The expression startroot 64 r superscript 8 baseline endroot can be written as (64)1/8r8.
This expression is asking for us to take the eighth root of 64, and then multiply it by 8. To solve this we can use the formula for radicals, which states that the nth root of a number a is equal to a1/n. In this case, n is equal to 8, and a is equal to 64. Therefore, the expression can be rewritten as 641/8 x 8. This simplifies to 8r2.
To calculate this, we first need to calculate the eighth root of 64, which can be done by raising the number to the power of the reciprocal of the root. In this case, we need to calculate 64^1/8. We can use a scientific calculator to find that the eighth root of 64 is 2. To finish the calculation, we simply multiply 2 by 8, which gives us 16. We can rewrite 16 as 8r2, which is the answer to the expression.
Therefore, the simplified expression is 8r2.
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The simplified form of expression √(64r^8) is 8r^4
The correct answer is an option (b)
In this question we have been given an expression startroot 64 r superscript 8 baseline endroot.
i.e., √(64r^8)
We need to simplify this expresison.
We know that 64 is square of 8.
8^2 = 64
So, we can write given expression as,
√(64r^8)
= √(8^2r^8)
= √[8^2r^(2 * 4)]
We know that for the properties of exponents i.e., non-zero numbers a, m,n
(a^m)^n = a^(m * n) ............(1)
So, √[8^2r^(2 * 4)]
= √[8^2(r^4)^2]
= √((8r^4)^2)
Square-root is nothing but the 1/2 power of number/expression.
i.e., √((8r^4)^2)
= [(8r^4)^2]^1/2
= (8r^4)^(2 * 1/2) ...........(from (1))
= (8r^4)^1
= 8r^4
Therefore, √(64r^8) = 8r^4
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Please answer asappp!!
Ty
Aiden's bank account has $160 in it. He plans to deposit a certain amount, m, each month
for the next year.
Aiden wants to have $400 at the end of the year. Which equation can he solve to find
the amount he should deposit each month?
160+12m = 400
160 + m = 12(400)
12(160+ m) = 400
160m | 12 = 400
The equation to find the amount deposited each month is 160 + 12m = 400.
The amount deposited each month is $20.
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,
Amount in account = $160
Amount at the end of the year = $400
Now,
There are 12 months in a year.
The amount deposited each month = m
Now,
160 + 12m = 400
Solve for m.
12m = 400 - 160
12m = 240
m = 20
Thus,
The equation is 160 + 12m = 400.
The amount deposited each month is $20.
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What is the midpoint of PQ, what is the value of M
The midpoint M of the line segment PQ is 14 units
How to determine the midpoint of the segment PQ?From the question, we have the following parameters that can be used in our computation:
A line segment PQ
The midpoint M
Using the above as a guide, we have the following:
P = 5
Q = 23
The midpoint M can be calculated using any of the following formulas
M = (Q - P)/2 + P or M = (P + Q)/2
Substitute the known values in the above equation, so, we have the following representation
M = (23 - 5)/2 + 5 or M = (23 + 5)/2
Evaluate the equations
M = 14
Hence, the value of M is 14 units
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In ABDC shown below, point E is on CD, and point F is on BD so that
ZBCD ZEFD. If FD=30, BC = 77, and EF = 35, find the
length of CD. Figures are not necessarily drawn to scale.
The length of the CD is 66.
What are similar triangles?Similar triangles are triangles that have the same shape but can be different sizes. Two triangles are similar if and only if the corresponding angles are congruent and the corresponding side lengths are in proportion. The symbol for similarity is '~' . Similarity can be determined by using the Angle-Angle (AA) similarity, the Side-Angle-Side (SAS) similarity, or the Side-Side-Side (SSS) similarity. If two triangles are similar, the ratio of the corresponding side lengths is called the scale factor. If this scale factor is k, then the ratio of any pair of corresponding sides is k.
In ΔBCD and ΔEFD,
side BC ≈ side EF ....(given E is on CD)
∠ BCD ≅ ∠EFD .....(given)
side CD ≈ side FD ......( given F is on BD)
∴ΔBCD ≈ ΔEFD ....(By Side Angle Side criteria)
[tex]\frac{BC}{EF} = \frac{CD}{FD}[/tex]
∴ [tex]\frac{77}{35} = \frac{CD}{30}[/tex]
∴ CD = 77 × 30/ 35
∴ CD = 66
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Given the Square JKLM, if the area of JKLM is 64 sq in.., what is the length of the diagonal KM?
The length of diagonal KM of square is 11.31 inch.
What is square?
A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can also be explained as a rectangle with two adjacent sides that are of equal length.
A square has four equal sides, four vertices, and is a closed, two-dimensional shape. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width.
Given:
The Square JKLM, the area of JKLM is 64 sq in.
We have to find the length of diagonal KM.
Since,
Area of square = (side)^2
64 = (side)^2
Side = 8
Length of each side of square is 8 in.
By using the Pythagorean theorem,
(KL)^2 + (LM)^2 = (KM)^2
8^2 + 8^2 = (KM)^2
64 + 64 = (KM)^2
128 = (KM)^2
KM = 11.31
Hence, the length of diagonal KM of square is 11.31 inch.
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What are angles for Grade 6?
In Grade 6, students typically learn about angles and their properties. Some of the key concepts that students may study include:
Understanding that an angle is formed by two rays with a common endpoint called the vertex.Identifying and labeling angles, using the vertex and the two rays that form the angle.Understanding that angles can be measured in degrees (°).Measuring angles with a protractor.Classifying angles as acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), or straight (exactly 180°).Identifying and drawing complementary and supplementary angles.Understanding the relationship between adjacent angles formed by parallel lines and transversals.Using angle properties to solve problems and prove geometric theorems.These are some of the key concepts that students may learn about angles in Grade 6, but the specific curriculum can vary depending on the school district and state.
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13 Jitesh made a square using 8 toothpicks of the same length as shown below. Arun made a bigger square. He also used some toothpicks of the same length. Which of these could be the number of toothpicks Arun used to make his square? A. 14 B. 16- D. 22
The number of toothpicks Arun could have used to make his bigger square than Jitesh's 8-toothpick square was B. 16.
How is the number of toothpicks determined?We are told that Jitesh made a square using 8 toothpicks.
The toothpicks have the same length as Arun's. We also know that Arun made a bigger square than Jitesh.
The same number of toothpicks must be on the four sides to make a square. Otherwise, it cannot form a perfect square.
Thus, it is unlikely that 14 toothpicks can make a square because 14 is not evenly divisible by 4, just like 22. However, 16 is evenly divisible by 4 and forms a perfect square of 4, giving each side an equal size.
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Here are some fractions.
9/12 6/8 18/24 10/16 15/20
One of these fractions is not equivalent to 3/4
Which fraction?
Fraction 10/16 is not equivalent to 3/4 among the other given fractions.
What is a fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given some fractions.9/12, 6/8, 18/24, 10/16, and 15/20.
Simplifying this given fraction by taking the common term out
[tex]\frac{9}{12}, \frac{6}{8} , \frac{18}{24} , \frac{10}{16} , \frac{15}{20}[/tex]
[tex]\frac{9/3}{1/3}, \frac{6/2}{8/2} , \frac{18/6}{24/6} , \frac{10/2}{16/2} , \frac{15/5}{20/5}[/tex]
Thus we will get
3/4, 3/4, 3/4, 5/8, 3/4
Therefore, Among the other fractions listed, fraction 10/16 is not equal to fraction 3/4.
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Find the slope-intercept equation of the line that passes through (1,-2) and has an undefined slope.
The slope - intercept equation of a line that would pass through (1,-2) and has an undefined slope, is y = -2 x
How to find the slope intercept equation?The slope - intercept equation takes the form:
y = mx + b
m = slope
b = y - intercept
When the slope is undefined, it means that there is no y - intercept as the slope is a vertical line which crosses the x - axis alone. The slope would therefore be :
y = mx
- 2 = 1 x
m = - 2
The slope - intercept form is:
y = -2 x
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Identify the restrictions on the domain of f(x) = quantity x minus 3 over quantity x plus 5.
The ratio of two values, x - 3 to x + 5, is the definition of the function f(x) = (x - 3)/(x + 5). The denominator (x + 5) of this function is defined for any values of x such that it is not equal to 0. The fraction would be undefined if the denominator was set to 0, which indicates that the function is not defined for that particular value of x.
For instance, the fraction would be undefinable if x = -5 because the denominator (x + 5) would be equal to 0. As a result, when x = -5, the function is not defined. The sole limitation on the function's domain is this one.
The domain of the function accepts all other values of x. The function is defined, for instance, for x = -4, -3, -2, and so forth.
In conclusion, x cannot be equal to -5, which is the only restriction on the domain of the function f(x) = (x - 3)/(x + 5). The domain of the function accepts all other values of x.
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What’s the algebraic expression if you have h more than 8?
Answer: h+8
Step-by-step explanation:
It’s simple h MORE than 8
Answer: h+8
Step-by-step explanation:
If you vertically compress the absolute value parent function f(x)= x by a factor of 3.
The equation of the new function, if we vertically compress the absolute value parent function, f(x) = |x| by a factor of 3: y = 1/x |x|
In this question we have been given an absolute value function f(x) = |x|
We need to find the equation of the function, if we vertically compress the absolute value parent function, f(x) = |x| by a factor of 3.
We know in function transformtaion there are two types of dilations.
1) Horizontal Dilation: a function y = f(x) into the form y = f(kx)
2) Vertical Dilation: a function y = f(x) into the form y = k f(x)
In both the cases, if k > 1, then the graph stretches and if 0 < k < 1, then the graph shrinks.
Since we vertically compress the absolute value parent function f(x) = |x| by a factor of 3, a scaling factor k must be 0 < k < 1
So, k = 1/3
And the required function wuld be, y = 1/3 * f(x)
y = 1/3 |x|
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The absolute value parent function is f(x)= x. When we vertically compress the absolute value parent function f(x)= x by a factor of 3, the new equation is f(x)=⅓x.
The vertical compression by a factor of 3 means that the original graph will be compressed to a vertically scaled-down version of the original graph. This means that the graph will be shorter by a factor of 3.
To calculate the new equation, we must first determine the value of the constant “a”. The equation of the original absolute value parent function is f(x)=x. When we vertically compress the absolute value parent function f(x)=x by a factor of 3, the new equation is f(x)=ax. The value of “a” is equal to ⅓. Therefore, the new equation of the absolute value parent function f(x)=x when it is vertically compressed by a factor of 3 is f(x)=⅓x.
The graph of the new equation is shown below. The graph is shorter than the original absolute value parent function by a factor of 3.
From the graph, we can also see that the new equation has a minimum value of -1/3, a maximum value of 1/3, and the graph is symmetrical along the y-axis.
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how many times does 5 go into 2.5
Answer:
.5
Step-by-step explanation:
2.5/5 = .5
On March 13, 2013, a Japanese printer presented the smallest book known at that date entitled "flowers of the four seasons". This square book has 22 pages of 0.75 mm on each side.
1) Calculate the area in m², of a page of this book answer : ???
The area of a page of the book, "flowers of the four seasons". would be = 5.6× 10^-⁷ m²
How to calculate the area of a book?To calculate the area of a book, the length and weight of the book must be determined which is then multiplied to give it's area in square metres or mm².
The number of pages that makes up the book, "flowers of the four seasons". = 22 pages.
Since the book has a square shape, the length and width is the same = 0.75 mm
To convert 0.75 mm to meter, divide by 1000= 0.00075m
The area of a page = Length× width = 0.00075×0.00075
= 0.0000005625= 5.6× 10^-⁷ m²
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Find the area of the shaded figure
The area of shaded figure is 272 square units
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.
Area of trapezium = (1/2)(a+b)*h
a=18 , b= 34, h - 16
So, area of trapezium = (1/2)(18+34)*16 = 52*8 = 416 square units
Area of unshaded triangle = (1/2) * base*height
= (1/2) * 18*16 = 18*8 = 144 square units
Area of shaded figure = area of trapezium - Area of unshaded triangle
= 416 - 144
= 272 square units
So, the Area of shaded figure = 272 square units
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Sonia finds a 3-full small bag of chips. She eats the rest of the chips
in the bag. Then she opens another small bag of chips. Sonia eats
of those chips. What fraction of a small bag of chips does Sonia
eat altogether?
The fraction of a small bag of chips does Sonia eat altogether if Sonia finds a 3/4- full bag of chips, she eats the rest of the chips in the bag, is 7 / 8.
What is a fraction?Only verbal descriptions of a portion of the whole were used to write fractions in ancient Rome. The numerator and denominator of fractions is first written in India with one number above the other but without a line. The line used to divide the numerator and the denominator were only added by Arabs.
Given:
Sonia finds a 3/4- full bag of chips, she eats the rest of the chips in the bag,
Calculate the fraction as shown below,
The Fraction of small bag of chips does Sonia eat altogether = total chips eat
The Fraction = 3/4 = 6/8
The Fraction = 6/8 + 1/8 = 7/8
Thus, the fraction is 7 / 8.
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The complete question is:
Sonia finds a 3/4- full bag of chips . she eats the rest of the chips in the bag. Then she opens another small bag of chips. Sonia eats 1/8 of those chips. what fraction of a small bag of chips does Sonia eat altogether?
13
5
L
N
M
Enter the ratio equivalent to tan(L).
tan (L) =
For right triangle LMN, the required ratio equivalent to tan(L) is 5 /13.
What is right angle triangle?The triangle is a geometric shape with three sides, and the sum of the interior angles should not exceed 180°.A right triangle also known as right-angled triangle, or more formally an orthogonal triangle, generally known as a rectangled triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.In this case, in order to find the ratio equivalent to tan (L).
tan(L) = opposite / adjacent side
tan(L) = NM /LN
Here given
NM = 5cm
LN = 13cm
We already know that tan(L) = perpendicular / adjacent
from given,
tan (L) = 5 / 13
As a result, the required ratio for triangle LMN is 5/13.
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everything in the picture
The measure of m∠6 is 123° and is equal to m∠1 because there are corresponding angles formed by parallel lines cut by a transversal.
What are corresponding anglesCorresponding angles are the angles that are formed when two parallel lines are cut or intersected by the transversal and they are equal.
The angles 1, 2, 3, 4, 5, 6, 7, and 8 all lie on a transversal line that cuts the parallel lines, hence m∠1 and m∠6 are corresponding angles are they are equal.
so;
m∠1 = (15x + 3)° = m∠6 = (10x + 43)°
collect like terms, we have;
15x - 10x = 43° - 3°
5x = 40°
divide through by 5
x = 40°/5
x = 8
m∠6 = [10(8) + 43]°
m∠6 = (80 + 43)°
m∠6 = 123°
Therefore, the corresponding angle m∠6 have the measure of 123°.
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Solve the inequality.
-4i + 28 > 8
The value of i for given inequality is i < 5.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a b indicates that an is smaller than b.
When a > b is used, it indicates that an is bigger than b.
A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.
Given,
-4i + 28 > 8
Dividing the equation by 4
-i + 7 > 2
Subtracting 7 from both sides,
- i > -5
i < 5
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time sensitive
20 points
Algebra 1
Answer:
c
Step-by-step explanation:
find 9 f(x) dx 0 if f(x) = 7 for x < 7 x for x ≥ 7 .
The function is 130/2.
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.
According to question,
[tex]\int\limits^9_0 {f(x)} \, dx \\ \int\limits^7_0 {f(x)} \, dx+\int\limits^9_7 {f(x)} \, dx\\ \int\limits^7_0 {7} \, dx + \int\limits^9_7 {x} \, dx\\ (7x)^{7} _{0} + (\frac{x^{2} }{2})^{9} _{7}[/tex]
7x7 - 7x0 + 81/4 - 49/4
49 + 32/2
130/2
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Find the area of the following trapezoid:
22cm, 12cm, 10cm, and 8cm
Answer:
Area of a Trapezoid = [tex]136cm^{2}[/tex]
Step-by-step explanation:
Area of a Trapezoid = [tex]\frac{1}{2} X(a+b)h[/tex]
Area of a Trapezoid = [tex]\frac{1}{2} X(12+22)8[/tex]
Area of a Trapezoid = [tex]\frac{1}{2} X34X8[/tex]
Area of a Trapezoid = [tex]136cm^{2}[/tex]
What is the difference between a line and a line segment Class 4?
Answer:
Answer Below
Step-by-step explanation:
The key difference between line and line segment is, a line is extended in both directions infinitely but a line segment has two endpoints.
Evaluate the following expressions.(a) \ln e ^ { -11 } =(b) e ^ {\ln 5 } =(c) e ^ {\ln \sqrt { 2 } } =(d) \ln ( 1/e^ { 4} ) =
The following logarithm expressions are,
(a) [tex]ln e^{-11}[/tex] = -11
(b) [tex]e^{ln5}[/tex] = 5
(c) [tex]e^{ln\sqrt{2} }[/tex] = 1.414
(d) [tex]ln^{\frac{1}{e^{4} } }[/tex] = -4
It is important to remember the following logarithm properties in order to solve the exercise:
[tex]ln(a) + ln(b) = ln(ab)[/tex]
[tex]ln(a) -ln(b) = ln(\frac{a}{b} )[/tex]
[tex]ln(a^{m})= m ln(a)[/tex]
[tex]ln(e)=1[/tex]
Given data,
(a) \ln e ^ { -11 }
[tex]ln e^{-11}[/tex] = [tex]ln_{e} ^{e^{-11} }[/tex]
[tex]ln e^{-11}[/tex] = -11
(b) e ^ {\ln 5 }
[tex]e^{ln5}[/tex] = 5
(c) e ^ {\ln \sqrt { 2 } }
[tex]e^{ln\sqrt{2} }[/tex] = [tex]\sqrt{2}[/tex]
[tex]e^{ln\sqrt{2} }[/tex] = 1.414
(d) \ln ( 1/e^ { 4} )
[tex]ln^{\frac{1}{e^{4} } }[/tex] = [tex]elne^{-4}[/tex]
[tex]ln^{\frac{1}{e^{4} } }[/tex] = -4
Therefore,
The following logarithm expressions are,
(a) [tex]ln e^{-11}[/tex] = -11
(b) [tex]e^{ln5}[/tex] = 5
(c) [tex]e^{ln\sqrt{2} }[/tex] = 1.414
(d) [tex]ln^{\frac{1}{e^{4} } }[/tex] = -4
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Andre says he can find the length of the third side of triangle ABC and it is 13 units. Mai disagrees and thinks that the side length is unknown. Who do you agree with? Show or explain your reasoning
On soloing the provided question we can say that - Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area. A = 210-123 = 87 sq unit
what is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
the sum of the areas of the circle, the triangle, and the square.
Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area.
A = 210-123 = 87 sq unit
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72 red and blue chairs in a class. The chair is selected at random from the class and the probability of selecting a blue chair is 2/3. If 4 red chairs and 2 blue chairs are taking out from the class, find the probability of selecting a red chair at random.
After 4 red chairs and 2 blue chairs are taken out from the class, there are 72 - 4 - 2 = 66 chairs remaining. Of these 66 chairs, 72 * 2/3 - 2 = 46 chairs are blue. Therefore, the probability of selecting a red chair at random is (66 - 46) / 66 = 20/66 = 5/16.
I don’t understand my homework
The Seed, where the range is 100, is the initial value of an algorithm used to produce a set of numbers.
Describe Range.Difference between the greatest and lowest value is referred to as the range. To get the range, find the variable's greatest observed value and deduct its lowest observed value. The data points in the center of the distribution are not taken into account; the range only considers these two values. Between the lowest and greatest values, there is a range of values. Values at each end of the range make up the range. Use the data set 4, 6, 10, 15, 18 as an example. Its range is 18-4 = 14, and its minimum and maximum values are 4, 4, and 4.
The term "seed" refers to the initial value of an algorithm used to produce a set of integers.
[tex]20, 25, 30, 45, 55, 90, 110,115,120[/tex]
Range = 120 - 20 = 100
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Solve the inequality:
x+2<20
m
0
Find the quotient 2+
27
4/²/7
13
317
土
1
3
You can use the model to help.
7
2/3
2
+
3
Answer: (D) --> 4 2/3
Step-by-step explanation:
1st --> Turn the problem into an improper fraction using the reciprocal
2nd --> Turn the improper fraction into a mixed answer
Help please ASAP[tex]\\\\\\[/tex]
y = (4/5)x - 1 is the equation of the line in slope-intercept form
How to write the equation of a line in slope-intercept form?
The equation of a line in slope-intercept form is y = mx + c.
Where m is the slope and c is the y-intercept (0, y)
slope = (y2-y1)/(x2-x1)
where (x1, y1) and (x2, y2) are the coordinates of two points that lie on the line
From the graph:
c = -1
x1 = 0, y1 = -1 and x2 = 5, y2 = 3
slope (m) = (3-(-1)) / (5-0) = 4/5
substitute m = 4/5 and c = -1 into y = mx + c:
y = (4/5)x - 1
Thus, the equation of the line in slope-intercept form is y = (4/5)x - 1
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What is the result when the number 63 Is decreased by 1.3%
Answer:
62.18
Step-by-step explanation:
The new value =
63 - The value of the percentage decrease =
63 - (1.3% × 63) =
63 - 1.3% × 63 =
(1 - 1.3%) × 63 =
(100% - 1.3%) × 63 =
98.7% × 63 =
98.7 ÷ 100 × 63 =
98.7 × 63 ÷ 100 =
6,218.1 ÷ 100 =
62.181 ≈
62.18
1/5/2023
7:00PM
