The sum of 26.541 + 14.2 is greater than the integer 40, as the sum is equivalent to 40 + 0.741.
How to prove that the sum of two real numbers is greater than an integer
In this problem we need to compare the sum of two real numbers with an integer, also a real number. The two real numbers can be written as the sum of an integer and excess decimal part. Then, the given sum can be rewritten as:
x = 26.541 + 14.2
x = (26 + 0.541) + (14 + 0.2)
This sum must be compared with an integer, 40.
x = (26 + 14) + (0.541 + 0.2)
x = 40 + 0.741
Then, by direct comparison, we see that the sum of 26.541 + 14.2 is greater than 40.
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Por el punto a(-3,-6) pasa una línea recta con pendiente m=2 obtén
a) la ecuación de la recta en su forma ordinaria
b) la ecuación de la recta en su forma general
Equation of line in ordinary form: y = 2x+0
Equation of line in standard (general) form: 2x - y = 3
What is Slope?
The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same).
a) Ordinary form =>
Slope Intercept Form:
y = mx+b
where m is the slope of the line
(Δy/Δx)
and b is the y-intercept.
For a line with slope 2 and point (-3,-6), plug 2 in for m, -3 for x, -6 for y, and solve for b.
-6 = 2(-3) + b
-6 = -6 + b
6 - 6 = b
b = 0
The equation in slope intercept form is
y = 2x+0
b) Standard form =>
Point Slope Form:
(y - y1) = m(x - x1)
Where m is the slope of the line
(Δy/Δx), y1 is the y coordinate of a point, and x1 is the x coordinate of a point.
For a line with slope 2 and point (-3,-6), plug 2 in for m, -3 for x1, -6for y1,
(y - (-6)) = 2(x - (-3))
Standard Form:
Ax + By = C
Where A, B, and C are integers. To write an equation in standard form, rewrite the equation in point slope form so that it fits the formula for standard form.
(y - (-6)) = 2(x - (-3))
(y + 6) = 2(x + 3)
y + 6 = 2x + 3
2x - y = 6 - 3
2x - y = 3
Hence, Equation of line in ordinary form is y = 2x+0
Equation of line in standard (general) form is 2x - y = 3
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Allan is buying grosces. they cost 87.64. Sale taxes is 7%. How much will the total sale be?
Please helpme!
The total sale based on cost of 87.64 and sales tax percentage of 7% is 93.77
What is sales tax?
Sales tax is the levy charged on goods and services that is remitted by the seller to the government, in some jurisdictions, it is known as value-added tax and it should be noted that it increases the sales, in essence, the total sale in this case is the cost of groceries which is 87.64 plus 7% of that amount which is sales tax on the cost of the groceries
cost of groceries=87.64
sales tax=7%*cost of groceries
sales tax=7%*87.64
sales tax=6.13
total sale=cost of groceries+sales tax
total sale=87.64+6.13
total sale=93.77
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Question 11(Multiple Choice)(05.06 MC)Using the graph of the function g(x) = log3 (x-4), what are the x-intercept and asymptote of g(x)?The x-intercept is 3, and the asymptote is located at x = 4.The x-intercept is 5, and the asymptote is located at x = 4.The x-intercept is 4, and the asymptote is located at y = 5.The x-intercept is 5, and the asymptote is located at y = 3.
Graph:
x intercept = where it crosses the x axis = 5
asymptote = never touches it = 4
Answer:
The x-intercept is 5, and the asymptote is located at x = 4.
Use the vertex ( h, k ) and a point on the graph ( x, y ) to find the standard form of the equation of the quadratic function:Vertex = (-4,2)Point = (-4,0)F( x )= Answer for coordinate 1 (x- Answer for coordinate 2 )^2 +Answer for coordinate 3
In order to find the quadratic equation, let's use the vertex form below:
[tex]y=a(x-h)^2+k[/tex]Where the vertex is located at (h, k).
So, if the vertex is (h, k) = (-4, 2) and using the point (x, y) = (-4, 0), we have:
[tex]\begin{gathered} y=a(x+4)^2+2 \\ 0=a(-4+4)^2+2 \\ 0=a\cdot0^2+2 \\ 0=2 \end{gathered}[/tex]Since the final statement is false, it's not possible to have a quadratic function with vertex (-4, 2) and with the point (-4, 0).
If we use the point (4, 0) instead, we would have:
[tex]\begin{gathered} y=a(x+4)^2+2 \\ 0=a(4+4)^2+2 \\ 0=a\cdot64+2 \\ 64a=-2 \\ a=-\frac{2}{64} \\ a=-\frac{1}{32} \end{gathered}[/tex]So the equation in this case would be:
[tex]y=(-\frac{1}{32})(x-(-4))^2+2[/tex]The empty spaces would be filled with the values -1/32, -4 and 2.
problem 4: Solve for x
The variable x has a value of 3 in the triangle
How to determine the solution of x?The given parameter represents the triangle(s) in the figure
In the triangle, we can see that:
There are two trianglesThe pair of triangles have parallel sidesAlso, the triangles are similar trianglesThe above means that:
The sides of the triangle are in equivalent ratio
This is represented as
4 : 5x - 4 = 4 : 3x + 2
This also means that
5x - 4 = 3x + 2
Collect the like terms
5x - 3x = 4 + 2
Evaluae
2x = 6
Divide
x = 3
Hence, the value of x is 3
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Could someone tell me the y intercept for the tables in questions 2 and 3
Using it's concept, the y-intercept for each table in this problem is given as follows:
2) y = 4.
3) y = -3.
What are the intercepts of a function?The x-intercept of a function is given by solutions of x to the equation f(x) = 0, that is, the value of x when the function crosses the x-axis.The y-intercept of a function is given by the value of f(x) when x = 0, that is, the value of y when the function crosses the y-axis, also called f(0).In the context of this problem, we are given two tables with pairs of values (x,y), hence the y-intercept for each case is given by the value of y when x = 0.
In item 2, when x = 0, y = 4, hence the y-intercept is of y = 4.In item 3, when x = 0, y = -3, hence the y-intercept is of y = -3.More can be learned about the y-intercept of a function at https://brainly.com/question/26249361
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Besides 39 and 1, what is one factor of 39?
Answer:
3 or 13
Step-by-step explanation:
1, 3, 13, and 39 are factors of 39
3 × 13 = 39
3 or 13 is a choice
I hope this helps!
A 25-foot ladder is leaning against the side of a house so that the bottom of the ladder is 15 feet from the base of the house. Will the ladder reach a window that is 21.5 feet above the ground?
From the given parameters using Pythagoras theorem, we can say that No, the ladder will not reach a window that is 21.5 feet above the ground.
How to use Pythagoras Theorem?
We are told that the ladder is 25 ft and leans against the wall and so this will be the hypotenuse of the right angle triangle formed with the building.
The horizontal distance from the base of the ladder to the building is 15 ft. Thus, this will be the base or adjacent side of the triangle.
I have drawn a triangle to show this measurements and so we can use Pythagoras theorem to find the vertical height from the top of the ladder to the ground.
BC² = AB² + AC²
25² = 15² + AC²
AC² = 25² - 15²
AC = √(25² - 15²)
AC = 20 feet
Since the ladder is a vertical height of 20 ft from the ground which is less than the height of the window from the ground then we cans ay that the ladder will not reach the window.
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Eddie needs 2 \displaystyle \frac{2}{3} 3 2 cups of flour for one batch of pancakes. How much flour does he need for 2 \frac{1}{2}2 2 1 batches? Make sure to put cups at the end of your answer.
The cups of flour that is needed for 2 1/2 cups of flour is 6 2/3 cups.
How much flour is needed?A mixed number is a fraction that has a whole number, a numerator and a denominator. The numerator usually has a smaller value when compared with the denominator. An example of a mixed number is 2 1/2.
In order to determine the cups of flour that is needed for 2 1/2 batches of pancakes, multiply 2 1/2 by 2 2/3. Multiplication is the mathematical operation that is used to determine the product of a number. The sign that represents multiplication is x.
Flour needed = batches to be made x amount of flour needed for one batch
2 2/3 x 2 1/2
8/3 x 5/2 = 20 / 3 = 6 2/3 cups
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please help me solve
The co-ordinate of B ( -3 , 2 )
What is the Mid Point of Line Halfway between the two end points is the midway?Its x value lies in the middle of the two x values.
Its y value lies in the middle of the two y values.
To figure it out:
Add the two "x" coordinates, then divide by two.
n order to divide by two, add the two "y" coordinates.
Mid point (X , Y) formula
X = ( x₁ + x₂ ) ÷ 2
Y = ( y₂ + y₂ ) ÷ 2
where ( x₁ , y₁) co- ordinate of A ( 7 , -2 )
(x₂ , y₂ ) co- ordinate of B
2 = ( 7 + x₂ ) ÷ 2
x₂ = -3
0 = ( -2 + y₂ ) ÷ 2
y₂ = 2
co- ordinate of B ( -3 , 2 )
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Find each of the missing sides of the right triangles using Pythagorean Theorem.
We need to apply the Pythagorean Theorem, which says that the square of the Hypothenuse is equal to the sum of the squares of the cathetus. So we have:
[tex]\begin{gathered} 41^2=x^2+9^2 \\ 1681=x^2+81 \\ x^2=1681-81 \\ x^2=1600 \\ x=\sqrt[]{1600} \\ x=40 \end{gathered}[/tex]The missing side is equal to 40.
A right circular cone has a radius of x+4 and a height 5 units less than its radius. Express the volume of the cone as a polynomial function. The volume of a cone is V=13πr2h for radius r and height h. Enter π as pi.
The equation of the volume function is V(x) = 1/3(x + 4)²(x - 1)
How to determine the volume function?The given parameters are
Radius, r = x + 4
Height, h = 5 units less than the radius
This means that
h = r - 5
So, we have
h = x + 4 - 5
Evaluate
h = x - 1
The volume of a cone is calculated as
V = 1/3πr²h
Substitute the known values in the above equation
V = 1/3 * (x + 4)² * (x - 1)
This gives
V = 1/3(x + 4)²(x - 1)
Express as a function
V(x) = 1/3(x + 4)²(x - 1)
Hence, the function is V(x) = 1/3(x + 4)²(x - 1)
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explain why the researchers used data from ten trials and averaged them, rather than data from a single trial.
Answer:
It meant that the results were more reliable and the average makes it more reliable.
Step-by-step explanation:
The researchers used data from ten trials and averaged them, rather than data from a single trial because the data from single trials are more likely to include errors.
What is the research?Research the issue utilizing data from a number of sources. It is critical to understand what one is attempting to achieve while designing an experiment.
The first method is to average identical successive trials, in which the researcher simply compares mean values across groups of patients or treatment effects. Averaging, to some extent, presume that the behavior is random. This premise is often ignored. If there is something systematic going on, such as a trial-by-trial change in response owing to adaptation/learning or weariness, this is potentially highly significant clinical information that is lost when the trials are averaged.
Thus, the data from single trials are more likely to include errors
Hence, the researchers used data from ten trials and averaged them, rather than data from a single trial.
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i’m doing a test and i’m looking for the answer to this problem -3/4 divided by 5
Answer:
-3/4÷5= -3/4*1/5
-3/20
-3/20 is the answer
Geometry Unit 5: Homework 1 Triangle Midsegments. Need help please!!
As per question no. 5 of the reference attached thereby along with the question statement, the solution for "x" is 15, solved using the similarity of triangles theorem.
As per the question statement, we are provided with a reference attachment, attached thereby,
And we are required to solve for "x", as per question no. 5 of the attachment.
To solve this question, first we need to know about the similarity of triangles.
Two triangles are said to be similar if they have the same ratio of corresponding sides and equal pairs of corresponding angles, that is, the two triangles will have the same shapes, but different sizes.Here, as per the similarity of triangles theorem, we can relate the question mentioned sides in the following equation:
[2(8x - 23) = (10x + 44)]
And solving the equation, we will be able to obtain the value of "x" which will be our desired answer, i.e.,
[2(8x - 23) = (10x + 44)]
Or, [(16x - 46) = (10x + 44)]
Or, [(16x - 10x) = (44 + 46)]
Or, (6x = 90)
Or, [x = (90/6)]
Or, (x = 15)
Triangles: A triangle is a two-dimensional, closed, geometric shape with three sides, and three interior angles, whose sum of these interior angles is always equal to 180 degrees.To learn more about Similarity of Triangles, click on the link below.
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Answer: 1. A)BD,AE B)BF,CE C)DF,CA
Step-by-step explanation:
THATS ALL I GOT
math help for homework
Answer:
[tex]f(x)=x+2[/tex]
Step-by-step explanation:
Given parameters:
f(0) = 2f(2) = 4Therefore, there are two points on the line:
(0, 2) and (2, 4)The linear relationship between the x and y values is:
The y-value is 2 more than the x-value.[tex]\implies f(x)=x+2[/tex]
To prove this algebraically, define the points:
(x₁, y₁) = (0, 2)(x₂, y₂) = (2, 4)Find the slope of the linear function by substituting the defined points into the slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-2}{2-0}=\dfrac{2}{2}=1[/tex]
Substitute the found slope and one of the points into the point-slope formula to create a linear function that satisfies the given parameters:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-2=1(x-0)[/tex]
[tex]\implies y-2=x[/tex]
[tex]\implies y=x+2[/tex]
Hence proving that the linear function is:
[tex]f(x)=x+2[/tex]
What is the domain/range of a parabola with the equation [tex]x=-2(y-2)^2+2[/tex]?
The quadratic function's domain for a given function is -2<x>2.
What is the Domain of a quadratic function?
When all of the x-values in the domain are assessed into the function, which is what is often referred to by the y-values, the range of a function is just the range of output values. This suggests that in order to clarify the range, the domain has to be determined.The domain of this quadratic function includes always all x values. This was very simple.The provided parabola, y = ax2 + bx + c, is in the Standard Form. Therefore, we should simplify the process by converting it to vertex form.Function given [tex]x=-2(y-2)^2+2[/tex]
The vertices are represented by the vertex form, y = an (x-h)^2+ k, and (h,k).
h=-2
k=+2
It is clear that this parabola has a minimum value of y = -2 and a maximum value of y=+2.
The quadratic function's domain for a given function is -2<x>2.
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find the gradient of lines a and b
Answer:
Line A: 4
Line B: -2
Step-by-step explanation:
Note: gradient means slope, or m, in this context
To find the slope of a line, use the formula:
[tex]m = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points on the line
Line A has points (2, 2) and (3, 6). To find the slope of the line, simply plug these values into the formula for m :
[tex]m_{\mathrm{line \, A}}=\dfrac{6-2}{3-2}=\dfrac{4}{1}=4[/tex]
So, the slope, or gradient, of line A is 4.
Next, do the same thing for Line B.
Find two points on the line:
(0, 8) and (1, 6)
And plug these values into the formula:
[tex]m_{\mathrm{line \, B}}=\dfrac{6-8}{1-0}=\dfrac{-2}{1}=-2[/tex]
So, the slope, or gradient, of line B is -2.
4 = -(x + 3) as a real world problem like renting a car if a deposit is paid and and there is an hourly charge
The equation to illustrate a word problem regarding the renting of a car is 60 + 3h.
What is an equation?It should be noted that an equation is simply used to illustrate the information given about the variables.
An example of word problem simply that can be illustrated by an equation will be that the initial deposit to rent a car is $50 and there's an hourly rate of $3.
Therefore, based on the above information, the equation to illustrate this will be:
= Initial cost + Hourly rate
Let the number of hours be represented by h.
= 50 + (3 × h)
= 50 + 3h
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what is slope from (6,-10),(-15,15)
Find the elapsed time Start 5:15am End time 12:04pm
Given that the start time is 5:15 am. It can be represented as,
[tex]S=5\colon15[/tex]Also given that the end time is 12:04 pm. It can be represented as.
[tex]E=12\colon04[/tex]The elapsed time (e) is equal to the difference between the end time and start time as given below,
[tex]e=E-S[/tex]Substitute the values,
[tex]e=12\colon04-5\colon15[/tex]Note that 04 minutes is greater than 15 minutes, so we have to borrow 1 hour from 12 hours and add it to the minutes,
[tex]12\colon04\equiv11\colon64[/tex]Replace the value and perform the subtraction,
[tex]\begin{gathered} e=11\colon64-5\colon15 \\ e=(11-5)\colon(64-15)_{} \\ e=6\colon49 \end{gathered}[/tex]Thus, the required elapsed time is 6:49, that is, 6 hours and 49 minutes.
what is the the slope of (20,15) (30,35)
Slope = 2
The slope of coordinates ( 20 , 15 ) and (30 , 35) = 2
What is slope?The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).The slope is defined as the ratio of the vertical change between two points, known as the rise, to the horizontal change between those same two points, known as the run.Determine the coordinates of two points on the line. Calculate the difference in y-coordinates between these two points (rise).Determine the x-coordinate difference between these two points (run). Divide the y-coordinate difference by the x-coordinate difference (rise/run or slope).Here given two points (20, 15) and (30 , 35)
Formula to find slope = y2 - y1 / x2 - x1
= 35 - 15 / 30 - 20
= 20 / 10
= 2 / 1
= 2
∴ Slope of (20 , 15) (30 , 35) = 2 .
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Find the slope and y intercept of
2y = 6x - 12 Show work
WILL GIVE BRAINLIEST!!!!
The slope and y-intercept of 2y = 6x - 12 are 3 and (-6) respectively.
What is the slope intercept form of a line?
The line with m as the slope, and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, c, denotes the y-coordinate of the location where the line's graph crosses the y-axis.
Given, the equation of the line is 2y = 6x - 12
Dividing the given equation by 2 we get, y = 3x - 6 ⇒ y = 3x + (-6)
Comparing the equation with the standard form of slope intercept form of a line as established in literature, we have:
Slope = m = 3 and y-intercept = c = -6
Thus, the slope and y-intercept of 2y = 6x - 12 are 3 and (-6) respectively.
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A right triangle has legs of 21 inches and 28 inches
whose sides are changing. The short leg is decreasing by 2
in/sec and the long leg is shrinking at 5 in/sec. What is the
rate of change of the area?
The rate of change of the area is -80.5 [tex]inches^{2}[/tex]/sec.
Given:
A right triangle has legs of 21 inches and 28 inches whose sides are changing.The short leg is decreasing by 2 in/sec and the long leg is shrinking at 5 in/sec.
Let's set the two legs as a and b, so the lengths are:
a = 21 - 2t
b = 28 - 5t
The area is:
area a = ab /2
= (21 - 2t) (28 - 5t)/2
= (588 - 105t - 56t + 10[tex]t^{2}[/tex]/2
a = 5[tex]t^{2}[/tex] - 161t/2 - 299
The rate of change of the area is:
da/dt = d(5[tex]t^{2}[/tex] - 161t/2 - 299)/dt
da/dt = 10t -161/2
And at t=0,
= 10(0) - 161/2
= - 80.5
so the rate of change of the area is -80.5 [tex]inches^{2}[/tex]/sec.
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What is the unit rate for a relationship A (the table)? (do not include units for this one)
PLEASE ANSWER ASAP
Answer:
it is per 1
Step-by-step explanation:
is -1 3/10 greater than -1.28
yes, because 3/10 is greater than .28
which of the following relations is a function? a( 5 ,1 )(,-2 4,) (1, 1) (-5, 2) b (1, 4) (-2, 2) 5,1) (-6,2) c (1, 01) (-2 3) ( 5, 1) (-2, 5) d )1, 4) (-2, 6) (1, 3) -6 2)
The relation is a function if every ordered pair has one value of x, which means x does not repeat
Let us study each relation
a) {(5, 1), (-2, 4), (1, 1), (5, 2)}
Since each ordered pair has a different value of x
There are 2 ordered pairs that have x = 5
This relation is not a function
b) {(1, 4), (-2, 2), (5, 1), (-6, 2)}
Since no repeated x in the ordered pairs
Then the relation is a function
c) There are 2 ordered pairs with x = -2
It is not a function
d) There are 2 ordered pairs with x = 1
It is not a function
The answer is b
For any line, if you draw two right triangles using the line as the hypotenuse, do the triangles have to be similar? why or why not?
For any line, if you draw two right triangles using the line as the hypotenuse, we can say that; Yes, the triangles have to be similar because the sides of both triangles will have the same ratio.
How to interpret congruent triangles?From the attached diagram, we will assume any two right triangles are drawn on the line OP, and AB and A'B' as the hypotenuse on the same line OP.
Now, due to the fact that the slope of the line OP is constant and assume that it makes x° with the positive x-axis, then we can say that;
tan x = AC/BC = A'C'/B'C'
Thus;
AC/A'C' = BC/B'C'
Therefore, we can say that the sides of the two right triangles are in the same ratio and as such, Δ ABC and Δ A'B'C' are similar.
Therefore, all the right triangles will be similar.
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I need help with 8, 9, and 10. Please help me I don’t want a 0.
1.Charles wants to invest $20,000. The investment firm is offering 8% interest compounded monthly. How much money will he have made if he leaves his money with the bank for 40 years?2.Lisa’s grandmother left her a $100,000 inheritance. She wants to invest themoney in an account paying 7.2% interest compounded continuously. How muchmoney will be in the account after 30 years?3.John saved $50,000. and wants to put the money into an Index Annuity that paysan average of 8.4% per year, compounded semi-annually. How long will it takehim to reach his goal of $1,000,000?4.Susie needs to make $100,000 to pay her home mortgage and has $10,000 toinvest. How much interest will she need if her bank compounds the interestannually to reach her goal?5.Betty wants to retire in 45 years. She needs $2,000,000. If she’s able to find aMutual Fund that offers 9.5% interest and compounds quarterly, how much willshe need for a deposit?
Apply the compound interest formula:
A= P (1+r/n)^nt
Where:
A: future value of the investment
P: Principal amount
r: interest rate (in decimal form)
n: number of compounding periods in each year
t: years
Replacing:
A= 20,000 (1+0.08/12)^12x40
A = 20,000 (1.0067)^480
A= 485,467.7116
