Answer:
The quadratic equations and their solutions are;
9 ± √33 /4 = 2x² - 9x + 6.
4 ± √6 /2 = 2x² - 8x + 5.
9 ± √89 /4 = 2x² - 9x - 1.
4 ± √22 /2 = 2x² - 8x - 3.
Explanation:
Any quadratic equation of the form, ax² + bx + c = 0 can be solved using the formula x = -b ± √b² - 4ac / 2a. Here a, b, and c are the coefficients of the x², x, and the numeric term respectively.
We have to solve all of the five equations to be able to match the equations with their solutions.
2x² - 8x + 5, here a = 2, b = -8, c = 5. x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(5) / 2(2) = 8 ± √64 - 40/4. 24 can also be written as 4 × 6 and √4 = 2. So x = 8 ± 2√6 / 2×2= 4±√6/2.
2x² - 10x + 3, here a = 2, b = -10, c = 3. x =-b ± √b² - 4ac / 2a =-(-10) ± √(-10)² - 4(2)(3) / 2(4) = 10 ± √100 + 24/4. 124 can also be written as 4 × 31 and √4 = 2. So x = 10 ± 2√31 / 2×2 = 5 ± √31 /2.
2x² - 8x - 3, here a = 2, b = -8, c = -3. x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(-3) / 2(2) = 8 ± √64 + 24/4. 88 can also be written as 4 × 22 and √4 = 2. So x = 8 ± 2√22 / 2×2 = 4± √22/2.
2x² - 9x - 1, here a = 2, b = -9, c = -1. x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(-1) / 2(2) = 9 ± √81 + 8/4. x = 9 ± √89 / 4.
2x² - 9x + 6, here a = 2, b = -9, c = 6. x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(6) / 2(2) = 9 ± √81 - 48/4. x = 9 ± √33 / 4 .
Step-by-step explanation:
Answer:
1.(2,-1)
2.\(y=(x+1)^{2} +2\)
3.\(y=(x-3)^{2} +1\)
Step-by-step explanation:
for $k \neq 0$, find the value of $k$ such that $f(x) = kx^4 -2k^3x^2$ has a local maximum at $x = 1$.
The values of k for local maxima is k = 1 and k = -1
The given function is,
f(x) = kx⁴ - 2k³x²
⇒ f'(x) = 4kx³ - 4k³x
⇒f''(x) = 12kx² - 4k³
To find a local maximum at x = 1, we need f'(1) = 0 and f''(1) < 0.
Therefore, set f'(1) = 0,
⇒4k(1)³ - 4k³(1) = 0
⇒4k - 4k³ = 0
⇒4k(1 - k²) = 0
From this, we can see that either k = 0 or k = ±1.
However, we have to check the second derivative to determine if these are local maximums,
⇒f''(1) = 12k(1)² - 4k³
For k = 0, f''(1) = 0, which means there isn't a local maximum.
For k = 1, f''(1) = 8 < 0, which means there is a local maximum.
For k = -1, f''(1) = -8 < 0, which means there is also a local maximum.
Therefore,
The values of k that give a local maximum at x = 1 are k = 1 and k = -1.
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maria bought a swimming pool with a circumference of 24 feet. she wants to buy a cover for her pool. what is the approximate size of the cover that maria will need to buy? round your answer to the nearest hundredth.
The approximate size of the cover that Maria will need to buy is 45. 84 square feet
How to determine the valueThe formula for calculating the circumference of a circle is expressed as;
Circumference = πr²
Where 'r' is the radius of the circle
Now, let's substitute the value of the circumference
24 = 2 × 3. 14 × r
r = 24/6. 28
r = 3. 82 feet
Formula for area = πr²
Substitute value of r
Area = 3. 14 × (3. 82)²
Area = 3. 14 × 14. 59
Area = 45. 84 square feet
Hence, the value is 45. 84 square feet
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Si una persona tiene que convivir 80 años y proyecta a terminar sus estudios cuanto tengo 1/3 de los años que vivirá. ¿A que edad termina sus estudios?
Answer:
terminan sus estudios cuando tienen 26 años y 2/3 años de edad
Unit 5: Systems of Equations & Inequalities Homework 2: Solving Systems by Substitution
By solving the system by substitution, we got the solutions:
x = 2/3, y = 8/3.
Solving the system of equations:
I guess we need to solve problem number 5, so let's do that.
Here we have the system of equations:
y = x + 2
3x + 3y = 6
To solve it by substitution, we need to isolate one of the variables in one of the equations and then replace that in the other equation.
For example, here we can see that "y" is already isolated in the first equation, so we can use that and replace it in the second equation.
3x + 3y = 6
3x + 3*(y = x + 2) = 6
3x + 3*(x + 2) = 6
Now we have an equation that only depends on x, so we can solve it:
3x + 3x + 2 = 6
6x + 2 = 6
6x = 6 - 2 = 4
x = 4/6 = 2/3.
Now we can use the first equation to find the value of y:
y = x + 2 = 2/3 + 2 = 2/3 + 6/3 = 8/3.
Then the solution is:
x = 2/3 and y = 8/3.
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which of the following would tend to decrease the width of a confidence interval? i. increasing the sample size ii. using a higher confidence level iii. using a lower confidence level
A. I only
B. II only
C. III only
D. I and II only
E. I and III only
Both increasing the sample size (i) and using a lower confidence level (iii) would tend to decrease the width of a confidence interval. The answer is: E.
Increasing the sample size provides more data points, which leads to a more precise estimate of the population parameter. With a larger sample size, the variability within the sample is reduced, resulting in a narrower confidence interval.
Using a lower confidence level means being less confident in the estimation and allowing for a greater margin of error. A lower confidence level requires a smaller interval width to accommodate the increased uncertainty, resulting in a narrower confidence interval.
On the other hand, using a higher confidence level (ii) would tend to increase the width of a confidence interval. A higher confidence level indicates a greater degree of confidence in the estimation, requiring a wider interval to capture the range of possible values for the population parameter.
Hence, the correct option is: E. I and III only.
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hi guys can you guys help me with this and answer and explain plss
Answer:
draw 3cm lines each sides and you get the rectangle
Step-by-step explanation:
it's 3cm because a rectangle has 4 side when you divide 12cm by 4cm you get 3cm
A couple is planning to have three children. Each child is equally likely to be a boy or a girl. If this couple's plan is successful, what is the probability that they will have exactly two girls?
Answer:
The probability of having exactly two girls is 3/8 or 0.375
Step-by-step explanation:
Since the likelihood is equal, the probability of having a boy = probability of having a girl = 1/2
In written form;
P(g) = P(b) = 1/2
We use the Bernoulli approximation to know the probability of having two girls.
Mathematically, that would be;
3C2 P(g)^2 P(b)^1
Inserting the values , we have;
3 * (1/2)^2 * (1/2)
= 3 * (1/2)^3 = 3/8 = 0.375
‼️‼️‼️Answer pls‼️‼️‼️
Answer:
C) 20 sq. ft.
Step-by-step explanation:
Using the formula given, we can find the answer. Substitute the diagonals given, 8 and 5, into the formula.
We then get 1/2*8*5 which equals 20 sq. ft.
Answer:
20 sq. ft.
Step-by-step explanation:
five hundred fifty five divided in five
Answer:
Well I'm not sure if its a joke but here is the answer anyways LOL Its 111
Step-by-step explanation:
Answer:
111
Step-by-step explanation:
If you think about it, 5 ÷ 5 = 1
So all the digits are 1
111
(Plus I just used a calculator)
Hope I helped :)
x+y=3
x^2+y^2=17
Solve the simultaneous equations
The possible solution set for the system is (- 1, 4) and (4, - 1).
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the equations as -
x + y = 3
x² + y² = 17
Refer to the graph of the function attached. The points of intersection represents the possible solution set.
Therefore, the possible solution set for the system is (- 1, 4) and (4, - 1).
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10.An order is written 700mg of ampicillin PO, the drug is supplied is liquid form as1g/3.5ml how much of the liquid should be given?
5.25ml 2.55ml 6.25ml 2.45ml
11.The order state meperidine 75mg IM every 6hours PRN pain. The pharmacy sends you a vial that states 25mg/2ml.how many ml can the nurse give in 24 hours?
12.The order state to give the patient 0.75g of antibiotic PO every 4 hours for 7 days The drug comes in 250mg tables. How many tablets should the patient take? 2tab. 3tab .4tab. 15tab.
13.Order is written for 1000ml of normal saline to be administered IV over 10hours.Thedrop factor on the IV tubing is 15gtt/ml. what is the IV rate?
50ml/hr.at50gtt/min 100ml/hr.at 25gtt/min 100ml/hr.at 100gtt/min 100ml/hr. at 15gtt/min
14.a post operative order is written for 15gr of codeine every 4 hours PRN for pain. Each dose given will contain how much milligrams of codeine
15.Robitussin cough syrup 225mg.PO is ordered the bottle read 600mg in 1oz how much cough syrup 225mg PO is ordered the bottle read600mg in 1oz how much cough syrup should be given in ml's?
Where the above are given,
10. The nurse should give 2.45ml of the liquid medication.
11. The nurse can give 24ml of meperidine in 24 hours.
12. The patient should take 42 tablets of the antibiotic.
13. The IV rate is 100ml/hr at 1500gtt/min with a 15gtt/ml drip factor.
14. Each dose of codeine contains 15000mg.
15. The patient should be given 2.67oz (approximately) of the cough syrup.
What is the explanation for the above ?10. To determine how much of the liquid should be given, we can set up a proportion
1g/3.5ml = 700mg/x
Cross-multiplying,
1g * x = 700mg * 3.5ml
x = (700mg * 3.5ml) / 1g
x = 2450mg*ml/g
Therefore, the amount of liquid to be given is 2.45ml.
11. The order states meperidine 75mg IM every 6 hours PRN pain, and the pharmacy sends a vial that contains 25mg/2ml. To calculate how many ml can be given in 24 hours, we need to consider the frequency and duration.
In 24 hours, there are 24/6 = 4 doses to be given. Each dose contains 75mg of meperidine.
To find the volume (ml) of each dose, we can set up a proportion -
25mg/2ml = 75mg/x
25mg * x = 75mg * 2ml
x = (75mg * 2ml) / 25mg
x = 6ml
12. To calculate the number of tablets the patient should take, we need to consider the dosage and the duration.
Each tablet contains 250mg of the antibiotic.
To find the number of tablets for the total dosage, we can set up a proportion -
250mg/1 tab = 0.75g/x
250mg * x = 0.75g * 1 tab
x = (0.75g * 1 tab) / 250mg
x = 0.003 tab
Since we cannot take a fraction of a tablet, the patient should take 1 tablet every 4 hours for 7 days, resulting in a total of 1 * 6 * 7
= 42 tablets.
13. To determine the IV rate, we need to calculate the number of drops per minute.
The formula to calculate the IV rate in drops per minute (gtt/min) is -
IV rate (ml/hr) = Total volume (ml) / Total time (hr)
IV rate (gtt/min) = IV rate (ml/hr) * Drop factor (gtt/ml)
IV rate (ml/hr) = 1000ml / 10hr = 100ml/hr
IV rate (gtt/min) = 100ml/hr * 15gtt/ml =
1500gtt/min
Therefore, the IV rate is 100ml/hr at 1500gtt/min.
14. To determine the amount of milligrams of codeine in each dose, we need to convert grams to milligrams.
1 gram (g) = 1000 milligrams (mg)
15 grams (gr) = 15 * 1000mg = 15000mg
Therefore, each dose contains 15000mg of codeine.
15. To calculate how much cough syrup should be given in ml's, we can set up a proportion -
225mg/1oz = x ml/600mg
225mg * x = 1oz * 600mg
x = (1oz * 600mg) / 225mg
x = 2.67oz
Therefore, 2.67oz of cough syrup should be given in ml's.
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Determine whether AB and CD are parallel, perpendicular, or neither. Graph each line to verify your answer. A(4, 2), B(-3, 1), C(6, 0), D(-10, 8)
The lines AB and CD are neither parallel nor perpendicular,
Determining the relationship between lines AB and CDFrom the question, we have the following parameters that can be used in our computation:
A(4, 2), B(-3, 1), C(6, 0), D(-10, 8)
The relationship between lines AB and CD can be determined using the slope formula
The slope of a line is calculated using
Slope = Change in y/Change in x
using the above as a guide, we have the following:
Slope AB = (1 - 2)/(-3 - 4)
Slope AB = 1/7
Slope CD = (8 - 0)/(-10 - 6)
Slope CD = -1/2
The above slopes are neither equal nor opposite reciprocals
This means that the lines AB and CD are neither parallel nor perpendicular,
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solve the system of equation
y= x +1
8x - 4y= 0
The answer is (1, 2)
Answer:
y=2
x=1
Slope:
y=x+1
y=2x
Step-by-step explanation:
y=x+1
8x-4y=0
-8x -8x
-4y=-8x
-------------
-4 -4
y=2x
If solving for x:
2x=x+1
-x -x
x=1
If solving for y:
y=1+1
y=2
Kegan wants to buy a new skateboard that will cost $140. So far, Kegan has saved $30 toward the purchase to the skateboard. To raise the remaining money needed, Kegan mows his neighbor’s lawn and charges $10 each time he completes the job. Write an equation to find x, the number of times Kegan mows his neighbor’s lawn. How many times will Kegan need to mow his neighbor’s lawn to have enough money to buy the skateboard?
Answer:
10x + 30=140. Kegan has to mow his neighbors lawn 11 times.
Answer:
11 more times.
Step-by-step explanation:
Ok, so what do we know?
We know that he wants to buy a skateboard that will cost $140.
He already saved $30.
To raise the remaining money needed, he mows his neighbor’s lawn and charges $10 each time he completes the job.
What do we want to find?
How many times Kegan needs to mow his neighbor's lawn to have enough money to buy the skateboard.
Ok we also need to write an equation.
$140-$30=$110
My equation will be 110 ÷ 10 = x.
Using this equation, I can solve for x.
110 ÷ 10 = 11.
So Kegan will need to mow 11 more times to have enough money for the skateboard.
In another right angle triangle the hypotenuse is 53, and the one of the side lengths is
28. Please find the missing side length,
A club with 13 members is to choose three officers: president, vice-president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?
Answer:
njj
Step-by-step explanation:
Suppose a student takes a 10-question true-false test, but they didn't study. What's the probability they get 3 problems correct by guessing
The probability that a student, who didn't study, gets 3 problems correct on a 10-question true-false test by guessing is approximately 0.117.
To calculate this probability, we can use the binomial probability formula. The formula is given by P(X = k) = (n C k) * p^k * (1 - p)^(n - k), where P(X = k) is the probability of getting k successes, n is the number of trials, p is the probability of success on a single trial, and (n C k) represents the number of combinations.
In this case, n = 10 (the number of questions), k = 3 (the desired number of correct answers), and p = 0.5 (since it's a true-false test and guessing has a 50% chance of being correct). We can calculate the probability using the formula as follows:
P(X = 3) = (10 C 3) * 0.5^3 * (1 - 0.5)^(10 - 3) ≈ 0.117
Therefore, the probability of getting 3 problems correct by guessing is approximately 0.117.
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Probability Distributions
This makes sense because the formula terms Probability Distributions are built upon one another, allowing us to utilise repeated reasoning to determine the value of Cn for any value of n.
What is inductive reasoning and deductive reasoning?Making generalisations using specific observations or data is known as inductive reasoning. Scientific research frequently bases ideas on patterns or trends that have been noticed. On the other hand, deductive reasoning entails applying broad concepts or rules to come to specific conclusions. It is frequently employed in logic and mathematics, where the premises are known to be valid and conclusions are reached by logical reasoning.
Using repeated reasoning we have:
C₁ = n = 1
C₋₁ = n = 1
C = 1
Cₙ in terms of C, C₁, and C₋₁:
Cₙ = 2C + C₁ + 3C₋₁
Substituting in the values we have for n = 1:
C₂ = 2(1) + 1 + 3(1) = 6
Now using n = 2, we have:
C₁ = n = 2
C₋₁ = n - 1 = 1
C = 1
Substituting in the formula again:
C₃ = 2(1) + 2 + 3(1) = 7
Now, for n = 3:
C₁ = n = 3
C₋₁ = n - 1 = 2
C = 1
C₄ = 2(1) + 3 + 3(2) = 11
This makes sense because the formula's terms are built upon one another, allowing us to utilise repeated reasoning to determine the value of Cn for any value of n.
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A system of two linear equations in two variables has no solution. What statement is accurate about these two linear equations?
Responses
The two linear equations never intersect.
The two linear equations never intersect.
The two linear equations graph the same line.
The two linear equations graph the same line.
The two linear equations do not cross the x-axis.
The two linear equations do not cross the x-axis.
The two linear equations do not cross the y-axis.
The two linear equations do not cross the y-axis.
The two linear equations intersect at exactly one point.
The right response is that the two linear equation never intersect , because the graph of these two linear equation will be two parallel lines.
How many types of solution are there for two linear equations ?
There are 2 types of solution :
Consistent :
A consistent system is said to be an independent system if it has a single solution.
A consistent system is said to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide, so the equations represent the same line. Each point on the line represents a pair of coordinates that fits the system. So there are an infinite number of solutions.
Non-consistent :
Another type of system of linear equations is the inconsistent system, in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no common points for both lines; therefore, there is no solution to the system and if we draw the graph of these equations then the graphs of both equation becomes parallel to each other.
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The two linear equations never intersect.
When a system of two linear equations in two variables has no solution, it means that there is no set of values for the variables that satisfies both equations simultaneously. Geometrically, this corresponds to the two lines represented by the equations being parallel. Since parallel lines never intersect, the statement "The two linear equations never intersect" accurately describes the situation.
If the two linear equations were graphed on a coordinate plane, they would appear as two distinct lines that run parallel to each other without ever crossing or intersecting. This indicates that there is no common point of intersection between the lines, and therefore no solution exists for the system of equations.
It is important to note that this scenario is different from the case where the two linear equations represent the same line. In that case, the equations would be equivalent, and every point on the line would satisfy both equations. However, when there is no solution, it means that the lines do not share any common points and never intersect.
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I have a proof and I need help!
Answer:
Step-by-step explanation:
can u please do step by step with this problem`-5(x-4)
Answer:
-5x+20
Step-by-step explanation:
Distribute the -5: -5(x) and -5(-4)
-5x+20
Since you cannot combine like terms, this is your final answer
Answer:
-5 × 4x = -20x
Step by Step Explanation:
Start with parenthesis
x - 4 = 4x
Multiply
-5 × 4x = -20x
4x - 5y = 1
x= -6
Solve for x and y
Step-by-step explanation:
44 is between what 2 numbers?
4 & 5
O 5 & 6
O 6 & 7
0 7 & 8
Answer:
\( \sqrt{36} < \sqrt{44} < \sqrt{49} \\ 6 < 6.6 < 7 \\ \\ it \: is \: betwen \: 6 \: and \: 7\)
4. Evaluate I = S 2x + 73 x² + 4x + 7 dx
The integral evaluates to:
∫(2x + 73x² + 4x + 7) dx = x^2 + (73/3) * x^3 + 2x^2 + 7x + C.
This is the general solution for the indefinite integral.
To evaluate the integral ∫(2x + 73x² + 4x + 7) dx, we can use the power rule of integration. By applying the power rule to each term of the integrand, we can find the antiderivative. This will give us the indefinite integral of the function. We will then add the constant of integration to obtain the final result.
To evaluate the integral ∫(2x + 73x² + 4x + 7) dx, we can use the power rule of integration, which states that the integral of x^n with respect to x is (1/(n+1)) * x^(n+1) + C, where C is the constant of integration.
Applying the power rule to each term of the integrand, we have:
∫2x dx = 2 * ∫x dx = 2 * (1/2) * x^2 = x^2
∫73x² dx = 73 * ∫x² dx = 73 * (1/3) * x^3 = (73/3) * x^3
∫4x dx = 4 * ∫x dx = 4 * (1/2) * x^2 = 2x^2
∫7 dx = 7x
Now, we can combine the individual antiderivatives to obtain the indefinite integral:
∫(2x + 73x² + 4x + 7) dx = ∫2x dx + ∫73x² dx + ∫4x dx + ∫7 dx
= x^2 + (73/3) * x^3 + 2x^2 + 7x + C,
where C is the constant of integration.
Therefore, the integral evaluates to:
∫(2x + 73x² + 4x + 7) dx = x^2 + (73/3) * x^3 + 2x^2 + 7x + C.
This is the general solution for the indefinite integral. If you have specific limits of integration, you can substitute those values into the antiderivative expression and subtract the corresponding values to find the definite integral.
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Write an equation of the line that passes through $\left(-1,\ 3\right)$ and is parallel to the line $y=-3x+2$ .
The equation of the line that passes through point (-1, 3) and parallel to line y = 3x + 2 is
y = 3x + 4How to find the line that passes through point point (-1, 3)As a parallel line part of the qualities include that the slopes of the lines are equal
The equation of line is y = 3x + 2
The slope intercept form of the form as
y = mx + c
where
m = slope
c = intercept
x = input variables
y = output variables
Line has slope, m = 3, a new parallel line of slope 3 passing through point (-1, 3)
(y - y₁) = m (x - x₁)
y - 3 = 3 (x - -1)
y = 3x + 1 + 3
y = 3x + 4
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Given that log (4)≈ 0.56 and log (3)≈ 0.44, evaluate each of the following:
a) log (0.75)
b) loga (√3)~
c) log (12)
d) log(64)~
e) log (48) ~
f) log (2.25)
The logarithmic values are given by:
a) log (0.75)= -0.12
b) log a (√3)≈log a+ 0.44
c) log (12)=1
d) log(64)≈1.68
e) log (48)≈1.56
f) log (2.25)=0.32
What are logarithmic functions?In mathematics, the logarithm is the inverse function of exponentiation. That is, the exponent to which b must be raised in order to obtain x is the logarithm of a number x to the base b. For example, because 1000 = 103, the logarithm base 10 of 1000 is three, or log10 (1000) = three.
Logarithmic functions are the inverses of exponential functions. The exponential equation x = ay is defined as the logarithmic function y = log ax.
Given,
log (4)≈ 0.56, log (3)≈ 0.44
a) log(0.75)=log(75/100)
=log(3/4)
=log 3 - log 4
= -0.12
b) log a(√3)=log a +log √3
=log a+ 0.44
c) log(12)= log(3×4)
=log 3+log 4
=0.44+0.56
=1.00
=1
d) log(64)= log(4³)
=3 log 4
=3(0.56)
=1.68
e) log(48)=log(3×16)
=log(3)+log(4²)
=log 3+2 log ²4
=0.44+2(0.56)
=1.56
f) log(2.25)=log(225/100)
=log(9/4)
=log(3²)-log 4
=2 log 3-log 4
=2(0.44)-0.56
=0.32
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jamie is 3 years less than three times Andys age. In five years the sum of their ages will be 59.How old are they now
Answer:
Andy : 13 years old and
Jamie: 36 years old
Step-by-step explanation:
Andy = x
Jamie = 3x - 3
In 5 years:
(X+5)+(3x-3+5) = 59
4x + 7 = 59
4x = 59 - 7
x = 52/4
x = 13
x+5y=5. 3x-5y=3. método de igualación porfa
Answer: (2,0.6)
Step-by-step explanation:
\(x+5y=5 \ \ \ \ (1)\\3x-5y=3\ \ \ (2)\\\\ Sum\ the\ equations\ (1)\ and \ (2):\\\\x+3x+0=5+3\\\\4x=8\)
Divide both parts of the equation by 4:
\(x=2\)
Substitute the value of x=2 into equation (1):
\(2+5y=5\\\\2+5y-2=5-2\\\\5y=3\)
Divide both parts of the equation by 5:
\(\displaystyle\\y=\frac{3}{5} \\\\y=0.6\)
Thus, (2,0.6)
Which expression shows the prime factorization of 36?
A. 2 x 2 x 3
B. 2 x 3 x 3
C. 2 x 2 x 2 x 3 x 3
D. 2 x 2 x 3 x 3
Answer:the answer is C
Step-by-step explanation:
: 1. Two equilateral triangles are always similar. 2. The diagonals of a rhombus are perpendicular to each other. 3. For any event, 0
Both the given statements are true
1. Two equilateral triangles are always similar: True.
An equilateral triangle is a triangle in which all three sides are equal. Since two equilateral triangles have the same shape and size, they are always similar. Similarity means that the corresponding angles are equal, and the corresponding sides are in proportion.
2. The diagonals of a rhombus are perpendicular to each other: True.
In a rhombus, opposite sides are parallel, and all sides have equal length. The diagonals of a rhombus bisect each other at right angles, which means they are perpendicular to each other. This property holds true for all rhombuses, regardless of their size or orientation.
Learn more about equilateral triangle here
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Given question is incomplete, the complete question is below
State true or false
1. Two equilateral triangles are always similar.
2. The diagonals of a rhombus are perpendicular to each other.