The ball travel horizontally 37 feet before it hits the ground.
What is Distance ?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
we have;
A(x) = -0.02x2 + 0.6x + 5
where
The horizontal distance, x, is given in feet.
The ball's height is indicated by the symbol A ---> in feet.
The fact that
The ball's altitude was zero when it landed on the earth.
so,
For A(x)=0
-0.02x^2 + 6x +5 = 0
'
the quadratic equation to be solved
The equation solving formula for a quadratic equation of the type;
ax^2 + bx + c = 0
this equation is equal to ;
[tex]x = \frac{-b\pm \sqrt{b^{2}- 4ac } }{2a}[/tex]
we have ;
-0.02x^2 + 0.6x +5 = 0
So,
a = -0.02
b = 0.6
c = 5
Subsititue this values in the formula;
[tex]x = \frac{-0.6\pm \sqrt{0.6^{2} -4 *(-0.02)(5) } }{2*(-0.02)}[/tex]
[tex]x = \frac{-0.6\pm \sqrt{0.76 } }{-0.04}[/tex]
[tex]x = \frac{-0.6\pm \ 0.87 }{-0.04}[/tex]
[tex]x = \frac{-0.6\ + \ 0.87 }{-0.04}= -6.75[/tex]
[tex]x = \frac{-0.6\ - \ 0.87 }{-0.04}= 36.75[/tex]
therefore
The ball travel horizontally 37 feet before it hits the ground.
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if distance between points p(3,a) and q(3,1 is 4 units find the value of a
Answer: -3 AND 7
Step-by-step explanation: very important to include the and, as it that point could be to the right or left of (3,1)
a cylinder is inscribed in a right circular cone of height 8 and radius (at the base) equal to 6.5. what are the dimensions of such a cylinder which has maximum volume?
The radius of such a cylinder will be 8 and height=8/3.
What is a cylinder?
Cylinder is one of the basic 3d shapes, in geometry, which has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center. The line segment joining the center of two circular bases is the axis of the cylinder. The distance between the two circular bases is called the height of the cylinder. LPG gas-cylinder is one of the real-life examples of cylinders.
Since, the cylinder is a three-dimensional shape, therefore it has two major properties, i.e., surface area and volume. The total surface area(TSA) of the cylinder is equal to the sum of its curved surface area and area of the two circular bases. The space occupied by a cylinder in three dimensions is called its volume(V).
V=πr²h and TSA=2πr²+2πrh where r=radius and h=height.
Now,
In any case, we can let the radius of the inscribed cylinder be x
. That must therefore mean that the height of the cylinder is 8−4/6x
. This makes the volume of the cylinder
V=πx^2(8−2/3x)=π(8x^2−2/3*x^3)
To find the maximum volume of the cylinder we take the derivative of V
with respect to x
and set it to 0
dV/dx=π(16x−2x^2)=0⇒16x−2x^2=2x(8−x)=0
x=0 leads to a trivial case, which leaves us with x=8
. This means that the height is 8−2/3*8=8/3
, and the volume is therefore
V=π⋅8^2⋅8/3
V=512/3π.
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Irene uses 6. 1 pints of white paint and blue paint to paint her bedroom walls.
3
4
of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?
After solving, 1.53 pints of blue paint she used to paint her bedroom walls.
Irene uses 6.1 pints of white paint and blue paint to paint her bedroom walls.
3/4 of this amount is white paint, and the rest is blue paint.
The combined amount of blue and white paint = 6.1 pints
Quantity of white paint applied to bedroom walls = 3/4
Quantity of blue paint applied to bedroom walls = 1 - 3/4
Quantity of blue paint applied to bedroom walls = 4/4 - 3/4
Quantity of blue paint applied to bedroom walls = (4 - 3)/4
Quantity of blue paint applied to bedroom walls = 1/4
Hence,
Blue paint were used to paint the bedroom's walls = 1/4 × 6.1
Blue paint were used to paint the bedroom's walls = 1.53
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The complete question is:
Irene uses 6. 1 pints of white paint and blue paint to paint her bedroom walls. 3/4 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?
16. Jake borrowed money to purchase a new bike. He has paid back $65 of the money he
borrowed, but he still owes $185. What was the total amount Jake originally borrowed?
Answer: $250
Step-by-step explanation:
If Jake still owes $185 and only just paid back $65, you need to add 185 and 65 together to get the total amount that he borrowed.
let p be the set of all people and let t(x,y) be the statement x trusts y. write the given statement using variables, quantifiers and symbols only
The given statement using variables, quantifiers and symbols only ∀x ∈ p, ∃y ∈ p, t(x,y).
Predicate variables are quantified using quantifiers. It contains a formula, a type of statement whose veracity depends on the values of various parameters.
A predicate turns into a proposition when we give it a definite value. Another way to put it is that the predicate will turn into a proposition if it is quantified.
Therefore, the phrase "quantify" refers to quantifiers like "all" or "some."
The two basic categories of quantifiers are existential and universal quantifiers.
Additionally, it demonstrates whether the predicate is true or false for all conceivable values or for specific value(s) inside the realm of discourse.
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Only variables, quantifiers, and symbols are used in the following statement: ∀x ∈ p, ∃y ∈ p, t(x,y).
Only variables, quantifiers, and symbols are used in the supplied statement.
Quantifiers are used to quantify predicate variables. It includes a formula, which is a sort of assertion whose truth is determined by the values of several factors.
When we assign a definite value to a predicate, it becomes a proposition. Another way to say it is that if the predicate is quantified, it becomes a proposition.
As a result, the term "quantify" refers to quantifiers such as "all" or "some."
Existential and universal quantifiers are the two primary types of quantifiers.
It also shows whether the predicate is true or false for all possible values or for specified value(s) inside the scope of discourse.
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Statistics Help! Will give Brainliest!
The z score that corresponds to the 90th percentile is 1.28. Option D
What is z-score?A z-score (also called a standard score) gives you an idea of how far from the mean a data point is. But more technically it’s a measure of how many standard deviations below or above the population mean a raw score is.
The 90th percentile refers to the value above 90 percent of the data. This is illustrated in the figure.
Therefore, using a z-table (also attached) or a technology, we can solve that getting the z=1.28.
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please help for algebra 1
Answer:
A: first choice
x^4
Step-by-step explanation:
When you divide two powers with the same base, you subtract the exponents, not divide.
The step x^8/x^4 is correct.
The next step should be x^(8 - 4), not x^8/4.
The correct simplification is x^4.
Answer:
A: first choice
x^4
A right triangle has a hypotenuse that is 21 inches long and a leg that is 15 inches long. How long is the other leg of the triangle?
Answer: In a right triangle, the length of the hypotenuse is the square root of the sum of the squares of the other two legs. So, using the Pythagorean theorem, the other leg would be the square root of (21^2 - 15^2) = (441 - 225) = 216 = 14.69 inches.
Step-by-step explanation:
A three-column table is given.
Part A C D
Part 14 28 63
Whole 50 B 90
What is the value of B in the table?
64
50
40
12
According to the information in the table, the value of B is 50 (option B)
How to find the value of B?To find the value of B we must calculate the constant, for that we have to perform the following operation:
constant = whole / partconstant = 50 / 28In this case, we use the values of another column to identify the constant that applies to all the values in the table and the result is the following:
constant = 1.78Additionally, to find the value of B we must perform the following operation:
whole = part * constantwhole = 28 * 1.78whole = 48.84 = 50According to the above, the correct answer would be 50 (option B).
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Need asap pls broooo
The angles in the quadrilateral are as follows:
g = 116 degrees
h = 64 degrees
How to find the angles of a quadrilateral?A quadrilateral is a polygon with 4 sides. The sum of angles in a quadrilateral is 360 degrees.
Therefore, let's find the angles g and h in the quadrilateral. According to the diagram, the quadrilateral has opposite side parallel to each other.
Therefore, the diagram can be regarded as a parallelogram.
Hence, adjacent angles of the diagram are supplementary.
Supplementary angles add up to 180 degrees.
Therefore,
116 + h = 180
h = 180 - 116
h = 64 degrees.
Therefore,
64 + g = 180
g = 180 - 64
g = 116 degrees.
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X is a positive integer.
33 + x is a positive integer.
Work out the four possible values of x, writing your values in ascending order.
smallest
value
largest
value
The possible values of x such that 33+x remains a positive integer in ascending order are 1,3,11 and 33.
An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.
Integer; ....-2, -1, 0, 1, 2, .....
Given the expression, 33+x
Now positive integers are whole numbers ( 1,2,3,...)
To 33/x be the whole number and x is also a positive integer.
33/1 = 33 (1,3 Positive integer)
33/3 = 11 (3,11 Positive integer)
33/11 = 3 (11,3 Positive integer)
33/33 = 1 (33,1 Positive integer)
Hence "The possible values of x such that 33+x remains a positive integer in ascending order are 1,3,11 and 33".
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The graph shows the population y of a certain city over the course of 10 years x. The equation of the trend line shown is y=1.9x+21
According to the equation of the trend line the population will reach 52900 in 27831 years.
What is an equation?A mathematical statement known as an equation is a combination of two expressions joined together by the equal sign.
The equation of the trend line is:
y = 1.9x + 21
where, y is the population and x indicate the year.
To find the number of years in which the population reach 52900, substitute y = 52900.
y = 1.9x + 21
52900 = 1.9x + 21
52900 - 21 = 1.9x
52879/ 1.9 = x
x = 27831
Hence, according to the equation of the trend line the population will reach 52900 in 27831 years.
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the tortoise and the hare are having a race. in this tale, the tortoise moves at feet per hour while the hare moves at feet per hour. the tortoise takes hours longer than the hare to finish. what was the distance of the race?
Distance of the race is 500 feet.
Given that tortoise moves at 50 feets per hour and hare moves at 250 feets per hour.
So speed of tortoise = 50 feets per hour.
Speed of hare = 250 feets per hour.
Let hare takes T hours to complete the race
Than tortoise will take (T + 8) hours to complete the race.
Total distance traveled by hare = speed * time = 250T
Total distance traveled by tortoise = speed * time = 50(T + 8)
Total distance traveled by both is same.
250T = 50(T + 8)
250T = 50T + 400
250T – 50T = 400
200T = 400
T = 2 hours
So, total distance of the race = 250T = 250 * 2 = 500 feet.
Therefore, total distance of the race is 500 feet.
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Graph the ordered pairs (time, distance) for the rows in the ratio table with missing values.
A graph of the ordered pairs (time, distance) for the rows in the ratio table is shown in the image attached below.
How to determine the ordered pairs (time, distance)?In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
y represents the distance.x represents the time.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 2/10
Constant of proportionality, k = 0.2
When time x = 20, the distance (y) is given by:
y = 20(0.2)
y = 4 miles.
When time x = 30, the distance (y) is given by:
y = 30(0.2)
y = 6 miles.
When time x = 40, the distance (y) is given by:
y = 40(0.2)
y = 8 miles.
Next, we would use an online graphing calculator to plot the ordered pairs as shown in the graph attached below.
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A et of even built-in bookhelve in to be contructed in a room. The floor-to-ceiling clearance i 9 ft 10 in. Each helf i 10 in. thick. An equal pace i to be left between helve. What pace hould there be between each helf and the next? ( There i no helf againt the ceiling and no helf on the floor. ) Pleae do not ue the rule for calculating with meaurement.
In order to leave an equal space between shelves, the distance between each shelf should be 9 feet 10 inches.
1. The floor-to-ceiling clearance is 9 feet 10 inches.
2. Each shelf is 10 inches thick.
3. To leave an equal space between shelves, the distance between each shelf should be the same as the floor-to-ceiling clearance, which is 9 feet 10 inches.
In order to ensure that there is an equal space between each of the shelves, the distance between each shelf should be 9 feet 10 inches. This is because the floor-to-ceiling clearance is 9 feet 10 inches, and the thickness of each shelf is 10 inches.
Therefore, in order to have an equal space between shelves, the total distance between each shelf should be 9 feet 10 inches. This is the best way to ensure that each shelf is equally spaced from the next.
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The distance from where Chris lives to willow lake is 48 miles.
Chris will take the train to willow lake. The train goes 60 miles an hour. If Chris takes the 2:20 train, about what time will he get to willow lake?
If Chris takes the 2:20 train, then he will get to willow lake at 2:28.
If Chris takes the 2:20 train, then we have to find at what time he will get to willow lake.
The distance from where Chris lives to willow lake is 48 miles.
Chris will take the train to willow lake. The train goes 60 miles an hour.
The distance = 48 miles
The speed of train = 60 miles an hour
Time = distance/speed
Time = 48/60
Time = 0.8 minutes
The train reach after 8 minutes in willow lake.
So the train reach 2:28.
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graph y=|x+4|
Please help!!
The graph for the points (-6, 2), (-5, 1), (-4, 0), (-3, 1) and (-2, 2) is plotted as below.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is y=|x+4|.
Graph the absolute value using the vertex and a few selected points.
Plot the points (-6, 2), (-5, 1), (-4, 0), (-3, 1) and (-2, 2)
Therefore, the graph for the points (-6, 2), (-5, 1), (-4, 0), (-3, 1) and (-2, 2) is plotted as below.
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You buy 4 mall candle and 2 large candle for $14. Your friend buy 5 mall candle and 3 large candle for $20. What i the cot of each mall candle? of each large candle?
The cost of 1 mall candle = $1 while the cost of 1 large candle = $5
Let the cost of 1 mall candle = x
Let us assume that the cost of 1 large candle = y
So, in case 1,
As I can buy,
4 mall candles and 2 large candles for $14
So, framing the equation,
We can rewrite it as:
4x+2y = 14-------(1)
As my friend can buy 5 mall candles and 3 large candles for $20
Now again framing the equation,
We can write it as:
5x+3y=20 -------(2)
From (1) and (2), for determining the value of x, we will first make the coefficient of y equal in both cases.
So, multiply the first equation by 3 and the second by 2
We will get,
12x+6y=42 -----(3)
10x+6y=40------(4)
Now subtracting (4) from (3)
We will get,
2x=2
=>x=1
So, for determining the value of y,
We will put the value of x in (1)
So, 4x+2y = 14-------(1)
=> 4+2y=14
=>2y=10
=>y=5
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The cost of a small candle is equal to $1, and the cost of each large candle is $5..
When I buy the candles,
Cost of 4 small and 2 large candles = $14
but when my friend purchse the candles , cost of 5 small and 3 large candles= $ 20 .
Let the cost of each small candle and each large candle be $x and $y respectively.
From first condition, when I can buy the candles,
Cost of 4 smalll candles = $4x
Cost of 2 large candles= $2y
=> $4x + $2y = $14
Reduce the equation, 2x + y = 7 ---(1) ( since, divided by 2)
In case Second, when my friend buy the candles,
Cost of 5 small candles= $5x
Cost og 3 large candles= $ 3x
=> $5x + $3y = $20 or 5x + 3y = 20 --(2)
Now, equation (1) and (2) made a system of linear equations. Linear equations are in two variables x and y . To solve the system of linear equation, we can use Elimination Method,
To make the same cofficient of y variable in both equtions, multiply the equation (1) by 3
=> 3(2x + y ) = 3× 7
=> 6x + 3y = 21 --(3)
Subtracts the eqution (2) from (3) to eliminate y,
=> 6x + 3y - ( 5x + 3y) = 21 - 20
=> 6x + 3y - 5x - 3y = 21 - 20
=> x = 1
from (1) , 2x + y = 7 => 2×1 + y = 7
=> y = 5
Hence, the cost of one small candle and one large candle are $1 and $5.
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which number line represents |x - 5| < 3?
Work Shown:
|x - 5| < 3
-3 < x-5 < 3
-3+5 < x-5+5 < 3+5
2 < x < 8
The graph will have open circles at 2 and 8, then shade between the open circles. The open circles indicate "do not include this endpoint". This is why choice A is the final answer.
GEOMETRY
this triangle has a depression of 10 degrees and it’s 1150 feet long. i’m supposed to find the height but i don’t know how !? pls help
I think this is it if not I'm sorry
78264 in
with two straight cuts, we can divide a flat pancake into four pieces: [asy] size(4 cm); draw(circle((0,0),1)); draw(rotate(45)*(1,0)--rotate(200)*(1,0),dashed); draw(rotate(150)*(1,0)--rotate(330)*(1,0),dashed); [/asy] what is the fewest number of straight cuts that will divide a flat pancake into $16$ pieces? (the pieces do not need to be the same shape or size.)
The fewest number of straight cuts needed to divide a flat pancake into 16 pieces is 5. This can be done by cutting the pancake into 4 pieces, then the 4 pieces into 4, and the resulting 16 pieces into 2.
The fewest number of straight cuts needed to divide a flat pancake into 16 pieces is 5. To do this, start by making one straight cut to divide the pancake into two equal pieces. Then make two more cuts, spaced evenly around the circumference, to divide the pancake into 4 equal pieces. Next, make two more cuts, spaced evenly around the circumference, to divide the 4 pieces into 4 even smaller pieces. Finally, make one last cut, spaced evenly around the circumference, to divide the 16 pieces into 2 equal pieces, giving you a total of 16 pieces. With this method, you can divide a flat pancake into 16 pieces with just 5 straight cuts.
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what expressions are equivalent to 3 (9p+2r)
Answer:
greetings
27p+6r, is an expression which is equivalent to 3 (9p+2r).
PLEASE SOMEONE HELP ME!!
I need this turned in by 10
Slope-intercept form (y=mx+b) of linear equations highlights the slope (m) and the y-intercept (b) of a line.
Define slope -intercept form?
The steepness of line is a slope (m). The point on the line is in the form of (x1, y1). The Point Slope Form Formula is, y – y1 = m (x – x1).Point-Slope Form of a LineSubstitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. Point-slope form = y − y 1 = m ( x − x 1 ) , where ( x 1 , y 1 ) is the point given and m is the slope given.A simple definition of point-slope form is an equation of a line written using one point on the line and the slope of the line. The point form is written as (x,y) and the slope is the rise over run, or the ratio of the change in the y values over the change in the x values.
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What is the midpoint to this line segment?
Answer:
I think 5
Step-by-step explanation:
One angle of an isosceles triangle measures 40°. What measures are possible for the other two angles? Choose all that apply.
40°
100°
20°
70°
Answer:
100° and 40°
Step-by-step explanation:
In an isosceles, 2 interior angles are equal.
If one angle is 40°, another one of its angles must be also 40°.
Fact of a triangle
Sum of interior angles of a triangle is 180°.
Let the unknown angle be x.
x + 40° + 40° = 180°
x + 80° = 180°
x = (180 - 80)°
x = 100°
So, the other angle is 100°
Hence,
100° and 40° are the possible measures for the other two triangles.
A high school drama department sold 238 tickets for their performance.
• An adult ticket cost $6. 75.
• A student ticket cost $3. 50.
• The high school drama department collected $1,252. 25 in ticket sales.
How many student tickets were sold?
The number of student tickets sold are 109.
As per the given data a high school drama department sold 238 tickets for their performance.
An adult ticket cost $6. 75.
A student ticket cost $3. 50.
Let the number of adult tickets be x.
Let the number of student tickets be y.
Then we know that the total number of tickets is 238.
x + y = 238 ... (1)
If we multiply the cost of a ticket by the number of tickets we can also get the total.
6. 75x + 3. 50y = 1252. 25(....... (2))
Now we have two equations and two unknowns and we can find the value for these unknowns
Lets use substitution method.
x + y = 238
x = 238 - y
Substitute x = 238 - y in equation (2)
6. 75(238 - y) + 3. 50y = 1252. 25
1606.5 - 6.75y + 3. 50y = 1252. 25
- 3.25y = - 354.25
3.25y = 354.25
y = 109
Substitute y = 109 in equation (1)
x + 109 = 238
x = 129.
Therefore number of student tickets are 109.
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a recipe calls for 112112 cups of mayonnaise and 3838 cups of pecans. how much mayonnaise should be used if 1 cup of pecans is used?
4 cups of mayonnaise should be used if 1 cup of pecans is used.
As per the given data:
A recipe calls for [tex]$1\frac{1}{2}[/tex] cups of mayonnaise and [tex]$\frac{3}{8}[/tex] cups of pecans.
First, convert the mixed fraction to an improper fraction.
[tex]$1\frac{1}{2}[/tex] cups of mayonnaise = [tex]$\frac{3}{2}[/tex]
Here we have to determine how much mayonnaise should be used if 1 cup of pecans is used.
This can be determined by using the unitary method.
We may determine the value of one unit from the value of many units and the value of many units from the value of one unit using the unitary technique.
The ratio of the amount of pecans comparing reality and the recipe is:
[tex]$= \frac{1}{\frac{3}{8} }[/tex]
= [tex]$\frac{8}{3}[/tex]
To find the amount of mayonnaise that should be added:
= [tex]$\frac{8}{3}[/tex] × [tex]$\frac{3}{2}[/tex]
= 4
Therefore 4 cups of mayonnaise is required.
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Find the Area of the figure below, composed of a parallelogram and two semicircles.
Round to the nearest tenths place.
16
5
18
The area of figure composing a parallelogram and two semicircles is 399.06 units².
What is a parallelogram?
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.
The base of the parallelogram is = 18 units
The height of the parallelogram is = 11 units
The area of a parallelogram is given as -
Area = Base × Height
Area = 18 × 11
Area = 198 units²
The diameter of the semicircle is = 16 units
The radius of semicircle is = 8 units
The area of the semicircle is given as -
Area = (1/2)πr²
Area = (1/2)π(8)²
Area = (1/2)π × 64
Area = 32π units²
The total area of the figure is given as -
Total Area = Area of Parallelogram + 2 (Area of semi-circle)
Total Area = 198 + 2(32)π
Total Area = 198 + 64π
Total Area = 198 + 201.06
Total Area = 399.06 units²
Therefore, the area of the figure is 399.06 units².
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Find the reflection of point A over the y-axis.
A (-3,-9)
The coordinates of point A after a reflection over the y-axis are given as follows:
A(3,-9).
How to obtain the coordinates of point A?The original coordinates of A are given as follows:
A(-3,-9).
The rule for a reflection over the y-axis is given as follows:
(x,y) -> (-x,y).
Meaning that the x-coordinate has the signal exchanged while the y-coordinate remain constant, hence the coordinates of point A after a reflection over the y-axis are given as follows:
A(3,-9).
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Select the correct answer from each drop-down menu.
The given equation has been solved in the table.
Step
Statement
& +5 – 5 = 23 – 5
į = 18
4. 5 = 4. 18
= 72
Use the table to complete each statement.
In step 2, the
In step 4, the
property of equality was applied.
property of equality was applied.
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In step 2. the addition property of equality was applied.
In step 2. the subtraction property of equality was applied.
We have solved the equation x/4 + 5 = 23.
In step second we subtract 5 on both side, this is the property of equality of addition.
In step 3 the expression is x/4 = 23
In step 4 we multiply 4 on both side, again using the property of equality of subtraction.
Now the value of x is 72.
Hence, using the property of equality in step 2 and 4 we solve the equation.
To learn more about property of equality link is here
brainly.com/question/13130806
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