50 PTS!!A right triangle has a leg measuring 16in. And 28in.
What is the length of the hypotenuse?
Round your answer to the nearest tenth.
1)23.0 in.
2)32.2 in.
3)44.0 in.
4)1040.0 in
Answers
Answer:
2) 32.2 in (nearest tenth)
Step-by-step explanation:
Pythagoras’ Theorem
[tex]\sf a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = 16 inb = 28 inc = hypotenuseSubstituting these values into the formula and solving for c:
[tex]\implies \sf 16^2+28^2=c^2[/tex]
[tex]\implies \sf 256+784=c^2[/tex]
[tex]\implies \sf c^2=1040[/tex]
[tex]\implies \sf c=\pm\sqrt{1040}[/tex]
[tex]\implies \sf c=\pm 32.2\:in\:(nearest\:tenth)[/tex]
As distance is positive, c = 32.2 in (nearest tenth)
Step-by-step explanation :
Here, A right angled triangle is given with the measure of two sides and we are to find the measure of the third side.
We'll find the measure of third side with the help of the Pythagorean theorem,
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (Hypotenuse {)}^{2}= (Base) {}^{2} + (Perpendicular {)}^{2} }}} \\ \\ [/tex]
Here,
The base (BC) is 16 inThe perpendicular (AB) is 28 inThe hypotenuse is AC.[tex] \: [/tex]
So, substituting the values in the formula we get :
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (AC {)}^{2}= (16) {}^{2} + (28 {)}^{2} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (AC {)}^{2}=256 + 784 }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (AC {)}^{2}=1040 }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad AC = \sqrt{1040} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\frak {\qquad AC = 32.24 }}} \\ \\[/tex]
Therefore,
The length of the hypotenuse (AC) is 32.2 in (Rounded to nearest tenth)
Related Questions
solve by completing the square: x^2+18x+45=0
Answers
Answer:
x = -3 , - 15
Step-by-step explanation:
Given:
x² + 18x + 45 = 0
Solve:
[tex]x_{1,\:2}=\frac{-18\pm \sqrt{18^2-4\cdot \:1\cdot \:45}}{2\cdot \:1}[/tex]
Simplify
[tex]-18\pm \sqrt{18^2-4\cdot \:1\cdot \:45=12[/tex]
[tex]x_{1,\:2}=\frac{-18\pm \:12}{2\cdot \:1}[/tex]
Separate the solution
[tex]x_1=\frac{-18+12}{2\cdot \:1},\:x_2=\frac{-18-12}{2\cdot \:1}[/tex]
[tex]x_1=\frac{-18+12}{2\cdot \:1}=-3[/tex]
[tex]x_2=\frac{-18-12}{2\cdot \:1}=-15[/tex]
Thus, the answer are:
[tex]x=-3,\:x=-15[/tex]
Kavinsky
The population of bacteria in a colony is increasing. The number of bacteria at time t
(in hours) is given by
P= 3000 x 1.15t
a)By what percentage is the number of bacteria increasing each hour?
b) What was the size of the population when t = 0?
C)What will be the size of the population after 24 hours?
Give your answer to a sensible degree of accuracy.
Step by step explanation please. <3
Answers
Step-by-step explanation:
a) if the population is 3000 and it is being multiplied 1.15 than it is 15%. I found this by multiplying 1.15 by 100 to make it percent than anything over 100 is an increase.
b)im not so sure on this one but I think if t = 0 than it would be p= 3000 x 1.15 x0 which would equal 0
c) p = 3000x 1.15 x 24 p = 82,800
3x−45=−12
What is the value of x?
Answers
Answer:
x=11
Step-by-step explanation:
3x−45=−12
Add 45 to each side
3x−45+45=−12+45
3x = 33
Divide each side by 3
3x/3 = 33/3
x=11
Someone please help and answer this please
Answers
Answer:
1) surface area = 2 · π · r · (r + h)
2) 8x5x6x14x8.94
3) surface area = 2 · π · r · (r + h)
4) 8x14x6
5) 4x4x8
6) 7x8.95x13
7) 3x4x11x3.61 divide by 2
8) 6x6x6 = 36x6 = 216
9) 3x4x10
Step-by-step explanation:
Its worth 20 points but i need it within 10 minutes or less!
Answers
The equation of a circle is shown. What is the radius? 22 + y2 - 10x + 8y + 16 = 0
Answers
Answer:
radius = 5
Step-by-step explanation:
Given
x² + y² - 10x + 8y + 16 = 0Using completing the square method
x² - 10x + 25 - 25 + y² + 8y + 16 (x + 5)² + (y + 4)² - 25 = 0(x + 5)² + (y + 4)² = 25Standard form for equation of a circle
(x - h)² + (y - k)² = r², where r is the radiusOn comparison to our equation in the question :
r² = 25radius = 5 [as distances cannot be -ve]Answer:
radius = 5
Step-by-step explanation:
Question[tex]x^2+y^2-10x+8y+16=0[/tex]
The equation of a circle is shown. What is the radius?
----------------------------------------------------------------------------------
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
(where (a, b) is the center and r is the radius)
Given equation:
[tex]x^2+y^2-10x+8y+16=0[/tex]
Collect like terms:
[tex]\implies x^2-10x+y^2+8y+16=0[/tex]
Subtract 16 from both sides:
[tex]\implies x^2-10x+y^2+8y=-16[/tex]
Complete the square for both variables.
Add 25 to both sides for x. Add 16 to both sides for y.
[tex]\implies x^2-10x+25+y^2+8y+16=-16+25+16[/tex]
[tex]\implies (x^2-10x+25)+(y^2+8y+16)=25[/tex]
Factor the two variables:
[tex]\implies (x-5)^2+(y+4)^2=25[/tex]
Therefore:
center of the circle = (5, -4)radius of the circle = √25 = 5please help asap!! i don't really understand this
Answers
Answer:
17*12 area of triangle is base*height
Answer:
Use the formula for the area of a triangle:
A = BH x 1/2
Where 'B' represents the base, 'H' the height, and multiplying by 1/2 just means dividing the product of those two lengths by 2.
What we know:
Base = 12 feetHeight = 17 feetWhich is all we need to know, so plug these values into our formula;
A = BH x 1/2
A = 12(17) x 1/2
Now just solve:-
A = 204 x 1/2
A = 204/2
A = 102, the area of this triangle is 102 ft²!
brelynn has a piece of ribbon that is 3/4 yard long. how many 1/12 yard pieces can she cut? help
Answers
The Brelynn can cut 9 pieces from the piece of ribbon that is 3/4 yard long of 1/12 yard.
What is a fraction?Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
Let's assume Brelynn can cut x pieces from the piece of ribbon that is 3/4 yard long.
So from the problem:
[tex]\rm \frac{\frac{3}{4} }{x} = \frac{1}{12}[/tex]
[tex]\rm \dfrac{3}{4} = \dfrac{x}{12}[/tex]
x = 9 pieces
Thus, the Brelynn can cut 9 pieces from the piece of ribbon that is 3/4 yard long of 1/12 yard.
Learn more about the fraction here:
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(10/2) / 3 = 10/ (2/3)
O A. True
O B. False
Answers
Answer:
It is False
Step-by-step explanation:
The answer is not the same.
Can anyone help with Discriminants in math??
(“number and types of solutions” is what the rest says)
Answers
#1
3x²-3x+2D:-
b²-4ac(-3)²-4(3)(2)9-24-15D<0 so unequal and un real roots
#2
b²-4ac(-10)²-4(1)(1)100-496D>0 so unequal and real roots
#3
(-4)²-4(4)(1)16-160Equal and real roots
Answer:
Discriminant
[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real solutions}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real solution}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real solutions}[/tex]
------------------------------------------------------------------------------------------------
Question 5
Given function: [tex]f(x)=3x^2-3x+2[/tex]
[tex]\implies a=3, \quad b=-3, \quad c=2[/tex]
Inputting these values into the discriminant:
[tex]\implies \textsf{discriminant}= (-3)^2-4(3)(2)=-15[/tex]
As -15 < 0 there are no real solutions
------------------------------------------------------------------------------------------------
Question 6
Given function: [tex]f(x)=x^2-10x+1[/tex]
[tex]\implies a=1, \quad b=-10, \quad c=1[/tex]
Inputting these values into the discriminant:
[tex]\implies \textsf{discriminant}= (-10)^2-4(1)(1)=96[/tex]
As 96 > 0 there are two real solutions
at [tex]x=5 \pm 2\sqrt{6}[/tex]
------------------------------------------------------------------------------------------------
Question 7
Given function: [tex]f(x)=x^2-4x+4[/tex]
[tex]\implies a=1, \quad b=-4, \quad c=4[/tex]
Inputting these values into the discriminant:
[tex]\implies \textsf{discriminant}= (-4)^2-4(1)(4)=0[/tex]
As 0 = 0 there is one real solution
at [tex]x=2[/tex]
1)
W
K
V
A) 20.8
C) 11
22.2
?
11
U
J
T
B) 16.6
D) 18
Answers
Answer:
1. A commercial air carrier determines that the maximum angle of depression of a plane descending to an airport is 11°. Determine horizontal distances
Step-by-step explanation:
The area of a circle is 49 pi cm^2 what is the radius of a circle
Answers
Answer:
The radius is 7 cm
Step-by-step explanation:
We know the area of a circle is given by
A = pi r^2
49 pi = pi r^2
Divide each side by pi
49 = r^2
Take the square root of each side
sqrt(49) = sqrt(r^2)
7 = r
The radius is 7 cm
Answer:
radius = 7 cm
Step-by-step explanation:
the area (A) of a circle is calculated as
A = πr² ( r is the radius )
given A = 49π , then
πr² = 49π ( divide both sides by π )
r² = 49 ( take square root of both sides )
r = [tex]\sqrt{49}[/tex] = 7
Let x = 0.147 and let y = 0.147
Answers
The value of y will be more as the number is repetitive, and both x and y initial three digits after the decimal are the same.
What is a rational number?A rational number is one that has the form p/q, where p and q are integers and q is greater than zero. Some rational number examples are 1/3, 2/4, 1/5, 9/3, and so on.
The complete question is, Let x = 0.147 and let y = [tex]0.\overline{147}[/tex]. Is x a rational number? Is ya rational number? Which is larger, x or y?
Given the value of x is 0.147. As it can be written in the form of a fraction,
[tex]0.147 = \dfrac{147}{1000}[/tex], we can conclude that x is a rational number.
The value of y = [tex]0.\overline{147}[/tex] can also be written in the form of a fraction,
[tex]0.\overline{147} = \dfrac{147}{999}[/tex], therefore, we can conclude that y is also a rational number.
The value of y will be more as the number is repetitive, and both x and y initial three digits after the decimal are the same.
Learn more about Rational Numbers:
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You work as an office administrator and are paid $18.65 per hour and work 80 hours in 2 weeks. How much is your straight time pay?
Answers
To find the straight time pay for two weeks,
we'll multiply the amount per hour to the number of working hours
hence,
Straight time pay ⇢$18.65 x 80Straight time pay⇢$ 1,492___________________________________
The Straight time pay of one week would be ,
⇢40 x $18.65⇢$746___________________________________
Straight time pay of a month would be,
⇢160 x $18.65⇢$2,984___________________________________
Weeks no is not of any use here
Straight time pay:-
18.65×80$1492A rectangular table top has length 1. 7 m and width 0. 9 m. A force of 750 N is applied to the whole table top. Calculate the pressure in N/m2 to the nearest integer
Answers
Step-by-step explanation:
pressure = F/A
= 750/ (1.7×9)
= 49 N/m²
She calculates two regression models. which is true? the linear model better represents the situation because the amount she owes is decreasing by about the same amount every 6 months. the linear model better represents the situation because according to the exponential model, the repayment amount will never be 0. the exponential model better represents the situation because the amount she owes decreases by about the same amount every 6 months. the exponential model better represents the situation because according to the linear model, the repayment amount will eventually be negative.
Answers
The answer is A.thus, this is a linear model. To check,you can see visually that the points are more fitted to the line than the curve.
What is linear regression?Linear regression is the most basic and commonly used predictive analysis. Regression estimates are used to describe data and to explain the relationship.
The difference between the linear model and the exponential model is the degree of difference of consecutive points. If their difference is constant, then it is more appropriate for the linear model. If their difference is increasing at a very fast rate, then that follows an exponential model. With that being said, let's look at the differences at every 6 month-intervals.
2700-2110 = 590
2110-1500 = 610
1500-870 = 630
870-220 = 650
Their differences are about the same having a mean of 620. Thus, this is a linear model. To check,you can see visually that the points are more fitted to the line than the curve. The answer is A.
To know more about Linear regression follow
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Answer:
A is the correct answer
Step-by-step explanation:
what is the area when the diameter is 94cm
Answers
Answer:
see below
Step-by-step explanation:
Area = pi r^2 r = radius
diamter = 94 then radius = 94/2 = 47 cm
area = pi (47)^2 = 2209 pi or 6939.78 cm^2
Answer:
A ≈ 6,939.8 cm²
Step-by-step explanation:
Given : " the diameter is 94cm "
d = 94
Radius is r = d/2 = 94/2 = 47 cm
Area of a circle is
A= π·r²
A = π·47² ≈ 6,939.8 cm²
there are 10 apples for every 6 bananas how many bananas are there if there are 20 apples?
What if there are 15 apples?
Answers
Suppose you carry out a significance test of h0: μ = 8 versus ha: μ > 8 based on sample size n = 25 and obtain t = 2. 15. Find the p-value for this test. What conclusion can you draw at the 5% significance level? explain.
a the p-value is 0. 2. We reject h0 at the 5% significance level because the p-value 0. 02 is less than 0. 5.
b the p-value is 0. 2. We fail to reject h0 at the 5% significance level because the p-value 0. 02 is less than 0. 5.
c the p-value is 0. 48. We reject h0 at the 5% significance level because the p-value 0. 48 is greater than 0. 5.
d the p-value is 0. 48. We fail to reject h0 at the 5% significance level because the p-value 0. 48 is greater than 0. 5.
e the p-value is 0. 52. We fail to reject h0 at the 5% significance level because the p-value 0. 52 is greater than 0. 5
Answers
Using a t-distribution calculator and finding the p-value, the correct option regarding the conclusion is given by:
a) the p-value is 0.02. We reject h0 at the 5% significance level because the p-value 0.02 is less than 0.05.
What is the relation between the p-value and the conclusion?It also involves the significance level, as follows.
If the p-value is less than the significance level, we reject the null hypothesis [tex]h_0[/tex].If it is more, we do not reject.In this problem, a t-distribution calculator for a right-tailed with t = 2.15 and 25 - 1 = 24 df is used to find a p-value of 0.02.
It is less than 0.05, hence option a is correct.
More can be learned about p-values at https://brainly.com/question/26454209
The three sides of a triangle are (x+5)cm ,(2x+4)cm and (2x-3)cm .
a.find the perimeter of the triangle
b. if x =10, find the perimeter of the traingle.
Answers
Hey ! there
Answer:
a. Perimeter = ( 5x + 6 ) cmb. Perimeter when x is equal to 10 = 56 cmStep-by-step explanation:
In this question we are given with three sides of a triangle that are as follows ,
( x + 5 ) cm ( 2x + 4 ) cm ( 2x - 3 ) cmAnd we are asked to :
a. find perimeter of triangle. b. find perimeter if x is equal to 10 .We know that for finding perimeter of any shape we must have to add all the sides of the shape or ,
[tex] \qquad \: \underline{\boxed{\frak{Perimeter = Sum \: of \: all \: sides}}}[/tex]
Solution : -
( a )
Now adding all the three sides of triangle to find the perimeter .
[tex] \hookrightarrow \quad \: ( x + 5 ) + ( 2 x + 4 ) + ( 2x - 3 ) [/tex]
[tex] \hookrightarrow \quad \: \: x + 5 + 2x + 4 + 2x - 3[/tex]
Combining like terms :
[tex] \hookrightarrow \quad \:x + 2x + 2x + 5 + 4 - 3[/tex]
Now , solving :
[tex] \hookrightarrow \quad \: \red{\underline{ \boxed{ \frak{(5x + 6) \: cm}}}}[/tex]
Therefore , perimeter of triangle is 5x + 6 centimetres .( b )
Now , we are finding perimeter of triangle when value of x is 10 . So substituting value of x in given sides of triangle ,
First Side :
x + 510 + 515 cmSecond Side :
2x + 42 ( 10 ) + 420 + 424 cmThird Side :
2x - 32 ( 10 ) - 320 - 317So , all the sides are 15 cm , 24 cm and 17 cm .
Now , adding all these to find perimeter .
[tex] \hookrightarrow \qquad \: 15 + 24 + 17[/tex]
[tex]\hookrightarrow \qquad \: 39 + 17[/tex]
[tex]\hookrightarrow \qquad \: \red{\underline{\boxed{\frak{56 \: cm}}}}[/tex]
Therefore , perimeter of triangle when value of x is 10 cm is 56 cm .Alternative Solution : -
As above we have find the perimeter of triangle in term of x that is ( 5x + 6 ) cm. So we can put value of x as 10 in this to get perimeter. So ,
5x + 65 ( 10 ) + 650 + 656 cmTherefore, perimeter of triangle is 56 cm .
#Keep LearningTo find the perimeter of a shape, we should add all sides , like so :
x+5+2x+4+2x-3
Combine the x's :
x+2x+2x+5+4-3
x+4x+9-3
5x+6
Perimeter :5x+6 cm
º º º º º º º º º º º º º º º º º º º º º º º º º º º º º º º º º º º º º º º º º º º º º
b.
Find the perimeter of the triangle if x = 10
Just write 10 instead of x :
5(10)+6
5(10) simplifies to 50 ↓
50+6
56
Perimeter of the triangle when x = 10 : 56 cmhope helpful ~
Suppose you own a home worth $185,325 and your property tax is 1.5%. How much are you liable to pay at the end of the year?
Answers
Answer:
$ 2779.88
Step-by-step explanation:
185 325 x 1.5 % =
185 325 x .015 = 2779.88
The mean of five numbers is 8. If one of the five numbers is removed, the mean becomes 9. What is the value of the number that was removed
Answers
Using the mean concept, it is found that the value of the number that was removed was of 4.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
The mean of five numbers is 8, hence, the sum of the numbers is given by:
S = 5 x 8 = 40.
If one of the five numbers is removed, the mean becomes 9, hence, the sum of the four numbers is given by:
S = 4 x 9 = 36.
The difference is:
40 - 36 = 4.
Hence, the value of the number that was removed was of 4.
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need help with question 8
Answers
Answer:
Asnwer is in explanation
Step-by-step explanation:
f' (x) = 2x
Hope this helps!
Rearrange 4x+2y=8 to make y the subject.
Answers
Step-by-step explanation:
y=(8-4x)/2
y=4-2x
I hope it helps
Answer:
y = 4 - 2x
Step-by-step explanation:
4x + 2y = 8
Subtract 4x on both sides,
2y = 8 - 4x
Divide 2 on both sides,
y = ( 8 - 4x ) / 2
y = 4 - 2x
3/4x= 12, what must x be?
x=16
x=4
x=3
x=48
Answers
Answer:
x=16
Step-by-step explanation:
12 is three fourths of x, there are three 1/4s that make up 12.
Divide 12 by three to find out 1/4 is.
Then simply multiply that by four.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
3/4
Step-by-step explanation:
If Ty and his brothers share a pizza equally, then the pizza is split into four parts because there are four people sharing it. That means that each person has 1/4 of the pizza.
Since Ty has 3 brothers, they share 3/4 of the pizza since 1/4 * 3 = 3/4.
A bowling ball has a diameter of 8.5 inches. If it is rolled down a 60-foot bowling lane, how many complete revolutions will it make? Round to the nearest tenth.
Worth 25 points!!
Answers
Answer:
27 revolutions
Step-by-step explanation:
Things to remember :
One revolution = distance of circumference coveredcircumference = 2πrdiameter = 2 x radiusSolving
One revolution = 2 x π x d/2 = πdOne revolution = 3.14 x 8.5One revolution = 26.69 inchesNo. of revolutions = Distance / one revolutionNo. of revolutions = 60 x 12 / 26.69No. of revolutions = 720 / 26.69No. of revolutions = 27 revolutionsplease help im not good with area and circumference when it comes to circles
Answers
1) r = 13cm
2) d = 27.2in
3) d = 24x
4) r = 24.5m
5) There is a circle inside a square, so the side of the square (16in), corresponds to the diameter of the circle.
radius = 8in
area = (pi)r^2 = 3.14 (8in)^2 = 3.14 (64in^2) = 200.96in^2
Circumference = 2(pi)r = 2(3.14)8in = 50.24in
6) The hypotenuse of the right triangle inside the circle is equal to the diameter of the circle. So we need to find it using the Pythagorean theorem.
d^2 = (10^2 + 24^2)cm
d^2 = (100 + 576)cm
d^2 = (676)cm
d = 26cm
So, radius = 13cm
Area = (pi)r^2 = 3.14 (13cm)^2 = 3.14 (169cm^2) = 530.66cm^2
Circumference = 2(pi)r = 2(3.14)(13cm) = 81.64cm
7) The diagonal of the square is equal to the diameter of the circle, so we need to find it using a formula.
d =[sqrt(2)] (5in)
I won’t calculate it now, because it’s a periodic number.
r = {[sqrt(2)] (5in)} : 2
Area = (pi)r^2 = 3.14 {[sqrt(2)(5in)]:2}^2 = 3.14 (12.5in^2)= 39.25in^2
Circumference = 2(pi)r = 2(3.14)(12.5in) = 78.5in
8) If a right triangle has two equal sides, it means that it is half of a square.
So we can apply the same formula as before.
d =[sqrt(2)] (8)
I won’t calculate it now, because it’s a periodic number.
r = {[sqrt(2)](8)}:2
Area = (pi)r^2 = 3.14 {[sqrt(2)(8)]:2}^2 = 3.14 (32) = 100.48
Circumference = 2(pi)r = 2(3.14)(32) = 200.86
{there aren’t units of measurement in this exercise}
I hope there are no accidental errors. :)
Emily is working with rolling a standard number cube (die) and flipping a quarter.
Which experiment can yield a 50% probability?
Answers
Answer:
flipping a quarter
Step-by-step explanation:
a quarter has two sides so the chance of getting one is 1/2
a dice has 6 sides so the chance of getting a certain number is 1/6
Simplify each of the expressions below. Which of the expressions have a value between 20 and 40? Select all that apply.
A)(6 −3)2+(5×3)
B)72 −(1×3)3
C)43 −5×8
D)102 −(5+2)2
Answers
Answer:
d
Step-by-step explanation: