Answer:
45.3°
Step-by-step explanation:
A right triangle is formed given the information above.
Angle of depression = x°
Distance between first bird and birdwatcher = opposite to angle x° = 32 ft
Distance between second bird and birdwatcher = hypotenuse of the right triangle formed = 45 ft
The trigonometric ratio formula to use is:
[tex] sin(x) = \frac{opp}{hypo} [/tex]
[tex] sin(x) = \frac{32}{45} [/tex]
[tex] sin(x) = 0.7111 [/tex]
[tex] x = sin^{-1}(0.7111) [/tex]
[tex] x = 45.3 [/tex] (nearest tenth)
Angle of depression = 45.3°
Answer:
45.3°
Step-by-step explanation:
Hope this helps :)
If a polygon has an area of 10 cm² and is dilated by a factor of 2, what will be the area of the dilated polygon?
Area depends on the product of sides,
so if the sides are shortened by a factor of 2, area will reduce by a factor of 4. (2×2)
new area = 10/4=2.5 cm²
The two-way frequency table below shows data on years working with the company and college degree status for Tom's coworkers. Complete the following two-way table of row relative frequencies. (If necessary, round your answers to the nearest hundredth.)
Answer:
Lets start with the top row.
First, add the two values.
5+14=19
Now, divide each value by the total.
5/19=0.26315789473
Round the decimal to the nearest hundredth.
5/19=0.26
14/19=0.73684210526
Round it to the nearest hundredth.
14/19=0.74
Now, The second row.
Add the two values.
16+7=23
Divide the first value by the total.
16/23=0.69565217391
Round it to the nearest hundredth.
16/23=0.70
Divide the second value by the total.
7/23=0.30434782608
Round to the nearest hundredth.
7/23=0.30
Done!
Answer:
Row 1: 0.26 0.74
Row 2: 0.70 0.30
Step-by-step explanation:
Khan
(b) The train is 61 cm long and travels at a speed of 18 cm/s.
It takes 4 seconds for the whole of the train to cross a bridge.
Calculate the length of the bridge.
Answer:
The length of the bridge is 72 cm
Step-by-step explanation:
In order to find the length of bridge, we have to apply distance formula which is D = S × T where S represents speed and T is time :
[tex]d = s \times t[/tex]
[tex]let \: s = 18,t = 4[/tex]
[tex]d = 18 \times 4[/tex]
[tex]d = 72 \: cm[/tex]
The length of the bridge is 11 cm .
What is relationship between distance time and speed ?When an object moves in a straight line at a steady speed, we can calculate its speed if we know how far it travels and how long it takes. This equation shows the relationship between speed, distance traveled and time taken:
Speed is distance divided by the time taken.
For example, a car travels 30 kilometers in 2 hours.
Its speed is 30 ÷ 2 = 15km/hr.
Formula used :
Distance = Speed * Time
Time = Distance / Speed
Speed = Distance / Time
According to the question
Length of train = 61 cm
Speed of train = 18 cm/s
Time taken to cross the bridge = 4 seconds
In this length traveled by train = length of train + Length of bridge
( as time given is to completely cross platform )
Therefore,
length traveled by train = 61 + Length of bridge
formula used
Distance = Speed * Time
61 + Length of bridge = 18 * 4
61 + Length of bridge = 72
Length of bridge = 72 - 61
Length of bridge = 11 cm
Hence, the length of the bridge is 11 cm .
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William and
Debra
Pierce are celebrating their
20th anniversary by having a reception at a local reception hall. They have budgeted
$2,000 for their reception. If the reception hall charges a
$50 cleanup fee plus
$36 per person, find the greatest number of people that they may invite and still stay within their budget.
Answer:
54
Step-by-step explanation:
i put in the calculator 50+36×54= and got this 1,994
If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (fog)(x)?
(3x + 2)(x2 + 1)
O 3x 2 + 1 + 2
(3x + 2)2 + 1
3(x2 + 1) + 2
Answer:
This means you would plug in g(x) into f(x).
Step-by-step explanation:
It would look like this:
[tex]3(x^{2} + 1) + 2[/tex]
By SAA conjecture, determine which triangles are congruent.
Answer:
The correct option is;
[B] ΔABF ≅ ΔEDF
Step-by-step explanation:
GIven that ∠FAE is congruent to ∠FEA
Therefore, triangle ΔFAE is an isosceles triangle (Definition of isosceles triangle)
Segment FA is equal to segment FE (Equal segments of isosceles triangle)
Angle ∠EFD is congruent to angle ∠AFB (Vertically opposite angles)
Therefore, triangle ΔABF is congruent to triangle ΔEDF (Angle Angle Side AAS rule of congruency)
The correct option is ΔABF ≅ ΔEDF.
what's 700.00divided by 120
Answer:
[tex]\Large \boxed{\frac{35}{6} }[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{700}{120}[/tex]
Reduce and simplify the fraction to lowest terms.
[tex]\displaystyle \frac{20(35)}{20(6)}[/tex]
[tex]\displaystyle \frac{35}{6}[/tex]
Which of these functions could have the graph shown below?
O A. f(x) = e^30x
O B. f(x) = 30^30x
O C. f(x) = 30^x
O D. f(x) = 30e^x
The functions could have the graph shown below will be y = 30eˣ. Then the correct option is D.
What is an exponent?Let a be the initial value and x be the power of the exponent function and e be the increasing factor.
The exponent is given as
y = a(e)ˣ
From the graph, the value of the exponent function at x = 0, will be 30.
Then the function will be
30 = a(e)⁰
30 = a
Then the exponent function is given as,
y = 30eˣ
Thus, the functions could have the graph shown below will be y = 30eˣ.
Then the correct option is D.
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Find the he value of n if 4n=6 4
Answer: 16
Step-by-step explanation:
64/4=16
n=16
Answer:
16
Step-by-step explanation:
4n = 64
n = 16 --------> Divide by 4 on each side
Suppose y varies jointly as x & z. If y = -180 when z = 15and x = -3,then find y when x = 7 and z = -5. 1 point
Answer:
y = - 140
Step-by-step explanation:
The statement
y varies jointly as x & z is written as
y = kxzto find y when x = 7 and z = -5 we must first find the relationship between the variables
when y = - 180
z = 15
x = - 3
- 180 = k(15)(-3)
-180 = - 45k
Divide both sides by - 45
k = 4
The formula for the variation is
y = 4xzwhen
x = 7
z = -5
y = 4(7)(-5)
y = 4(-35)
y = - 140Hope this helps you
Evaluate the expression for the given value of the variable. −3x3, when x = 4
Answer:
The answer is - 192Step-by-step explanation:
The expression
- 3x³
To find the value of the expression when
x = 4 substitute the value of x that's 4 into the expression
We have
- 3(4)³
= - 3( 64)
The final answer is
- 192Hope this helps you
Clinton is having a coin drive. Each class has a goal of 600 pennies.Layla has already collected 338 pennies. How many more pennies does Layla need to collect to reach their goal. PLEASE SHOW YOUR WORK I WILL MARK YOU BRAINLIEST PLEASE AND EXPLAIN HOW YOU GOT YOUR ANSWER
Answer:
262 pennies
Step-by-step explanation:
If Layla already has 388 pennies and she needs 600 pennies total, all she needs to do is is take the amount she already has away from 600:
Solve the simultaneous equation
X+3y=13
X-y=5
Answer:
x = 7
y = 2
Step-by-step explanation:
In the above question, we are given 2 equations which are simultaneous. To solve this equation, we have to find the values of x and y
x + 3y = 13 ........ Equation 1
x - y = 5...........Equation 2
From Equation 2,
x = 5 + y
Substitute 5 + y for x in Equation 1
x + 3y = 13 ........ Equation 1
5 + y + 3y = 13
5 + 4y = 13
4y = 13 - 5
4y = 8
y = 8/4
y = 2
Since y = 2, substitute , 2 for y in Equation 2
x - y = 5...........Equation 2
x - 2 = 5
x = 5 + 2
x = 7
Therefore, x = 7 and y = 2
PLEASE help me with this question! This is really urgent! No nonsense answers please, and answer with full solutions!
Answer:0.80
Step-by-step explanation:please i don't really know how to explain this i am very sorry
Convert to slope-intercept from: y-4=9(x-7)
Answer:
y = 9x - 59
Step-by-step explanation:
y - 4= 9(x-7)
y - 4 = 9x - 63
y - 4 + 4 = 9x - 63 + 4
y = 9x - 59
Answer:
Below
Step-by-step explanation:
● y-4 = 9(x-7)
Multiply 9 by (x-7)
● y-4 = 9x - 63
Add 4 to both sides
● y-4+4 = 9x-63 +4
● y = 9x - 59
(If gets it right get's brainliest)If the hypotenuse of an isosceles right triangle is 14, what is the area of the triangle?
Answer:
49 unit²
Step-by-step explanation:
Right triangle with equal legs given, let the leg be x.
Hypotenuse of isosceles right triangle is
√x² + x² = x√2Area of triangle:
1/2ah= 1/2x²Since we have hypotenuse = 14 units:
x√2=14x= 14/√2Then area:
1/2x² = 1/2*(14/√2)² = 1/2*14²/2 = 7² = 49 unit²A classroom floor has an area of
(30x^3 + 8x^2, with a width of 2x feet.
What is the length of the floor?
Answer:
15x² + 4x feet
Step-by-step explanation:
We need to calculate (30x³ + 8x²) / 2x.
(30x³ + 8x²) / 2x
= 30x³ / 2x + 8x² / 2x
= 15x² + 4x
What is the width of the rectangle shown below?
4x + 3
A = 8x2 – 10x – 12
Answer:
2x-4Step-by-step explanation:
Area of a rectangle = Length * Width
Given parameters
Area A = 8x2 – 10x – 12
Length of the rectangle = 4x+3
Required
Width of the rectangle.
Substituting the given parameters into the formula
8x2 – 10x – 12 = (4x+3)*width
width = 8x2 – 10x – 12 /4x+3
S
Factorizing the numerator
8x² – 10x – 12
= 2(4x²-5x-6)
= 2(4x²-8x+3x-6)
= 2(4x(x-2)+3(x-2))
= 2(4x+3)(x-2)
Width = 2(4x+3)(x-2)/4x+3
Width = 2(x-2)
Width = 2x-4
Hence the width of the rectangle is 2x-4
Please answer this question now
Answer:
AB = 72°
Step-by-step explanation:
The inscribed angle ADC is half the measure of its intercepted arc, thus
56° = [tex]\frac{1}{2}[/tex] ( m ABC ) ← multiply both sides by 2
112° = ABC
ABC = AB + BC = AB + 40, so
AB + 40 = 112 ( subtract 40 from both sides )
AB = 72°
Given that p=x^2-y^2/x^2+xy
I. Express p in the simplest form
ii. Find the value of p if x=-4 and y=-6
Answer:
p = - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given
p = [tex]\frac{x^2-y^2}{x^2+xy}[/tex] ( factorise numerator and denominator )
x² - y² ← is a difference of squares and factors as (x - y)(x + y)
x² + xy ← factor out x from each term
= x(x + y) , thus
p = [tex]\frac{(x-y)(x+y)}{x(x+y)}[/tex] ← cancel (x + y) on numerator/ denominator
= [tex]\frac{x-y}{x}[/tex] ← substitute x = - 4, y = - 6
= [tex]\frac{-4-(-6)}{-4}[/tex]
= [tex]\frac{-4+6}{-4}[/tex]
= [tex]\frac{2}{-4}[/tex] = - [tex]\frac{1}{2}[/tex]
Which of the following systems has (1,−1) as a solution? 1. 3x−2y=1 5x+3y=8 2. 3x+2y=1 5x+3y=−8 3. 3x+2y=1 5x−3y=8 4. 2x+3y=1 5x−3y=−8
2. 3x+2y= 1 and 5x+3y=-8
solution: In picture.
You own a farm and have several fields in which your livestock grazes. You need to order barbed-wire fencing for a small pasture that has a length of 5 yards and a width of 3 yards. The barbed wire must be long enough to be placed on all four sides of the outside pasture. How many yards of barbed-wire should you order?
Answer:
16 yards of barbed wire
Step-by-step explanation:
Length=5 yards
Width=3 yards
Perimeter of the pasture=2(length + width)
=2(5 yards +3 yards)
=2(8 yards)
=16 yards
You should order 16 yards of barbed wire for fencing the pasture
Each packet of the cooking oil weighs 2/5th of a kilogram and one kilogram of the cooking oil costs $6.5. Sara went to the grocery shop to buy some items to stock her kitchen. If she bought 8 packets of the cooking oil, how much money did she spend? A $19.60 B $18.20 C $20.80 D $23.40
Answer:
C) $20.80
Step-by-step explanation:
1 kg of cooking oil = $6.5
1 packet of cooking oil =2/5 kg
If 1 kg of cooking oil = $6.5
2/5kg of cooking oil = $X
Cross Multiply
1kg × $X = 2/5kg × $6.5
$X = 13/5
$X = 2.6
Hence 2/5kg of oil cost $2.6
Since 1 packet of oil = 2/5kg of oil , 1 packet of oil cost $2.6
The amount she spent if she bought if she bought 8 packets of the cooking oil is calculated as:
1 packet of oil = $2.6
8 packets of oil =
$2.5 × 8
= $20.80
Therefore,if Sara bought 8 packets of oil, the amount she would spend = $20.80
I need help with multistep equations
Answer:
1 2/3 = m
Step-by-step explanation:
2/3 = m+3/5 -8/5
Combine terms
2/3 = m-5/5
2/3 = m -1
Add 1 to each side
2/3 +1 = m-1+1
2/3 +3/3 = m
5/3 = m
1 2/3 = m
Answer:
[tex]\large \boxed{\sf m = \frac{5}{3} }}[/tex]
Step-by-step explanation:
2/3 = m + 3/5 - 8/5
Subtract the fractions since the denominators are same.
2/3 = m -5/5
Simplify the equation.
2/3 = m - 1
Add 1 to each side.
5/3 = m
how many 6-digit numbers can be created using8, 0, 1, 3, 7, and 5 if each number is used only once?
Answer:
600 numbers
Step-by-step explanation:
For six-digit numbers, we need to use all digits 8,0,1,3,7,5 each once.
However, 0 cannot be used as the first digit, because it would make a 5-digit number.
Therefore
there are 5 choices for the first digit (exclude 0)
there are 5 choices for the first digit (include 0)
there are 4 choices for the first digit
there are 3 choices for the first digit
there are 2 choices for the first digit
there are 1 choices for the first digit
for a total of 5*5*4*3*2*1 = 600 numbers
Which equation represents the line that is perpendicular to y=3/4x+1 and passes through (-5,11)
Will give brainliest!!
Answer:
y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{13}{3}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{3}{4}[/tex] x + 1 ← is in slope- intercept form
with slope m = [tex]\frac{3}{4}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex] , thus
y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation
To find c substitute (- 5, 11) into the partial equation
11 = [tex]\frac{20}{3}[/tex] + c ⇒ c = 11 - [tex]\frac{20}{3}[/tex] = [tex]\frac{13}{3}[/tex]
y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{13}{3}[/tex] ← equation of perpendicular line
The equation of the line that passes through (-5, 11) and perpendicular to y = (3/4)x + 1 is
y = -2x + 1
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
y = (2/4)x + 1 is in the form of y = m(2)x + c
So,
m(2) = 2/4 = 1/2
The equation of the line y = m(1)x + c is perpendicular to y = (2/4)x + 1.
So,
m(1) x m(2) = -1
m(1) = -1/(1/2)
m(1) = -2
Now,
y = -2x + c passes through (-5, 11).
This means,
11 = -2 x (-5) + c
11 = 10 + c
11- 10 = c
c = 1
Thus,
The equation of the line is y = -2x + 1.
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In the first quadrant you start at 5, 6 and move 4 units down. What point will you end up at? Thanks for your help! - Someone who's better at English than math
Answer:
(5, 2)
Step-by-step explanation:
(5, 6) go down 4 units means subtract 4 from the y
(5, 2)
The point to end up will be (5, 2).
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
In the first quadrant you start at (5, 6 ) and move 4 units down.
Now,
Since, In the first quadrant you start at 5, 6 and move 4 units down.
Hence, The end up point = (5, 6 - 4)
= (5, 2)
Thus, The point to end up will be (5, 2).
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7 liters of gasoline between their 4 cars. How many liters of gasoline should each car get?
Answer:
1.75 liters for each car.
Step-by-step explanation:
Divide:
*7 / 4 = 1.75.
Check:
*1.75 x 4 = 7.
Write an equation for the line in the graph that passes through the points (0,4) and (12,16).
Answer:
We have,
y-y1=m(x-x1)
or,y-4=-1(x-0)
or,y-4=-x
or,x+y=4 is the required equation
Step-by-step explanation:
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A VERTICAL POLE OF CAST A SHADOW OF 4.5m LONG AT THE SAME TIME A TREE OF HEIGHT 24m LONG CAST A SHADOW OF 6m LONG. FIND THE HEIGHT OF THE POLE.
Answer:
18 metres
Step-by-step explanation:
4.5/6 = x/24
¾= x/24
x = 18 m