Answers
Answer:
u = 2\(\sqrt{5}\) v = \(\sqrt{15}\)
Step-by-step explanation:
longer leg of a 30-60-90 triangle is shorter leg times \(\sqrt{3}\) and the hypotenuse of a 30-60-90 triangle is shorter leg times 2.
So, the length of the shorter leg = \(\sqrt{5}\)
Therefore, u = 2\(\sqrt{5}\) and v = \(\sqrt{3} \sqrt{5} = \sqrt{15}\)
Related Questions
The Black Panther looks for Vibranium to put in his spear. He spends 3/5 of an hour searching. Over 4 days, about how many hours doe
gemstones? (NF 4 828)
between 2 and 3 hours
between 4 and 5 hours
between 6 and 7 hours
o
between 8 and 9 hours
Answers
Answer:
Between 2 and 3 hours
Step-by-step explanation:
Given
\(Time = \frac{3}{5}\ hours\ daily\)
\(Days = 4\)
Required
Determine the total hours
This is calculated by multiplying the number of days by the time per day;
\(Duration = \frac{3}{5} * 4\)
\(Duration = \frac{3 * 4}{5}\)
\(Duration = \frac{12}{5}\)
\(Duration = 2.4\)
2.4 is a number between the interval of 2 and 3.
Hence, option (A) is the solution to the question
What is an example of "A one-to-one function of P onto Q is an isomorphism of P and Q "?
Answers
An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.
How to Identify a One-to-One Function?An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.
This function is one-to-one because for every element x in P, there is a unique element 2x in Q. It is onto because every element y in Q has a preimage x in P such that f(x) = y (e.g., y/2 = x).
Furthermore, this function preserves the group structure between P and Q, as it satisfies the properties of an isomorphism. In this case, the group structure is addition, and the function f preserves addition: f(x + y) = 2(x + y) = 2x + 2y = f(x) + f(y) for all x, y in P.
Therefore, the function f: P -> Q defined as f(x) = 2x is an example of a one-to-one function that is an isomorphism between sets P and Q.
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A door with width 4.20 has an arc as shown in the diagram. Find: a the radius of the arc, to the nearest cm b the length of the arc, to the nearest cm. 225° is the central angle
Answers
Answer:
The arc length is 4 cm to the nearest cmStep-by-step explanation:
The diagram is not given in this question, but we can proceed anyways.
from the problem statement we can observe that the radius of the arc is same as the width of the door
a. the radius is 4.2 cm
b. the length of the arc given that the central angle is 25° can be gotten using the formula stated bellow
arc length = 2 π r *(∅/360)
substituting we have
arc length = 2*3.142*(225/360)
arc length= 6.284*0.625
arc length=3.92 cm
Approximately the arc length is 4 cmWhich graph represents the solution to the inequality 0.5 is greater than or equal to the product of a number and −0.25?
A. number line with closed circle on 0.5 with arrow shaded right
B. number line with open circle on point on negative 0.5 with arrow shaded left
C. number line with closed circle on negative 2 with arrow shaded right
D. number line with open circle on 2 with arrow shaded left
Answers
Option C i.e. number line with closed circle on negative 2 with arrow shaded right represents the solution to the inequality.
What is inequality?
An inequality is a comparison relationship between two or more mathematical expressions.
We are given an inequality as 0.5 is greater than or equal to the product of a number and −0.25.
Let the number be x.
So, from the above information, we get the inequality as
0.5 ≥ -0.25x
Now, on solving the above inequality, we get the following
0.5 ≥ -0.25x
On multiplying by -1, we get
⇒-0.5 ≤ 0.25x
On dividing both sides by 0.25, we get
⇒-2 < x
Hence, Option C i.e. number line with closed circle on negative 2 with arrow shaded right represents the solution to the inequality.
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An article in the November 1983 Consumer Reports compared various types of batteries. The average lifetimes of Duracell Alkaline AA batteries and Eveready Energizer Alkaline AA batteries were given as 4.1 hours and 4.5 hours, respectively. Suppose these are the population average lifetimes.
Required:
Let x̄ be the sample average lifetime of 64 Duracell and ȳ be the sample average lifetime of 64 Eveready Energizer batteries. What is the mean value of x̄- ȳ(i.e., where is the distribution of -centered)?
Answers
Answer:
The mean is of -0.4 hours.
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Mean of the sample of 64 Duracell:
By the Central Limit Theorem, 4.1 hours.
Mean of the sample of 64 Eveready:
By the Central Limit Theorem, 4.5 hours.
Mean of the difference?
Subtraction of normal variables, so we subtract the means.
4.1 - 4.5 = -0.4
The mean is of -0.4 hours.
7.6.AP-6
Find the surface area of the prism.
The surface area is
(Type an integer or a decimal.)
4 m
3.7 m-
3m
4 m
3.2 m
Answers
The Total surface area of the given prism is: 46.3 sq.m
What is the surface area of the prism?The surface area of the prism is gotten by finding the areas of all surfaces and adding up to get the total surface area. Thus:
We know that formula to find the area of a triangle is:
Area of triangle = ¹/₂*base*height
Area of rectangle = length * width
Thus:
Total surface area = 2(¹/₂* 3 * 3.7) + 2(4 * 3.2) + (3 * 3.2)
Total surface area = 11.1 + 25.6 + 9.6
Total surface area = 46.3 sq.m
Thus, that is the total surface area of the given prism with dimensions
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round decimal to the nearest whole number.
12.1
Answers
Answer:
12
Step-by-step explanation:
12.1 to the nearest whole number is 12.
Answer:
12
Step-by-step explanation:
12.1 there is no number behind the one, therefore it becomes 12
You are playing in the NBA Playoffs and attempt a 3-point shot as the buzzer sounds for the end of the
game, if you make the shot your team wins! Your basketball is is traveling on a path described by the
following function: b(x) = -x2 +1.36x + 2. The net is on a level described by the following function:
n(x) = 3 between (8 < x < 8.5). Will you make the shot and win the playoffs?
You may work alone or in a group of up to 3 students total.
BONUS: How high in the air will the basketball be at its highest point?
UNITS: x is in meters, y is in meters
Answers
Since we do not know the value of u, we cannot find the time taken by the basketball to travel a distance of 8.5 meters. We cannot find the height of the basketball at its highest point.
Given that n(x) = 3 for 8 < x < 8.5.It is impossible to determine whether the shot will be made or not based solely on this information. Winning the playoffs depends on various factors, such as the score, time remaining, and the overall performance of the team.
Therefore, additional information is required to determine the outcome of the playoffs.However, to find the height of the basketball at its highest point, we need to know the equation of the trajectory of the basketball.
Assuming that the basketball follows a parabolic path, we can use the formula:
y = ax² + bx + c,
where y is the height of the basketball, and x is the horizontal distance traveled by the basketball.
To find the values of a, b, and c, we need to know three points on the trajectory of the basketball. Let's assume that the basketball is thrown from a height of 1.5 meters and lands on the floor after traveling a horizontal distance of 8.5 meters.
Therefore, the points on the trajectory of the basketball are:
(0, 1.5), (8.5/2, h), and (8.5, 0),
where h is the height of the basketball at its highest point.Substituting these values in the equation of the trajectory,
we get:
1.5 = a(0)² + b(0) + c...(1)0 = a(8.5)² + b(8.5) + c...(2)h = a(8.5/2)² + b(8.5/2) + c...(3)
Simplifying equations (1) and (2),
we get:
c = 1.5...(4)b = -a(8.5)²/8.5...(5)
Substituting equation (4) in equation (3), we get:
h = a(8.5/2)² + b(8.5/2) + 1.5h = a(8.5/2)² - a(8.5)²/8.5 + 1.5h = -29.375a + 1.5
Substituting the value of a from equation (5) in the above equation,
we get:
h = -29.375(-a(8.5)²/8.5) + 1.5h = 0.5a(8.5)² + 1.5
Therefore, to find the height of the basketball at its highest point, we need to find the value of a. Since we know that the basketball lands on the floor after traveling a horizontal distance of 8.5 meters,
we can use the formula:
x = ut + 0.5at²,
where u is the initial horizontal velocity of the basketball, and t is the time taken by the basketball to travel a distance of 8.5 meters.
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Jennifer bought some tulips, lilies, and roses to make bouquets. She bought the same number of tulips as lilies. She bought three more roses than tulips and lilies combined. She paid 18 cents for each tulip. The lilies were 27 cents per flower, and the roses cost 55 cents each. How many of each kind of flower did Jennifer buy if she paid $17.15 in all?
Answers
Answer: 10 tulips, 10 lilies and 23 roses.
Step-by-step explanation:
Let's define the variables:
T = number of tulips that Jennifer bought
L = number of lilies that Jennifer bought
R = number of roses that Jennifer bought
Each tulip costs $0.18
Each lily costs $0.27
Each rose costs $0.55
We know that:
"She bought the same number of tulips as lilies."
T = L
" She bought three more roses than tulips and lilies combined."
R = T + L + 3
"she paid $17.15 in all"
T*$0.18 + L*$0.27 + R*$0.55 = $17.15
Then we have a system of 3 equations:
T = L
R = T + L + 3
T*$0.18 + L*$0.27 + R*$0.55 = $17.15
The first step to solve this is to replace the first equation into the other two, and get:
R = 2*L + 3
L*$0.18 + L*$0.27 + R*$0.55 = $17.15
Now we can replace the first equation into the second:
L*$0.18 + L*$0.27 + (2*L + 3)*$0.55 = $17.15
Now we can solve this for L.
L*($0.18 + $0.27 + 2*$0.55) + 3*$0.55 = $17.15
L*$1.55 + $1.66 = $17.15
L*$1.55 = $17.15 - $1.66 = $15.50
L = $15.50/$1.55 = 10
Then Jennifer bought 10 lilies.
And by the other two equations:
T = L = 10
She bought 10 tulips.
R = L + T + 3 = 10 + 10 + 3 = 23
She bought 23 roses
I need the answer fast I am in schoool pls
Answers
Answer:
288
Step-by-step explanation:
To solve, we need to find the area of the four triangle sides and add that to the square base's area.
Area of triangle sides: base * height * 0.5
Area of square base: base * height
Substitute the values
8 * 14 * 0.5 = 56
There are four of these sides, so the area of all the triangles is 224.
The square base is 8 * 8, or 64
Add these two values together.
64 + 224 = 288
Thus, the answer is 288
There were 6 dogs at the dog park last Saturday, and 2 of them were German shepherds. Considering this data, how many of the next 12 dogs to arrive at the park next Saturday should you expect to be German shepherds?
Answers
Answer:
Its 4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Add and subtract, whichever comes first, from left to right.
activity
Simplifying Expressions
Use the order of operations to simplify the following expressions.
6. (3 + 4) - 2 + (6 + 3)
9.3 x 6 + 4 =
7. 5(2 + 4) + (8 – 2) = .
10. 20 – 6:3 + 8 =
8. 6 + 2(10 = 5) – 1 =
www.harcourtschoolsupply.com
24
ts
Chapter 1: Bev
Cinancial Math 1
Answers
Answer:
6. (3 + 4) - 2 + (6 + 3)
=7−2+6+3
=5+6+3
=5+9
=14
7. 5(2 + 4) + (8 – 2)
=(5)(6)+8−2
=30+8−2
=30+6
=36
8. 6+2(10 ÷ 5)-1
=6+(2)(2)−1
=6+4−1
=10−1
=9
9. 3x6+4
(3)(6)+4
=18+4
=22
10.
20-6 ÷ 3+8
=20-2+8
=18+8
=26
Multiple 7/9 to the sum of 8 3/7 and 5 11/14
Answers
\( \frac{7}{9} \times (8 \frac{3}{7} + 5 \frac{11}{14}) = \\ \)
\( \frac{7}{9} \times (8 \frac{6}{14} + 5 \frac{11}{14} ) = \\ \)
\( \frac{7}{9} \times (13 \frac{6 + 11}{14}) = \\ \)
\( \frac{7}{9} \times (13 \frac{17}{14}) = \\ \)
\( \frac{7}{9} \times (14 \frac{3}{14}) = \\ \)
\( \frac{7}{9} \times ( \frac{14 \times 3 + 3}{14}) = \\ \)
\( \frac{7}{9} \times ( \frac{42 + 3}{14}) = \\ \)
\( \frac{7}{9} \times ( \frac{45}{14}) = \frac{7 \times 45}{9 \times 14} = \frac{5}{2} \\ \)
_________________________________
And we're done.
Thanks for watching buddy good luck.
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Answer:
\(\displaystyle \frac{199}{18}\)
Step-by-step explanation:
Fraction Operations
Before attempting to operate with the given fractions, we need to express all of them in the form a/b, because the last 2 fractions are in mixed form.
\(\displaystyle 8\frac{3}{7}=8+\frac{3}{7}=\frac{8*7+3}{7}=\frac{59}{7}\)
\(\displaystyle 5\frac{11}{14}=5+\frac{11}{14}=\frac{5*14+11}{14}=\frac{81}{14}\)
Now for the sum of the last two fractions:
\(\displaystyle \frac{59}{7}+\frac{81}{14}\)
Make both denominators equal by multiplying by 2 both parts of the first fraction:
\(\displaystyle \frac{59}{7}+\frac{81}{14}=\frac{118}{14}+\frac{81}{14}\)
\(\displaystyle =\frac{118+81}{14}=\frac{199}{14}\)
Now multiply by 7/9:
\(\displaystyle \frac{199}{14}*\frac{7}{9}=\frac{199}{18}\)
MARS On Mars, the gravity acting on an object is less than that on Earth. On Earth, a golf ball hit with an initial upward velocity of 26 meters per second will hit the ground in about 5.4 seconds. The height h of an object on Mars that leaves the ground with an initial velocity of 26 meters per second is given by the equation h=−1.9t2+26t
. How much longer will it take for the golf ball hit on Mars to reach the ground? What is the maximum height of the golf ball on Mars? Round your answer to the nearest tenth.
It takes about
seconds longer for the golf ball hit on Mars to reach the ground.
The maximum height of the golf ball on Mars is about
meters.
Answers
The maximum height of the golf ball on Mars is about 48.8 meters.
To find how much longer it would take for the golf ball hit on Mars to reach the ground, we can use the given equation h = -1.9t² + 26t, where h is the height of the object and t is the time in seconds. First, we need to find the time it takes for the golf ball to reach the ground on Mars. Setting h = 0, we get:
0 = -1.9t² + 26t
Solving for t using the quadratic formula, we get t = 13.684 or t = 0.856. Since the golf ball is launched upward, we need the positive value of t, so it takes about 13.7 seconds for the golf ball to reach the ground on Mars. Therefore, it takes 13.7 − 5.4 = 8.3 seconds longer for the golf ball hit on Mars to reach the ground than the golf ball hit on Earth.
To find the maximum height of the golf ball on Mars, we can use the formula h = -1.9t² + 26t, where t is the time when the height is maximum. Since the formula is a quadratic equation, the maximum height occurs at the vertex of the parabola, which is at t = -b/2a.
In this case, a = -1.9 and b = 26, so the time at maximum height is t = -26 / 2(-1.9) = 6.842. Plugging this value into the equation for h, we get:
= -1.9(6.842)² + 26(6.842) ≈ 48.8 meters
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1 3/8 minus 1/2 thanks
Answers
Answer:
0.833
Step-by-step explanation:
Maria paid $2.85 for 3
pounds of apples. How
much did it cost for one
pound of apples?
Answers
Answer:
$0.95
Step-by-step explanation:
Since it cost $2.85 for 3 pounds of apples, dividing 2.85 by 3 will give us one pound of apples.
2.85/3 = $0.95
Hope this helps! Please comment if it does or not. :)
That’s your answer
Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.3 years with a standard deviation of 1.1 years.
Step 1 of 2: If a sampling distribution is created using samples of the ages at which 35 children begin reading, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary.
Answers
Answer:
The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3 years.
give thanks for more! your welcome!
Step-by-step explanation:
Multiply the following and combine terms where possible. -a(a-b-3)
Answers
Answer:
-a^2 +ab +3a
Step-by-step explanation:
-a(a-b-3)
Distribute
-a*a -a*(-b) -a *(-3)
-a^2 +ab +3a
The area of the hexagonal base is 58 square inches.
The height is 6.25 inches.
What is the volume the hexagonal prism? cubic inches
Do not round the height or the answer.
Answers
Answer:
362.5 in^3
Step-by-step explanation:
V = (face [surface] area)(height)
V = 58(6.25) = 362.5
The measures of two complementary angles are in the ratio 7:3. What is the measure of the smaller angle?
Answers
mathmatically indication example with solution
Answers
A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.
How to solve the equation ?Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.
The equation would be 3 x + 2 = 14.
So we can solve for the equation to be :
3x + 2 - 2 = 14 - 2
3x = 12
3 x / 3 = 12 / 3
x = 4
In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.
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how much money deposited now will provide payment of Rs. 15000 at the end of each half year for 10 years, if interest is 16% compounded six-monthly
Answers
The interest is 16% compounded semi-annually, is Rs. 121,179.10.
To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.
Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)
So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:
Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.
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Find the value of x.
Answers
Answer:
These x-values are known as the “roots” or “zeros” of the quadratic. To find these roots, we simply set the quadratic equal to zero and solve for x
Step-by-step explanation:
Anita incorrectly wrote z =w-18 to describe the pattern in the table. Choose the best description of Anitas error
Answers
409.0113 x230.2190931
Answers
Answer:
9.416221055365203 x 10^4
Step-by-step explanation:
You just multiply
Which problem has a greater (bigger) answer? Solve both, choose the one that has the bigger answer and explain (1-2 sentences) how you found your
answer.
1) (2 + 3) (5 + 5)
2)2 + 3 x 5 + 5 =
I need so much helppppp pleaseeeee
Answers
Answer:
Problem 1 has a greater answer.
Step-by-step explanation:
Solve problem 1 using the order of operatiobs PEMDAS (Parentheses, Exponents, multiplication/division, and addition/subtraction):
Multiplication/division depends from left to right of the expression, the same goes to addition/subtraction.
(2 + 3) (5 + 5)
= (5)(10)
= 50
SOLVE problem 2 using PEMDAS:
2 + 3 x 5 + 5
= 2 + 15 + 5
= 17 + 5
= 22
Answer 1 (50) compared to Answer 2 (22):
50 > 22
HOPE THIS HELPS!
Which best describes the range of the function #(x) = 2(3)x? O y>0 O y≥0 O y = 2 O y≥2
Answers
Answer:
The range of the function f(x) : is y > 0.
The correct option is (A)
Step-by-step explanation:
The definition of range is the set of all possible values that the function will give when we give in the domain as input.
Given function is :
If we draw the graph for this, then we can see that the horizontal asymptote is 0.
So, the range is real numbers higher than 0.
Hence, the range should be y > 0.
what is the property of 3x(5x7)=(3x5)7
Answers
The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.
In the equation you provided: 3x(5x7) = (3x5)7
The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.
Please help quick I need it
Answers
The area of the composite figure is 122.24 units².
How to find the area of a composite figure?The composite figure consist of a rectangle and two semi circles. Therefore, the area of the composite figure is the sum of the area of the individua shapes.
Hence,
area of the composite figure = area of the rectangle + 2(area of semi circle)
Therefore,
area of the composite figure = 9 × 8 + 2(1 / 2 πr²)
area of the composite figure = 72 + πr²
where
r = 8 / 2 = 4 units
Therefore,
area of the composite figure = 72 + 3.14 × 4²
area of the composite figure = 72 + 3.14 × 16
area of the composite figure = 72 + 50.24
area of the composite figure = 122.24 units²
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Question 3 of 10
Which of the following shows the polynomial below written in descending
order?
5x3x+9x7+4+3x11
OA. 9x² + 5x³+4+3x¹¹ - x
OB. 3x¹¹ +9x7 + 5x³ − x + 4
OC. 3x¹1 +9x7-x+4+5x³
D. 4+ 3x¹¹+
D. 4+ 3x¹1 +9x7 + 5x³ - x
Answers
Answer:
B. 3x¹¹ +9x⁷ +5x³ −x +4
Step-by-step explanation:
You want to identify the polynomial that has terms written in descending order of their degree.
DegreeThe degree of a term is the exponent of x in that term. In the given polynomial, the term degrees are 3, 1, 7, 0, 11.
When these are put into descending order, that order is ...
11, 7, 3, 1, 0
Standard formThe answer to this question will be the polynomial with terms written in the order of their degree as shown above:
3x¹¹ +9x⁷ +5x³ −x +4
__
Additional comment
When the exponent of x is 0, the value of the term x^0 is 1. That is why we can say the constant term is a term that has the variable to degree 0.
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