Answer: if the iguana is five feet it would be 60 inches
3. A projectile is fired from ground level with an initial velocity of 35 m/s at an angle of 35° with the horizontal. How long will it take for the projectile to reach the ground?
Answer: 4.10s
t=2Vi*sin(theta)/g
Vi=initial velocity=35m/s
g=9.8m/s^2
t=2*35*sin(35)/9.8=4.10s
Answer:
4.1 seconds to the nearest tenth.
Step-by-step explanation:
The vertical component of the velocity = 35 sin 4.935 m/s.
The relation between the height (h) of the projectile and time is given by:
h = ut + 1/2 g^2 where u = initial velocity, t = the time and g = acceleration due to gravity which we can take to be 9.8 m/s/s. When the projectile hits the ground h = 0 .
So we have h = 35sin35 t - 4.9t^2 = 0
t(35sin35 - 4.9t) = 0
4.9t = 35 sin35
t = 35 sin 35 / 4.9
= 4.097 seconds
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Tammy knows that the factors of a polynomial are ƒ(x) = (x − 2)(x − 1)(x + 4) and the solutions are x = −4, 1, and 2. Which graph models this polynomial?
The answer would be D, where all of the given x values touch the x axis
Answer: D)
Step-by-step explanation:
The equation is: (x - 2)(x - 1)(x + 4) = 0
We can find the x-intercepts by Applying the Zero Product Property:
x - 2 = 0 x - 1 = 0 x + 4 = 0
x = 2 x = 1 x = -4
Which graph shows the curve crossing the x-axis at these points? D
Vector u has its initial point at (-7, 2) and its terminal point at (11, 5). Vector v has a direction opposite that of vector u, and its magnitude is three times the magnitude of u. What is the component form of vector v?
A. [tex]v= \ \textless \ -54, 63\ \textgreater \ [/tex]
B. [tex]v= \ \textless \ -162, -63\ \textgreater \ [/tex]
C.[tex]v= \ \textless \ -54, 21\ \textgreater \ [/tex]
D. [tex]v= \ \textless \ -162, 21\ \textgreater \ [/tex]
Here,
the initial point of vector u(x1,y1)=(-7,2)
the final point of vector u (x2,y2)=(11,5)
so the component of vector u(x,y)=(x2,y2)-(x1,y1)
=(11+7,5-2)=(18,3)
according to the question, the magnitude of vector is thrice the magnitute of vector u and is opposite ot the ditecrion of vector u.
so the component of vector v is -3(x,y)
=-3(18,3)=(-54,-9)
A car will be traveling a total distance of 520 miles. The first part of the trip takes 2 hours, and the car’s average rate is 65 miles per hour. If the entire trip takes 8 hours, what is the car’s average rate, in miles per hour, during the second part of the trip?
49
57
50
65
Final answer:
The car's average rate during the second part of the trip is 65 miles per hour, which is calculated by dividing the remaining distance of 390 miles by the remaining travel time of 6 hours.
Explanation:
We need to find the average rate of the car during the second part of the trip. We know the total distance of the trip is 520 miles and the total time for the trip is 8 hours. Since the first part of the trip was at 65 miles per hour for 2 hours, the car would have covered 130 miles (65 miles/hour * 2 hours).
We subtract the distance covered in the first part of the trip from the total distance to find the distance covered during the second part of the trip: 520 miles - 130 miles = 390 miles. The remaining time for the second part of the trip is 8 hours - 2 hours = 6 hours.
To find the average speed during the second part of the trip, we divide the remaining distance by the remaining time:
Average rate = Distance / Time = 390 miles / 6 hours = 65 miles per hour.
An anthropologist finds that a prehistoric bone contains less than 8.1% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did the person die? (The constant for Carbon-14 is 0.00012.)
19,000 years
20,944 years
21,048 years
23,028 years
Answer:
20,944 years
Step-by-step explanation:
The formula you use for this type of decay problem is the one that uses the decay constant as opposed to the half life in years. We are given the k value of .00012. If we don't know how much carbon was in the bones when the person was alive, it would be safer to say that when he was alive he had 100% of his carbon. What's left then is 8.1%. Because the 8.1% is left over from 100% after t years, we don't need to worry about converting that percent into a decimal. We can use the 8.1. Here's the formula:
[tex]N(t)=N_{0} e^{-kt}[/tex]
where N(t) is the amount left over after the decay occurs, [tex]N_{0}[/tex] is the initial amount, -k is the constant of decay (it's negative cuz decay is a taking away from as opposed to a giving to) and t is the time in years. Filling in accordingly,
[tex]8.1=100e^{-.00012t}[/tex]
Begin by dividing the 100 on both sides to get
[tex].081=e^{-.00012t}[/tex]
Now take the natural log of both sides. Since the base of a natual log is e, natural logs and e "undo" each other, much like taking the square root of a squared number.
ln(.081)= -.00012t
Take the natual log of .081 on your calculator to get
-2.513306124 = -.00012t
Now divide both sides by -.00012 to get t = 20,944 years
Determine whether each set of side lengths could be the sides of a right triangle. Drag and drop each set of side lengths to the correct box. 10.5cm,20.8cm,23.3cm
6cm, 22.9cm,20.1cm
Answer:
10.5cm,20.8cm,23.3cm — yes6cm, 22.9cm,20.1cm — noStep-by-step explanation:
If the sides form a right triangle, the sum of the squares of the shorter two sides will equal the square of the longest side.
1. 10.5^2 + 20.8^2 = 23.3^2 . . . . . true algebraic statement; right triangle
__
2. 6^2 +20.1^2 = 440.01 ≠ 22.9^2 = 524.41 . . . . . this is an obtuse triangle
Juan drew a right triangle with leg lengths of 6 centimeters and 8 centimeters. He wants to draw another right triangle that is similar to the first one. Which could be the lengths of the legs?
The lengths of the legs of a similar triangle to the one Juan drew, which has leg lengths 6cm and 8cm, could be 12 cm and 16 cm because the sides of similar triangles are proportional.
Explanation:Juan's right triangle has leg lengths of 6 centimeters and 8 centimeters. To find a similar right triangle, we need ratios of corresponding sides to be equivalent or proportional. As these are right triangles, we can use the Pythagorean theorem which states that a² + b² = c². If the original triangle has sides 6 cm and 8 cm, then triangle with proportional sides could have sides that are multiple of these dimensions, such as 12 cm (which is 6cm x 2) and 16 cm (which is 8cm x 2). So, one example of a similar triangle could have leg lengths of 12 cm and 16 cm.
Learn more about Similar Triangles here:https://brainly.com/question/34830045
#SPJ12
What is the probability of getting a spade or a red card?
Answer:
3/4
Step-by-step explanation:
1/2 the deck is red cards.
1/4 of the deck is spades.
There are no spades that are red cards, so the probability of drawing a red card or a spade at random from a well-shuffled deck is ...
1/2 + 1/4 = 3/4
There are rabbits and chickens in Sally's backyard: 22 heads and 76 legs. How many rabbits and how many chickens are there?
there is 6 chickens and 16 rabbits, need the work tho?
6 chickens 16 rabbits
One jar of jelly costs $2.32 for 16 ounces. Another jar costs $2.03 for 13 ounces. Which is the better buy? Why? The jelly that costs $____ for ____ ounces is the better buy. The unit rate for this jar of jelly is $____, or approximately $____ per ounce. The unit rate for the second jar of jelly is $____, or approximately $____ per ounce. Question 4 options: Blank # 1 Blank # 2 Blank # 3 Blank # 4 Blank # 5 Blank # 6
Answer:
The jar of jelly that costs $2.32 for 16 ounces is the better buy, because the unit rate is less
Step-by-step explanation:
step 1
Find the units rate
One jar of jelly costs $2.32 for 16 ounces
so
The unit rate is equal to [tex]\frac{2.32}{16}= 0.145\frac{\$}{ounce}[/tex]
Another jar costs $2.03 for 13 ounces
so
The unit rate is equal to [tex]\frac{2.03}{13}= 0.156\frac{\$}{ounce}[/tex]
step 2
Compare the unit rates
[tex]0.145\frac{\$}{ounce} < 0.156\frac{\$}{ounce}[/tex]
therefore
The jar of jelly that costs $2.32 for 16 ounces is the better buy, because the unit rate is less
The jelly that costs $2.32 for 16 ounces is the better buy. The unit rate for this jar of jelly is $0.145 or approximately $0.15 per ounce. The unit rate for the second jar of jelly is $0.156 or approximately $0.16 per ounce
Cody hiked at an average speed of 1 mile per hour for 5 hours on Saturday. He hiked an average speed of 2 miles per hour for 3 hours on Sunday. Which explanation correctly tells how to calculate the total number of miles that Cody hiked in two days? Step 1: Divide 1 ÷ 5. Step 2: Divide 2 ÷ 3. Step 3: Subtract the two quotients. Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Add the two products. Step 1: Divide 1 ÷ 5. Step 2: Divide 2 ÷ 3. Step 3: Add the two quotients. Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Subtract the two products.
Answer:
Step 1: Multiply 1x5 Step 2: Multiply 2x3 Step 3: Add the two products
d=v*t
d=distance
v=velocity(speed)
t=time
distance is equal to the product of velocity and time, equation form;
d=vt
Any questions please feel free to ask. Thanks!
The equation (x + 6)^2 + (y + 4)^2 = 36 models the position and range of the source of a radio signal. Describe the position of the source and the range of the signals
Answer:
position: (-6, -4)
range: 6
Step-by-step explanation:
The equation is that of a circle centered at (-6, -4) with a radius of √36 = 6. We presume that the "position" is that of the circle's center, and the "range" is the radius of the circle.
___
The standard form equation of a circle with center (h, k) and radius r is ...
(x -h)^2 +(y -k)^2 = r^2
Matching parts of the equation, we find ...
h = -6, k = -4, r = √36 = 6.
The source of the radio signal is at the point (-6, -4), and the range of the signals is within a circular area with a radius of 6 units.
The equation given, (x + 6)² + (y + 4)² = 36, is a mathematical representation of a circle in a Cartesian plane. This equation indicates that the source of the radio signal is at the center of the circle, which is the point (-6, -4).
The number 36 on the right side of the equation is the square of the radius of the circle, which implies that the radius of the circle is 6 units. Hence, the range of the signals emitted from the source is limited to a circular area with a radius of 6 units around the point (-6, -4).
Please please help!!
Answer:
240.3
Step-by-step explanation:
Tan(31) = y/400ft
400 tan (31) = y
y = 240,3
he points A, B, C, and D are on a number line, not necessarily in that order. If the distance between A and B is 18 and the distance between C and D is 8, what is the distance between B and D ? (1) The distance between C and A is the same as the distance between C and B. (2) A is to the left of D on the number line. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient. Next Help End Review Review Screen
Answer:
Statements (1) and (2) TOGETHER are NOT sufficient.
Step-by-step explanation:
If the point order is DCAB or CDAB (or the reverse of either of these), then the BD distance will be 36±8 units. It cannot be determined.
__
If the point order is AD(BC) or A(BC)D, then the BD distance is the same as the CD distance, which is given as 8. In this scenario, point B and C lie at the same place on the number line.
__
So, we have 3 possible values of BD, even when both statements are used together. TOGETHER, the statements aren NOT sufficient.
Seth and Eva are biking on a trail. Seth begins 8 miles ahead of Eva and bikes at an average speed of 4 miles per hour. Eva bikes at an average speed of 6 miles per hour. How much time will it take for Eva to catch up with Seth on the trail?
Answer:
4 hours
Step-by-step explanation:
0:8
6:12
12:16
18:20
24:24
Answer: 4 hours
Step-by-step explanation:
2(3y − 1)(y − 3) is the factored form of
Answer:
6 y² - 20 y + 6
Step-by-step explanation:
Multiply step by step the terms inside the brackets:
3y * y
3y * -3
-1 * y
-1 * -3
add those up to get 3y² - 10 y + 3
multiply all terms of the result by 2
Answer:
6y^2 - 20y + 6.
Step-by-step explanation:
2(3y − 1)(y − 3)
= 2 [ 3y(y - 3) - 1(y - 3)]
= 2 (3y^2 - 9y - y + 3)
= 2(3y^2 - 10y + 3)
= 6y^2 - 20y + 6.
Brianna and Maddie rode their bikes on Saturday. Maddy rode twice as much as Brianna. Together they rode for 162 minutes. How many minutes did each girl ride?
Answer: brianna rode for 54 minutes and maddie rode for 108 minutes.
Step-by-step explanation:
let the time for which brianna rode be = x
(since maddie rode twice as brianna then,)
let the time for which maddie rode be = 2x
(together they rode for 162 minutes. so,)
x + 2x = 162
3x = 162
x = 162/3
=>x = 54
=>2x = 54*2 = 108
hope it helps
Please give details on how to do this:
Given the translation T(-2, 5), translate the given ordered pairs: (2, 5) and (-1, 7
Answer:
It is 15.
Step-by-step explanation:
What is the area of a circle with radius of 3 inches? Use pie =3.14 A .18.84 square roots B .28.26 square roots C .9.42 square roots D .113.04 square roots
Answer:
B. 28.26
Step-by-step explanation:
First you have to find the circumference:
R²= 3²=9
Then you multiply your circumference by 3.14 to get you answer:
9·3.14=28.26
Really need answer, don't understand what it want:
Answer:
y ≈ - 3.8
Step-by-step explanation:
Given the 2 equations
5x + 2y = 21 → (1)
- 2x + 6y = - 34 → (2)
To eliminate the terms in x , multiply (1) by 2 and (2) by 5
10x + 4y = 42 → (3)
- 10x + 30y = - 170 → (4)
Add (3) and (4) term by term
(10x - 10x) + (4y + 30y) = (42 - 170)
34y = - 128 ( divide both sides by 34 )
y ≈ - 3.8 ( to the nearest tenth )
What is the volume of the space between the cylinder and the sphere?
500/3π cubic inches
500π cubic inches
250/3π cubic inches
750π cubic inches
250π cubic inches
Answer:
250/3π cubic inches
Step-by-step explanation:
we know that
The volume of the space between the cylinder and the sphere is equal to the volume of the cylinder minus the volume of the sphere
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]h=10\ in[/tex]
[tex]r=5\ in[/tex]
substitute
[tex]V=\pi (5)^{2} (10)[/tex]
[tex]V=250\pi\ in^{3}[/tex]
step 2
Find the volume of the sphere
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=5\ in[/tex]
substitute
[tex]V=\frac{4}{3}\pi (5)^{3}[/tex]
[tex]V=(500/3)\pi\ in^{3}[/tex]
step 3
Find the difference
[tex]250\pi\ in^{3}-(500/3)\pi\ in^{3}=(250/3)\pi\ in^{3}[/tex]
I really really REALLY NEED HELP ON this!!!
Simplify: 4^sqrt(400)/4^sqrt(5) Show your work.
Answer:
[tex]2\sqrt[4]{5}[/tex]
Step-by-step explanation:
First, you calculate the quotient which is [tex]\sqrt[4]{80}[/tex]
Then you simplify the radical which is [tex]2\sqrt[4]{5}[/tex]
Inputting this in a calculator will give you 2.99 which is also correct.
How do you use a system of equations to find the solution algebraically?
Answer:
Pemdas
Step-by-step explanation:
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
You go from left to right and solve in the order called Pemdas.
To use a system of equations to find the solution algebraically, follow these steps: identify the unknowns and knowns, write down the equations, solve for one variable, substitute the expression into the other equation(s), solve for the remaining variables, and check your answer(s) for reasonableness.
Explanation:Using a System of Equations to Find the Solution Algebraically1. Identify the unknowns and knowns.
2. Write down the equations that represent the given information.
3. Solve one of the equations for one variable in terms of the other.
4. Substitute this expression into the other equation(s), replacing the variable.
5. Solve the resulting equation(s) to find the value(s) of the remaining variable(s).
6. Check your answer(s) to ensure they make sense in the context of the problem.
Which of the following equations represents Exponential Decay?
y=−3x+5
y=3(0.8)x
y=−3x−5
y=0.8(3)x
Answer:
y=3(0.8)x
Step-by-step explanation:
An exponential function is a function of the form;
[tex]y=ab^{x}[/tex]
The explanatory variable x is the exponent, a is the initial value and b the base of the exponential function.
The function is said to be an exponential decay function if the base is between 0 and 1;
0<b<1
Therefore, y=3(0.8)^x is the required function. The values of y become smaller as x increases.
Jivesh also has a more powerful Model B rocket. For this rocket, he uses the equation h=-490t^2+1260t. When is the height of the Model B rocket 810 centimeters? ( it also includes number 19, but I need 20)
Answer:
1.29 s
Step-by-step explanation:
h = -490t² + 1260t
810 = -490t² + 1260t
490t² - 1260t + 810 = 0
49t² - 126t + 81 = 0
(7t - 9)² = 0
7t - 9 = 0
t = 9/7
t ≈ 1.29
To find the time when the rocket is at a height of 810 cm, set the equation -490t^2 + 1260t equal to 810 and solve for t using the quadratic formula. The quadratic formula will give two solutions: choose the positive solution as we cannot have negative time.
Explanation:We are given the equation h=-490t^2+1260t to represent the height of the rocket. We're also told that the height h is 810 cm and we are asked to solve for time t when this is the case.
To find the time when the rocket's height is 810 cm, we can first set the equation equal to 810: -490t^2 + 1260t = 810.
We can then simplify that to -490t^2 + 1260t - 810 = 0 and solve for t using the quadratic formula t = [-b ± sqrt(b² - 4ac)] / 2a, where a = -490, b = 1260 and c = -810.
This will give us the two points in time at which the rocket is at a height of 810 cm. Remember, the negative solution is likely extraneous as we cannot have negative time, so you should consider only the positive solution.
Learn more about Quadratic Equations here:https://brainly.com/question/34196754
#SPJ2
The faces of triangular pyramid have a base of 5cm and a height of 11cm what is the lateral area of the pyramid
Answer:
55cm
Step-by-step explanation:
11 x 5 = 55, so the area of the pyrmid is 55cm.
Answer:You will have to multiply 55 x 5 because if the base if 5 cm and the height is 11 cm which equals to 55 and a pyramid has 5 faces, so the answer will be 220. I hoped this helped! :)
Step-by-step explanation:
A certain country's consumer price index is approximated by a(t) = 100e0.024t, where t represents the number of years. use the function to determine the year in which costs will be 50% higher than in year 0.
Answer:
[tex]\boxed{\text{Year 17}}[/tex]
Step-by-step explanation:
[tex]a(t) = 100e^{0.024t}[/tex]
Data:
a(t) = 150
a(0) = 100
Calculations :
[tex]\begin{array}{rcll}150 & = & 100e^{0.024t} & \\\\1.50 & = & e^{0.024t} & \text{Divided each side by 100}\\0.4055 & = & 0.024t & \text{Took the ln of each side}\\t & \approx & \mathbf{17} & \text{Divided each side by 0.024}\\\end{array}[/tex]
[tex]\text{The consumer price index will be 50 \% higher in } \boxed{\textbf{year 17}}[/tex]
Two search teams spot a stranded climber on a mountain. The first search team is 0.5 miles from the second search team. If the angle of elevation from the first search team to the stranded climber is 15° and the angle of elevation from the second search team is 22° to the stranded climber, what is the altitude of the climber if both search teams are standing at an altitude of 1 mile high?
Answer:
The altitude of the climber is 1.40 miles
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In the right triangle BCD
tan(22°)=h/(x-0.5)
h=tan(22°)*(x-0.5) ----> equation A
In the right triangle ACD
tan(15°)=h/x
h=tan(15°)*(x) ----> equation B
Equate equation A and equation B and solve for x
tan(22°)*(x-0.5)=tan(15°)*(x)
tan(22°)*x-tan(22°)*0.5=tan(15°)*x
x[tan(22°)-tan(15°)]=tan(22°)*0.5
x=tan(22°)*0.5/[tan(22°)-tan(15°)]
x=1.48 miles
Find the value oh h
h=tan(15°)*(1.48)=0.40 miles
therefore
The altitude of the climber is equal to
0.40+1=1.40 miles
Answer:
Step-by-step explanation:
Just solved a similar problem and figured it out, the angle of elevation is somewhat unintuitive as the angle of the second search team needs to be flipped. The diagram should look more like this:
This isn't an explanation of the math but more of a visualization for those that just needed the 2D representation. The real answer would be 1.081 miles (:
I have a vase that is shaped like a rectangular prism. The height is 10 inches. The length of the base is 6 inches. The width of the base is 5 inches. What is 2/3 of the volume of the vase? If necessary, round to the nearest whole number.
Answer:
[tex]200in^3[/tex]
Step-by-step explanation:
To solve this, we are using the formula for the volume of a rectangular prism:
[tex]V=whl[/tex]
where
[tex]w[/tex] is the width of the base
[tex]l[/tex] is the length of the base
[tex]h[/tex] is the height of the prism
We know from our problem that the height is 10 inches. The length of the base is 6 inches. The width of the base is 5 inches.
Replacing values
[tex]V=(5in)(10in)(6in)[/tex]
[tex]V=300in^3[/tex]
Now, to find 2/3 of that volume, we just need to multiply it by 2/3
[tex]\frac{2}{3} V=\frac{2}{3} 300in^3[/tex]
[tex]\frac{2}{3} V=200in^3[/tex]
We can conclude that 2/3 of the volume of the vase is 200 cubic inches.
What is the product of these numbers?
(1 + 2i)(2 + i)
1 − 5i
1 + 5i
0 − 5i
0 + 5i
Answer:
0 + 5i
Step-by-step explanation:
Multiply these the way you would any binomials, then replace i² with -1.
(1 +2i)(2 +i) = 1·2 +1·i +(2i)·2 +(2i)·i
= 2 + i + 4i + 2i² . . . . . the partial products
= 2 +5i -2 . . . . . . . . . . after replacement of i² = -1
= 0 +5i