The equation equivalent to the equation x + y = 3 is 6x + 6y = 18.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
x + y = 3
Multiply 6 on both sides.
6x + 6y = 18
Thus,
The equation that is equivalent is 6x + 6y = 18.
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x^y=y^x and x=2y prove that y=2.
Answer:
[tex] {x}^{y} = {y}^{x} \: - - - (1)[/tex]
[tex]x = 2y \: - - - (2)[/tex]
Substitute (2) into (1):
[tex] {2y}^{y} = {y}^{2y} [/tex]
Log both sides:
[tex]lg(2 {y}^{y} ) = lg(y^{2y} )[/tex]
[tex]y \: lg(2y) = 2y(lg \: y)[/tex]
[tex]y \: lg(2) + y \: lg(y) = 2y \: lg(y)[/tex]
[tex]y \: lg(2) = 2y \: lg(y) - y \: lg(y)[/tex]
[tex]y \: lg(2) = y \: lg(y)[/tex]
Divide by y on both sides:
[tex]lg(2) = lg(y)[/tex]
[tex] {10}^{lg(2)} = {10}^{lg(y)} [/tex]
2= y
y= 2 (proved)
Explanation:
• step 5: lg(m)^n= nlg(m)
• Step 6: lg(mn)= lg(m) +lg(n)
Triangle ABC has coordinates A(-2, -3), B(1, 1), and C(2, -1). If the triangle is
translated 1 unit right and 3 units up, what are the coordinates of A?
Unit rates are ALL AROUND US. If you have a phone, take a picture of a unit rate that you find at the grocery store, gas station, or as you are simply out and about. For your post, describe the picture and where you found your unit rate and what the unit rate was.
For your replies, think back and see if you recall seeing unit rates in those places. Describe how a unit rate could be used at the location where it was found.
A unit rate I found at the grocery store was 10 bananas/ $5 this describe the price for 10 bananas but can also be used to identify the price for 1 banana.
What is a unit rate?In mathematics, a unit rate can be defined as a mathematical expression that includes two units to show the rate of a specific activity. For example, the expression 50 kilometers/2 hours shows a car covers a distance of 50 kilometers in two hours, which can be simplied as 25 kilometers per hour.
What is an example of a unit rate that you can find at a grocery store?A unit rate I could observe last weekend while buying fruits and vegetables was 10 bananas/ $5. This unit rate is mainly used to inform buyers about the price of 10 bananas. However, this can also be simplified as $0.5 per banana and this would inform the buyers about the price per unit.
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BANKING Twin brothers Amare and Jermaine each received $1000 for graduation. Amare invests his money in an account that pays 2.25% compounded daily. Jermain invests his money in an account that pays 2.25% compounded
annually.
Part A
Which brother will have more money at the end of 10 years?
A) Amare
B) Jermaine
C) The accounts will be equal.
Part B
To the nearest cent, how much more money? $
A) Amaire have more money than Jermaine after 10 years.
B) By [tex]5.387*10^{11}[/tex]% Amaire has more money than Jermaine.
What is compound interest?
The interest charged on a loan or deposit is known as compound interest. It is the idea that we employ the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest.
Amare and Jermaine has initial amount = $1000
Amare spend his money that pays 2.25% compounded daily.
where are Jermain invest his money that pays 2.25% compounded annually.
Formula of Compound interest that compounded daily
final amount = [tex]A(1+\frac{r}{365})^{365t}[/tex]
where A is initial amount and t is time in years .
final amount after 10 years
final amount = [tex]1000(1+\frac{2.25}{365})^{365*10}[/tex]
final amount = 1000×[tex]1.00616^{3650}[/tex]
final amount = 1000×5.51×[tex]10^{9}[/tex]
final amount = $5.51 ×[tex]10^{12}[/tex]
Formula of Compound interest that compounded annually
final amount = [tex]A(1+\frac{r}{100})^{t}[/tex]
where A is initial amount and t is time in years .
final amount after 10 years
final amount = [tex]1000(1+\frac{2.25}{1000})^{10}[/tex]
final amount = 1000×[tex]1.00225^{10}[/tex]
final amount = 1000×1.0227
final amount = $1022.7
Part A :
Amare has more money after 10 years.
part B :
percent more money = [($5.51 ×[tex]10^{12}[/tex] - 1022.7)/1022.7]*100=[tex]5.387*10^{11}[/tex]%
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What are sin 0 and cos 0 for each value of 0?
Answer:
a. sin 300 = -∛3/2, cos 300 = 1/2
b. sin -225 = √2/2, cos -225 = √2/2
c. sin 5π/6 = 1/2, cos 5π/6 = -3√2
d. sin -4π/3 = √3/2, cos -4π/3 = -1/2
Step-by-step explanation:
See unit circle
A $280 suit is marked down by 30%. Find the sale price.
Answer:
To find the sale price of the suit, we need to first calculate the discount. The discount is equal to the original price multiplied by the discount rate, which in this case is $280 * 30% = $84.
Then we subtract the discount from the original price to find the sale price: $280 - $84 = $196.
So the sale price of the suit is $196.
Step-by-step explanation:
HELP!! I'M COMFUSED!
The mass of particle A is approximately 6.5 x 10^-8 grams and the mass of particle B is 8.8 x 10^-27 grams. Approximately how many of particle B have the same mass as one of particle A?
Answer:
Take the ratio of the 2 numbers:
[tex] \frac{6.5 \times {10}^{ - 8} }{8.8 \times {10}^{ - 27} } = 7.4 \times {10}^{18} [/tex]
This means that it takes 7.4×10^18 particle Bs to equal the mass of particle A.
Which number is the prime factorization for: 2 x 3 x 3 x 5
Answers:
90
180
18
95
Answer:
90
Step-by-step explanation:
2*3*3*5=
90
Answer:
90
Step-by-step explanation:
2 × 3 × 3 × 5
2 × 3 × 15
2 × 45
90
I need help with this please
Answer:
pls give me the brainliest
the answer is in the attached document
Answer:
1 13/15
You need to turn the mixed number into an improper fraction to multiply.
What is the XYZ axis called?
The XYZ axis is called as X-axis, Y-axis, and Z-axis, respectively.
The term axis in math is defined as a line with respect to which a curve or figure is drawn, measured, rotated, etc.
Here we have given that XYZ axis, in math are no standard names for the coordinates in the three axes
Based on these the coordinates are often denoted by the letters X, Y, and Z, or x, y, and z.
And these axes may then be referred to as the X-axis, Y-axis, and Z-axis, respectively.
Here in the graph x-axis and y-axis represent the first two dimensions where as the z-axis, the third dimension. Which is also defines the x and y denote width and height and the z denotes depth.
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Find the measure of the missing angles.
Answer:
c = 77
b = 77
Step-by-step explanation:
c and b are equal because they are vertically opposite.
In addition, they both form a supplementary pair with 103 (but not at the same time).
c + 103 = 180 c and 103 form a supplementary pair.
c = 180 - 103
c = 77
c = b = 77
HELP ME PLEASE aAA REEE NO SCAMS
Answer:
5
Step-by-step explanation:
Each value of ADCB is 2x as much as EHGF
Which table represents the statement “A car is traveling at a rate of 60 miles per hour”? A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled miles with entries 60, 30, 10. A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled miles with entries 60,61, 62. A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled miles with entries 60, 65, 70. A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled miles with entries 60, 120, 180.
Answer:
Option DStep-by-step explanation:
The given statement represents the equation:
y = 60xFor the values of x = 1, 2, 3 the value of y would be:
y = 60, 120, 180Correct table to reflect this is D.
A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled miles with entries 60, 120, 180.Answer:
The declaration is the equation:
and = 60x
In terms of values x = 1, 2, 3 y is: Y
Y = 60. 120.
This is shown by the right table D.
Table with 3 rows in 2 columns.
The hours of entries 1, 2, 3 are shown with Column 1.
Miles containing the items 60, 120, 180 are shown in column 2.
0 Thank you.
Step-by-step explanation:
In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. The scatterplot displays the data the teacher collected along with the least-squares regression line. One student with a handspan of 23 cm grabbed 38 pretzels. This point is circled on the graph.
What effect will the circled point have on the y-intercept?
The y-intercept will not change with the addition of this point.
The y-intercept will decrease because the point pulls the least-squares regression line toward it.
The y-intercept will increase because the point pulls the least-squares regression line toward it.
The y-intercept will increase because this point represents an extremely high number of pretzels grabbed with the dominant hand.
answer is B
We can see here that the effect that the circled point will have on the y-intercept is: B. The y-intercept will decrease because the point pulls the least-squares regression line toward it.
What is an intercept?In statistics, an intercept is the value of the dependent variable when the independent variable(s) is equal to zero. It is often represented by the symbol "b" in a linear equation.
For example, a simple linear equation has the form y = mx + b, where "y" is the dependent variable, "x" is the independent variable, "m" is the slope of the line, and "b" is the y-intercept. The y-intercept is the point where the line crosses the y-axis.
We see here that the answer above is the correct answer.
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Complete the table with the perimeter for each given side length. Then, write a rule for a function, P, that gives the perimeter of the paper in feet when the side length in feet is l. Use function notation.
what does P(11) represent in this situation? What is its value?
For a roll of paper with dimensions 3 feet cut to any desire length,
a) The value of perimeter when cut to 2.5 feet is 11 feet.
b) The complete table with filled perimeter column is present above . The function notation for perimeter is , P =2(L+ W)
c) P(11) , represents the length of paper cut to 11 feet in this situation. It's value i.e., P(11) = 28 feet .
Perimeter is defined as the sum of all boundary length of any geometry. We have a roll of paper with dimensions 3 feet ( i.e, width) is cut to any length. From, it we conclude that that paper is like quadrilateral shape but not square.
a) when the paper cut in a length of 2.5 feet , so, length (L) = 2.5 feet
The perimeter of quadilateral ( rectangle in this case ) is 2(L+W) so, perimeter
= 2( 2.5 + 3)
= 11.0 feet
b) Now, we have to complete "perimeter coulmn ," in the table and side lengths are provided.
Width (w) = 3 feet
length (l) = 1 feet
perimeter = 2(4) = 8
similarly, side lengths (ft.) perimeter ( ft.)
2.5 11
1 8
2 10
11 28
L 2( L + W)
The functional notation for perimeter is
P = 2(L+W) .
c) P(11) represents the length of paper in feet when the paper is cut at a length of 11 feet . It's value is 28 feet . So, the value of P(11) is 28 feet.
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Complete question:
A roll of paper that is 3 feet wide can be cut to any length.
a. If we cut a length of 2.5 feet, what is the perimeter of the paper?
b. Complete the table with the perimeter for each given side length. Then, write a rule for a function, P, that gives the perimeter of the paper in feet when the side length in feet is L, use a function notation.
c) what does P(11) represent in this situation? What is its value?
Pls help question 9,10 and 11. And can u explain or show how u make the equation ?
No links will mark brainliest if correct!
12,000$Step-by-step explanation
Suppose that there are some spiders in a tank and each spider has 8 legs
x=the number of spiders
y=the total number of legs on all the spiders
Which equation is correct
a. x-87
b. y=x/8
c. x=y/8
d. y=8x
Answer:
d. y=8x
Step-by-step explanation:
since y = the number of legs and spiders = x
each spider has 8 legs
so y = 8*x
which is y=8x
The point P(2k, k) i equiditant from A(-2, 4) and B (7,-5). Find the value of k.
The value of k is 3. We have to equal the distance between PA and PB and then solve the equation by squaring both side.
Given is that P(2k, k) is equidistance from A(-2, 4) and B(7, -5).
First, we try to understand what is distance formula between 2 points
let's suppose we have 2 points (x1, y1) and (x2, y2).
Find the distance between them.
The separation between two points the coordinates of two points in space are used in the formula. In coordinate geometry, a two-dimensional or three-dimensional space can be used to calculate the distance between two points using the distance formula. The Pythagoras theorem is also applied to the distance formula for two points.
The length of the line segment bridging two points on a plane is known as the distance between the points. d=√(x2 - x1)^2 + (y2 - y1)^2 is a common formula to calculate the distance between two points. This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.
Given that PA = PB.
First, find what is PA
[tex]\sqrt{(2k+2)^2 + (k-4)^2}[/tex]
Here we will use the formula of
(a + b)^2 = a^2 + 2ab + b^2
(a - b)^2 = a^2 -2ab + b^2
[tex]\sqrt{4k^2+8k + 4 + k^2 -8k + 16}[/tex]
[tex]\sqrt{5k^2+20}[/tex].
Now find what is PB.
[tex]\sqrt{(2k-7)^2 + (k+5)^2}[/tex]
[tex]\sqrt{4k^2 + 49 -28k + k^2 + 25 + 10k}[/tex]
[tex]\sqrt{5k^2 - 18k + 74}[/tex]
PA = PB.
[tex]\sqrt{5k^2 + 20 } = \sqrt{5k^2 -18k + 74}[/tex]
squaring both sides.
5k^2 + 20 = 5k^2 -18k + 74
18k = 74-20
18k = 54
k = 3.
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Need help with this as well tyy
Answer:
<F =~ <LGH/KL = FH/JL<G =~ <KHope that helps! :)
-Aphrodite
Step-by-step explanation:
PLEASE HELP ASAP!!! no bots
Answer:
Vertex: (-3, -5)
Axis of Symmetry: x = -3
Step-by-step explanation:
Heres the sketch:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
A third-grade student is asked to find the best estimated answer for the problem below by rounding to the nearest ten. 162 287 395 The student gets an answer of 840. Which of the following best describes the student's error
The error is that the student rounded off the outcome after combining the numbers.
What is rounding off?When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number.
For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.
So, we have:
162 + 287 + 395 = 840
The error:
After adding the numbers, the student rounded the result.
If the learner had added the numbers first and then rounded the result, they would have received the correct answer of 850 instead of 840.
When estimating totals, students should be taught to round numbers first before adding them.
Therefore, the error is that the student rounded the outcome after combining the numbers.
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Correct question:
A third-grade student is asked to find the best-estimated answer for the problem below by rounding to the nearest ten.
162 + 287 + 395
The student gets an answer of 840. Which of the following best describes the student's error?
which of these functions is linear?
Answer:
Function 2, y = x - 5
Step-by-step explanation:
Function 1 is called an Absolute Value Function (where there is absolute value symbol around the whole or a part of the equation, its parent function is; y = |x| )
Function 2 is called a Linear Function (which could be written as y = mx + b, here m and b are integer values, b value is the y-intercept, m is the slope)
Function 3 is called an Inverse Function ( where a value is divided by a variable like "x", it's parent function is; y = [tex]\frac{1}{x}[/tex] )
Function 4 is called a Quadratic Function (it's a function where the variable is squared, it's parent function is; y = x² )
Hope this helps!
The function that represents the linear function is y = x - 5. Then the correct option is B.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let's check all the options, then we have
A) y = |x| - 5, the function is an absolute function.
B) y = x - 5, the function is a linear function.
C) y = 1/x - 5, the function is a rectangular hyperbolic function.
D) y = x² - 5, the function is a quadratic function.
The function that represents the linear function is y = x - 5. Then the correct option is B.
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Una tribu de indios observa que la manada de búfalos del territorio donde se han instalado se reduce según una función de decrecimiento exponencial dada por f(x)=kax. Hace 12 lunas contabilizaron 1944 búfalos y actualmente hay 1296 búfalos en la manada. Si se mantiene el decrecimiento exponencial, calcular dentro de cuántas lunas tendrán que abandonar la pradera, sabiendo que esa tribu cambia de territorio cuando quedan menos de de 100 búfalos.
Answer:
88 lunas
Step-by-step explanation:
El número inicial de búfalos, a = 1,944
El número de búfalos después de 12 semanas, y₁₂ = 1296
La forma general de una función decreciente exponencial se presenta como sigue;
y = a · bˣ
Dónde;
x = El número de lunas
b <1
a = El primer término = 1,944
Por lo tanto, tenemos;
1.296 = 1.944 × b¹²
b¹² = 1.296 / 1.944 = 2/3
b = e ^ (ln (2/3) / 12) ≈ 0,967
Cuando queden 100 búfalos, tenemos;
100 = 1.944 × (0,967)ˣ
x = ln (100 / 1.944) / ln (0,967) ≈ 87,82 ≈ 88
El número de lunas que tendrían que dejar el prado, x ≈ 88 lunas
find the value of x and y (2x+5) , (5x-17) and (3x-11)
The value of x and y in the diagram are 26° and 9° respectively.
What is linear pair theorem?Two adjacent angles formed a linear pair.
The linear pair property:
The sum of the angle measure of both the angles is 180°.
Given:
Using linear pair theorem,
(5x - 17)° + (3x - 11)° = 180°.
8x - 28°= 180°
8x = 180° + 28°
8x = 208°
x = 208/8
x = 26°
The value of x is 26°.
Now,
3x - 11° = 3×26°-11°
= 67°
Linear pair theorem,
67° + 90° + (2y+5)° = 180°
157°+2y+5° = 180°
2y + 162° = 180°
2y = 180° - 162°
2y = 18°
y = 9°
The value of y is 9°.
Therefore, the value of x is 26° and y is 9°.
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The complete question is given in the attached image.
PLEASE PLEASE HELP ME WILL MARK BRAINLISTS!!!!!!
PLEASE HELP
PLEASE HELP
PLEASE HELP
PLEASE HELP
PLEASE HELP
PLEASE HELP
PLEASE HELP
PLEASE HELP
PLEASE HELP
Answer:
All of them approach 9 when x=0
Step-by-step explanation:
During a science experiment, a chemist boils a liquid and then sets it on the lab table and records the temperatures as it cools. The graph shows , the temperature in degrees Centigrade, and is the number of after the liquid is set on the table. Liquid Temperature Time () Which equation is the best model for this data?
The exponential function that best models this data is given as follows:
C. y = 80(0.75)^x + 20.
How to define the exponential function?An exponential function, considering it's asymptote, is defined as follows:
y = a(b)^x + c.
In which the parameters are given as follows:
a is used to define the initial value.b is the rate of change.c is the horizontal asymptote.From the graph, the horizontal asymptote is at y = 20, hence the parameter c is defined as follows:
c = 20.
When x = 0, y = 100, hence the parameter a is obtained as follows:
100 = a(b)^0 + 20
a + 20 = 100
a = 80.
When x = 5, y = 40, hence the parameter b is obtained as follows:
40 = 80b^5 + 20
80b^5 = 20
b^5 = 1/4
b = (1/4)^(1/5)
b = 0.75. (approximately).
Hence the function is defined as follows:
y = 80(0.75)^x + 20.
Meaning that the correct option is given by option C.
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6. A phone company charges $67 for monthly
access and $14 for each gigabyte of data
used. If you sign a two-year contract and
use 147.5 gigabytes of data, which value is
the closest approximation to the total
amount you will pay for phone service?
147.5 times 14 = 2065
And they want an estimate so just round the 147.5 to 150.0 and the 14 to a 15 and your answer is 2250
Estimate : 2250
Actual answer is : 2065
If you have any questions comment under this post
Have a wonderful day<3
to
5.2.2 Guided Instruction: Solutions to the
Products and Quotients of Polynomials on a
Graph
Graphs can be used to determine the products and
quotients of polynomials similarly to using graphs when
adding and subtracting polynomials.
The functions a(x) and b(x), and their product, a(x) b(x),
represented by c(x), are shown on the coordinate plane.
35A
(10, 34)
-10
-30
-25-(-0,24)
MATH
20
(0.805, 105)
10
(1.5, 6)
0
(0-3)
b(x10
-15
(8,13)
C(x)
(6.5, 10)
5
(0-8)
(10, 17)
(8.695-10)
3. Find the value of c(10).
2. What is the product of a(10) · b(10)?
10, 2
15
(8,0)
-20
1. Describe how to use the graph to determine the value
of a (10) b(10).
20
25
Thus, the choice that best describes the graph is A cubic function on a coordinate plane has an inflection point at x = 5 and crosses the x-axis at x = 5.
Definition of the cubic function .f(x)=ax3+bx2+cx+d, where 0 and the coefficients a, b, c, and d are complex numbers, and where the variable x has real values. In other words, it is both a three-degree polynomial function and a real function.
Here,
Our role in this situation is:
y = ∛(x - 5) (x - 5)
so the cubic root is given.
In this case, we see that when x = 0, we have:
The y-intercept is y = -5.
And if x = 5, we get:
Because of the sign change, the x-intercept and inflection point are both equal to y = ∛0 = 0
Thus, the choice that best describes the graph is A cubic function on a coordinate plane has an inflection point at x = 5 and crosses the x-axis at x = 5.
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Find the height of the triangle.
Answer:
72.83
Step-by-step explanation:
61²+x²=95²
3721+x²=9025
x²= 5304
x= 72.83