The given set of side lengths 11, 24, and 26 does not form a right triangle.
Determining whether the set of side lengths form a right triangleTo determine whether the set of side lengths form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have side lengths 11, 24, and 26. Let's check whether they satisfy the Pythagorean theorem.
Using the theorem, we have:
26^2 = 11^2 + 24^2
Simplifying the right-hand side, we get:
676 = 121 + 576
Therefore, the equation is false, and the set of side lengths satisfies the Pythagorean theorem.
This means that the given set of side lengths does not form a right triangle.
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the scatterplot below shows the relationship between the grams of fat and total calories in different food items. the equation for the least-squares regression line to this data set is y with hat on top equals 13.198 x plus 153.6. what is the predicted number of total calories for a food item that contains 25 grams of fat?
The predicted total number of calories for a food containing 25 grams of fat is approximately 483.55.
The equation for the least-squares regression line is:
z = 13.198x + 153.6
where ŷ= predicted value of y (total calories), x = value of the predictor variable (grams of fat), 13.198= slope of the line, and 153.6= y-intercept of the line.
To find the predicted total calories for a food with 25 grams of fat, simplify by substituting x = 25 into the equation.
z = 13.198x + 153.6
ŷ = 13.198(25) + 153.6
ŷ = 329.95 + 153.6
z = 483.55
Therefore, the predicted total number of calories for a food containing 25 grams of fat is approximately 483.55.
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Finding the mean , helpppp
The sum of the squares of two nonnegative numbers is 327. The product of the two numbers is 101. What is the sum of the two numbers?
The sum of the two number is 23.
Let's call the two numbers x and y. We know that:
x^2 + y^2 = 327
xy = 101
We want to find x + y.
We can start by squaring the equation x + y:
(x + y)^2 = x^2 + 2xy + y^2
Substituting in the values we know:
(x + y)^2 = x^2 + y^2 + 2xy
(x + y)^2 = 327 + 2(101)
(x + y)^2 = 529
Taking the square root of both sides:
x + y = ±23
Since both x and y are non-negative, we know that x + y must be positive. Therefore:
x + y = 23
So the sum of the two numbers is 23.
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plssss helppp asappp
Answer:
I think it's 13. The side that is equal to 13 is also equal to x.
i need to know this answer, i don’t understand probability
Answer:
67%
Step-by-step explanation:
add the yes and no values of 35 to 49
267+131= 398
267/398 = 0.6708542714
Estimate 0.6708542714 = 0.67
0.67 x 100 = 67%
explain whether the mean or the median is amore appropriate measure of center for this data set?
The mean and median are both measures of center, but which one is more appropriate depends on the data set.
What is appropriate?Appropriate behavior is behavior that is socially acceptable and respectful of others. This includes treating others with kindness, politeness, and respect, refraining from using offensive language, and not engaging in hurtful or violent behavior. Appropriate behavior also means following established rules, laws, and cultural norms. Examples of appropriate behavior include being honest and trustworthy, showing respect for others and their property, and being courteous and polite.
The mean is the average of the data set and is affected by extreme values. The median is the middle value in the data set and is not affected by extreme values. If the data set has extreme values, the median is usually the more appropriate measure of center. If the data set does not have extreme values, the mean is usually the more appropriate measure of center.
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Approximately how much of the area under a standard curve is within one standard deviation of the mean?
99%
95%
68%
80%
Answer:
Approximately 68% of the area under a standard normal distribution curve is within one standard deviation of the mean, also known as the 68-95-99.7 rule.
Specifically, the rule states that:
Approximately 68% of the area under the curve falls within one standard deviation of the mean.Approximately 95% of the area under the curve falls within two standard deviations of the mean.Approximately 99.7% of the area under the curve falls within three standard deviations of the mean.This means that if we have a normally distributed dataset with a mean of 0 and a standard deviation of 1, approximately 68% of the data points will fall within the range of -1 to +1 standard deviations from the mean.
please help me on this question.
Substituting the given values, we get:
sin M = 21/25 = 0.8400 (exact value)
Hence, sin M ≈ 0.8400 (four-decimal approximation)
What is the Trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships and properties of angles and triangles.
Given:
Opposite side (MK) = 21
Adjacent side (KL) = 2√46
Hypotenuse (LM) = 25
We can use the following trigonometric ratios in a right triangle:
sin M = Opposite/Hypotenuse
cos M = Adjacent/Hypotenuse
tan M = Opposite/Adjacent
Substituting the given values, we get:
sin M = 21/25 = 0.8400 (exact value)
Hence, sin M ≈ 0.8400 (four-decimal approximation)
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The pattern continues. Fill in the blanks.
2 x 4 + 1 = 3 x 3
3 x 5 + 1 = 4 x 4
4 x 6 + 1 = __ + __
__ x 7 + 1 = __ x __
__ x __ + __ = __ + __
Describe patterns that you see.
What will the equation look like when the first term is 25?
Based on the given pattern:
2 x 4 + 1 = 3 x 3
3 x 5 + 1 = 4 x 4
4 x 6 + 1 = __ + __
__ x 7 + 1 = __ x __
__ x __ + __ = __ + __
The general pattern is that the first term is multiplied by one more than itself, and then 1 is added to the result, which is equal to the second term squared.
When the first term is 25, the equation would look like:
25 x 26 + 1 = __ + __
The first blank would be filled with 26, and the second blank would be filled with 676 (which is 26 squared). So the complete equation would be:
25 x 26 + 1 = 26 + 676
two shaded identical rectangular decorative tiles are first placed (one each) at the top and at the base of a door frame for a hobbit's house, as shown in figure 1. the distance from w to h is 45 inches. then the same two tiles are rearranged at the top and at the base of the door frame, as shown in figure 2. the distance from y to z is 37 inches. what is the height of the door frame, in inches?
The height of the door frame is approximately [tex]68.2 + 2t = 68.2 + 2\sqrt(131.2) \approx95.1[/tex]inches.
Basic geometry concepts.
Firstly, we need to recognize that the two identical rectangular tiles form a vertical rectangle in both figure 1 and figure 2.
Let's call the height of this rectangle "h" and the width "w".
In figure 1, we can see that the distance from the top of the rectangle to the top of the door frame is "h".
Similarly, the distance from the bottom of the rectangle to the bottom of the door frame is also "h".
Therefore, the height of the door frame is simply the sum of the height of the rectangle and the height of the two tiles.
Height of door frame = h + 2t
"t" is the height of one tile.
Next, we can use the same logic for figure 2.
The distance from the top of the rectangle to the top of the door frame is now "y".
Similarly, the distance from the bottom of the rectangle to the bottom of the door frame is "z".
Therefore, we can write:
[tex]Height of door frame = (h - t) + 2t[/tex]
Where (h - t) is the height of the rectangle above the tiles.
Now, we can equate the two expressions for the height of the door frame:
[tex]h + 2t = (h - t) + 2t[/tex]
Simplifying, we get:
h = 3t
We are given that the distance from w to h is 45 inches, so we can use Pythagoras' theorem to find the length of the rectangle:
[tex]w^2 + h^2 = 45^2[/tex]
Substituting h = 3t, we get:
[tex]w^2 + 9t^2 = 2025[/tex]
Similarly, we can use the information in figure 2 to get another equation:
[tex]w^2 + 4t^2 = 1369[/tex]
Now we have two equations with two variables (w and t), which we can solve simultaneously.
Subtracting the second equation from the first, we get:
[tex]5t^2 = 656[/tex]
Therefore,
[tex]t^2 = 131.2[/tex]
And
[tex]h = 3t = 3sqrt(131.2)[/tex][tex]\approx68.2 inches[/tex]
Finally, we can use the Pythagorean theorem again to find the length of the door frame:
[tex]w^2 + h^2 = 45^2[/tex]
Substituting h = 68.2, we get:
[tex]w^2 + 68.2^2 = 2025[/tex]
Solving for w, we get:
[tex]w \approx 41.2 inches[/tex]
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How is this image rotating in degrees brainlest
The given image is rotated by 180 degrees.
What is rotation?The term "rotation" describes how an object or a point rotates around a fixed axis or center. In mathematics, rotation is a transformation where an object is twisted or spun in one direction or another around a fixed point known as the centre of rotation.
The center, angle, and direction of a rotation can all be identified in terms of geometry. Either clockwise or anticlockwise rotation is possible. A 360-degree rotation is a full turn or full revolution, while a 90-degree anticlockwise rotation is also referred to as a quarter-turn.
For the given quadrilateral when the image is rotated along the axis of symmetry the other image is obtained at 180 degree rotation.
Thus, the given image is rotated by 180 degrees.
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8 students are enrolled in a competition. they all solve the same 8 qs. after correction, it can be seen that each problem has been correctly solved by exactly 5 students. show that there are 2 students who, together, have solved all the problems?
Let's label the 8 questions as Q1, Q2, Q3, Q4, Q5, Q6, Q7, and Q8.
Let's label the 8 students as A, B, C, D, E, F, G, and H.
Since each problem has been correctly solved by exactly 5 students, we can say that the following is true:
Q1: A, B, C, D, E
Q2
PLSSSS HELP IF YOU TURLY KNOW THISSS
1. Multiply both sides by 2. 4 + 3x = 5 * 2
2. Simplify. 4 + 3x = 10
3. Subtract 4 from both sides to single out x. 3x = 10 - 4
4. Simplify. 3x = 6
5. Divide by 3. x = 6/3
6. Simplify. x = 2
Input 2 into the original equation to check this answer and you will get 5 = 5 which means that x = 2 is your final answer.
Answer: x = 2
Step-by-step explanation:
To solve for x, we will isolate the variable (x).
Given:
[tex]\displaystyle \frac{4+3x}{2}=5[/tex]
Multiply both sides of the equation by 2:
4 + 3x = 10
Subtract 4 from both sides of the equation:
3x = 6
Divide both sides of the equation by 3:
x = 2
The expression 0.9x represents the amount of pure copper sulfate in x liters of 90% copper sulfate solution.
a. Write an expression for the amount of pure copper sulfate in 3x liters of 25% copper sulfate solution.
b. A chemist added x liters of 90% copper sulfate solution to 3x liters of 25% copper sulfate solution. Use division to find the percentage of pure copper sulfate in the resulting solution.
The percentage of pure copper is
.
a) The expression for the amount of pure copper sulfate in 3x liters of 25% solution is 0.675x.
b) The percentage of pure copper sulfate in the resulting solution is 39.375%.
Percent compositionTo find the amount of pure copper sulfate in 3x liters of 25% copper sulfate solution, we can first calculate the amount of copper sulfate in the solution and then multiply by the percentage of pure copper sulfate.Since the solution is 25% copper sulfate, we know that there are 0.25(3x) = 0.75x liters of copper sulfate in the solution.
The amount of pure copper sulfate in the solution is given by 0.9 times the amount of copper sulfate. Therefore, the expression for the amount of pure copper sulfate in 3x liters of 25% copper sulfate solution is:
0.9(0.75x) = 0.675x
To find the percentage of pure copper sulfate in the resulting solution, we need to calculate the total amount of pure copper sulfate in the solution and divide by the total volume of the solution.The amount of pure copper sulfate added from the 90% copper sulfate solution is 0.9x liters.
The amount of pure copper sulfate in the 25% copper sulfate solution is 0.675x liters.
The total amount of pure copper sulfate in the resulting solution is:
0.9x + 0.675x = 1.575x
The total volume of the resulting solution is:
x + 3x = 4x
To find the percentage of pure copper sulfate in the resulting solution, we divide the amount of pure copper sulfate by the total volume of the solution and multiply by 100:
(1.575x / 4x) * 100 = 39.375%
Therefore, the percentage of pure copper sulfate in the resulting solution is 39.375%.
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Need help with this!
Answer
Number 14: 7 faces, 15 edges, and 10 vertices.
Number 15: 10 faces, 24 edges, and 16 vertices.
Number 16: 7 faces, 12 edges, and 7 vertices.
:D
Step-by-step explanation:
What is the answer to this problem?
The area of the shaded area is 3.27 ft²
How to the area of the shaded area?We can find the area of the shaded area by subtracting the area of the triangle from the area of the sector. That is;
Area of shaded area = Area of sector - area of triangle
Area of shaded area = (60/360 * π * 6²) - (1/2 * 6 * 6 * sin 60)
Area of shaded area = (60/360 * 22/7 * 36) - (1/2 * 36 * 0.866)
Area of shaded area = 3.27 ft²
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Shannon and Leslie want to carpet is 16 1/2‘ x 16 1/2‘ square room. They cannot put carpet under the entertainment system that jets out. In square feet, what is the area of the space with no carpet?
The area of space with no carpet is 268.25 sq ft.
In order to calculate the area of square room we have to subtract the section that is not carpeted from the total area of the room.
The given dimensions of the room is 16 1/2‘ x 16 1/2‘ square room
therefore,
16.5 x 16.5 = 272.25 sq ft
now if we consider that the entertainment system is 2 feet in measurement then,
2 x 2 = 4 sq ft
hence, the space with no carpet is
271.25 - 4
= 268.25 sq feet
The area of space with no carpet is 268.25 sq ft.
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So, a line parallel to y =ax + c will have a slope of
A. a
B. A number not equal to a
C. 1/a
Answer:
A
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = ax + x ← is in slope- intercept form
with slope m = a
• Parallel lines have equal slopes
then the slope of a line parallel to y = ax + c is
slope = a
A random sample of size is selected from a population with. A. What is the expected value of (to 2 decimals)? B. What is the standard error of (to 2 decimals)? C. Show the sampling distribution of (to 2 decimals). D. What does the sampling distribution of show? Blank
A) The expected value of the sampling distribution is 0.40.
B) The standard error is 0.05.
C) The sampling distribution will be centered around the population proportion of 0.40, with a spread given by the standard error of 0.05.
D) By examining the sampling distribution, we can see how likely it is to obtain a certain sample proportion by chance alone, and therefore make conclusions about the population based on the sample.
A) The expected value (also called the mean) of a sampling distribution is equal to the population parameter being estimated. In this case, the population parameter is the proportion, p, which is 0.40.
B) The standard error is the standard deviation of the sampling distribution. For a proportion, the formula for the standard error is √((p(1-p))/n), where p is the population proportion and n is the sample size. Plugging in the values given, we get √((0.40(1-0.40))/100) = 0.049.
C) The sampling distribution of a proportion is approximately normal if both np and n(1-p) are greater than or equal to 10. In this case, np = 1000.40 = 40 and n(1-p) = 100*0.60 = 60, so the conditions for normality are met.
D) The sampling distribution of a proportion shows the distribution of all possible sample proportions of a given size that could be drawn from a population with a known proportion.
The sampling distribution allows us to make inferences about the population proportion, such as constructing confidence intervals or conducting hypothesis tests.
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Complete Question:
A random sample of size 100 is selected from a population with p =0 .40.
A. What is the expected value (to 2 decimals)?
B. What is the standard error (to 2 decimals)?
C. Show the sampling distribution (to 2 decimals).
D. What does the sampling distribution of show?
an actuary determines the following regarding an individual auto policyholder: the probability that the auto policyholder will file a medical claim is 0.30. the probability that the auto policyholder will file a property claim is 0.42. the probability that the auto policyholder will file a medical claim or a property claim is 0.60. calculate the probability that the auto policyholder will file exactly one type of claim, given that the policyholder will not file both types of claims
The probability that the auto policyholder will file exactly one type of claim is 0.40.
How to calculate the probability?To calculate the probability, let M be the event that the policyholder files a medical claim and P be the event that the policyholder files a property claim. We are given:
P(M) = 0.30
P(P) = 0.42
P(M or P) = 0.60
We want to calculate the probability that the policyholder files exactly one type of claim, given that the policyholder will not file both types of claims. This can be expressed as:
P(exactly one type of claim | not both types of claims) = P((M and not P) or (not M and P)) / P(not both types of claims)
We can use the fact that:
P(not both types of claims) = P(M or P) - P(M and P)
To calculate the numerator, we have:
P((M and not P) or (not M and P)) = P(M and not P) + P(not M and P)
We can use the fact that:
P(not P) = 1 - P(P)
To calculate:
P(M and not P) = P(M) - P(M and P)
Putting everything together, we get:
P(M and not P) = 0.30 - P(M and P) = 0.30 - (0.60 - 0.30) = 0.00
P(not M and P) = P(P) - P(M and P) = 0.42 - (0.60 - 0.30) = 0.12
P((M and not P) or (not M and P)) = 0.00 + 0.12 = 0.12
P(not both types of claims) = 0.60 - 0.30 = 0.30
Therefore:
P(exactly one type of claim | not both types of claims) = 0.12 / 0.30 = 0.40
So the probability that the auto policyholder will file exactly one type of claim, given that the policyholder will not file both types of claims, is 0.40.
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Quadrilateral JKLM has vertices J(3,5), K(7,8), L(13,5), and M(13,0). Which statements are true? Select all that apply.
~a.) Line Segment KL ║ Line Segment JM
~b.) Line Segment KL ≅ Line Segment JM
~c.) Line Segment JK ≅ Line Segment LM
~d.) Line Segment JK ║ Line Segment LM
~e.) Quadrilateral JKLM is a trapezoid.
~f.) Quadrilateral JKLM is an isosceles trapezoid.
The statements that are true are:
→ Line Segment KL ≅ Line Segment JM
→ Quadrilateral JKLM is a trapezoid.
What is a trapezoid?A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs.
According to the given informationIn the quadrilateral JKLM
Using the distance formula, we can find the lengths of the line segments:
JK = √[(7-3)² + (8-5)²] = √58
KL = √[(13-7)² + (5-8)²] = √58
LM = √[(13-13)² + (0-5)²] = 5
JM = √[(13-3)² + (0-5)²] = √109
From this, we can analyze each statement:
a.) Line Segment KL ║ Line Segment JM
We can see from the sketch that the two line segments are not parallel. Therefore, statement a is false.
b.) Line Segment KL ≅ Line Segment JM
We found that the length of KL is equal to the length of JM. Therefore, statement b is true.
c.) Line Segment JK ≅ Line Segment LM
We can see from the sketch that the two line segments are not congruent. Therefore, statement c is false.
d.) Line Segment JK ║ Line Segment LM
We can see from the sketch that the two line segments are perpendicular. Therefore, statement d is false.
e.) Quadrilateral JKLM is a trapezoid.
A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. We can see from the sketch that line segments KL and JM are not parallel, but line segments JK and LM are parallel. Therefore, statement e is true.
f.) Quadrilateral JKLM is an isosceles trapezoid.
An isosceles trapezoid is defined as a trapezoid with congruent base angles and congruent non-parallel sides. We can see from the sketch that neither the base angles nor the non-parallel sides are congruent. Therefore, statement f is false.
Therefore, the statements that are true are b and e.
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Answer:
A) KL⎯⎯⎯⎯⎯∥JM⎯⎯⎯⎯⎯
C) JK⎯⎯⎯⎯⎯≅LM⎯⎯⎯⎯⎯⎯
E) Quadrilateral JKLM is a trapezoid.
F) Quadrilateral JKLM is an isosceles trapezoid.
Step-by-step explanation:
These where the correct answer I got when taking the assignment with that question
Shopping While shopping for clothes, Tracy spent $34 less than 3 times what Jaclyn spent. Tracy spent $26. Write and solve an equation to find how much Jaclyn spent. Let x represent how much Jaclyn spent. The equation that can be used to determine how much Jaclyn has spent is
PLEASE HELP!! 20 POINTS
Select the correct answer from each drop-down menu. Consider this equation. 1/x + 2/x+10 =1/3 Complete the statements to make them true. The least common denominator is . The equation will have valid solutions.
Answer: The least common denominator is 3x(x+10)
The equation will have 2 valid solutions
Step-by-step explanation: sorry if wrong
The radius of a circle is 10 cm. Find its area in terms of π.
The area of a circle is given by the formula:
A = πr^2
where r is the radius of the circle.
Substituting the value of the radius as r = 10 cm, we get:
A = π(10)^2
A = 100π
Therefore, the area of the circle with radius 10 cm is 100π square centimeters.
~~~Harsha~~~
Exit
6-3: PRACTICE Part 2 Logarithms in Equations Algebra 2
Michael invests $1,000 in an account that earns a 4.75% annual percentage rate compounded continuously. Peter invests $1,200 in an account that earns a 4.25% annual
percentage rate compounded continuously. Which person's account will grow to $1,800 first?
Michael's account will grow to $1,800 after about year(s). Peter's account will grow to $1,800 after about year(s). So,
(Round to the nearest whole number as needed.)
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account will grow to $1,800 first.
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Answer: To solve this problem, we need to use the continuous compound interest formula:
A = Pe^(rt)
where A is the amount in the account, P is the initial principal, e is the mathematical constant e (approximately 2.71828), r is the annual interest rate (as a decimal), and t is the time in years.
For Michael's account, we have:
A = 1000e^(0.0475t)
For Peter's account, we have:
A = 1200e^(0.0425t)
We want to find the time it takes for each account to reach $1,800. So we can set up the following equations:
1000e^(0.0475t) = 1800
1200e^(0.0425t) = 1800
We can solve each equation for t by taking the natural logarithm of both sides and isolating t:
ln(1000) + 0.0475t = ln(1800)
ln(1200) + 0.0425t = ln(1800)
Subtracting ln(1000) or ln(1200) from both sides, we get:
0.0475t = ln(1800) - ln(1000)
0.0425t = ln(1800) - ln(1200)
Dividing both sides by the interest rate and simplifying, we get:
t = (ln(1800) - ln(1000)) / 0.0475 ≈ 10.16 years for Michael's account
t = (ln(1800) - ln(1200)) / 0.0425 ≈ 10.62 years for Peter's account
Therefore, Michael's account will grow to $1,800 first, after about 10 years (rounded to the nearest whole number).
Step-by-step explanation:
help would be absolutely appreciated
Thus, the given quadratic equation has two real roots x = 3 and x = -2.
Explain about the solution of quadratic function:A function or mathematical statement of degree two is a quadratic function. This indicates that two is the function's highest power. The roots of all quadratic functions are two.
The quadratic formula is employed to solve a quadratic to discover its roots, which can either be distinct or the same. A quadratic function must first be converted into a quadratic equation by being made equal to zero in order to be solved.Given equation:
x² - x - 6 = 0
Using the quadratic formula:
x = [-b ± √(b² - 4ac) ] / 2a
a = 1 , b = -1 and c = -6
x = [1 ± √((-1)² - 4*1*(-6) ] / 2*1
x = [1 ± √(1 + 24) ] / 2
x = [1 ± 5 ] / 2
Now,
x = (1 + 5)/2 = 3
x = (1 - 5)/ 2 = -2
Thus, the given quadratic equation has two real roots x = 3 and x = -2.
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complete question:
Check whether the given equation has, one solution, two solution ,many solution or no real solution.
x² - x - 6 = 0
The height of another frog over time is modeled by the function y= -16t^2 + 10t +0.3. How many seconds is this frog in the air before landing on the ground? Round your answer to the nearest hundredth.
please answer quickly
Step-by-step explanation:
y will equal 0 when the frog hits on the ground after being in the air:
0 = -16t^2 + 10 t + 0.3
Use quadratic formula with a = -16 b = 10 c = 0.3
to find t = .65 seconds
Which of these expressions are equivalent to p/3
Answer:
B) 3p/9
D)1/3p
Step-by-step explanation:
Given that £1 = $1.62
a) How much is £650 in $?
b) How much is $405 in £?
Answer:
a 1053
b 250
multiply 650 by 1.62 for part a.
for part b divide by 1.62 since pound is less than dollar
hope this helps :)
I need help, I thought I understood it but this doesn't make any sense
Answer:
The corresponding sides:
[tex]NO[/tex]≅[tex]ZW[/tex]
[tex]PM[/tex]≅[tex]XY[/tex]
[tex]MN[/tex]≅[tex]YZ[/tex]
[tex]OP[/tex]≅[tex]WX[/tex]
The corresponding angles:
[tex]< M[/tex]≅[tex]< Y[/tex]
[tex]< P[/tex]≅[tex]< X[/tex]
[tex]< O[/tex]≅[tex]< W[/tex]
[tex]< N[/tex]≅[tex]< Z[/tex]