Given:
Length of the ladder = 20 ft
Distance between base of the ladder and wall = 4 ft
To find:
The angle measure of the ladder to the ground to the nearest degree.
Solution:
Ladder is the hypotenuse of a right triangle. Here, we have,
Hypotenuse = 20 ft
Base = 4 ft
In a right angle triangle,
[tex]\cos \theta=\dfrac{Base}{Hypotenuse}[/tex]
[tex]\cos \theta=\dfrac{4}{20}[/tex]
[tex]\cos \theta=\dfrac{1}{5}[/tex]
Taking cos inverse on both sides, we get
[tex] \theta=\cos^{-1}\dfrac{1}{5}[/tex]
[tex] \theta=78.46304^\circ[/tex]
[tex] \theta\approx 78^\circ[/tex]
Therefore, the correct option is A.
Pls help
An airplane can Seat up to 175 passengers the airplane has already sold 87 tickets for a flight on the airplane which graph represents the solution to the inequality that find a number of tickets the air line can still sell
Answer:
the third graph is the answer
Answer:
It's A.
Step-by-step explanation:
Since 175-87 is 88, there is 88 or less available tickets left. So it is A.
Hope this helps.
Please help :(((((((((((((
16 is what percent less than 489?
hope this helps. Please mark me brainliest
Answer:
3.27
16 is what percent of 489? = 3.27.
If I had 15 acres and I got $237,000 for it, how much is each acre?
For the price per acre do 237,000 / 15 = $15800 per acre
Question 5 of 27
What is the measure of ZC in the parallelogram shown?
Answer:
C.35⁰
Step-by-step explanation:
C= 180⁰-145⁰= 35⁰
15. In the diagram AB is parallel to CD.
Calculate the value of a.
NOT TO
SCALE
Step-by-step explanation:
sorry can't help u because I can't see any picture
If the side lengths of a cube are 15 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form? (2 points)
Group of answer choices
15 ⋅ 15 ⋅ 15
15 ⋅ 3
315
153
The expression to represent the volume of the cube in exponential form is 15^3
How to write the expression to represent the volume of the cube in exponential form?The length is given as:
Length = 15 feet
The volume of the cube is calculated as:
Volume = Length^3
So, we have:
Volume = 15^3
Hence, the expression to represent the volume of the cube in exponential form is 15^3
Read more about expressions at:
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What is the area of the polygon given below?
ANSWER:
B. 525 square units
SOLUTION:S= 27+14+9×14+3×7
S= 525
[tex]{{hope it helps}}}[/tex]
Answer:
Option B 525 Square units
Step-by-step explanation:
7x3=21
27x14=378
14x9=126
21+378+126=525
Can someone help with this and help me understand this as well?
Answer:
<K ≅ <N
Step-by-step explanation:
JKL ≅ MNP
That means the angles are the same
<J ≅< M
<K ≅ <N
<L ≅<P
The sides are also congruent
JK ≅ MN
KL ≅ NP
JL ≅ MP
Please help
Sketch the graph of y = (x – 1)2 + 2 and identify the axis of symmetry.
Answer:
The axis of symmetry is (0,0)
Step-by-step explanation:
This is the picture
Troy spends $9.75 on chicken feed
each week. He has 48 chickens and
each chicken lays one egg a day. At
the end of the week, Troy keeps one
dozen eggs for himself and sells the
rest at the farmer's market for $4.00 a
dozen. What is Troy's weekly profit?
A $98.25
B $102.25
© $112
D $192
Answer:
A
Step-by-step explanation:
Total eggs in lay in one week = 48 * 7 = 336
total eggs sold = 336 - 12 = 324
Total dozen = 324 : 12 = 27
Total profit = 27 * 4 = $108
Profit without chicken feed = 108 - 9.75 = $98.25
A person deposited Rs. 80,000 in bank 'P' for 2 years at the rate of 10% annual compound interest. But after one year bank has changed the policy and decided to pay semi-annual compound interest at the same rate. What is the percentage difference between compound interests of the first year and second year? Give reason with calculation:
Answer:
compound interest in year 2 is 12.75% than compound interest in year 1. This is because semi annual compounding yield a higher compound interest
Step-by-step explanation:
compound interest = future value - present value
The formula for calculating future value:
FV = P (1 + r/m)^nm
FV = Future value
P = Present value
R = interest rate
N = number of years
m = number of compounding
compound value in the first year = 80,000(1.1)^1 = 88,000
compound interest = 88,000 - 80,000 = 8,000
compound interest in the second year = 88,000(1 + 0.01/2)^2 = 97,020
compound interest = 97,020 - 88,000 = 9020
Percentage change = (9020 / 8,000) - 1 = 12.75%
a freight elevator has a weight limit of 2 tons. Each crate that is loaded weighs 80 pounds. What is the greatest number of crates that can be loaded on to the elevator?
25
500
250
50
Please help meh TvT
Answer:
50 crates
Step-by-step explanation:
First we need to convert 2 tons into pounds; 2 short tons = 4000 pounds, so the greatest number of crates that can be loaded onto the elevator is 4000 Hope this helps >:D
What type of function is represented by the table of values below? X:1,2,3,4,5 X:4,8,12,16,20 A.cubic B.exponential C.quadratic D. Linear
Answer:
c
Step-by-step explanation:
Parallel maze puzzle
Answers:
d) verticalc) alternate interiorf) supplementarye) alternate exteriorg) correspondinge) alternate exteriorf) supplementaryc) alternate interiore) alternate exteriorLetters 'a', b, and h are never used.
Letters c and f show up twice each; e shows up 3 times.
=====================================================
Explanations:
Angles 1 and 2 are vertical angles because they are opposite one another in this X configuration. Vertical angles are always congruent.These angles are alternate interior angles because they are inside the parallel lines (hence the "interior") and they are on alternating sides of the transversal cut.The two angles shown here form a straight line, so that's what makes them supplementary. Supplementary angles add to 180 degrees.Angle 4 and angle 5 are on alternating sides of the transversal, but this time they are outside the parallel lines. So that's why we go for alternate exterior this time. Angles 5 and 6 are in the same southwest corner of each four-corner configuration, which makes them corresponding angles.It's the same idea as problem 4Same idea as problem 3.Same idea as problem 2.Same idea as problems 4 and 6.---------------
None of the angle pairs mentioned are consecutive interior angles. These types of angles are on the same side of the transversal, and inside the parallel lines. So we never use option 'a'. We cross off option h as well for pretty much identical reasoning. Options 'a' and h are the same thing, just slightly different wording.
We cross off option b as well because none of the angles add up to 90 degrees.
The diagram below represents the net of a triangular prism.
3
6 cm
12 cm
6 cm
8 cm
10 cm
6 cm
(not drawn to scale]
What is the surface area of the triangular prism?
A
288 square centimeters
B
312 square centimeters
с
336 square centimeters
D
368 square centimeters
Answer:
yes
Step-by-step explanation:
Answer:
336cm2
Step-by-step explanation:
The diagram is divided ninto 5 parts that is rectangles ABCD, CHGD, GFEH and triangles CIH and DGJ.
Area of rectangle ABCD= lxb
=12x6=72cm2
Area rectangle CDHG=lxb
12x8=96cm2
Area rectangle HGFE= lxb
=10x12=120cm2
Area of triangles CIH and DIG= 2x1/2xbxh
=6x8=48cm2
Surface area of the triangular prism=Area of rectangle ABCD+Area rectangle CDHG+Area rectangle HGFE+Area of triangles CIH and DIG
72+96+120+48=336cm2
One piece of wood has a rectangular bottom that is 30 cm long and 56 mm wide. The block is said to weigh 80 N. Calculate the pressure that the block exerts on the surface
Answer:
4762 N/m^2
Step-by-step explanation:
Find area.
30x5.6=168
Convert to m^2
168cm^2=0.0168m^2
Use pressure formula to get answer
P=F/A
P=80/0.0168
P=4762 N/m^2
logo y = x means: log base b of y equals x.
True
False
If you meant to write [tex]\log_{b}(y) = x[/tex] then the statement is true.
As a more concrete example, something like [tex]\log_3(81) = 4[/tex] would be read out as "log base 3 of 81 is equal to 4".
Find the exact surface area of the figure.
Otto used 6 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used
to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the
values of x and y?
y=6x, x is any integer greater than or equal to 0, and y is an integer greater than or equal to 6.
O y=6x, x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6.
y=x+6; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 6.
O y=x+6; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6.
Answer:
y = x + 6
x is any real number greater than or equal to 0,
and y is any real number greater than or equal to 6.
The formula to determine the value of y, or the total amount of flour that Otto used in the recipe, is y=6x.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
The correct equation is y = 6 + x, where y is the total amount of flour and x is the amount of white flour used.
The constraints on the values of x and y are x ≥ 0 (because you cannot use negative flour) and y ≥ 6 (because the minimum amount of flour used is 6 cups, and that is when x = 0).
Any real number more than or equal to 0 and any real number higher than or equal to 6 are the restrictions on the values of x and y, respectively.
So the correct answer is: y = x + 6; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6.
Learn more about algebraic Expression here:
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PLEASE ANSWER ASAP
expand and simplify the following:
a) (√6+√3)(√6-√3) b)(√5-√2)(√2+√5)
Answer:
[tex]{ \bf{a).}} \\ { \tt{( \sqrt{6} + \sqrt{3} )( \sqrt{6} - \sqrt{3}) }} \\ { \tt{ = ( { \sqrt{6} )}^{2} - {( \sqrt{3}) }^{2} }} \\ { \tt{ = 6 - 3}} \\ { \tt{ = 3}} \\ \\ { \bf{b).}} \\ { \tt{( \sqrt{5} - \sqrt{2})( \sqrt{2} + \sqrt{5} )}} \\ { \tt{ = ( { \sqrt{5} }^{2}) - { (\sqrt{2} }^{2}) }} \\ { \tt{ = 5 - 2}} \\ { \tt{ = 3}}[/tex]
Answer:
(6-3)(5-2)=3×3=9
Step-by-step explanation:
[tex]x ^{2} - {y}^{2} = (x - y)(x + y)[/tex]
[tex]( \sqrt{6} - \sqrt{3} )( \sqrt{6} + \sqrt{3} ) = ( { \sqrt{6} }^{2} - { \sqrt{3} }^{2} ) = 6 - 3 = 3[/tex]
Please Helppp!! 50 Points
Compute the sum
10235
I just typed it in a calculator
the answer is in the above image
Answer:
Step-by-step explanation:
5* (2⁰ + 2¹ + 2 ²+ 2³+ ........+ 2¹⁰)
Sum of geometric series = [tex]a*\frac{r^{n}-1}{r-1}[/tex]
a -> first term = 1
r- ratio = 2
n --> number of terms = 11
5* (2⁰ + 2¹ + 2 ²+ 2³+ ........+ 2¹⁰)=
[tex]5*[1*\frac{2^{11}-1}{2-1}]\\\\=5 *[1*(2048-1)]\\\\= 5 * 2047\\= 10235[/tex]
Which is equivalent to (square root 10) ^3/4?
Answer:
2nd option
Step-by-step explanation:
Using the rule of exponents/ radicals
[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex](\sqrt[n]{a}) ^{m}[/tex] , then
[tex]\sqrt{10} ^{\frac{3x}{4} }[/tex]
= [tex](\sqrt[4]{10}) ^{3x}[/tex]
Complete parallel side 2
Height = 8mm
parallel side 1= 5mm
parallel side 2=?
Area = 72 mm
Step-by-step explanation:
Assume length of side 2 = L
Area of parallelogram is Height x L
So, 72 = 8 x L
L = 9
In 2 Year 6 classes, 2/5 of the children are girls. There are 39 boys. How many children are there in the class?
Solve the following system of equations.
\begin{aligned} -5x+4y &= 3\\\\ x&=2y-15 \end{aligned}
−5x+4y
x
=3
=2y−15
x=?
y=?
Step-by-step explanation:
The first president of the United States was
[tex]\begin{aligned} -5x+4y &= 3\\\\ x&=2y-15 \end{aligned}[/tex]
Answer:
x=9
y=12
Step-by-step explanation:
mmmmm hey can you explain my math?
Answer:On June 17
the explanation is in the picture
the sum of ages of two brothers A and B is 35 A is two thirds of B's age find their ages
Answer:
let the ages of the brothers be 2x and 3x
2x +3x=35
5x=35
x=35÷5
x=7
now,
A=2x=2×7=14
B=3x=3×7=21
this is the answer
Move point b some more as you move point b the angle formed between ab and cd varies if you want to make an perpendicular to cd what do you need to do explain in terms of BEC
Answer:
Following are the response to the given question:
Step-by-step explanation:
Move b a bit further if the angle between cd and ab changes when you move b if you want to make a perpendicular point to cd The angle BEC is 90 ° for making the AB line perpendicular to the line CD to transfer point B to the angle between the two lines.
prove that: sin8A/1-cos8A=cot4A
Step-by-step explanation:
Recall the identity
[tex]\tan \frac{A}{2}= \dfrac{1 - \cos A}{\sin A}[/tex]
We can see that
[tex]\dfrac{\sin 8A}{1 - \cos 8A} = \dfrac{1}{\tan 4A}= \cot 4A[/tex]