is
df/ds = (V(Vs + 1) - (Vs - 1)V)/(Vs + 1)^2
= (V^2 -1)/(Vs + 1)^2
Help please quickly thank you
Answer: y=x/3-6
Step-by-step explanation: ✨Math sucks doesn’t it darling✨
Which of the following expression has the value 37?a) 10 x 3 + (5 + 2)
b) 10 X 4+ (5-2)
c) 10 x 3 + 3
d)(9 x 3) + 27
Answer:
a is the answer.
10x3 is 30 plus (5+2) is 37. using the order of operations.
Triangle NOP is formed by connecting the midpoints of the side of triangle
KLM. The measures of the interior angles of triangle KLM are shown.
Find the measure of ZMOP. Figures not necessarily drawn to scale.
K
34°
P
M
72°
N
74
L
ZMOP must have a measure of 60°.
What is triangle?A triangle is a three-sided polygon that is one of the most basic shapes in geometry. It is defined by three points, known as its vertices, and the straight lines connecting them. Triangles come in many different shapes and sizes, and can be classified by their angles, sides, and area. Triangles have many uses in mathematics, for example, to calculate interior angles, calculate area and perimeter, or to prove certain geometric theorems.
In order to find the measure of ZMOP, we must first look at the structure of triangle NOP. Since it is formed by connecting the midpoints of the sides of triangle KLM, it can be classified as an equilateral triangle. This means that all three of its interior angles are equal in measure. Therefore, ZMOP must have a measure of 60°. This is because the sum of all three interior angles of an equilateral triangle is 180°, and since the other two angles have measures of 34° and 74°, the third angle must have a measure of 180° - (34° + 74°) = 60°.
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What is the equation of the central street pq
-7x+3y=-21.5
The function can be written as - y = (7/3)x - (21.5/3).
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the equation as -
- 7x + 3y = - 21.5
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.The set X is called the domain of the function and the set Y is called the codomain of the function.Functions whose domain are the non - negative integers, known as sequences, are often defined by recurrence relations.The given equation is -
- 7x + 3y = - 21.5
3y = - 21.5 + 7x
y = - (21.5/3) + (7/3)x
y = (7/3)x - (21.5/3)
Therefore, the function can be written as -
y = (7/3)x - (21.5/3).
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En la ciudadela de soacha de ciudad verde se identifico que el 60% de las familias residentes tienen vehiculo propio. Si se desea realizar una investigacion de mercado con dicha poblacion sobre consumo de gasolina. Cual debe ser el tamaño de la muestra teniendo en cuenta un nivel de confianza del 95% y de error de 0. 03?
The size of the exhibition is roughly 717 families.
Error is the difference between a genuine value and an estimate, or approximate, representation of that value in practical mathematics. The discrepancy between the mean of the complete population and the mean of a sample taken from that population is a frequent example in statistics.
Datos:
a 95% confidence level
Significance level = 1-0,95 = 0,05
Zα = -1,64
e = 0,03
p = 0,6
q= 0,4
The size of the display for an infinite population is:
n= Zα²*p*q/e²
n = (1,64)² *0,6*0,4/(0,03) (0,03)²
n = 717
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What is the equation written in vertex from of a parabola with a vertex of (4, –2) that passes through (2,0)?
The equation of parabola is y=1/2(x-4)^2-2.
Vertex of (4, –2) that passes through (2,0)
We can use the vertex form of the quadratic equation:y = a(x - h)² + k
k=-2,h=4
Substitute these values into the vertex form to solve for a:
y = a(x - h)² + k
When x=2,y=0
a=1/2
Therefore, the quadratic equation in vertex form is:y = a(x - h)² + k
k=-2,h=4
The equation of such a parabola is y=1/2(x-4)^2-2
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Solve please:
1/4x + 1/2 - 8 = 3x - 3/4
Answer:
x=-27/11
Step-by-step explanation:
This answer is x=-27/11
3. A quadrilateral will be dilated on a coordinate grid to
create a larger polygon. The polygon is dilated using the
origin as the center of dilation. Which rule could represent
this dilation? 8.3C
A.(x,y) (0.5x, 0.5y)
B. (x,y) → (1/2x, 1/2y)
C. (x,y) → (7/5x,7/5 y)
D. (x,y) → (0.4x, 0.4y)
Therefore , the solution of the given problem of quadrilateral comes out to be the centre of dilatation to produce a smaller polygon (0.9x, 0.9y).
Describe a quadrilateral.In geometry, a four-sided object having four corners is referred to as a quadrilateral. The word comes from either the Latin quad or portfolio of innovative (meaning "side"). Four corners, four states, and four corners are the three dimensions of a rectangle. Concave and convex surfaces come in essentially two varieties. Convex quadrilaterals also include the subclasses of trapezoids, parallelograms, angles, rhombuses, and squares.
Here,
The rule that can describe this is (x, y). The polygon is expanded to use the beginning as the point of dilatation to generate a smaller polygon. (0.9x, 0.9y)
A point is transformed when it is moved from its original location to something like a new one. Reflection, rotation, translation, and dilation are examples of different transformations.
The term "dilation" refers to an alteration in a figure's size.
The clear element is A' if a position A(x, y) is stretched by a factor k. (kx, ky). It is a decrease if k 1 and an enlargement if k > 1.
The rule that can describe this is (x, y). The hexagon is dilated to use the beginning as the centre of dilatation to produce a smaller polygon.
(0.9x, 0.9y)
Therefore , the solution of the given problem of quadrilateral comes out to be the centre of dilatation to produce a smaller polygon (0.9x, 0.9y).
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