A rectangular book measures 4 x 7, the length of its diagonal is √65.
Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In mathematical terms, if a and b represent the lengths of the two shorter sides (also known as legs) of a right triangle, and c represents the length of the hypotenuse, then the Pythagorean theorem can be expressed as:
a² + b² = c²
Given:
Base = 4
Length = 7.
To determine the length of diagonal by using Pythagorean theorem.
Diagonal² = Base² + Length²
Plugging the values in Pythagorean theorem.
Diagonal² = 4² + 7²
Diagonal = √(16 + 49) =√65.
Therefore, the length of diagonal of book is √65.
Learn more about Pythagorean theorem here:
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Please help I don’t understand
how many groups of 9 are there in 45
the answer is 5
Step-by-step explanation:
45÷9=5
How do you know square root c is a right angle?
Answer:
angle c is right angle because,
it is proved by Pythagoras theorem....
now,we check that
[tex] {10 }^{2} = {8}^{2} + {6}^{2} \\ 100 = 6 + 36 \\ 100 = 100 \\ lhs = rhs \\ hence \: \: proved \: angle \: c \: is \: right \: angle[/tex]
2 consecutive numbers that add up to 719
Answer:
359+360
Step-by-step explanation:
Answer:
359+360
Step-by-step explanation:
Here we will use algebra to find three consecutive integers whose sum is 719. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 719. Therefore, you can write the equation as follows:
(X) + (X + 1) + (X + 2) = 719
What can be said about the discriminant of the graph below?
A. The discriminant is positive, so there are no solutions.
B. The discriminant is 0, so there is one solution.
C. The discriminant is negative, so there are no solutions.
D. The discriminant is positive, so there are 2 solutions.
True or False.
If
F(x) = ∫ -23x sin(t) dt
then the second fundamental theorem of calculus can be used to evaluate F '(x) as follows
F '(x) = sin (3x)
Answer:
False.
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Integration
IntegralsDefinite IntegralsIntegration Constant CIntegration Rule [Fundamental Theorem of Calculus 2]: [tex]\displaystyle \frac{d}{dx}[\int\limits^x_a {f(t)} \, dt] = f(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle F(x) = \int\limits^{3x}_{-2} {sin(t)} \, dt[/tex]
Step 2: Differentiate
Chain Rule: [tex]\displaystyle F'(x) = \frac{d}{dx}[\int\limits^{3x}_{-2} {sin(t)} \, dt] \cdot \frac{d}{dx}[3x][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle F'(x) = \frac{d}{dx}[\int\limits^{3x}_{-2} {sin(t)} \, dt] \cdot 3\frac{d}{dx}[x][/tex]Basic Power Rule: [tex]\displaystyle F'(x) = \frac{d}{dx}[\int\limits^{3x}_{-2} {sin(t)} \, dt] \cdot 3x^{1 - 1}[/tex]Simplify: [tex]\displaystyle F'(x) = 3\frac{d}{dx}[\int\limits^{3x}_{-2} {sin(t)} \, dt][/tex]Integration Rule [Fundamental Theorem of Calculus 2]: [tex]\displaystyle F'(x) = 3sin(3x)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
find the area of the adjoining figure.
please help and find it
i really need it my exam is tomorrow
i will mark you the brainlliast
first lets find Area of triangle bellow
(SRT triangle):
FORMULA: (Base×height)/2
(18×5)/2=90/2=45 cm²
now lets find area of trapezoid (PQSR):
FORMULA: ((base+base)/2)×height
((18+20)/2)×4=19×4=76cm²
now lets add both of the figure's areas to get final answer:
45+76=121 cm²
area of figure is 121cm²
please mark❤️
The law of cosines is a2 +62 - 2abcosC = (2. Find the value of 2abcosC.
2
4
B
A
5
Answer:
[tex]2abcosC = 37[/tex]
Step-by-step explanation:
Given
[tex]a^2 + b^2 - 2abcosC = c^2[/tex]
Required
[tex]2abcosC[/tex]
[tex]a^2 + b^2 - 2abcosC = c^2[/tex]
Add [tex]2abcosC[/tex] to both sides
[tex]a^2 + b^2 - 2abcosC+2abcosC = c^2+2abcosC[/tex]
[tex]a^2 + b^2 = c^2+2abcosC[/tex]
Subtract [tex]c^2[/tex] from both sides
[tex]a^2 + b^2 -c^2= c^2 -c^2+2abcosC[/tex]
[tex]a^2 + b^2 -c^2= 2abcosC[/tex]
From the attachment:
[tex]a = 4[/tex] [tex]b = 5[/tex] and [tex]c = 2[/tex]
So, we have:
[tex]4^2 + 5^2 -2^2= 2abcosC[/tex]
[tex]16 + 25 -4= 2abcosC[/tex]
[tex]37= 2abcosC[/tex]
i.e.
[tex]2abcosC = 37[/tex]
Answer:
A. 37
Step-by-step explanation:
(a) The perimeter of a rectangular garden is 314 m.
If the length of the garden is 85 m, what is its width?
(b) The area of a rectangular window is 4800 cm
2
If the width of the window is 64 cm, what is its length?
Answer:72 for the garden and 75 for the window
Step-by-step explanation:
Can someone pretty please help me... it’s only 2 questions! :(
Answer:
9. C 10. C
Step-by-step explanation:
Please gimme brainliest
Answer: c for both
Step-by-step explanation:
Promote means support, and the “general welfare” is the general good of the people.
The Preambles of the constitution at the beginning of it, so it couldn’t be a a conclusion, and there were no indexes in the Constitution. It had to be a summary or an introduction, Ndola it’s an introduction, it did not explain everything in the document like a a bunch, but it did state that it was a constitution.
Also, the question end should with an, so it had to be an answer starting with a vowel, so one of the last two, since the last one I saw wrong, it had to be c.
Can anyone help me with these? It's a yes or no question...
Answer:
Yes
Step-by-step explanation:
If you insert the numbers it will turn out something like this:
5+6=11
2+18=20
And those are all true.
I hope this helps :)
Answer:
Yes it is
Step-by-step explanation:
x=1 y= 6
(5 × 1) + 6 = 11
(2×1) +(3×6) =20
A 29-m tall building casts a shadow . The distance from the top of the building to the top of the shadow is 32m. Find the length of the shadow.
Margo can purchase tile at a store for $.99 per tile and rent a tile saw for $10. At another store she can borrow the tile saw for free if she buys tiles there for $1.49 per tile. How many tiles mushy by for the cost to be the same at both stores?
Answer:
The indifference point is 20 tiles.
Step-by-step explanation:
First, we need to establish the total cost formulas for each store:
Store 1:
Total cost= 10 + 0.99*x
Store 2:
Total cost= 1.49*x
x= number of tiles
Now, we equal both formulas and isolate x:
10 + 0.99x = 1.49x
10= 0.5x
10/0.5=x
20=x
The indifference point is 20 tiles.
6 cm
8 cm
what’s the hypotenuse
Answer:
10 cm
Step-by-step explanation:
This is the Pythagorean triple 3, 4, 5, in which the two legs are multiples of 3 and 4, while the hypotenuse is a multiple of 5. Observing the given numbers it can be deduced that the second multiple of 5 is what is needed to complete this triple, therefor the hypotenuse must be 10 cm.
What is the solution set for the inequality.
t - 10 ≥ 7
A
{18, 19, 20, 21}
B
{17, 3, 14, 25}
C
{17, 20, 30, 44}
D
{8, 11, 15, 17}
Hope you get the right answer
Step-by-step explanation:
Will mark Brianliest !!!!!!! Please helppp!!!!!!!!!! Show your work correctly !!!!!!!!!!!!
two-base angle are equal
let take a base angle as x
2x + 98 = 1802x = 180 - 98x = 2/2x = 1help im confused!! i need to find the x
A cylinder and a cone have the same base and altitude. If the volume of the cone is 30 cubic inches, what is the volume of the cylinder?
Answer:
im not completely sure but I'd say 30
Step-by-step explanation:
well I'm not sure but if they have the same base and altitude you'd think they might have the same volume, but I'm not exactly sure
What is the sum of all prime numbers beetween 30 to 60?
Answer:
311
Step-by-step explanation:
Please give me brainliest and thank me
Answer:
311
Step-by-step explanation:
31+37+41+43+47+53+59=311
please mark me as brainliest, i'd really appreciate it!<3
3 There are 8 teams in the
recreational soccer league. Each
team is comprised of 9 fourth-
grade students and 5 fifth-grade
students. Which expression could
be used to find the total number of
students in the soccer league?
A. (8 + 9) * 5 =
B. (8 x 9) + 5 =
C. 8 + (9x5) =
D. 8 (9 + 5) =
Answer:
On each team there is the same number of teammates, the answer is D. 8 (9 + 5).
Step-by-step explanation:
If you add up the amount of teammates then multiply that by the number of teams.
Therefore, D. 8 (9 + 5) is the answer.
Carl earns $3.25 per hour walking his neighbor’s dogs. He walks them 1/3 of an hour in the morning and 1/2 of an hour in the afternoon.
a. How much time does Carl spend dog walking every day?
b. How much time does Carl spend dog walking in a week?
c. Ten minutes is equal to 1/6 of an hour. How many minutes does Carl work dog walking each week?
d. How much money does Carl earn each week?
Plz help I’ll appreciate it plz help
Answer:
x = 36
Step-by-step explanation:
Here, we want to get the value of x
As we can see on the markings, the base angle are equal
Thus, the other base angle is x too
mathematically, the sum of all the interior angles of a triangle = 180
thus;
3x + x + x = 180
5x = 180
x = 180/5
x = 36
Can someone please help me. It’s hard and I don’t understand.
9513 1404 393
Answer:
changes by 120 for each copyis 1800 if none are soldStep-by-step explanation:
Let's look at the second question first.
x is the number of copies Chau sells. If he doesn't sell any copies, then x = 0. To find Chau's pay, we use x=0 in the equation, and solve for y.
120×0 +1800 = y
0 +1800 = y
1800 = y
Chau's pay when he sells no copies is $1800.
__
If Chau sells 1 copy, then his pay is ...
120×1 +1800 = y = 1920 . . . . . . . use the equation with x = 1
The increase in Chau's pay is 1920 -1800 = 120.
Chau's pay changes by $120 for each copy he sells.
what percent of 18 is 24
SIDE NOTE:its not 75%
2019 like “I live my life in fast forward, but they haters wanna rewind me”
Um how is this related to homework?
Evaluate 7b-b when b=4
Thank you!!
Answer:
The correct answer is 24.
Step-by-step explanation:
What is the value of Angle 'a'?
a
47°
Answer:
133
Step-by-step explanation:
180-47=133
Answer: if the shape is a triangle, 180-47=133
if it is any other shape, 360-47=313
Step-by-step explanation:
Which angle number is adjacent to angle to MNJ?
Answer:
I think it is ACB
Step-by-step explanation:
Please don't come after me if i'm wrong
A hummingbird can flap its wings an average of 1800 times every 30 seconds. What is the rate of change of wing flaps?
3t+7=3t+6 pls help ...
Answer:
There are no values of t that make the equation true.
No solution
Step-by-step explanation: