The length of the ladder nearest hundredth of a foot is 23 feet.
We have given that,
An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 20 feet up.
The ladder makes an angle of [tex]77^{\circ}[/tex] the ground.
What is the sin ratio?[tex]sin(\theta)=\frac{perpendicular \ side}{hypotenous}[/tex]
Therefore we get,
[tex]\implies\frac{22}{H} =sin(77)[/tex]
[tex]\implies H=22/sin(77)[/tex]
[tex]\implies 22.59ft\\\\=23ft[/tex]
Therefore, The length of the ladder nearest hundredth of a foot is 23 feet.
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Solve the equation for all values of x by completing the square.
x2 + 8.0 + 15 = 0
Answer:
x= -3
x= -5
Step-by-step explanation:
x^2 + 8x + 15 = 0
find which 2 numbers when multiplied equal 15 and when added equal 8
they are 3 and 5
(x+3)(x+5)
x+3 =0
x+5=0
x= -3
x= -5
I need help on 11A, I got the answer as 5.046cm but the book says it's 8.37 cm
Answer:
[tex]\textsf{Area of a triangle}=\dfrac{1}{2} ab \sin C[/tex]
(where [tex]a[/tex] and [tex]b[/tex] are the sides, and [tex]C[/tex] is the included angle)
[tex]\textsf{Area of a sector}= \dfrac{\theta}{360} \pi r^2[/tex]
(where [tex]\theta[/tex] is the angle in degrees and [tex]r[/tex] is the radius)
Therefore, using the above formulas:
[tex]\begin{aligned}\textsf{Area of segment } \rm (A) & = \textsf{area of sector}- \textsf{area of triangle}\\& = \dfrac{\theta}{360} \pi r^2 - \dfrac{1}{2}r^2 \sin \theta\\\end{aligned}[/tex]
Given:
[tex]\theta[/tex] = 90°A = 20 cm²Substitute the given values into the formula and solve for r:
[tex]\begin{aligned}\implies 20 & = \dfrac{90}{360} \pi r^2 - \dfrac{1}{2}r^2 \sin 90\\\\20 & = \dfrac{1}{4} \pi r^2 - \dfrac{1}{2}r^2 (1)\\\\20 & = \left(\dfrac{1}{4} \pi -\dfrac{1}{2}\right)r^2\\\\20 & = \left(\dfrac{\pi -2}{4}\right)r^2\\\\r^2 & = 20\left(\dfrac{4}{\pi -2}\right)\\\\r^2 & =\dfrac{80}{\pi-2}\\\\r & =\sqrt{\dfrac{80}{\pi-2}}\\\\r & = 8.37\: \sf (2\:dp)\end{aligned}[/tex]
23h−13h+11=8
please help me
Answer:
h = - [tex]\frac{3}{10}[/tex]
Step-by-step explanation:
23h - 13h + 11 = 8 ( subtract 11 from both sides )
10h = - 3 ( divide both sides by 10 )
h = - [tex]\frac{3}{10}[/tex]
Your answer(s) will be:
0.3 (Decimal Form)
or
3/10 (Fraction Form)
i need to find the value of each variable in the following parallelograms
201 ft
15 ft 6
200 ft
Find the perimeter of the triangle
Answer: 6416
Step-by-step explanation:
The perimeter of this triangle is 416 centimeters
How much work is done by a man who uses a force of 7 Newtons to push a box 3 meters across the room?
Answer: 21 J (Joules) of work done.
Step-by-step explanation:
W = Fs, where F is force and s is displacement.
F = 7 N
s = 3 m
W = 7 N * 3 m = 21 N*m, or 21 J
21 N/m of work is done by a man to push the box.
What is Work done?The displacement plus a component of the applied force of the item in the direction of displacement make up the work done by a force. Work is accomplished when we push a block with some force; the body moves more quickly.
We have,
Force = 7 Newton
Distance = 3 m
We know, Work done = Force x distance
Work done = 7 x 3
Work done = 21 N/m
Thus, the amount work done is 21 N/m.
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What is the median?
Answer:
6
Step-by-step explanation:To find the median, first order your data. Then calculate the middle position based on n, the number of values in your data set. If n is an odd number, the median lies at the position (n + 1) / 2. If n is an even number, the median is the mean of the values at positions n / 2 and (n / 2) + 1.
Answer:
6
Step-by-step explanation:
How much paper is used for the label on the can of peas?
Answer:
here
Step-by-step explanation:
find the circumference of the lid (this is like a side length of a rectangle)
2*pi*2= 12.566in
Then multiply by 3 (the other side length)
12.566*3= 37.7in squared :)
Use each table to find the requested ratio. ITEM BANK: Move to Bottom
1:2 1:4 1:5 2:1 4:1 5:1
Answer:
See below ~
Step-by-step explanation:
Table 1
⇒ Side length : Perimeter = 1 : 4
⇒ Perimeter : Side length = 4 : 1
Table 2
⇒ Radius : Diameter = 1 : 2
⇒ Diameter : Radius = 2 : 1
Table 3
⇒ Number of people : Number of tables = 5 : 1
⇒ Number of tables : Number of people = 1 : 5
Please Help! Cube Roots
3 square root 56 + 3 square root 189
Step-by-step explanation:
cubic root(56) + cubic root(189) =
= cubic root(7×8) + cubic root(27×7) =
= 2×cubic root(7) + 3×cubic root(7) = 5×cubic root(7) =
= 9.564655914...
What is the area, in square meters, of the shaded part of the rectangle below?
Answer:
45.5 m²
Step-by-step explanation:
Area (Shaded) = Area (Rectangle) - Area (Trapezoid)
Area (Shaded) = lb - 1/2 x (a + b) x hArea (Shaded) = 17 × 13 - 1/2 × (10 + 17) × 13Area (Shaded) = 13 (17 - 27/2)Area (Shaded) = 13 × 7/2Area (Shaded) = 91/2Area (Shaded) = 45.5 m²Area of trapezoid:-
1/2(sum of parallel side)×Height1/2(10+17)(13)1/2(27)(13)13.5(13)175.5m²Area of triangle:-
1/2BH1/2(13)(17-10)1/2(13)(7)91/245.5m²Which part is shaded not said so both shaded regions area calculated
Cscx=cscx+secx/1+tanx
Answer:
[tex]\csc \left(x\right)=\frac{\csc \left(x\right)+\sec \left(x\right)}{1+\tan \left(x\right)}[/tex]
[tex]=\frac{1}{\sin \left(x\right)}[/tex] (expressed with sine and cosine)
[tex]\frac{1}{\sin \left(x\right)}=\csc \left(x\right)[/tex]
[tex]=\csc \left(x\right)[/tex]
Therefore, the identity has been proven true.
Please help me on this!
The positive integer for which g(x) first exceeds f(x) is 178 according to the number line.
What is the function of f(x)?The function f of (x) is used to denote a linear algebra that can be represented on the graph.
Given that:
f(x) = 2x + 15[tex]\mathbf{g(x) = 11(1.02)^x}[/tex]We are to determine a positive integer for which g(x) first exceeds f(x). Using the following option;
f(x) = 2(371) + 15 = 757g(x) = 11(1.02)³⁷¹ = 17063.04f(x) = 2(177) + 15 = 369g(x) = 11(1.02)¹⁷⁷ = 366.11f(x) = 2(370) + 15 = 755g(x) = 11(1.02)³⁷⁰ = 16728.47f(x) = 2(178) + 15 = 371g(x) = 11(1.02)¹⁷⁸ = 373Therefore, we can conclude that the positive integer for which g(x) first exceeds f(x) is 178 according to the number line.
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Jamie drove to the beach. She started driving at 11:50 a.m. It took her 4 hours and 25 minutes to get to the beach.
Which clock shows the time Jamie arrived at the beach?
What is the decimal that is grater than 3/10 and less than 2/5.
The options are 0.32 , 0.035, 0.4 , 0.24
Answer:
0.32
Step-by-step explanation:
3/10=0.3
2/5=0.4
0.32 is between these two numbers.
Hope this Helps
if f(c)=2x^2-x, find f(-4) - f(9)
Answer:
-13f
Simplify by combining the sum of 4 + 9 with the term "f" and assume integers will be negative.for each pair of functions, find f(g(x)) and g (f(x)).
1. f(x)= x^3 g(x)= 2x
2. f(x)= 3x+5 g(x)= 4x-2
3. f(x)= 2x+5 g(x)= x^2+2
I'd like an answer and explanation pleasee
Answer:
its 3
Step-by-step explanation:
id ont know the formula but im certain im a very smart 6th grader!
What is the length of the hypotenuse of the triangle when x=14
The length of the hypotenuse will be equal to H=122.25 when value of x=14.
What is pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal the square of the sum of the other two sides.
It is given that:
Value of x=14
The perpendicular is =6x+5=6x14+5=89
The base is =6x=84
So by using the Pythagorean theorem:-
[tex]H^2=P^2+B^2\\\\\\H^2=89^2+84^2\\\\\\H=\sqrt{89^2+84^2}\\\\\[/tex]
Hence the value of hypotenuse will be H=122.25
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Consider the function. F(x, y) = 9x2y3 (a) find 3 f(x, y) dx
The integration of the function f(x, y) = 2x²y³ from 0 to 3 with respect to x is 27y³.
What is integration?It is the reverse of differentiation.
The function f(x, y) is given below.
f(x, y) = 2x²y³
Then the integration of the function from 0 to 3 with respect to x.
[tex]\begin{aligned} \rm \int_{0}^{3}f(x, y)dx &= \rm \int_{0}^{3}9x^2y^3 dx \\\\&= \rm 9y^3 \ \int_{0}^{3} x^2 dx\\\\&= \rm 9y^3 (\dfrac{x^3}{3}) _{0}^{3}\\\\&= \rm3y^3 (3^3 - 0 ^3)\\\\&= \rm 3y^3 \times 9\\\\&= \rm 27y^3 \end{aligned}[/tex]
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Name the following triangle: 11in 77˚ 11in
Answer:
an acute triangle im guessing ik its not a right and the degrees and the inches are small So it can't be absolute thats just what i was thinking but i might be wrong
Step-by-step explanation:
14. Find the area under the normal curve to the right of z = 1.84.
A. 0.9671
B. 0.0329
C. 0.2005
D. 0.7995
Answer:
B is the correct answer from my understanding
Step-by-step explanation:
help me pls it will help me alot
Answer:
h > 1600
Step-by-step explanation:
Since the elevation at which it is difficult for Matt to breathe (h) has to be *higher* than 1600, h is greater than 1600.
how do i do this I forgot how to do this and I have a test tomorrow
Answer:
Step-by-step explanation:
(1 + 11)/(-2+5)= 12/3=4
y + 11 = 4(x + 5)
y + 11 = 4x + 20
y = 4x + 9
how many times greater is the vuale in 4 in 547 than 4 in 84
Answer:
10 times
Step-by-step explanation:
4 in 547 is equal to 40
4 in 84 is equal to 4
When you separate that number into smaller parts
Ex: 547 = 500 + 40 + 7
Mrs. Eaton's dass is participating in the "Box Teps for Education campaign. On the first day, her
class collected 2 lops. On the third day, her dass collected 8 tope. Let D represent each collection
day and N represent the number of tops collected on that day.
Based on the situation, John daims the number of tops colected can be modeled by an exponential
function. Riley disagrees and claims the number of tops can be modeled with a linear function. What
Is the number of tops collected on the abath day based on the exponential model? What is the
number of tops collected on the sixth day based on the linear model?
Number of tops on 6th day based on exponential model:
Number of tops on the 6th day based on the linear model:
The number of tops on the 6th day based on the exponential model is 64, and the number of tops on the 6th day based on the linear model is 17.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]
where a is a constant and a>1
First day class collected = 2 tops
Third day class collected = 8 tops
The exponential function can be modelled:
[tex]\rm D(N) = 2^N[/tex]
D(1) = 2 (first day)
D(3) = 8 (third day)
D(6) = 64 (sixth day)
The linear function can be modeled:
D(N) = 3N -1
D(1) = 2 (first day)
D(3) = 8 (third day)
D(6) = 17 (sixth day)
Thus, the number of tops on 6th day based on exponential model is 64, and the number of tops on the 6th day based on the linear model is 17.
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please help asap!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
30.96
Step-by-step explanation:
First you must find the diameter of the circle which is 12
Then you must use the formula A=πr²
So it should be = to A = 3.14 ×144 which is 30.96
[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{✰\:Notes }}}[/tex]
★ Concept ★➣ A square with sides 12m➣then a circle in between➣nd it's diameter is 12m bcz of side of square is equal to radius➣soo here things we to find is the area of circle and then square then by subtracting their will give us the area of shaded part in image[tex] \rule{70mm}{2.9pt}[/tex]
[tex] \large\underline{ \boxed{ \sf{✰\: formule\: used\:✰ }}}[/tex]
[tex]{ \boxed{✟\underline{ \boxed{ \sf{\: Area \: of \: circle = \pi {r}^{2} \: }}}✟}}[/tex]
[tex]{ \boxed{✟\underline{ \boxed{ \sf{\: Area \: of \: square = side \times side \: or \: ( {s}^{2}) \: }}}✟}}[/tex]
[tex] \rule{70mm}{2.9pt}[/tex]
✛ 1st taking out the the area of circle✛
➣ value of pi = 3.14➣ diameter = 12m (have to find radius we know that radius is half of diameter) which is[tex] \qquad \rm{➛ \: radius(r) = \frac{12}{2} } \\ \\ \qquad \rm{➛ \: radius(r) = \frac{ \cancel{12}}{ \cancel2} } \\ \\ \qquad \rm{➛ \: radius(r) =6m}[/tex]
★ Hence radius of circle is 6m★ let's substitute values now ★[tex] \\ \qquad \rm{➛Area \: of \: circle = 3.14 \times {6}^{2} \:} \\ \\ \qquad \rm{➛Area \: of \: circle = \:3.14 \times 36} \\ \\ \qquad \rm{➛Area \: of \: circle = \:113.04 {m}^{2} }[/tex]
[tex] \rule{70mm}{2.9pt}[/tex]
✛ now finding the area of square✛
➣ here two given side are 12m★ let's substitute values now ★[tex]\\ \qquad \rm{➛Area \: of \:square = 12×12} \\ \\ \\ \qquad \rm{➛Area \: of \:square = 144 {m}^{2} }[/tex]
✞ Now according to given ques we have to find area of shaded part soo let's solve ! ✞[tex]\\ \rm{➛Area \: of \:shaded \: part = \: area \: of \: circle - area \: of \: squre} \\ [/tex]
★ Let's substitute value ★
[tex]\\ \rm{➛Area \: of \:shaded \: part =113.04-144} \\ \\ \qquad \rm{➛Area \: of \:shaded \: part =30.96 {m}^{2} }[/tex]
[tex] \rule{70mm}{2.9pt}[/tex]
★ Hence area of shaded part =
[tex]{ \boxed{✜\underline{ \boxed{ \sf{ \: 30.96 {m}^{2} \green✓\: }}}✜}}[/tex]
★ note here we neglect minus (-)
[tex] \rule{70mm}{2.9pt}[/tex]
Hope it helps !
evaluate the expression [tex](-0.3)^4[/tex]
the value of the expression is
The value of the expressions (-0.3)⁴ equal to 0.0081.
What is a mathematical expression?A mathematical expression is the representation of numbers in the form of powers or mathematical signs.
Here we have the (-0.3)⁴
Now by evaluating the expression we will get:
(-0.3)⁴=(-0.3x-0.3x-0.3x-0.3)
Hence the value of the given expression will be 0.0081
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Evaluate:
(34x3)+7+ 24/6
Answer: 113 ( 34x3+11
Step-by-step explanation:
Step 1- Divide the numbers34x 3 on top + 7 + 24/6
34 x 3 on top + 7 = 4
Step 2- Add the numbers34 x 3 on top + 7 + 4
34 x 3 on top + 11
34 x 3 on top + 11
Andrea recorded the points she scored in her last eight basketball games:
28, 32, 47, 16, 40, 35, 38, 54.
Give an example of a statistical question you could answer using the mean or the median. Explain your reasoning.
Answer:
You could ask what her average score is using mean (which is 36.25)
Step-by-step explanation:
Answer:
You could ask what her average score is using mean (which is 36.25)
Step-by-step explanation:
Four transformations of the Function f(x)=2^x are given below.
For each transformation drag the expression that shows the result of that transformation to the box under it.
After applying operations between functions, we find the following four transformations for the function [tex]f(x) = 2^{x}[/tex]:
a) 6 · f(x) - [tex]g(x) = 6 \cdot 2^{x}[/tex]
b) f(6 · x) - [tex]g(x) = 2^{6\cdot x}[/tex]/[tex]g(x) = 2^{6}\cdot f(x)[/tex]
c) f(x + 6) - [tex]g(x) = 2^{x+6}[/tex]/[tex]g(x) = 2^{6}\cdot f(x)[/tex]
d) f(x) + 6 - [tex]g(x) = 2^{x}+6[/tex]
How to determine the transformations of a function
Mathematically speaking, transformations are operations applied on a function such that its domain or range are altered. There are five operations for functions:
AdditionSubtractionMultiplicationDivisionCompositionLet suppose that [tex]f(x) = 2^{x}[/tex], the images of this function are, respectively:
a) 6 · f(x) - Multiplication between two functions
[tex]g(x) = 6 \cdot 2^{x}[/tex]
b) f(6 · x) - Composition between two functions
[tex]g(x) = 2^{6\cdot x}[/tex]
[tex]g(x) = (2^{x})^{6}[/tex]
[tex]g(x) = (f(x))^{6}[/tex]
c) f(x + 6) - Composition between two functions
[tex]g(x) = 2^{x+6}[/tex]
[tex]g(x) = 2^{x}\cdot 2^{6}[/tex]
[tex]g(x) = 2^{6}\cdot 2^{x}[/tex]
[tex]g(x) = 2^{6}\cdot f(x)[/tex]
d) f(x) + 6 - Addition between two functions
[tex]g(x) = 2^{x}+6[/tex]
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