9514 1404 393
Answer:
∠CAB = 86°
∠ABC = 43°
∠BCA = 51°
Step-by-step explanation:
This can be done a couple of different ways (as with most math problems). We can use the distance formula to find the side lengths, then the law of cosines to find the angles. Or, we could use the dot product. In the end, the math is about the same.
The lengths of the sides are given by the distance formula.
AB² = (4-1)² +(-3-0)² +(0-(-1)) = 16 +9 +1 = 26
BC² = (1-4)² +(2-(-3))³ +(3-0)² = 9 +25 +9 = 43
CA² = (1-1)² +(0-2)² +(-1-3)² = 4 +16 = 20
From the law of cosines, ...
∠A = arccos((AB² +CA² -BC²)/(2·AB·CA)) = arccos((26 +20 -43)/(2√(26·20)))
∠A = arccos(3/(4√130)) ≈ 86°
∠B = arccos((AB² +BC² -AC²)/(2·AB·BC)) = arccos((26 +43 -20)/(2√(26·43)))
∠B = arccos(49/(2√1118)) ≈ 43°
∠C = arccos((BC² +CA² -AB²)/(2·BC·CA)) = arccos((43 +20 -26)/(2√(43·20)))
∠C = arccos(37/(4√215)) ≈ 51°
The three angles are ...
∠CAB = 86°
∠ABC = 43°
∠BCA = 51°
_____
Additional comment
This sort of repetitive arithmetic is nicely done by a spreadsheet.
Explain how to divide a decimal by a decimal
Answer:
To divide a decimal by another decimal:
Move the decimal point in the divisor to the right until it is a whole number.
Move the decimal point in the dividend to the right by the same number of places as the decimal point was moved to make the divisor a whole number.
Then divide the new dividend by the new divisor
Step-by-step explanation:
see in the example
What is the value of y?
Enter your answer, as an exact value, in the box.
Answer:
y=4√3 units
Step-by-step explanation:
Hi there!
We are given ΔABC, which is a right triangle (m<C=90°), m<A=60°, AB=8, and BC=y
We need to find the value of y (BC)
The side AB is the hypotenuse of the (the side opposite from the right angle).
BC is a leg, which is a side that makes up the right angle.
Now, if we have a right triangle that has one of the acute angles as 60°, the side OPPOSITE from that 60° angle (in this case, BC) is equal to [tex]\frac{a\sqrt{3}}{2}[/tex], where a is the length of the hypotenuse
Since we have the hypotenuse given as 8, the length of BC (y) is [tex]\frac{8\sqrt{3}}{2}[/tex], or 4√3
so y=4√3 units
Hope this helps!
when price of indomie noodles was lowered from #50 to #40 per unit, quantity demanded increases from 400 to 600 units per week. calculate the coefficient of price elasticity of demand and determine whether by lowering price this firm has made a wise decision
Answer:
The price elasticity of demand is -10
Step-by-step explanation:
Given
[tex]p_1,p_2 = 50,40[/tex]
[tex]q_1,q_2 = 400,500[/tex]
Solving (a): The coefficient of price elasticity of demand (k)
This is calculated as:
[tex]k = \frac{\triangle q}{\triangle p}[/tex]
So, we have:
[tex]k = \frac{500 - 400}{40 - 50}[/tex]
[tex]k = \frac{100}{-10}[/tex]
[tex]k = -10[/tex]
Because |k| > 0, then we can conclude that the company made a wise decision.
Probabilityyyyyyyyyyyyyyy
Answer:
Reduce if needed, asked or necessary
Step-by-step explanation:
1. 4/10
2. 2/6
3. 4/10
4. more likely
Answer:
Since Probability Is Usually Written In Fraction Form OR Ratios
(Although It Really Doesn't Matter):
1. 4/10 (2/5)
2. 2/6 (1/3)
3. 6/10 (3/5)
(All Fraction Form)
Last Question:
I can't really see the bottom but probably its 'More likely' since you can already see a bunch of red marbles.
Step-by-step explanation:
This is the basic fraction form : ____ / ____
Based on what they ask, like the probability of picking out a black marble, count the number of black marbles in the particular bag and put that number as the numerator. The denominator is the total amount of marbles in that particular bag. Hope this helps!
HELP HELP HELP MATH⚠️⚠️⚠️⚠️⚠️
Find four consecutive integers with the sum of 2021
Answer:
This problem has not solution
Step-by-step explanation:
lets the integers be:
x
x+1
x+2
x+3
so:
x+(x+1)+(x+2)+(x+3)=2021
x+x+x+x+1+2+3=2021
4x+6=2021
4x=2021-6=2015
x=2015/4=503.75
x is not a integer
Need help with this really fast
Answer:
6
Step-by-step explanation:
You can apply the proportion of 9/6 to 4 to get 6:
6*(9/6)= 9
So
4*(9/6) = Length LA
6= Length LA
Answer:
Option C, or [tex]2\frac{2}{3}[/tex]
Explanation:
We can see that the Line FM in the smaller triangle dialates to Line LK in the bigger triangle by the scale factor of:
FM/LK
6/9 or 2/3
So we would know that to find out the value of LA in the bigger triangle we would have to dialate it’s corresponding side FI in the smaller triangle by the same scale factor:
4 * 2/3
=> [tex]2\frac{2}{3}[/tex] = LA
Hope this helps!
Simplify. v80
A. 16v5
B. 5v4
C. 4v5
D. 20v4
Hi!
√80 = √(16 • 5) = √(4² • 5) = 4√5
In a family of 3 children, what is the probability that there will be exactly 2 boys assuming that the sexes are equally likely to occur in each birth
Answer:
There is a 60.00 percent probability of a particular outcome and 40.00 percent probability of another outcome.
FREE
Circle O has a circumference of approximately 250 ft.
What is the approximate length of the diameter, d?
O 40 ft
O 80 ft
O 125 ft
O 250 ft
Save and Exit
Next
Submit
Mark this and return
Answer:
Step-by-step explanation:
circumference = πd ≅ 250 ft
d ≅ 250/π ≅80 ft
f(x)=2x1 + 16x2 + 7x3 + 4x4 -> min
Step-by-step explanation:
f(x)=(2x-1)square=0
it can be 0 or greater than 0
Hence,maximum value of (2x- 1)square=0
maximum value of (2x- 1square)+3=0+3=3
ab=6cm ac=12 calculate the length of cd
Answer:
is that the full question?
Answer:
Solution:-
Given,
ab =perpendicular (p)= 6cm
ac =hypotenuse (h)= 12cm
cd =base (b)= ?
using , Pythagoras theorem we have ,
b²=√h²-p²
or,cd²=√ac²-ab²
= √12²-6²
= √144-36
=√108
=√10.8²
=10.8cm
the length of cd is 10.8 cm
hope it is helpful to you
sets A and B have 3 and 6 elements respectively. what can be the minimum number of elements in AUB
Answer:
6
Step-by-step explanation:
n(AUB) = n(A) + n(B) - n(AnB)
n(AUB) can have the minimum number of elements if n(AnB) has the maximum number of elements.
n(AnB) maximum = 3
so n(AUB) = 3+6-3 = 6
5. In 2015, Texas led the nation in the percentage of people who lacked health insurance (21.6% of the population). It is known that, nationally, 5% of patients account for 50% of the costs of healthcare. These are the “high cost” patients Assume* that: Being a high cost patient and being uninsured are independent characteristics Insured and uninsured people become “patients” at the same rate The uninsured and high cost patients in Texas are evenly distributed across the state, and that high cost patients are evenly distributed across insured and uninsured patient populations a. What is the probability that a patient in a Texas healthcare facility will be a high cost patient who is uninsured?
Answer: 0.108
Step-by-step explanation:
Since the probability of the uninsured is 21.6% of the population, then the probability of insured will be:
= 1 - 21.6%
= 78.4%
The probability of high cost patients is 5%. Therefore, the probability that a patient in a Texas healthcare facility will be a high cost patient who is uninsured will be:
= 5% × 21.6%
= 0.05 × 0.216
= 0.108
For a particular species of wolf, 55% are female, 20% hunt in medium-sized packs, and 15% are both female and hunt in medium-sized packs. What is the percent of wolves that are female but do not hunt in medium-sized packs?
HELP ASAP! I don’t know how to solve this problem nor where to start. Can someone please help me out here?
===============================================
Explanation:
It might help to draw out the picture as shown below. The pool itself (just the water only) is the inner rectangle. The outer rectangle is the pool plus the border of those 1 by 1 tiles.
The pool is a rectangle 90 feet by 80 feet. If we add on the tiles, then we get a larger rectangle that is 90+2 = 92 feet by 80+2 = 82 feet.
We add on 2 since we're adding two copies of "1" on either side of each dimension.
The larger rectangle's area is 92*82 = 7544 square feet
The smaller rectangle's area is 90*80 = 7200 square feet
The difference in areas is 7544-7200 = 344 square feet.
Each 1 by 1 tile is of area 1*1 = 1 sq foot, meaning that 344 tiles will get us the 344 square foot border around the pool.
Which would result in a lower price to first discount an item by 10% and then by a further 15%, OR to first discount an item by 15% and then by a further 10%. Justify your reasoning.
Answer:
Neither one. They will both result in the same price.
Step-by-step explanation:
To discount an item 10%, you charge 90% of the price of the item. To find 90% of a price, you multiply the price by 0.9.
To discount an item 15%, you charge 85% of the price of the item. To find 85% of a price, you multiply the price by 0.85.
Since multiplication is commutative, multiplying a number by 0.9 and then by 0.85 is the same as multiplying the number by 0.85 first and then by 0.9.
Let's say the item costs x.
Take off the 10% discount first: 0.9x
Now take off the 15% discount: 0.85 * (0.9x)
Now do it the other way.
Take off the 15% discount first: 0.85x
Now take off the 10% discount: 0.9 * (0.85x)
Since 0.85 * 0.9 * x = 0.9 * 0.85 * x, the results are the same.
Answer: neither
if cosA=3√2/5,then show that cos2A=11/25
Answer:
Step-by-step explanation:
Cos 2A = 2Cos² A - 1
[tex]= 2*(\frac{3\sqrt{2}}{5})^{2}-1\\\\=2*(\frac{3^{2}*(\sqrt{2})^{2}}{5^{2}})-1\\\\=2*\frac{9*2}{25} - 1\\\\=\frac{36}{25}-1\\\\=\frac{36}{25}-\frac{25}{25}\\\\=\frac{11}{25}[/tex]
The following figure appears in a math workbook. Students are asked to reflect the polygon across the line, then rotate it 90 degrees clockwise . Which figure shows the result of the two transformations?
Answer:
C
Step-by-step explanation:
tracing paper is your friend
What is the value of x in the figure below? If necessary, round your answer to
the nearest tenth of a unit.
X
15
D 4 B
A. 7.7
B. 3.8
O C. 15
D. 4
Answer:
Step-by-step explanation:
when a force of 400N is applied on a body at angle of 60 degree to the horizontal displacement,the body covers a distance of 8m.what is the work done?
Answer:
1600N
Step-by-step explanation:
Force = 400 N
Angle with horizontal = 60°
Displacement in horizontal direction = 8 m
work done formula when angle is included: Force * distance * cos(angle)
400 * 8 * cos(60)
= 400 * 8 * 1/2
= 1600N
i need help solving this .
Answer:b
Step-by-step explanation:
Answer:
just be smart trust me u dont need us to give u the answer ur super smart
Step-by-step explanation:
make me brainliest to help people be encourage
The half-life of a newly discovered radioactive element is 30 seconds. To the nearest tenth of a second, how long will it take for a sample of 9 grams to decay to 0.72 grams
Answer:
It will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.
Step-by-step explanation:
We can write a half-life function to model our function.
A half-life function has the form:
[tex]\displaystyle A=A_0\left(\frac{1}{2}\right)^{t/d}[/tex]
Where A₀ is the initial amount, t is the time that has passes (in this case seconds), d is the half-life, and A is the amount after t seconds.
Since the half-life of the element is 30 seconds, d = 30. Our initial sample has nine grams, so A₀ is 9. Substitute:
[tex]\displaystyle A=9\left(\frac{1}{2}\right)^{t/30}[/tex]
We want to find the time it will take for the element to decay to 0.72 grams. So, we can let A = 0.72 and solve for t:
[tex]\displaystyle 0.72=9\left(\frac{1}{2}\right)^{t/30}[/tex]
Divide both sides by 9:
[tex]\displaystyle 0.08=\left(\frac{1}{2}\right)^{t/30}[/tex]
We can take the natural log of both sides:
[tex]\displaystyle \ln(0.08)=\ln\left(\left(\frac{1}{2}\right)^{t/30}\right)[/tex]
By logarithm properties:
[tex]\displaystyle \ln(0.08)=\frac{t}{30}\ln(0.5)[/tex]
Solve for t:
[tex]\displaystyle t=\frac{30\ln(0.08)}{\ln(0.5)}\approx109.3\text{ seconds}[/tex]
So, it will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.
F(x) =-2x-4 find x if f(x)=14
Answer:
14=-2x-4
18=-2x
x=-9
Hope This Helps!!!
What is the volume of a cone with a height of 27 cm
and a radius of 13 cm? Round your answer to the
nearest tenth.
Use the button on your calculator to complete this
problem.
V=
cm3
Answer:4778.3 cm^3
Step-by-step explanation: The formula for volume of a cone is V=1/3h pi r^2. By plugging in the height and the radius we get our answer.
Answer:
4778.4 :)
Step-by-step explanation:
Create a circle such that its center is point A and B is a point on the circle.
Answer:
The center of a circle is the point in the circle which is equidistant to all the edges of thr circle. The point a is the center, while point b is an arbitrary point in the circle. Find attachment for the diagram.
for a science fair project javier is recording the amount of water that evaporate from a bucket in a month he creates a table like this i will give point for the best answer
week 1 2/16 inch
week 2 1/16 inch
week 3 3/16 inch
week 4 2/16 inch
how much water had evaported from the bucket at the end of week 2
what was the total amount of water that evaported in the four weeks
if javier orignally put 4 inches of water in the bucket how many inches of water were left after the experment was completed
Answer: [tex]\dfrac{3}{16},\ \dfrac{1}{2}, \dfrac{7}{2}\ \text{inch}[/tex]
Step-by-step explanation:
Given
Javier created a table for the amount of water evaporated in each week
After two weeks, the amount of water evaporated is
[tex]\Rightarrow \dfrac{2}{16}+\dfrac{1}{16}\\\\\Rightarrow \dfrac{2+1}{16}=\dfrac{3}{16}\ \text{inch}[/tex]
Total amount of water evaporated in four weeks is
[tex]\Rightarrow \dfrac{2}{16}+\dfrac{1}{16}+\dfrac{3}{16}+\dfrac{2}{16}\\\\\Rightarrow \dfrac{2+1+3+2}{16}=\dfrac{8}{16}\\\Rightarrow \dfrac{1}{2}\ \text{inch}[/tex]
If Javier originally puts 4 inches of water, amount of water left in the bucket
[tex]\Rightarrow 4-\dfrac{1}{2}\\\\\Rightarrow \dfrac{4\times 2}{2}-\dfrac{1}{2}\\\\\Rightarrow \dfrac{8-1}{2}=\dfrac{7}{2}\ \text{inch}[/tex]
I’ll mark u plz help
Answer:
D is the answer
Step-by-step explanation:
all sides and angles are equal
hope it helps!! let me know if it does
A boy leaves station X on a bearing of 035' to station Y. which is 21km away. He then travels to another station Z on a bearing of 125 degrees . If Z is directly East of X, what is the distance from X to his present position?
9514 1404 393
Answer:
36.6 km
Step-by-step explanation:
We assume the initial bearing of the boy is 35°. Then he will make a 90° turn to a heading of 125°. A diagram shows the distance of interest is the hypotenuse of a right triangle in which 35° is the angle opposite the side of length 21 km.
The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(35°) = (21 km)/XZ
XZ = (21 km)/sin(35°) ≈ 36.61 km
The distance from X to Z is about 36.61 km.
_____
The attached diagram has the angles measured in the usual way for a Cartesian plane: CCW from the +x axis. This will correspond to bearing measures if we relabel the axes so that +x is North, and +y is East.
if side of square is 4.05 find its area
Answer:
A
≈
16.4
please give brain listWhich of the following is a like radical to cube rt of 7x
Answer:
[tex]\sqrt[3]{7x}[/tex]
Step-by-step explanation:
Given
[tex]7x[/tex]
Required
The radical statement
Cube root is represented as:
[tex]\sqrt[3]{}[/tex]
Considering [tex]7x[/tex], the expression is:
[tex]\sqrt[3]{7x}[/tex]
