Answers
The system of equations is y = 4x - 3 and y = -1/3x + 4 and the solution is (21/13, 45/13)
How to determine the system of equations?From the question, we have the table of values as the parameters that can be used in our computation:
From the table, we have
Table 1
(x, y) = (0, -3) and (4, 13)
A linear equation is represented as
y = mx + c
Where
Slope = m
c = y when x = 0
This means that
c = -3
So, we have
y = mx - 3
The point (4, 13) implies that
13 = m * 4 - 3
So, we have
4m = 16
m = 4
So, the equation is
y = 4x - 3
Table 2
(x, y) = (0, 4) and (4, 6)
A linear equation is represented as
y = mx + c
This means that
c = 4
So, we have
y = mx + 4
The point (4, 6) implies that
6 = m * 4 + 4
So, we have
4m = -2
m = -1/3
So, the equation is
y = -1/3x + 4
Substitute y = -1/3x + 4 in y = 4x - 3
-1/3x + 4 = 4x - 3
So, we have
-x + 12 = 12x - 9
Evaluate the like terms
13x = 21
Divide
x = 21/13
y = -1/3x + 4 implies that
y = -1/3 x 21/13 + 4
So, we have
y = -7/13 + 4
Evaluate
y = 45/13
So, the solution is (21/13, 45/13)
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Related Questions
During summer, the height of the water in Scott's pool decreases by 4 inches each week, due to evaporation. How many weeks does it take for the water to decrease by 20 inches?
Responses
A −5
B 5
C 20
D −20
Answers
Answer:
5 weeks
Step-by-step explanation:
20 inches / ( 4 inches/week ) = 5 weeks
3) Juakali used Kingo's computer to type a report document which had 123 pages, and
each page occupied by 70 lines. 36 of 70 lines had 14 words while the remaining lines
had 18 words each. He wanted to take the document with him, and he had only a flash
disk with 256 KB as free space. Can he successfully save the document on the device?
Why?
Answers
To determine whether Juakali can successfully save the document on the flash disk, you can calculate the total number of words in the document and compare it to the amount of free space on the flash disk.
First, calculate the total number of lines in the document by multiplying the number of pages by the number of lines per page:
Total number of lines = 123 pages * 70 lines/page
= 8610 lines
Next, calculate the number of lines with 14 words by multiplying the total number of lines by the proportion of lines with 14 words:
Number of lines with 14 words = 8610 lines * 36/70
= 4380 lines
Calculate the total number of words in the lines with 14 words by multiplying the number of lines by the number of words per line:
Total number of words in lines with 14 words = 4380 lines * 14 words/line
= 61320 words
Calculate the number of lines with 18 words by subtracting the number of lines with 14 words from the total number of lines:
Number of lines with 18 words = 8610 lines - 4380 lines
= 4230 lines
Calculate the total number of words in the lines with 18 words by multiplying the number of lines by the number of words per line:
Total number of words in lines with 18 words = 4230 lines * 18 words/line
= 76140 words
Finally, add the total number of words in the lines with 14 words and the total number of words in the lines with 18 words to find the total number of words in the document:
Total number of words = 61320 words + 76140 words
= 137,460 words
To determine whether Juakali can successfully save the document on the flash disk, you can compare the total number of words in the document to the amount of free space on the flash disk. Since the flash disk has 256 KB of free space and there are 137,460 words in the document, Juakali will not be able to save the document on the flash disk. This is because the document is larger than the amount of free space available on the flash disk.
It is important to note that the capacity of a storage device is usually measured in bytes, and 1 KB is equal to 1024 bytes.
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raphael drives to his office which is 75km away from his house what is his speed if it takes him 1 hour and 15 minutes to get to his office
Answers
Answer:
1km\h
Step-by-step explanation:
like in physics, the calculation of speed is total distance divided by total time, you should do the same in math, and so you do 1 hour (60 minutes) + 15 minutes which gives you 75 minutes, and then you divide 75 km by the time so it should look something like this:
[tex]\frac{75 km}{75 minutes}[/tex] which gives you 1
so raphael is going 1 km\h
Answer:
[tex]\huge\boxed{\sf v = 60\ km/hr}[/tex]
Step-by-step explanation:
Given:Distance = S = 75 km
Time = t = 1.25 hours
Required:Speed = v = ?
Formula:v = S/t
Solution:v = 75/1.25
v = 60 km/hr
[tex]\rule[225]{225}{2}[/tex]
if three sides of a triangle are in ratio of 3:5:7 and the perimeter of the triangle is 12xm. what is the length of the longest side?
Answers
The required length of the longest side will be 28/5 cm in the triangle.
What is the perimeter of a triangle?The perimeter of a triangle is defined as the addition of the lengths of the triangle's three sides.
We have been given that the three sides of a triangle are in the ratio of 3:5:7
Let's assume the sides are 3x, 5x, 7x
Since the perimeter of the triangle is 12 cm.
So, 3x+5x+7x = 12
Apply the addition operation,
15x = 12
x = 12/15
Reduce the above fraction to the simplest form
x = 4/5
So, longest side = 7x = 28/5 cm
Thus, the required length of the longest side will be 28/5 cm in the triangle.
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Solve the following equation. Answer as a reduced, mixed number.
9(x − 6) = 8(x + 6)
Answers
The value of x in the equation 9(x − 6) = 8(x + 6) is 102.
How to calculate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It should be noted that from the information given, the equation is illustrated as:
9(x − 6) = 8(x + 6)
9x - 54 = 8x + 48
Collect the like terms
9x - 8x = 48 + 54
x = 102
The value of x is 102.
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please help ASP WIIL GIVE Brilliance
Answers
Answer:
2. Definition of Midpoint
3. Vertical Angles Theorem
Step-by-step explanation:
Definition of Midpoint is the middle point of a line segment
Vertical Angles Theorem is proving angles that are opposite each other and formed by two intersecting straight lines, are congruent.
am i doing well on this
Answers
Answer:
The last option is the correct answer.
Step-by-step explanation:
lake front company is considering investing in a new dock that will cost 560,000 the company expects to use the dock for 5 years after which it will be sold for 300,000 lake front aticipates annual cash flows of 110,000 resulting from the new dock the companys borrowing rate is 8% while its cost of capital is 10% calculate the net present value of the dock and indicafe whether lake front should make the investment
Answers
The lakefront company should make the investment as in 5 years they'll have a profit of 10000.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, the lakefront company is considering investing in a new dock that will cost 560,000.
So, a Capital cost of 10% is (560000/10) = 56000
The company's borrowing rate is 8%.
∴ SI = (560000×8×5)/100.
SI = 5600×8×5.
SI = 224000.
So, The total cost is (560000 + 56000 + 224000) = 840000.
After 5 years they can sell it for 300000.
And has a cash flow of 110000, so in 5 years it is 550000.
So, total earnings is (300000 + 550000) = 850000.
Total profit is (850000 - 840000) = 10000 so it is profitable.
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Mrs.Barrera learned that 21 of her 25 students ride the school bus every morning.What percent of her students ride the school bus every morning?
Answers
The percentage of her students that ride the school bus every morning would be = 84%
What is percentage expression?A percentage expression is an representation of a data set to a fraction of 100.
The total number of students = 25 students
The number of students that ride the school bus = 21
To calculate the percentage of the students that ride the bus the following is done;
= 21/25 × 100
= 2100/25
= 84%
Therefore, the percentage of her students that ride the school bus every morning is 84%
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how do i find x? please help me, I tried everything :(
Answers
We are given an isosceles triangle because two sides are marked congruent, and therefore, the base angles opposite those sides are congruent. First we need to calculate the angles of the triangle using the Isosceles Triangle Theorem.
We are given a 110° angle with a ray that forms a straight line. Straight lines measure 180° by definition. So, we can calculate the vertex angle in the triangle by creating this equation:
110+x=180
110 degrees plus x creates a 180 degree line. Now, solve for x:
x=70
We have our first angle in the triangle, and we know a triangle must sum up to 180°. We also know the triangle is isosceles, and so the two base angles are congruent. We can create another equation to find all angles in the triangle:
70+2x=180
Remember, we have one angle and because the two base angles are congruent, we can denote them with the same variable and multiply by 2 because the angles will add to each other twice. Solve for x:
2x=110
x=55
So, we now have all there angles and can solve for “x.” Like we did before, a straight line forms one of the rays of the angle. So, we can create the equation:
55+x=180
55° plus x° sums up to 180. Now, solve for “x:”
x=125
The length of a rectangle is 3 less than twice the width. If the perimeter of the rectangle is 78 inches, find the dimensions (length and width) of the rectangle.
Answers
Length of the rectangle is 25 and width of the rectangle is 14.
What do you mean by algebraic expression?
A combination of terms through addition, subtraction, multiplication, division, and other operations is known as an algebraic expression (or variable expression). An algebraic expression is composed of various parts.
Any algebraic expression's variables, constants, terms, and coefficients.
A variable is a symbol that doesn't have a set value. Any value may be used.
It is given that the length of a rectangle is 3 less than twice the width and the perimeter of the rectangle is 78 inches.
Let the width of the rectangle be x
Length of the rectangle become 2x - 3
Perimeter of rectangle = 2(length + width)
78 = 2(2x - 3 + x)
78 = 2(3x - 3)
78 = 6x - 6
78 + 6 = 6x
84 = 6x
x = 84/6
x = 14
length of the rectanle is 2x - 3 = 2(14) - 3 = 28 - 3 = 25
Width of the rectangle is x = 14
Therefore, length of the rectangle is 25 and width of the rectangle is 14.
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The graph of g(x) is a transformation of the graph of f(x) = 2².
Enter the equation for g(x) in the box. g(x) =
Answers
3=k
G(x)=2^ˣ-k
Solution
G(x)=2ˣ - 3
19. The amount of money in a savings account increases from $ 250 to $ 270 in one month. If the percent increase is the same for every month, how much money will be in the account at the end of the next month?
(A) $ 291.60
(B) $ 295
(C) $ 289.60
(D) $ 300
Answers
Answer:
the answer will be the options A
ANALYZE PROBLEMS The midpoints of the sides of a triangle are located at (a, 0),(2 a, b) and (a, b). If one vertex is located at the origin, what are the
coordinates of the other vertices?
,( ______0) and (______,______)
Answers
The coordinates of the other vertices of the triangle are (2a, 0), (2a, b), and (a, b).
What are the coordinates of the vertices of the triangle?
The coordinates of the vertices of a triangle are (x1,y1), (x2,y2), and (x3,y3). The line joining the first two is divided in the ratio l:k and the line joining this point of division to the opposite angular point is then divided in the ratio m:k+l.
To find the coordinates of the other vertices of the triangle, you can use the fact that the midpoint of a line segment is located at the average of the coordinates of the endpoints of the segment.
If the midpoint of one side of the triangle is located at (a, 0), then the coordinates of the two endpoints of this side must be (a, 0) and (2a, 0). The coordinates of one of the vertices is (2a, 0), and since this vertex is not the one located at the origin, the coordinates of the other vertex must be the origin, or (0, 0).
If the midpoint of another side of the triangle is located at (2a, b), then the coordinates of the two endpoints of this side must be (2a, b) and (2a, 0). One of the endpoints is (2a, 0), which we already know is a vertex of the triangle. The other endpoint, (2a, b), is also a vertex of the triangle.
Finally, if the midpoint of the third side of the triangle is located at (a, b), then the coordinates of the two endpoints of this side must be (a, b) and (0, 0). One of the endpoints is (0, 0), which we already know is a vertex of the triangle. The other endpoint, (a, b), is also a vertex of the triangle.
Hence, the coordinates of the other vertices of the triangle are (2a, 0), (2a, b), and (a, b).
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Determine how many digits are to the right of the decimal point in the answer from multiplying: 0.3568 x 0.042
Responses
A. 5
B. 9
C. 7
D. 3
Answers
The number of the digits after the decimal point is 7. The correct option is C.
What is a number system?A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols. In several numeral systems, the same set of symbols may represent various numbers.
Given that the numbers are 0.3568 and 0.042. The multiplication of the two numbers will be done as,
P = 0.3568 x 0.042
P = 0.0149856
The number of the digits after the decimal is 7.
Therefore, the number of the digits after the decimal point is 7. The correct option is C.
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Need answer will mark Brainliest
Answers
Answer:
see explanation
Step-by-step explanation:
from the table we can obtain that
f(x ) = 6x³ + 8x - 12 ( 6 0 8 - 12 , being the coefficients of the polynomial )
f(x) is divided by (x + 7) , since evaluated at - 7
the quotient is
6x² - 42x + 302 ( 6 - 42 302, are the coefficients of the quotient )
with remainder - 2126
It takes Eddie 2 hours to shovel the snow from a driveway and sidewalk. Brad can shovel the snow from the same driveway and sidewalk in 5 hours. How long would it take them working together to shovel the snow?
How do I solve it?
Answers
Eddie and Brad together shovel the snow in 1 hour 26 minutes.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that it takes Eddie 2 hours to shovel the snow from a driveway and sidewalk.
Brad can shovel the snow from the same driveway and sidewalk in 5 hours.
We now find how long would it take them working together to shovel the snow.
Eddie does 1/2 in 1 hour or x/2 in x hours
Brad does 1/5 in 1 hour or x/5 in x hours
the sum is 1 full job
(x/2)+(x/5)=1
multiply both sides by 10
7x=10
x=(10/7) hours or 600/7 minutes =86 minutes
As we know 1 hour has 60 minutes.
We can write 86 minutes as 1 hour and 26 minutes.
Hence, 1 hour 26 minutes is the time taken by Eddie and Brad to shovel the snow.
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Solve using quadratic formula: 5x^2+9=4x+5
Answers
Answer:
No real solutions.
Step-by-step explanation:
No real solutions.
Which statement is true about the diagram?
R
S
يحة
Ο Δ QRC ~Δ SCU
O ARQCA SUC by SSS
O A CRQA CSU by SAS
O No triangles are congruent
U
Answers
Answer:
[tex]\triangle CRQ \cong \triangle CSU[/tex] by SAS
Step-by-step explanation:
[tex]\angle QCR \cong \angle SCU[/tex] because of vertical angles.
Solve.
9^(3x+1) = 27^2x
Answers
Answer: the equations has no solution
Step-by-step explanation:
[tex]9^{3x+1}=27^{2x}\\\\(3^2)^{3x+1}=(3^3)^{2x}\\\\3^{2(3x+1)}=3^{3(2x)}\\\\3^{6x+2}=3^{6x}\\\\Hence,\\\\6x+2=6x\\\\6x+2-6x=6x-6x\\\\2\neq 0\\\\Thus,\ the\ equations\ has\ no\ solution[/tex]
Write the equation of the line which passes
through the point (2. −3) and has a slope of -2/5
A. 2x + 5y = 4
C. 2x+ 5y = −11
B. 2x+5y = −9
D. 2x-5y = −16
Show work for this question please & thank u
Answers
y = -2/5 x -11/5 is the equation of line with slope -2/5 that passes through the point (2, -3).
What is the equation of line?The slope of the line is the rise to run ratio, or the rise divided by the run. It expresses the slope of a line in the coordinate plane.
The standard form of an equation is y = mx+c.
Here given,
A line with a slope of -2/5 that passes through the point (2, -3).
Simplify y = mx+c with m=2/5 and (x, y)=(2, -3). That is to say,
-3 = -2/5 (2)+c
⇒ -3 = -4/5 +c
⇒ c = -3 + 4/5
⇒ c = (-15 + 4) / 5
=> c = -11/5
When m = -2/5 and c = -11 /5 are substituted in y = mx+c, we get
y = -2/5 x -11/5
As a result, an equation for a line with a slope of -2/5 that passes through the point (2,-3) is y = -2/5 x -11/5.
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Answer:
C. 2x+ 5y = −11
Step-by-step explanation:
You want the equation of the line with slope -2/5 through point (2, -3).
Point-slope equationThe equation of a line with slope m through point (h, k) can be written as ...
y -k = m(x -h)
Then the equation of the line with slope -2/5 through point (2, -3) will be ...
y +3 = -2/5(x -2)
Standard formWe can put this in standard form by ...
5(y +3) = -2(x -2) . . . . . multiply by 5
5y +15 = -2x +4 . . . . . . eliminate parentheses
2x +5y = -11 . . . . . . . . . add 2x-15 to both sides
The desired equation is 2x +5y = -11.
is 2/5 equivalent to 25
Answers
Answer:
2/5 ≠ 25
Step-by-step explanation:
Given question,
→ Is 2/5 equivalent to 25?
Let's check the problem,
→ 2/5 = 25
→ 0.4 ≠ 25
The equivalent fractions of 2/5 are,
→ 2/5 = 4/10
→ 2/5 = 6/15
→ 2/5 = 8/20
→ 2/5 = 10/25
Hence, 2/5 is not equivalent to 25.
The replacement set for an equation is {10, 24, 25, 36}.
The equation is represented by the sentence, "5/6 of a number is 30."
What is the solution set of the equation?
options:
Responses
{10}
{24}
{25}
{36}
ill give brainleist
Answers
{25} is the solution set of the equation {10, 24, 25, 36}.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given set of equation is {10, 24, 25, 36}
Since, The equation is represented by the sentence that is 5/6 of a number is 30.
So the required solution,
5/6 of the number 30 = 25
The solution set of the equation is {25}.
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Question 10
What is the equation of the line shown?
Answers
does it want the answer in a specific form?
slope intercept form; y = mx + b
slope = 2
b = -1
plug the values in
y = 2x -1 or y = 2/1x -1
Find the inverse function to y=f(x)= 8-9x/5-4x
x=g(y)=
Answers
Therefore , the inverse function to y=f(x)= 8-9x/5-4x is 8-5x /-4x+9 .
A function is what?In mathematics, a function from a set X to a set Y assigns each item in X exactly one element in the other set. The sets X and Y represent the function's domain and codomain, respectively.
Here,
Given :
function :8-9x/5-4x
To find the inverse ,
Inverse of 8-9x. 8-5x 5 4x -4x+9
Steps Function Inverse definition A function g is the inverse of function F if for y=√(x), x=g(v)
y= 8-9x 5-4x
Replace x with y
x = 8-9y/ 5-4y
Solve for y,
x = 8-97/ 5-4y
=>8-5x /-4x+9
Therefore , the inverse function to y=f(x)= 8-9x/5-4x is 8-5x /-4x+9 .
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help meeeeeeeeeee pleaseee
Answers
The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.
What is an expression?An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.
Calculation:It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as
f(x) = 0.48 ln(x+2) + 27
Here x is the distance in miles from the eye of the hurricane.
f(x) is the pressure of the mercury in a barometer in inches
So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is
(Here f(x) = 28)
f(x) = 0.48 ln(x+2) + 27
⇒ 28 = 0.48 ln(x+2) + 27
⇒ 0.48 ln(x+2) = 28 - 27
⇒ ln (x+2) = 1/0.48
⇒ ln(x+2) = 2.0833
Applying exponential base "e" on both sides, we get
(x+2) = [tex]e^{2.0833}[/tex]
⇒ x + 2 = 8.0309
⇒ x = 8.0309 - 2 = 6.0309
When the result is rounded to the nearest whole number, we get x = 6 miles.
Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.
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Help with this plsss !!!
Answers
Answer:
:))
Step-by-step explanation:
The maximum value is 22 as the last small line (end of the "whisker") is marked at 22. Hope this helps!! Pls mark as brainliest and lots of points, help ya girl out!!!
In how many ways can a person order one ice cream cone with 3 different
flavors of ice cream if there are 14 flavors to choose from and it matters to
the person how the 3 flavors are stacked on the one cone? That is, which
flavor is on the top, middle, and bottom.
Answers
Answer:
2184
Step-by-step explanation:
You want to know the possible number of ways 3 flavors can be chosen from 14 when order matters.
PermutationsThe number of permutations of 14 flavors taken 3 at a time is ...
14 × 13 × 12 = 2184
There are 14 ways to choose the bottom flavor, then 13 ways to choose a different middle flavor, and finally 12 ways to choose a different top flavor. Each flavor can go with any combination of the others, so the total number is the product of 14·13·12, or 2184.
The formula for the number of n things taken k at a time is ...
P(n, k) + n!/(n-k)!
For n=14, k=3, this is the product shown above.
how many tens are in 7x30 or 30x7
Answers
There are 3 tens in 7x30 or 30x7.
What is an equation?
A mathematical statement is referred to as an equation when two expressions are connected by the equal sign. A mathematical equation serves as the connection between two expressions on each side of the sign. Usually, there is only one variable and an equal sign.
Equations can be categorized as identities or conditional equations. An identity holds true regardless of the value given to the variables. A conditional equation's variables can only have specific values that produce the truth.
An equation is created by joining two expressions with an equal sign. The solution to an equation is a number that may be used as the variable to generate a true number statement.
Here, we have
7x30 = 7 x 10 x 10 x 10
The value of 7x30 = 210
Hence, there are 3 tens in 7x30 or 30x7.
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If both dimensions are doubled then which of the following statements about it’s perimeter will be true
Refer to this rectangle
4mm
9mm
The new perimeter will be 3 times larger then the old perimeter
The new perimeter will be 2 times larger then the old perimeter
The new perimeter will be 1/3 times larger then the old perimeter
The new perimeter will be 4. Times larger then the old perimeter
Answers
The new perimeter will be 2 times larger then the old perimeter, if both dimensions of rectangle are doubled.
What is perimeter ?The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width.
The figure's length is essentially revealed by the perimeter. Assume that the perimeter of a square with equal sides will be four times that square's sides. The perimeter of a circle, which is determined by its radius, is known as its circumference.
The new dimensions of rectangle = 4mm and 9mm
The original dimension = 2mm and 4.5 mm
Perimeter of rectangle = P=2(l+w) = 2 (4.5 +2 ) = 13 mm
Perimeter of rectangle after doubled dimension = 2 (9 + 4) = 26
So, the new perimeter will be 2 times larger then the old perimeter
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