Answer:
6. x° is approximately 21.04°
7. x° is approximately 39.56°
8. x° is approximately 58.03°
9. x° is approximately 72.85°
Step-by-step explanation:
6. In the given right triangle (a triangle with the measure of one of the interior angles equal to 90°, indicated by the small square between two sides) , we have;
The hypotenuse side length = 15
The adjacent side to the given reference angle, x° = 14
By trigonometric ratio, we have;
[tex]cos\angle X = \dfrac{Adjacent\ leg \ length}{Hypotenuse \ length}[/tex]
[tex]\therefore cos(x^{\circ}) = \dfrac{14}{15}[/tex]
To find the value of x°, we make use of the inverse cosine function, arccos found on a scientific calculator, as follows;
x° = arccos(14/15) ≈ 21.04°
x° ≈ 21.04°
7. In the given right triangle, we have;
The length of the opposite side to the given reference angle, x° = 19
The length of the adjacent side to the given reference angle, x° = 23
By trigonometric ratios, we have;
[tex]Tan(\angle X) = \dfrac{Opposite \, side \ length}{Adjacent\, side \ length}[/tex]
[tex]\therefore tan(x^{\circ}) = \dfrac{19}{23}[/tex]
Therefore;
x° = arctan(19/23) ≈ 39.56°
x° ≈ 39.56°
8. In the given right triangle, the adjacent side to the reference angle, x° and the hypotenuse side are given, therefore, we have;
x° = arccos(9/17) ≈ 58.03°
x° ≈ 58.03°
9. The opposite side to the reference angle and the hypotenuse side are given
By trigonometric ratio, we have;
[tex]sin\angle X = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length}[/tex]
[tex]\therefore sin(x^{\circ}) = \dfrac{43}{45}[/tex]
x° = arcsin(43/45) ≈ 72.85°
x° ≈ 72.85°.
What is the total percent of a pie or circle graph
Answer:
100%
Step-by-step explanation:
WHICH EXPRESSION HAS THE GREATEST VALUE
Answer:
The second, 16^3/2
Step-by-step explanation:
The first is equal to 16
The second is equal to 64
The third is equal to 16
The fourth is equal to 16
The required, greatest volume among the given number is [tex]16^{3/2}[/tex].
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.
Here,
The given number,
∛64² simplified to 16,
[tex]16^{3/2}[/tex] simplified to 64.
√16² simplified to 16
∛8⁴ simplified to 16
Thus, the required, greatest volume among the given number is [tex]16^{3/2}[/tex].
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ3
The grocery store has 19.2 pounds of rice. If the rice is divided equally into 8 bags, how many pounds of rice will be in each bag?
Answer:
2.4 pounds
Step-by-step explanation:
19.2 pounds÷ 8 bags= 2.4 pounds per bag
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How many diagonals does a convex angle have?
A cube has edge lengths of 11 ft. What is the volume of the cube?
Answer:
1331 ft³
Step-by-step explanation:
The volume of a cube = (edge length)³
From the above question,
Edge length = 11 ft
The volume of the cube = (11 ft)³
= (11 ft × 11 ft × 11 ft)
= 1331 ft³
The volume of the cube = 1331 ft³
Multiple of 30 degrees
Answer:
69
Step-by-step explanation:
Answer:
Step-by-step explanation:
Incomplete question!
But here are some "multiples of 30 degrees:"
60, 90, 120, 180, 150, and so on. Start with "30 degrees" and multiply that by various positive integers: 2, 3, 4, 6, 5, and so on, to obtain "multiples of 30 degrees."
whats 10.50x +64=300
Answer:
74.5
Step-by-step explanation:
A piling for a high-rise building is pushed by two bulldozers at exactly the same time. One bulldozer exerts a force of 1850
pounds in a westerly direction. The other bulldozer pushes the piling with a force of 3250 pounds in a northerly direction. What
is the direction of the resulting force upon the piling, to the nearest degree?
Answer: I got this answer from the internet hopefully this helps
Resultant force will act on 65° N of W.
Step-by-step explanation:
The direction of the resulting force upon the piling, to the nearest degree is gotten as; A = 60°
What is the direction of the resultant force?As given in the question one bulldozer exerts force of 1850 pounds in western direction and another pushes with a force of 3250 pounds in northern direction.
Now, we have to find angle A which is an angle between 1850 pounds of force and resultant force F.
Thus;
tan A= Force on North direction/ Force on west direction
tan A = 3250/1850
tan A = 1.7568
A = tan⁻¹1.7568
A = 60.35°
To the nearest degree is A = 60°
Read more about resultant force direction at; https://brainly.com/question/14626208
Which quadrant of the coordinate plane has ordered pairs in the form of a positive number
and a negative number, (+,-)?
Y у
quadrant IV
10
-9
quadrant III
8
7
6
Quadrant
quadrant 11
Quadrant
II
5
4
quadrant 1
2
- 1
2
-Z
3
5
6
7
8
9
-10-9-8-7-6-5-4-3
10
-1 0
-1
-2
-3
-4
-5
Quadrant
III
Quadrant
IV
-6
-7
-8
-9
-10
Answer:
Quadrant IV
Step-by-step explanation:
On the graph, the x-axis numbers are positive and the y-axis numbers are negative
Given triangle ADE shown below with overline BC || overline DE . if AB=16, BD=8, and DE = 30, which of the following is the length of overline BC
1) 20
2) 60
3) 15
4) 22
Calculate the average of the numbers shown. 23.8, 12.1 ,-17.6, 31.3
A)12.4
B)12.8
C)13.4
D)13.8
Answer:A.
Step-by-step explanation:
add the numbers together
23.8 + 12.1 + -17.6+ 31.3 = 49.6
then divide by number of numbers(4)
49.6/4=12.4
how do i factor this trinomial 5y^2 — 7y — 6
Answer:
(5y+3) x (y-2)
Step-by-step explanation:
5y^2-7y-6
5y^2+3y-10y-6
y(5y+3(-2(5y+3)
(5y+3) x (y-2)
What is the common ratio between successive terms in the sequence? 27,9,3,1, 1/3, ,1/9, 1/27
Answer:
1/3
Step-by-step explanation:
Take the second term and divide by the first
9/27 = 1/3
Take the third term and divide by the second
3/9 = 1/3
Check each subsequent ratio, we can see the common ratio is 1/3
Who is correct?
PLease answer ASAP!! pls (:
Answer: Isaiah is correct because you can never be sure whether it’s gonna be a queen but you can be sure that the card could be red
Step-by-step explanation:
Find the lateral area of the cone to the nearest whole
number.
Answer:
lateral area = pi x radius x slant height
slant height = 40^2 + 30^2 = 1600 + 900= [tex]\sqrt{2500}[/tex] = 50
3.14 x 30 x 50 = 4710m^3
Hope that answers your question
Don't hesitate to leave a comment if you are confused about something
Step-by-step explanation:
put these fractions from least to greatest please!! 2/3 7/12 17/24 3/4
Answer:
7/12 < 2/3 < 17/24 < 3/4
Step-by-step explanation:
least to greatest
You want to estimate the number of students in your school who support extra funding for the music club. You survey every second student who enters the school.
Determine whether the sample is biased or unbiased.
Answer: It’s UNBIASED!
Step-by-step explanation:
Please help,
NO LINKS PLEASE
Answer:the photo is to bleary
Step-by-step explanation:
Which number is the additive inverse of 47? Hi. SI56 -47 1 W om 04
Answer:
4 [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
The additive inverse is the value that must be added to the number to give zero.
- 4 [tex]\frac{1}{4}[/tex] + 4 [tex]\frac{1}{4}[/tex] = 0
↑ additive inverse
What is the angle measure of 2x+1°
Answer:
25 degrees
Step-by-step explanation:
Haha, awesome! Just did a problem like this!
All angles add up to 180, so set it up like this:
2x + 1 + 5x + 5 + 90 = 18
Combine like terms.
7x + 96 = 180
7x = 84
x = 12
Plug x back into 2x + 1
2(12) + 1
24 + 1
= 25 degrees
While we're at it...
5(12) + 5
60 + 5
= 65 degrees (for the other angle)
25 + 65 + 90 = 180
Math checks out & we're good to go!
Hope this helped. :) <3
The volume of a cylinder is 117.1 cubic feet, and its height is 15 ft. Find the diameter of the base of the cylinder.
Answer:
3.15 ft
Step-by-step explanation:
V
Volume of a cylinder: πr²h. Solving for r², we get r² = ---------
πh
Here, we get r² = (117.1 ft³) / (3.14·15 ft) = 2.48 ft² and r = √(2.48 ft²), or
1.58 ft, so that the diameter is 2r, or 3.15 ft
The diameter of the base of the cylinder is 3.15 ft.
Callie uses leather cord to make necklaces. She has a piece of leather cord that has a length of 4 yards. Each necklace will have a length of 28 inches. How many necklaces can Callie make?
A. 32
B. 24
C. 4
D. 5
What is the median of 8, 7.5, 6, 5.75, 10.25, 13.75, 6.5, 8.75, 9, 8, 9.25, 10, 8.25, 8.25, 9.25, 11, 6.75, 7, 9.5, 8.5
Answer:
8.375
Step-by-step explanation:
5.75,6, 6.5, 6.75, 7, 7.5, 8, 8, 8.25, 8.25, 8.5, 8.75, 9, 9.25, 9.25, 9.5, 10, 10.25, 11, 13.75
8.25 + 8.5 = 16.75
16.75/2 = 8.375
-6 ( x – 8) = 60
can you explain it step by step for me
Answer:
-2
Step-by-step explanation:
-6(x-8)=60
x-8=60/-6
x-8=-10
x=-10+8
x=-2
TRUE OR FALSE (answer these two questions)
800 is a compatible number that is close to 704
Spencer should add compatible numbers to fund the estimate. (The number is 704)
el valor de mis acciones ,tras subir un 5% es de 20,000 ¿Cuál era el valor anterior ?
Answer:
400,000
Step-by-step explanation:
Ok so, su ecusión es 0.05p = 20,000 p = 400,000
lo siento si esto está mal no soy genial con el español.
A culture of 100 bacteria grows at a continuous rate of 20%. Two hours later. 60 of the same type of bacteria are placed in a culture that allows a 30% growth rate. After how many hours do both cultures have the same population? Explain your answer.
Answer:
Both cultures will have the same population after 11 hours.
Step-by-step explanation:
Exponential equation for population growth:
The exponential equation for population growth is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial population and r is the growth rate, as a decimal.
A culture of 100 bacteria grows at a continuous rate of 20%.
This means that [tex]P(0) = 100, r = 0.2[/tex]. So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P_{1}(t) = 100(1+0.2)^t[/tex]
[tex]P_{1}(t) = 100(1.2)^t[/tex]
The other culture starts to hours later, and we want to take that time as a parameter. So
[tex]P_{1}(2) = 100(1.2)^2 = 144[/tex]
Which means that when culture 2 growth starts, the population size of culture 1 is described by the following equation:
[tex]P_{1}(t) = 144(1.2)^t[/tex]
Two hours later 60 of the same type of bacteria are placed in a culture that allows a 30% growth rate.
This means that [tex]P(0) = 60, r = 0.3[/tex]. So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P_{2}(t) = 60(1+0.3)^t[/tex]
[tex]P_{2}(t) = 60(1.3)^t[/tex]
After how many hours do both cultures have the same population?
This is t for which:
[tex]P_{1}(t) = P_{2}(t)[/tex]
So
[tex]144(1.2)^t = 60(1.3)^t[/tex]
[tex]\frac{(1.3)^t}{(1.2)^t} = \frac{144}{60}[/tex]
[tex](\frac{1.3}{1.2})^t = \frac{144}{60}[/tex]
[tex]\log{(\frac{1.3}{1.2})^t} = \log{\frac{144}{60}}[/tex]
[tex]t\log{\frac{1.3}{1.2}} = \log{\frac{144}{60}}[/tex]
[tex]t = \frac{\log{\frac{144}{60}}}{\log{\frac{1.3}{1.2}}}[/tex]
[tex]t = 11[/tex]
Both cultures will have the same population after 11 hours.
PLZ HELP!!!!!
Calculate x
Answer:
x = 31
Step-by-step explanation:
The two triangles are similar, so [tex]\triangle{NPO} \sim \triangle{YZO}[/tex].
Vertex N matches up with vertex Y.
Vertex P matches up with vertex Z.
Vertex[tex]\frac{NO}{YO}=\frac{1}{4}\\\\\frac{x}{124}=\frac{1}{4}\\\\4x=124\\\\x=31[/tex] O matches up with itself.
Corresponding sides are in proportion. To find the proportion between the two triangles, you use known sides from each.
[tex]\frac{NP}{YZ}=\frac{23}{92}=\frac{1}{4}[/tex] meaning the small triangle is 1/4 the size of the large one.
To find x , notice that it is side NO which corresponds to side YO from the large triangle.
Peter has an average daily balance on his credit card of $127.50. His credit card charges 14.99% annual interest. What will his monthly finance charge be
Answer:
$1.59
Step-by-step explanation:
monthly finance charge = average daily balance x monthly interest
monthly interest = 14,99% / 12 = 1.249%
1.249% x $127.50 = $1.59