The real zeros of the polynomial function P(x) = x⁵ − 50x³ + 49x are -1, 0, and 1.
To find the zeros of this function, we can factor it by first factoring out an x to get P(x) = x(x⁴ − 50x² + 49). Then, we can factor the quadratic expression inside the parentheses using the difference of squares formula, which gives us P(x) = x(x² − 1)(x² − 49). Simplifying further, we have P(x) = x(x − 1)(x + 1)(x - 7)(x + 7).
Therefore, the zeros of P(x) are the values of x that make each factor equal to zero. This gives us x = -7, -1, 0, 1, and 7. Since all of these values are real, we conclude that the number of real zeros of P(x) is 5.
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Answer quickly?
Please
The quadratic function g(x) = - 3 · (x + 5)² + 12 is the result of the following rigid transformations:
Horizontal translation.Vertical dilation.Reflection about x-axis. Vertical translation.How to modify a quadratic equation by rigid transformations
In this problem we find a quadratic equation that must be modified by means of rigid transformations. The most known rigid transformations are listed below:
TranslationDilationRotationReflectionIf we know that f(x) = x², then the resulting functions are found by using the following steps:
1) Write the entire function:
f(x) = x²
2) Horizontal translation:
f'(x) = (x + 5)²
3) Vertical dilation:
f''(x) = 3 · (x + 5)²
4) Reflection about x-axis:
f'''(x) = - 3 · (x + 5)²
5) Vertical translation:
g(x) = - 3 · (x + 5)² + 12
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Help as much as you can please!
Answer:
Step-by-step explanation:
Find the equivalent for each
1. R
2. S
3. Q
4. QS put a line over this
5. QR put a line over
6. MN put a line over
7. LN put a line over
8. RS put a line
9. 2
10. 6
11. 3y+5=14
3y=9
y=3
12. 2
Incorrect
2 tries left. Please try again.
Find mZN.
54
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(5x +9)°
P
(6x)
(3y + 8)°
(6y-1)°
M
N
The measure of the angle N is 17 degrees
How to determine the angleFrom the information given in the parallelogram, we have the angles written as;
m<N = 3y + 8
m<M = 6y - 1
m< P = 6x
m< L = 5x + 9
Then, we can say that;
m< M = m<N
Substitute the values, we get;
6y - 1 = 3y + 8
collect the like terms
6y - 3y = 8 + 1
add the values
3y =9
Divide both sides by the coefficient of the variable, y , we have;
y = 9/3
Divide the values
y = 3
Then, m<N = 3y + 8 = 3(3) + 8 = 17 degrees
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#A-B= 56 78 and B = 2-1 3-4 then find A+B.
The calculated value of the expression A + B is 60
From the question, we have the following parameters that can be used in our computation:
A - B = 56
B = 2
Substitute the known values of B in the above first equation
So, we have the following representation
A - 2 = 56
Evaluate the sum
A = 58
Add B to both sides
A + B = 58 + B
So, we have
A + B = 58 + 2
Evaluate
A + B = 60
Hence the solution is 60
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Determine if the point is part of the line: y = 7-2x ; (5,1)
To determine if the point (5,1) is part of the line y = 7-2x, we need to substitute x=5 and y=1 into the equation of the line and check if it is a true statement:
y = 7 - 2x
1 = 7 - 2(5)
1 = 7 - 10
1 = -3
Since -3 is not equal to 1, the point (5,1) is not part of the line y = 7-2x.
which of the following is not part of the validation testing stage?group of answer choicestesting begins before finishing the integration testing in order to validate it.testing begins at the end of integration testing.testing begins when the software is completely assembled.testing begins when individual components have been tested.
The correct option is A, Testing begins before finishing the integration testing in order to validate it is NOT part of the validation testing stage.
Validation testing is a software testing technique that evaluates a system or application to ensure that it meets the specified requirements and satisfies the customer's needs. The main goal of validation testing is to verify whether the software meets the intended purpose and functions as expected in the real-world scenario.
In validation testing, the system is tested against the user requirements, specifications, and business needs. This type of testing focuses on the overall performance and functionality of the system, including usability, reliability, and security. It helps to ensure that the software meets the user's expectations and is ready for deployment. The validation testing process typically involves a series of tests, including system testing, acceptance testing, and regression testing.
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Complete Question:-
Which of the following is NOT part of the validation testing stage?
a. Testing begins before finishing the integration testing in order to validate it.
b. Testing begins at the end of integration testing.
c. Testing begins when individual components have been tested.
d. Testing begins when the software is completely assembled
Estimation Without calculating, estimate the relationship
between the larger figure and the smaller figure, its image
after a dilation. Then find the scale factor.
18-
16
14
4
12
22
20-
10
+
6
12 14 16 18
ou
Which statement best describes the two figures?
OA. The edge lengths of the smaller figure are more
than half those of the larger figure.
OB. The edge lengths of the two figures are the same.
OC. The edge lengths of the smaller figure are less
than half those of the larger figure.
OD. The edge lengths of the smaller figure are about
half those of the larger figure.
The scale factor for the side lengths in this dilation is
(Simplify your answer.)
The statement that describes the relationship between the larger figure and the smaller figure, its image after a dilation is given as follows:
C. The edge lengths of the smaller figure are less than half than those of the larger figure.
The scale factor is given as follows:
k = 1/4 = 0.25.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The side lengths are given as follows:
Larger figure: 16 - 4 = 12 units.Smaller figure: 4 - 1 = 3 units.Hence the scale factor is given as follows:
k = 3/12
k = 1/4
k = 0.25.
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Which set of measurements cannot be the lengths of the three sides of a triangle?
A. 5 inches, 7 inches, 9 inches
B.5 inches, 9 inches, 9 inches
C.4 inches, 5 inches, 9 inches
D.4 inches, 4 inches, 7 inches
Iris loves Hibachi and will be having her birthday dinner at Lil Buddha Friday night. The chicken and shrimp dinner cost $25 before taxes and tip. ( T )Taxes are 10% and she will be leaving a 20% tip ( t ). Which equation below represents how much money Iris will pay for her bill?
The correct equation is $25 + 0.1($25) + 0.2($25)
Iris should first figure out how much tax she will be responsible for paying.
Her supper will set you back $25 before taxes and gratuity, and the tax percentage is 10%.
Thus, she will pay the following amount in taxes:
taxes = 0.1 * $25 = $2.50
Secondly, determine how much Iris will leave in tips. Since she will leave a 20% tip, tip is :
0.2 * $25 =$5.00.
Iris will pay her bill in full, which will include taxes, a gratuity, and the price of her dinner:
Dinner price plus taxes and tip equals the final bill.
The total due is $25 plus $2.50 plus $5.00.
$32.50 is the entire cost.
So, $25 + 0.1($25) + 0.2($25) is the equation that indicates the amount of money Iris will pay for her bill.
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Shortcut You walk along the edge of a park. Then you take
a shortcut represented by PQ on the graph. What is the
length of the shortcut in meters?
Waking Through the Park
200-
QH1582
80
✓
CID
The length of the shortcut ism.
(Round to the nearest tenth as needed.) no
suppose a new employee has had 13 hours of training. what would be the 99% prediction interval for the number of defects per countertop? round your answer to two decimal places.
The 99% prediction that number of defects per countertop is (-19.68, 9.13), under the given condition that new employee have had 13 hours of training.
Let us assume a linear regression model where the number of defects per countertop is projected based on the number of hours of training an employee has received. The 99% prediction interval for the number of defects per countertop can be evaluated applying the formula
y' ± t(α/2,n-2) × s[y"]
here
y' = predicted value of y,
t(α/2,n-2) = t-critical value for a given level of confidence (in this case 99%)
(n-2) =degrees of freedom ,
s[y"] = standard error of the estimate.
Utilizing the given data, we can evaluate y'
y' = 6.717822 - 1.004950 × 13
= -5.276
Therefore, the standard error of the estimate is given as 1.229787.
Applying a t-distribution table with n-2 degrees of freedom (n=1), we can get that t(α/2,n-2) = 12.706. Then, the evaluated 99% prediction interval for the number of defects per countertop is
-5.276 ± 12.706 × 1.229787
= (-19.68, 9.13)
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A farmer has 1,440 feet of fencing available to enclose a rectangular
area bordering a river. No fencing is required along the river. Let x
represent the length of the side of the rectangular enclosure that is
perpendicular to the river. Complete parts a. through c.
The length of the side of the rectangle perpendicular to the river is
c. What is the maximum area?
X
The maximum area is
River
a. Create a function, A(x), that describes the total area of the rectangular enclosure as a function of x, where x is the lem
A(x)=
(Simplify your answer.)
b. Find the dimensions of the fence that will maximize the area.
...
and the length of the side of the rec
Step-by-step explanation:
Maximum area enclosed will be a square enclosure
since the river is one side , the other three sides of the square will be
1440 / 3 = 480 ft long
Square with sides 480 ft
area =480 x 480 = 230 400 ft^2
Gabe goes to the mall. If n is the number of items he bought, the expression 18. 91x + 21 gives the amount he spent in dollars at one store. Then he spent 23 dollars at another store. Find the expression 18. 91x + 21 which represents the amount Gabe spent at the mall. Then estimate how much Gabe spent if he bought 2 items
Gabe spent approximately $81.82 at the mall if he bought 2 items.
The expression given to us is 18.91x + 21, where x represents the number of items Gabe bought at one store. We can interpret this expression as follows: For each item Gabe buys, he spends $18.91, and he also spends an additional $21 regardless of the number of items he buys. Therefore, if he buys n items at this store, he would spend 18.91n + 21 dollars.
Now, we are told that Gabe spent $23 at another store. To find the expression that represents the total amount he spent at the mall, we add the amount he spent at both stores. Therefore, the expression we are looking for is:
Total amount = 18.91x + 21 + 23
Simplifying this expression, we get:
Total amount = 18.91x + 44
This expression represents the total amount Gabe spent at the mall based on the number of items he bought at the first store.
To estimate how much money Gabe spent if he bought 2 items, we can substitute x = 2 into the expression we just derived:
Total amount = 18.91(2) + 44
Total amount = 37.82 + 44
Total amount = 81.82
Therefore, if Gabe bought 2 items, he would have spent approximately $81.82 at the mall.
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the wild wind stadium seat 25,000 people. it has 25 exits and can be evacuated in 20 minutes. the time to exit the stadium varies directly with thee number of people and inversely with the number of exits used. how long would it take to evacuate 21,000 people if only 15 exits are used?
It would take 28 minutes to evacuate 21,000 people from the Wild Wind Stadium using only 15 exits
The time to evacuate the stadium varies directly with the number of people and inversely with the number of exits used. This means that the time it takes to evacuate the stadium is proportional to the number of people and inversely proportional to the number of exits used.
Let t be the time it takes to evacuate 21,000 people if only 15 exits are used. Let k be a constant of proportionality. Then we have
t = k × (number of people) / (number of exits)
We know that it takes 20 minutes to evacuate the stadium with all 25 exits in use. This gives us another equation
20 = k × 25000 / 25
Simplifying this equation, we get
20 = 1000k
k = 0.02
Now we can use this value of k to find the time it takes to evacuate 21,000 people with only 15 exits
t = 0.02 × 21000 / 15
t = 28 minutes
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If you draw from the cards 100 times, what is the theoretical probability that you would draw a spade?
the theoretical probability that you would draw a spade is 1/4
What is the theoretical probability that you would draw a spade?From the question, we have the following parameters that can be used in our computation:
Drawing a spade
In a sample space of 52 cards, we have
Spade = 13
So, we have
Probability = 13/52
Evaluate
Probability = 1/4
Hence, the probability is 1/4
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Three softball players discussed their batting averages after a game.
Probability
Player 1 four sevenths
Player 2 five eighths
Player 3 three sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1)
Player 3 is more likely to hit the ball than Player 1 because P(Player 3) > P(Player 1)
Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)
Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1). Then the correct option is B.
Given that:
P(Player 1) = 4/7 = 0.57
P(Player 2) = 5/8 = 0.625
P(Player 3) = 3/6 = 0.50
The probabilities are arranged in ascending order as,
P(Player 3) < P(Player 1) < P(Player 2)
Player 2 is more likely to hit the ball than Player 1 and Player 1 is more likely to hit the ball than Player 3.
Thus, the correct option is B.
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Help me with this problem please!
Help solve this problem quickly
This is an exercise in solving problems involving quadratic functions, which is an important topic in mathematics and is used in many fields, including physics, engineering, and economics. In general, one seeks to find the critical points of a quadratic function, such as the vertex or the roots, to understand the behavior of the function in different situations.
To find the vertex of a quadratic function, we use the canonical form of the quadratic equation, which is f(x) = a(x - h)^2 + k, where (h, k) are the coordinates of the vertex. It is also possible to find the vertex using the formula -b/2a, which is derived from the general form of the quadratic equation.
In addition to finding the vertex, it is also common to find the roots of a quadratic function, which are the values of x where the function vanishes. This can be done using the general formula of the quadratic equation or by completing the square.
Solving our exercise, in which we are asked to calculate the vertex:
f(x) = 2(x + 8)² - 2
First we write the quadratic function in standard form.
Using (a + b)² = a² + 2ab + b², expand the expression.
f(x) = 2(x² + 16x + 64) - 2
We distribute the 2 to the terms that are between the parentheses.
f(x) = 2x² + 32x + 128 - 2 ⇒ subtract 2
f(x) = 2x² + 32x + 126
Now we identify the coefficients a and b of the quadratic function.
a = 2, b = 32
We find the x-coordinate of the vertex by substituting a = 2 and b = 2 into x = - (b)/(2a).
x = - (32)/(2 × 2) = - 32/4 = -8
x = -8
Find the y-coordinate of the vertex by evaluating the function for x = -8.
f(x) = 2(x + 8)² - 2, x = -8
We substitute x = -8 in the equation.
f(-8) = 2(-8 + 8)² - 2
The sum of two opposite numbers is equal to 0. The Inverse Property of Addition states that the sum of two opposite numbers is equal to 0.
f(-8) = 2 x 0² - 2
0 raised any positive power is equal to 0. We remember that a power represents a repeated multiplication of the base.
Therefore, the power 0² means that 0 is multiplied by itself 2 times, resulting in 0.
f(-8) = 2 × 0 - 2
Any expression multiplied by 0 equals 0.
f(-8) = 0 - 2
Removing the 0 does not change the value, so we remove it from the expression.
f(-8) = -2
The vertex of the graph of the quadratic function is at (-8, -2).
(-8,-2)
The vertex of the quadratic function f(x) = 28(x + 8)² - 2 is (-8,-2), the last option being correct.
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Which shows an equivalent decimal, fraction and percent
A-0. 125,1/8,12. 5%
B-0. 20,1/10,20%
C-0. 45,4/5,45%
D-0. 60,2/3,66%
An equivalent decimal, fraction and percent is C) 0.45, 4/5, 45%.
To understand why this is the correct choice, we need to look at how decimals, fractions, and percentages are related. Decimals are just another way of representing fractions, where the denominator is a power of 10. For example, 0.45 is the same as 45/100 or 9/20.
Percentages, on the other hand, are just a way of representing fractions with a denominator of 100. So, 45% is the same as 45/100 or 9/20.
The other options do not have equivalent representations of decimals, fractions, and percentages.
In conclusion, understanding the relationships between decimals, fractions, and percentages is essential to solving problems like these. The key is to remember that they are just different ways of representing the same value, and with a bit of practice, it becomes second nature to recognize equivalent representations.
Therefore, option C shows an equivalent decimal (0.45), fraction (4/5), and percent (45%).
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can someone please help me with these 4 questions ill do anything im currently failing math
Account x pays 2.1% simple annual interest
Based on the concepts of simple interest and compound interest, the TRUE statement about these two accounts after 5 years is b) Account Y would earn Monica $62.70 more interest than Account X.
What is the difference between simple interest and compound interest?Under the simple interest system, interest is computed on only the principal for each period.
Under the compound interest system, interest is computed on both the principal and accumulated interest for each period.
Simple Interest:Principal = $3,000
Interest Rate = 2.1%
Period = 5 years
Simple Interest = $315.00 ($3,000 x 2.1% x 5)
Compound Interest:N (# of periods) = 5 years
I/Y (Interest per year) = 2.4%
PV (Present Value) = $3,000
PMT (Periodic Payment) = $0
Results:
FV = $3,377.70
Total Compound Interest =$377.70
Difference in Interest = $62.70 ($377.70 - $315.00)
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Complete Question:Monica wants to open a savings account with a deposit of $3,000. Monica will not make any further withdrawals or deposits after she opens the account. Her bank offers two different savings accounts.
Account X pays 2.1% simple annual interest.Account Y pays 2.4% interest compounded annually.Which statement about these two accounts after 5 years is true?
Options:
a) Account X would earn Monica $62.70 more interest than Account Y.
b) Account Y would earn Monica $62.70 more interest than Account X.
c) Account X would earn Monica $45.00 more interest than Account Y.
b) Account Y would earn Monica $45.00 more interest than Account X.
What’s the anwser née help asap please
The surface area of the cone is 650.54 mi²
What is the surface area of the cone?Surface area of a cone is the total area covered by its surface. The total surface area will cover the base area and lateral surface area of the cone. Cone is defined as a three-dimensional solid structure that has a circular base.
The formula of surface area of a cone is given as;
S.A = πr(r + √h² + r²)
h = height of the coner = radius of the coneπ = 3.14The diameter of the base is given as 16 mi
radius = diameter / 2
radius = 16 /2
radius = 8 mi
The slant height is given as 17.9 mi and we can use Pythagorean theorem to find the height of the cone.
h² = 17.9² - 8²
h = 16.01mi
Using the height and radius, we can calculate the surface area of the cone.
S.A = πr(r + √h² + r²)
S.A = 3.14 * 8 (8 + √(16.01² + 8²)
S.A = 650.54 squared miles
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Justine used unit cubes to build a rectangular prism that is 10 units tall and has a volume of 160 cubic units. Larry used half as many unit cubes to build a rectangular prism that is the same height as Justine's prism. What is the area of the base of Larry's prism?
The volume of Justine's rectangular prism is: 8 units
How to solve for the volumeV = l x w x h = 160 cubic units
Since the height of Justine's prism is 10 units, we can solve for the area of the base by dividing the volume by the product of the height and the length:
lw = V/h = 160/10 = 16 square units
So the area of the base of Justine's prism is 16 square units.
V' = V/2 = 160/2 = 80 cubic units
To find the area of the base of Larry's prism, we can use the same formula as before:
lw = V'/h = 80/10 = 8 square units
So the area of the base of Larry's prism is 8 square units.
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The park manager wants to make a timetable for buses and minibuses leaving the park at different times of the day from 8:00am to 5:00pm. Buses and minibuses leave the park at intervals of 40mins and 50mins respectively after loading. Both vehicles start loading at the same time. Task. Help the park manager to; draw a departure timetable for the 2 vehicles from 8:00 to 5:00pm. Identify any time of the day when the two vehicles will leave the park at the same time. How can traffic jam be controlled
The time of the day when two vehicles will leave park at same time is 11:20 a.m.
Traffic can be controlled by adjust the departure times, use a reservation system, limit the number of vehicles , and promote carpooling.
To create the departure timetable,
Start by listing the times at which the first bus and minibus will leave the park.
From there, add 40 and 50 minutes respectively to each departure time to find the next departure time for each vehicle.
Here is the timetable,
Departure time Bus interval Minibus interval
8.00 a.m. 40min 50min
8.40 a.m. 40min 50min
9.20 a.m. 40min 50min
10.00 a.m. 40min 50min
10.40 a.m. 40min 50min
11.20 a.m. 40min 50min
12.00 p.m. 40min 50min
12.40 p.m. 40min 50min
1.20 p.m. 40min 50min
2.00 p.m. 40min 50min
2.40 p.m. 40min 50min
3.20 p.m. 40min 50min
4.00 p.m. 40min 50min
4.40 p.m. 40min 50min
To identify any time of the day when the two vehicles will leave the park at the same time.
When the time of the intervals of the two vehicles overlap.
The least common multiple LCM of 40 and 50 is 200.
The two vehicles will leave the park at the same time every 200 minutes, or 3 hours and 20 minutes.
The first time this happens is at,
8:00am + 200 mins = 11:20am
So, at 11:20am both vehicles will leave the park at the same time.
To control traffic jam the park manager can consider the following strategies,
Adjust the departure times,
If the departure times are causing congestion,
The manager can adjust the intervals or the departure times to spread out the flow of vehicles.
Use a reservation system,
The manager can use a reservation system to stagger the departure times of the vehicles.
Ensuring that there are no backlogs at the loading area.
Limit the number of vehicles,
The manager can limit the number of vehicles that are allowed in the park at any given time.
To reduce the number of vehicles on the road and prevent congestion.
Promote carpooling,
The manager can encourage visitors to carpool to the park to reduce the number of vehicles on the road.
This can be done through promotional campaigns or by offering incentives for carpooling.
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two birds are flying in the air. bird A is currently 500 feet in the air and is decending at a constant rate of 75 ceet per minute. bird b who is originally 100 feet in the air begins to increse in altitude at a constant rate of 25 feet per minute. bird a begins to asend in the air at the same time bird b begins to desend in the air
Questions:
What is bird A’s height above the ground?
What is bird B’s height above the ground?
After how many minutes did the two birds reach the same height?
When is bird A above bird B?
When is bird B above bird A?
after 1 minute what is the difference in height between the birds?
The difference between the two high altitudes is therefore 300 feet.
How to solveLet 't' denote the time in minutes when both birds are at the same height. If both of these fowls are traveling, one descending and the latter ascending, then we obtain a formulaic value for t using the equations below.
Distance descended by bird A = 75tDistance ascended by bird B = 25tOriginal altitude-distance difference = 500 - 100 = 400 feetTherefore, if we solve: 75t - 25t = 400, it follows that 50t = 400 and t = 8 minutes.
Given this information, after 8 minutes, the two birds reach the same height.
Consequently, before the 8-minute interval, bird A is situated at a higher level than bird B since the prior's rate of descent is less than the current bird's ascent.
Once they have reached the shared altitude, bird B is above bird A given its continuous upward elevation, contrasting against bird A's descending course.
Their heights after only 1 minute has elapsed; the Height of bird A after 1 minute is calculated to be 425 feet - (500 - 75(1)) and for bird B it is 125 feet - (100 + 25(1)).
The difference between the two high altitudes is therefore 300 feet.
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Find the value of x, y, and z using radicals
Answer:
x = 14, y = 7√3, z = 7√2
Step-by-step explanation:
In an isosceles right triangle, the length of the hypotenuse is √2 times the length of a leg. In a 30°-60°-90° right triangle, the length of the longer leg is √3 times the length of the shorter leg, and the length of the hypotenuse is twice the length of the shorter leg. So x = 14, y = 7√3, and
z = 7√2.
The slope of the line below is
Answer:
B
Step-by-step explanation:
• a line sloping upwards from left to right is positive
• a line sloping downwards from left to right is negative
• a horizontal line parallel to the x- axis has a slope of zero
the line here is sloping upwards from left to right, thus has a positive slope.
Answer:
Step-by-step explanation:
B
if the line makes an angle less than or equal to 90 with the horizontal has a positive slope
A family has a unique pattern in their tile flooring on the patio. An image of one of the tiles is shown.
A quadrilateral with a line segment drawn from the bottom vertex and perpendicular to the top that is 5 centimeters. The right vertical side is labeled 3 centimeters. The portion of the top from the left vertex to the perpendicular segment is 5 centimeters. There is a horizontal segment from the left side that intersects the perpendicular vertical line segment and is labeled 6 centimeters.
What is the area of the tile shown?
53 cm2
45.5 cm2
42.5 cm2
36.5 cm2
The area of the tile shown is 42.5 [tex]cm^2[/tex]. So, the correct option is (c) 42.5 [tex]cm^2[/tex].
What is area of triangle?
The area of a triangle can be calculated using the formula:
A = (1/2)bh
where A is the area of the triangle, b is the length of the base of the triangle, and h is the height of the triangle.
To find the area of the quadrilateral, we need to split it into two triangles and a rectangle.
First, we find the area of the rectangle: 5 cm × 6 cm = 30 [tex]cm^2[/tex].
Next, we find the area of the left triangle: (1/2) × 5 cm × 3 cm = 7.5 [tex]cm^2[/tex].
Finally, we find the area of the right triangle: (1/2) × 5 cm × 2 cm = 5 [tex]cm^2[/tex].
Adding up the areas of the two triangles and the rectangle, we get:
30 [tex]cm^2[/tex] + 7.5 [tex]cm^2[/tex] + 5 [tex]cm^2[/tex] = 42.5 [tex]cm^2[/tex]
Therefore, the area of the tile shown is 42.5 [tex]cm^2[/tex].
So, the correct option is (c) 42.5 [tex]cm^2[/tex].
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When Sarah finished the next level of her video game, she gained 10
points for each of the four targets she hit and lost 105 points for
taking too long. Write the total change to her score as an integer.
Answer:
If Sarah received 10 points for each of the four targets she hit, her total point gain from hitting targets would be:
4 targets x 10 points = 40 points
If Sarah loses 105 points for taking too long, her total loss is -105 points (due to the negative change in her score).
As a result, the total change in Sarah's score may be determined by adding her point gain from hitting targets to her point loss from taking too long:
Total difference = 40 points minus 105 points
-65 points total change
As a result, Sarah's score dropped by 65 points after completing the following level of her video game.
The measure of ∠ROS in △ROS
below is 60 degree
a. The curved arrow represents the rotation of OR, beginning from the positive x-axis Through how many degrees has OR rotated?
b. If OR=1, what are the exact lengths of OS and SR?
c.what are the exact coordinates of point R?
Step-by-step explanation:
a. Since the measure of ∠ROS is 60 degrees and OR is the initial side of the rotation, OR has rotated 60 degrees counterclockwise.
b. Using the Law of Cosines in △ROS:
OS² = OR² + SR² - 2(OR)(SR)cos(∠ROS)
Since OR=1 and ∠ROS=60 degrees, we have:
OS² = 1² + SR² - 2(SR)(cos(60))
OS² = 1 + SR² - SR
Substituting SR = 1 - OS from the equation above, we get:
OS² = 1 + (1 - OS)² - (1 - OS)
Simplifying and solving for OS, we get:
OS² - 2OS + 1 = 0
(OS - 1)² = 0
So, OS = 1 and SR = 0.
c. Since OR=1 and the measure of ∠ROS is 60 degrees, we can use trigonometry to find the coordinates of point R. Let (x,y) be the coordinates of R. Then we have:
sin(60) = y/1
y = √3/2
cos(60) = x/1
x = 1/2
Therefore, the exact coordinates of point R are (1/2, √3/2).