The height of the tree to the nearest hundredth is 122.49 feet
Application of SOH CAH TOAThese are used to determine the sides and angle of a right triangle
Given
Angle of elevation= 54 degrees
Base distance = 89 feet
Required
Height of tree
Using the SOH CAH TOA
tan 54 = H/89
H = 89tan54
H = 122.49
Hence the height of the tree to the nearest hundredth is 122.49 feet
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Aisha has a piece of string that she cuts into smaller pieces. This line plot shows the length of each piece. Juan has a piece of string that is 12 as long as Aisha's seventh-longest piece. (Note: The problem states the seventh-longest piece, not the seventh-longest length.)
How long is Juan's piece of string?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
2 5/8 inches
Step-by-step explanation:
There are 2 pieces 5 3/4 inches long.
There is 1 piece 5 1/2 inches long.
There are 4 pieces 5 1/4 inches long.
The seventh longest piece is one of the pieces measuring 5 1/4 inches.
Juan's piece is 1/2 as long as 5 1/4 inches.
1/2 × 5 1/4 inches = 1/2 × 21/4 = 21/8 inches = (16/8 + 5/8) = 2 5/8 inches
A number x is at least 5 and is at most 8
Answer:
[tex]5 \leqslant x \leqslant 8[/tex]
Over the last 3 months, Janet exercised a total of 101 hours. She exercised 4 hours more during the second month than the first month. In the third month, she exercised 3 hours less than the second month.
Create an equation that represents this situation, where h represents the number of hours Janet exercised during the first month.
In 1st month let she exercised h hours
in second month she exercised h+4 hours
in third month she exercised h+4-3=h+1 hours
Now
h+h+4+h+1=1013h+5=1013h=96h=32hoursAnswer:
Let's say the unknown variable is h
In 1st month let she exercised h hours
in the 2nd month she exercised h+4 hours
in the 3rd month she exercised h+4-3=h+1 hours
Now, to display the sequence:
h+h+4+h+1=101
3h+5=101
3h=96
h=32hours
A music company offers a loan to buy a drum set for $1800.
-15.25% simple interest
-Equal monthly payment for 4 years.
What is the monthly payment?
The monthly payment is $____
Using it's formula, it is found that the value of the monthly payment for the loan to buy the drum set is of $50.32.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.In this problem, the parameters are given as follows:
P = 1800, r = 0.1525, n = 4 x 12 = 48.
Hence:
r/12 = 0.1525/12 = 0.01270833.
Hence, the monthly payments will be of:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 1800\frac{0.01270833(1 + 0.01270833)^{48}}{(1 + 0.01270833)^{48} - 1}[/tex]
A = 50.32.
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Work out the area of this circle.
Take pi to be 3.142 and give your answer in 2 decimal places.
Answer: 63.63 m²
Explanation:
Area of circle:
π(radius)²Here given:
radius: (diameter/2) = (9/2) = 4.5 m
π should be taken as 3.142
So area of circle:
3.142(4.5)² = 63.6255 ≈ 63.63 (rounded to two decimal place)Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the area of this circle.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
→ [tex]\bf{Area_{circle}=\pi r^{2}}[/tex]
Notice that we are asked to use 3.142 for [tex]\pi[/tex] (pi).
The radius isn't given to us; what we have instead is...the diameter.
To find the radius, we divide the diameter by 2.
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{\bf{To\;find\;the\;radius,\;we\;divide\;the\;diameter\;by\;2}}[/tex]
Thus, the radius is
[tex]\bf{9\div2=4.5}[/tex]
Now substitute the values (3.142 for pi and 4.5 for r):
[tex]\bf{A=3.142\times4.5^{2} }[/tex]
Simplifying,
[tex]\bf{A=3.142\times20.25}[/tex]
Simplifying,
[tex]\bf{A=63.6255\:m}[/tex]
Rounding to 2 decimal places (D.P.):
[tex]\bf{A=63.63\:m}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
~Just a smiley person helping fellow students :)
If set A contains four distinct numbers and set B contains seven distinct letters, how many elements are in (A U B)?
There are 11 elements are in (A U B)
How to determine the number of elements?The given parameters are:
n(A) = 4
n(B) = 7
The number of elements in (A U B) is calculated using:
n(A U B) = n(A) +n(B) - n(A U B)
Given that the sets have distincts elements, we have:
n(A U B) = 4 + 7 - 0
Evaluate
n(A U B) = 11
Hence, there are 11 elements are in (A U B)
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Answer: There are 11 elements are in (A U B)
Step-by-step explanation:
A rectangular patio has a length of 12 1\2 feet and an area of 103 1\8 square feet. What is the width of the patio?
Answer:
8.25 feet
Step-by-step explanation:
to find the width, you divide the area by the length
103 1/8 / 12 1/2 = 8.25
Give brainliest, please!
Hope this helps :)
In the following exercises, translate into an equation and solve
Kindergarten Connie’s kindergarten class has 24 children. She wants them to get into 4 equal groups. How many children will she put in each group?
Answer: 6 children
Step-by-step explanation:
Given:
Children - 24
Groups - 4
Number of children per group - x
Solve:
24 ÷ 4 = x
x = 6
Hope it helps!!! Please mark as brainliest. Thanks :D
Thank you for your help. The question is in the screenshot
Answer:
Hi,
Step-by-step explanation:
Using the pythagorean theorem , let's calculate the apothem of a side:
a²=26²-10²=57=24²
Area of a side: 24*10*2/2=240 (ft²)
Lateral area=240*4=960(ft²)
Area of the base: 20²=400 (ft²)
Total area=1360(ft²)
p and q are complex numbers such that |p|=7√3 and |p+q|=12√2. On what interval must |q| fall on?
The interval where |q| will fall will be[ 12√2−7√3,∞ ).
What are complex numbers?A complex number is an element of a number system that contains the real numbers and a specific element.
In this case, p and q are complex numbers such that |p|=7√3 and |p+q|=12√2. The interval where |q| will fall will be[ 12√2−7√3,∞ ).
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Please answer quick. Will mark whoever is first brainliest. The x intercept of the line is either A. (5,0) or B. (10,0) and it’s Y intercept is either A. (0,1/20) or B (0,20)
Answer:#1 A, #2 B
Step-by-step explanation:
Heres the proof
The production supervisor at a particular office products company finds that it takes 3 hours to manufacture each table for one of its special dining room sets. Each
chair
takes 8 hours to manufacture. A total of 6000 hours is available to produce tables and chairs of this style. The linear equation that models this situation is
3x+8y=6000, where x represents the number of tables produced and y the number of chairs produced.
a. Complete the ordered pair solution (0.) of this equation. Describe the manufacturing situation that corresponds to this solution.
The ordered pair is (0…)
The ordered pairs of the equation are
0 tables, 750 chairs2000 tables. 0 chairsHow to find the ordered pairs of the equationThe equation is given as
3x + 8y = 6000
We have x = number of tables
y = number of chairs
When x = 0
3(0) + 8y = 6000
8y = 6000
y = 750
When y = 0
3x + 8(0) = 6000
3x = 6000
x = 2000
The ordered pairs of the products are:
0 table 750 chairs
200 tables, 0 chairs.
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Which statements are true?
Select each correct answer.
All trapezoids are quadrilaterals.
All rhombuses are squares.
All rhombuses are parallelograms.
All quadrilaterals are parallelograms.
Answer:
all rhombuses are parallelograms, all trapezoids are quadrilaterals
Step-by-step explanation:
rhombuses have all equal sides, 2 sets of parallel lines and are a diamond shape. a quadrilateral is a shape with 4 sides (quad means 4) therefore, all rhombuses are parallelograms. we know that all trapezoids have 4 sides, so we can conclude that all trapezoids are quadrilaterals i hope this helped because i know that end of year tests are super hard.
if the sine ratio is given, then how can sin 0/2 be determined?
Step-by-step explanation:
If you know, the sine. You must find the cos ratio, using the Pythagorean trig theorem.
Next, you use the half angle identity for sin
[tex] \sin( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos(a) }{2} } [/tex]
Example.
[tex] \sin( \alpha ) = \frac{ \sqrt{3} }{2} [/tex]
We must find
[tex] \sin( \frac{ \alpha }{2} ) [/tex]
First, use the Pythagorean identity
[tex] \sin {}^{2} ( \alpha ) + \cos {}^{2} ( \alpha ) = 1[/tex]
[tex]( \frac{ \sqrt{3} }{2} ) {}^{2} + \cos {}^{2} (a) = 1[/tex]
[tex] \frac{3}{4} + \cos {}^{2} (a) = 1[/tex]
[tex] \cos {}^{2} (a) = \frac{1}{4} [/tex]
[tex] \cos( \alpha ) = \frac{1}{2} [/tex]
Now use the half angle identiy
[tex] \sin( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos( \alpha ) }{2} } [/tex]
[tex] = \frac{ \sqrt{1 - \frac{1}{2} } }{ \sqrt{2} } [/tex]
[tex] = \frac{ \sqrt{ \frac{1}{2} } }{ \sqrt{2} } [/tex]
[tex] = \frac{ \sqrt{ \frac{1}{2} } }{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{ \sqrt{1} }{ \sqrt{4} } = \frac{1}{2} [/tex]
So the answer for our example is 1/2
Solve for x.
(x−2)^2+2=38
x= ___ or x= ___
Answer:
[tex]x \: = \: \boxed{ \bold{ - 4 }}\: \: \text{or} \: \: x \: = \: \boxed{ \bold{ 8}}[/tex]
Step-by-step explanation:
[tex](x \: - \: 2 {)}^{2} \: + \: 2 \: = \: 38[/tex]
[tex] {x}^{2} \: - \: 4x \: + \: 4 \: + \: 2 \: = \: 38[/tex]
[tex] {x}^{2} \: - \: 4x \: + \: 6 \: = \: 38[/tex]
[tex] {x}^{2} \: - \: 4x \: + \: 6 \: - \: 38 \: = \: 0[/tex]
[tex] {x}^{2} \: + \: 4x \: - \: 8x \: - \: 32 \: = \: 0[/tex]
[tex]x \: \times \: (x \: + \: 4) \: - \: 8(x \: + \: 4) \: = \: 0[/tex]
[tex](x \: + \: 4) \: \times \: (x \: - \: 8) \: = \: 0[/tex]
When it happens that the product of the factors is the same as zero. It is divided into two possible cases.[tex]x \: + \: 4 \: = \: 0 \\ x \: - \: 8 \: = \: 0[/tex]
We solve the two equations:[tex]x \: = \: - 4 \\ x \: = \: 8[/tex]
Answer:[tex]x \: = \: - 4 \\ x \: = \: 8[/tex]
MissSpanishUsing the net below, find the surface area
of the triangular prism.
6 cm
8 cm
15 cm
15 cm
6 cm 8 cm
6 cm
Surface Area
[?] cm²
10 cm
Enter
Find the value of x and the measure of angleMNQ.
3x − 11°62°
The value of x is
90
° and the measure of angleMNQ is
180
°.
Answer:
180
Step-by-step explanation:
Find the value of x and the measure of angleMNQ.
3x − 11°62°
The value of x is
90
° and the measure of angleMNQ is
180
°.
The diameter of a circle is m. What is the area
Answer:
[tex] (\frac{{m}^{2} }{4} )\pi[/tex]
Step-by-step explanation:
we can find the radius from the diameter by dividing the diameter by 2 (radius is half the diameter)
the formula for the area of a circle is r²π (with r being radius) but since we must use diameter we have to replace r with (m/2)
this gives us our new formula of (m/2)²π, which simplifies to (m²/4)π
that is the answer
- kan academy advance
If you roll a standard number cube 95 times, how many times do you expect the cube to show a one or a three?
Answer:
32 times
Step-by-step explanation:
the probability in getting a certain number is you first find out the chance of rolling one side on a die. There are six sides, and there is two numbers on it you want a 3 and a 1. so you would get 2/6 would be the fraction of what you what most likely get, so you would multiply 95 by 2/6 you get the correct answer
In the triangle below, what is the measure of B?
A. 18°
B. 56°
C. 90°
D. 28°
The measure of the angle B from the isosceles triangle is equal to 28°. (Correct choice: D)
What is the measure of the missing angle?
In this problem we have the case of an isosceles triangle, that is, a triangle with two sides of equal length and two angles of same measure. By properties from isosceles triangles, we know that the measures of sides AC and BC are the same and angles B and C are the same.
Then, if we know that AC = AB = 10 and m ∠C = 28°, then the measure of the angle B is equal to 28°.
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The marked price of a watch is 30% above the cost price. When it is sold allowing 20% discount on it, there is a gain of Rs 150. Find the marked price and the cost price of them.
Answer:
Marked price: Rs. 4875
Cost price: Rs. 3750
Explanation:
(i) Cost price: 100%
(ii) Marked price: (100% + 30%) = 130%
(i) Let the cost price be p
(ii) Marked price: 130% × p = 1.3p
Given, 20% discount then sold at 80%
Discount price: (130% × 80%) × p = 1.04p - discounted price
Gain price: 1.04p - p = 0.04p
Cost price:
0.04p = 150
p = 150/0.04 = 3750 ← This is the cost price.
Marked price:
1.3p = 1.3(3750) = Rs. 4875
which of the following is located over the center of the base of a regular pyramid
A vertex
B slant height
C face
D edge
Answer:
vertex
Step-by-step explanation:
The graph of y=cosx is translated by (30,-1). What is the equation of the translated graph?
The equation on the graph is shown (I really hope this helps)
Equation of the translated graph is;
⇒y = cos(x - 30) - 1
What is equation of translated graph?
Equation of the translated graph is solved as;
g(x) = f(x + k) + C
Where, k and C are points.
Given that;
The equation is;
y = cos x
Since, Graph of function y = cosx is translated by (30, -1).
So, Equation of translated graph will be;
y = cos(x - 30) - 1
Hence, The equation of the translated graph will be;
⇒ y = cos(x - 30) - 1
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Which of these is a recurring cost of car ownership?
A. Windshield replacement
B. Driver's license application fee
C. Gas
O D. Bumper replacement
please help will give brainlest
Answer:
18
Step-by-step explanation:
Here,
given,
a=3 and b=6
Then
4a+b=?
Put respective values on 4a+b
4*3+6
=12+6
=18
Answer:
18
Step-by-step explanation:
step 1:4a+b=
step 2:(4x3)+6=
step 3:12+6=
answer=18
hope this helps
The Pythagorean theorem can only be used with witch type of triangle
Answer:
Right Triangles
Step-by-step explanation:
A quart of stain covers 100 square feet. How many quarts should you buy to stain the wheelchair ramp? (Assume you do not have to stain the bottom of the ramp.)
This shows that the number of quarts she should you buy to stain the wheelchair ramp is 9 quart
Surface area of a pyramidThis the sum of all the area of the surfaces. The given figures is made of 3 rectangles and 2 triangles
Determine the surface area
TSA = (25*25) + (2 * 5*301/12) + (5*2.08333)
TSa = 625 + 258.33333 + 10.41665
TSA = 893.74995
If a quart of stain covers 100 square feet, the total nuber to buy is given as:
Number to buy = 894/100 = 8.94
This shows that the number of quarts she should you buy to stain the wheelchair ramp is 9 quart
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What is the range of function g if g(x) =-2f(x-3)
Answer:
If you entered the function correctly there is not a range
Step-by-step explanation:
Answer: {y|-♾<y<0}
Step-by-step explanation: i’m taking this summer school class
please answer this !!
uhm i dont know sorry but i can't help you
factorize
2x²-x²-x
Please help me fast to solve this problem.
Answer: x (x - 1)
Step-by-step explanation:
[tex]2x^{2} - x^{2} -x[/tex]
[tex]x^{2} -x[/tex]
x (x - 1)