Clear y from both equations to find the slope y intercept form of the equations
[tex]\begin{gathered} 4x-9y=-5 \\ -9y=-4x-5 \\ y=\frac{-4x-5}{-9} \\ y=\frac{4}{9}x+\frac{5}{9}\text{ (Eq. 1)} \\ -x-4y=-2 \\ -4y=x-2 \\ y=\frac{x-2}{-4} \\ y=-\frac{x}{4}+\frac{1}{2}\text{ (Eq. 2)} \end{gathered}[/tex]Now, find the equation for the line that is perpendicular to Eq. 1 and has the same y intercept as Eq. 2
[tex]\begin{gathered} m1\cdot m3=-1 \\ m3=-\frac{1}{m1} \\ m3=-\frac{1}{\frac{4}{9}} \\ m3=-\frac{9}{4} \\ y=-\frac{9}{4}x+\frac{1}{2}\text{ (Eq. 3)} \end{gathered}[/tex]Eq. 3 is the equation for the line
Qsn 1.4.1 have never done a problem of this kind before so will need background explanation for every step in the answer.
Answer
Maximum area = 4900 m²
Step-by-step explanation
1.4.1 The perimeter of a rectangle is calculated as follows:
[tex]P=2(l+w)[/tex]where l is the length and w is the width of the rectangle.
Substituting P = 280 m, l = 2x meters, and w = y meters, and solving for y:
[tex]\begin{gathered} 280=2(2x+y) \\ \frac{280}{2}=\frac{2(2x+y)}{2} \\ 140=2x+y \\ 140-2x=2x+y-2x \\ 140-2x=y \end{gathered}[/tex]The area of a rectangle is calculated as follows:
[tex]A=l\cdot w[/tex]Substituting l = 2x and w = y = 140 - 2x:
[tex]\begin{gathered} A=2x(140-2x) \\ A=2x(140)-2x(2x) \\ A=280x-4x^2 \end{gathered}[/tex]1.4.2 Given that Area's formula is a quadratic function, its maximum is placed at its vertex. The x-coordinate of the vertex is found as follows:
[tex]x_V=\frac{-b}{2a}[/tex]where a is the leading coefficient and b is the x-coefficient of the function. In this case, the coefficients are a = -4 and b = 280, then:
[tex]\begin{gathered} x_V=\frac{-280}{2(-4)} \\ x_V=\frac{-280}{-8} \\ x_V=35 \end{gathered}[/tex]Evaluating the Area at x = 35, the maximum Area is:
[tex]\begin{gathered} A=280(35)-4(35)^2 \\ A=4900\text{ m}^2 \end{gathered}[/tex]The coordinate plane shows rectangle PQRS . The length of side QR is 4 units. What is the area of PQRS?
QR = 4 unit
Let us find RS, which is the length of the rectangle . Therefore
[tex]\begin{gathered} RS=\sqrt[]{(1-5)^2+(-4-6)^2} \\ RS=\sqrt[]{16+100} \\ RS=\sqrt[]{116} \end{gathered}[/tex][tex]\begin{gathered} \text{area}=lw \\ \text{area}=\sqrt[]{116}\times4 \\ \text{area}=4\sqrt[]{116\text{ }}unit^2 \end{gathered}[/tex]Multiple Representations of a Story Juan is ordering a flower arrangement online for Valentine's Day. Each rose costs $5 and the vase sells for $10. enter the equation of the line
Let:
r be the number of roses
c be the cost of a flower arrangement
Let's consider that a flower arrangement has 1 vase and "r" roses.
Then, the cost of a flower arrangement is:
c = cost of vase + cost of roses
c = 10 + 5r
Which is the same as
c = 5r + 10
Answer:
c = 5r + 10
(-x) + (-3) = x + 3
x =
Answer:
x = -3
Step-by-step explanation:
-x +- 3 = x + 3
-x - 3 = x + 3 (+- is equal to -)
- 3 = 2x + 3 (add x to both sides, to remove the x on the left side)
- 6 = 2x (subtract 3 on both sides)
x = -3 (divide by 2)
The graph of a linear function is shown on the grid.Y(-3, 3.6(5,2)XYo -2What is the rate of change of y with respect to x for this function?Choose the grid that is labeled and bubbled with the correct answer.
(x, y) = (-3, 3.6); (5, 2)
Slope (m) = (y2 - y1) / (x2 - x1)
m = (2 - 3.6) / (5 - - 3) = - 1.6/8
m = -0.2
Isabella's baby weighed 8.5 lbs
when it was first born. 20 days
later, it weighed 10.8 lbs. what is the rate of change of the baby's weight per day?
0.115 lbs/day is the rate of change of baby's weight.
What is rate of change ?When anything changes over time, it does so at a certain rate, or ROC. Therefore, rather than the size of each change individually, it is the pace of change—or, more specifically, its acceleration or deceleration. Rate of change in the financial world is utilized to comprehend price returns and spot trend momentum.
Calculationrate of change in baby's weight will be = (10.8 - 8.5)/ 20
= 2.3 / 20
= 0.115 lbs/day
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Estimate the side length of a square that has a 9 cm long diagonal. ( The perimeter of a square is typically 2.8 times bigger than the diagonal)
The diagonal and two adjacent sides of the square form an isosceles right triangle.
By the Pythagorean theorem
[tex]\begin{gathered} s^2+s^2=9^2 \\ 2s^2=81 \\ s^2=\frac{81}{2} \\ s=\sqrt[]{\frac{81}{2}} \\ s=\frac{9}{\sqrt[]{2}} \\ s=6.36\text{ cm} \end{gathered}[/tex]Use the following function rule to find f(9).
f(x) = x + 6
f(9) = [
What does f(9) =
Answer:
f(9) = 15Step-by-step explanation:
In order to find f(9) we substitute the value of x that's 9 into f(X) that's where there's x we substitute it with 9 and calculate.
We have
[tex]f(x) = x + 6[/tex]
[tex]f(9) = 9 + 6 \\ = 15[/tex]
We have the final answer as
f(9) = 15Hope this helps you
The graph of the system of linear equations below is shown in the coordinate plane.
4y = -3x - 1
2y = x - 13
why is the point (5,-4) a solution to the system?
The point, (5, -4), is the solution to the given system of equations because the lines intersect at the point.
Graph of system of linear equationsFrom the question, we are to determine why the given point is a solution to the system of equations
The given system of equations is
4y = -3x - 1
2y = x - 13
When solving system of equations by the graphical method, the point where the lines intersect gives the solution to the system of equations.
From the given graph,
The two lines intersect at the point where x = 5 and y = -4.
That is,
The lines intersect at (5, -4), and thus, (5, -4) is the solution to the system of equations.
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Mr. A drove to a city in New Jersey
that is 200 miles away. He got
there in 2 hours. What is his
2 rate of change (At what Speed
was Mr. A driving)
Answer:
100 miles per hour
Step-by-step explanation:
He drives 200 miles in 2 hours so just divide 200 by 2 to get the unit rate/ miles per hour
During the 2003-2004 season, Kevin Weekes of the Carolina
Hurricanes saved 1506 out of 1652 shots on goal. To the nearest
what part of the time did Weekes save shots on goal?
Part of the time weekes save shots on goal is 0.911.
Given,
Total number of shots on goal=1652
Number of shots saved=1506
Part of time weekes save shots on goal,
[tex]\frac{Number of shots saved}{Total number of shots on goal}\\\\\\=\frac{1506}{1652}\\ \\=0.911[/tex]
Thus, Part of the time weekes save shots on goal is 0.911.
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Please help asap now please Ik this easy for u not for me I’m not good whit shapes
The shape has some right angles .
The correct option is (D).
Given,
In the question:
Complete the sentences :
The shape has ____
Now, According to the question:
From the figure,
There are four option:
Select the one option according to the figure.
To see that :
The figure says that :
Correct Answer is some right angles because the sides are not exactly the same .
Hence, The shape has some right angles .
The correct option is (D).
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NEED HELP AGAIN FASTTT FOR GEOMETRY my time is running out
Answer:
d
Step-by-step explanation:
Answer:4/5
Step-by-step explanation:
sin is opposite/hypotenuse so its 16/20 which reduces to 4/5
An elf drew a picture of a reindeer using the scale 3 inches = 2 feet. If the reindeer in the picture was 6 %. Inches tall, how tall is the actual reindeer?
He drew a picture of reindeer . He used a scale 3 inches = 2 feet. The reindeer in the picture is 6 % inches tall . The height of the actual reindeer can be calculated below
[tex]\begin{gathered} 6\text{ \% of an inch tall = }0.06\text{ inches} \\ 3\text{ inches = 2 f}eet \\ 0.06\text{ inches =?} \\ \text{actual height of the reind}eer=\frac{0.06\times2}{3}=\frac{0.12}{3}=\text{ }0.04\text{ fe}et \end{gathered}[/tex]-7/3 divided by 1/3 plus one
Factor the expression using the GCF.
84+28
Answer:
28(3 +1)
Step-by-step explanation:
You want the expression 84+28 to be factored using the GCF.
GCFThe Greatest Common Factor (GCF) of 84 and 28 can be found by looking at the remainder from division of 84 by 28.
84 ÷ 28 = 3 r 0
The remainder is 0, so 28 is a factor of 84. Since it is also the largest factor of itself, it is the GCF of the two numbers.
Distributive propertyFactoring out 28, we have ...
84 +28 = 28·3 +28·1 = 28(3 +1)
The factored expression is 28(3 +1).
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can you help with this
In the given parallelogram ABCD:
CD=5x-18
BC=3x-6
AB=2x+12
From the properties of parallelogram: The opposite sides of parallelogram are equal
Pair of opposite sides are:
AB & CD
BC & DA
Opposite sides are equal:
[tex]\begin{gathered} AB=CD \\ 2x+12=5x-18 \\ 5x-2x=12+18 \\ 3x=30 \\ x=\frac{30}{3} \\ x=10 \end{gathered}[/tex]x = 10
Substitute the value of x = 10 in the expression of BC
BC = 3x - 6
BC = 3(10) - 6
BC = 30 - 6
BC = 24
Opposite sides are equal: BC = DA
BC = 24 = DA
DA = 24
Answer: DA = 24
The number of men and women receiving bachelor's degrees each year has been steadily increasing. For the years 1970 through the projection of 2014, the number of men receiving degrees (in thousands) is given by the equation y= 3.6x + 444 and for women, the equation is y= 14.2x + 315 where x is the number of years after 1970.
The solution to the system of equations is x = 12
Equal number of men and women have received bachelor's degrees up till 1982Women have a higher rate of receiving bachelor's degrees each year than menThe solution to the system of equationsThe system of equations is given as
y = 3.6x + 444
y = 14.2x + 315
Substitute y = 14.2x + 315 in y = 3.6x + 444
14.2x + 315 = 3.6x + 444
Evaluate the like terms
10.6x = 129
Divide both sides by 10.6
x = 12
Interpret the result in (a)In (a), we have
x = 12
Where
x is the number of years after 1970.
This means that
Year = 1970 + 12
Evaluate
Year = 1982
So, it means that the total number of men and women that have received bachelor's degrees up till 1982 are equal
The trend for men and womenSee attachment for the graph
On the graph, we can interpret the trends to be:
More women receive bachelor's degrees each year than men
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Missing part in the question
A. Use the substitution method to solve this system of equations. (Round your final results to the nearest whole numbers.)
B. Explain the meaning of your answer to part (a).
C. Sketch a graph of the system of equations. Write a sentence describing the trends for men and women receiving bachelor degrees.
In parallelogram EFGH the measure of angle E is (2x+3) and the measure of angle F is (3x-33) what’s is the measure of angle E
The measure of ∠E = 87° and ∠F = 93°.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a parallelogram in which EFGH the measure of angle E is (2x+3) and the measure of angle F is (3x - 33).
We can write -
2(2x + 3) + 2(3x - 33) = 360°
4x + 6 + 6x - 66 = 360°
10x - 60 = 360
10x = 420
x = 42
∠E = 2 x 42 + 3 = 84 + 3 = 87°
∠F = 3 x 42 - 33 = 126 - 33 = 93°
Therefore, the measure of ∠E = 87° and ∠F = 93°.
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a health-conscious student faithfully wears a device that tracks his steps. suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. what percent of the time does he exceed 13,000 steps? group of answer choices 0.0228 0.05 0.95 0.972
The percentage of time he exceeds 13,000 steps is 2.28% or 0.0228.
Percentage
Use the percentage formula to express a number or percentage in terms of 100. % simply indicates one out of one hundred. An expression for a number between 0 and 1 can be made using the percentage formula. It is a number that is represented as a fraction of 100. The sign % is used to denote it and it is mostly used to compare and calculate ratios. The formula for percentage increases is the ratio of the increased value to the original value multiplied by 100. It is described in percentage form. If anything is valued more highly, both its value and proportion will rise.
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How many possible outcomes are therefor any set of linear systems?
The answer is three
None, one or infinitely many solutions
angles
FIND THE VALUE OF THE GIVEN ALPHABET.
Answer:
y=75
Step-by-step explanation:
2y=150y=150/2y=72The height of an iceberg above the
water is 23 meters. The bottom of the
iceberg is 15 meters below sea level.
What is the total height and depth of
the iceberg.
The total height of the iceberg is 38 meters and the total depth of the iceberg is 15 meters.
What is meant by height and depth?Height is a mathematical term that refers to the vertical distance between an object's top and base. Sometimes, it has the designation altitude. The measurement of an item along the y-axis in coordinate geometry is referred to as height in geometry.
The depth of an object is the separation between its closest and farthest ends. Jane, for instance, measures a box. Jane estimates the depth of the box by calculating the distance between the end of the box that is closest to her and the end that is farthest away.
Given, the height of an iceberg above the water is 23 meters.
And also given that the bottom of the iceberg is 15 meters below sea level.
Total height = above the water + below the water
Total height=23+15=38 meters
Depth= total height - iceberg above the water
Depth=38-23=15 meters
The total height of the iceberg is 38 meters.
The total depth of the iceberg is 15 meters.
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Simplify and determine the coefficient of (-x)(5y)(-2x).
Answer:
10x^2y
Step-by-step explanation:
Write an equation of the line that passes through (-5,0) and is parallel to the line y=-2/3x-1
The equation of the line that passes through (-5,0) and is parallel to the line y = -2/3x - 1 is y = - 2 / 3 x - 10 / 3
How to find the equation of a line?The equation of a line can be represented in different form such as point slope form, slope intercept form, standard form and general form.
The equation of a line in slope intercept form is as follow:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line passes through (-5,0) and is parallel to the line y = -2/3x - 1.
Parallel line has the same slope.
Therefore, the slope of the line is - 2 / 3.
Hence, let's find the y-intercept using (-5, 0)
0 = - 2 / 3(-5) + b
b = - 10 / 3
Therefore, the equation is y = - 2 / 3 x - 10 / 3
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The table below represents the number of paintings, y, that Jordan completed in x years. Jordan's Paintings Year (x) Paintings (y) 1 4 2 7 3 10 4 13 Which equation describes the relmionship between the number of paintings and the year? A. y = x+3 B. y = 3x + 1 D.y = 4x + 3 C. y = 3x + 4
Method 1
Concept
Pick two points and find the equation of a line.
Point ( 1. 4 ) and ( 2, 7 )
Step 2: Represent each point
[tex]\begin{gathered} x_1\text{ = 1} \\ y_1\text{ = 4} \\ x_2\text{ = 2} \\ y_2\text{ = 7} \end{gathered}[/tex]Step 3: Substitute the values in the two points equation of a line formula
[tex]\frac{y-y_1}{x-x_1}\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} \frac{y\text{ - 4}}{x\text{ - 1}}\text{ = }\frac{7\text{ - 4}}{2\text{ - 1}} \\ \frac{y\text{ - 4}}{x\text{ - 1}}\text{ = }\frac{3}{1} \\ \frac{y\text{ - 4}}{x\text{ - 1}}\text{ = 3} \\ \text{Cross multiply} \\ y\text{ - 4 = 3(x - 1)} \\ y\text{ - 4 = 3x - 3} \\ y\text{ = 3x - 3 + 4} \\ y\text{ = 3x + 1} \end{gathered}[/tex]Step 4: Final answer
y = 3x + 1 Option B
Solving Systems of linear equations by elimination
The solution of the systems of linear equations is x = 13.81 and y = 73.381. The average salaries were equal in the year 1999. The average salary that year was about $73381.
What is the system of linear equation?
A collection of two or more linear equations is a system of linear equations. The graph of a system of two equations is a pair of lines in the plane for two variables (x and y).
The intersection point of the lines is ( 13.81, 73.381).
The average salaries were equal after 14 years since 1985.
The average salaries were equal (1985 + 14) = 1999.
The average salary that year was about $73381.
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Please help! I need explanation on why the answer is what it is.
I can’t understand slope :(
The correct equation that represents the slope equation using the given information will be (B) y = -5x + 2.
What exactly are slopes?The slope of a line can be used to gauge how steep it is.Divide the change in y by the change in x, or "rise over run," to find the slope in mathematics.Locate two locations along the chosen line and find their coordinates.Find the y-coordinate difference between these two places (rise).Find the difference between the x-coordinates of these two points (run).Subtract the difference in y-coordinates from the difference in x-coordinates (rise/run or slope).So, the slope equation will be:
Slope form: y = MX + bM is -5 and points are (-1, 2).Now, the correct question will be:
y = MX + by = -5x + 2Therefore, the correct equation that represents the slope equation using the given information will be (B) y = -5x + 2.
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Correct questions:
Get the correct equation of the slope -5 and points (-1, 2).
(A) y = 5x + 2
(B) y = -5x + 2
(C) y = -5x - 2
(D) y = 5x - 2
m = 4 through (3,-2)
The equation of the line is y = 4x - 14
The slope of the line m = 4
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the function
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
The point is (3, -2)
Substitute the values in the point slope form
y - (-2) = 4(x-3)
y + 2 = 4x - 12
Rearrange the equation and make slope intercept form
y = 4x - 12 -2
y = 4x - 14
Hence, the equation of the line is y = 4x - 14
The complete question is
Write the equation of the line when m = 4 and the passing through the point (3, -2)
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shelbyblanchard15, this is the solution:
e. (7 * 10^6) * (8 * 10^5) = 5.6 * 10 ^12
f. 10,000,000 * 0.000 005
10,000,000 = 10 ^7
0.000 005 = 5 * 10 ^ -6
5 * 10^1 = 5 * 10
g. 30,000/0.0004
30,000 = 3 * 10^4
0.0004 = 4 * 10^-4
3 * 10^4/4 * 10^-4 = 7.5 * 10^7