Final answer:
To determine if the points (-1,3), (4,-2), and (1,-5) form a right triangle, plot them on a coordinate plane, use the distance formula to calculate the lengths of the sides, and then apply the Pythagorean theorem.
Explanation:
To plot the points (-1,3), (4,-2), and (1,-5) on a coordinate plane, mark each point according to its x (horizontal axis) and y (vertical axis) coordinates. Connect these points to form a triangle. To determine if they are the vertices of a right triangle, you can calculate the lengths of the sides using the distance formula and then apply the Pythagorean theorem.
The distance formula is √((x₂-x₁)² + (y₂-y₁)²), and the Pythagorean theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
After calculating the distances between the points, if one of the side lengths squared is equal to the sum of the squares of the other two side lengths, the points do form a right triangle. If not, they do not form a right triangle.
Julia won the race by one hundredth of a second Write the amount of time she won by as a fraction
Answer:
1/100
Step-by-step explanation:
50 POINTS!!! PLEASE HELP PLEASE HURRY !!!
Also ignore what the picture says just find the area of the figure
What is the area of the figure:
Answer:
144
Step-by-step explanation:
Height and Length are A and Hypotenuse is Asqrt(2)
Set hyp = 24 and solve for a.
a = 24/sqrt(2)
Area of Tri = 1/2*(A^2)
Answer:
144
Step-by-step explanation:
A ladder leans against a building, making a 70° angle of elevation with the ground. The top of the ladder reaches a point on the building that is 39 feet above the ground.
To the nearest tenth of a foot, what is the distance between the base of the building and the base of the ladder?
Question 4 options:
13.3 ft
14.2 ft
36.6 ft
41.5 ft
Question 5
A bird fountain is located 6 m from the base of Joey's apartment building. From his window, Joey can see it at a 51° angle of depression.
To the nearest tenth of a meter, how far up the building is Joey's window?
Question 5 options:
4.9 m
7.4 m
7.7 m
9.5 m
➷ It would help if you drew it out as a triangle
You will notice that you need to use tan
tan70 = 39/x
x = 39/tan70
x = 14.194
The correct option would be 14.2 ft
You will need to use tan
tan51 = 6/x
x = 6/tan51
x = 4.8587
The correct option would be 4.9m
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Solve the problem be using proper methods. Show work.
If you invest $1200 at an interest rate of 1.3% compounded continuously,
a) How much will you have in 5 years?
b) How long will it take for your investment to double?
Answer:
$1280.59
53 years
Step-by-step explanation:
To find how much we will get in 5 years, we use the formula:
[tex]A=Pe^{rt}[/tex]
P = $1200
r = 1.3% or 0.013
t = 5
Now that we have our values, let's plug them into the formula.
[tex]A=1200e^{0.013(5)}[/tex]
[tex]A=1200e^{0.065}[/tex]
[tex]A=1280.59[/tex]
We will have $1280.59 after 5 years.
Now to find how long it will take for our investment to double.
t = ln(A/P)/r
A = 2400
P = 1200
r = 1.3 or 0.013
Let's plug it in.
t = ln(2400/1200)/0.013
t = ln(2)/0.013
t = 53.32 or 53 years
could someone please just help me out. i’m struggling pleasee
Answer:
NO = 4.5
MO = 3.5
LN = sqrt(44)
Step-by-step explanation:
Since the value of the base of the triangles is 8, and the value of NO is 4.5, the value of MO is MN - NO, which is 8 - 4.5, which comes out to 3.5.
Then, we apply the quadratic formula to triangle MLO to find that the middle line value is sqrt(23.75). Then we use the quadratic formula on traingle OLN to find the LN is sqrt(44).
once again text is for min word req the problem is in the image again
Set the two equations to equal each other and solve:
3x-2 = x+2
Subtract x from each side:
2x -2 = 2
Add 2 to each side:
2x = 4
Divide both sides by 2:
x = 4/2 = 2
Now replace x with 2 in one of the equations and solve for y:
y = 3x -2 = 3(2) - 2 = 6-2 = 4
X = 2, Y = 4
(2,4)
Two-thirds of the students in Hannah's homeroom plan to do some volunteering this summer. Of these students,3/5 plan to volunteer at the community center. What fraction of students in Hannah's homeroom plan to volunteer at the community center this summer
Answer:
2/5 of the students
Step-by-step explanation:
Let the total number of students be x. Two-Thirds of the students plan to do some volunteering. Two-Thirds in fraction can be written as 2/3. So the portion of the students which plan to do some volunteering is:
[tex]\frac{2x}{3}[/tex]
From these students, 3/5 plan to volunteer at community center. So the students who plan to volunteer at community center will be:
[tex]\frac{2x}{3} \times \frac{3}{5}\\\\ = \frac{2x}{5}[/tex]
This means, among x students, 2/5 of the students plan to volunteer at the community center this summer.
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 270. (a) Find an expression for the number of bacteria after t hours. P(t) = (b) Find the number of bacteria after 4 hours. (Round your answer to the nearest whole number.) P(4) = bacteria (c) Find the rate of growth after 4 hours. (Round your answer to the nearest whole number.) P'(4) = bacteria per hour (d) When will the population reach 10,000? (Round your answer to one decimal place.) t = hr
Answer: [tex]\bold{a)\ P(t)=P_o\cdot e^{t\cdot ln(2.7)}}[/tex]
b) 5314
c) ln 2.7
d) 4.6 hrs
Step-by-step explanation:
[tex]P(t) = P_o\cdot e^{kt}\\\\\bullet \text{P(t) is the number of bacteria after t hours} \\\bullet P_o\text{ is the initial number of bacteria}\\\bullet \text{k is the rate of growth}\\\bullet \text{t is the time (in hours)}\\\\\\270=100\cdot e^{k(1)}\\2.7=e^k\\ln\ 2.7=\ln e^k\\\boxed{ln\ 2.7=k}\\\\\text{So the equation to find the number of bacteria is: }\boxed{P(t)=P_o\cdot e^{t\cdot ln(2.7)}}\\\\\\P(4)=100\cdot e^{4\cdot ln(2.7)}\\.\qquad =\boxed{5314}[/tex]
[tex]10,000=100\cdot e^{t\cdot ln(2.7)}\\100=e^{t\cdot ln(2.7)}\\ln\ 100=ln\ e^{t\cdot ln(2.7)}\\ln\ 100=t\cdot ln(2.7)\\\dfrac{ln\ 100}{ln\ 2.7}=t\\\\\boxed{4.6=t}[/tex]
Final answer:
The question involves solving an exponential growth problem, often modeled by the equation P(t) = P0ekt, to determine the bacterial population at specific times and the growth rate after 4 hours, as well as the time it takes to reach a certain population size.
Explanation:
The student's question falls into the realm of differential equations and specifically pertains to exponential growth in the context of a bacteria population. When dealing with bacterial growth, the formula used is P(t) = P0ekt, where P0 is the initial population, e is the base of the natural logarithm, k is the rate constant, and t is the time in hours.
To find the expression for P(t), we first need to determine the value of k using the information that after one hour the population has increased from 100 to 270 cells. We can then use this value to determine P(4), the population after 4 hours, and P'(4), the rate of growth after 4 hours. Finally, to find when the population reaches 10,000 cells we solve P(t) = 10,000.
Here are the steps we follow:
Since P(1) = 270 and P0 = 100, we solve the equation 270 = 100ek to find k.After finding k, we plug it into the exponential model to find P(4).To find the rate of growth after 4 hours, P'(4), we take the derivative of P(t) with respect to t and evaluate it at t = 4.Lastly, we solve the equation P(t) = 10,000 for t to find out when the population reaches 10,000 cells.Shawn drew a rectangle that was 2 units wide and 6 units long. Draw a different rectangle that has the same perimeter area.
Answer:
A square that has sides of 4.5 units, or a rectangle that is 1 unit wide and 8 units long.
Step-by-step explanation:
First, you need to find the perimeter in the first place. Since there are two sides of the same number, you would double each number.
2 would become 4
6 would become 12
Add 4+12=18
So, our rectangle has to have a perimeter of 18 units. Because a square is a rectangle, you can divide 18 and 4, since a square has 4 sides. You get 4.5. Each side can be 4.5 units.
Or, you can have a rectangle. What I thought first was a length of 9, but I knew that wouldn't work. I drew a rectangle and tried 8. If I put it on the top and bottom, which you need to to find the perimeter, it was only 16. Then I knew I could use 1 as a side length. If you added the sides, it would equal 2, and when you add 16 and 2, it's 18. So, you can use a rectangle that has a length of 8 units and a width of 1 unit.
A cylinder has a radius of 10cm and a height of 9cm. A cone has a radius of 10cm and a height of 9 cm. Show that the volume of the cylinder is three times the volume of the cone.
Answer:
The answer in the procedure
Step-by-step explanation:
step 1
Find the volume of the cylinder
The volume of the cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=10\ cm[/tex]
[tex]h=9\ cm[/tex]
substitute
[tex]V=\pi (10)^{2}(9)=900\pi\ cm^{2}[/tex]
step 2
Find the volume of the cone
The volume of the cone is equal to
[tex]V=(1/3)\pi r^{2} h[/tex]
we have
[tex]r=10\ cm[/tex]
[tex]h=9\ cm[/tex]
substitute
[tex]V=(1/3)\pi (10)^{2}(9)=300\pi\ cm^{2}[/tex]
therefore
we have
[tex]Vcylinder=900\pi\ cm^{2}[/tex]
[tex]Vcone=300\pi\ cm^{2}[/tex]
so
[tex]Vcylinder=3Vcone[/tex]
What is the length of AB¯¯¯¯¯, to the nearest tenth of a centimeter?
Answer:
13.43
Step-by-step explanation:
Law of Sines
x/sin50 = 12/sin42
solve for x and don't forget to put calculator into degree mode
Answer:
[tex]AB\approx13.7cm[/tex] to the nearest tenth.
Step-by-step explanation:
We know two angles and a given side, we can use the sine rule to find the required length.
[tex]\frac{AB}{\sin(50\degree)}=\frac{12}{\sin(42\degree)}[/tex]
We solve for the AB by multiplying both sides by [tex]\sin(50\degree)[/tex].
This implies that;
[tex]AB=\frac{12}{\sin(42\degree)}\times \sin(50\degree)[/tex]
[tex]AB=13.738[/tex]
[tex]AB\approx13.7cm[/tex] to the nearest tenth.
A share of stock in a pharmaceutical company was worth $30.46 on Monday. On Wednesday, the stock price changed to $45.83. What is the net change in the stock price from Monday to Wednesday?
A.
-$76.29
B.
-$15.37
C.
$15.37
D.
$60.92
E.
$76.29
The price increased so it would be a positive net change.
Subtract the new price from the original price:
45.83 - 30.46 = 15.37
The net change was C. $15.37
Answer:
C) 15,37
Step-by-step explanation:
You can to obtain the net change in the stock price with a substract:
Vt = [Pf - Pi]
Vt = [$45.83 - 30.46]
Vt = 15.37
Its a positive variation
Best regards
Please Help! I'm having a lot of trouble with this question!!!
Kayla wants to find the distance, AB, across a creek. She starts at point B and walks along the edge of the river 62 ft and marks point C. Then she walks 93 ft further and marks point D. She turns 90° and walks until her final location and marks point E. Point E, point A, and point C are collinear.
(a) Can Kayla conclude that ∆ABC and ∆EDC are similar? Why or why not?
(b) Suppose (DE) ̅=125 ft. Calculate the distance of (AB) ̅ to the nearest tenth of a foot. Show your work. Don’t forget to label your answer.
Answer:
a ∆ABC and ∆EDC are similar
b. AB = 83.3 ft
Step-by-step explanation:
a. We need to determine if ∆ABC and ∆EDC are similar.
We know B = D = 90
We know C = C because they are vertical angles and vertical angles are equal
Therefore A = E because they are triangles, and if 2 angles in a triangle are equal the third angles must be equal.
∆ABC and ∆EDC are similar
b. We know that because they are similar triangles
AB BC
------ = ---------
ED DC
Substituting in
AB 62
------ = ---------
125 93
Using cross products
93 AB = 62*125
93 AB = 7750
Divide by 93
AB = 7750/93
AB = 83.3333333333(repeating)
Rounding to the nearest tenth ft
AB = 83.3 ft
Quadrilateral PQRS is similar to Quadrilateral LMNO.
Find the value of x.
A 10
B 1.5
C 2.5
D 8
Answer:
2.5
Step-by-step explanation:
so LM is 3 right, right?
so PQ is 6
what they did to get that is they doubled 3 so 3x2=6
so if we divide 5 by 2 we get 2.5 because 2.5+2.5= 5
and that is how i got 2.5
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If the ratio of the edges of two cubes is 3:2, what is the ratio of the volume of the larger cube to the volume of the smaller one?
Answer:
81 : 8
Step-by-step explanation:
Cube 1 has side lengths of 3, so it's volume is 3³ = 81
Cube 2 has side lengths of 2, so it's volume is 2³ = 8
So the ration of volume of the larger cube to the smaller cube is 81 : 8
One angle of a triangle is 30 degrees more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.
Answer:
The measures would be 30, 60, and 90 degrees.
Step-by-step explanation:
60 is 30 more than 30, and 90 is the sum of 30 and 60. Also the sum of the measures of triangle is always 180, and 30 + 60 + 90 = 180.
If One angle of a triangle is 30 degrees more than the smallest angle. The largest angle is the sum of the other angles. Then 30, 60 and 90 are
measures of all three angles.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given,
One angle of a triangle is 30 degrees more than the smallest angle.
x=30+y
The largest angle is the sum of the other angles
z=x+y
By angle sum property the sum of three angles is 180 degrees
x+y+z=180
30+y+y+z=180
30+y+y+30+y+y=180
60+4y=180
Subtract 60 from both sides
4y=120
Divide 4 on both sides
y=30
Now substitute y value in x
x=60
z=90
Hence the measure of all three angles are 30,60 and 90 degrees.
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GUYS PLS HELP URGENT
Answer:
[tex]\boxed{0.2}[/tex]
Step-by-step explanation:
Put -2 where x is in the function and do the arithmetic. Any number of calculators will compute this for you.
x ≈ 0.23781036584 ≈ 0.2
_____
Comment on the above result
The number above came from the Google calculator (2nd attachment). Surprisingly, it is rounded incorrectly in the last displayed digit. To 20 significant digits, the value is ...
0.23781036584658190876
It appears the Google calculator didn't carry enough digits to get the answer correct in the last displayed decimal place.
Answer:
your answer would be 0.2
Step-by-step explanation:
Are there less than 1 million, exactly 1 million, or greater than 1 million milligrams in 1 kilograms?
Answer: There is exactly 1 million in 1 kilogram
Step-by-step explanation:
Answer:
ello mate
Step-by-step explanation:
does this graph show a function?Explain how you know.
Check the picture below.
Answer:
The correct option is A.
Step-by-step explanation:
A relation is called a function if for each values of x, there exist a unique value of y.
A graph show a function if it passes the vertical line test. It means the function intersect each vertical at most once.
From the given graph it is clear that the graph passes the vertical line test because the the function intersect each vertical at most once and for each values of x, there exist a unique value of y.
Hence the correct option is A.
Given: -1/2x > 6.
Choose the solution set.
Answer:
x < -12
Step-by-step explanation:
-1/2x > 6
Multiply by -2 to isolate x
Remember that when multiplying by a negative, we flip the inequality
-2 * -1/2x < 6*-2
x < -12
Solve the equation. Round to the nearest hundredth. Show work.
[tex]5^{-2x-1} = 4^{4x+3}[/tex]
Answer:
Final answer is approx x=-0.66.
Step-by-step explanation:
Given equation is [tex]5^{-2x-1}=4^{4x+3} [/tex].
Now we need to solve equation [tex]5^{-2x-1}=4^{4x+3} [/tex] and round to the nearest hundredth.
[tex]5^{-2x-1}=4^{4x+3} [/tex]
[tex]\log(5^{-2x-1})=\log(4^{4x+3}) [/tex]
[tex](-2x-1)\log(5)=(4x+3)\log(4) [/tex]
[tex]-2x \log(5)- \log(5)=4x \log(4)+3 \log(4) [/tex]
[tex]-2x \log(5) -4x \log(4)=3 \log(4) +\log(5)[/tex]
[tex]x=\frac{\left(3\log(4)+\log(5)\right)}{\left(-2\log(5)-4\log(4)\right)}[/tex]
Now use calculator to calculate log values, we get:
[tex]x=-0.65817959094[/tex]
Round to the nearest hundredth.
Hence final answer is approx x=-0.66.
Find the surface area of the pyramid to the nearest whole number.
D) 408 in^2 is your answer.
The surface area of the pyramid is approximately 345 square inches.
The base of the pyramid is a polygon, and in this case, it is a square since it has 12-inch sides. The formula to find the area of a square is side length squared. Therefore, the area of the square base can be calculated as follows:
Area of base = side length * side length = 12 in * 12 in = 144 square inches.
Since we have the slant height of the pyramid (11 inches) and the base side length (12 inches), we can find the height of the triangle (distance from the base to the apex) using the Pythagorean theorem.
Let 'h' be the height of the triangle:
h² + (1/2 * base)² = slant²
h² + (1/2 * 12)² = 11²
h² + 36 = 121
h² = 121 - 36
h² = 85
h = √85 ≈ 9.22 inches (rounded to two decimal places).
Now that we have the height of the triangular face, we can calculate its area using the formula:
Area of triangle = (1/2 * base * height)
= (1/2 * 12 in * 9.22 in) ≈ 55.32 square inches
Find the Total Surface Area
To find the total surface area of the pyramid, we add the area of the base and the four triangular lateral faces:
Total Surface Area = Area of base + 4 * Area of triangle
Total Surface Area = 144 square inches + 4 * 55.32 square inches
Total Surface Area ≈ 345.28 square inches
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HELPPPPPPPP................................................................................................................
Answer:
Step-by-step explanation:
see attached
An office manager needs to decide between two tables for the conference room. One is rectangular, 5 feet wide by 10 feet long. The other is a circle with an 8-foot diameter.
Which table can seat more people? Explain your answer be sure to support your answer using facts about the tables.
Answer:
Circle table
Step-by-step explanation:
More people will fit around the circle table then the rectangle table. You can find the distance around using the circumference.
C = πr² = π(4)²=16π = 50.24 feet
The perimeter of a rectangle table is P = 2l+2w = 2(10) + 2(5) = 30 feet.
With more than 20 feet more, the circle table will fit more.
Please help me out!!!!!!!!!!!!!!! :)
Assuming that N is the midpoint of QR, its coordinates are the average of the coordinates of Q and R. So, we have
[tex] N = \left(\dfrac{0+2c}{2},\dfrac{2b+0}{2}\right)=(c,b)[/tex]
A store which formerly sold peppers at 3 pounds for $2.00 changed the price to 2 pounds for $1.50. If x is the percent increase in the price per pound x=
A)25%
B)20%
C)16 2/3%
D)12 1/2%
Answer:
D 12½%
Step-by-step explanation:
∆=1.5/2-2/3
=4.5/6-4/6
=0.5/6
∆=0.083 $/lb
X=∆/(original price)•100
=0.083/(2/3)•100
=0.1245•100
X=12.45%
A horizontal plane intersects a cylinder parallel to its base. What 2-D cross section is formed? A square b circle c triangle d rectangle
Previous balance = $102.35 Finance charge = $1.24 New purchases = $15.73 Payments/credits = $12.00 New balance = $______
Answer:
$97.38
Step-by-step explanation:
Subtract the finance charge and new purchases from the previous balance.
102.35 - 1.24 - 15.73 = 85.38
Add the payment/credit
85.38 + 12 = 97.38
Answer:
$107.32
Step-by-step explanation:
GivenNew balance = previous balance + finance charge + purchases - payments
Previous balance = $102.35
Finance charge = $1.24
Purchases = $15.73
Payments = $12.00
FindNew balance
SolutionFill in the given information and do the arithmetic.
... New balance = previous balance + finance charge + purchases - payments
... New balance = $102.35 + $1.24 + $15.73 - $12.00
... New balance = $107.32
The measurement of one angle of a right triangle is 42°. What is the measurement of the third angle?
Answer:
48°
Step-by-step explanation:
The sum of the three angles of a right triangle is 180°.
If one angle is 90° and another is 42°, then
90° + 42° + x = 180°
132° + x = 180°
x = 180° - 132° = 48°
The third angle is 48°.
Which statement below is incorrect? The mean is not affected by the existence of an outlier. The median is not affected by the existence of an outlier. The standard deviation is affected by the existence of an outlier. The interquartile range is unaffected by the existence of an outl
Answer:
https://brainly.com/question/3346907
Step-by-step explanation: