Answer:
31.2 ft
Step-by-step explanation:
sin = opp/hyp
sin64 = 28/hyp
hyp = 28/sin64
use calculator
hyp = 31.15285433330529
Rounded
31.2 ft
The length of the ladder needed to reach an electric box 28 feet up is 31.2 feet.
The ladder, the distance from the wall to the base of the ladder and the distance from the ground to the electric box forms a right angled triangle.
Trigonometric ratios shows the relationship between the sides and angles of a right angled triangle.
Let x represent the length of the ladder, hence:
sin(64) = 28 feet/x
x = 28 feet / sin(64)
x = 31.2 feet
Hence the length of the ladder needed to reach an electric box 28 feet up is 31.2 feet.
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I really need help with this question as fast as possible
Answer:
-1625
Step-by-step explanation:
→ (-125) × 5 + (-125) × 8
Taking (-125) as in common,
→ (-125) × (8 + 5)
→ (-125) × 13
→ -1625
−6⋅20.1x=−100
Which of the following is the solution of the equation?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
x
=
2
(
50
)
2
(
3
)
x=
log
2
(3)
log
2
(50)
x, equals, start fraction, log, start base, 2, end base, left parenthesis, 50, right parenthesis, divided by, log, start base, 2, end base, left parenthesis, 3, right parenthesis, end fraction
(Choice B)
B
x
=
10
2
(
50
3
)
x=10log
2
(
3
50
)x, equals, 10, log, start base, 2, end base, left parenthesis, start fraction, 50, divided by, 3, end fraction, right parenthesis
(Choice C)
C
x
=
10
2
(
50
)
2
(
3
)
x=
log
2
(3)
10log
2
(50)
x, equals, start fraction, 10, log, start base, 2, end base, left parenthesis, 50, right parenthesis, divided by, log, start base, 2, end base, left parenthesis, 3, right parenthesis, end fraction
(Choice D)
D
x
=
2
(
50
3
)
x=log
2
(
3
50
)x, equals, log, start base, 2, end base, left parenthesis, start fraction, 50, divided by, 3, end fraction, right parenthesis
Answer:
The answer (D)
x=log2(50/3)
Thus, [tex]x=10log_{2}\frac{50}{3}[/tex] so option (B) is the correct answer.
What is a logarithm?"A logarithm tells what exponent (or power) is needed to make a certain number, so logarithms are the inverse (opposite) of exponentiation. Just as an exponential function has three parts, a logarithm has three parts as well: a base, an argument, and an answer (also called power)".
For the given situation,
The equation is
[tex]-6(2)^{0.1x} = -100[/tex]
The equation can be expressed in logarithm as
[tex]a^{x}=b\\[/tex]
⇒ [tex]x=log_{a}b[/tex]
So, [tex]-6(2)^{0.1x} = -100[/tex]
⇒ [tex]2^{0.1x}=\frac{-100}{-6} \\[/tex]
⇒ [tex]0.1x=log_{2}\frac{50}{3}[/tex]
⇒[tex]\frac{1}{10}x=log_{2} \frac{50}{3}[/tex]
⇒[tex]x=10log_{2}\frac{50}{3}[/tex]
Hence we can conclude that [tex]x=10log_{2}\frac{50}{3}[/tex] option (B) is the correct answer.
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7.2 cm
6 cm
15 cm
8 cm
Answer:
i need to know the answer or the question plz
Which function has zeros at x = -2 and x = 5?
Answer:
f(x) = x² - 3x - 10
Step-by-step explanation:
Given zeros x = - 2 and x = 5, then the corresponding factors are
(x + 2) and (x - 5) , so
f(x) = (x + 2)(x - 5) ← expand using FOIL
= X² - 3X - 10
Answer:
f(x) = x² - 3x - 10
(option D)
Step-by-step explanation:
Brian spends 3 5 of his wages on rent and 1 3 on food. If he makes £735 per week, how much money does he have left?
Answer :
Brian has $49 left.
Step by step explanation :
Step 1 : Find how much money Brian spends on rent and food.
First question we should be asking is what is 3/5 of 735?
Let's find that.
[tex]\frac{3}{5}[/tex] * [tex]\frac{735}{1}[/tex]
= [tex]\frac{(3)(735)}{(5)(1)}[/tex]
= [tex]\frac{2205}{5}[/tex]
= 441
We know Brian spends $441 on rent. Now we find how much he spends on food.
[tex]\frac{1}{3} * \frac{735}{1}[/tex]
= [tex]\frac{(1)(735)}{(3)(1)}[/tex]
= [tex]\frac{735}{3}[/tex]
= 245
Brian spends $245 on food.
Step 2 : Add what he spends on rent and food together.
$441 + $245 = $686
Step 3 : To find out how much money Brian has left, we subtract $686 from $735.
$735 - $686 = $49
Conclusion : Brian has $49 left.
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A leading automobile magazine has 60 pages and 4,50,000 copies are printed every month. How many pages in all are printed in the month of April?
Answer:
See the explanation below
Step-by-step explanation:
Number of months =4
Number of copies =450000
Number of pages =60
Number of copies in 4 months =450000*4
=1800000
Number of pages is
=1800000 *60
=108,000,000
Area of base=
A)8 square units
B)6 square units
C)12 square units
Answer:
its 8
Step-by-step explanation:
4 times 2 is 8 and you cant get 6 or 12
Answer:
A
Step-by-step explanation:
Area of base = length x width = 4 * 2 = 8 square units
Please help me !!!
What is the image of (-8,-1) after a reflection over the line y = -x?
Answer:
Step-by-step explanation:
Reflection of (-8 , -1) over y = -x is (-1 , 8)
Image of (x , y) over the line y = -x is (y, -x)
Answer:
reflection on the y axis (x,y)=(-x,y)
(-8,-1)=(8,-1)
Step-by-step explanation:
hope this is helpful
Find the area of triangle.
Answer:
16cm2
Step-by-step explanation:
(1/2) × 8 ×4=16cm2
the answer is 16 cm squared
Answer:
The area is 16 cm^2
Why? Below I explain.
Step-by-step explanation:
In that triangle, there are 2 sides, so you need to use this formula:
B * H / 2
Using those values:
4 * 8 / 2 is equal to 16.
The points A, B, C and D lie on a circle centre O.
Angle AOB = 90° angle COD= 50° and angle BCD= 1239
The line DT is a tangent to the circle at D.
Find
(a) angle OCD
The measure of angle OCD from the given figure is 58°.
Given that, the points A, B, C and D lie on a circle Centre O.
What is the circle?A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
Here, OC and OB are radius of a circle, then BOC is isosceles triangle
Now, ∠BOC+∠OBC+∠OCB=180°
50°+∠OBC+∠OBC=180°
⇒ 2∠OBC=130°
⇒ ∠OBC=65°
Here, ∠OCD=∠BCD-65°
⇒ x=123-65=58°
Hence, the measure of angle OCD from the given figure is 58°.
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Which steps can be done to both sides of the equation to determine the value of x ?
3.2.2 - 9.6 = 38.4
A. subtract 9.6, then multiply by 3.2.
B. Add 9.6, then multiply by 3.2.
C. Add 9.6, then divide by 3.2.
D. Subtract 9.6, then divide by 3.2.
Answer:
C. Add 9.6, then divide by 3.2.
Step-by-step explanation:
[tex]3.2x−9.6=38.4[/tex]
[tex]3.2x=38.4+9.6[/tex]
[tex]3.2x=48[/tex]
[tex]x = \frac{48}{3.2} [/tex][tex]x = 15[/tex]
Hope it is helpful...If a,b, and c are three different numbers, which of the following equations has no solutions?
A. ax= bx+c
B. ax+b=ax+c
C. ax+b=ax+b
Answer:
C
Step-by-step explanation:
if you divide both sides by ax+b you get 1=1 which is not a solution for x.
Patty’s gymnastics class is 5
6
of an hour long. Patty practices five different skills and spends the same amount of time on each skill. How can you find how much time she spent on each skill?
Explain how to use an area model to solve the problem.
Answer:
possibly 11 hours on each which is embarrassing
The expression
3(x+6)-x
can be simplified to the form
2x + a)
What is the value of a?
Answer:
a = 18
Step-by-step explanation:
3(x+6)-x = 2x + a
Distribute
3x +18 -x = 2x+a
2x +18 = 2x+a
Subtract 2x from each side
18 = a
Estimate the perimeter and area of the figure to the nearest whole number. Please help!!
Answer:
29 ; 37
Step-by-step explanation:
The figure is composed by a square, a rectangle, and a right triangle
The perimeter of the square is 6 units
The perimeter of the rectangle is 10 units
The triangle is composed by a side of 6 units and a side of 5 units
The third side can be find with the Pythagorean theorem
[tex]\sqrt{6^2 + 5^2} = \sqrt{36 + 25} = \sqrt{61}[/tex] = 7,81025
The total perimeter is
6 + 10 + 5 + 7,81025 = 28,81025 = 29
Area of the square = 2^2 = 4 square units
Area of the rectangle = 6 x 3 = 18 square units
Area of the triangle = (5 x 6)/2 = 15 square units
Total area = 4 + 18 + 15 = 37 square units
part A: Which expression can be used to find the value of x in the triangle shown?
part B: write the value of x to the nearest tenth.
Answer:
D and x=11.55
Step-by-step explanation:
helppppppp really please.
Answer:
x ≈ 101.5
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan44 = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{98}{x}[/tex] ( multiply both sides by x )
x × tan44° = 98 ( divide both sides by tan44° )
x = [tex]\frac{98}{tan44}[/tex] ≈ 101.5 ( to the nearest tenth )
Sum one helpppp meeeee
Answer:
Step-by-step explanation:
total cost of the meal = $120
tip = 20%
tip amount = ?
total cost of the meal with tip = ?
tip amount = tip% 0f total cost of the meal
=20/100 * $120
=$2400/100
=$24
total cost of the meal with tip = total cost of the meal without tip + tip amount
=$120 + $24
=$144
Find the zeros of the function f(x) = (x + 2)(x - 3)(x + 12)
Step-by-step explanation:
f(x) = (x + 2)(x - 3)(x + 12) = 0
(x + 2)(x - 3)(x + 12) = 0
so, the zeros of the function :
=> x1 = -2
=> x2= 3
=> x3 = -12
Manipulate the radius of the sphere, setting it to different values. In the table below, record each radius you chose and the exact volume of the sphere (in terms of π). Also calculate the decimal value of each volume, and verify that it matches the volume displayed by the tool. (You might see some discrepancies in the tool due to rounding of decimals.)
Answer:
641654654
Step-by-step explanation:
Answer:
1) r=9 v=972
2) r=6 v=288
3) r=12 v=2,304
Step-by-step explanation:
Sample Answer on edmentum
does anyone know how to solve this?
Answer:
[tex]x=360[/tex]
Step-by-step explanation:
The inscribed angles theorem states that when given a circle, with an angle that has its vertex at the center of the circle, the measure of the angle is congruent to the measure of the arc surrounding it. One can apply this knowledge here by stating the following,
[tex]m<MON = MN\\[/tex]
Substitute,
[tex]x=2\pi[/tex]
However, this answer is in radians, it is the literal measurement. One must convert into degrees so that the answer fits the format of the question. The conversion rate to switch between radians and degrees is the following,
[tex]degree=\frac{\pi}{180}radians[/tex]
Substitute,
[tex]degree=\frac{180}{\pi}(x)\\\\degree=\frac{180}{\pi}(2\pi)\\[/tex]
Simplify,
[tex]degree=\frac{180*(2\pi)}{\pi}\\degree=360[/tex]
Answer:
x = 45°
Step-by-step explanation:
Given arc length = 2π cm
Radius, r = 8 cm
[tex]Arc \ Length = 2 \pi r (\frac{x}{360})[/tex]
[tex]2 \pi = 2 \pi \times 8 \frac{ x}{360}\\\\\frac{2 \pi}{16 \pi} = \frac{x }{ 360}\\\\\frac{1}{8} = \frac{x}{360}\\\\\frac{360}{8} = x\\\\x = 45^\circ[/tex]
Amber works as a waitress at a restaurant. She earns an hourly wage and also earns tips. One night, she worked 6 hours and earned a total of $69.20, which included tips of $15.50. Explain how the equation 6w + 15.5 = 69.2 represents this situation. Then, calculate Amber’s hourly wage.
Answer:
Hey there!
The given equation helps us understand the relationship between Amber's tips earned and the money she earned through her hourly wage. This information will add up to equal a grand total of $69.20.
We know that Amber earns $15.50 in tips during her 6 hour shift. Therefore, this is not considered part of her wage. This would be one of the constants of our equation.
We also know that Amber earns a fixed hourly wage, but we don't know what this wage is. We need to find w.
[tex]6w+15.5=\$69.20[/tex]
Subtract 15.5 from both sides of the equation (and get rid of the currency symbol).
[tex]6w=69.20-15.5\\6w=53.7[/tex]
Divide both sides of the equation by 6.
[tex]\displaystyle \frac{6w}{6}=\frac{53.7}{6}\\\\w=8.95[/tex]
Therefore, Amber's hourly wage is $8.95.
A line has the equation 3x–4y–12=0 what is the slope of this line
Answer:
The slope of this line is 3/4.
Step-by-step explanation:
Solving this equation 3x–4y–12=0 for y puts the equation into the form
y = mx + b, where m is the slope of the line.
One way of solving for 4y here is to add 4y to both sides, obtaining:
3x - 12 = 4y
Dividing all three terms by 4 yields
y = (3/4)x - 3
The slope of this line is 3/4.
Which row in the table is the closest to the actual solution?
Answer:
0.8
Step-by-step explanation: 6 22 6 06
I plotted both sides of the equation using DEMOS graphing calculator and located the intersection at (0.779, 2.135) I found that easier than finding the delta difference of both sides of the equation for the table or solving for x.
If a +b+c=9 and a square +b square +square =1 then ab+bc+ca
Answer:
ab + bc + ca = 40
Step-by-step explanation:
Using the expansion identity
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca) , that is
9² = 1 + 2(ab + bc + ca)
81 = 1 + 2(ab + bc + ca) ← subtract 1 from both sides
80 = 2(ab + bc + ca) ← divide both sides by 2
40 = ab + bc + ca
can someone help please
Answer:
3a. (i). Sequence [tex]V_{n}[/tex] is in Arithematic
(ii). Sequence [tex]W_{n}[/tex] is in Geometric
3b. 2520 Sum of First 20 Arithmetic Sequence
3c. 98292 Sum of First 13 Geometric Sequence
Step-by-step explanation:
According to the Question,
3a. (i) Arithmetic Sequence ([tex]V_{n}[/tex]) = 12 , 24 , 36 , 48 .....
it is a sequence of numbers such that the difference between the consecutive terms is same. example → 24+12=12 , 36-24=12 , 48-36=12 ∵Common Difference=12
(ii) Geometric Sequence ([tex]W_{n}[/tex]) = 12 , 24 , 48 , 96 .....
A geometric series is a series for which the ratio of each two consecutive terms is a constant function. example → 24/12= 2 , 48/24= 2 , 96/48= 2 ∵Common Ratio=2
3b. Sum of first 20 terms of Arithematic sequence, [tex]S_{n}=\frac{n}{2}[2a + (n-1) d][/tex]
(Where, a=first term of sequence , n= number of term & d=common difference)
[tex]S_{n}[/tex]=10[2×12 + 19×12]
[tex]S_{n}[/tex] =10×252 ⇔ 2520
3c. Sum Of First 13 term of a geometric sequence, [tex]S_{n}= \frac{a(r^{n}-1) }{r-1}[/tex]
(Where, a=first term of sequence , n= number of term & r= common ratio)
[tex]S_{n}[/tex]=12([tex]2^{13}[/tex]-1) / 2-1
[tex]S_{n}[/tex]=12×8191 ⇔ 98292
Write this number in scientific rotation. 1,490,000.
Answer and explain.
Answer:
4.9 x 10^5
Step-by-step explanation:
the answer is 4.9 x 10^5
Which of the equations below represents a line perpendicular to the yaxis?
A. y= -6
B. x= 6
C. y=6x
D. y=x
Answer:
A. y=-6
Step-by-step explanation:
Using the answer, it would make a horizontal line which would be perpendicular to the y axis.
At the start of 2014, Mike's car is worth 12000. the car depreciates by 30 percent every year. how much is his car worth in 2017
Answer:
$4,116
Step-by-step explanation:
Worth of Mike's car at the start of 2014 = $12,000
If the car is said to depreciates every year by 30% = 30/100 = 0.3
The worth of the car at the start of 2017 is what we are to determine.
This means that the car depreciated by 30% (0.3) for 3 years since 2014 (2017 - 2014 = 3 yrs)
The worth at the start of 2017 would be calculated as follows:
12,000 × (1 - 0.3)³
= 12,000 × (0.7)³
= 12,000 × 0.343
= 4,116
Worth of the car at the start of 2017 would be $4,116
the perimeter of a rectangle is 56 meters. Find the dimensions of the rectangle if they are in the ratio 1:3
Answer:
length= 7m and breadth= 21m
Step-by-step explanation:
Perimeter=56m
Perimeter of a rectangle= 2(l+ b)
Dimensions in the ratio 1:3
1:3= 1x and 3x
Take length as 1x and breadth as 3x
2(1x+3x)= 56m
2(4x)= 56
8x=56
x= 56/8 = 7m
length= 1x= 7m
breadth= 3x= 3*7 = 21m
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