The slope intercept form of the given line whose coordinate of point is (- 5,9) and slope is - 5 would be y = -5x - 16.
Equation of a straight line: y = mx + b ------(i)
Given that
y = 9, x = -5
and slope, m = - 5
By putting above values in equation (i)
9 = -5 (-5) + b
9 = 25 + b
-16 = b
b = -16
y = -5x - 16
The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.
The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.
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Question content area top
Part 1
Write an equivalent expression without parentheses. Then simplify the result.
m−(8−3m)
using exponents, On simplifying the equation, we get =4m+8.
The PEMDAS order of operations must be followed when you want to simplify a mathematical equation without using parenthesis (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). There are no parenthesis in the expression, so you may start looking for exponents. If it does, first make that simpler.
What is the main objective of simplification?Work simplification is to develop better work processes that boost output while cutting waste and costs.
What does simplifying mean in algebra?Simplifying an expression is the same as solving a mathematical issue. When you simplify an equation, you essentially try to write it as simply as you can. There shouldn't be any more multiplication, dividing, adding, or deleting to be done when the process is finished.
Given equation,
m-(8-3m)
=m-8+3m
=4m+8
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What is the most prescise classification of this shape?
Answer:
the answer for this question isnparallelogram
Answer:
Parallelogram
Step-by-step explanation:
a 95% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (3%, 9%). what is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?
The point estimator of the mean percentage of airline reservations canceled on the day of the flight is the midpoint of the 95% confidence interval, which is (3% + 9%) / 2 = 6%.
The point estimator of the mean percentage of airline reservations being canceled on the day of the flight is the midpoint of the confidence interval, which is (3% + 9%) / 2 = 6%. Therefore, the point estimator of the mean percentage of reservations that are canceled on the day of the flight is 6%.
This means that based on the data, we can estimate that the mean percentage of airline reservations being canceled on the day of the flight is around 6%. However, since this is a point estimate, there is some uncertainty associated with it. The 95% confidence interval provides a range of values within which we can be 95% confident that the true mean percentage of cancellations falls. In this case, we can be 95% confident that the true mean percentage of cancellations on the day of the flight falls between 3% and 9%.
Overall, the interval and the point estimator provide us with useful information about the mean percentage of airline reservations being canceled on the day of the flight and allow us to make informed decisions and predictions about future cancellations.
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Which equation represents the slope-intercept form of the line below?
I really need help with the bottom half only
. suppose the sides of a rectangle are changing with respect to time. the first side is changing at a rate of 2 in./sec whereas the second side is changing at the rate of 4 in/sec. how fast is the diagonal of the rectangle changing when the first side measures 16 in. and the second side measures 20 in.? (round answer to three decimal places.)
Diagonal of rectangle is changing by the rate of 4.373 in. /sec.
What is rate of change ?Rate of change (ROC) is the rate at which a variable changes over a particular period of time
To find the average rate of change, divide the change in the y-values by the change in the x-values . Finding the average rate of change is especially useful for identifying changes in measurable values such as average speed or average velocity.
A ratio is a special ratio in which the two terms have different units.
Calculationthe calculation part is shown in the below picture attached .
so after seeing the solution we come to an answer of = 4.373 in./sec
therefore diagonal of rectangle is changing by the rate of 4.373 in. /sec
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Estimate the measure of the angle formed by the following city or location listed, the North Pole, and the Prime Meridian.
b. Fairbanks, Alaska
The estimated measure of the angle is 25.1622°.This means that the angle formed by Fairbanks, the North Pole, and the Prime Meridian can be estimated as 25.1622°.
1. Determine the latitude of Fairbanks, Alaska.
2. Calculate the difference between the latitude of Fairbanks and the latitude of the North Pole.
3. The angle formed by Fairbanks, the North Pole, and the Prime Meridian is equal to the difference in latitude.
To estimate the measure of the angle formed by Fairbanks, Alaska, the North Pole, and the Prime Meridian, we need to consider the latitude of Fairbanks and the latitude of the North Pole. Fairbanks, Alaska, is located at approximately 64.8378° N.
The North Pole, on the other hand, is situated at 90° N. To find the difference in latitude, we subtract the latitude of Fairbanks from the latitude of the North Pole: 90° - 64.8378° = 25.1622°. This means that the angle formed by Fairbanks, the North Pole, and the Prime Meridian can be estimated as 25.1622°.
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3/14 x 3/14 as a fraction
Answer:
((3 / 14) * 3) / 14 = 9 / 196
Step-by-step explanation:
Reduce 9/196 to lowest terms 9 196 is already in the simplest form. It can be written as 0.045918 in decimal form (rounded to 6 decimal places).
the question is in the picture below
Answer:
The missing value is \(14\).
Step-by-step explanation:
Divide the known denominator by its numerator.
\(4\div2=2\)
Now multiply the quotient by the other numerator (\(7\)).
\(2×7=14\)
or
First, find the factor by which the numerators have been multiplied.
\(2x=7→x=3.5\)
Now, do the same for the denominators.
\(4(3.5)=14\)
Asap!! step by step pls! After a new firm starts in business, it finds that it’s rate of profit (in hundreds of dollars) after t years of operations is given by P’(t)=3t^2+10t+6. Find the profit in year 4 of the operation.
Answer:
$ 7800
Step-by-step explanation:
P'(t) = 3t² + 10t + 6
\(P(t) = \int\limits^a_b {P'(t)} \, dt\)
For the 4th year, the limits are [3,4]
\(P(t) = \int\limits^4_3 {3t^2 + 10t + 6} \, dt\\\\= [\frac{3t^3}{3} + \frac{10t^2}{2} + 6t]^{^4}__{3}\\\\\)
\(=[\frac{3(4)^3}{3} + \frac{10(4)^2}{2} + 6(4)]-[\frac{3(3)^3}{3} + \frac{10(3)^2}{2} + 6(3)]\\\\=[\frac{3(64)}{3} + \frac{10(16)}{2} + 24]-[\frac{3(27)}{3} + \frac{10(9)}{2} + 18]\\\\= [64 + 5(16) + 24]-[27+5(9) + 18]\\\\= 168-90\\\\= 78\)
= $ 7800
Eastside Gym charges a $60 initial fee and $28.50 per month. Valley Gym charges $36 per month, and no initial fee. After how many months of use would Eastside cost less than Valley
answer: after 6 months
Please help I need to finish this in 2 days
The angle subtended at the center of the arc is 102⁰
What is the length of the arc?Recall that to find the length of an arc on a circle, we can use the formula L = r *, where r is the radius of the circle, is the central angle, and is the angle between the ends of the arc. If the central angle is measured in degrees, we can use the formula L = r *, where r is the radius of the circle, is the central angle, and is the angle between the ends of the arc.
Lenght of arc = A/360 *2пr
A = angle at center = ?
п = 22/7 r = radius = 840 feet
⇒1500 = A/360 2 *22/7 * 840
1500 = 36960A/2520
3780000= 36960A
making A the subject we have
3780000/36960 = A
A = 102.27
A= 102⁰
The angle is 102⁰
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If the area and perimeter of a right triangle are 30 cm^2 and 30 cm, respectively, what is the length of the hypotenuse (the side opposite the right angle)?
If the area and perimeter of a right triangle are 30 cm² and 30 cm, respectively, the length of the hypotenuse is 13 cm.
Given that, the area of the right-angled triangle is 30 cm² and the perimeter is 30 cm.
Let a, b, and c be the lengths of the sides and assume that c is the hypotenuse.
Area = 30 cm²
1/2×a×b = 30
ab = 60.
Perimeter = 30 cm
Perimeter is the sum of the sides of the triangle.
a + b + c = 30.
a + b = 30 - c
Squaring on both sides
a²+b²+2ab = 900+c²-60c
In a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the adjacent side and the opposite side.
So, a²+b²=c²
c²+2ab = 900 + c²-60c
c²+120 = 900+c²-60c [we know that ab=60]
Subtracting c² on both sides.
60c = 780
c = 13.
Therefore, the length of the hypotenuse is 13 cm.
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A triangle is placed in a semicircle with a radius of 8 cm as shown below
To find the area of the shaded region:
1. Find the area of the semicircle:
\(\begin{gathered} A=\frac{\pi *r^2}{2} \\ \\ A=\frac{3.14*(8cm)\placeholder{⬚}^2}{2}=\frac{3.14*64cm^2}{2}=100.48cm^2 \end{gathered}\)2. Find the area of the triangle:
the base of the triangle is the diameter of the semicircle (twice the radius)
\(\begin{gathered} A=\frac{1}{2}b*h \\ \\ A=\frac{1}{2}(16cm)(8cm)=\frac{128}{2}cm^2=64cm^2 \end{gathered}\)3. Subtract the area of the triangle from the area of the semicirle:
\(A_{shaded}=100.48cm^2-64cm^2=36.48cm^2\)Then, the area of the shaded region is 36.48 square centimetersWhile making desserts for Fun Day, Methuki used 5/6 of a scoop of brown sugar as well as 1/2 of a scoop of white sugar. How much more brown sugar did she use?
Hey there! I'm happy to help!
We want to find how much more 5/6 is than 1/2. To do this, we simply subtract 1/2 from 5/6. This will show us how much more 5/6 is.
First, we multiply 1/2 by 3/3 so that the denominator is 6.
1/2×3/3=3/6
Now, we subtract this from 5/6.
5/6-3/6=2/6
We can simplify this to 1/3.
Therefore, Methuki used 1/3 scoop more of brown sugar than white sugar while making desserts for Fun Day.
Have a wonderful day! :D
Fred's net worth is shown in the table below.
Assets are positive numbers and liabilities are negative
numbers If Fred's net worth is $74,000 how much
does he owe in credit card debt?
Item
House (current value)
Checking Account
Credit Card Debt
Vehicle (current value)
Student Loans
Personal Loans
Savings Account
Value
$105,900
$375
$13,500
-$32,000
-$800
$1,275
A) $6,725
B) $7,560
C) $9,750
D) $12,500
E) $14,250
F) $17,325
Fred owes $14,250 in credit card debt.
We must total up all of Fred's assets and liabilities, then subtract them to arrive at the amount he owes on his credit cards.
Let's figure it out:
Total Assets:
House (current value) = $105,900
Checking Account = $375
Vehicle (current value) = $13,500
Savings Account Value = $1,275
Total Liabilities:
Credit Card Debt = ?
Student Loans = $32,000
Personal Loans = $800
Total Assets - Total Liabilities = Net Worth
105,900 + 375 + 13,500 + 1,275 - (Credit Card Debt + 32,000 + 800) = 74,000
Solving for Credit card debt =
Credit Card Debt = 74,000 - 88,250
Credit Card Debt = -14,250 [The negative sign identifies it as a liability, as you can see.]
Therefore, Fred owes $14,250 in credit card debt.
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A
1
The angle that is an
alternate interior
angle with angle 1
is angle [?]
2.
D
3
A. 1
B. 2
C. 3
D. 4
Answer:
angle 2
Step-by-step explanation:
alternate interior angles are angles formed when two parallel or non parallel line are intersected by a transversal ....
anbody know what this x means
Answer: x would be 6
Step-by-step explanation: x is a variable, its being used as multiplication here and u need to find the number x is representing
with 2x = 12
divide both sides by 2
2x divided by 2, 12 divided by 2
ur left with
x = 6
How many perpendicular bisectors are required to be constructed to devide a line segment into four equal parts?
Answer:
Three perpendicular bisectors are required
Step-by-step explanation:
A perpendicular bisector of a line segment is a line that cuts the line segment at a 90° angle, dividing it into two equal halves.
In this example, one bisector produces two equal parts of the segment
two bisectors produce three segments and three bisectors, four segments as shown in the diagram.
Perpendicular bisectors are constructed using a compass and a pencil, you can check out how to construct one, it is pretty interesting.
Solve h+p=7(k -4) for k.
Answer:
k= h/7 + p/7 +4
Find the domain of the relation represented on the mapping diagram:
3-------> -1
6-------> 4
8-------> 4
Explain how to do it please!!
{3, 6, 8} is the domain of the relation R={(3,-1)(6,4)(8,4)}
What is Function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
A function has three important parts, domain, codomain and Range.
The domain of the relation R is the set of arguments i.e. first members of each ordered pair and the codomain is the set of which the values i.e. second members of all the ordered pairs.
In the Given relation
R={(3,-1)(6,4)(8,4)}
All the values in x place are domain values.
The domain equals all of the x values which are r on the left in a ordered pair
x= {3, 6, 8}
Hence {3, 6, 8} is the domain of the relation R={(3,-1)(6,4)(8,4)}
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square root of 1000 (simplified)
Answer:
10 √10
Step-by-step explanation:
Answer:
\(10\sqrt{10}\)
Step-by-step explanation:
The largest perfect square of the factors of 1000 is 100. We can therefore convert √1000 like this:
√100 × 10
Next, we separate the numbers inside the √ as such:
√100 × √10
√100 is a perfect square that equals 10. We can therefore put 10 outside the radical and get the final answer to square root of 1000 in simplest radical form as follows:
10√10
pure acid is to be added to a 20% acid solution to obtain 52L of a 40% acid solution.What amounts of each should be used?
Let's define the following variables:
x = the amount of pure acid (100%) in liters
y = the amount of 20% acid in liters
If mixing the two liquids makes 52 L, then we can say that: (equation1)
\(x+y=52\)In addition, 100% of x liters + 20% of y liters will make 52L of 40% solution then, we can also say that: (equation 2)
\(\begin{gathered} 1(x)+0.2(y)=0.4(52) \\ x+0.2y=20.8 \end{gathered}\)Using this two equations, we can solve for the values of x and y using elimination. Here the steps:
1. Subtract equation 2 from equation 1.
\(\begin{gathered} x+y=52 \\ x+0.2y=20.8 \\ \text{Subtract similar terms in the two equations above.} \\ 0.8y=31.2 \end{gathered}\)2. Divide both sides of the equation by 0.8.
\(\begin{gathered} \frac{0.8y}{0.8}=\frac{31.2}{0.8} \\ y=39 \end{gathered}\)Therefore, the value of y = 39. The amount of 20% acid solution added to the mixture is 39 liters.
3. Plug in the value of y in the equation 1 to solve for x.
\(\begin{gathered} x+y=52 \\ x+39=52 \\ x=52-39 \\ x=13 \end{gathered}\)The value of x is 13. Hence, the amount of pure acid that was added to the mixture is 13 liters.
If you subtract 17 from my number and multiply the difference by -5 , the result is -25 ." What is 's number?
Answer:
22
Step-by-step explanation:
-23.94 divided by 10.5
Triangle inequality
Answer:
DF
EF
DE
Step-by-step explanation:
First, we need to figure out the third angle.
Angles in a triangle add up to 180, so
180 = 61 + 59 + DEF
DEF = 180 - (61 + 59) = 180 - 120 = 60
In a triangle, the smallest angle is always opposite the shortest side, and the largest angle opposite the longest.
The three angles are 61, 60, and 59.
Since DEF(61) is the largest, DF is the longest.
Next is EDF(60), so EF is the next.
Finally, DFE(59) is the smallest angle, so DE is the shortest.
DF, EF, DE
12−(−85)+45+(−36)
This is integer question
Solve it
12-(-85)+45+(-36)
negative 1 multiply negative 85 will leave an positive 85 and positive 1 multiply negative36 will also leave negative answer then you simplify to get 106
I need help pls asap I cant figure it out
There are 24 sticks in pattern 6. The diagram indicates that one pattern is made up of one box built from four sticks.
What is the geometric pattern?A geometric pattern is a pattern made out of geometric forms that are generally repeated, much like a wallpaper design.
The given figure shows that one pattern consists of one box formed from the 4 sticks.
Pattrern 1 = 1 box
Pattern 2 = 2 box
Pattern 6 = 6 box
1 box = 4 stick
Pattern 6 = 6 box = 6 ×4 = 24 sticks
Hence,there are 24 sticks in pattern 6.
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a wire that is centimeters long is shown below. the wire is cut into two pieces, and each piece is bent and formed into the shape of a square. suppose that the side length (in centimeters) of one square is , as shown below. (a) find a function that gives the total area enclosed by the two squares (in square centimeters) in terms of . (b) find the side length that minimizes the total area of the two squares. (c) what is the minimum area enclosed by the two squares?
The total area enclosed by the two squares is 2x² - 16x - 64.
What is a square?A square has four equal sides, four vertices, and is a closed, two-dimensional object. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width.
A two-dimensional shape's area is determined by how much space it would occupy if kept on a flat surface, such as a table.
Area of square is equal to side * side = side².
Given that the length of wire is 32cm.
The wire is cut into two pieces, and each piece is bent and formed into the shape of a square. So the length of one piece of wire is perimeter of that square.
The length of side of one square is x cm, so the perimeter of that square is 4x.
So the length of second piece of wire is 32-4x.
This is the perimeter of second square. so the length of side of second square is (32-4x)/4 = 8-x cm
Now the area of first square is A = x *x
A = x²
and the area of second is A = (8-x) *(8-x)
A = (8-x)²
A = x² - 16x + 64
So that the total area of two square is
A = x² + x² - 16x + 64
A = 2x² - 16x + 64
To find the minimum value of Area we find A'(x) = \(\frac{dA}{dx}\)
A'(x) = \(\frac{d}{dx}[x^2 +(8-x)^2]\)
A'(x) = 2x - 2(8-x).1
A'(x) = 2x - 16 + 2x
A'(x) = 4(x - 4)
To find the length of wire pieces so that the total area is minimum
A'(x) = 0
4(x - 4) = 0
x - 4 = 0
x = 4cm
So, the side of second square is 8 -4 = 4cm
So that, both square have equal measure.
The Total area enclosed by the two squares = 2 * side²
A = 2 * 4²
A = 2*16
A = 32cm²
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(3xy)^2x^4y/x^5
A. 3y^3
B. 3xy^3
C. 9xy^3
D. 9x^5y^3
Answer:
It is the third one
Step-by-step explanation
3 times 3 equals 9.
By solving Power equation, answer of the equation \(\frac{(3x)^2x^4y}{x^5}\) is 9xy³.
What is Power equation?The power is "a number says how many times to use the number in a multiplication".
According to the question,
\(\frac{(3x)^2x^4y}{x^5}\) = \(\frac{9x^2y^2x^4y}{x^5}\) [using power equation]
= 9xy².
Hence, By solving Power equation answer of the equation \(\frac{(3x)^2x^4y}{x^5}\) is 9xy³
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