Write the equation of a slope intercept form with a slope of 9 and a y-intercept of -3
Answer:
y = 9x-3
Step-by-step explanation:
since the slope intercept form is in the y=mx+b form, you just have to plug in the slope for m and the y-intercept for b.
What are the similarities between the sine, cosine,
and tangent ratios? What are the differences?
Answer:
Similarities: All the trigonometric functions are periodic functions. All these trigonometric function values can be found by using special right triangles from the unit circle. Diffferences: The tangent has different domain and range values from sine and cosine. The tangent function is not a continuous function, unlike sine and cosine.
Step-by-step explanation:
The similarities and differences between the sine, cosine, and tangent ratios are given.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The sine, cosine, and tangent are three trigonometric ratios used in geometry to relate the angles of a right triangle to the lengths of its sides.
Similarities:
All three ratios involve comparing two sides of a right triangle to each other.
They are all functions of an angle and are dependent on the measure of the angle and not the size of the triangle.
They are all defined as ratios of two sides of a right triangle, and the values of these ratios depend on the angle in question.
Differences:
The sine and cosine ratios are periodic functions with a period of 2π, while the tangent ratio is not periodic, and its graph has vertical asymptotes.
The sine and cosine ratios are always between -1 and 1, while the tangent ratio can take any value, positive or negative.
The cosine of an angle is equal to the sine of its complement, while the tangent of an angle is equal to the sine of the angle divided by the cosine of the angle.
Hence, the similarities and differences between the sine, cosine, and tangent ratios are given.
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a bag contains 2 coins. some of them are 10 cents coins and all of the others a 5 cent coins.
i) if the number of 10 cent coins is x, write down an expression for the number of 5 cent coins
ii) write down a expression, in terms of x, for the total value, in cents of the 24 coins
Answer:
i) 24 - x
ii) 5x + 120
Step-by-step explanation:
i) There are a total of 24 coins. We see that x of these 24 are 10 cent coins. The rest must be 5 cent coins, so they must be all the 24 coins that are NOT included in the x: 24 - x
ii) We know that there are x 10 cent coins, which are each 10 cents. There are also (24 - x) 5 cent coins, which are each 5 cents. In order to find their total value, we need to multiply the value of the denomination by how many there are of each denomination. So:
10x + 5(24 - x) = 10x + 120 - 5x = 5x + 120
Hope this helps!
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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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
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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Find the gradient of the line segment between the points (4,3) and (5,7)
Answer:
gradient = 4
Step-by-step explanation:
Calculate the gradient m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 3) and (x₂, y₂ ) = (5, 7)
m = [tex]\frac{7-3}{5-4}[/tex] = 4
The gradient of the line segment between the points (4,3) and (5,7) is 4
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The gradient of the line is also called as slope of line
Gradient of the line segment between the points (4,3) and (5,7)
Gradient = 7-3/5-4
=4/1
Hence, the gradient of the line segment between the points (4,3) and (5,7) is 4
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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.
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.
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
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
Please help me out! And please show your work!!
|
|
|
v
Answer:
Ratio of perimeters = 5:2
Ratio of areas: 25:4
Step-by-step explanation:
20/8 = 5/2 (ratio of lengths is equal to ratio of perimeters)
[tex](5/4) ^{2}[/tex] = 25/4 (ratio of areas is the square of ratio of lengths)
90 with a exponent 30 divided by 9 with a exponent as 8
Answer:
90^30/43046721
Step-by-step explanation:
Which of the following is an irrational number? A. 16 B. 0.4 C. 4 D. 16
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:
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].
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
In order to answer the question correctly, please use the following image below:
Find the value of x.
X=(Blank)
Please show all the work on how you got your answer.
Answer:
106°
Step-by-step explanation:
(152 + 60)/2
212/2
106°
(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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Match the formulas to the correct text. I. A equals the product of B or H, divided by 2. II. A equals the product of B times H, divided by 2. III. D equals P sub T plus the quantity 2 times T, divided by 3. IV. D equals P sub T times the quantity 2 times T, divided by 3. V. R sub T equals R sub 1 plus R sub 2. VI. R sub T equals R sub 1 plus the sum R sub 2.
The correct matches are as follows:
Formula | Text
I. A equals the product of B or H, divided by 2. | Incorrect
II. A equals the product of B times H, divided by 2. | Correct
III. D equals P sub T plus the quantity 2 times T, divided by 3. | Correct
IV. D equals P sub T times the quantity 2 times T, divided by 3. | Incorrect
V. R sub T equals R sub 1 plus R sub 2. | Correct
VI. R sub T equals R sub 1 plus the sum R sub 2. | Incorrect
Here is a more detailed explanation of each match:
II. A equals the product of B times H, divided by 2.
This formula is correct for the area of a triangle, where A is the area, B is the base, and H is the height.
III. D equals P sub T plus the quantity 2 times T, divided by 3.
This formula is correct for the average distance traveled, where D is the total distance traveled, P sub T is the starting point, and T is the time taken.
V. R sub T equals R sub 1 plus R sub 2.
This formula is correct for the total resistance in a parallel circuit, where R sub T is the total resistance, and R sub 1 and R sub 2 are the resistances of the two parallel resistors.
The other formulas are incorrect. For example, formula I states that A is equal to the product of B or H, divided by 2. This is not correct, because A cannot be equal to two different things at the same time. Formula IV is incorrect because it states that D is equal to P sub T times the quantity 2 times T, divided by 3.
This is not correct, because the average distance traveled cannot be equal to the starting point multiplied by the time taken. Formula VI is incorrect because it states that R sub T is equal to R sub 1 plus the sum R sub 2.
This is not correct, because the total resistance in a parallel circuit cannot be equal to the sum of the resistances of the two parallel resistors.
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Item 4 Find the median, first quartile, third quartile, and interquartile range of the data. 132,127,106,140,158,135,129,138 median: first quartile: third quartile: interquartile range
The median of this data set is 133.5, the first quartile (Q₁) is 128, the third quartile (Q₃) is 139, and the interquartile range (IQR) is 11.
Explanation:First, arrange the data in ascending order: 106, 127, 129, 132, 135, 138, 140, 158.
Median: The median is the middle value of a data set. Since there are 8 numbers, the median is the average of the 4th and 5th values: (132+135) ÷ 2 = 133.5.
First Quartile (Q₁): This is the median of the lower half of the data. Here, it is the average of the 2nd and 3rd values: (127+129) ÷ 2 = 128.
Third Quartile (Q₃): This is the median of the upper half of the data, which is the average of the 6th and 7th values: (138+140) ÷ 2 = 139.
Interquartile Range (IQR): You find the IQR by subtracting Q₁ from Q₃, hence IQR = 139 - 128 = 11. The IQR represents the middle 50% of the values when ordered from lowest to highest.
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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!!!
A water tank is in the shape of a cylinder with a diameter of 20 feet and a height of 20 feet. The tank is 70% full. About how many gallons of water are in the tank? Round your answer to the nearest whole number.
Answer:
32901 gallons
Step-by-step explanation:
First, we find the volume of the cylindrical water tank when it is full.
The volume of a cylinder is given as:
V = [tex]\pi r^2h[/tex]
where r = radius and h = height of the cylinder
The diameter of the tank is 20 feet, hence, its radius is 10 feet.
Volume, V, is therefore:
V = [tex]\pi * 10^2*20 = 6283.19 ft^3[/tex]
This is the volume of the tank, when it is full.
When it is 70% full, the volume will be:
[tex]\frac{70}{100} * 6283.19 = 4398.23 ft^3[/tex]
1 cubic foot ([tex]ft^3[/tex]) is 7.48 gallons.
Therefore, the volume of the 70% full tank in gallons will be:
4398.23 * 7.48 = 32901.05 gallons ≅ 32901 gallons
The tank contains 32901 gallons of water.
Answer:
32886.476 gal
Step-by-step explanation:
Given:
Diameter of tank 'd'= 20 ft
∴radius 'r'= d/2=> 20/2=> 10ft
Height 'h' = 20 ft
Volume of cylinder can be determined by
V= π r² h
Substituting the values in above equation
V= π (10)² (20) =>π(100)(20)
V=2000π ft³
When the tank is 70% full.
70% of 2000π =>0.7 x 2000π
1400π ft³
As we know that, 1ft³ = 7.481 gal
1400π ft³= 1400π x 7.481 gal
1400π ft³= 32886.476 gal
Therefore, if the tank is 70% full then 32886.476 gallons of water are in the tank
What is............What is 60% of 1200
Answer: [tex]720[/tex]
Multiply
60%×1200=720
Note: When finding the percent of a number always multiply the percent times the number.
Answer:
[tex]720[/tex]
Step-by-step explanation:
[tex]1200 \times \frac{60}{100} \\ = \frac{72000}{100} \\ = 720[/tex]
hope this helps you...
Which expression is equivalent to x4 + 4x² – 45?
Answer:
Step-by-step explanation:
x4 + 4x² – 45 = x^4 + 4x^2 - 45. Use " ^ " to indicate exponentiation.
Temporarily substitute p for x^2. Then we have:
p^2 + 4p - 45, or
(p + 9)(p - 5)
But p = x^2.
Therefore, our expression becomes
(x^2 + 9)(x^2 - 5)
We could stop here or we could factor further.
Hint: x^2 - 5 = (x - √5)(x + √5); (x^2 + 9) factors into imaginary roots.
Simplify: (5mn3)3 • (5mn)3
Answer:
photomath said 375m³n³
Step-by-step explanation:
-use exponent rules 3×(5mn)³
- calculate the product 3×125m³n³
-Solution 375m³n³
decrease 160 by 6% .
Answer:
150.4
Step-by-step explanation:
whcih point on the number line represents the problem. point a point b point c or point d
Answer:
its D 100%
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Miss Penny inherits £910.
She decides to save some of the
money and spend the rest.
The ratio of savings to spending
money is 7:6
How much does she save and how
much does she spend?
Savings
£
[2]
Spending money £
[2]
Answer:
Sacing 490 spending 420
Step-by-step explanation:
If a is a fraction
Saving 7a Spending 6a
7a + 6a = 910
13a = 910
a = 910/13
a = 70
Saving 7×70 = 490
Spending 6×70 = 420
The sum is 490 + 420 is equal to 910
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