The statement which is true regarding the values of x and y is option C; x=y+360n , for any positive integer n.
What are Coterminal angles?The algebraic sum of Coterminal angles at a point is 360°.
From the given information;
Angle x is coterminal with angle y.
If the measure of angle x is greater than the measure of angle y.
Then, the statement which is correct is will be as;
x = y + 360n , for any positive integer n.
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Dimitri determined that the ordered pair (2, –2) is a solution to the system of linear equations 7x + 9y = –4 and 5x – 2y = 6 as shown.
He mixed up the coordinates of the ordered pair when substituting it into the equations 7x + 9y = –4 and 5x – 2y = 6.
He checked the equation 7x + 9y = –4 first when he should have checked first.
He made a mistake in his calculations when substituting the ordered pair into the equation 7x + 9y = –4 and simplifying.
He made a mistake in his calculations when substituting the ordered pair into the equation 5x – 2y = 6 and simplifying.
Answer: D. He made a mistake in his calculations when substituting the ordered pair into the equation 5x -2y =6 and simplifying.
Step-by-step explanation: I got the answer correct on a test. Hope this helps!
Name the relationship: complementary, or supplementary.
Answer:
See below.
Step-by-step explanation:
1. a and b are supplementary ( they add up to 180 degrees as they are on a straight line).
2,3 and 4 are complementary as in each case a + b = 90 degrees.
Answer:
Complementary angles are the angles which add up to 90°. example - 60° + 30° = 90° . Supplementary angles are those angles which add up to 180° . example - 110° + 70° = 180°.
Step-by-step explanation:
(5b^3 +9b+4)−(9b−4) Subtract. standard form
Answer:
the answer is 5b^3+8
Step-by-step explanation:
To subtract (5b^3 +9b+4)−(9b−4) in standard form, distribute the negative sign, combine like terms, and simplify the expression.
To subtract (5b^3 +9b+4)−(9b−4) in standard form, we need to remove the parentheses and combine like terms. Distribute the negative sign to both terms in the second parentheses, which changes the sign of each term inside.
This gives us 5b^3 + 9b + 4 - 9b + 4.
Combining like terms, we have 5b^3 + 4b + 8.
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The area of the triangle is 35 square feet. Use a quadratic equation to find the length of the base. Round your answer to the nearest tenth.
Answer:
10.6 ft
Step-by-step explanation:
The complete question is:
The area of the triangle is 35 square feet. Use a quadratic equation to find the length of the base. Round your answer to the nearest tenth.Base=x+4 Height=x
SOLUTION:
As you know, Area of triangle 'A' = 1/2 x b x h
Where,
Base 'b' = x+4
Area 'A' = 35 ft²
Height 'h'= x
35 = (1/2)(x+4)x
35 =(x² + 4x)/2
2 * 35 =x² + 4x
70 = x² + 4x
x² + 4x - 70=0
Formula for the quadratic equation is
x = [- b ± √(b² - 4ac)]/2a
Where,
a=1, b= 4, c=-70
Plugging in the values.
x = [- 4 ± √4² - (4 × 1 × - 70)] / (2 × 1 )
x = [- 4 ± √(16 + 280)]/2
x = [- 4 ± √296]/2
x = (- 4 + 17.2)/2 or x = (- 4 - 17.2)/2
x = 13.2/2 or x = - 21.2/2
As, we choose to ignore negative value of 'x'
Therefore, x = 13.2/2 = 6.6
And, Length of the base will be:
x + 4 = 6.6 + 4 => 10.6 ft
The base is approximately 10.6 feet when rounded to the nearest tenth.
We know the area of the triangle is 35 square feet, the base is x + 4, and the height is x.
The formula for the area of a triangle is:
Area = 1/2 × base × height
1. Substitute the given values into the formula:
35 = 1/2 × (x + 4) × x
2. To simplify, multiply both sides by 2 to eliminate the fraction:
70 = (x + 4) × x
3. Expand the equation:
70 = [tex]x^{2}[/tex] + 4x
4. Rearrange into a standard quadratic form:
[tex]x^{2}[/tex] + 4x - 70 = 0
5. To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √([tex]b^{2}[/tex] - 4ac)) / 2a
6. Here, a = 1, b = 4, and c = -70. Plug these values into the formula:
x = (-4 ± √([tex]4^{2}[/tex] - 4(1)(-70))) / 2(1)
x = (-4 ± √(16 + 280)) / 2
x = (-4 ± √296) / 2
x = (-4 ± 17.2) / 2
7. This gives us two potential solutions:
x = (-4 + 17.2) / 2 ≈ 6.6
x = (-4 - 17.2) / 2 ≈ -10.6 (This solution is not valid since the height cannot be negative)
8. So, the height (x) is 6.6 feet. Therefore, the length of the base is:
Base = x + 4 ≈ 6.6 + 4 = 10.6 feet.
Question- The area of the triangle is 35 square ft. Use a quadratic equation to find the length of the base. Round your answer to the nearest tenth. Base = x + 4, Height = x.
Work out the area of this semicircle take pie to be 3.142 and write down all the digits given by your calculator 18cm
Final answer:
The area of the semicircle is 0.051 square meters.
Explanation:
The area of a semicircle can be found using the formula A = πr²/2, where r is the radius of the semicircle. In this case, the radius is given as 18 cm. So, substituting this value into the formula, we get A = 3.142 x (18 cm)²/2. Now, let's calculate the area step by step:
Convert the radius to meters: 18 cm = 0.18 m
Square the radius: (0.18 m)² = 0.0324 m²
Multiply by π and divide by 2: 0.0324 m² x 3.142 / 2 = 0.051 m²
Therefore, the area of the semicircle is 0.051 square meters.
Ben is filling his cylinder shaped pool up to 80% of its capacity. If his pool is 6 feet deep and has a diameter of 18 feet, how much water will he put in the pool?
Answer:
34601 liters
Step-by-step explanation:
Given:
Ben is filling his cylinder shaped pool up to 80% of its capacity.
His pool is 6 feet deep and has a diameter of 18 feet.
Question asked:
How much water will he put in the pool?
Solution:
First of all we will find volume of cylinder:
Diameter = 18 feet
Radius, r = [tex]\frac{Diameter}{2} =\frac{18}{2} =9\ feet[/tex]
Height, h = 6 feet
As we know:
[tex]Volume\ of \ cylinder=\pi r^{2} h[/tex]
[tex]=\frac{22}{7} \times(9)^{2} \times 6\\ \\=\frac{22}{7} \times81 \times 6\\ \\ =\frac{10692}{7} \\ \\ =1527.42\ cubic\ feet[/tex]
Now, as given that pool is being filled up to 80%, we have to find quantity of water he will put in the pool:-
Quantity of water filled = 80% of the volume of the pool
[tex]=\frac{80}{100} \times1527.42\\ \\ =1221.93\ cubic feet[/tex]
Now, convert it into liters.
1 cubic feet = 28.31 liters
1221.93 cubic feet = 28.31 [tex]\times[/tex] 1221.93 = 34,601.20 liters
Therefore, he will put about 34601 liters water in the pool.
There are 86 calories in 100g of banana.
There are 89 calories in 100g of yogurt.
Amanda has 70g of banana and 140g of yogurt for breakfast.
Work out the total number of calories in this breakfast. Show your full working out.
Answer:
[tex]60.2 + 124.6 = 184.8 \: calories[/tex]
The total number of calories in this breakfast is 184.8 calories if there are 86 calories in 100g of banana and there are 89 calories in 100g of yogurt.
What is a fraction?
Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
There are 86 calories in 100g of banana.
In 1 g = 0.86 calories
In 70 g
= 0.86×70 = 60.2 calories
There are 89 calories in 100g of yogurt.
1g = 0.89 calories
In 140g yogurt:
= 140×0.89
= 124.6 calories
Total calories = 60.2 + 124.6 = 184.8 calories
Thus, the total number of calories in this breakfast is 184.8 calories if there are 86 calories in 100g of banana and there are 89 calories in 100g of yogurt.
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Match the sequence (term) with the correct type of sequence (definition). (4 points) Group of answer choices 128, 32, 8, 2, ... 1, 3, 9, 27, ... 5, 10, 15, 20, ... 20, 17, 14, 11, …
Answer:
Step-by-step explanation:
In an arithmetic sequence, the consecutive terms differ by a common difference, d. Therefore,
d = Term 2 - Term 1 = Term 3 - Term 2
In an geometric sequence, the consecutive terms differ by a common difference, r. Therefore,
r = Term 2 /Term 1 = Term 3 / Term 2
1) 128, 32, 8, 2, .. Is a geometric sequence
r = 32/128 = 1/4
2) 1, 3, 9, 27, .. Is a geometric sequence
r = 3/1 = 3
3) 5, 10, 15, 20, ...is an arithmetic sequence
d = 10 - 5 = 5
4) 20, 17, 14, 11, … is an arithmetic sequence
d = 17 - 20 = - 3
What is the slope of the line that passes through the points (3, 6)(3,6) and (1, 2) ?(1,2)
Answer:
-2
Step-by-step explanation:
Using the slope theorem:
[tex]m=\frac{y_{1}-y_{0}}{x_{1}-x_{0}}[/tex]
[tex]\frac{6-2}{1-3} = \frac{4}{-2} =-2[/tex]
The slope of a line passing through two points can be calculated using a formula. In this case, the slope of a line passing through (1, 0.1) and (7, 26.8) is found to be 4.45.
The slope of a line passing through two points (x₁, y₁) and the (x₂, y₂) can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Plugging in the values of the points (1, 0.1) and (7, 26.8) into the formula, we get:
m = (26.8 - 0.1) / (7 - 1) = 26.7 / 6 = 4.45
Therefore, the slope of the line passing through the points (1, 0.1) and (7, 26.8) is 4.45.
Suppose that in solving an equation over the interval [0 comma 360 degrees )[0,360°), you reach the step sine theta equals negative one halfsinθ=− 1 2. Why is minus−30degrees° not a correct answer?
The angle -30 degrees is not a correct answer because it falls outside of the given interval [0, 360 degrees). The correct answer is theta = 210 degrees, which satisfies the equation sine theta = -1/2 over the interval. In the fourth quadrant, the angle whose sine is -1/2 should be in the third quadrant to satisfy the inequality sine theta <= 0.
Explanation:In solving the equation Σ theta = -1/2, the student is looking for the values of theta that satisfy the equation over the interval [0, 360 degrees). The value -30 degrees is not a correct answer because it falls outside of the given interval. To find the correct answer, we need to determine the values of theta that make sine of theta equal to -1/2.
To find an angle whose sine is -1/2, we can look at the unit circle. In the first and second quadrants, the sine function is positive, so we need to look in the third and fourth quadrants.In the third quadrant (180 to 270 degrees), the sine function is negative. The angle whose sine is -1/2 in this quadrant is theta = 210 degrees.In the fourth quadrant (270 to 360 degrees), the sine function is positive again. However, the angle whose sine is -1/2 should be in the third quadrant to satisfy the inequality sine theta <= 0. Therefore, -1/2 is not a valid value for sine theta in the fourth quadrant.Learn more about Solving Equations here:https://brainly.com/question/29050831
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The time is 1:25 A.M. What time will it be in 6 hours and 55 minutes?
Answer:
8:20 am
Step-by-step explanation:
find the area of the shape shown below.
Answer:
Ok so lets start with finding the equations or the steps:
so for a trapazoid the formula is A= A+B/2 SO the area is 6
Step-by-step explanation: For more info on how i did this just contact me or reply to this also inform it if its wrong Thanks! have a good day
Answer:
10
Step-by-step explanation:
The area of a triangle is given by the formula [tex]\frac{(base)(height)}{2}[/tex].
The first triangle has 4 units in base and 2 in height, in the formula is
[tex]\frac{(4)(2)}{2}[/tex] = 4
The second triangle has 2 units in base and 2 in height, in the formula is
[tex]\frac{(2)(2)}{2}[/tex] = 2
The area of a square is given by the formula base x height = 2 x 2 = 4.
The sum of the areas is 10.
Rosa picked some peaches from one tree, and then she picked 8 peaches from a different tree. She gave 10 peaches to Sten. She has 12 peaches left. How many peaches did Rosa pick from the first tree?
Answer:
14
Step-by-step explanation:
she had 22 in all take away 8 then you get 14.
take away 8 because they came from another tree
Answer:
14 peaches
Step-by-step explanation:
10-8=2+12=14
Juan drove his car on a vacation trip. His odometer Read 1460.3 when he began and 1830.2 at the end. If he used 20 gallons of gas how many miles per gallon did he get
Answer:
Juan got 18.50 miles per gallon.
Step-by-step explanation:
We are given the following in the question:
Odometer in the beginning of trip = 1460.3 miles
Odometer at the end of trip = 1830.2
Gallons of gas used for trip = 20 gallons
Distance of trip =
= Odometer at the end of trip - Odometer in the beginning of trip
[tex]=1830.2-1460.3\\=369.9\text{ miles}[/tex]
Thus, the trip was of 369.9 miles.
Miles per gallon =
[tex]=\dfrac{\text{Distance cover in trip}}{\text{Gallons of gas used}}\\\\=\dfrac{369.9}{20}\\\\=18.495\approx 18.50\text{ miles per gallon}[/tex]
Thus, Juan got 18.50 miles per gallon.
The sum of two numbers is 39. The sum of twice the larger number and three times the smaller number is 93. Find the smaller number.
Answer:3 * (n + 4) = 93
3n + 12 = 93
Subtract 12 to both sides:
3n = 81
Divide 3 to both sides:
n = 27
Step-by-step explanation:
Final answer:
The smaller number is 15.
Explanation:
To find the smaller number, let's assign variables to the two numbers. Let's call the larger number 'x' and the smaller number 'y'. According to the given information, we have two equations:
x + y = 39
2x + 3y = 93
To solve this system of equations, we can use the method of substitution.
Rearrange the first equation to get x = 39 - y.
Substitute this expression for x into the second equation:
2(39 - y) + 3y = 93
Now, simplify and solve for y:
78 - 2y + 3y = 93
y = 15
Therefore, the smaller number is 15.
a 50 gram sample of a substance thats used to treat thyroid disorders has a k value of 0.1133
Answer:
6.1
Step-by-step explanation:
a line passes through the point (-9,7) and has a slope of -4/3 write an equation in point slope form for this line
if you apply 20 newtons of force to do 60 joules of work on an object moves a distance of ---------- meters
Answer:
3 metres
Step-by-step explanation:
Work done = Force × displacement
60= 20×d
d= 60/20
d= 3 metres
Uisng the relationship between force, work and distance, the distance moved by the object would be 3 meters
Given the Parameters :
Workdone = 60 joules Force applied = 20 NewtonRecall :
Workdone = Force × DistanceSubstituting the values into the formula :
60 = 20 × Distance
Distance = 60 / 20
Distance = 3
Therefore, the object moves a distance of 3 meters
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Sally has 2 cats and each cat eats 1/4 of a tin of cat food each day.
Sally buys 9 tins of cat food.
For how many days will the cat food feed her 2 cats?
Please show your working.
Answer:
18 days
Step-by-step explanation:
Each cat eats 1/4 of the thin in a day, so between the two cats they eat:
of the tin in one day.
if the two cats eat 1/2 of the tin in one day, this means that in 2 days they eat a whole tin of cat food.
we can represent this as follows
days tins of cat food
2 1
and because she has 9 tins of cat food, and x represents the quantity of days:
days tins of cat food
2 1
x 9
thus, we must multiply cross quantities from the table and divide by the remaining amount:
x = 2*9/1 = 18
the 9 tins of cat food will last 18 days
pls mark me brainliest
There are 27 chocolates in a box, all identically shaped. There 4 are filled with nuts, 8 with caramel, and 15 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting a solid chocolate candy followed by a nut candy.
Answer:
Therefore the required probability is [tex]\frac{30}{351}[/tex].
Step-by-step explanation:
Two events are dependents event if the occurrence of one of them has effect on the probability of the other.
If A and B are dependents,
then,
P(AB)=P(A)P(B).
Given that,
There are 27 chocolates in a box.
Number of nuts chocolates = 4
Number of caramel chocolates = 8
Number of solid chocolates= 15.
The probability of that a solid candy is drawn is
[tex]=\frac{\textrm{Number of solid chocolate}}{\textrm{Total number of chocolate}}[/tex]
[tex]=\frac{15}{27}[/tex].
After selecting a solid chocolate, the number of chocolate is= (27-1)=26.
The probability that a nut candy is drawn is
[tex]=\frac{\textrm{Number of nut chocolate}}{\textrm{Total number of chocolate}}[/tex]
[tex]=\frac{4}{26}[/tex]
[tex]=\frac{2}{13}[/tex]
Therefore the required probability is
[tex]=\frac{15}{27}\times\frac{2}{13}[/tex]
[tex]=\frac{30}{351}[/tex]
48 divided by 4,756
im really behind-
Answer:
0.0100925147183
Step-by-step explanation:
Answer:
48/4,756= 0.010
Step-by-step explanation:
USE THE GOLDEN RATIO!!!!!!!!!!!
Suppose you want to use synthetic turf as the surface for a rectangular playground. The design calls for a golden rectangle where the ratio of the longer length to the width is (1+√5) :2. If the longer length is 16 feet, which expression, in simplified form, represents the width of the playground?"
A. 8+8√5 ft
B. 16+16√5 /3 ft
C. −8+8√5 ft
D. 4√5+20 /5 ft
Answer:
The correct option is option C.
The width of the rectangular playground is [tex]-8+8\sqrt5[/tex] ft.
Step-by-step explanation:
Area of rectangular plot is = length × wide.
Given that,
The ratio of longer length to the width of the rectangular playground is
(1+√5): 2
Let the length and width of the rectangular playground be (1+√5)x and 2x.
But the length of the longer side of the rectangular playground is = 16 feet.
According to the problem,
(1+√5)x= 16
[tex]\Rightarrow x= \frac{16}{1+\sqrt5}[/tex]
[tex]\Rightarrow x= \frac{16(1-\sqrt 5)}{(1+\sqrt5)(1-\sqrt 5)}[/tex] [ rationalize]
[tex]\Rightarrow x= \frac{16(1-\sqrt 5)}{(1)^2-(\sqrt5)^2}[/tex] [ (a+b)(a-b)=a²-b²]
[tex]\Rightarrow x= \frac{16(1-\sqrt 5)}{1-5}[/tex]
[tex]\Rightarrow x= \frac{16(1-\sqrt 5)}{-4}[/tex]
[tex]\Rightarrow x=-4(1-\sqrt 5)}[/tex]
[tex]\Rightarrow x=-4+4\sqrt 5[/tex]
Then the width of the playground is = 2x
[tex]=2(-4+4\sqrt5)[/tex] ft
[tex]=-8+8\sqrt5[/tex] ft
show that the cube of positive integer is 6q+r ,where q is an integer & r=0,1,2,3,4,5
Answer:
6(6)² + 0 = 6³
6(0) + 1 = 1³
6(1) + 2 = 8 = 2³
6(4) + 3 = 27 = 3³
6(10) + 4 = 64 = 4³
6(20) + 5 = 125 = 5³
What is the probability that a randomly selected day of the year happens to be in December or January?
The probability that a randomly selected day of the year is in December or January is [tex]\( \frac{62}{365} \)[/tex].
To find the probability that a randomly selected day of the year is in December or January, we need to consider the total number of days in December and January and divide it by the total number of days in a year.
Total number of days in December:December has 31 days.
Total number of days in January:January also has 31 days.
Total number of days in a year:A non-leap year has 365 days, and a leap year has 366 days.
Assuming we're considering a non-leap year for simplicity, the total number of days in a year is 365.
Now, let's calculate the probability:
Probability = [tex]\frac{\text{Number of days in December} \ + \ \text{Number of days in January}}{\text{Total number of days in a year}}[/tex]
Probability = [tex]\frac{31 + 31}{365}[/tex]
Probability = [tex]\frac{62}{365}[/tex]
Now, we can simplify this fraction if needed, but to keep it in the most accurate form, we can leave it as [tex]\( \frac{62}{365}[/tex].
The set of all real numbers x that satisfies 5<_ x<_ 8 is given by the following interval notation:
[5, 8].
Answer:
true
Step-by-step explanation:
Answer:
True is the answer
Step-by-step explanation:
got it correct on my quiz
PreCalc help with sums. I will mark brainliest. (also can you explain WHY you got what answer you got? Thanks)
Answer:
8
Step-by-step explanation:
a = -4
r = 16/-4 = -4
Sn = a(r^n - 1)/(r - 1)
52428 = -4[(-4)^n - 1]/(-4-1)
(-4)^n - 1 = 65535
(-4)^n = 65536
Means n is even
(4)^n = 65536
nln(4) = ln(65536)
n = 8
90 with a exponent 30 divided by 9 with a exponent as 8
Answer:
90^30/43046721
Step-by-step explanation:
construct a 95% prediction interval for y given x=-3.5, ^y= 2.097x - .552 and se= .976
Answer:
95% Confidence interval for y
= (-9.804, -5.979)
Lower limit = -9.804
Upper limit = -5.979
Step-by-step explanation:
^y= 2.097x - 0.552
x = -3.5
Standard error = 0.976
Mathematically,
Confidence Interval = (Mean) ± (Margin of error)
Mean = 2.097x - 0.552 = (2.097×-3.5) - 0.552 = - 7.8915
(note that x=-3.5)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value for 95% confidence interval = 1.960
Standard Error of the mean = 0.976
95% Confidence Interval = (Mean) ± [(Critical value) × (standard Error of the mean)]
CI = -7.8915 ± (1.960 × 0.976)
CI = -7.8915 ± 1.91296
95% CI = (-9.80446, -5.97854)
95% Confidence interval for y
= (-9.804, -5.979)
Hope this Helps!!!
+30 POINTS FOR THIS QUESTION
1. I just bought a kite at the departmnet store for $5.95. The owner of the store bought it from a wholesaler for $3.10. Which price is retail price?
The $5.95 is retail price because the owner got it for wholesale.
2. What precentage of the retail price is the whole sale price in #1?
3. If the sandals cost $58.00 wholesale and $105.00 retail, what is the markup in dollars?
4.The markup in #3 is what percent of the retail?
5.What precent of the wholesale in #3 is the markup?
6. A dozen eggs are purchased from the farmer at $1.05 per dozen. They are then sold to the consumer for $1.45. What percent of the retail is the markup.
1. I just bought a kite at the department store for $5.95. The owner of the store bought it from a wholesaler for $3.10. Which price is retail price?
Answer: The $5.95 is retail price because that's what I paid for it at the store
2. What percentage of the retail price is the wholesale price in #1?
3.10 / 5.95 = 0.52100 = 52.1%
3. If the sandals cost $58.00 wholesale and $105.00 retail, what is the markup in dollars?
markup = 105 - 58 = $47
4.The markup in #3 is what percent of the retail?
47/105 = 0.44761904761904764 = 44.8%
5.What percent of the wholesale in #3 is the markup?
47/58 = 0.8103 = 81.0%
6. A dozen eggs are purchased from the farmer at $1.05 per dozen. They are then sold to the consumer for $1.45. What percent of the retail is the markup.
(145-105)/145 = 0.2758620 = 27.6%
Answer:
uh what he said (:
Step-by-step explanation:
decrease 160 by 6% .
Answer:
150.4
Step-by-step explanation: