The product of the inverse of these elementary matrices gives us the original matrix A:
A = E1^(-1)E2^(-1)E3^(-1)E4^(-1) =
[ 1 2 0 ]
[ -4 8 0 6 ]
[ 0 1 0 ]
Consider the given Gauss-Jordan reduction:
A =
[ 1 2 0 ]
[ -4 8 0 6 ]
[ 0 1 0 ]
We need to find the elementary matrices E1, E2, E3, and E4 such that:
A = E1^(-1)E2^(-1)E3^(-1)E4^(-1)
First, we can use an elementary matrix E1 to subtract 4 times the first row from the second row:
E1 =
[ 1 0 0 ]
[ -4 1 0 ]
[ 0 0 1 ]
Next, we can use an elementary matrix E2 to add -2 times the second row to the first row:
E2 =
[ 1 -2 0 ]
[ 0 1 0 ]
[ 0 0 1 ]
Then, we can use an elementary matrix E3 to subtract the third row from the second row:
E3 =
[ 1 0 0 ]
[ 0 1 -1 ]
[ 0 0 1 ]
Finally, we can use an elementary matrix E4 to divide the second row by 8:
E4 =
[ 1 0 0 ]
[ 0 1/8 0 ]
[ 0 0 1 ]
Therefore, the product of the inverse of these elementary matrices gives us the original matrix A:
A = E1^(-1)E2^(-1)E3^(-1)E4^(-1) =
[ 1 2 0 ]
[ -4 8 0 6 ]
[ 0 1 0 ]
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A grain silo has a cylindrical shape. Its diameter is 17 ft , and its height is 42 ft . What is the volume of the silo?
The volume of the silo is approximately 9,685.73 cubic feet.
What is volume of a cylinder?
The volume of a cylinder can be calculated using the formula:
[tex]V = \pi r^2h[/tex] where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.
We are given that the diameter of the silo is 17 feet. The radius, which is half the diameter, is therefore:
r = 17/2 = 8.5 feet
We are also given that the height of the silo is 42 feet.
Using the formula for the volume of a cylinder, we can calculate the volume of the silo:
[tex]V = \pi r^2h[/tex]
[tex]= \pi(8.5)^2(42)[/tex]
≈ 9,685.73 cubic feet
Therefore, the volume of the silo is approximately 9,685.73 cubic feet.
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If a random variable X has exponential distribution with mean 1 then P[X > 2] is
a. 1- e^-2 b. e^2 c. e^-2
d. 1-e²
The correct answer is option a. 1 - e^-2.
To find the probability of a random variable X with exponential distribution, we use the following formula:P[X > x] = e^(-λx)Where λ is the rate parameter and x is the value we are trying to find the probability of.
In this case, we are given that the mean of the distribution is 1, so we can use this information to find the rate parameter:λ = 1/mean = 1/1 = 1Now, we can plug in the values for λ and x into the formula to find the probability:P[X > 2] = e^(-1*2) = e^-2 = 0.1353Therefore, the correct answer is option a. 1 - e^-2.
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Find f ∘ g, g ∘ f, and g ∘ g.
f(x) = x4, g(x) = 1/x
(a)
f ∘ g
(b)
g ∘ f
(c)
g ∘ g
Hello there! To find f ∘ g, g ∘ f, and g ∘ g, let's first recall the definition of function composition: given two functions f and g, their composition f ∘ g is defined as the function that results from applying g to the result of applying f to its argument. Specifically, for a given input x, we can express the composition f ∘ g as follows: (f ∘ g)(x) = f(g(x)).
Given f(x) = x4 and g(x) = 1/x, we can find each composition as follows:
(a) f ∘ g = f(g(x)) = f(1/x) = (1/x)4
(b) g ∘ f = g(f(x)) = g(x4) = 1/(x4)
(c) g ∘ g = g(g(x)) = g(1/x) = 1/(1/x) = x
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which equation of the least squares regression line most closely matches the data set?
The equatiοn οf the least squares regressiοn line which mοst clοsely matches the data set is y = 3.5 x + 43.8
Hοw tο sοlve fοr the data set?Tο sοlve fοr the data set, lets lοοk at the table,
X 1190 1992 1994 1996 1998
Y 45 51 57 61 75
Let the equatiοn that shοws the abοve data be
y = b + a x ---------(1)
Where, a = Σy Σx² - Σx Σxy
And, b = (Σxy - Σx Σy) / n Σx² -(Σx)²
By the abοve table,
Σx=20
Σxy = 1296
Σx² = 120
Σy=289
By substituting these values in the abοve value οf a and b,
We get b = 43.8 and a = 3.5
Substitute this value in equatiοn (1)
We get, the equatiοn that shοws the given data is,
y = 3.5 x + 43.8
Therefοre, οptiοn 3 is cοrrect.
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A cart weighing 40 lb is placed on a ramp inclined at 15° to the horizontal. The cart is held in place by a rope inclined at 60° to the horizontal, as shown in the figure. Find the force that the rope must exert on the cart to keep it from rolling down the ramp.
Answer:
11.97 lb
Step-by-step explanation:
To find the force that the rope must exert on the cart to keep it from rolling down the ramp, we need to resolve the forces acting on the cart along the direction of the ramp and perpendicular to the ramp.
First, we resolve the weight of the cart into its components. The weight of the cart acting vertically downwards can be resolved into a component perpendicular to the ramp and a component parallel to the ramp.
The component perpendicular to the ramp is given by:
W_perp = W * cos(theta) = 40lb * cos(15°) = 38.6lb
The component parallel to the ramp is given by:
W_parallel = W * sin(theta) = 40lb * sin(15°) = 10.4lb
where W is the weight of the cart, and theta is the angle of inclination of the ramp.
Next, we resolve the force exerted by the rope into its components. The force exerted by the rope can be resolved into a component perpendicular to the ramp and a component parallel to the ramp.
The component perpendicular to the ramp is given by:
F_perp = F * cos(phi) = F * cos(60°) = 0.5F
The component parallel to the ramp is given by:
F_parallel = F * sin(phi) = F * sin(60°) = 0.87F
where F is the force exerted by the rope, and phi is the angle of inclination of the rope.
To keep the cart from rolling down the ramp, the force exerted by the rope must balance the weight of the cart along the direction of the ramp. That is,
F_parallel = W_parallel
0.87F = 10.4lb
Solving for F, we get:
F = 11.97lb
Therefore, the force that the rope must exert on the cart to keep it from rolling down the ramp is approximately 11.97lb.
The question is in the screenshot:
We can deduce that 3pi/4<5pi/3<2pi
The angle is in the 4th quadrant. To find the angle you just do:
[tex]2\pi -\frac{5\pi }{3}=\frac{\pi }{3}[/tex]
The answer to your question is B. I hope that this is the answer that you were looking for and it has helped you.
Peter mows 7 lawns in 11 hours. If he continues at the same rate, how many lawns will Peter mow in 55 hours?
If Peter mows 7 lawns in 11 hours, then the number of lawns Peter can mow in 55 hours is 35.
How many lawns can he mow?The first step is to determine how many lawns Peter can mow in 1 hour. To do this, divide 7 by 11.
Division is the process of determining the quotient of two or more numbers. It entails putting a number into equal groups using another number.
Number of lawns that Peter can mow in 1 hour = 7 / 11To determine the number of lawns that can be mowed in 55 hours, multiply the fraction derived in the previous step by 55.
Multiplication is the process of determining the product of two or more numbers.
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Last week, Cindy's Diner sold 7 milkshakes with whipped cream on top and 18 milkshakes without whipped cream. What percentage of the milkshakes had whipped cream?
Answer: The total number of milkshakes sold is 7 + 18 = 25.
The number of milkshakes sold with whipped cream is 7.
To find the percentage of milkshakes with whipped cream, we can use the formula:
percentage = (part/whole) x 100
Substituting the values, we get:
percentage = (7/25) x 100
percentage = 28
Therefore, 28% of the milkshakes had whipped cream.
Step-by-step explanation:
In 1968 the remains of a young boy buried with over 100 tools of stone and antlers were found by accident by a construction worker on private property owned by the Anzick family in Montana. The bones were determined by radiocarbon-dating to be 12,600 years old. The half-life of Carbon-14 is 5730 years. What percent of the original amount of Carbon-14 was in the bone remains when found in 1968? Show how you obtained your equation and how you solved it. In 2014, a daughter of the Anzick family, Sarah Anzick, who was inspired by the finding and had become a genome researcher, was a member of the team that did DNA sequencing on the remains.
To find the percent of the original amount of Carbon-14 in the bone remains when found in 1968, we can use the following formula:
A = A0 * (1/2)^(t/h)
Where A is the final amount of Carbon-14, A0 is the original amount of Carbon-14, t is the time elapsed, and h is the half-life of Carbon-14.
Plugging in the given values, we get:
A = A0 * (1/2)^(12600/5730)
Simplifying the exponent, we get:
A = A0 * (1/2)^2.199
Using a calculator, we find that (1/2)^2.199 is approximately 0.153, so:
A = A0 * 0.153
This means that the final amount of Carbon-14 is 15.3% of the original amount of Carbon-14. Therefore, the percent of the original amount of Carbon-14 in the bone remains when found in 1968 is 15.3%.
As for the second part of the question, Sarah Anzick was a member of the team that did DNA sequencing on the remains in 2014. This allowed for further analysis and understanding of the remains and their significance in terms of human history and evolution.
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Someone please answer my question
Answer:
Point D is the solution to the system of equations.
Step-by-step explanation:
When asked for a solution involving 2 equations, the goal is to find a point (x,y) that would be a solution to both equations. Any point on a line that is defined by an equation is a solution to that equation. For an equation of y = 2x + 2, possible solutions are (1,4), (2,6), (5,12) etc. These points all lie on the line formed by that equation. There are an infinite number of possible solutions. If a second eqaution is added, there is now a constraint on the possible answers. The goal is to find a point that satisfies both equations.
If a seond equation of y = 1x + 3 were matced with y=2x+2, both are straight lines, but with different slopes. So they will intersect at some point. One may either solve mathematically using substitution, or by graphing, as was done here.
Matematically:
y = 2x + 2
y = 1x + 3
Rearrange either equation to isolate a variable, x or y. These are already isolated (since I made them up) so go to the next step of substituting one expression of y into the other:
y = 1x + 3
2x + 2 = 1x + 3
x = 1
Now use this value of x to find y:
y = 2x + 2
y = 2*(1) + 2
y = 4
The point these two lines intersect is (1,4) and is the "solution" to this series of equations.
See the attached graph.
Exercise 12. Let X and Y be independent random variables satisfying E|X+Y|^n < [infinity] for some a > 0. Show that E|X|^n < [infinity].
E|X|n < ∞
Let X and Y be independent random variables satisfying E|X+Y|n < ∞ for some a > 0. We can show that E|X|n < ∞ using the triangle inequality.
Let b = a/2. Since E|X+Y|n < ∞, we know that E|X+Y| < ∞. Then by the triangle inequality, we have E|X| < |X+Y| + |Y| < ∞.
Raising both sides of the inequality to the nth power gives us E|X|n < (|X+Y| + |Y|)n < ∞.
Therefore, E|X|n < ∞.
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Rectangle PQRS is plotted on a coordinate plane. The coordinates of P
are (-1, -3) and the coordinates of Q are (-1, 2). Each unit on the
coordinate plane represents 1 centimeter, and the perimeter of
rectangle PQRS is 20 centimeters. Find the coordinates of points R and
S given these conditions:
a) Points R and S are to the left of points P and Q.
PLS HELP I NEED IT TO HE SMPLE
[tex]PQ = 2 - (-3) = 2 + 3 = 5 \ cm[/tex]
[tex]RS = PQ \implies RS = 5 \ cm[/tex]
the perimeter of rectangle PQRS is 20 centimeters ⇒
[tex]QR = SP = 5 \ cm[/tex]
⇒ PQRS is square
[tex]x_{R} = x_{Q} - 5 = -1-5 = -6[/tex]
[tex]y_{R} = y_{Q} = 2[/tex]
[tex]\implies R(-6,2)[/tex]
[tex]x_{S} = x_{R} = -6[/tex]
[tex]y_{S} = y_{P} = -3[/tex]
[tex]\implies Q(-6,-3)[/tex]
find the missing side of the triangle
The missing side of the triangle is 16 mm.
What is Trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common uses for an angle in trigonometry.
As per the given diagram:
The sides and angles of the right-angled triangle is given:
To find v using the trigonometric ratio:
sinθ = (P/H) {P is perpendicular and H is hypotunese}
for θ = 30°
sin30° = (8/v)
1/2 = 8/v
v = 16 mm
Hence, the missing side of the triangle is 16 mm.
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The continuous random variable X has probability density function given by f(x) = 0.1 + kx where 0 ≤ x ≤ 5 0 otherwise (a) Find the value of the constant, k, which ensures that this is a proper density function. (b) Evaluate E[X], and var[X]. (c) If G = 5X − 6, obtain the mean and standard deviation of G. (d) If H = 5 − 6X, obtain the mean and standard deviation of H.
a) The value of k is 0.04.
b) The value of E[X] is 3.3333 and the value of var[X] is 1.3889.
c) The standard deviation of G is 5.8916.
d) The standard deviation of H is 7.0711.
(a) To find the value of k that ensures that f(x) is a proper density function, we need to ensure that the integral of f(x) over its domain is equal to 1:
∫05 (0.1 + kx) dx = 1
0.5 + 12.5k = 1
12.5k = 0.5
k = 0.04
Therefore, the value of k is 0.04.
(b) To find E[X], we need to evaluate the integral of x*f(x) over its domain:
E[X] = ∫05 x(0.1 + 0.04x) dx
E[X] = 0.5 + 0.02(125/3) = 3.3333
To find var[X], we need to evaluate the integral of (x - E[X])2*f(x) over its domain:
var[X] = ∫05 (x - 3.3333)2(0.1 + 0.04x) dx = 1.3889
(c) If G = 5X - 6, then E[G] = 5E[X] - 6 = 11.6667 and var[G] = 52var[X] = 34.7225. The standard deviation of G is the square root of var[G], which is 5.8916.
(d) If H = 5 - 6X, then E[H] = 5 - 6E[X] = -14.9998 and var[H] = 62var[X] = 49.9994. The standard deviation of H is the square root of var[H], which is 7.0711.
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See Solution Bcore: 5 Penalty: None gleton Operations on Functions 6:13PM f(x)=x^(2)-5x-50 and g(x)=x+5, find (f-g)(x)
The value of (f-g)(x) is x^(2)-6x-55.
What are Mathematical operations on a function?Mathematical operations on a function involve the manipulation or transformation of the function, such as adding, subtracting, multiplying, dividing, and integrating the function. These operations can be done either to the function itself or to the domain or range of the function. This can be used to find the inverse of a function, calculate the area under the curve, or find the first or second derivative of a function.
To find (f-g)(x), we need to subtract the function g(x) from the function f(x).
(f-g)(x) = f(x) - g(x)
= (x^(2)-5x-50) - (x+5)
= x^(2)-5x-50 - x - 5
= x^(2)-6x-55
Therefore, (f-g)(x) = x^(2)-6x-55.
This is the final answer for the difference between the two functions f(x) and g(x).
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How long of a chain can Jill make by attaching a 13 3 4 -inch chain to a 15 2 4 -inch chain? Select all the possible sums. A. 13 3 4 + 15 2 4 = 28 5 4 B. 13 3 4 + 15 2 4 = 29 1 4 C. 13 3 4 + 15 2 4 = 29 D. 13 3 4 + 15 2 4 = 117 4 E. 13 3 4 + 15 2 4 = 28 5 8 I NEED THIS ASAP
The correct option representing possible sum for the long chain is B. 13 3 4 + 15 2 4 = 29 1 4.
Firstly let us convert the mixed fraction to fraction. So, the length of first chain = (13×4)+3/4
Length of first chain = 55/4 inches
Length of first chain = 13.75 inches
Length of second chain = (15×4)+2/4
Length of second chain = 62/4
Second chain length = 15.5 inches
So, total length = length of first chain + length of second chain
Total length = 13.75 + 15.5
Total length = 29.25 inches
Converting the decimal back to mixed fraction -
Total length = 29 1/4 inches
Thus, the correct answer B. 13 3 4 + 15 2 4 = 29 1 4.
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A circle moves through 145 degrees in 25 seconds. If the radius
of the circle is 21 cm, find the linear and angular speeds.
The linear speed of the circle is 2.125 cm/s and the angular speed of the circle is 0.1012 rad/s.
The linear speed of the circle can be found by calculating the length of the arc traveled in 25 seconds. The length of an arc is given by the formula L = rθ, where r is the radius of the circle and θ is the central angle in radians. Converting the given angle from degrees to radians, we have:
θ = 145 degrees * π/180 = 2.53 radians
Substituting the values into the formula, we get:
L = 21 cm * 2.53 = 53.13 cm
Therefore, the linear speed of the circle is:
v = L/t = 53.13 cm/25 s = 2.125 cm/s
The angular speed of the circle can be found by dividing the central angle by the time taken to travel that angle. Therefore, the angular speed of the circle is:
ω = θ/t = 2.53 radians/25 s = 0.1012 rad/s
Hence, the linear speed of the circle is 2.125 cm/s and the angular speed of the circle is 0.1012 rad/s.
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Use a calculator to approximate the measure of the acute angle A to the nearest tenth of a degree. sin A = 0.9659
a. 60.3 Degrees
b. 56 Degrees
c. 75 Degrees
d. 55.5 Degrees
Answer:
OPTION C
Step-by-step explanation:
There are 3 sides in a triangle. 2 of them are legs, and one of them is the Hypotenuse. "Sin" refers to Opposite/Hypotenuse.
To find A given a sine value, we must use inverse sin. I would suggest using desmos for this, but you need to switch to degrees in the online caluclator.
So the Equation is: [tex]sin^{-1} (0.9659)[/tex]
After plugging that into desmos, we get 74.994 degrees. Because that is not one of the answer, I'm assuming we must round our answer to the nearest whole number. In that case, your answer is 75 degrees, or OPTION C
Which of the following are subspaces of R3 ?
(i) {(x,y,z)| z = (x+y)2}
(ii) {(x,y,z)| x=10z}
None of the other choices is correct
(ii) only
(i) and (ii)
(i) only
The correct answer is (i) and (ii). Both of the sets are subspaces of R3 because they satisfy the three criteria of a subspace. The first set, {(x,y,z)| z = (x+y)2}, is a set of all triplets (x,y,z) such that z = (x+y)2. The second set, {(x,y,z)| x=10z}, is a set of all triplets (x,y,z) such that x = 10z. Neither of the other choices are correct.
A watch was bought for 2,700 including 8% VAT. Find its price before the VAT was added.
Answer:
Let's assume that the price before adding the VAT is x.
We know that the VAT rate is 8%, which means that the VAT amount is 8% of x, or 0.08x.
The total price including VAT is the sum of the price before VAT and the VAT amount, so we can write:
Total price = price before VAT + VAT amount
or
2,700 = x + 0.08x
Simplifying this equation, we can combine like terms on the right-hand side to get:
2,700 = 1.08x
To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 1.08:
x = 2,700 / 1.08
x = 2,500
Therefore, the price before VAT was added is 2,500.
A restaurant serves x meals of chicken quarters daily and makes soup each day 1/2 using of a chicken. The chef expresses the number of chickens she uses each day as 1/4 * x + 1/2 How many chickens does she use in three days?
Answer: 1 1/4
Step-by-step explanation:
1/4 * 3 = 3/4
3/4 + 1/2 =
3/4 + 2/4 = 5/4 = 1 1/4
What is the slope of the line that contains the points (2, −7) and (−1, 5)?
−4
negative one fourth
one fourth
4
Answer:
The answer is -4
Step-by-step explanation:
The slot of the line can be calculated using the formula : y2 - y1/ x2 - x1.
So, you would plug in the values making the equation 5 - (-7)/ -1 - 2 and solve.
suppose a house painter rests a 20-foot ladder against a building, then decides the ladder needs to rest 1 foot higher against the building.Will moving the ladder 1 foot towards the building do the job?If it needs to be 2 feet lower, will moving the ladder 2 feet away from the building do the trick? Let's investigate
Moving the ladder 1 foot towards the building will not be enough to raise it by 1 foot, and moving it 2 feet away from the building will not be enough to lower it by 2 feet.
The relationship between the distance the ladder is moved along the ground (run) and the resulting change in height (rise) is determined by the ladder's angle of inclination, which is constant. This angle can be calculated using trigonometry, specifically the tangent function:
[tex]angle = arctan(rise/run)[/tex]
For a 20-foot ladder, the angle of inclination is approximately 75.96 degrees. If the painter moves the ladder 1 foot towards the building, the run will decrease from 20 feet to 19 feet, which means the rise will decrease proportionally according to the tangent function:
[tex]new rise = tan(angle) * new run[/tex]
[tex]new rise = tan(75.96) * 19[/tex]
new rise ≈ 18.7 feet
So, moving the ladder 1 foot towards the building will only raise it by about 0.3 feet, not enough to achieve the desired 1-foot increase. Similarly, moving the ladder 2 feet away from the building will increase the run from 20 feet to 22 feet, causing the rise to increase proportionally according to the tangent function:
new rise = tan(angle) x new run
new rise = tan(75.96) x 22
new rise ≈ 21.3 feet
Therefore, moving the ladder 2 feet away from the building will only lower it by about 1.3 feet, not enough to achieve the desired 2-foot decrease.
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Jay has an album that holds 800 hockey cards. Each page of the album holds 8 hockey cards. If 22% of the album is empty, how many pages are filled with hockey cards?
Using the given percentage we can see that there are 78 filled pages.
How many pages are filled with hockey cards?We know that there are 800 cards and each page holds 8 cards, then the number of pages is:
N = 800/8 = 100
And we know that 22% of the album is empty, then 78% (the complement) of the album is filled, this means that the number of filled pages is given by the formula below.
F = 100*(78%/100%) = 100*0.78 = 78
We divide the percentage by 100% to make it a decimal number, so we can use it in the operation.
There are 78 filled pages in the album.
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Help me solve this question
Hypothesis: The P-value for this test is 0.026251 which is less than the significance level of 0.05.
What is Hypothesis?Hypothesis is a statement or explanation proposed to explain a phenomenon. It is a logical conjecture, based on observations or experiments, made in order to draw out and test its consequences. In scientific research, a hypothesis is used as a starting point for further investigation and is tested through the scientific method. A hypothesis must be testable and falsifiable, meaning it can be tested and disproved using scientific evidence.
Therefore, we can reject the null hypothesis that there is no difference in the proportions of almonds in the new and old recipes. This means that the proportion of almonds in the new recipe is greater than in the previous recipe.
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What mice would be the “fittest” to do the forest environment? Why?
Answer:
The "fittest" mice to survive in a forest environment would depend on various factors such as the specific characteristics of the forest, availability of resources, and the predators and other species present in the area.
Generally, mice that are well adapted to forest environments would possess certain traits such as:
Good sense of smell: Forest environments are often dense and may provide cover for predators. Mice with a good sense of smell are better equipped to navigate and find food in such environments.
Good vision: Some mice species have adapted to have good vision to better navigate through their environment and avoid predators.
Climbing ability: Mice that are able to climb trees and other obstacles can better avoid predators and find food sources.
Ability to burrow: Some mice may dig burrows to escape predators or find shelter, and those that are well adapted to digging will be better equipped to do so in a forest environment.
Based on these criteria, mice such as the white-footed mouse and the deer mouse are well-suited to forest environments. These species possess a good sense of smell and vision, can climb and burrow when necessary, and are able to find food sources such as nuts, seeds, and insects in the forest. However, there may be other mouse species that are better adapted to a specific forest environment, and the "fittest" mice would ultimately depend on the specific characteristics of the forest in question.
if I get an annual income of 420 600,000 and get an increase of 8.2% calculate my new income
Answer:
Step-by-step explanation:
To calculate your new income after an increase of 8.2%, you can use the following formula:
New income = Old income + (Percentage increase * Old income)
Plugging in the values given in the problem, we get:
New income = 420,600,000 + (8.2% * 420,600,000)
New income = 420,600,000 + (0.082 * 420,600,000)
New income = 420,600,000 + 34,524,120
New income = 455,124,120
Therefore, your new income after an increase of 8.2% would be 455,124,120.
4. The middle school is located at (0, 0) on
a coordinate plane. Town Hall is located
4 miles directly east of the middle
school. The fire station is located 2 miles
directly north of Town Hall.
How many miles long is a straight
line between the school and the fire
station? Round to the nearest tenth.
The distance between the middle school and the fire station is 4.5 miles
What is Pythagoras theorem?Pythagoras theorem states that, in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
The distance between the middle school and the fire station is is the hypotenuse
therefore;
c² = 2² + 4²
c² = 4 + 16
c² = 20
c = √20
c = 4.5 miles(nearest tenth)
therefore the distance between the middle school and fire station is 4.5 miles
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What is the measure of angle P? q is 65° P is 67°
this IXL is due tomorrow so I need help fast make sure to explain
Check the picture below.
Who can help me please
The similarity statements are;
SV/RS = TV/TU
AC/AB = CE/ED
What are similar triangles?Formally, two triangles ABC and DEF are similar if and only if:
Their corresponding angles are congruent, meaning that angle A is equal to angle D, angle B is equal to angle E, and angle C is equal to angle F.
The corresponding sides are in proportion to each other, meaning that the ratio of the length of side AB to side DE is equal to the ratio of the length of side BC to side EF, which is also equal to the ratio of the length of side AC to side DF.
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