Answers
or 23.4 rounded to the nearest tenth.
[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]
[tex] \large\underline{ \boxed{ \sf{✰\:Note }}}[/tex]
★ 1st let's know what is the given figure is and it's related concepts for solving !
➣ Given Triangle is a right angled triangle
➣ It is having 3sides let's know what are the name of these sides
➣ 1st AB is know as hypotenuse
➣ 2nd AC and is called Base of the triangle
➣ 3rd BC whích is know as perpendicular of the triangle
➣ Hypotenuse(H):-The side of a right triangle opposite the right angle.
➣ Perpendicular(P):- Exactly upright; extending in a straight line.
➣ Base(B):- it also known as the side opposite to hypotenuse
➣Perpendicular and base are know as the leg of right angled triangle
➣ We can easily find length of one missing side by using a theorem name as "Pythagorean theorem"
➣ Pythagorean theorem :- A mathematical theorem which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of those of the two other sides
★ Note :- The Pythagorean theorem only applies to right triangles.
[tex] \rule{70mm}{2.9pt}[/tex]
★ Writing this theorem mathematically ★
[tex] { \boxed{✫\underline{ \boxed{ \sf{Pythagorean \: theorem \: ⇒ {Hypotenuse }^2={ Base }^2+ {Height }^2}}}✫}}[/tex]
★ Here ★
➣ Base (AC)= 22cm
➣ Perpendicular (height) (BC)= 8cm
[tex] \rule{70mm}{2.9pt}[/tex]
✝ Assumption ✝
➣ let Hypotenuse ( AB ) = "x"
[tex] \boxed{ \rm{ \pink ➛AB^2= AC^2+BC^2}}[/tex]
[tex] \rule{70mm}{2.9pt}[/tex]
✝ let's substitute values ✝
[tex]\rm{ \pink ➛x^2=22 ^2+8^2} \\ \rm{ \pink ➛x^2 = 484+ {64} } \\ \rm{ \pink ➛ {x}^{2} = 548 } \\ \rm{ \pink ➛= {x} = \sqrt{548} } \\ \rm{ \pink ➛ x = 2\sqrt{137} \: or23.4} \\ [/tex]
[tex] \rule{70mm}{2.9pt}[/tex]
Hence Hypotenuse (AB) in the given triangle is of
[tex] { \boxed{✛\underline{ \boxed{ \sf{2\sqrt{137} \: or23.4\green✓}}}✛}}[/tex]
[tex] \rule{70mm}{2.9pt}[/tex]
Hope it helps !
Related Questions
Can someone solve this venn diagram for x please. Giving brainiliest
Answers
Answer:
x = 38
Step-by-step explanation:
Intersection is occupied by xremaining part of set A = 149 - xremaining part of set B = 160 - xNow,
(149 - x) + (x) + (160 - x) + (2x + 3) = 350149 - x + x + 160 - x + 2x + 3 = 350312 + x = 350x = 350 - 312x = 38Type the correct answer in the box. Use numerals instead of words. 5 The surface area of a cone is 2167 square units. The height of the cone is 3 times greater than the radius. What is the length of the radius of the cone to the nearest foot? The radius is about ___ feet.
Answers
The surface area of the cone is the amount of space on it, the radius of the cone is about 13 feet
How to determine the radius?The given parameters are:
Surface Area, A = 2167Height (h) = 3 * radius (r)The surface area is calculated using:
[tex]A =\pi r(r + \sqrt{h^2 + r^2})[/tex]
So, we have:
[tex]A =\pi r(r + \sqrt{(3r)^2 + r^2})[/tex]
Substitute 2167 for A
[tex]2167 =\pi r(r + \sqrt{(3r)^2 + r^2})[/tex]
Evaluate the sum
[tex]2167 =\pi r(r + \sqrt{10r^2})[/tex]
Divide both sides by [tex]\pi[/tex]
[tex]689.78 =r(r + \sqrt{10r^2})[/tex]
Evaluate the exponent
[tex]689.78 =r(r + 3.16r)[/tex]
Evaluate the sum
689.78 =r(4.16r)
Open the bracket
689.78 = 4.16r²
Divide both sides by 4.15
r² =165.8125
Take the square root of both sides
r = 13 (approximated)
Hence, the radius of the cone is about 13 feet
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A ball is thrown vertically upwards from the ground. It rises to a height of 10m and then falls and bounces. After each bounce, it vertically 2/3 the height of which is fell.
i) Find the height to which the ball bounces after the nth impact
ii) Find the total distance travelled by the ball from the first throw to the nth impact with the ground
Answers
[tex]{\huge{\fcolorbox{yellow}{red}{\orange{\boxed{\boxed{\boxed{\boxed{\underbrace{\overbrace{\mathfrak{\pink{\fcolorbox{green}{blue}{Answer}}}}}}}}}}}}}[/tex]
(i)
[tex] \sf{a_n = 20 \times {( \frac{2}{3} )}^{n - 1} }[/tex]
(ii)
[tex] \sf S_n = 60 \{1 - { \frac{2}{3}}^{n} \} [/tex]
Step-by-step explanation:
[tex]\underline\red{\textsf{Given :-}}[/tex]
height of ball (a) = 10m
fraction of height decreases by each bounce (r) = 2/3
[tex] \underline\pink{\textsf{Solution :-}}[/tex]
(i) We will use here geometric progression formula to find height an times
[tex]{\blue{\sf{a_n = a {r}^{n - 1} }}} \\ \sf{a_n = 20 \times { \frac{2}{3} }^{n - 1} }[/tex]
(ii) here we will use the sum formula of geometric progression for finding the total nth impact
[tex] \orange {\sf{S_n = a \times \frac{(1 - {r}^{n} )}{1 - r} }} \\ \sf S_n = 20 \times \frac{1 - ( { \frac{2}{3} })^{n} }{1 - \frac{2}{3} } \\ \sf S_n = 20 \times \frac{1 - {( \frac{2}{3}) }^{n} }{ \frac{1}{3} } \\ \sf S_n = 3 \times 20 \times \{1 - ( { \frac{2}{3}) }^{n} \} \\ \purple{\sf S_n = 60 \{1 - { \frac{2}{3} }^{n} \}}[/tex]
1
suppose you deposit $1,500 in a savings account that pays interest at an annual rate of 5%. if no money is added or withdrawn from the account, answer the following questions.
a. how much will be in the account after 4 years?
b. how much will be in the account after 17 years?
c. how many years will it take for the account to contain $2,000?
d. how many years will it take for the account to contain $2,500?
a. after 4 years, the amount in the account will $
(do not round until the final answer. then round to the nearest cent as needed.)
Answers
Answer:
a. After 4 years there will be $1,823.26.
b. After 17 years there will be $3,438.03.
c. It will take 6 years with a total balance of $2,010.14.
d. It will take 11 years with a total balance of $2,565.51.
Step-by-step explanation:
Henry has a box in the shape of a
square pyramid. He wants to wrap
the box with paper. If the base has
side lengths of 5 in. and the lateral
height is 8 in., about how much
wrapping paper will he need?
Answers
The amount of wrapping paper that he needs to cover the pyramid will be 105 square inches.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Henry has a box in the shape of a square pyramid.
He wants to wrap the box with paper.
If the base has side lengths of 5 in. and the lateral height is 8 in.
Then the amount of the wrapping paper that he needs to cover the pyramid will be
[tex]\rm Area = 4 \times \dfrac{1}{2} \times 5 \times 8 + 5 \times 5\\\\\\Area = 80 + 25\\\\\\Area = 105 \ in^2[/tex]
Thus, the amount of wrapping paper that he needs to cover the pyramid will be 105 square inches.
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PLEASE HELP!!!!!!!!!!!!
Answers
Answer:
Yes you are correct it is a constant rate of -800
Step-by-step explanation:
Hope this helps. :-)
The students in Classroom 101 consist of 13 girls and 7 boys. The students in Classroom 103
consist of 8 girls and 12 boys. You randomly choose one student from each classroom. Find the
probability of the events.
8. Choosing a boy from both classrooms
9. Choosing a girl from Classroom 101 and a boy from Classroom 103
10. Choosing a boy from Classroom 101 and a girl from Classroom 103
11. You randomly choose 2 students from Classroom 101 to compete in
a competition.
a. First Choice: girl Second Choice: girl
b. First Choice: boy
Second Choice: girl
c. First Choice: girl
Second Choice: boy
Answers
The probability of choosing a boy from both classrooms is 19/20, the probability of choosing a girl from Classroom 101 and a boy from Classroom 103 is 39/100, and the probability of choosing a boy from Classroom 101 and a girl from Classroom 103 is 7/50
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Total number of students in classroom 101 = 13+7 = 20
Total number of students in classroom 103 = 8+12 = 20
The probability of choosing a boy from both classrooms:
= 19/20
Choosing a girl from Classroom 101 and a boy from Classroom 103:
Since both are independent event.
Probability of choosing a girl from Classroom 101 = 13/20
Probability of choosing a boy from Classroom 103 = 12/20
The probability of choosing a girl from Classroom 101 and a boy from Classroom 103:
= (13/20)(12/20)
= 156/400
= 39/100
Similarly, the probability of Choosing a boy from Classroom 101 and a girl from Classroom 103:
= (7/20)(8/20)
= 56/400
= 7/50
Similarly, we can find remaining probability.
Thus, the probability of choosing a boy from both classrooms is 19/20, the probability of choosing a girl from Classroom 101 and a boy from Classroom 103 is 39/100, and the probability of choosing a boy from Classroom 101 and a girl from Classroom 103 is 7/50
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Triangles L O N and L M N share common side L N. Angles O L N and N L M are congruent.
What additional information would be needed to prove that the triangles are congruent using the ASA congruence theorem?
ON ≅ MN
∠LON ≅ ∠LMN
LN ≅ NM
∠LNO ≅ ∠LNM
Answers
Answer:
Step-by-step explanation:
Answer:
D. ∠LNO ≅ ∠LNM
Step-by-step explanation:
Have a good day!
Solve the system of linear equations by elimination. Check your solution.
3x - 4y = 17
7x - 4y = 13
Answers
Answer:
( - 1, - 5)
Step-by-step explanation:
Elimination Method:
A method for solving a system of linear equations where you add or subtract equations to eliminate a variableEliminating one variable by combining two equations with a common term with adding or subtractingMultiply the second equation by -1, then add the equations together.
(3x−4y=17)
−1(7x−4y=13)
Becomes:
3x−4y=17
−7x+4y=−13
Add these equations to eliminate y:
−4x=4
Then solve−4x=4for x:
−4x=4
-4x / -4 = 4/-4 (Divide both sides by -4)
x= −1
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
3x−4y=17
Substitute−1forxin3x−4y=17:
(3)(−1)−4y=17
−4y−3=17(Simplify both sides of the equation)
−4y−3+3=17+3(Add 3 to both sides)
−4y=20
-4y/ -4 = 20/ -4 (Divide both sides by -4)
y=−5
Answer:
x=−1 and y=−5
A boy’s height is 133 cm at the end of a year. His height increased by 5%. Find the height at the
beginning of the year.
Answers
Answer:
126.35cm
Step-by-step explanation:
quick use of a calculator
Answer:
26.6 cm
Step-by-step explanation:
height= 133/5
height of year= 26.6 cm
actually help... if u dont hve the answer, dont respond.
Answers
Answer:
y = 1/3*x -3
Step-by-step explanation:
Method 1:
Grab two random points from the line.
(0,-3) and (3,-2)
Using the Point-Slope Form solve for m.
(-3 - (-2)) = m * (0 - (3))
-1 = m * (-3)
m = 1/3
Turning Point-Slope form into Slope intercept Form.
(y - (-3)) = 1/3 * (x - 0)
y + 3 = 1/3x
y = 1/3 - 3
Method 2:
Look at the y-intercept since y-int becomes our b. b = -3
From the y-int count rise/run as thats our Slope m. m = 1/3
Slope-intecept Form:
y = 1/3*x -3
Answer:
y=1/3x-3
rise/run= 1/3
y-int. is -3
Step-by-step explanation:
You start at (7, 8). you move left 3 units and right 3 units. where do you end?
Answers
Answer:
You end back at where you started (7,8)
Step-by-step explanation:
You move left so you subtract 3 from (7) because it is x, (8) is Y
Left: 7-3=4
Right: 4+3-7
A group of 300 middle school students were asked whether they prefer playing video games or watching TV in their spare
time. The genders of the students and their responses are reported in the following table.
Playing video
Watching TV
games
Girls
45
108
Boys
84
63
(a) What percentage of the students prefer playing video games?
(b) What percentage of the students are boys?
X 5 ?
(a) [%
(b) 1%
Answers
Answer:
(a) 43%
(b) 49%
Step-by-step explanation:
Add a total column and a total row to the table:
[tex]\begin{tabular}{| c | c | c | c |}\cline{1-4} & Playing video games & Watching TV & Total\\\cline{1-4} Girls & 45 & 108 & 153\\\cline{1-4} Boys & 84 & 63 & 147\\\cline{1-4} Total & 129 & 171 & 300\\\cline{1-4}\end{tabular}[/tex]
Part (a)Percentage of students who prefer video games:
[tex]=\dfrac{\textsf{total no. of students who play video games}}{\textsf{total no. of students}} \times \sf 100\%[/tex]
[tex]=\sf \dfrac{129}{300} \times 100 \%[/tex]
[tex]= \sf 43 \%[/tex]
Part (b)Percentage of students who are boys:
[tex]=\dfrac{\textsf{total no. of students who are boys}}{\textsf{total no. of students}} \times \sf 100\%[/tex]
[tex]=\sf \dfrac{147}{300} \times 100 \%[/tex]
[tex]= \sf 49 \%[/tex]
Answer:
total num playing video games/total no of studen×100
a) 43%
b) 49%
(2x+3,2+y)=(y+4,3x+2) find the value of x and
Answers
Answer:
x = -1
y = -3
Step-by-step explanation:
[tex]\begin{cases}2x+3=y+4\\ 2+y=3x+2\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}2x-y=1&\left( 1\right) \\ 3x-y=0&(2)\end{cases}[/tex]
(2) - (1) ⇒ (3x - y) - (2x - y) = 0 - 1 ⇒ x = -1
(1) ⇒ 2x - y = 1 ⇒ y = 2x - 1 = 2(-1) - 1 = -3
At a football stadium, 10% of the fans in attendance were teenagers. If there were 150 teenagers at the football stadium, what was the total number of people at the stadium?
Answers
Answer:
1500 people.
Step-by-step explanation:
100% of the fans are not known,
So let the total number of fans or 100% of the fans be X
SINCE 10% ••••••••••• 150
100% ••••••••••••X
we're going to Cross multiply
= 10×X = 100 × 150
10X = 15000
dividing bothsides by 10
10X/10 = 15000/10
X = 1500 people.
hope this helps....please let me know is was really helpful by rating and marking it as brainliest!!!Write it in exponential form, with only positive exponents
Answers
Answer:
the answer is 27 if you have to evaluate
" " " 3 cubed if you have to simplify
Step-by-step explanation:
Translate the sentence into an inequality.
The difference of twice a number and 3 greater than or equal to 19.
Use the variable c for the unknown number.
Answers
Answer:
2c - 3 >= 19
Step-by-step explanation:
Solving it:
2c >= 22
c >= 11
an outfielder throws a ball to home plate. the balls path is modeled by the graph of y=x/5-x^2/1000 where x represents the horizontal distance of the ball from the outfield and y represents the balls vertical distance above the ground. what are the coordinates of vertex of the ball's path?
Answers
Answer:
(100,10)
Step-by-step explanation:
25 POINTS
Which equation does the graph of the systems of equations solve? two linear functions intersecting at 3, 2 −one thirdx + 1 = 2x − 4 one thirdx + 1 = −2x − 4 one thirdx + 1 = 2x − 4 −one thirdx − 1 = −2x − 4
^-^
the answer is [tex]\frac{1}{3} x + 1 = 2x - 4[/tex]
Answers
The equation that the given graph of the system of equations solves is: 1/3x + 1 = 2x - 4.
What is the Equation of a Line?Where m is the slope and b is the y-intercept, the equation of a line in slope-intercept form is expressed as y = mx + b.
Equation of the Blue Line:
Slope (m) = change in y / change in x = 2/1 = 2
y-intercept (b) = -4.
Equation: y = 2x - 4
Equation of the Red Line:
Slope (m) = change in y / change in x = 1/3
y-intercept (b) = 1
Equation: y = 1/3x + 1
The equation that the graph of the systems of equations solve would be: 1/3x + 1 = 2x - 4.
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The midpoint of AB is M(4,-2). If the coordinates of A are (3, -6), what are the
coordinates of B?
Answers
Answer:
okay here we go
Step-by-step explanation:
[tex]in \: vectos \: ab \: means \: ob - oa \\ but \: the \: midpoint \: m \: is \: equal \: to \: a \: half \: of \: ab \\ \\ therefore \: m = \frac{1}{2} ab \\ = \frac{1}{2} (ob - oa) \\ = \frac{1}{2} (ob - (3. - 6)) \\ (4. - 2) = \frac{1}{2} (ob - (3. - 6)) \\ (8. - 4) = (ob - (3. - 6)) \\ ob = (11. - 2)[/tex]
Answer this question to get 10 pts!
Answers
Answer:
10x8=80 not 800 the answer should be
Step-by-step explanation:
5x8=40
5x50=250
10x8=80 not 800
10x50=500
500+250=750
750+40=790
790+80=870
-1/8d - 3 = -3/8
please help
Answers
Answer:
d=-21
Step-by-step explanation:
please help, will mark brainliest!!!
Answers
Answer:
$ 3513. 63
Step-by-step explanation:
Plug in the numbers :
3200 * e ^(.017 * 5.5) = 3513.63
Explain how you solve each problem. Show all your work. Marissa is 3 years older than her younger brother. Her older brother is twice as old as her younger brother. Her older brother is 18. How old are Marissa and her younger brother?
Answers
The age of Marissa and her younger brother.
Solution:Younger brother:We know that the older brother's age is 18 and he is twice older than the younger brother.
Let the unknown be "x"
[tex] x=\frac{18}{2} [/tex]
[tex]\large\boxed{\sf{x=9 \: years}}[/tex]
Marissa:Now, we know that the younger brother's age is 9 and Marissa is 3 years older than him.
Let the unknown be "x"
[tex]x=9 + 3[/tex]
[tex]\large\boxed{\sf{x=12 \: years}}[/tex]
Therefore, Marissa is 12 and her younger brother is 9
Answer:
Marissa's age = 12
Younger brother's age = 9
Step-by-step explanation:
Let age of Marissa be x, and her younger brother's y.
Equations formed :
x = y + 32y = 18Finding age of younger brother using Equation 2 :
⇒ 2y = 18
⇒ 2y/2 = 18/2
⇒ y = 9 years old
Substituting y in Equation 1 :
⇒ x = y + 3
⇒ x = 9 + 3
⇒ x = 12 years old
Marissa's age = 12
Younger brother's age = 9
A 5ft slide will be installed on a playground. The top of the slide will be 3 ft above the ground. What angle does the slide make with the ground? Round your final answer to the nearest degree.
Answers
Answer:
Its 37ft
Step-by-step explanation:
Apple estimates that 2.8 million square feet of the building is used for office space. Is their estimate reasonable? Below is the floor plan (each floor has a similar floor plan). Only the blue area is office space. Justify your response.
Answers
The estimate that 2.8 million square feet of the building is used for office space is not reasonable
How to determine the true statement?From the plan, the width of the building is:
Width = 230 feet
The building has a circular area, and it has four floors
So, the estimate of the building area is:
Area= 4πR²
So, we have:
Area= 4 * 3.14 * 230²
Evaluate
Area= 664424
The above value cannot be approximated to 2.8 million
Hence, the estimate used for office space is not reasonable
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Which
equation represents a line that passes through (-2, 4) and has a slope of 2/5?
Answers
Answer:y - 4 = 2/5(x + 2)
Step-by-step explanation:
Mark me brainliest
If the length of minute hand of a clock is 42m . How much distance minute hand will cover in 15 minutes ?
Answers
Answer: We minutes hand moves for 20minutes ,it makes 120° central angle
Length=x/360×2πr
=120/360×2×22/7×42
On simplyfing
Length=88cm
Step-by-step explanation:
The scatter plot shows the profit by the month for a new company during its first year of operation. Which equation most closely models the line of best fit for the scatter plot? A) y = 5x B) y = 2.5x C) y = 5x + 1000 D) y = 2.5x + 1000
Answers
The equation most closely models the line of best fit for the scatter plot is y = 2.5x
Equation of a line graphsA line is the defines as the minimum distance between two points. The equation of a line is given in the form y =mx + b
where:
m is the slopeb is the interceptIn order to determine the required equation, we can use the coordinate (3, 5000) and (9, 20000)
Determine the slope
Slope = 20000-5000/9-3
Slope = 15000/6 = 2500
Determine the y-intercept
5000 = 2500(3) + b
b = 5000 - 7500
b = -2500
Determine the equation
y = 2.5x - 2.5
Therefore the equation most closely models the line of best fit for the scatter plot is y = 2.5x
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Can someone help me answer this?
Answers
Answer:
m<S = 68 degrees.
m<D = 112 degrees
Step-by-step explanation:
Opposite angles of a parallelogram are equal so:
4x - 4 = 3x + 14
4x - 3x = 14 + 4
x = 18.
So m < S = 4(18) - 4
= 72-4
= 68 degrees.
Angles on the same side of a parallelogram are supplementary, so
m < D = 180 - 68
= 112 degrees.