Answer:
13
Step-by-step explanation:
volume of pad : 8x8x1=64
64/5=12.8
so you would need 13 bags
Answer:
Step-by-step explanation:
Since the pad frame is a square frame measuring 8 feet long and 1 foot high, we would determine its volume by applying the formula for determining the area of a cuboid which is expressed as
Volume = length × width × height
Volume of pad frame = 8 × 8 × 1 = 64 cubic feet
Since each bag of cement will fill 5 cubic feet, then the number of bags that you will need to buy to ensure enough to fill the entire frame is
64/5 = 16.8
Approximately 17 bags
Jared and Zach are practicing their free throws. Jared attempted x shots and made 75% of them. Zach attempted 10 more shots than Jared did and made 80% of them. Together, they made a total of 101 shots. Which equation represents this situation? How many balls did Jared and Zach throw.
Answer:
D. 0.75x + 0.8(x + 10) = 101
Step-by-step explanation:
Answer:
0.75x + 0.8(x + 10) = 101
Step-by-step explanation:
They both made 101 shots.
Jared attempted 60 shots.
Zach attempted 70 shots.
hellp i am bad at math
Answer:
16
Step-by-step explanation:
its a cube, so all the sides are 16.
hope you pass surface area it has ALOT of formulas ( :
Answer:
15
Step-by-step explanation:
the yellow side without the small one is 16 but since the face of the small one is 1 we must subtract it
IMPORTANT! ANSWER QUESTION NOW. Will award brainliest. Find the value of x. Give reasons to justify your solution.
Answer:
48 degrees for A and 7 12 degrees for B
Step-by-step explanation:
As you can see in the first picture, C and x share the same angle and the angle is 48 degrees. On the second picture the answer is 12 because 3*4=12.
If A = 8! and B = 8P8, then which one of the following is true: A > B not enough information A < B A = B
Answer:
A = B
Step-by-step explanation:
A = 8! = 8*7*6*5*4*3*2*1 = 40320
B = 8P8 = 8! / ( 8-8)! = 8! = 0! = 8! /1 = 8! = 40320
A = B
PLEASE HELP!!!! FAST THANK YOU FOR YOUR HELP!!!
With steps please!
Answer:
The nearest whole number you need to round to is: $3,094.00
Step-by-step explanation:
If Ava deposited the $400.00, which is four-hundred dollars and zero cents each month for here monthly deposits each month, then she would have to have 3.35% compound which is three point thirty-five percent compound price times the number of her monthly deposit of four-hundred dollars and zero cents which is $400.00 she would get the result that $3,094.00 which is three-thousand, ninety-four dollars and zero cents, which is the answer because if you round it with $1,250.00 which is one-thousand, two-hundred and fifty dollars and zero cents then it doesn't work out. So in the end, it would be: $3,094.00!
Identify the sequence as arithmetic or geometric. 14, 11, 8, 5,
Answer:
sequence is arithmetic
Step-by-step explanation:
A geometric sequence has a common ratio r between consecutive terms.
An arithmetic sequence has a common difference d between consecutive terms, thus
11 ÷ 14 ≠ 8 ÷ 11 ≠ 5 ≠ 8 ← not geometric
11 - 14 = - 3
8 - 11 = - 3
5 - 8 = - 3
There is a common difference d between consecutive terms
Thus sequence is arithmetic.
Answer:
Step-by-step explanation:
This is an arithmetic sequence.
First term = a = 14
Second term = 11
Common difference = second term - first term
= 11 - 14
= - 4
Each term is got by adding (-4) to the previous term
Third term = 11 + (-4) = 11 -4 = 8
The two non-parallel sides of an isosceles trapezoid are each 7 feet long. The longer of the two bases measures 22 feet long. The sum of the base angles is 140°. a. Find the length of the diagonal. b. Find the length of the shorter base. Round your answers to the nearest hundredth. show work please!
Answer:
Step-by-step explanation:
as the non parallel sides are equal and it is a trapezoid.∴ base angles are equal.each base angle=1/2×140=70°let the foot of perpendicular from end of shorter side is at distance x from nearest end of longer side.[tex]\frac{x}{7}=cos ~70\\x=7 \times cos~70 \approx 2.394\\2x \approx 4.788 \approx 4.79\\[/tex]shorter side=22-4.79=17.21 ftto find diagonal use cos formula[tex]cos ~70=\frac{22^2+7^2-d^2}{2*22*7} \\308 cos~70=484+49-d^2\\d=\sqrt{533-308~cos~70} \approx~20.68\\where ~d~is~diagonal.[/tex]d=20.68 fta. The length of the diagonal is approximately 15.74 feet.
b. The length of the shorter base is approximately 27.77 feet.
a. To find the length of the diagonal (d), we can use the given information and the formulas mentioned. Let's substitute the values into the formula:
h = (7/2) * tan(140°)
h ≈ (7/2) * (-1.376381920471173)
h ≈ -4.796335681196056
Now, substitute the values into the formula for the diagonal:
[tex]d = \sqrt{(22 - x)^2 + [(7/2) * tan(140\°)]^2}\\\\d = \sqrt{(22 - 7)^2 + [(-4.796335681196056)]^2}\\\\d = \sqrt{15^2 + 23.011228900189124}\\\\d = \sqrt{225 + 23.011228900189124}\\\\d = \sqrt{248.011228900189124}\\\\d = 15.74[/tex]
Therefore, the length of the diagonal is approximately 15.74 feet.
b. To find the length of the shorter base (b), we can use the given information and the law of cosines:
[tex]b^2 = 7^2 + 22^2 - 2 * 7 * 22 * cos(140\°)\\\\b^2 = 49 + 484 - 2 * 7 * 22 * cos(140\°)\\\\b^2 = 533 - 308 * cos(140\°)\\\\b^2 = 533 - 308 * (-0.766044443118978)\\\\b^2 = 533 + 236.924\\\\b^2 = 769.924\\\\b = 27.77[/tex]
Therefore, the length of the shorter base is approximately 27.77 feet (rounded to the nearest hundredth).
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The price, t, of a lawn mower at Turf Cutters is $240 less than twice the price, d, of the same lawn mower at Lawn Masters. The difference in price between the mower at Turf Cutters and Lawn Masters is $320. Which system of equations can be used to determine the price of the mower at each store? A. t - 2d = -240 t - d = 320 B. 2t - 2d = 240 t + d = 320 C. 2t - d = 240 t - d = -320 D. t - 2d = -240 t - d = -320
Answer: A. t - 2d = -240 t - d = 320
Step-by-step explanation:
Let t be the price of a lawn mower at Turf Cutters and d be the price of the same lawn mower at Lawn Masters.
As per given , we have
The price, t, of a lawn mower at Turf Cutters is $240 less than twice the price, d, of the same lawn mower at Lawn Masters.
[tex]2d-240=t\\\\\Rightarrow\ t-2d=-240 ...(i)[/tex]
The difference in price between the mower at Turf Cutters and Lawn Masters is $320.
[tex]t-d=320 ...(ii)[/tex]
So, the system of equations can be used to determine the price of the mower at each store is
[tex]t-2d=-240\\\\t-d=320[/tex]
Hence, the correct option is "A."
Triangle A"B"C" is formed using the translation (x + 2 y + 0) and the dilation by a scale factor of from the origin. Which equation explains the relationship between AB and A"B"?
Answer:
segment a double prime b double prime = segment ab over 2
Step-by-step explanation:
Triangle A″B″C″ is formed using the translation (x + 2, y + 0) and the dilation by a scale factor of one half from the origin. which equation explains the relationship between segment ab and segment a double prime b double prime?
coordinate plane with triangle ABC at A (- 3, 3), B (1, - 3), and C (- 3, -3).
segment a double prime b double prime = segment ab over 2
segment ab = segment a double prime b double prime over 2
segment ab over segment a double prime b double prime = one half
segment a double prime b double prime over segment ab = 2
Answer: If triangle ABC at A (- 3, 3), B (1, - 3), and c (- 3, -3) is translated using (x + 2, y + 0), then the new coordinates of triangle ABC would be at A'(- 3 + 2, 3), B'(1 + 2, - 3), and C'(- 3 + 2, -3) Which is A'(- 1, 3), B'(3, - 3), and C'(- 1, -3). The dilation by a scale factor of from the origin gives A″ (-1/2, 3/2), B″ (3/2, -3/2) and C″(-1/2, -3/2) = (-0.5, 1.5), B″ (1.5, -1.5) and C″(-0.5, -1.5)
The distance AB and A"B" are given as:
[tex]AB=\sqrt{(1-(-3))^2+(-3-3)^2} =\sqrt{5 2} \\\\A"B"=\sqrt{(1.5-(-0.5))^2+(-1.5-1.5)^2} =\sqrt{13}[/tex]
AB = √52 = √(4×52) = 2√13 = 2A"B"
A"B" = AB/2
Answer:
What The Other Guy Said Was Correct
Step-by-step explanation:
2 + 2 = 4
[tex]solve for x if 4 x+1-9(2 ^{2} +2=0[/tex]
Answer:
mark my answer as the brainliest
Step-by-step explanation:
x = 53/4
Answer:
4×+1-9 (2^)+2)=0
4×+1-9 (4+2)=0
4×+1(-36-18)=0
4×+1 (-54)=0
4×-54=0
4×=54
×=54÷4
×=13.5
Match each set of ordered pairs on the left with the correct description of the relation
given by the set on the right. The descriptions on the right will be used more than
once.
{(13,6), ( – 8,3), (21, – 4), ( – 6,0), (9, – 4)}
function
{(– 32,0), ( – 16,8), (4, 56), ( - 16, – 8), (8, – 72)}
not a
function
{(500, 312), (325, 129), (103, 202), (304, 418), (325, 911)}
{( - 43, – 75), (61, – 75), (- 35, – 75), (82, - 75), (28, – 75)}
Answer:
{(13,6), ( – 8,3), (21, – 4), ( – 6,0), (9, – 4)} function
{(– 32,0), ( – 16,8), (4, 56), ( - 16, – 8), (8, – 72)} not a function
{(500, 312), (325, 129), (103, 202), (304, 418), (325, 911)} not a function
{( - 43, – 75), (61, – 75), (- 35, – 75), (82, - 75), (28, – 75)} function (but flat-lined !)
Step-by-step explanation: To be a function, each x-value must have a unique y-value
In the set {(– 32,0), ( – 16,8), (4, 56), ( - 16, – 8), (8, – 72)} —16 has both 8 and –72 as y values so it is not a function
In the set {(500, 312), (325, 129), (103, 202), (304, 418), (325, 911)} 325 has both 129 and 911 so it is not a function.
It is ok for y-values to be repeated, but only for different x-values
Write an expression of 4 less than twice a number
Answer:
2x-4
Step-by-step explanation:
you can't really explain this, is just have the meaning 4 less twice a number.
I wish this is the correct one and will help you!
Answer:
2x-4
Step-by-step explanation:
Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. c 22 and 15 Answer: < 3rd side
Answer:
| a - b | < length of third side < a + b
Step-by-step explanation:
Visualize the two given sides of the triangle (let's call then a and b), joined at the vertex of the triangle, and forming an angle. We can join the other free end of these two segments, with another segment whose length would vary according to how tiny or large the angle is. We can spread the aperture of the angle they form as much as we can just below [tex]180^o[/tex] (not reaching this angle measure, because in such case, there will be no triangle of tangible area. In such case, the length of the joining segment will be limited by the addition of the two sides:
length of third side < a + b
In the case the aperture of the angle formed by the two given sides is diminished as much as possible to still form a measurable triangle, the angle has to be just larger than zero, and in such case, the segment joining the other to ends of a and b would be just larger than the absolute value of the difference between a and b:
length third side > | a - b|
These are the two extreme cases, and the length of the third side must be within these limits.
Answer:
7<x<37
Step-by-step explanation:
Here is the formula to solve range questions:
22-15<x<22+15
Solve : 3x + 9 < 4(x-5) -x + 3 + 2x
Answer:
x > 13Step-by-step explanation: I tried to work it out well.
I Hope it helps:)
[tex]3x + 9 < 4(x-5) -x + 3 + 2x\\\mathrm{Group\:like\:terms}\\3x+9<-x+2x+4\left(x-5\right)+3\\\mathrm{Add\:similar\:elements:}\:-x+2x=x\\3x+9<x+4\left(x-5\right)+3\\Expand ; x+4\left(x-5\right)+3\\=x+4x-20+3\\=5x-17\\3x+9<5x-17\\\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}\\3x+9-9<5x-17-9\\Simplify\\3x<5x-26\\\mathrm{Subtract\:}5x\mathrm{\:from\:both\:sides}\\3x-5x<5x-26-5x\mathrm{Simplify}\\-2x<-26\\[/tex]
[tex]Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)\\\left(-2x\right)\left(-1\right)>\left(-26\right)\left(-1\right)\\Simplify\\2x>26\\\mathrm{Divide\:both\:sides\:by\:}2\\\frac{2x}{2}>\frac{26}{2}\\\\x>13[/tex]
Lin solved the equation 8 (x - 3) +7= 2x (4 - 17) incorrectly.
Find the 2 errors in her solution.
What should her answer have been?
Answer:
Her final answer should have been x = 1/2.
Step-by-step explanation:
Her 2 errors were that she didn't distribute the 2x to both 4 and -17 and that she made the 13 positive instead of negative when she added 4 and -17 together.
Correct solution:
8(x-3)+7=2x(4-17)
8x-24+7=8x-34x
-17=-34x
The negatives on both sides cancel each other out
x = 1/2
Answer:
x=1/2
Step-by-step explanation:
8(x-3)+7=2x(4-17)
8(x-3)+7=2x(-13)
This is where Lin's first mistake appears, 4-17 is -13, not positive 13.
Next, Lin distributes.
8x-24+7=26x
This is right with Lin's equation, since Lin got 13 instead of -13.
However, if we were doing it correctly from the start, it should be:
8x-24+7=-26x
Okay, after 8x-24+7=26x Lin simplifies again to:
8x-17=26x
She then tries to eliminate 8x.
What she does wrong here, is that she subtracts 8x from the left, and adds 8x to the right.
This makes it so that the equation is not equal anymore, because what you do to one side, you must do to the other.
This is Lin's second mistake.
What she should have gotten is
-17=18x.
Okay, now that we have found her mistakes, let's solve this correctly.
8(x-3)+7=2x(4-17)
8(x-3)+7=2x(-13)
Distribute.
8x-24+7=-26x
8x-17=-26x
Add 17 to both sides.
8x=-26x+17
Add 26x to both sides.
34x=17
x=1/2
Her answer should have been 1/2.
Solve 7x = 49 for x. Thank you however answer’s this
Answer:
x=7
Step-by-step explanation:
To solve for x, we need to isolate it by itself. We can do that by getting rid of the 7. Since the 7 is being multiplied with the x, we need to divide by 7 to cancel it out. When doing something to one side of the equation, we must always to the same to the other.
Divide both sides by 7
x=7
Answer:
x = 7
Step-by-step explanation:
All you have to do to solve this question is divide 7 on both sides so,
7x / 7 = 49 / 7
7x / 7 = 1 or x
49 / 7 = 7
So your answer will be,
x = 7
Hope this helps!!
Please help with step by step. Thank you.
Answer:
A) 90 degrees
B) 110 degrees
C) 78.5 in. sq.
D) 15.3 in. sq.
Step-by-step explanation:
A) 90 degrees by the two-tangent theorem
B) 360-90-90-70=110
C) A=pi r-squared
A=3.14x5x5
A=78.5
D) 70/360=0.1944
78.5x0.1944=15.3
Help please and thank you >:D
Answer:
E. 4 shifts
Step-by-step explanation:
L.C.M. of 18 and 24
18=2×3×3
24=2×2×2×3
L.C.M.=2×2×2×3×3=72
so after 72 hours time will be same
or 72/18=4 shifts
How many solution does this following equation have? -7x-10-15x=-22x+83 A. No solution B. Exact 1 solution C. Infinite solution
Answer:
A. No Solution
Step-by-step explanation:
To solve for x we would just simplify the equation so it is easier to work with. First we will combine the -7x and the -15x and when you combine then you will get -22x so the equation will look like this [tex]-22x-10=-22x+83[/tex] now we would add 22x to both sides and our equation will be [tex]-10=83[/tex] and that is not correct so the answer would be A. No solution
Answer:
A. No solution
Step-by-step explanation:
-7x - 10 - 15x = -22x + 83
-22x - 10 = -22x + 83
0 = 93
Zero doesn't equal to 93, so there are no solutions.
Charley sold 12 fruit baskets fir the school fund raiser. Maria sold 15 and Paul sold 18. If each fruit basket cost $18, how much money did they raise altogether
Answer:
$810 total raised
Step-by-step explanation:
Charley:
12 * $18 = $216
Maria:
15 * $18 = $270
Paul:
18 * $18 = $324
Total:
$324 + $270 + $216 = $810
Answer:
pls appreciate my efforts by markinf my answer as the brainliest......
Step-by-step explanation:
Charley raised = 12 *18 =$216
Maria raised =15*18 = $270
Paul raised = 18*18 = $ 324
total amount raised = $ 810
Chad washes windows after school to make some extra money. He charges $5.50 to wash each window. If the customer provides the supplies, Chad deducts $3.25 from the total cost. One customer paid a total of $35.25 and did provide supplies. Which equation could be used to find the number of windows, w , that Chad washed for this customer? A) 5.5 w + 3.25 = 35.25 B) 5.5 w - 3.25 = 35.25 C) 5.5 w = 35.25 D) 5.5 - 3.25 w = 35.25
Answer: D is correct if it is really (5.5-3.25)w=35.25
(Without parenthesis it doesn't work)
Answer:
B) 5.5 w - 3.25 = 35.25
Step-by-step explanation:
Chad charges $5.50 per window. ( 5.50w )
Since Chad's customer brought supplies, Chad would deduct $3.25. ( - 3.25)
The customer would be charged $35.25 at the end. ( = 35.25 )
So, the total of the cost of the windows minus the discount would be $35.25.
5.50w - 3.25 = 35.25
Option B's equation would be most appropriate to solve for w.
please help answer this question as soon as possible!
Answer:
[tex]a_{n}[/tex] = 10.5 - 3n
Step-by-step explanation:
The explicit rule for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
A recursive formula has the form
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d ( where d is the common difference )
Given
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 3 ⇒ d = - 3
Thus explicit rule with a₁ = 7.5 and d = - 3
[tex]a_{n}[/tex] = 7.5 - 3(n - 1) = 7.5 - 3n + 3 = 10.5 - 3n
Can someone help me with the question please
Answer:
Purple line: 4
Red dashed line: 2
Blue line: 1/2
Step-by-step explanation:
The purple line is the steepest line, therefore it has the biggest constant of proportionality or slope. Since 4 is the biggest number among the others, we attribute it to the purple line (the one with the point C on it).
Think of it this way:
[tex]y = ax+b \\[/tex]
here [tex]b = 0[/tex] so [tex]y = ax[/tex]
The greater a is, the greater y is. So for any value of x, y will be become bigger and bigger if we increase the value of a.
Take for example this one:
[tex]y = 2x \\[/tex]
Take [tex]x=2\\[/tex] therefore [tex]y =4[/tex]
Now take [tex]y = 4x[/tex] and take [tex]x =2[/tex] therefore [tex]y = 8[/tex]
When we increased this constant of proportionality, as you can see from 2 to 4, the value of y increase from 4 to 8.
Hope this is helpful. Think of it really carefully, and I'm sure you'll grasp the concept.
two fifths of a number equals 564. what is the number
Answer:
1410
Step by step explanation:
2/5x=564
5/2*2/5x=564*5/2
x=1410
Proof: 2/5*1410=564
Hope it helps <3
Answer:
1410
Step-by-step explanation:
A region is said to be____if it is completely
enclosed by its constraints.
Answer:
Step-by-step explanation:
A region is said to be closed if it is completely
enclosed by its constraints
A region is said to be a closed area if it is completely enclosed by its constraints.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. For example, the space occupied by the circle in a two-dimensional plane is called the area of the circle.
The area of the circle is given by the formula below:-
Area = πr²
Where r is the radius of the circle.
Therefore, the region is said to be a closed area if it is completely enclosed by its constraints.
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Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a $ 7.50 delivery fee and $ 14 per pizza. She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under $ 60. Each pizza is cut into 8 slices, and she wonders how many total slices she can afford. Let P PP represent the number of pizzas that Jacque buys. 1) Which inequality describes this scenario? Choose 1 answer: (Choice A,) 7.50 + 14 P < 60 (Choice B) 7.50 + 14 P > 60 (Choice C) 14 + 7.50 P < 60 (Choice D) 14 + 7.50 P > 60 2) What is the largest number of slices that Jacque can afford?
Answer: Choice A
Step-by-step explanation:
She can only buy 3 pizzas. 14 times 3 is 42. 42 plus 7.50 is 49.50. Another 14 dollars would be over. So 24 SLICES she can afford.
Here, we are required to identify the inequality that describes Jacque's pizza purchase scenario and also the largest number of slices that Jacque can afford
Choice 1 which is ;
Choice 1 which is ;7.50 + 14 P < 60Choice 1 which is ;7.50 + 14 P < 60Jacque can afford to buy 30slices of pizza
First,
Since the restaurant charges a fixed $ 7.50 for delivery and charges $ 14 per pizza.and she also needs to keep the delivery fee plus the cost of the pizzas under $ 60The inequality which describes the scenario is :
Choice 1 which is ;
7.50 + 14 P < 60And to determine the largest number of slices that Jacque can afford, we have to solve for P first.
Therefore, 14P < 60 - 7.50P = 52.50/14P = 3.75Therefore, Jacque can only buy 3.75 pizzasHowever, the question requires that we determine how many slices she can afford to buy,
Since each pizza is cut into 8 slicesJacque can afford to buy 3.75 × 8 slices of pizza.
Jacque can afford to buy 30slices of pizza
Read more:
https://brainly.com/question/19003099
Which method correctly solves the equation using the multiplication property of equality and the reciprocal of One-third?
Answer: -third
Step-by-step explanation:
HELP!!! ANSWER SOON!!!! Which graph shows the solution set for 2 x + 3 greater-than negative 9? A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the right of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the right of the circle is shaded.
We can solve the inequality 2x + 3 > -9 by first subtracting 3, then dividing by 2:
2x > -12
x > -6
This graph should have an open circle at negative 6 (this is a strict inequality, so x cannot equal -6), with everything to the right shaded (since x is greater than -6).
Answer:
C
Step-by-step explanation:
Did test on edge
Use the diagram to answer the question. Triangle A B C. Segment B C measures 13. Segment A C measures 15. Angle B is a right angle. What is the measure of ∠A?
Answer:
angle A= 59.997
Step-by-step explanation:
SinA=13/15
sinA=0.866
A=inverse sin (0.866)
A=59.997
help pls
с LG ZX
D ZH ZY
BB HWY
mm CZW=2)
DHE ZY
4. Determine if the triangles below are congruent. If
so, what properties are used in your logic?
3. Determine if the triangles below are congruent. If
so, what properties are used in your logic?
4
triangle congruence
5. State what additional information is required to
prove AUML = AKLM by SAS.
6. State what additional information is required to
prove AJHI AUSI by SAS.
M
Answer:
1). x = 10 m
2). x = 15 cm
3). x = 5 yd
4). AB = 10 units
Step-by-step explanation:
1). By Pythagoras theorem in the given triangle,
a² + b² = c²
Where 'c' = Hypotenuse
a and b = Legs of the right triangle
By substituting measures of the sides in the formula,
x² = 8² + 6²
x = [tex]\sqrt{100}[/tex]
x = 10 m
2). By using Pythagoras theorem in this triangle,
x² = 9² + (12)²
x² = 81 + 144
x = [tex]\sqrt{225}[/tex]
x = 15 cm
3). By Pythagoras theorem,
(13)² = x² + (12)²
169 = x² + 144
169 - 144 = x²
25 = x²
x = 5 yd
4). If BD is a perpendicular bisector of AC,
AD = CD = 6 cm
By Pythagoras theorem in ΔABD,
AB² = BD² + AD²
AB² = 8² + 6²
AB = [tex]\sqrt{100}[/tex]
AB = 10 units