Note that in the above scenario, the original dimensions of the piece of metal that is rectangular are:
Length: 32 InchesWidth: 15 InchesWhat is the rationale for the above solution?Let x equal the width of the box and x + 15 equal the length of the box.
Subtract 6 (the amount cut out) from both of these to get the following terms: (x+9) and (x-6).
These are the length and width of the box respectively. We also know that the height of the box is 3. Plugging these into the formula for the volume of a box gives you:
3(x+9)(x-6)=858
If the above is expanded, we have:
3x²+9x-162=858
Subtract 858 from both sides to make the quadratic equation equal zero. Plug the a, b and c coefficients into the quadratic formula (or factor) to find x.
3x²+9x-162- 858 = 0
⇒ 3x²+9x -1020= 0
At the stage we solve for x:
3x2+9x−1020 = 0
Factor left side of the equation.
3(x−17)(x+20)=0
Set factors equal to 0.
x−17=0 or x+20=0
x=17 or x=−20
We can't get a negative side, so the answer that makes sense is x =17 recall that the metal is 15 inches longer than its width.
So if the Width is x and the Lenght is x +15
Then Width is 17 while the length is 17 + 15 = 32inces.
Thus the original dimensions of the metal are:
Length: 32 Inches
Width: 15 Inches
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graph the function
X+6, X ≤-2
f(x)= x², -2≤ x ≤ 1.
-2x, x > 1
Answer:
Step-by-step explanation:
To graph the function, we'll break it down into three parts based on the given conditions.
For x ≤ -2:
The function f(x) = x + 6 is valid in this range. We'll plot a straight line with a slope of 1 and a y-intercept of 6. Since x ≤ -2, we'll extend the line towards the left indefinitely.
For -2 ≤ x ≤ 1:
The function f(x) = x² is valid in this range. We'll plot a curve representing a quadratic function. The graph starts at the point (-2, 4), curves upward, and ends at the point (1, 1).
For x > 1:
The function f(x) = -2x is valid in this range. We'll plot a straight line with a negative slope of -2. Since x > 1, we'll extend the line towards the right indefinitely.
Combining these three parts, we get the graph of the function as follows:
23(2+2+3+372+27272+"
Find all Solutions of the equation
Answer:
[tex]\textsf{D)} \quad x=-\dfrac{\pi}{3}, 0, \dfrac{\pi}{3}, \dfrac{\pi}{2}[/tex]
Step-by-step explanation:
To find the solutions of the given trigonometric equation, begin by factoring out the common term sin 2x:
[tex]\begin{aligned}2 \sin 2x \cos x - \sin 2x & = 0\\\sin 2x(2 \cos x - 1)&=0\end{aligned}[/tex]
Set each factor equal to zero and solve for x using the unit circle.
[tex]\begin{aligned}\sin 2x & = 0\\2x & = \sin^{-1}(0)\\2x&=0+ 2\pi n, \pi + 2 \pi n\\ x&=\pi n, \dfrac{\pi}{2}+\pi n \end{aligned}[/tex]
[tex]\begin{aligned}2\cos x - 1 & = 0\\2 \cos x& = 1\\\cos x&=\dfrac{1}{2}\\x&=\cos^{-1}\left(\dfrac{1}{2}\right)\\x&=\dfrac{\pi}{3}+2\pi n, \dfrac{5\pi}{3}+2 \pi n\end{aligned}[/tex]
Therefore, the solutions in the given interval -π/2 < x ≤ π/2 are:
[tex]\boxed{x=-\dfrac{\pi}{3}, 0, \dfrac{\pi}{3}, \dfrac{\pi}{2}}[/tex]
If f(1) = 0, what are all the roots of the function f (x) = x cubed + 3 x squared minus x minus 3? Use the Remainder Theorem.
The roots of the cubic function:
f(x)= x³ + 3x² - x - 3
are x = 1, x= -1, x = -3
How to find the roots of the function?We want to find the roots of the function:
f(x)= x³ + 3x² - x - 3
We know that x = 1 is a root, because f(1) = 0.
Then we can write that function as:
(x - 1)*(x - a)*(x - b)
Where a and b are the other two roots, then we need to solve:
x³ + 3x² - x - 3 = (x - 1)*(x - a)*(x - b)
Expanding the right side, we will get:
x³ + 3x² - x - 3 = x³ + (-a - b - 1)x² + (a + b + ab)x + (-ab)
Comparing like terms, we can see that:
(-a - b - 1) = 3
(a + b + ab) = -1
(-ab) = -3
The third equation gives:
ab = 3
Replacing that in the second one we get:
a + b + 3 = -1
a + b = - 1 - 3 = -4
a + b = -4
a = -4 - b
Replacing that in the relation above:
ab = 3
(-4 - b)*b = 3
-4b - b² = 3
b² + 4b + 3 = 0
The zeros of that function are:
[tex]b = \frac{-4 \pm \sqrt{4^2 -4*3*1} }{2*1} \\\\b = \frac{-4 \pm 2}{2}[/tex]
Then if b is the value when we take the positive sign:
b = (-4 + 2)/2 = -1
the value of a is:
a = -4 - b = -4 + 1 = -3
These are the other two roots.
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A toy ball can be modeled as a sphere. Jeriel measures its diameter as 21.9 cm. Find
the ball's volume in cubic centimeters. Round your answer to the nearest tenth if
necessary.
Answer:
Step-by-step explanation:
Solve the following system of equations using the elimination method
y + 2x = 1
3x - 2y = 5
The solution to the system of equations is x = 1,y = -1 by using the elimination method.
To solve the system of equations using the elimination method, we'll eliminate one variable by adding or subtracting the equations. Here's how:
Multiply the first equation by 2 to make the coefficients of y in both equations opposite each other:
Equation 1: 2(y + 2x) = 2(1) => 2y + 4x = 2
Rewrite the second equation as:
Equation 2: 3x - 2y = 5
Now, we can add the modified Equation 1 to Equation 2 to eliminate y:
(2y + 4x) + (3x - 2y) = 2 + 5
Simplifying, we get:
4x + 3x = 7
7x = 7
Divide both sides of the equation by 7 to solve for x:
x = 7/7
x = 1
Substitute the value of x into either of the original equations. Let's use the first equation:
y + 2(1) = 1
y + 2 = 1
Subtract two from both sides of the equation to solve for y:
y = 1 - 2
y = -1
Therefore, the solution to the system of equations is:
x = 1
y = -1
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jureks brother is 6 years older than him .Together they are 22 years old ,how old are the brothers.Write down the correct equation?
Answer:
Jurek is 8. His brother is 14
Step-by-step explanation:
let's call Jurek J, and let's call his brother B.
his brother is 6 years older than Jurek.
So, B = J + 6.
B + J = 22
(J + 6) + J = 22
2J + 6 = 22
2J = 16
J = 8
so Jurek is 8
B + J = 22, B = 22 - J = 22 - 8 = 14.
Brother is 14
Please help me right now!
Thank you so much
The length of the arc KL in the given circle is 3.49 units
How to find the length of the arc KL?In a circle whose radius is R, the length of an arc defined by an angle x is given by:
Length = (x/360)*2*3.14*R
Here we know that the radius is 2 units, and the angle for the arc KL is 100°, then we can replace these values in the formula above so we get that the length of the arc is:
Length = (100/360)*2*3.14*2
Lenght = 3.49 units.
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kylie is wrapping a book for her sister.The box is 20" x 12"x 2 1/2. the book she wants to put it in is 18" x 3 1/2 x 8.How much empty space will be in the box once kyile puts the book inside
Answer:
96 cubic inches
Step-by-step explanation:
To calculate the empty space that will be left in the box once the book is inside, we need to find the difference between the volume of the box and the volume of the book.
Volume of the box:
20" x 12" x 2 1/2" = 600 cubic inches
Volume of the book:
18" x 3 1/2" x 8" = 504 cubic inches
Empty space in the box:
600 cubic inches - 504 cubic inches = 96 cubic inches
Therefore, there will be 96 cubic inches of empty space left in the box once Kylie puts the book inside.
PQ and QR are 2 sides of a regular 12-sided polygon
Answer:
Step-by-step explanation:
HELPPPPPPPP!!!!!!!!!!!!! Answer this please
The surface area of the cuboid that has length = 4 yd, width = 2 yd and height = 3 yd is 44 square yards.
To find the surface area of a cuboid, we need to add up the area of all six faces. The formula for the surface area of a cuboid is:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h represent the length, width, and height of the cuboid, respectively.
Substituting the given values, we get:
Surface Area = 2(4 x 2) + 2(4 x 3) + 2(2 x 3)
Surface Area = 8 + 24 + 12
Surface Area = 44
This means that there are 44 square yards of material needed to cover all six faces of the cuboid.
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what is 300 in word form
Answer:
Three Hundred.
What is the value of c?
Answer:
84°
Step-by-step explanation:
opposite angles in a cyclic quadrilateral (4-sided shape) add up to 180.
c + 96 = 180
c = 180 - 96 = 84°
Select the correct answer.
Which statement best defines a circle?
OA the set of all points in a plane that are the same distance from a given point called the center
OB. the set of all points that are the same distance from a given point called the center
OC points in a plane that surround a given point called the center
OD. the set of all points in a plane that are the same distance from each other surrounding a given point called the center
Reset
Next
Answer:
A. the set of all points in a plane that are the same distance from a given point called the center
Step-by-step explanation:
I have a deck of 52 cards, from which I draw 3 cards and I would like to make a probability tree diagram, with two events, drawing a spade, and not drawing a spade. These two events have to branches which are the same, drawing a spade and not drawing a spade. Once again these two branches have two more branches for each, drawing another spade and not drawing a spade. I need a tree diagram which includes these branches and events.
The probability is solved and the tree diagram is given
Given data ,
The tree diagram to draw 3 cards out of 52 cards from the given probability details are:
The two events, drawing a spade, and not drawing a spade. These two events have to branches which are the same, drawing a spade and not drawing a spade. Once again these two branches have two more branches for each, drawing another spade and not drawing a spade.
_______ Draw a Spade _______
/ \
______/______ ______\_______
/ \ / \
/ \ / \
/ \ / \
Spade Not Spade Spade Not Spade
| | | |
Draw another Spade Not Draw a Spade Draw another Spade Not Draw a Spade
Hence , the probability of deck of cards is solved
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6
Select ALL the true statements about 388.33.
The value of the tens digit, 80, is 10 times the value of the ones digit, 8.
The value of the hundredths digit, 0.03, is 10 times the value of the tenths
digit, 0.3.
C. The value of the ones digit, 8, is the value of the tens digit, 80.
D.
The value of the hundredths digit, 0.03, is to the value of the tenths
digit, 0.3.
A.
B.
E. O The value of the tenths digit, 0.3, is 10 times the value of the hundredths
digit, 0.03.
The true statements about 388.33 are:
The value of the hundredth digit, 0.03, is 10 times the value of the tenth digit, 0.3.
The value of the tenth digit, 0.3, is 10 times the value of the hundredth digit, 0.03.
We have,
The statement "The value of the tens digit, 80, is 10 times the value of the one's digit, 8" is incorrect. The tens digit is actually 3, not 80.
The statement "The value of the hundredths digit, 0.03, is 10 times the value of the tenths digit, 0.3" is true.
The hundredth digit is 3 times smaller than the tenth digit, which means that the tenth digit is 10 times larger than the hundredth digit.
The statement "The value of the one's digit, 8, is the value of the tens digit, 80" is incorrect.
The tens digit is 3, not 80.
The statement "The value of the hundredths digit, 0.03, is to the value of the tenths digit, 0.3" is unclear and not a proper comparison, so it cannot be determined whether it is true or false.
Thus,
The true statements about 388.33 are:
The value of the hundredth digit, 0.03, is 10 times the value of the tenth digit, 0.3.
The value of the tenth digit, 0.3, is 10 times the value of the hundredth digit, 0.03.
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I 10. The sides of a square are increased by a scale factor of 3. The area of the larger square is what percent of tne area of the smaller square?
The area of the larger square is 900% of the area of the smaller square.
Let's assume that the side of the smaller square is "s". Therefore, the area of the smaller square will be:
Area of smaller square = s²
Now, the sides of the square are increased by a scale factor of 3, which means that the new side length of the larger square will be 3s. The area of the larger square will be:
Area of larger square = (3s)² = 9s²
To find the percentage of the larger square with respect to the smaller square, we need to divide the area of the larger square by the area of the smaller square, and then multiply by 100:
(9s²/s²) x 100 = 900%
This means that the larger square is 9 times the area of the smaller square.
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Lai Lal Chinese Restaurant has seven items in its breakfast menu. The management of Lai Lai has just acquired some data and they would like to find out both popularity and profitability of its breakfast menu items based on their selling price, food cost percentage, sales volume and contribution margin (CM) from the past period. The financial data for the selling price, sales volume, and individual food cost dollar amounts are presented in the table below:
Breakfast Selling Price Food Cost Menu Item ($) (52 Sales Volume А $10.00 $3.00 250 B $16.00 $6.00 50 с $18.45 $8.00 60 D $14.75 $4.25 300 E $8.75 $2.50 80 F $12.50 $5.75 180 G $9.00 $2.60 280 TOTAL 1.200
Based on the information given in the table above, what are the specific classification of the breakfast menu items based on their profitability and popularity in order?
Based on the contribution margin and the sales volume, Menu Item D is the most profitable and popular.
What is the contribution margin?The contribution margin is the profitability that is shown in the difference between the selling price and the variable cost per unit of an item.
The contribution margin can be computed per unit or in total. Using the sales volume to multiply the contribution margin per item gives the total contribution margin in dollars.
Breakfast Selling Price Food Cost Sales Contribution Margin
Menu Item ($) ($) Volume Unit Total
А $10.00 $3.00 250 $7.00 $1,750
B $16.00 $6.00 50 $10.00 $500
C $18.45 $8.00 60 $10.45 $627
D $14.75 $4.25 300 $10.50 $3,150
E $8.75 $2.50 80 $6.25 $500
F $12.50 $5.75 180 $6.75 $1,215
G $9.00 $2.60 280 $6.40 $1,792
TOTAL 1,200
Thus, we can conclude that Menu Item D enjoys the highest profitability and popularity.
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1
4
(
8
−
6
x
+
12
)
?
1
4
(
8
−
6
x
+
12
)
?
A.
7
2
x
7
2
x
B.
−
13
2
x
−
13
2
x
C.
−
6
x
+
14
−
6
x
+
14
D.
−
3
2
x
+
5
The equivalent expression is 5 - 3x/2. Option D
What are algebraic expressions?Algebraic expressions are described as expressions that are made up of variables, their coefficients, factors and constants.
these algebraic expressions are also composed of mathematical operations. These operations includes;
BracketParenthesesSubtractionMultiplicationDivisionAdditionFrom the information given, we have that;
1/ 4(8 - 6x + 12)
expand the bracket, we have;
Add the like terms
1/4(20 - 6x)
now, multiply the values, we have;
20 - 6x/4
Divide by the denominator
5 - 3x/2
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The complete question:
Simply the expression:
1/ 4(8 - 6x + 12)
From a point x, the bearing of a hill is 200⁰ and from another point Y 170km due east of x ,the bearing of the hill is 255⁰. Calculate the distance between the hill and Y
Answer:
Step-by-step explanation:
Need help in solving this problem I’m stuck on it. Pls help me?????? If you can see the numbers it’s 3ft, 7ft, 5ft, 4ft.
Answer:
20 square feet
Step-by-step explanation:
area of a triangle = (1/2) base x height
The "base" for this one gigantic triangle is the 'top' of the diagram - - - - it's the entire 3+7 = 10 side. (We can calculate the area of the whole thing at once. We don't have to do the left and the right halves separately!!!)
The height is 4.
So area = (1/2) base x height
= (1/2) * 10 * 4
= 20 square feet
Simplify (2x + 3)(x − 4) = ? A. 2x² - 5x + 12 O B. 2x²5x - 12 O C. 2x² + 5x + 12 O D. 2x² + 5x - 12
Answer:
2x^2-5x-12
Step-by-step explanation:
(2x+3)(x-4) can be simplified using the acronym FOIL, which stands for "first, outer, inner, last." This means that you multiply the first terms in each group, the the outer terms, then the inner terms, and lastly the last terms in each group.
2x*x=2x^2
2x*-4=-8x
3*x=3x
3*-4=-12
Combine those and you get 2x^2-8x+3x-12. Combine like terms, and your final answer is 2x^2-5x-12
A rectangular prism with a square base has a height of 17.2 cm and a volume of 24.768 cm² What is the side length of its base?
If rectangular prism with a square base has a height of 17.2 cm and a volume of 24.768 cm², the side length of the square base is 1.2 cm.
Let's denote the side length of the square base as x cm. Then, the volume of the rectangular prism can be expressed as V = x² * 17.2 cm³, and its surface area can be expressed as S = 2x² + 4x * 17.2 cm².
We are given that the volume of the rectangular prism is 24.768 cm³, so we can write the equation:
x² * 17.2 cm³ = 24.768 cm³
Simplifying this equation, we get:
x² = 24.768 cm³ / 17.2 cm² = 1.44 cm²
Taking the square root of both sides, we get:
x = 1.2 cm
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a moving streaming service offers two types of subscriptions
A moving streaming service offers two types of subscriptions: a basic subscription and a premium subscription.
The moving streaming service provides customers with two distinct types of subscriptions to cater to their viewing preferences and needs. The first option is the basic subscription, which offers access to a limited selection of movies and TV shows. This subscription provides users with a basic streaming experience, allowing them to enjoy a range of popular titles at a lower cost.
On the other hand, the second option is the premium subscription, which provides subscribers with a more extensive and premium streaming experience. With the premium subscription, users gain access to a wider library of content, including exclusive movies, TV series, and original productions. Additionally, premium subscribers often enjoy additional features such as ad-free streaming, simultaneous streaming on multiple devices, and the ability to download content for offline viewing.
By offering these two subscription options, the moving streaming service aims to cater to a diverse range of users, providing them with flexibility and choice based on their preferences and budget.
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Gabrielle is 13 years older than Mikhail. The sum of their ages is 97. What is Mikhail's age?
Answer: 42
Step-by-step explanation:
The best way to solve this is to set up an equation. In this problem, we can use "x" for Mikhail's age, so that Gabrielle's age becomes "x+13." Now, we can write, "x+x+13=97," because Mikhail's age (x) plus Gabrielle's age (x+13) is equal to 97. When we solve for x, we get x=42, so Mikhail's age is 42.
thanks so much for the help!! you don't have to put the showed work!
Answer:
75 points ( more than?? you didn't add the drop-down list ) today's score.
Hope this helps!
Step-by-step explanation:
y = mx + b
y = 5x + b
(50) = 5(6) + b -> b = 20
y = 5x + 20
If Carlos plays the game today for 0 min, he will get a score of 20 ( odd... how is that possible )
But tomorrow, he plans to play for an extra 15 min, so he will get a score of 95 ( ( 5 × 15 ) + 20 ). The question asks for how much his score will change so his score will change by 75 points ( 95 - 20 ).
You could also just do 15 × 5 to get 75 :)
Thirty-four percent of workers in the Unites States are college graduates. Suppose a random sample of 120 workers is obtained and 35 of them have a college degree.
a) What are the mean and standard deviation of the number of workers with a college degree respectively?
b) What is the probability that the number of workers with a college degree is at least 35?
The mean number of workers with a college degree is 40.8, and the standard deviation is 5.37.
The probability that the number of workers with a college degree is at least 35 is 0.976, or 97.6%.
Given Sample size (n) is 120 workers
Proportion of workers who are college graduates (p): 34% or 0.34
a) Mean and Standard Deviation:
The mean (μ) of a binomial distribution is given by μ = np, and the standard deviation (σ) is given by σ =√np(1 - p).
Substituting the values:
μ = 120 ×0.34 = 40.8
σ = √120 × 0.34 × (1 - 0.34)) = 5.37
To find the probability that the number of workers with a college degree is at least 35
we need to calculate the cumulative probability of the binomial distribution from 35 to the maximum possible value, which is 120 in this case.
Using a binomial probability calculator or a statistical software, we can find this probability.
Assuming a binomial distribution with parameters n = 120 and p = 0.34, the probability can be calculated as follows:
P(X ≥ 35) = 1 - P(X < 35)
The probability that the number of workers with a college degree is at least 35 is 0.976, or 97.6%.
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4. Maria also wants to study the relationship between the weight of puppies at birth
and their adult weight (at two years old). She collected data from five randomly
selected small-breed dogs and displayed the data in the table.
Birth weightAdult weight
(pounds) (pounds)
1.5 10
317
18
2.5 14
Birth weight Adult weight
(pounds) (pounds)
0.75 5
Part A. Use the data in the table to create a scatterplot. (5 points)
Part A.
(5 points)
Dog Birth and Adult Weights
Answer:
y = 4.87x + 2.28 Is the answer
Step-by-step explanation:
( i see a little bit of part b but do not see the FULL QUESTION which is a problem and i cannot answer.. )
using a:
THE ULTIMATE LINEAR REGRESSION CACLAULTOR
yes it is the epic i get:
y = 4.87x + 2.28
Nothing more noting less ikr
y = 4.87x + 2.28 Being the answer
Haleigh decides that instead of throwing away old candles, she can use the last bit of wax combined together to make new candles. Each candle has 10% of it's original wax left. How many 5 ounce candles can she make if she has five 20 oz candles, 5 five ounce candles, and twenty-five one-ounce candles?
We cannot have a fractional number of candles, Haleigh can make a maximum of 2 five-ounce candles using the available wax from the 20-ounce and 1-ounce candles.
To determine the number of 5-ounce candles Haleigh can make using the remaining wax from her existing candles, we need to calculate the total amount of wax available and divide it by the amount of wax needed for each 5-ounce candle.
Let's calculate the total amount of wax available:
The five 20-ounce candles have 10% of their original wax remaining, so each candle has 2 ounces of wax left.
Therefore, the total wax from the five 20-ounce candles is 5 candles [tex]\times[/tex] 2 ounces = 10 ounces.
The five 5-ounce candles already have wax, so we don't need to consider them.
The twenty-five 1-ounce candles have 10% of their original wax remaining, so each candle has 0.1 ounces of wax left.
Therefore, the total wax from the twenty-five 1-ounce candles is 25 candles * 0.1 ounces = 2.5 ounces.
Adding up the wax from the 20-ounce and 1-ounce candles, we have a total of 10 ounces + 2.5 ounces = 12.5 ounces of wax available.
To determine how many 5-ounce candles can be made, we divide the total available wax by the amount of wax needed for each 5-ounce candle:
Number of 5-ounce candles = Total available wax / Wax needed per 5-ounce candle
Number of 5-ounce candles = 12.5 ounces / 5 ounces
Number of 5-ounce candles ≈ 2.5 candles.
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Help me !!!! Please I’m offering points
The statement that justifies that ΔBAE ≅ Δ DAE is Side-Side-Angle Postulate. The best option from the statements given is "Classify A triangle". That is definition of a triangle.
What is the Side-Side- Angle Postulate?The Side Side Angle Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Between both triangles, here are the congruent sides and angles:
AB ≅ AD - Given
AE = EA - Reflexive Property. Note that AE is shared by both triangles so we have Two congruent sides.
AC ⊥ BD - that means ∠AEB = ∠AED = ∠BEC = ∠CED = 90°
(perpendicular bisector theorem)
A perpendicular bisector is a line segment that cuts another line segment at 90 degrees. A perpendicular bisector, in other terms, meets another line segment at 90° and splits it into two equal halves.
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PLEASE HELP
The triangle above has the following measures.
q = 6 yd
m/Q=43°
Find the length of side r.
Round to the nearest tenth and include correct units.
Show all your work.
Answer:
r=5.9
Step-by-step explanation: