Answer:
Step-by-step explanation:
If you were to sit in the very top of said tree and look directly straight, your line of vision would be parallel to the ground. The angle of depression is in between your line of vision and the rock. When you look down at the rock, your line of vision to the rock is a transversal between the 2 parallel lines. With this being the case, the angle of depression is alternate interior with the angle made on the ground from the rock to the top of the tree. See the illustration I attached below.
We are looking for the distance on the ground between the tree and the rock, which we will call x. The side opposite the reference angle is the height of the tree and the side adjacent to the reference angle is x. Side opposite over side adjacent is the tangent ratio. Therefore,
[tex]tan(49)=\frac{18.5}{x}[/tex] and
[tex]x=\frac{18.5}{tan(49)}[/tex] and on your calculator in degree mode, you will find that
x = 16.08 m
factorise:x²+30x+216
Answer: (x + 12)(x + 18)
Step-by-step explanation: x² + 30x + 216
12 + 18 = 30
12 x 18 = 216
(x + 12)(x + 18)
Answer:
answer would be (x + 12)(x + 18).
Step-by-step explanation:
Let's factor x^2 + 30x + 216
x^2 + 30x + 216
Answer:
(x + 12) (x + 18)
Given: PQRS is a rectangle. Put a checkmark in every box that must be true. You will put more than one checkmark. Use calculations and words to show this quadrilateral meets the definition of a kite.
Answer:
The true options are:
2) Has exactly one pair of parallel sides
4) Has exactly one pair of congruent sides
5) Both pairs of opposite sides are congruent
7) There are right angles at all 4 vertices
9) The diagonals are congruent
10) The diagonals bisect each other.
A polygon is regular when all angles are equal and all sides are equal
True or False
Answer:
True
Step-by-step explanation:
True, because a polygon have all angles that are equal and all lengths are the same length.
find the perimeter of the triangle defined by the coordinates (9,0) , (-5,0) and (-10,6)
Answer:
PERIMETER = 41.73 units
Step-by-step explanation:
To find the perimeter of the triangle, we will follow the steps below:
Let the coordinate of the triangle be ABC, that is
A(9,0) B(-5,0) and C(-10,6)
We will first find distance AB, BC and CA using the distance formula
|D| = √(x₂-x₁)² +(y₂-y₁)²
A(9,0) B(-5,0)
x₁ =9 y₁=0 x₂=-5 y₂=0
substitute the values into the formula
|AB| = √(-5-9)² +(0-0)²
= √(-14)² +(0)²
=√196
=14
|AB| = 14 units
B(-5,0) C(-10,6)
x₁ =-5 y₁=0 x₂=-10 y₂=6
substitute the values into the formula
|BC| = √(-10+ 5)² +(6-0)²
=√(-5)² +(6)²
=√25 + 36
=√61
≈7.81
|BC| ≈7.81 units
C(-10,6) A(9,0)
x₁ =-10 y₁=6 x₂=9 y₂=0
substitute the values into the formula
|CA| = √(9+10)² +(0-6)²
= √(19)² +(-6)²
=√361 +36
=√397
≈19.92 units
|CA|≈19.92 units
Perimeter of triangle = |AB|+|BC|+|CA|
=14+7.81+19.92
=41.73
PERIMETER = 41.73 units
Nancy wants to receive the most return on a $50,000 investment. She has two options. Option 1 gives annual interest at 5% compounded yearly. Option 2 gives annual interest at 3.5% compounded monthly. Which option is better after 3 years, and what is the difference in earned interest? 1Option 2 earns more interest by $3,581.52. Option 2 earns more interest by $2,396.13. Option 1 earns more interest by $2,396.13. Option 1 earns more interest by $3,581.52.
Answer:
Option 1 earns more interest by $2396.13
Step-by-step explanation:
Step 1: Determine the prices
50000(1 + 0.05)^3 = 57881.30
50000(1 + 0.0035/12)^36 = 55527
Step 2: Determine which pays higher
Step 3: Find difference
57881.30 - 55527 = 2396.13
And we have our final answer!
What is the surface area of the cube below?
A. 508 units2
B. 512 units2
C. 320 units2
D. 384 units2
Answer:
D
Step-by-step explanation:
because one side surface area is 8x8=64, and there is 6 sides so 64x6 = 384 units2
Answer:
D. 384 units^2
Step-by-step explanation:
The surface area of a cube can be found using the following formula:
S=6s^2
where s is the side length.
In this case, the side length of the cube is 8 units.
s=8 units
Substitute 8 units in for s.
S=6*(8 units)^2
First, evaluate the exponent.
(8 units)^2=8 units * 8 units= 64 units^2
S=6* 64 units^2
Multiply 6 and 64
S=384 units^2
The surface area of the cube is 384 square units, therefore D. 384 units^2 is correct.
What is the next term in the sequence?
1,-3,9,-27
Begin by studying the pattern.
Here, notice that 1 × -3 is equal to -3.
-3 × -3 is equal to 9.
9 × -3 is equal to -27.
Continuing the same pattern, -27 × -3 is equal to 1.
So the next term in the pattern is 81.
So, we multiply by -3 each time.
ggefv23ehwdg1uhigvfgwuiderfghvwh4eryu
Answer:
1. 15+63= 78 ft cubed
2. 5.5+33= 38.5 m cubed
The diagram shows a floor in the shape of a trapezium. Tim is going to paint the floor. Each 5 litre tin of paint costs £16.99 and 1 litre of paint covers an area of 1.9 m2 How much would it cost to buy all the paint he needs? You must show how you get your answer. 0 m 16m £16.99
Answer: £186.89
Step-by-step explanation:
-We are given that each 5l tin of paint costs £16.99 . We therefore divide the paint used by 5 and multiply by £16.99:
Hence, it will cost £186.89 to buy all the paint
Answer:
=£186.89
Step-by-step explanation:
A=1/2(a+b)h
a||b dimensions
A=1/2(16+10)×7.6
=98.8m²
Given that 1 litre of paint covers an area of 1.9 sq m, we divide the area of the trapezium by this and multiply by the price per liter to get total cost:
paint used= Area/paint m²
98.8/1.9
=52 litres
We are given that each 5l tin of paint costs £16.99 . We therefore divide the paint used by 5 and multiply by £16.99
52/2
=10.4
11tins
cost=11×16.99
=£186.89
Chris is driving his car at a rate of 32 miles per hour. Albert is driving his car at a rate of 36 miles per hour. Both started driving at the same time. If you were to graph each linear relationship, what would be the difference in the slopes of the lines?
Answer:
Use the formula r = d/t. Your rate is 24 miles divided by 2 hours, so: r = 24 miles ÷ 2 hours = 12 miles per hour. Now let's say you rode your bike at a rate of 10 miles per hour for 4 hours.
Step-by-step explanation:
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.7 days and a standard deviation of 2.4 days. What is the 90th percentile for recovery times? (Round your answer to two decimal places.)
Answer: the 90th percentile for recovery times is 8.77 days.
Step-by-step explanation:
Let x be the random variable representing the recovery time of patients from a particular surgical procedure. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 5.7 days
σ = 2.4 days
The probability for the 90th percentile is 90/100 = 0.9
The z score corresponding to the probability value on the normal distribution table is 1.28
Therefore,
1.28 = (x - 5.7)/2.4
Cross multiplying, it becomes
1.28 × 2.4 = x - 5.7
3.072 = x - 5.7
x = 3.072 + 5.7 = 8.77 days
James is following this recipe to make flapjacks. James uses 600 g of margarine. How many flapjacks is James making? Recipe: Makes 15 flapjacks 120 g sugar 150 ml syrup 200 g oats 120 g margarine 40 g sultanas
Answer:
75 Flapjacks
Step-by-step explanation:
You must divide 120 by 600 in order to get your answer. As it says 120 margirine to make 15 flapjacks which is equal to one batch, you must then divide 600 by 120 and then multiply 5 by 15 to get 75. I hope this helped.
(brainliest?)
Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data. What do the results tell us? 83 45 80 53 46 24 79 34 55 10 44 Rangeequals 73 (Round to one decimal place as needed.) Sample standard deviationequals 23.4 (Round to one decimal place as needed.) Sample varianceequals 547.2 (Round to one decimal place as needed.) What do the results tell us? A. The sample standard deviation is too large in comparison to the range. B. Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless. C. Jersey numbers on a football team do not vary as much as expected. D. Jersey numbers on a football team vary much more than expected.
Answer: B. Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.
Step-by-step explanation:
Given the following list of data:
83 45 80 53 46 24 79 34 55 10 44
Range :
(Highest - Lowest) value
83 - 10 = 73
Sample Variance :
[Summation of (x - mean)^2] / number of observation - 1
Mean = (83+45+80+53+46+24+79+34+55+10+44) / 11
= 553 / 11 = 50.3
Check attached picture for computation of variance and standard deviation.
In football, jersey numbers do not imply any statistical relevance or importance
How to solve -5 + 13y = -7
Answer:
y = -2/13
Step-by-step explanation:
-5 + 13y = -7
Add 5 to each side
-5+5 + 13y = -7+5
13y = -2
Divide by 13
13y/13 = -2/13
y = -2/13
Which triangles are similar? d a b c
Answer:
b and d
Step-by-step explanation:
If lines p and q are parallel then the value of x is
Answer:
The answer is A. 10
Step-by-step explanation:
The two angles are alternate interior angles so they are congruent. Since they are congruent, you can write it in an equation.
5x - 25 = 3x - 5
subtract 3x from each side
2x - 25 = -5
add 25 to each side
2x = 20
divide 2 from each side
x = 10
Also, if you want to check your answer, you can plug 10 back into the equation to see if they're equal.
The relation between the given angles is given by the alternate interior
angles theorem.
If lines p and q are parallel then the value of x is A. 10°
Reason:
The given parameters are;
Condition; Line p, and line q, are parallel.
The angles (3·x - 5)° and (5·x - 25)° are alternate interior angles.
According to alternate interior angles theorem, we have the alternate
angles are congruent, where line p, and line q are parallel.
Therefore;
(3·x - 5)° ≅ (5·x - 25)° By alternate interior angles
(3·x - 5)° = (5·x - 25)° By definition of congruency
Solving, we get;
(3·x - 5)° + 25° = (5·x - 25)° + 25°
3·x + 20° - 3·x = 5·x - 3·x = 2·x
20° = 2·x
[tex]x = \dfrac{20^{\circ}}{2} = 10^{\circ}[/tex]
The correct option is A. 10°
Learn more here:
https://brainly.com/question/18242590
Estimate the solution to the following system of equations by graphing. A. B. C. D.
Answer:
Um where is the question
Step-by-step explanation:
Answer:
b. -1/3,1/2
Step-by-step explanation:
Given that tan theta = -9/4, where 270° ≤ theta ≤ 360° a)state the 5 trigonometric ratios as a fraction b) determine the value of theta to the nearest degree
Answer:
Step-by-step explanation:
θ lies in 4th quadrant.
cos θ and sec θ are positive all other trigonometric ratios are negative.
sin θ/cos θ=-9/4
sin θ=-9/4 cos θ
we know sin² θ +cos ² θ =1
(-9/4 cos θ)²+cos ² θ =1
cos ² θ (81/16+1)=1
cos ²θ((81+16)/16)=1
cos² θ=16/97
cos θ=4/√97
sin θ=-9/4*4/√97=-9/√97
sec θ=1/cos θ=√97/4
cosec θ=1/sin θ=-√97/9
cot θ=1/tan θ=-4/9
[tex]\ theta=tan^{-1}(-9/4) \approx 294 ^\circ[/tex]
Can someone please help me with this please I need the right answer if you don’t know how to do geometry then don’t do this please thank you
Answer:
3. Reflexive property of congruence
(since the statement states that a segment is congruent to itself)
4. SSS
(since 3 sides of one triangle are congruent to three sides of the other triangle)
4) Every 10 years in April, the population of Boston is recorded. In 1990, Boston had a
population of 4,500 people. From 1990 to 2000, the population increased by 15%. From 2000
to 2010, the population decreased by 4%. That was Boston's population in 2010?
A
4,527
B
4,968
с
4,995
D
5,382
4500 increase it by 15%=675
4500+675=5175
Decrease 4% from 5175
4% of 5175=207
5175-207=4868
Answer=I think it’s b
Employees from A and company B receive annual bonuses. What information would you need to test the claim that the difference in annual bonuses is greater than $100 at the 0.5 level of significance? Write out the hypothesis and explain the testing procedure in details
Answer:
1. The required information are
The average annual bonuses, [tex]\bar {x}_1[/tex] received by employees from company A
The average annual bonuses, [tex]\bar {x}_2[/tex] received by employees from company B
The standard deviation, σ₁, of the average annual bonuses for employees from company A
The standard deviation, σ₂, of the average annual bonuses for employees from company A
The number of employees in company A, n₁
The number of employees in company B, n₂
2. The null hypothesis is H₀: [tex]\bar {x}_1[/tex] - [tex]\bar {x}_2[/tex] ≤ 100
The alternative hypothesis is Hₐ: [tex]\bar {x}_1[/tex] - [tex]\bar {x}_2[/tex] > 100
Step-by-step explanation:
1. The required information are
The average annual bonuses, [tex]\bar {x}_1[/tex] received by employees from company A
The average annual bonuses, [tex]\bar {x}_2[/tex] received by employees from company B
The standard deviation, σ₁, of the average annual bonuses for employees from company A
The standard deviation, σ₂, of the average annual bonuses for employees from company A
The number of employees in company A, n₁
The number of employees in company B, n₂
2. The null hypothesis is H₀: [tex]\bar {x}_1[/tex] - [tex]\bar {x}_2[/tex] ≤ 100
The alternative hypothesis is Hₐ: [tex]\bar {x}_1[/tex] - [tex]\bar {x}_2[/tex] > 100
The z value for the hypothesis testing of the difference between two means is given as follows;
[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\frac{\sigma_{1}^{2} }{n_{1}}-\frac{\sigma _{2}^{2}}{n_{2}}}}[/tex]
At 0.5 level of significance, the critical [tex]z_\alpha[/tex] = ± 0
The rejection region is z > [tex]z_\alpha[/tex] and z < -[tex]z_\alpha[/tex]
Therefore, the value of z obtained from the relation above more than or less than 0, we reject the null hypothesis, and we fail to reject the alternative hypothesis.
Find the following for the function f(x)=3x2+2x−2. (a) f(0) =
Answer:
-2
Step-by-step explanation:
when x= 0
f(0)= 3*(0)² + 2*0 - 2
= 0 + 0-2
= -2
a) x2 - 2 = 0 resolver por factorizacion
Answer:
x = ± √2 = ± 1.4142
Step-by-step explanation:
Which inequality represents all the solutions of 10(3x + 2) > 7(2x − 4)?
Answer:
x>-3
Step-by-step explanation:
Answer:
x > -3
Step-by-step explanation: First you have to distribute the 10 to 3x +2 and 7 to 2x -4 . 10 times 3x + 2 is 30x + 20. 7 times 2x -4 is 14 x -28 . Subtract 20 from both sides, which is 30x = 14x-48 , because -28 minus 20 is -48. Subtract 14 x from both sides which is gonna be 16x >-48 , divide both sides by 16 which is x > -3.
What is the root of -100 or √−100
Answer:
The root of -100 is 10i
Step-by-step explanation:
Ten I
Where is g decreasing ? Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!!
Answer:
x≥ -1 or (-1, ∞)
Step-by-step explanation:
g is decreasing where the slope is negative so after max at -1 so x≥ -1
What is the product of (x-2)(x+2)?
Answer:
The difference of squares is (a - b)(a + b) = a² - b². Since a = x and b = 2, the answer is x² - 4.
Witch value of x makes the equation x + 7 = 21 true ?
Answer:
x=14
Step-by-step explanation:
x+7=21
x=14
Which interval contains a local minimum for the graphed function?
A. [-4, -2.5]
B. [-2, -1]
C. [1, 2]
D. [2.5, 4]
Answer:
A
Step-by-step explanation:
the answer is a why do not ask
What two number multiply to -21 and add to 20
Answer:
-1 and 21
Step-by-step explanation:
Let the numbers be x and y.
x + y = 20
xy = -21
Solve the first equation for x and substitute in the second equation.
x = 20 - y
(20 - y)y = -21
20y - y^2 = -21
y^2 - 20y - 21 = 0
(y - 21)(y + 1) = 0
y - 21 = 0 or y + 1 = 0
y = 21 or y = -1
For y = 21:
x = 20 - y
x = 20 - 21
x = -1
For y = -1:
x = 20 - y
x = 20 - (-1)
x = 21
Solutions: (-1, 21) and (21, -1)
Answer: the numbers are -1 and 21