Answers
Answer:
[tex]\boxed {\boxed {\sf 53}}[/tex]
Step-by-step explanation:
This is a right triangle, which we know because of the little square in the corner.
We can use the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
where a and b are the legs and c is the hypotenuse.
In this triangle, 28 and 45 are the legs, because they make up the right angle. The unknown side is the hypotenuse, because it is opposite the right angle.
[tex]a=28 \\b=45 \\[/tex]
[tex](28)^2+(45)^2=c^2[/tex]
Solve the exponents.
(28)²= 28*28= 784[tex]784+(45)^2=c^2[/tex]
(45)²=45*45=2025[tex]784+2025=c^2[/tex]
Add the two numbers.
[tex]2809=c^2[/tex]
Solve for c by isolating it on one side of the equation. c is being squared. The Inverse of a square is the square root. Take the square root of both sides of the equation.
[tex]\sqrt{2809} =\sqrt{c^2}[/tex]
[tex]\sqrt{2809} = c[/tex]
[tex]53=c[/tex]
The third side and hypotenuse of the triangle is 53
[tex]\pink{\sf Third \: side \: of \: the \: triangle = 53}[/tex]
Solution :As, the given triangle is a right angled triangle,
Hence, We can use the Pythagoras' Theorem,
[tex]\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}[/tex]
Here,
H = Hypotenuse of triangleB = Base of triangle P = Perpendicular of triangleIn given triangle,
Base = 45 Perpendicular = 28 Hypotenuse = ?Now, by Pythagoras' theorem,
[tex]\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}[/tex]
[tex] \sf : \implies H^{2} = (45)^{2} + (28)^{2}[/tex]
[tex] \sf : \implies H^{2} = 45 \times 45 + 28 \times 28[/tex]
[tex] \sf : \implies H^{2} = 2025 + 784[/tex]
[tex] \sf : \implies H^{2} = 2809[/tex]
By squaring both sides :
[tex] \sf \sqrt{H^{2}} = \sqrt{2809}[/tex]
[tex] \sf : \implies H^{2} = \sqrt{2809}[/tex]
[tex] \sf : \implies H^{2} = \sqrt{(53)^{2}}[/tex]
[tex] \sf : \implies H^{2} = 53 [/tex]
[tex]\pink{\sf \therefore \: Third \: side \: of \: the \: triangle \: is \: 53}[/tex]
━━━━━━━━━━━━━━━━━━━━━
Related Questions
A store buys a video game for the wholesale price of $29.95. The markup on the game is 80%. If sales tax is 7.5%, how much money would you need to buy the game?
Answers
Answer:
57.9532
Step-by-step explanation:
Given that:
Wholesale price = 29.95
Markup = 80%
Sales tax = 7.5%
Retail price of the game :
Price before sale tax:
Wholesale price * ( 1 + markup %)
29.95 * (1 + 0.8)
29.95 * (1.8)
$53.91
Sales tax = 7.5%
53.91 * (1 + 0.075)
53.91 * (1.075)
= 57.9532
Hence, $57.9532 will have to be paid
help math 7th grade.........
Answers
Answer:
6/7
Step-by-step explanation:
Answer: 6/7
Step-by-step explanation:
Jenna has 3 red balloons and 5 blue balloons.
what is the ratio of the blue balloons. she adds 2 red balloons and remove 1 blue balloons what is the new ratio of the number of red balloons to the number of blue balloon
Answers
Answer:
5: 4
Step-by-step explanation:
original ratio: 3:5
new ratio: 5:4
hope it helps!
Two trains leave stations 320 miles apart at the same time and travel toward each other. One train travels at 105 miles per hour while the other travels at 95 miles per hour. How long will it take for the two trains to meet?
Answers
Answer:
1.6 hours / 1 hour 36 minutes
Step-by-step explanation:
105+95=200 miles
This is the distance that the trains could travel in an hour.
320÷200=1.6 hours
Our Answer is 1.6 hours / 1 hour 36 minutes
Given DFG, mD=48° mF=75°, FG= 20 Find DF,DG
Answers
Answer:
DF=22.57
DG=26
Step-by-step explanation:
sinF/DG=sinD/FG
sin75/DG=sin48/20
DG*sin48/sin48=20*sin75/sin48
DG=26
D^+F^+G=180(sum of int. angles of triangle)
G^=180-48-75
G^=57
sinG/DF=sinD/FG
sin57/DF=sin48/20
DF*sin48/sin48=20*sin57/sin48
DF=22.57
The value of DF and DG is 22.57 units and 25.9956 units respectively.
Given to us,
∠D = 48°,
∠F = 75°,
FG = 20,
According to sine rule, in a triangle the length of a side of the triangle and the angle opposite to it is always in ratio. therefore,
[tex]\dfrac{A}{sin\alpha}= \dfrac{B}{sin \beta}= \dfrac{C}{sin\gamma}[/tex]
So,
[tex]\dfrac{DF}{sin (G)}= \dfrac{FG}{sin (D)}= \dfrac{GD}{sin(F)}[/tex],
For ∠G,
∠D + ∠F + ∠G = 180°,
48° + 75° + ∠G = 180°,
∠G = 180° - ( 48° +75°),
∠G = 57°,
Now using the sine rule,
[tex]\dfrac{DF}{sin (G)}= \dfrac{FG}{sin (D)}= \dfrac{DG}{sin(F)}\\\\\\\dfrac{DF}{sin (57)}= \dfrac{20}{sin (48)}= \dfrac{DG}{sin(75)}\\\\\\\dfrac{DF}{sin (57)}= \dfrac{20}{sin (48)}\\\\DF = 22.57\ units\\\\\\ \dfrac{20}{sin (48)}= \dfrac{DG}{sin(75)}\\\\DG = 25.9956\ units[/tex]
Hence, the value of DF and DG is 22.57 units and 25.9956 units respectively.
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For 6 consecutive days, Alejandro studied for 5 minutes more each day than he did the previous day. Which best represents the change in the amount of time that Alejandro studied on the first day to the amount of time he studied on the last day?
–30 minutes
–11 minutes
11 minutes
30 minutes
Answers
Answer:
30 minutes
Step-by-step explanation:
Option A.30 minutes.
The change in the amount of time that Alejandro studied on the first day to the amount of time he studied on the last day is 30 minutes.
Step-by-step
The computation of the change in the amount of time is shown below = Number of consecutive ways * number of minutes more each day = 6 days ~ 5 minutes = 30 minutes
Hence, the change in the amount of time is 30 minutes Therefore the correct option is D.
We simply applied the above formula so that the correct value could come, and the same is to be considered(the answer is 30 ).
Learn more about consecutive days at
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#SPJ2
Please help ASAP PLEASE AND THANK YOUUU ❤️
Answers
Step-by-step explanation:
[tex] {7}^{ - 3} \times {7}^{ - 5} \times 7 {}^{ - 1} [/tex]
[tex] \frac{1}{7 {}^{3} } \times \frac{1}{ {7}^{5} } \times \frac{1}{7 } \\ \frac{1}{ {7}^{3 + 5 + 1 } } \\ \frac{1}{ {7}^{9} } \\ [/tex]
Step-by-step explanation:
[tex] = {7}^{ - 3} \times {7}^{ - 5} \times {7}^{ - 1} [/tex]
[tex] = {7}^{( - 3 - 5 - 1)} [/tex]
[tex] = {7}^{ - 9} [/tex]
[tex] = \frac{1}{ {7}^{9} } [/tex]
This year, Carlos planted 6 more than one-third of the cucumber plants he planted last year. How many cucumber plants
did he plant this year if last year he planted 12 plants?
06
9
O 10
O 12
Answers
Answer:
10.
Step-by-step explanation:
6+1/3*12=6+4=10
Answer: 10
Step-by-step explanation:
Tyrese bought 35 tickets to use at the carnival. He used some of the tickets to ride the bumper cars and play some games. now he has 28 tickets left what is the percent of decrease in the number of ticket that he has?
Answers
Answer:
20%?
Step-by-step explanation:
Help !! No work is needed to be shown
Answers
Step-by-step explanation:
By Law of Indices, a^m / a^n = a^(m-n).
Therefore a² / a⁸ = a^(-6).
x = -6.
Joe baked 27 dozen cookies and 24 dozen brownies. There are 12 treats in 1 dozen. About how many treats did he bake? Explain.
Answers
Answer:
612
Step-by-step explanation:
you multiply 27 x 12 and 24 x 12, and add up the products, and you get 612
Answer: 612 Treats
Work: To find out how many treats he baked, you do 27 x 12 and 24 x 12. After doing so, you get 324 and 288. Add those up, and you get 612.
I hope this helps, and Happy Holidays! :)
I need help with Thai question
Answers
[tex] \Large{\boxed{\sf n = 8}} [/tex]
[tex] \\ [/tex]
Explanation:The perimeter of a rectangle is given by the following formula:
[tex] \Large{\sf P = 2L + 2W } [/tex]
Where:
P is the perimeter of the rectangle.L is its length.W is its width.[tex] \\ [/tex]
[tex] \Large{\boxed{\sf Given \text{:} } \begin{cases} \sf L &=\sf 3n - 9 \\ \sf W &=\sf n + 5 \\ \end{cases} } [/tex]
[tex] \\ [/tex]
Substitute these values into our formula:
[tex] \sf P = 2(3n - 9) + 2(n + 5) [/tex]
[tex] \\ [/tex]
Expand the expression of the perimeter using the following distributive property.
[tex]\green{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \blue{ \sf\boxed{ \sf Distributive \: property \text{ : } }} \\ \\ \sf\star \: \red{ \large{ a (b + c) = ab + ac }} \end{array}}\\\end{gathered} \end{gathered}}[/tex]
[tex] \\ [/tex]
We get:
[tex] \sf P = 2(3n) + 2(-9) + 2n + 2(5) \\ \\ \sf P = 6n - 18 + 2n + 10 \\ \\ \boxed{\sf P = 8n - 8 } [/tex]
[tex] \\ [/tex]
Since the perimeter is equal to 56, the value of n satisfies the following equality:
[tex] \sf 8n - 8 = 56 [/tex]
[tex] \\ [/tex]
To solve this equation, let's add 8 to both sides:
[tex] \sf 8n - 8 + 8 = 56 + 8 \\ \\ \sf 8n = 64 [/tex]
[tex] \\ [/tex]
Now, divide both sides of the equation by 8:
[tex] \sf \dfrac{8n}{8} = \dfrac{64}{8} \\ \\ \\ \boxed{\boxed{\sf n = 8}} [/tex]
[tex] \\ \\ [/tex]
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There are 60 marbles in a bowl. Their colors are red, blue, and yellow. 1/3 of the marbles are yellow, 1/4 of the marbles are blue. How many red marbles are there in the bowl
Answers
Answer: 25 red marbles
Step-by-step explanation:
Fraction of yellow marbles = 1/3
Fraction of blue marbles = 1/4
Fraction of red marbles = 1 - (1/3 + 1/4) = 5/12
Therefore, the number of red marbles that are there in the bowl would be:
= 5/12 × 60
= 25 red marbles
otieno is k years old.He is 5 years older than kidole what will be their age fours to come
Answers
Answer:
Otieno's age in 4 years: [tex]k+4[/tex]
Kidole's age in 4 years: [tex]k-1[/tex]
Step-by-step explanation:
[tex]k[/tex] = Otieno's age
[tex]k-5[/tex] = Kidole's age
Their ages will increase by 4 years when 4 years pass.
[tex]k+4[/tex] = Otieno's age in 4 years
[tex]k-5+4[/tex] = Kidole's age in 4 years
[tex]k-1[/tex] = Kidole's age in 4 years (after simplifying the expression)
I hope this helps!
What are the domain and range of the function represented by the set of ordered pairs? \ (-6,5),(-3,2),(-1,0),(5,-4)\
Answers
Answer:
The domain and the range of the function represented by the set of ordered pairs are {-6, -3, -1, 5} and {5, 2, 0, -4}
Step-by-step explanation:
In any set of ordered pairs,
The domain is the values of x (set of x) ⇒ the first number in each ordered pairThe range is the value of y (set of y) ⇒ the second number in each ordered pairLet us solve the question
∵ The set of ordered pairs is {(-6, 5), (-3, 2), (-1, 0), (5, -4)}
∵ The first number in each ordered pair represents x
∴ x = -6, -3, -1, 5
∵ The set of x is the domain of the function
∴ The domain of the set of ordered pairs = {-6, -3, -1, 5}
∵ The second number in each ordered pair represents y
∴ y = 5, 2, 0, -4
∵ The set of y is the range of the function
∴ The range of the set of ordered pairs = {5, 2, 0, -4}
The domain and the range of the function represented by the set of ordered pairs are {-6, -3, -1, 5} and {5, 2, 0, -4}
Answer:
Domain: {-6,-3,-1,5}
Range: {-4,0,2,5}
Step-by-step explanation:
11y+2 Help me please
Answers
Answer:
what does it equal ?? x???
Step-by-step explanation:
Salma's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Salma $5.15 per pound, and type B coffee costs $4.10 per pound. This month, Salma made 147 pounds of the blend, for a total cost of $659.40. How many pounds of type A coffee did she use?
Answers
.........................
Answer: 54 pounds
Step-by-step explanation:
1. Adressing the variables:
x=number of pounds of type A
y=number of pounds of type B
2. Equations:
x+y=147 pounds
5.15x+4.1y=659.40
3. Subsitution:
y=147-x =>5.15x+4.1(147-x)
4. Solve:
5.15x+602.7-4.1x=659.4
=> 1.05x=56.7 => x=54
5. Solution:
x=54; y=93
If matrix C represents (A-B)+A, the value of the entry represented by C41 is
Answers
Answer:
The value of the entry represented by [tex]c_{41}[/tex] is 12.
Step-by-step explanation:
Let [tex]A = \left[\begin{array}{ccc}-5&3&8\\3&6&-5\\5&-9&0\\7&3&4\end{array}\right][/tex] and [tex]B = \left[\begin{array}{ccc}-7&-8&-5\\7&9&2\\2&5&-7\\2&8&-7\end{array}\right][/tex]. The sum of equal-sized matrices consist in the sum of each pair of corresponding elements. If [tex]C = (A-B)+A[/tex], then:
[tex]C = 2\cdot A -B[/tex] (1)
Then, [tex]c_{41}[/tex] is the element of matrix C located in the fourth row and first column and is defined by the following expression:
[tex]c_{41} = 2\cdot a_{41}-b_{41}[/tex] (2)
If we know that [tex]a_{41} = 7[/tex] and [tex]b_{41} = 2[/tex], then [tex]c_{41}[/tex] is:
[tex]c_{41} = 2\cdot (7)-2[/tex]
[tex]c_{41} = 12[/tex]
The value of the entry represented by [tex]c_{41}[/tex] is 12.
Identify the two equations that have no solution?
Answers
Answer:
1st option and last option
thats all of my points plz help me
Reuben is making a replica of the US flag for his school project.
He uses a scale of 0.5 centimeter to 1 inch to draw the flag. The length of the scale drawing is 2.5 centimeters, and its width is 4.75 centimeters.
The perimeter of the scale drawing is (a7.25, b 11.875, c 14.5 d 47.5)centimeters
The perimeter of the actual flag is(a 14.5 b 29 c 47.5 d 95
Answers
Given: U.S Flag - rectangle in shape
scale of 0.5 cm = 1 in
length of the scale 2.5 cm
width of the scale 4.75 cm
perimeter of the scale = 2(L+W) = 2(2.5+4.75) =
2(7.25) = 14.5cm
perimeter of the actual flag is:
14.5cm * 1in/0.5cm = 29 inches
hope it helps!
Step-by-step explanation:
Perimeter of scale drawing
= 2 * (Length + Width)
= 2 * (2.5cm + 4.75cm)
= 2 * 7.25cm
= 14.5cm. (C)
Scale length to Actual length = 0.5cm : 1 in
Hence,
Perimeter of actual drawing
=> (1/0.5) * Perimeter of scale drawing
=> (1/0.5) * 14.5cm
=> 29 in. (B)
100 points with work
Answers
Answer:
jacky 12 809 n-t
Step-by-step explanation:
Answer:
he said it not me
Can you help me out with this question pls
Answers
-16>-f , if f =15 true or false
Answers
Answer:
false 15 is a positive number
Combine Like Terms
5+2x+5+7x=3
Answers
Answer:
9x + 10 = 3
General Formulas and Concepts:
Algebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define Equation
5 + 2x + 5 + 7x = 3
Step 2: Simplify
Combine like terms (x): 9x + 5 + 5 = 3Combine like terms (Z): 9x + 10 = 3Answer:
9x+10=3
Explantion
(2x+7x)+(5+5)=3
= 9x+10=3
I am confused on these 2
Answers
Answer:
1) x=20 degrees
2) x=25 degrees
Step-by-step explanation:
1) there is 9x if you add all of the angles together and there is 180 degrees in a triangle so 180 divided by 9 equals 20 degrees.
2)there is 7x and 5 dgress in total so we can make an equation:
7x+5=180
7x=175
x=25
An object of mass 20kg is dropped from a height . Find the potential and kinetic energy if the heights are 4,3,2,1, just above the ground. (Take value of g as 10 m/s-2
Answers
Answer:
At 4 meters, the potential energy is 800 Joules
At 3 meters, the potential energy is 600 Joules
At 2 meters, the potential energy is 400 Joules
At 1 meter, the potential energy is 200 Joules
Step-by-step explanation:
The given mass of the object = 20 kg
The Potential Energy of an object at a height is. P.E. = m × g × h
Where;
m = The mass of the object
g = The acceleration due to gravity taken as 10 m/s²
h = The height of the object
The potential energy if the height is 4 meters is given as follows;
P.E. = 20 kg × 10 m/s² × 4 m = 800 Joules
The potential energy if the height is 3 meters is given as follows;
P.E. = 20 kg × 10 m/s² × 3 m = 600 Joules
The potential energy if the height is 2 meters is given as follows;
P.E. = 20 kg × 10 m/s² × 2 m = 400 Joules
The potential energy if the height is 1 meter is given as follows;
P.E. = 20 kg × 10 m/s² × 1 m = 200 Joules.
How long will it take l to catch up to c lauren can run 24 feet in 3 seconds clara can run 20 feet in 5 seconds clara has a 40 foot head start l will catch c in how many seconds after running how many feet
Answers
Answer:
They both will meet each other when they both have been running for 10 seconds
Lauren will run [tex]x=80\ \text{ft}[/tex] and Clara will run [tex]40\ \text{ft}[/tex]
Step-by-step explanation:
Velocity of Lauren
[tex]v_l=\dfrac{24}{3}\\\Rightarrow v_l=8\ \text{ft/s}[/tex]
Velocity of Clara
[tex]v_c=\dfrac{20}{5}\\\Rightarrow v_c=4\ \text{ft/s}[/tex]
Let distance traveled by Lauren be [tex]x[/tex]
As Clara has a 40 feet head start distance she will travel is [tex]x-40[/tex]
[tex]\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}[/tex]
The time that will have passed when they both will meet will be the same for both of them so
[tex]\dfrac{x-40}{4}=\dfrac{x}{8}\\\Rightarrow 8x-320=4x\\\Rightarrow 8x-4x=320\\\Rightarrow 4x=320\\\Rightarrow x=\dfrac{320}{4}\\\Rightarrow x=80\ \text{ft}[/tex]
Time they will meet is [tex]\dfrac{80-40}{4}=\dfrac{80}{8}=10\ \text{s}[/tex].
So, Lauren will run [tex]x=80\ \text{ft}[/tex] and Clara will run [tex]x-40=80-40=40\ \text{ft}[/tex].
A line passes through (-2,5) and has slope. What is an equation of the line in point-slope form?
Answers
Answer:
Step-by-step explanation:
since the question does not have a given slope you can just put the point into the point slope formula y-y1 = m(x-x1)
y-5 = m(x-(-2))
y-5 = m(x+2)
since the slope is not given, leave it like that
1) △ABC has A(-2,-2), B(-1,2) and C(2,1). After a dilation centered at the origin, △A'B'C' has A'(-4,-4), B'(-2,4) and C'(4,2). What is the scale
factor of the dilation?
a) -2
C) 2
b) -1/2
d) 1/2
Answers
Answer:
Option (C)
Step-by-step explanation:
If a point is dilated by a scale factor of 'k' about the origin,
Rule for the dilation,
(x, y) → (kx, ky)
By this rule, if ΔABC is dilated to form image triangle as ΔA'B'C',
A(-2, -2) → A'[2×(-2), 2×(-2)]
B(-1, 2) → B'[2×(-1), 2×(2)]
C(2, 1) → C'[2×(2), 2×(1)]
Therefore, scale factor of the dilation of the dilation will be k = 2
Option (C) will be the answer.
Winston wants to put some very thick books on his bookshelf. Each book is 3 inches
thick. His bookshelf is 16 inches wide. How many thick books can he put on the
bookshelf? (There will be space left over.)
5
1
15
6