the "sum of" means we add.
So the sum of n and 12 means we add n and 12:-
n+12
or
12+n (both of these expressions mean the same thing)
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
solve- cbb to work it out
➝ Hypotenuse of triangle ( a ) = 21.63 mm
➝ Hypotenuse of triangle ( b ) = 150 mm
➝ Hypotenuse of triangle ( c ) = 111.80 mm
[tex] \quad\rule{300pt}{1.5pt}\quad[/tex]
Solution:We have to find the length of hypotenuse in the given 3 triangles, which can be done by using Pythagoras theorem.
Pythagoras theorem states that :" In a right angled triangle, the square of hypotenuse side is equal to the sum of square of other two sides "
[tex] \qquad \bull \:{\pmb{\mathfrak{ h^2 = b^2 + p^2}}}[/tex]
And we have to convert the answer to the units indicated in red i.e, in mm.
Since 1cm = 10 mm, we will convert the given values of length of side in mm before putting the values in the formula
For triangle ( a )[tex] :\implies\qquad \sf{ h^2 = b^2 + p^2}[/tex]
[tex] :\implies\qquad \sf{ h =\sqrt{b^2 + p^2}}[/tex]
[tex] :\implies\qquad \sf{h=\sqrt{ (12)^2 + (18)^2 }}[/tex]
[tex] :\implies\qquad \sf{ h= \sqrt{144 + 324}}[/tex]
[tex] :\implies\qquad \sf{ h = \sqrt{468}}[/tex]
[tex] :\implies\qquad\underline{\underline{\pmb{ \sf{ h = 21.63 mm}}}}[/tex]
For triangle ( b )[tex] :\implies\qquad \sf{ h^2 = b^2 + p^2}[/tex]
[tex] :\implies\qquad \sf{h =\sqrt{b^2 + p^2} }[/tex]
[tex] :\implies\qquad \sf{ h = \sqrt{(90)^2+(120)^2}}[/tex]
[tex] :\implies\qquad \sf{ h=\sqrt{8100+14400}}[/tex]
[tex] :\implies\qquad \sf{ h =\sqrt{22500}}[/tex]
[tex] :\implies\qquad\underline{\underline{\pmb{ \sf{h = 150mm}}} }[/tex]
For triangle ( c )[tex] :\implies\qquad \sf{h^2 = b^2 + p^2 }[/tex]
[tex] :\implies\qquad \sf{ h=\sqrt{b^2 + p^2}}[/tex]
[tex] :\implies\qquad \sf{ h =\sqrt{(100)^2)+(50)^2}}[/tex]
[tex] :\implies\qquad \sf{ h=\sqrt{10000+2500}}[/tex]
[tex] :\implies\qquad \sf{ h =\sqrt{12500}}[/tex]
[tex] :\implies\qquad \underline{\underline{\pmb{\sf{h = 111.80mm}}} }[/tex]
Hypotenuse of triangle ( a ) = 21.63 mm
Hypotenuse of triangle ( b ) = 150 mm
Hypotenuse of triangle ( c ) = 111.80 mm
Explanation :find the length of hypotenuse in the given 3 triangles, which can be done by using Pythagoras theorem.
[tex]h^2 = b^2 + p^2[/tex]
And we have to convert the answer to the units indicated in red i.e, in mm.
Since 1cm = 10 mm, we will convert the given values of length of side in mm before putting the values in the formula
[tex]For \: \: triangle ( a )
\qquad \sf{ h^2 = b^2 + p^2}[/tex]
[tex]\qquad \sf{ h =\sqrt{b^2 + p^2}}[/tex][tex]\qquad \sf{h=\sqrt{ (12)^2 + (18)^2 }}[/tex][tex]\qquad\sf{h=\sqrt{ (12)^2 + (18)^2 }} \\ \\ \qquad \sf{ h= \sqrt{144 + 324}} \\ \\ \qquad \sf{ h = \sqrt{468}}
\\ \\\qquad\underline{\underline{\pmb{ \sf{ h = 21.63 mm}}}} \\ \\ For \: \: triangle ( b ) \qquad \sf{ h^2 = b^2 + p^2} \\ \\ \qquad \sf{h =\sqrt{b^2 + p^2} } \\ \\ \qquad \sf{ h = \sqrt{(90)^2+(120)^2}} \\ \\ \qquad \sf{ h=\sqrt{8100+14400}} \\ \\
\qquad \sf{ h =\sqrt{22500}} \\ \\\qquad\underline{\underline{\pmb{ \sf{h = 150mm}}} } \\ \\ For \: \: triangle ( c ) \qquad \sf{h^2 = b^2 + p^2 } \\ \\ \qquad \sf{ h=\sqrt{b^2 + p^2}} \\ \\\qquad\sf{ h=\sqrt{(100)^2)+(50)^2}} \\ \\\qquad\sf{ h=\sqrt{10000+2500}} \\ \\ \qquad \sf{ h =\sqrt{12500}} \\ \\
\qquad\underline{\underline{\pmb{\sf{h = 111.80mm}}} } [/tex]
the half life of a radioactive substance is the time it takes for a quantity of the substance to decay to half of the initial amount . The half-life of the radioactive gas radon is approximately 3.8 days. The initial amount of radon used in an experiment is 75 grams. if N represents the number of grams of radon remaining t days after the start of the experiment,
a. Write an equation that gives N in terms of t.
b. How much gas radon approximately remains after 3.8 days?
c. approximately when will the amount of radon remaining be 10 grams?
Using an exponential function, it is found that:
a) [tex]N(t) = 75(0.5)^{\frac{t}{3.8}}[/tex]
b) 37.5 grams of the gas remains after 3.8 days.
c) The amount remaining will be of 10 grams after approximately 11 days.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.Item a:
We start with 75 grams, and then work with a half-life of 3.8 days, hence the amount after t daus is given by:
[tex]N(t) = 75(0.5)^{\frac{t}{3.8}}[/tex]
Item b:
This is N when t = 3.8, hence:
[tex]N(t) = 75(0.5)^{\frac{3.8}{3.8}} = 37.5[/tex]
37.5 grams of the gas remains after 3.8 days.
Item c:
This is t for which N(t) = 10, hence:
[tex]N(t) = 75(0.5)^{\frac{t}{3.8}}[/tex]
[tex]10 = 75(0.5)^{\frac{t}{3.8}}[/tex]
[tex](0.5)^{\frac{t}{3.8}} = \frac{10}{75}[/tex]
[tex]\log{(0.5)^{\frac{t}{3.8}}} = \log{\frac{10}{75}}[/tex]
[tex]\frac{t}{3.8}\log{0.5} = \log{\frac{10}{75}}[/tex]
[tex]t = 3.8\frac{\log{\frac{10}{75}}}{\log{0.5}}[/tex]
[tex]t \approx 11[/tex]
The amount remaining will be of 10 grams after approximately 11 days.
More can be learned about exponential functions at https://brainly.com/question/25537936
PLEASE I NEED HELP!!! BRAINLIEST FOR THE FASTEST ANSWER
Answer:
883.125
Step-by-step explanation:
First, use the formula for volume of a sphere (4/3 * pi * r^3) to get the volume of the full sphere, then divide it by 2 to get the volume of half of the sphere.
Hopefully this helps- let me know if you have any questions!
A ________ is a set of points that extends infinitely in both directions.
Answer:
line
Step-by-step explanation:
A line is a set of points that extends infinitely in both directions.
An equilateral triangle has an area of 50 units 2. What is the length of each side?
Answer:
Length of each side of equilateral Traingle is 10.75 unitsStep-by-step explanation:
Given that area of an equilateral traingle 50 square units.
Let the length of side of equilateral traingle be 'x' units. To calculate length of each side we will use the formula of area of equilateral traingle:
[tex] \: \: { \underline { \boxed{\pmb { \sf{ \purple {Area_{(equilateral \: traingle)} = \dfrac{\sqrt 3}{4} \times (Side)^2}} }}}} \\ [/tex]
By substituting the values in above formula:
[tex]~[/tex]
[tex] : \implies \sf \: \: 50 = \dfrac{ \sqrt{3} }{4} \times {(x)}^{2} \\ \\ \\ : \implies \sf \: \: {(x)}^{2} = \dfrac{50 \times 4}{ \sqrt{3} } \\ \\ \\ : \implies \sf \: \: {(x)}^{2} = \dfrac{200}{ \sqrt{3} } \\ \\ \\ : \implies \sf \: \: x = \sqrt{ \dfrac{200}{ \sqrt{3} } } \\ \\ \\ : \implies \: \: { \boxed{\pmb{ \frak{ x = 10.75 \: units }}}}\\ \\ \\ [/tex]
Hence, Length of each side of equilateral Traingle is 10.75 unitsHere are clues for a puzzle involving two numbers.
Seven times the first number plus six times the second number equals 31.
Three times the first number minus ten times the second number is 29.
PART A
What are the two numbers?
Answer:
the first number is 5 1/2the second number is -1 1/8Step-by-step explanation:
The relations describing the two numbers can be written as equations. First, we need to assign variables: let x and y represent the first and second numbers, respectively.
The given relations are then ...
7x +6y = 31
3x -10y = 29
__
Such a system of equations can be solved many ways. One that is usually convenient is to use a graphing calculator. It tells us ...
the first number is 5 1/2the second number is -1 1/8A lifeguard fills a pool with water at a constant rate. After 1/2 hour, 1/3 of the pool is filled.
At this rate, what fraction of the pool is filled per hour?
A. 1/6 of the pool
B. 1/3 of the pool
C. 1/2 of the pool
D. 2/3 of the pool
Answer:
D
Step-by-step explanation:
1/2 hour -> 1/3 pool
multiply this by 2
1 hour -> 2/3 pool
so D 2/3 pool
The fraction of the pool that would be filled per hour at the given rate is: D. 2/3 of the pool.
What is a Constant Rate?A constant rate can be described as a quantity that changes steadlity over time.
The rate that the pool gets filled is given as:
1/2 hr = 1/3 of the water that would be filled in the pool
1 hr would be: 1/3 × 2 = 2/3
Therefore, the fraction of the pool that would be filled per hour at the given rate is: D. 2/3 of the pool.
Learn more about rate on:
https://brainly.com/question/25184007
Indicate whether the two functions are equal. If the two functions are not equal, then give an element of the domain on which the two functions have different values
The function f(x) = x² and g(x) = |x|² are the same since they both give a positive value.
How to interpret the function?From the complete information, it should be noted that the function f(x) = x² and g(x) = |x|² are the same since they both give a positive value.
Also, f(x) = x³ and g(x) = |x|³ are not equal. This is because both functions are not equal for x < 0. This can be illustrated when x = -1. In this case, f(x) = -1 and g(x) = 1.
Learn more about functions on:
https://brainly.com/question/22340031
The function f(x) = x² and g(x) = |x|² are the same since they both give a positive value.
What is the equality of the two functions?Two functions are equal if they have the same domain and codomain and their values are the same for all elements of the domain.
The function f(x) = x² and g(x) = |x|² are the same since they both give a positive value.
Also, f(x) = x³ and g(x) = |x|³ are not equal.
This is because both functions are not equal for x < 0.
This can be illustrated when x = -1. In this case, f(x) = -1 and g(x) = 1.
Hence, the function f(x) = x² and g(x) = |x|² are the same since they both give a positive value.
Learn more about functions on:
brainly.com/question/22340031
#SPJ4
Evaluate the expression 120n+160,500120n+160,500 when n=32n=32.
Answer: The answer should be 164,340.
More help please! IF YOU DON'T KNOW THE ANSWER THEN DO NOT ANSWER!
Answer:
8/3 < 8/2
D
Step-by-step explanation:
8/3 = 2.67
8/2 = 4
So, when fractions have equivalent (same) numerators, the one with the lesser denominator is the greater fraction.
There is more left if 8 is divided by 2 than when it is divided by 3
[Answer]8/3 < 8/2
[Answer] D
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
The half-life of a radioactive substance is the time it takes for a quantity of the substance to decay to half of the initial amount. The half-life of the radioactive gas radon is approximately 2.8 days. The initial amount of radon used in an experiment is 74 grams. If N represents the number of grams of radon remaining t days after the start of the experiment,
Answer:
N = 74(1/2)^(t/2.8)
Step-by-step explanation:
The exponential function expressing a half-life relation can be written ...
amount = (initial amount) × (1/2)^(t/(half-life))
For the numbers given in this problem, this is ...
N = 74(1/2)^(t/2.8)
__
Some folks like to express these relations in the form ...
N = 74e^(-kt)
In this form, the value of k is ...
k = ln(2)/(half-life) ≈ 0.693147/2.8 ≈ 0.24755
N = 74e^(-0.24755t)
Help if you understand thanks
Step-by-step explanation:
Table A represents an arithmetic sequence with a common difference d=+7.5
so for x=4, it's y³+7.5=25+7.5=32.5
for x=5, it's y⁴+7.5=32.5+7.5=40
Table B represents a geometric sequence with a common ratio r=4, so you're essentially multiplying by 4.
for x=4, y⁴=y³×4=160×4=640
for x=5, y⁵=y⁴×4=640×4=2560
Mr. Wilson bought a bag of birdseed and put half of it in his bird feeder. He split the other half equally among his 4 pet birds. How much of the bag did each pet bird get?
Answer:
each pet bird got 1/8 of the bag of birdseed
Step-by-step explanation:
the easiest way to do this is to divide the bag into eighths. if you divide the bag into eighths, 4/8 of the bag, being half, goes into the bird feeder. the other 4/8 of the bag is divided among Mr. Wilson's four pet birds, leaving each bird to get 1/4 of the bag when split evenly.
hope this helps
what is the slope of line AB
Answer:
2,3
Step-by-step explanation:
you count up 2,then count over three
ABCD is an irregular quadrilateral. The sum of all the interior angles is 360 degrees. What is the measure of angle D?
A. 60°
B. 120°
C. 180°
D. Need more information
please hurry! first CORRECT answer gets brainliest! :)
Answer:
D. Need more informationStep-by-step explanation:
The given information is not sufficient to determine each angle measure since the quadrilateral is irregular.
It would be good to see the picture at least.
Possible options are A or B but we can't confirm without additional detals, option C can't be a correct choice as 180° represents a straight line.
20. Joseph has a shadow that is 7 feet long. If the
angle of elevation of the sun is 48°, how tall is
Joseph?
Answer:
7.8 feet
Step-by-step explanation:
Use the formula of tan to find his height.
tan Θ = [tex]\frac{opposite}{adjacent}[/tex]
tan 48 = [tex]\frac{x}{7}[/tex]
x = tan 48 × 7
x = 7.8 ft
the measures of the angles in a triangle are in a ratio 1:5:6. find the measures of the angles
Answer:
The required angles are 15, 75 and 90
Step-by-step explanation:
1x + 5x+ 6x = 180
or 12x = 180
180 ÷ 12 = 15
hence,
15, 75, 90.
help me please I will mark as brainlist
Answer:
[tex] \frac{ \alpha + \beta + \gamma }{ - d} [/tex]
Step-by-step explanation:
If we simplify that fraction, we get
[tex] \frac{ \alpha + \beta + \gamma }{ \alpha \beta \gamma } [/tex]
Keep that in mind.
If y, a ,b are zeroes of the cubic polynomial, then that means
[tex](x - \alpha )(x - \beta )(x - \gamma )[/tex]
make up the polynomial.
Notice that leading xoeffeicent will be 1, so the roots will multiply to
[tex] - d[/tex]
so
[tex] \alpha \beta \gamma = - d[/tex]
which gives us
[tex] \frac{ \alpha + \beta + \gamma }{ - d} [/tex]
Proof:
Consider the function
[tex](x - 2)(x - 3)(x - 5)[/tex]
The roots are 2, 3, 5.
D is -30 so we get
Using the value,
[tex] \frac{2 + 3 + 5}{ 30} = \frac{1}{3} [/tex]
If we use the orginal equation, we get
[tex] \frac{1}{6} + \frac{1}{10} + \frac{1}{15} = \frac{10}{30} = \frac{1}{3} [/tex]
Answer:
Hey,mate
Notice that leading xoeffeicent will be 1, so the roots will multiply to
The roots are 2, 3, 5.
[tex]\sqrt{2} \sqrt{3} \sqrt{5}[/tex]
D is -30
simplify 35x-35
over 14x-49
Answer: Distributive property a(b+c) = ab + ac
-5(7)x + 7(7) = -35x + 49 (D)
It is now 11:15 A.M. What time will it be in three quarters of an hour?
A) noon
B) 11:45 A.M.
C) 11:45 P.M.
D) midnigh
Answer:
Ur mom
Step-by-step explanation:
Ur mom JK here's the answer 11:45 A.M. because 15 + 15 + 15 = 45 15 is a quarter so yeah Bois is 11:45 A.M Good luck
The ratio of the measures of the three angles in a triangle is 15:8:13. Find the measure of the three angles.
Answer: 75, 40, 65
Step-by-step explanation:
Let the angles measure 15x, 8x, and 13x.
Since the sum of the angles of a triangle is 180 degrees,
15x+8x+13x=180, meaning that x=5.
So, the angles are 15(5)=75 degrees, 8(5)=40 degrees, and 13(5)=65 degrees.
It’s a 4 digit number. The tens are double the ones. The thousands are double the tens. The sum of the digit is 19
URGENT
BRAINLIEST HURRY HURRY By your cell phone contract, you pay a monthly fee plus some money for each minute you use the phone during the month. In one month, you spent 280 minutes on the phone, and paid $23.80. In another month, you spent 340 minutes on the phone, and paid $25.90.
Let x be the number of minutes you talk over the phone in a month, and let y be your cell phone bill, in dollars, for that month. Use a linear equation to model your monthly bill based on the number of minutes you talk over the phone.
This linear model’s slope-intercept equation is_______ .
If you spent 160 minutes over the phone in a month, you would pay _____.
If in a month, you paid $30.80 of cell phone bill, you must have spent _____ minutes on the phone in that month.
Answer:Y = Co + C*x.22.45 = Co + C*200,Co = 22.45 - 200C.29.65 = Co + C*350.Co = 29.65 - 350C. = 22.45 - 200C150C = 7.20, C = 0.048/min.Co = 22.45 - 200*0.048 = $12.85/mo. = Initial cost.Y = 0.048x + 12.85.2. Y = 0.048*110 + 12.85 = $18.13.3. 34.10 = 0.048x + 12.85, X = ?.
Step-by-step explanation:
line d has a slope of 7/3. line e is perpendicular to line d. what is the slope of line e?
Perpendicular lines have slopes that are opposite reciprocals.
This means we take a number, flop it over, and change its sign.
Here we have the number:-
[tex]\boxed{\frac{7}{3}}[/tex]
Flop it over:-
[tex]\boxed{\frac{3}{7} }\longleftarrow\sf{the~numerator~and~denominator~switch~places}[/tex]
Change its sign:-
[tex]\boxed{-\frac{3}{7}}[/tex]
Hence, the slope of line e is:-
[tex]\bigstar{\boxed{\pmb{Slope=-\frac{3}{7}}}}[/tex]
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
A square with side length s has an area of 324 square centimeters. This equation shows the area of the square ^{s^2}is 324
Answer:
the side s is 18
Step-by-step explanation:
s=?
Area of square(A)=324
Now,
A=s²
324=s²
√(324)=s
s=18
Jocelyn is pregnant and needs to eat at least 500 more calories a day than usual. when buying groceries one day with a
budget of $15 for the extra food, she buys bananas that have 90 calories each and chocolate granola bars that have 150
calories each. the bananas cost $0. 35 each and the granola bars cost $2. 50 each.
4/9 x 5/6 simplest form
5/6 x 4/9 = 10/27 as a fraction form. The work for 5/6 times 4/9 as a fraction provides more insight of how to find what is 5/6 times 4/9 in fraction form and the different variations of such problems.
An animal group adopted out 1,526 cats last year. this year, they found homes for 1,214 cats. what is the percent decrease in the number of cats adopted from last year to this year?
Answer: 20.4% decrease
Step-by-step explanation:
First, find how many fewer cats were adopted out this year: 1,526 - 1214 = 312.
Now, find what percent of 1,526 312 is: 1,526 * x = 312 → x = .204 * 100 = 20.4% :)
PLS HELP WILL GIVE BRAINLIEST
Answer:
y=2x+b
Step-by-step explanation:
What is the Greatest Common Factor for 39 and 57?
Answer:
3
Step-by-step explanation:
As you can see when you list out the factors of each number, 3 is the greatest number that 39 and 57 divides into.