Answer:
1.03921568627
Step-by-step explanation:
An observer on the top of a lighthouse observes the angles of depression of two ship at anchor to be 75 and 45 respectively. Find the distance between the two ships if the line joining them points to the base of the light house which is 100 meters high. (use tan 15 = 0.27) Answer should be 73 meter.
Answer:
Distance between two ships = 73 units
Step-by-step explanation:
Note:
tangent = opposite / hypotenuse
Referring to diagram,
Distance of ship A from tower = 100 tan(90-45) = 100 units
Distance of ship B from tower = 100 tan(90-75) = 100 tan (27) = 27 units
Distance between two ships = 100-27 = 73 units
At a pond, there were 24 ducks swimming. The ratio of ducklings to adult ducks is 5:1. How many ducklings were swimming at the pond?
Answer:
Hey there!
The ratio of ducklings to adult ducks is 5:1.
This means for every six ducks, five are ducklings and one is an adult.
If there are 24 ducks, then 5 times 4 = 20 ducklings and 4 adults.
Thus, there are 20 ducklings.
Hope this helps :)
Answer:
20 ducklings.
Step-by-step explanation:
Thanks a lot... Plz answer with steps
24 and 16
Step-by-step explanation:
let's assume two part be x and (40 - x)
According to Question,
[tex] x\dfrac{1}{4} = (40 - x) \dfrac{3}{8} [/tex]
[tex] x= \dfrac{3(40 - x)}{2} [/tex]
[tex]2 \times x = 120 - 3x [/tex]
[tex]2x + 3x = 120[/tex]
[tex]5x = 120[/tex]
[tex] \cancel{5}x= \cancel{120}[/tex]
[tex]x = 24[/tex]
Hence one part is 24 and other is (40 - 24) = 16 .
Answer: 24 and 16
Step-by-step explanation:
I REALLY need help with this! Could someone please help me?
Answer:
It's the first option
Step-by-step explanation:
The Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle (in this case AB and AC) is parallel to the third side (BC) and half as long.
. A used car dealer says that the mean price of a two-year old sedan (in good condition) is at least $20,500. You suspect this claim is incorrect and find that a random sample of 14 similar vehicles has a mean price of $19,850 and a standard deviation of $1084. Is there enough evidence to reject the dealer's claim at a significance level (alpha) =0.05?
Answer: There is sufficient evidence to reject the dealer's claim that the mean price is at least $20,500
Step-by-step explanation:
given that;
n = 14
mean Ж = 19,850
standard deviation S = 1,084
degree of freedom df = n - 1 = ( 14 -1 ) = 13
H₀ : ц ≥ 20,500
H₁ : ц < 20,500
Now the test statistics
t = (Ж - ц) / ( s/√n)
t = ( 19850 - 20500) / ( 1084/√14)
t = -2.244
we know that our degree of freedom df = 13
from the table, the area under the t-distribution of the left of (t=-2.244) and for (df=13) is 0.0215
so P = 0.0215
significance ∝ = 0.05
we can confidently say that since our p value is less than the significance level, we reject the null hypothesis ( H₀ : ц ≥ 20,500 )
There is sufficient evidence to reject the dealer's claim that the mean price is at least $20,500
What is the angle formed by the line y=2x−1 and x-axis?
Answer:
63.4°
Step-by-step explanation:
y = 2x - 1
dy/dx = 2
∴ The angle is arc tan(2) = tan^-1(2) = 63.4°
What is the slope of the line?
3(y - 1) = 2x + 2
Answer:
The slope is 2/3
Answer:
2/3
Step-by-step explanation:
This is written in point slope form
y - y1 = m(x-x1)
3(y - 1) = 2x + 2
Divide each side by 3
(y - 1) = 1/3(2x + 2)
Factor out a 2
(y - 1) = 2/3(x - -1)
The slope is 2/3
Instructions: Use the given information to answer the questions and interpret key features. Use any method of graphing or solving. * Round to one decimal place, if necessary.*
The trajectory of a golf ball in a chip from the rough has a parabolic pattern. The height, in feet, of the ball is given by the equation h(x)=−.25x2+4.3x, where x is the number of feet away from the golf club (along the ground) the ball is.
1) The ball starts (blank/answer) feet above the ground.
2)The ball reaches a maximum height of (Blank/answer) feet at a horizontal distance of (blank/answer) feet away from the golf club it was hit with.
3)The ball returns to the ground at about (blank/answer) feet away.
Answer:
1.) Zero ( 0 )
2.) 55.47 feet , 8.6 feet
3.) 17.2 feet
Step-by-step explanation:
The height, in feet, of the ball is given by the equation h(x)=−.25x2+4.3x, where x is the number of feet away from the golf club (along the ground) the ball is.
1.) Since the equation has no intercept,
The ball will start zero feet above the ground.
2.) The distance of the ball at the maximum height will be achieved by using the formula
X = -b/2a
Where b = 4.3, a = -0.25
Substitutes both into the formula
X = -4.3 / 2( - 0.25 )
X = - 4.3 / - 0.5
X = 8.6 feet
Substitute X into the function to get the maximum height
h(x) = −.25(8.6)^2 + 4.3(8.6)
h(x) = 18.49 + 36.98
h(x) = 55.47 feet
3) As the ball returns to the ground, the height will be equal to zero, therefore,
0 = -0.25x^2 + 4.3x
0.25x^2 = 4.3x
X = 4.3/0.25
X = 17.2 feet
The ball returns to the ground at about 17.2 feet away
Help please asap!!
What are the units and degrees that u need to put in ?
Answer:
This question is unanwserable without the "Spider Tool" If you would like to revise it i'd be happy to help
Step-by-step explanation:
But the units are degrees
Write the point-slope form of an equation of the line through the points (6, -1) and (5, -7).
A. Y- 6 = 6(x + 1)
B.y - 5 = 6(x + 7)
C.Y+7= 6(x + 5)
D.y +1 = 6:1-6)
Answer:
D.y + 1 = 6(x - 6)
Step-by-step explanation:
The general form of a straightline equation is given as
y = mx + c
where m is the slope and c is the intercept
m = Δy/Δx
from the given points
m = (-7 - -1)/(5 - 6)
= -6/-1
= 6
Considering the points x₁ and y which are 6 and -1
and using the formular
m = (y - y₁)/(x - x₁)
6 = (y - -1)/(x - 6)
y + 1 = 6(x - 6)
how do you know if the solutions to a quadratic equation are inside, outside, on, inside and on, or outside and on the parabola??
Answer:
Plug in the x and y values into the equation
Step-by-step explanation:
A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than in the first. The tax in the first city was 4.5%, and the tax in the second city was 3.5% . The total hotel tax paid for the two cities was $317.50. How much was the hotel charge in each city before tax? First city: Second city:
Answer:
$3750 and $4250
Step-by-step explanation:
x + 500 = y
.045x + .035y = 317.50
.045x + .035(x + 500) = 317.50
.045x + .035x + 17.5 = 317.50
.08x = 300.00
x = 3750
y = 4250
Write the point-slope form of an equation of the line through the points (-1, 4) and (-2, 2)
A. y + 2 = 2(x - 2)
B. y 4 20 + 1)
c. y + 1 = 2(3-4)
D. y 2 233 - 2)
Answer:
The answer is option BStep-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find an equation of a line given two points first find the slope / gradient
Slope of the line using points (-1,4) and (-2,2) is
[tex]m = \frac{2 - 4}{ - 2 + 1} = \frac{ - 2}{ - 1} = 2[/tex]
So the equation of the line using point (-1,4) is
y - 4 = 2( x + 1)Hope this helps you
Three triangles have sides of lengths 3, 4, and 5. Their respective perimeters are 6, 8 and 10. The triangles are similar to each other.
True or false
Answer:
'll tell you where the problem lies - it is IMPOSSIBLE to form triangles like this.
If the perimeter of the smallest triangle is 6 and one side is 3, then the sum of the other two sides can only be 6 - 3 = 3
One property to enable you to form a triangle is that NO ONE SIDE can be greater or equal to the sum of the other two sides. In the smallest triangle 1 side of length 3 equals the other two sides.
In the middle triangle one side of length "4" equals the sum of the other two sides and
In the large triangle one side of length "5" equals the other two sides.
Therefore when I say "triangle" above I am not actually correct because it is IMPOSSIBLE to form triangles with those dimensions of 1 side and with those perimeters
Linda sells cookies for $2 and hamburgers for $3. She sold 25 items and made $60. How many cookies did she sell ?
Answer:
10 cookies
Step-by-step explanation:
10 x 3 = 30
15 x 2 = 30
30 + 30 = $60
The number of cookies sold by Linda will be 10 cookies.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Linda sells cookies for $2 and hamburgers for $3. She sold 25 items and made $60.
The number of cookies sold by Linda will be calculated as below:-
10 x 3 = 30
15 x 2 = 30
30 + 30 = $60
Therefore, the number of cookies sold by Linda will be 10 cookies.
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f(x) = x^2 - 4x + 3 f(x) = 1/2x + p The system of equations above, when graphed in the xy-coordinate plane, intersects at the point (4, q). What is p?
Answer:
p = 1
Step-by-step explanation:
Given that the system intersect at (4, q) then this point satisfies both equations, that is
q = 4² - 4(4) + 3
q = [tex]\frac{1}{2}[/tex] (4) + p
Equating both gives
16 - 16 + 3 = 2 + p, that is
3 = 2 + p ( subtract 2 from both sides )
p = 1
A student stands 20 m away from the footof a tree and observes that the angle of elevation of the top of the tree, measured from a table 1.5 m above the ground, is 34°28'. Calculate the height of the tree tothe nearest metre.
Answer:
6 to the north
Step-by-step explanation:
mark as brainliest
Please help.............
.
Answer:
The length of arc is (7/12)π cm.
Step-by-step explanation:
Given that the formula to find the length of arc is Arc = (θ/360)×2×π×r where θ represents degrees and r representa radius. Then you have to substitute the following values into the formula :
[tex]arc = \frac{θ}{360} \times 2 \times \pi \times r[/tex]
[tex]let \: θ = 30 \\ let \: r = 3.5[/tex]
[tex]arc = \frac{30}{360} \times 2 \times \pi \times 3.5[/tex]
[tex]arc = \frac{1}{12} \times 7 \times \pi[/tex]
[tex]arc = \frac{7}{12} \pi \: \: cm[/tex]
As mountain climbers know, the higher you go, the cooler the temperature gets. At noon on July 4th last summer, the temperature at the top of Mt. Washington — elevation 6288 feet — was 56◦F. The temperature at base camp in Pinkham Notch — elevation 2041 feet — was 87◦F. It was a clear, still day. At that moment, a group of hikers reached Tuckerman Junction — elevation 5376 feet. To the nearest degree, calculate the temperature the hikers were experiencing at that time and place. When you decided how to model this situation, what assumptions did you make?
Answer:
The temperature at 5376 ft is approximately 63°F
The assumption made was that the temperature varies linearly with elevation
Step-by-step explanation:
The parameters given are;
Temperature at 6288 feet = 56°F = 286.5
Temperature at 2041 feet = 87°F = 303.71
We are to find the temperature at 5376 feet
Let the temperature be the y-coordinate value and the elevation be the x-coordinate value, to find the temperature, we have the temperature gradient given by the relation;
[tex]m = \dfrac{y_2-y_1}{x_2 - x_1} = \dfrac{303.71-286.5}{2041 - 6288}= -4.05 \times 10^{-3} \ K/ft[/tex]
The temperature at 5376 ft will be the temperature at 2041 added to the decrease in temperature from climbing to 5376 ft
The increase in elevation is 5376 - 2041 = 3335 ft
The decrease in temperature = 3335 ft × (-4.05 × 10⁻³) K/ft = -13 .5 K
The temperature at 5376 ft will then be 303.71 - 13.5 = 290.196 K = 62.68°F ≈ 63°F
The assumption made was that the decrease in temperature with elevation is linear.
R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)} which is a domain
Answer:
Domain { -3, -1 ,1}
Step-by-step explanation:
The domain is the input values
We write them in order from smallest to largest with out repeating any numbers
Domain { -3, -1 ,1}
Which rule describes the x-coordinates in the translation below?. On a coordinate plane, triangle A B C is shifted 6 units up.
Answer:
The answer is A: x + 0
Step-by-step explanation:
I got it correct on Edge. Please give 5 stars and have a great day! :)
The translation of the x-coordinate is written as x⇒0 for the triangle ABC.
What is translation?A translation in mathematics moves a shape left, right, up, or down but does not turn it. The translated (or image) shapes appear to be the same size as the original shape, indicating that they are congruent. They've just moved in one or more directions.
A coordinate system is a two-dimensional number line, such as two perpendicular axes. This is an example of a typical coordinate system: The horizontal axis is referred to as the x-axis, and the vertical axis is referred to as the y-axis.
Given that on a coordinate plane, triangle A B C has shifted 6 units up. The x translation for the triangle is zero.
The x-coordinate translation is written as,
x ⇒ 0
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State the number of possible triangles that can be formed using the given measurements.
Answer: 39) 1 40) 2
41) 1 42) 0
Step-by-step explanation:
39) ∠A = ? ∠B = ? ∠C = 129°
a = ? b = 15 c = 45
Use Law of Sines to find ∠B:
[tex]\dfrac{\sin B}{b}=\dfrac{\sin C}{c} \rightarrow\quad \dfrac{\sin B}{15}=\dfrac{\sin 129}{45}\rightarrow \quad \angle B=15^o\quad or \quad \angle B=165^o[/tex]
If ∠B = 15°, then ∠A = 180° - (15° + 129°) = 36°
If ∠B = 165°, then ∠A = 180° - (165° + 129°) = -114°
Since ∠A cannot be negative then ∠B ≠ 165°
∠A = 36° ∠B = 15° ∠C = 129° is the only valid solution.
40) ∠A = 16° ∠B = ? ∠C = ?
a = 15 b = ? c = 19
Use Law of Sines to find ∠C:
[tex]\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \rightarrow\quad \dfrac{\sin 16}{15}=\dfrac{\sin C}{19}\rightarrow \quad \angle C=20^o\quad or \quad \angle C=160^o[/tex]
If ∠C = 20°, then ∠B = 180° - (16° + 20°) = 144°
If ∠C = 160°, then ∠B = 180° - (16° + 160°) = 4°
Both result with ∠B as a positive number so both are valid solutions.
Solution 1: ∠A = 16° ∠B = 144° ∠C = 20°
Solution 2: ∠A = 16° ∠B = 4° ∠C = 160°
41) ∠A = ? ∠B = 75° ∠C = ?
a = 7 b = 30 c = ?
Use Law of Sines to find ∠A:
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b} \rightarrow\quad \dfrac{\sin A}{7}=\dfrac{\sin 75}{30}\rightarrow \quad \angle A=13^o\quad or \quad \angle A=167^o[/tex]
If ∠A = 13°, then ∠C = 180° - (13° + 75°) = 92°
If ∠A = 167°, then ∠C = 180° - (167° + 75°) = -62°
Since ∠C cannot be negative then ∠A ≠ 167°
∠A = 13° ∠B = 75° ∠C = 92° is the only valid solution.
42) ∠A = ? ∠B = 119° ∠C = ?
a = 34 b = 34 c = ?
Use Law of Sines to find ∠A:
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b} \rightarrow\quad \dfrac{\sin A}{34}=\dfrac{\sin 119}{34}\rightarrow \quad \angle A=61^o\quad or \quad \angle A=119^o[/tex]
If ∠A = 61°, then ∠C = 180° - (61° + 119°) = 0°
If ∠A = 119°, then ∠C = 180° - (119° + 119°) = -58°
Since ∠C cannot be zero or negative then ∠A ≠ 61° and ∠A ≠ 119°
There are no valid solutions.
Given that ACAB - ACED, lind the value of y to 1 dermal place
Answer:
y = 15
Step-by-step explanation:
The triangles CAB and CED are similar (Using the case AA), so we can write the following relations:
[tex]\frac{12}{28} =\frac{15}{x}=\frac{y}{35}[/tex]
Using the first two fractions, we can find the value of x:
[tex]\frac{12}{28} =\frac{15}{x}[/tex]
[tex]12x = 28*15[/tex]
[tex]12x = 504[/tex]
[tex]x = 504/12 = 42[/tex]
Using the first and last fractions, we can find the value of y:
[tex]\frac{12}{28} =\frac{y}{35}[/tex]
[tex]28y = 12*35[/tex]
[tex]28y = 420[/tex]
[tex]y = 420/28 = 15[/tex]
the sum of x and y is twice x. y=
Answer:
y is x because if x+y is 2x then y must equal x
The sum of x and y is twice x. Then the value of y will be equal to x.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
It is given that sum of x and y is twice x. Then the value of y will be calculated as below:-
x + y = 2x
y = 2x - x
y = x
Therefore, the sum of x and y is twice x. Then the value of y will be equal to x.
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i need help quick i will mark brainilest
Answer:
x-y
Step-by-step explanation:
X is greater than y so we are subtracting the smaller number from the bigger number
That means we do not need the absolute value signs since x-y will be positive
|x-y| when x> y
x-y
Using numbers
| 5-2| 5>2
5-2
Two similar cylindrical cans hold 2 litres and 6.75 litres of liquid. If the diameter of the smaller can is 16cm, find the diameter of the larger can.
Step-by-step explanation:
It is given that,
Volume of the cylindrical can 1 is 2 litres and that of cylindrical can 2 is 6.75 litres. The diameter of the smaller can is 16 cm. We need to find the diameter of the larger can.
The formula of the volume of a cylinder is given by :
[tex]V=\pi r^2h[/tex]
So,
[tex]\dfrac{V_1}{V_2}=\dfrac{r_1^2}{r_2^2}[/tex]
Diameter, d = 2r
[tex]\dfrac{V_1}{V_2}=\dfrac{(d_1/2)^2}{(d_2/2)^2}\\\\\dfrac{V_1}{V_2}=(\dfrac{d_1^2}{d_2^2})[/tex]
V₁ = 2 L, V₂ = 6.75 L, d₁ = 16 cm, d₂ = ?
[tex]\dfrac{2}{6.75}=(\dfrac{16^2}{d_2^2})\\\\d_2=29.39\ cm[/tex]
So, the diameter of the larger can is 29.39 cm.
the square root of 5 is
Step-by-step explanation:
The square root of 5 can be approximately found by doing the square root of 4 to get 2, and the square root of 9 to get 3. Then, because 5 is closer to 4 than 9, the square root of 5 is about 2.2.
Otherwise, simply do sqrt(5) in a calculator to get 2.23606798
Hope it helps <3
Which values for A and B will create infinitely many solutions for this system of equations?
4 x minus A y = 15. Negative 4 x + 6 y = B.
A = negative 6, B = 15
A = 6, B = 15
A = 6, B = negative 15
A = negative 6, B = negative 15
Answer: C) A = 6, B = -15
Step-by-step explanation:
In order to have infinitely many solutions, you must end up with 0 = 0 when adding the equations together.
4x - Ay = 15
-4x + 6y = B
(6 - A)y = 15 + B
↓ ↓
6 - A = 0 15 + B = 0
6 = A B = -15
Answer:
C
Step-by-step explanation:
TOOK THE TEST
if (x)= 2x square minus 1,then f(-3)
Answer:
17.
Step-by-step explanation:
f(x) = 2x^2 - 1
f(-3) = 2(-3)^2 - 1
= 2 * 9 - 1
= 18 - 1
= 17
Hope this helps!
Hope it will help u....
SOMEONE PLS HELP ASAP!!!
The exponential function h, represented in the table, can be written as h(x)=a⋅b^x.
x h(x)
0 10
1 4
Complete the equation for h(x) h(x)=?
Answer: [tex]h(x)=10(0.4)^x[/tex]
Step-by-step explanation:
The exponential function h, represented in the table, can be written as [tex]h(x)=ab^x[/tex]
From table, at x=0, h(x) =10
Put theses values in equation,, we get
[tex]10=a.b^0\\\\\Rightarrow\ 10= a (1)\\\\\Rightarrow\ a= 10[/tex]
Also, for x= 1 , h(x) = 4, so put these values and a=10 in the equation , we get
[tex]4=10b^1\\\\\Rightarrow\ b=\dfrac{4}{10}\\\\\Rightarrow\ b= 0.4[/tex]
Put value of a and b in the equation ,
[tex]h(x)=10(0.4)^x[/tex] → Required equation.