The slope of the line is a measure of the rate of change between two points and is calculated by dividing the change in y-values by the change in x-values. In this case, the slope is -6, which means that for every 1 unit increase in x, there is a 6 unit decrease in y.
The slope of the line is a measure of the rate of change between two points. It is calculated by dividing the change in y-values by the change in x-values. To find the slope of the line represented by the table of values, we need to first identify two points on the line. We will use the points (x1, y1) and
(x2, y2).
We can choose any two points, but for this example, we will use
(x1, y1) = (-7, 9) and (x2, y2) = (8, -15).
The slope of the line is then calculated by finding the difference between the y-values
(y2 - y1 = -15 - 9 = -24)
and the difference between the x-values
(x2 - x1 = 8 - (-7) = 15)
and dividing these two values:
-24/15 = -6.
This means that for every 1 unit increase in x, there is a 6 unit decrease in y.
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A parallelogram is shown on this coordinate plane.
What is the perimeter, in units, of the parallelogram?
A) 24
B) 36
C) 48
D) 64
The perimeter, in units, of the parallelogram exists 48.
What is meant by coordinate plane?Two number lines combine to produce the coordinate plane, a two-dimensional surface. The x-axis is the name given to one horizontal number line. The y-axis is the name given to the other number line, which is vertical. At a place known as the origin, the two axes collide. The coordinate plane allows us to graph points, lines, and more.
A coordinate plane is a framework for describing and graphing points and lines. The coordinate plane is composed of two axes, one vertical (y) and one horizontal (x). The coordinate plane has four quadrants. The origin is the location where these lines converge (0, 0).
Therefore, the correct answer is option C) 48.
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Twenty-five households are surveyed and the number of children is recorded. The data is summarized in the frequency table below. Use the frequency table to compute the mean of the observations.
An average mean of 1.72 children can be found on every house
What is frequency table?One method for making data more comprehensible is to put it in a frequency distribution table. Consider having a list of IQ results for a talented class at a certain elementary school. The frequency of a value in a set of data is how frequently it appears.
Victor, for instance, made nine attempts to obtain a red gumball. The quantity of gumballs in each hue that were produced would be the frequency in this situation. The distribution of observations based on a variable's possible values is displayed in a frequency table.
frequency = 10 + 4 + 2 + 3 + 4 + 2
= 25
Sum of children
= (10 × 0)+(4 ×1)+(2 × 2)+(3 × 3)+(4 × 4)+(2 × 5)
= 43
Mean = 43/25
= 1.72
Thus, An average mean of 1.72 children can be found on every house.
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16
d
out of
What is the solution set to the following
equation?
4m² - 8m +9=0
Select one:
O a. m = 1 + 4i√√/5
2+i√/5
O b. m =
2
O c. m = -1 ± 4i√√5
O d. m =
-2+i√/5
2
The solutions of the quadratic equation are:
m = 1 ± i*√(5)/2
The correct option is b.
How to find the solutions of the quadratic equation?Here we want to solve the quadratic equation:
4m² - 8m +9 = 0
Replacing the coefficients on the quadratic formula, we will see that the solutions are:
[tex]m = \frac{8 \pm \sqrt{(-8)^2 - 4*4*9} }{2*4} \\\\m = \frac{8 \pm \sqrt{-80} }{8}\\\\m = 1 \pm\sqrt{-80/64} \\\\m = 1 \pm\sqrt{-5/4} \\\\m = 1 \pm\sqrt{-5}/2\\\\m = 1 \pm\sqrt{5}i/2[/tex]
These are the solutions.
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PLEASE HELP ME
A circular mulch bed has a radius of 1.6 feet. A bag of mulch contains 2 cubic feet of mulch. If all of the mulch is spread evenly on the bed, what is the mulch's depth to an appropriate number of significant digits? A. 0.249 foot B. 0.2 foot C. 0.25 foot D. 0.2487
PLEASE SHOW WORK!!!
If a circular mulch bed has a radius of 1.6 feet. A bag of mulch contains 2 cubic feet of mulch. The mulch's depth to an appropriate number of significant digits is: C. 0.25 foot.
How to find the depth?The volume of the mulch bed is given by the formula for the volume of a cylinder:
V = π * r^2 * h
Where:
r = radius (1.6 feet)
h= the height (the depth of the mulch).
Since we have 2 cubic feet of mulch, and want to spread it evenly over the bed, we can set 2 = π * r^2 * h and solve for h:
h = 2 / (π * r^2) = 2 / (π * 1.6^2)
h ≈ 0.25 feet
Therefore the depth of the mulch is approximately 0.25 feet.
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What is the range of integer value in C?.
The range of integer value in C is: -2,147,483,647 to 2,147,483,647
We know that the range of data types means the maximum and minimum value that can be stored inside the variable of a given type.
In C programming, the primitive data types are:
char – this data type hold a single character
float – this data type hold single-precision types of floating-point.
int – this data type hold integers
double - this data type hold double-precision types of floating-point
The int i.e., integer data type holds whole numbers that range from -2,147,483,647 to 2,147,483,647.
The number 2,147,483,648 cannot be used.
The integer value is stored as a signed binary integer.
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formula to solve any quadratic equation
A goat is tethered to a stake at the edge of a circular field with radius 1 unit. How long should the rope be so that the goat can graze over half of the field?
Based on the information provided, the length of the rope for the goat to graze over half of the field is 0.5 units.
What is the radius of a circle?The radius of a circle can be defined as a straight line that goes from any of the borders of the circle to its center of it.
How is the radius related to the lenght of the rope?The radius and the proportion of the field that the goat can graze is proportional. In this case if the length is 1 unit the goat can graze all the field; therefore, if we cut the graze to 0.5 the goat will graze only half of the field.
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Set up a proportion to solve for x in the following similar triangles.
Answer:
9/6=12/x-4
Step-by-step explanation:
Three friends shared 2 chocolate chip cookies. Four friends shared 3 oatmeal raisin cookies. Who got more cookie: the friends who shared the chocolate chip cookies or the friends who shared the oatmeal raisin cookies
Answer: The friends who shared 2 chocolate chip cookies.
Step-by-step explanation: 3/2= 1.5 and 4/3= 1.3
1.5>1.3
Nata is solving 42 × 15. Lulu stops her after the third step to ask her why she wrote what she did. Lulu asks why she wrote a 20. Complete the sentences to explain Nata’s work
Nata was using the partial products method to solve the multiplication problem 42 × 15. She likely wrote 20 because she was finding the product of 42 and 10, which is 420. Writing 20 was likely a shorthand for the digit 2 in 420.
What is the product about?In the partial product method, each digit of one number is multiplied by each digit of another number, keeping each digit in its original place. Place value is typically used to calculate the partial product. To get the product of two-digit numbers, we employ the partial product method.
The partial products method involves breaking down one factor into its place value components and multiplying each component separately, then adding the products together to get the final answer.
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19. Sketch the graph of x² + y² + 4x - 2y - 31 = 0.
Write the center and radius under the graph. (show all work)
For given equation of circle radius is 6 unit and center is at (-2,1).
What is a circle?
A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.
The equation of circle in the plane is given as:
(x-h)^2 + (y-k)^2 = r^2
where (x, y) are the coordinate points
(h, k) is the coordinate of the center of a circle
and r is the radius of a circle.
Now,
As shown in graph the graph by taking two points on graph
(-2,7) and (-2,-5)
Center will be at (-2-2)/2, (7-5)/2
i.e. (-2,1)
And for radius take magnitude of points from y-coordinate
(7+5)/2=6 unit
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3. Solve this system by elimination
-5x - 10y = 20
-5x - 8y = 14
6. Solve this system by substitution
x = 4
-4x - 5y = 4
Answer:
3. (-4/5, -3) 6. (4, 12/-5)
Step-by-step explanation:
3. so first we have
-5x - 10y = 20
-5x - 8y = 14
so first we have to have the x's be opposite so we multiply the top one by -1 which gets us
5x + 10y = -20
-5x - 8y = 14
then we cancel out the x's and subtract 10 by 8 and -20 by 14 so it's now
2y = -6
then we divide by 2 on both sides so it's
y = -3
but now we have to solve for x so we substitute y in on the bottom equation so now it is
-5x - 8(-3) = 20
now we multiply
-5x + 24 = 20
subtract 24 from both sides
-5x = -4
divide by -5
x = -4/5
then put it in coordinates
(-4/5, -3)
6. so we have
x = 4
-4x - 5y = 4
so first we have to substitute the top in for the bottom so now we have
-4(4) - 5y = 4
distribute
-8 - 5y = 4
add 8 to both sides
-5y = 12
divide
y = 12/-5
coordinates
(4, 12/-5)
HELP ME PLS >>>>>>>>>
The value of the length of side UX for the right triangle formed by sides tangent to the circle is equal to 3.4 using the Pythagoras rule.
What is the Pythagoras ruleThe Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The side XV is perpendicular to the side UV tangent to the circle, which makes the triangle a right triangle.
so by evaluation we derive the value for the hypotenuse UX as follows;
UX = √(3² + 1.6²)
UX = √(9 + 2.56)
UX = √11.56
UX = 3.4
Therefore, the length of side UX for the right triangle is equal to 3.4 using the Pythagoras rule.
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Polynomial from Description
Use the information below to answer the questions.
Find the value of a,b,c and d. Note: b < d for grading purposes.
:b- type your answer....
a- type your answer....
type your answer.....
d- type your answer.....
Next
The polynomial, so d can be any value less than b.
What is polynomial?A polynomial is an expression made up of multiple terms, each of which is a number, a variable, or the product of a number and one or more variables. Polynomials are typically used to model real-world scenarios including, but not limited to, population growth, force and acceleration, and angles of elevation. Each term of the polynomial is separated from the others by an addition or subtraction sign.
Given the polynomial 4x^3 + ax^2 + bx + c,
a = 4, b = -3, c = 5, d = -2.
To find the values of a, b, c, and d, we need to compare the coefficients of the polynomial to the given values.
The coefficient of the term with the highest degree (x^3) is 4, so a = 4.
The coefficient of the next degree (x^2) is a, so a = -3.
The coefficient of the next degree (x) is b, so b = 5. The coefficient of the constant term is c, so c = -2. Finally, d is not given in the polynomial, so d can be any value less than b.
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A piece of artwork appreciate by 1. 28% in value every year. It wa purchaed for $1500. State the equation that can be ued to determine the value of the artwork in ""x"" year
the equation that can be used to determine the value of the artwork in "x" year is A = 1500(1 + 0.0128)^x.
An equation that can be used to determine the value of the artwork in "x" years is a compound interest equation. This type of equation is used to calculate the value of an investment over time, taking into account the initial investment amount and the interest rate.
Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It can be contrasted with simple interest, which is calculated only on the principal amount.
Compound interest is considered to be more beneficial for savers and investors, as it allows for interest to be earned on previously earned interest, leading to faster growth of the principal.
In this case, the artwork appreciates by 1.28% in value every year and was purchased for $1500. The formula for compound interest is:
A = P(1 + r)^n
Where:
A = the future value of the artwork
P = the initial investment (the purchase price of $1500)
r = the interest rate (1.28% per year)
n = the number of years
To use this equation, we need to convert the interest rate from a percentage to a decimal. We do this by dividing the interest rate by 100. So, 1.28% as a decimal is 0.0128.
Now we can substitute the values into the equation:
A = 1500(1 + 0.0128)^x
Therefore, the equation that can be used to determine the value of the artwork in "x" year is A = 1500(1 + 0.0128)^x.
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3. Triangle DEF with vertices D(0, 6), E(3, 5), and F(1, 1):
90° counterclockwise about the point (5,2)
The vertices of the triangle DEF after the 90º counterclockwise rotation about the point (5,2) are given as follows:
D'(-11, -2), E'(-10, 1) and F'(-6, -3).
What are the rotation rules?The five more known rotation rules are given as follows:
90° clockwise rotation: (x,y) -> (y,-x)90° counterclockwise rotation: (x,y) -> (-y,x)180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y)270° clockwise rotation: (x,y) -> (-y,x)270° counterclockwise rotation: (x,y) -> (y,-x)Considering the 90º counterclockwise rotation about the point (5,2), the rule is given as follows:
(x,y) -> (-y - 5, x - 2).
Hence the vertices are given as follows:
D'(-11, -2), E'(-10, 1) and F'(-6, -3).
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“growth or decay right” it cut out the picture
Help! i’ve been stuck on these problems for a bit now
Answer:
Growth
Growth
Decay
Decay
How do you graph y =- 7?.
Graph y=-7 by plotting y-intercept (0,-7) and all points have y=-7, it is a horizontal line.
What is graph ?
A graph is a mathematical structure used to represent relationships between objects. In a graph, objects are represented by vertices (or nodes) and relationships are represented by edges (or arcs). Graphs can be used to model a wide variety of real-world systems, including networks of roads, social networks, and the internet.
To graph y = -7, you can start by plotting the y-intercept, which is the point at which the line crosses the y-axis. In this case, the y-intercept is (0, -7) because when x = 0, y = -7.
To graph the line, you can then pick any other x-value, substitute it into the equation, and find the corresponding y-value. For example, if you pick x = 1, then y = -7. So, you can plot the point (1,-7) on the graph.
You can repeat this process with different x-values and plot more points on the graph.
Graph y=-7 by plotting y-intercept (0,-7) and all points have y=-7, it is a horizontal line.
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There are two bags A and B.
Bag A has 6 red counters and 4 green counters. Bag B has 3 red counters and 7 green counters.
A counter is removed from Bag a and placed into Bag B. A counter is then removed from Bag B.
Work out the probability the counter removed is red.
The probability that the counter removed is red is given as follows:
18/55.
How to obtain the probability?A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.
The probabilities of a red counter being removed from Bag B is obtained considering these following scenarios:
Red from A: 4/11 of 6/10.Green from A: 3/11 of 4/10.Hence the probability that the counter removed is red is calculated as follows:
p = 4/11 x 6/10 + 3/11 x 4/10 = 36/110 = 18/55.
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GIVING 20 POINTS! FOR CORRECT ANSWER!
(1 + √2)^2
Can someone please give a step-by-step on how to solve this? Thanks!
What is the value of the expression shown below? 3 over 5 to the power of 2 + 4 × 3 − 2 (4 points)
anyone?? help....
[tex]( \frac{3}{5} ){}^{2} + 4 \times 3 - 2[/tex]
[tex] \frac{9}{25} {}^{} + 12- 2[/tex]
[tex] \frac{9}{25} {}^{} + 10[/tex]
[tex] \frac{9 + 10(25)}{25} [/tex]
[tex] \frac{9 + 250}{25} [/tex]
[tex] \frac{259}{25} [/tex]
Each pair of points is on the graph of an inverse variation. Find the missing value.
(3.5,16) (x,8)
The missing value for x is 7.
How to find the missing valueThe inverse variation relationship between two variables x and y is described by the equation y = k/x,
where k is a constant.
We can use this equation to find the missing value, using the information given.
First, we'll use the first set of points to find the constant k:
y = k/x
16 = k/3.5
16 * 3.5 = k
56 = k
Next, we'll use the constant k and the second set of points to find the missing x value:
y = k/x
8 = 56/x
8 * x = 56
x = 56/8
x = 7
hence x is 7
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a trinagle is shown. what is y?
Answer:
82+54=136°
Step-by-step explanation:
the value of the extreior angle in a tringle equals to the sum of the further two angles in the tringle
43p72 transmath 4eme
The value of {p} is equivalent to 1.68.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression -
43p = 72
The given equation is -
43p = 72
{p} = 72/43
{p} = 1.68
Therefore, the value of {p} is equivalent to 1.68.
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Amrita had to travel 20 km to attend a function. She had covered 17km 50 m when her car broken down. How much ditance remained to be covered
The distance remained to be covered by amrita to attend a function is 2950 meters or 2.95 kilometers.
Given,
Total distance to be covered by Amrita = 20 KM = 20000 m
Distance covered by her car before broken = 17 Km 50 meter = 17050m
We know that,
1 Kilometer = 1000 meter
Remaining Distance = (20000 - 17050)m
= 2950 m
= 2.95 KM
Therefore, the distance remaining to be covered by amrita is 2950 meters or 2.95 Kilometers.
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Please help, I already did the rest I just need help with the last one.
Find 4½ x 2½ write the product as a mixed number
Answer: 11 1/4
Step-by-step explanation:
4 1/2 * 2 1/2
= 9/2 * 5/2
= 45 / 4
= 11 1/4
HELP.
If the lengths of two sides of a triangle measure 7 and 12, the length of the third side could
measure:
(b) 19
(c) 3
(d) 5
(a)16
Answer: (A) 16
must be less than 19
and more than 5
Step-by-step explanation:
A cannonball i fired directly upward from a height of 0 feet with an initial velocity of 208 feet per econd. When will the cannonball be at a height of 640 feet for the firt time?
12 econd
5 econd
The cannonball will be at a height of 640 feet for the first time after 6.5 seconds.
Acceleration, is a rate at which velocity changes with time, in terms of both speed and direction.
The time it will take for the cannonball to reach a height of 640 feet for the first time can be found using the equation:
t = (vf - vi) / a
where:
t = time (in seconds)
vf = final velocity (in feet per second) = 0 (at the top)
vi = initial velocity (in feet per second) = 208
a = acceleration (in feet per second squared) = -32 (upwards)
Plugging in the values:
t = (0 - 208) / (-32) = 6.5 seconds.
So, the cannonball will be at a height of 640 feet for the first time after 6.5 seconds.
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