The ordered pairs of Nicole and Ian's sequence pattern are:(5,1),(17,3),(53,5),(161,10),(485,20).
Given that Nicole uses the rule multiply by 3 then add 2 starting with it and Ian uses the rule add 1/2 then multiply by 2 starting from 0,
We ar rquired to find the ordered pairs of Nicole's and Ian's rules.
We are told that Nicole's pattern is multiply by 3 then add 2 starting with 1.
Thus Nicole's pattern is :5,17,53,161,485.
Ian's pattern is add 1/2 then multiply by 2 and starting with 0.Thus the numbers are :1,3,5,10,20.
If we combine the numbers of both the person'rule then we will get the ordered pairs which can be written as under:
The ordered pairs are (5,1),(17,3),(53,5),(161,10),(485,20).
Hence the ordered pairs are (5,1),(17,3),(53,5),(161,10),(485,20).
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You ride your bike for 3 days in a row. On Monday , you ride 3 and 2/3 miles. On Tuesday, you ride 1 and 1/2 times further. On Wednesday, you ride 1 and 1/4 miles less than Tuesday. Find the total number of miles.
Taking the given ride lengths for 3 consecutive days and adding them the total number of miles ridden by the rider is 14.67 miles.
How is the distance traveled on Tuesday related to Monday's distance?On Tuesday, the distance traveled is 1 and 1/2 times further than Monday's distance. This means that the distance traveled on Tuesday is 1.5 times the distance traveled on Monday.
How can we find the total distance traveled over a period of multiple days?To find the total distance traveled over a period of multiple days, we can add up the distances traveled on each day. This can be done by summing up all the individual distances traveled on each day. This can be done either in fraction or decimal. If the distances are in mixed numbers, it is good to convert them into fractions before adding them. This will give the total distance traveled over the period of multiple days.
On Tuesday, you ride 1 and 1/2 times further than on Monday, which is 3 and 2/3 miles * 1 and 1/2 = 5 and 1/2 miles.
On Wednesday, you ride 1 and 1/4 miles less than on Tuesday, which is 5 and 1/2 miles - 1 and 1/4 miles = 4 and 1/4 miles.
The total number of miles you rode on Monday, Tuesday, and Wednesday is:
3 and 2/3 miles + 5 and 1/2 miles + 4 and 1/4 miles = 13 and 5/6 miles
You can convert the mixed numbers to fraction to find the total miles.
3 and 2/3 miles = (33 + 2)/3 = 11/3 miles
5 and 1/2 miles = (52 + 1)/2 = 11/2 miles
4 and 1/4 miles = (4*4 + 1)/4 = 17/4 miles
So, the total number of miles you rode on Monday, Tuesday, and Wednesday is :
11/3 + 11/2 + 17/4 = (114 + 113 + 172)/12 = 11/3 + 33/4 = (114 + 11*3 + 34)/12 = 44/3 = 14.67 miles
You rode 14.67 miles in total for 3 days.
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what kind of motion should you impart to the nozzle of a garden hose so that the resulting stream of water approximates a sine curve?
In order to make the stream of water from a garden hose approximate a sine curve, the nozzle of the hose should be moved in an up-and-down motion.
The reason is because a sine curve is a smooth wave-like pattern that oscillates between positive and negative values. If the nozzle is moved up and down, it will cause the water to be released in a similar wave-like pattern, creating a stream that approximates a sine curve. This is due to the nozzle moving in a sinusoidal motion, which causes the water to be released in the same motion. This kind of motion is known as a harmonic motion, and it's the same motion that causes a wave to have a sinusoidal shape.
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A right triangle has a leg of 11 cm and a hypotenuse of 17 cm. What is the length of the other leg? round to the nearest tenth. Responses 6. 0 cm 6. 0 cm 13. 0 cm 13. 0 cm 20. 2 cm 20. 2 cm 168. 0 cm.
The length of the other leg of a right triangle, as per the Pythagoras theorem, is option B: 13.0 cm.
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse. The calculation of the other leg of tbe triangle is given as follows.
According to the Pythagoras theorem:
(Hypotenuse)² = (Base)² + (Height)²
As per the question,
The height or the length of a leg of a right triangle is given equal to 11 cm and hypotenuse is given 17 cm. The other leg, or the base can be calculated as:
(Base)² = (Hypotenuse)² - (height)²
b² = (17)² - (11)²
b² = 289 - 121
b² = 168
b = √168
b = 12.96
or b = 13cm.
Thus, the base or the other leg of the right triangle is equal to 13 cm.
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Two angles are complementary. The measure of
one angle is 125% of the other. Find the
measures of both angles.
Answer:
2
Step-by-step explanation:
Maths, would it be congruent or alternate??
Therefore , the solution of congruency problem is its two congruent halves are LJ and LI. The sections' sizes and forms must be consistent to be considered congruent.
What is congruence?Using the Side-Angle-Side Congruity Theorem (SAS), two triangles are believed to be compatible with one another if their corresponding two sides and included angle are the same. A defined angle is found to be present on 2 sections that are being taken into account. Therefore, it is insufficient to use the SAS Congruity Theorem to establish the congruence of two triangles based just on the presence of two pairs of reciprocals and one set of points of intersection.
Here,
Given: The illustration shows a congruent link between
the two portions LI and LJ.
The segments will be identical in terms of size and shape if they are congruent.
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What happens when the base of an exponential function is negative?
Answer:
in ℤ, successive values alternate signs
Step-by-step explanation:
You want to know what happens when the base of an exponential function is negative.
Powers of a negative numberConsider the exponential function ...
y = a·b^x
For b < 0 and integer values of x, the signs of the corresponding values of y will alternate.
Example
y = 2·(-1)^x
A table of values will be ...
[tex]\begin{array}{ccccccc}x&-1&0&1&2&3\\y&-2&2&-2&2&-2\end{array}[/tex]
Roots of a negative numberFor non-integer values of x, the values of y become more complicated. For fractional values of x, where x has an even denominator, the equation does not produce a real value. Instead, you get a complex number.
For fractional values of x where x has an odd denominator, the power is defined, and the sign will depend on whether the numerator is even or odd.
For irrational values of x, the function value in general is complex.
Of course, there are an infinite number of rational numbers between any pair of numbers on the number line, so the graph will have both positive and negative values, but will not be continuous. The attached graph can give you the idea. It is not in any way a complete graph of the function, but plots selected values.
__
Additional comment
The second attachment shows one of the uses of an exponential factor with a negative base. It creates the alternate signs of the series expansion of the sine function. Only whole number exponents are used in this case.
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
-3
Step-by-step explanation:
to make it easier try 8-5 and then add a negative sign
9. unit 7 homework 5 solve for x. round to the nearest tenth
x
54
12
The angle x in a right-angled triangle is 12.8°.
What is a right-angled triangle?
A triangle is said to have a right angle if one of the angles is 90 degrees. Right triangles are those with angles at 90 degrees, which are referred to as right angles.
The diagram shows a right-angled triangle with opposite = 12 units and hypotenuse as 54 units.
To find the angle x, apply the formula -
sin(x) = opposite/hypotenuse
sin(x) = 12/54
x = sin^-1(12/54)
x = sin^-1(2/9)
x = 12.84°
Rounding it to nearest tenth gives x = 12.8°.
Therefore, the value of x is 12.8°.
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How do you find the domain and range of a function in Class 12?
In Class 12, to find the domain and range of a function, you can use the following steps:
Domain: The domain of a function is the set of all input values for which the function is defined. To find the domain of a function, you need to look at the function and identify any values of x that would make the function output undefined. These values of x are not in the domain of the function.For example, if the function is f(x) = 1/x, the domain of the function is all real numbers except 0, because dividing by 0 is undefined. In this case, the domain of the function is (-∞,0) U (0,+∞)
Range: The range of a function is the set of all possible output values of the function. To find the range, you can look at the function and identify any restrictions on the output values.For example, if the function is f(x) = √x, the domain of the function is all non-negative real numbers, because √x is only defined for non-negative values of x. In this case, the range of the function is [0,+∞)
Note that some functions may have more complex expressions, in such cases, you may have to use algebraic methods to find the domain and range.
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28. If a 20-foot ladder makes a 65° angle with the wall, how many feet up a wall will it reach, rounded to the
nearest hundredth? For maximum points, draw the picture, label the sides as H (hypotenuse), O
(opposite) and A (adjacent), write the trig ratio and select your answer.
A. 8.45 ft
B. 22.07 ft
C. 18.13 ft
D. 47.32 ft
On solving the provided question, we can say that We can use the trigonometry sine to solve for the other side: sin 65 = y/20 => y = 18.126
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study.
We can arrange a right triangle with 20 feet as the hypotenuse and 65 degrees as the angle between the hypotenuse and adjacent side assuming that the ground and wall meet at a 90 degree angle. The side across from the angle would be the amount of feet the ladder extends up the wall
We can use the trigonometric function sine to solve for the other side:
sin 65 = y/20
y = sin(65) . 20
y = 18.126
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Please answer the question.
The rate at which the distance is decreasing is - 30 centimeters per second. Ravi's distance from the first floor when he stepped on escalator is 1250 centimeters.
What is rate?The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one thing by the equal amount of change in another.
a. From the table we can observe that as time increases, his distance from the first floor decreases.
The rate at which the distance is decreasing is given by:
Rate = (d2 - d1)/ (t2 - t1)
= (980 - 1070) / (9 - 6)
= -90 / 3
= -30
Hence, the rate at which the distance is decreasing is - 30 centimeters per second.
b. Ravi's distance from the first floor when he stepped on escalator is calculates as:
d - d1 = m(t - t1)
where, m is the rate.
Here, m = -30.
d - 1070 = (- 30) (t - 6)
d = -30t + 180 + 1070
d = -30t + 1250
The time when he stepped on escalator is 0.
d = -30(0) + 1250
d = 1250
Hence, Ravi's distance from the first floor when he stepped on escalator is 1250 centimeters.
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Nathan buys 9 items that cost b dollars each. She gives the cashier $100 dollars. Write
an expression for the change she should receive.
An expression for the change she will receive is 8b - 100 = 100
What is an expression?You should be aware that an expression in math is a sentence with a minimum of two numbers or variables and at least one math operation
The given parameters are
Nathan buys 9 items
She gives the cashier $100
The expression 8(b) -100 = 100%
Where 100 is the full amount payable
Therefore, the expression becomes 8b -100=100
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40. The area of a square is 45 m², what is the measurement of its side? (no choices)
41.) What is the square root of -4? a. 2 b.-2 c.0 d.undefined
42.) Which of the following DOES NOT belong to the group?
a. (3/4)-2 b. 9/16 c. 16/9 D.9 m
43.) Evaluate 8x0.
a.0 b.1 c.8 d.x
44.) If y varies directly as x, and y is 15 when x-3, find y when x-5.
a. 25 b. 15 C.45 D.35
45. If N varies inversely as M, and N=5 when M-3, find N when M=10.
a. 3/2 b. 15 c. 5/3 d. 5
46.)If y varies jointly as x ad z, and y-6 when x-10 and z-8, find y when x-4 and 2-40. a. 12 b. 10 c. 8 d. 16
47.) If z varies directly as x and inversely as y, and z-9 when x-6 and y=2, find z when x=8 and y=12. a. 2 b. 4 c. 6 d. 16
48. If 3 men can do a portion of a job in 8 days, how many men can do the same job in 6 days? a. 7 b. 6 c. 5 d. 4
49.) Jordan's income varies directly as the number of days that he works. If he earns 8,000 pesos in 20 days, how much will he earn if he worked 3 times long? a. 26,000 b. 24,000 c. 20,000 c. 16,000
50.) The amount of gasoline used by a car varies jointly as the distance travelled and the square root of the speed. Suppose a car used 25 litres on a 100 km trip at 100 kph, about how many litres will be use on a 1000 km trip at 64 kph? a. 100 L b. 200 L c. 300 L c. 400 L
The solutions to the different sides and values of square are given below. The length of the side of the square is 6.71m.
What is a square?Square is a polygon which four equal sides and all angles are right- angles.
Given area of square = 45 m²
Area = side²
Side = √Area = √45 = 6.71 m
Therefore side of the square is 6.71m.
41) Negative numbers do not have square roots.
Therefore √-4 is undefined.
42) Option D is correct as it is not a fraction.
43) Any number multiplied by zero is zero.
Therefore (a) is the correct option.
44) When y = 15, x = 3
For direct variation, y =kx
so k = y/x =15/3 = 5
When x=5, y = kx =5*5 = 25
Therefore (a) is correct.
45) For inverse variation
MN = k
Given 5*3 = k
k=15
When M = 10 , N = k/M = 15 /10 = 3/2
Therefore option a is correct.
48) Let the amount of work be W
For 3 men,
8 days = W
1 day = W/8
Now work done by 1 man in one day = (W/8) /3 =W/24
In six days, work done by one man = W/24 * 6 = W/4
Therefore for the work to be completed, the number of men required is 4 (W/4 *4 = W).
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can someone help me solve this?
The answer is B: 1/16
what is the Least common denominator of 7/10 and 1/15
Answer:
30
Step-by-step explanation:
10 = 2 × 5
15 = 3 × 5
LCD = 2 × 3 × 5 = 30
20 POINTS TO WHOEVER CAN ANSWER THIS!!!!!
please answer with the given image.
Answer: 0
Step-by-step explanation: if the 5 doesn't change at all, it doesn't change at all. Common sense.
Answer:
the answer is 1 I just know cause ima genius and smart also I'm like 6'7 how could i.be wrong
Step-by-step explanation:
look
2(3p-2) - (p+4) = 3p
Please help immediately. Will mark brainiest for correct answer.
Answer:
[tex]2(3p - 2) - (p + 4) = 3p \\ \\ \dashrightarrow \: 6p - 4 - p - 4 = 3p \\ \\ \dashrightarrow \: 5p - 8 = 3p \\ \\ \dashrightarrow \: 5p - 3p = 8 \\ \\ \dashrightarrow \: 2p = 8 \\ \\ \dashrightarrow \: p = 4[/tex]
hope helpful :-;
An architect creates a drawing in which a rectangular desk is 11 inches long and 6 inches wide. The drawing is at a scale of 1 inch = 2 feet. what is the actual area, in square feet, off the desk
The actual area of the rectangular desk is 264 feet²
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Scaling is used to increase or decrease the size of a figure by a scale factor.
The drawing is at a scale of 1 inch = 2 feet.
11 inches = 11 inches * 2 feet per 1 inch = 22 feet
6 inches = 6 inches * 2 feet per 1 inch = 12 feet
Area of the desk = length * width = 22 feet * 12 feet = 264 feet²
The actual area is 264 feet²
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how to solve simplify rational expressions
Which value of X satisfies both -9X + 4Y = 8 and -3X - Y = 4 given the same value of Y
The value of X that satisfies both -9X + 4Y = 8 and -3X - Y = 4 given the same value of Y is X = -8/7.
What is an equation?An equation is a mathematical statement that shows that two mathematical algebraic expressions are equal. For example, x + 7 = 10 is an equation, in which x + 7 and 10 are two expressions separated by an 'equal to' sign.
An equation also has two sides, the let hand side and the right hand side.
Solving the two equations simultaneously we have:
-9x + 4y = 8 --- (1)
-3x - y = 4 --- (2)
Multiply 2 by 3 and subtract from (1) as shown below
-9x + 4y = 8
-9x - 3y = 12
------------------
0 + 7y = - 4
7y = -4
y = -4/7
Substituting the value of y in equation 2 we get the value of x.
-3x - (- 4/7) = 4
-3x + 4/7 = 4
-3x = 4 - 4/7
-3x = 24/7
x = -8/7
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The first term of a sequence is 4.
1. Choose a growth factor and list the next 3 terms of a geometric sequence.
2. Choose a different growth factor and list the next 3 terms of a geometric sequence.
1. The sequence is 2, 8, 16, 32.
2. The sequence is 4, 16, 64, 256.
What is Sequence?A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts.
For example, 3, 7, 11, 15, ... is a sequence as there is a pattern where each term is obtained by adding 4 to its previous term.
Given:
The first term of a sequence is 4.
1. let the common ratio 2.
Then, second term= 4 x 2= 8
third term = 8 x2 =16
fourth term = 16 x 2= 32
So, the sequence is 2, 8, 16, 32..
2. let the common ratio 4.
Then, second term= 4 x 4 = 16
third term = 16 x 4 = 64
fourth term = 64 x 4 = 256
So, the sequence is 4, 16, 64, 256.
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7) What is the (x, y) solution for the following s [y=-4x+2 [y=6x-8
solution for the two equation is x = 1, and y = - 2
What is solution?
It is a mathematical term that acts as the substitute of variables present in one or more equations. It is the value of unknown numbers that makes an equation true.
What is the (x, y) solution for the following equation bellow?
equation given, y = - 4x + 2
y = 6x - 8
if we use addition method then y = - 4x +2
y = 6x -8
- - +
0 = - 10x + 10
10 x = 10
x = 1
putting the value of x in one of the above equations we get the y value.
y = 6×1 -8
y = -2
the solution is the x = 1 and y = - 2
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Please somebody help with this question!
According to angle symmetry, the value of x=125°
What is an example of an alternate angle?The two parallel lines intersected by a transversal form alternate angles. Consider the following figure, where EF and GH are two parallel lines. The transversal line RS intersects EF at L and GH at M. If a transversal cuts two parallel lines, the alternate angles are equal.
Since, AK and BL are parallel lines.
Hence,
∠ADC=∠BED=72°
∠EIH=∠DHG=55°
∠DHG+∠GHK=180°
∠GHK=180°-55°
∠GHK=125°=x
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please answer this question i am stuck 82 x 19 ≈80
Answer:1558
Step-by-step explanation:
Answer:1558
Step-by-step explanation:
[tex]82\\19[/tex]
put a line under it multiply the 9x2 and then 9x8 make sure to carry
put a zero under the 8 and multiply 1x2 and 1x8
now add the the numbers together
you get 1558
4. Complete the table. (10 points: 1 point for each row)
a. Identify the actual number of sales at each price.
b. Use your line of best fit to calculate the predicted sales at each price. Round
the predicted sales to the nearest tenth.
c. Calculate the residuals at each price by subtracting predicted sales from actual
sales.
Price
1.5
1.6
1.8
2.0
2.1
2.2
2.5
2.7
2.9
3.0
Actual sales
96
94
91
85
83
79
73
70
64
63
Coffee:
Predicted sales
96
94
89
85
83
80
74
69
64
62
Residual I have to figure out the residual by subtracting the Actual sales by the predicted sales .but I need someone to help me put them back in the decimal form at first when they were first calculated
For this kind of issue, you can select any option and the procedure will remain the same. Let's choose coffee as the beverage to analyse for the purposes of this response.
What does a 0.5 Pearson correlation indicate?When a correlation coefficient's magnitude is between 0.5 and 0.7, it means that the variables are moderately correlated. Low correlation between the variables is indicated by correlation coefficients with magnitudes between 0.3 and 0.5.
In this equation, x stands for price, and y for sales.
-22.7x+130.3
The slope indicates the number of units that the sales would change by if we raised the price by one unit. Since our slope is -22.7, this indicates that a 1 unit price increase would result in a 22.7 decrease in sales.
The scatterplot's points are all intersected by the line of best fit, as can be seen. We can also calculate the Pearson correlation coefficient, which gives us -0.998, to add to the evidence. This suggests a very adverse relationship.
For this item we will just need the equation for the line of best fit and the data that has been given in the problem. For the actual sales, we will just refer to the given while we will compute for the predicted sales using the line of best fit.
PRICE ACTUAL SALES PREDICTED SALES
1.5 96 96
1.6 94 94
1.8 91 89
2.0 85 85
2.1 83 83
2.2 79 80
2.5 73 74
2.7 70 69
2.9 64 64
3.0 63 62
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How do you compare complex numbers with real numbers?
Complex numbers and real numbers cannot be directly compared as they are from different number systems.
Complex numbers have both a real and an imaginary component, whereas real numbers only have a real component. However, you can compare the magnitudes (absolute values) of complex numbers with real numbers.
The magnitude of a complex number is the distance from the origin in the complex plane, represented by the absolute value or modulus of the complex number, which is always a positive real number. By comparing the magnitudes of complex numbers, you can determine which one is larger or smaller.
For example, the magnitude of 3 + 4i is 5, and the magnitude of 2 + 3i is 3.5. Therefore, 3 + 4i has a larger magnitude than 2 + 3i.
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find the scale factor
Answer:
[tex]\dfrac{2}{3}[/tex]
Step-by-step explanation:
Method 1To find the scale factor of the dilation of a figure, simply divide the x-value (or y-value) of a vertex of the dilated image Q'R'S'T' by the x-value (or y-value) of the corresponding vertex of the pre-image QRST.
[tex]\implies \sf Scale\;factor=\dfrac{x_{Q'}}{x_{Q}}=\dfrac{-2}{-3}=\dfrac{2}{3}[/tex]
[tex]\implies \sf Scale\;factor=\dfrac{y_{T'}}{y_{T}}=\dfrac{4}{6}=\dfrac{2}{3}[/tex]
Therefore, the scale factor is 2/3.
Method 2To find the scale factor of the dilation of a figure, first find the lengths of corresponding sides using the distance formula.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
From inspection of the given diagram:
Q = (-3, 9)R = (3, 6)[tex]\implies QR=\sqrt{(x_R-x_Q)^2+(y_R-y_Q)^2}[/tex]
[tex]\implies QR=\sqrt{(3-(-3))^2+(6-9)^2}[/tex]
[tex]\implies QR=\sqrt{(6)^2+(-3)^2}[/tex]
[tex]\implies QR=\sqrt{36+9}[/tex]
[tex]\implies QR=\sqrt{45}[/tex]
[tex]\implies QR=3\sqrt{5}[/tex]
From inspection of the given diagram:
Q' = (-2, 6)R' = (2, 4)[tex]\implies Q'R'=\sqrt{(x_{R'}-x_{Q'})^2+(y_{R'}-y_{Q'})^2}[/tex]
[tex]\implies Q'R'=\sqrt{(2-(-2))^2+(4-6)^2}[/tex]
[tex]\implies Q'R'=\sqrt{(4)^2+(-2)^2}[/tex]
[tex]\implies Q'R'=\sqrt{16+4}[/tex]
[tex]\implies Q'R'=\sqrt{20}[/tex]
[tex]\implies Q'R'=2\sqrt{5}[/tex]
To find the scale factor of dilation that maps QRST onto Q'R'S'T', divide the length of Q'R' by the length of QR:
[tex]\implies \dfrac{Q'R'}{QR}=\dfrac{2\sqrt{5}}{3\sqrt{5}}=\dfrac{2}{3}[/tex]
Therefore, the scale factor is 2/3.
What is the motion of displacement?
Displacement is the change in the position of an object relative to a reference point over a period of time.
It is usually represented by a vector quantity and is measured in meters (m). The formula for displacement is displacement = final position - initial position. Mathematically, displacement is denoted by s and is equal to the final position (x2) minus the initial position (x1), or s = x2 - x1. As an example, if a person walks a path of length 10 meters, starting at the origin (x1 = 0) and ending at x2 = 10, then their displacement would be s = 10 - 0 = 10 meters. To calculate displacement, we need to know the initial and final positions of the object, and the direction in which it moves.For example, if an object moves from position 5 m to position 10 m, the displacement is 5 m. This can be calculated by subtracting the initial position (5 m) from the final position (10 m). The result is 5 m, which is the displacement of the object.
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How do you plot y =- 2x on a graph?
Answer:
below
Step-by-step explanation:
make the ordered pairsso if x=1 then y is... it's -2so if x=2 then y is... it's -4so if x=3 then y is... it's -6so now you have the ordered pairs (1,-2) and (2,-4) and (3,-6)Now plot them(2,-1) y=1/4x+8 in slope-intercept form
Answer: Here is my question
Step-by-step explanation: