The value of g(-6) is 42
What is a linear function?A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.
For example if f(x) = 3x-2, the value of f(3) is derived by substituting 3 for x In the function. Therefore f(x) = 3(3) -2 = 9-2 = 7
Similarly to solve g(-6) we substitute -6 for x in the function
g(-6) = -6² -(-6)
g(-6) = 36 + 6
g(-6) = 42
therefore the value of g(-6) = 42
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Graph the function.
f(x)=-2x²
Plot five points on the graph of the function: one point with x=0, two points with negative x-values, and two points with positive x-values.
Answer: The graph of the function f(x) = -2x² is a parabola that opens downward, with its vertex at the origin (0,0). The x-axis is the axis of symmetry for this parabola.
To plot five points on the graph of the function, we can substitute different x-values into the function and solve for y:
For x = 0, y = f(0) = -2(0)² = 0
For x = -2, y = f(-2) = -2(-2)² = 8
For x = -3, y = f(-3) = -2(-3)² = 18
For x = 2, y = f(2) = -2(2)² = -8
For x = 1, y = f(1) = -2(1)² = -2
So, the five points on the graph of the function are (0,0), (-2,8), (-3,18), (2,-8), (1,-2).
It's important to note that, the graph of f(x)=-2x² will be a parabola opening downward and passing through the points that we found.
Step-by-step explanation:
this is a camera toy
edge of the cube = 5cm
cylinder diameter = 4cm and
cylinder height = 20cm
1) find the clay required to make this toy
2)find the area to be painted
The total clay required is 376.2 cm³and area to be painted is given by 300.7 cm²
What is the area and volume of a right circular cylinder?The volume of a Right Circular Cylinder. In general, the volume of a right cylinder is the area of the base times the height of the cylinder. The area of the circular base is given by the formula A = πr2. Substitute to get V = πr2h.
Given here: The dimensions of the edge of the cube as 5cm and the cylinder diameter is 4cm with a height of 20cm
We know the volume of the cube is given by a³ where a is the measure of the length of the cube
Thus a³=5³
=125 cm³
and surface area of the cube is given by 6a²=6×25
=150 cm²
Again the volume of the cylinder and surface area of the given cylinder is as follows:
Volume= 22/7×2²×20
=251.2 cm³
surface area = 2·π·2·10+2·π·22≈150.79645cm²
Thus the clay required to make the toy is=125+251.2
=376.2 cm³
And the area to be painted is given by =150.7+150
=300.7 cm²
Hence, The total clay required is 376.2 cm³and area to be painted is given by 300.7 cm²
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Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number
Ivanna earns $2,400 if she doesn't sell any copies of history is fun.
What is the difference between positive and negative number?Ivanna makes an extra $120 ($120) for each additional copy she sells and a loss of $120 ($120) for each fewer copy.
If Ivanna doesn't sell any copies of History is Fun, her total compensation is $2,400.
Ivanna makes a total salary of y = 2,400 + 120x, where x is the quantity of copies of her book History is Fun she sells.
We compare the compensation for two successive values of y to determine the change in Ivanna's pay.
We must estimate y when x exists of consecutive values i.e. 1, 2, 3, 4
We compute the value of y when x = 1, 2 and 3.
When x = 1, y = 2,400 + 120 (1) = 2,400 + 120 = $2,520.
When x = 2, y = 2,400 + 120 (2) = 2,400 + 240 = $2,640.
When x = 3, y = 2,400 + 120 (3) = 2,400 + 360 = $2,760.
To estimate the increase in her pay for a copy, we subtract y when x = 2 from y when x = 3.
(y when x = 3) - (y when x = 2) = $2,760 - $2,640 = $120.
So for every extra copy, Ivanna gets an extra $120.
To estimate the decrease in her pay for a copy, we subtract y when x = 3 from y when x = 2.
(y when x = 2) - (y when x = 3) = $2,640 - $2,760 = -$120.
So for every less copy, Ivanna loses $120.
To estimate her pay when she doesn't sell any copies of history is fun, we substitute the value of x as 0 in y.
When x = 0, y = 2,400 + 120 (0) = $2,400.
So Ivanna earns $2,400 if she doesn't sell any copies of history is fun.
The complete question is:
Ivanna is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of History is Fun she sells. Suppose that x and y are related by the equation 2400+120x = y.
Answer the questions below.
Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What is the change in Ivanna's total pay for each copy of History is Fun she sells?
What is Ivanna's total pay if she doesn't sell any copies of History is Fun?
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15. An airplane is traveling at a fixed altitude with a negligible wind factor. The airplane is headed N 30° W at a speed of 500 miles per hour. As the airplane reaches a certain point, It encounters a wind with a velocity of 70 mph in the direction of N 45' E.
What are the resultant speed and direction of the airplane?
The resultant speed is 52.48 and the direction of the airplane is west to north.
The resultant velocity of an object is defined as the sum of its individual vector velocities, and the sum of the vector forces on an object is equal to the scalar product of the object's mass and its acceleration vector.
Given
The plane is initially flying with a velocity of magnitude v=500mph.
at an angle of 30° North toward the west
The velocity of the plane airplane can be written as:
[tex]v_a=-500(sin 30i+cos30j)[/tex]
Now the wind is encountered with the speed of v=70mph at an angle of N 45°E
[tex]v_w=70(cos45i+sin45j)\\[/tex]
resultant velocity:
[tex]v_R=v_a=v_w\\\\[/tex]
[tex]v_R=-500(sin 30i+cos30j)+70(cos45i+sin45j)\\\\v_R=i(-250+49.49)+j(433.01+49.49)\\\\v_R=i(-200.51)+j(482.5)\\\\tan\alpha =\frac{482.5}{-200.51} \\\\tan\alpha =2.406\\\\\alpha =tan^-^1(2.406)[/tex]
α=52.48° west of North.
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May I have help on this please?
Answer:
yeah you can
Step-by-step explanation:
what do you need help with lol
For questions 1-2, use the following scenario:
Some wooden chests are in a store. A green chest has a length of 180 centimeters (cm), a width of 75 cm, and a height of 20 cm.
1. If another box, a blue box, is proportional in size, what is its length if its width is 15 cm?
2. If another box, a red box, is proportional in size, what is its height if its length is 13 cm?
The measures are given as follows:
1. Length of 36 cm.
2. Height of 1.44 cm.
How to obtain the measures?The measures are obtained applying the proportions in the context of this problem.
The ratio between the length and the width is given as follows:
Length/Width = 180/75
Length/Width = 2.4
Length = 2.4 Width.
For a width of 15 cm, the length is given as follows:
15 x 2.4 = 36 cm.
The ratio between the length and the height is given as follows:
Length/Height = 180/20
Length/Height= 9
Length = 9Height
Height = Length/9
Hence the height if the length is of 13 cm is given as follows:
13/9 = 1.44 cm.
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Which of the following is a solution set for the following graph?
Substitute the sign for the symbol to graph the provided inequality.
What is the graph?Replace the symbol with the = sign to graph the specified inequality.
Create a table now.
y= 8x - 6.
Assume a random integer for x to determine y.
x y= 8x - 6.
-2 -4
0 -4
-6 8
We are now graphing the points. Connect the spots with the dotted line.
Now, we'll do shading.
Use the test point (8,6)
Therefore, we darken the area that doesn't include (8,6)
We are now graphing the points. Connect the spots with the dotted line.
Substitute the = sign for the symbol to graph the provided inequality.
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Drag each set of column entries to the correct location in the augmented matrix. Not all sets of entries will be used.
Mac traveled to three cities on one highway. The total distance one way was 320 miles. The distance from his original location to the first city was 20 miles more than half
the distance from the first city to the second city. The distance from the second city to the third city was 75 miles less than the distance from the first city to the second
city. Let xrepresent the distance from the original location to the first city, y represent the distance from the first city to the second city, and z represent the distance from
the second city to the third city. Place the correct sets of column entries in the augmented matrix that models Mac's situation,
Vital phrases there are more than and lesser than, so if he went, say, 75 miles from his residence to the first city the first one they would claim that he actually traveled 10 miles less between the first and second cities.
The total distance is 320 miles because, according to the very last sentence, the initial distance between the first and second cities was approximately 75 miles, and if the distance between the second and third cities was the same, the equation would be (160*2)+75. In order to solve this equation correctly, you must use P.E.M.D.A.S., which stands for parenthesis, exponents, multiplying, dividing, and adding subtracting.
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The local Farmers Market sells peppers at five for $2. 25.
Complete the rate table.
Number of Peppers
0
1
2
3
4
5
10
15
20
Cost ($)
0
0. 45
0. 90
1. 35
1. 8
$2. 25
4. 5
6. 75
9 What is the constant rate of change (CROC)? How do you know?
Is this a proportional relationship? How do you know?
The proportionality is 0.45, then the equation is C = 0.45 n. The number of peppers you buy for $20 will be 44.44. Then the table is completed below.
What are proportion and ratio?
A collection of consecutively ordered numbers a and b expressed as a/b, where b is never equal to zero, is referred to as a ratio. A statement is considered proportionate when there is equality between two items.
Let n be the number of peppers and C be the price. The proportionality is then provided as,
C ∝ kn
With n = 5 and a cost of C = 2.25, we obtain
2.25 = k (5) (5)
k = 2.25 / 5
k = 0.45
The equation is then presented as,
C = 0.45 n
You will be told how many peppers you get for your $20 purchase as,
20 = 0.45 n
n = 44.44
Then the table is completed below.
Number of peppers Cost
1 $0.45
2 $0.90
3 $1.35
4 $1.80
5 $2.25
10 $4.50
15 $6.75
20 $9
100 $45
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Given: e || f and g is a transversal Prove: 1 8 Given that e || f and g is a transversal, we know that 4 5 by the alternate interior angles theorem. We also know that 1 4 and 8 5 by the corresponding angles theoremalternate interior angles theoremvertical angles theoremalternate exterior angles theorem. Therefore, 1 8 by the transitive property
We also know that 1 4 and 8 5 by the vertical angles theorem.
Vertical angles, also known as vertically opposite angles, are the opposing angles formed when two lines converge. Angles that are vertically opposite one another are always equal to one another. A vertical angle and the angle it is near to are also supplementary angles, which means their combined angle is 180 degrees.
The opposite angle, for example, is 45° when two lines intersect to form an angle, say X=45°. And the angle next to angle X will be 180 – 45, or 135 degrees.
Correct Question :
Given: e || f and g is a transversal.
Prove: 1 8 Given that e || f and g is a transversal, we know that 4 5 by the alternate interior angles theorem. We also know that 1 4 and 8 5 by the (corresponding angles theorem / alternate interior angles theorem / vertical angles theorem / alternate exterior angles theorem). Therefore, 1 8 by the transitive property.
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on a radio, min turned the dial until it was set to 96.3.what is 96.3 rounded to the nearest whole number?
In the given scenario, 96.3 rounded to the nearest whole number is 96.
A whole number is a number that does not have a fractional or decimal part, and is an integer greater than or equal to zero.
Whole numbers are often used to represent the count of discrete objects or items.
Examples of whole numbers include: 0, 1, 2, 3, 4, 5, and so on. Whole numbers are a subset of the set of integers.
To round a decimal number to the nearest whole number, look at the digit to the right of the decimal point.
If the digit is less than 5, round down. If the digit is 5 or greater, round up.
Rounding off is a method of approximating a number to a specified number of significant digits or decimal places.
The basic idea behind rounding off is to keep only the most significant digits of a number and discard the rest.
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Mrs. Wu uses a 25% off coupon to buy 1 adult ticket and 1 child ticket to a movie. She pays a total amount of $9.00. A child ticket without the coupon costs $4.00. Write an equation that can be used to find the cost of an adult ticket, x, without the coupon.
Answer:
$9 = (1-25%) * (x + 4)
Step-by-step explanation:
$9 = (1-25%) * (x + 4)
aspen has 306 306306 green beads and 210 210210 silver beads. for every 5 cm 5cm5, start text, c, m, end text of a belt that aspen sews, they use 40 4040 green beads and 24 2424 silver beads. after how many centimeters of the belt will aspen have equal numbers of green and silver beads left?
After 30 cm of the belt sewn, Aspen will have equal numbers of green and silver beads left.
Aspen has 306 green beads and 210 silver beads.
For every 5 cm of a belt that Aspen sews, they use 40 green beads and 24 silver beads.
We can set up an equation to determine when Aspen will have equal numbers of green and silver beads left.
Let x be the number of centimeters of the belt Aspen will have sewn when they have equal numbers of green and silver beads left.
We can use the following equation:
306 - (40/5)x = 210 - (24/5)x
Solving for x, we get:
x = (306-210)/(40/5-24/5) = (96)/(16/5) = 96*5/16 = 30 cm
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Alan Louden deposits $615.00 in a savings account. The account pays an annual interest rate of 5%. He makes no other deposits and withdrawals. After 3 months, the interest is calculated. How much simple interest did his money earn?
Answer:
The interest earned on the account would be $30.75. (6150.053/12=30.75)
Step-by-step explanation:
a certain museum has five visitors in two minutes on average. let a poisson random variable denote the number of visitors per minute to this museum. find the probability that this museum gets at least three visitors in a minute (round off to second decimal place).
The exact probability that this museum gets at least 3 visitors in a minute is approximately 0.224
A Poisson distribution is a probability distribution that models the number of times an event occurs within a given time or space, if these events are rare and independently of the time since the last event. The Poisson distribution is characterized by the mean number of occurrences λ in a given interval.
In this case, the mean number of visitors per minute is λ = 5 visitors / 2 minutes = 2.5 visitors per minute.
We can use the Poisson probability mass function to find the probability that this museum gets at least 3 visitors in a minute.
To find the probability that this museum gets at least 3 visitors in a minute by using:
1 - P(X < 3)
Where X is the number of visitors in a minute and 3 is the lower limit of the number of visitors we want to include in the sample.
Thus, P(X>=3) = 1 - P(X < 3) = 1 - 0.776 = 0.224
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Find the proportion relating the side lengths of smaller quadrilateral to the lager quadrilateral
The ratio of the lengths of the smaller quadrilateral to the larger quadrilateral will be 4:5.
What is a quadrilateral?The quadrilateral has four sides and four angles. The sum of internal angles is 360 degrees.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The quadrilateral MLKJ is similar to the quadrilateral ABCD. Then the ratio of the lengths of the smaller quadrilateral to the larger quadrilateral will be given as,
Ratio = 12 / 15
Ratio = 4/5
The ratio of the lengths of the smaller quadrilateral to the larger quadrilateral will be 4:5.
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The radius of a circle is 8 cm. Find its area to the nearest whole number.
Answer: 50.24 or 50
Step-by-step explanation:
the radius is half of a circle so the diameter is 16, the formula for area is diameter x pi
pi= 3.14
16 x 3.14 =50.24
A team of 9 dodgeball players needs to choose
The function that would be needed for the team of dodgeball players to choose a co - captain and a captain would be a permutation.
When is a permutation needed ?The techniques used to determine how many outcomes are conceivable in certain circumstances are permutation and combination. Combinations and permutations are referred to as selections and arrangements, respectively. The sum rules and product rules, which are based on the basic concept of counting, make counting simple to use.
When an order or sequence of arrangement is required, permutations are used. There is an order that needs to be used here and that order is that a captain is picked to have more authority than a captain.
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The full question is:
Permutation, combination, or neither? A team of 9 dodgeball players needs to choose a co-captain and captain.
If C = G - 3F, find the trinomanial that represents C when F = 2x^2+6x-5 and G = 3x^2+4
The trinomial expression that represents C is
C = -3x² - 18x + 19
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
C = G - 3F ______(1)
F = 2x² + 6x - 5
G = 3x² + 4
Substituting F and G in (1)
C = 3x² + 4 - 3(2x² + 6x - 5)
C = 3x² + 4 - 6x² - 18x + 15
C = -3x² - 18x + 19
Thus,
The trinomial expression is
C = -3x² - 18x + 19
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The outside tempature dropped 20°F from the time arianna ate breakfast until the time she ate dinner. When she ate dinner the tempature was 35°F. Write and solve an equation to find the outside tempature t when arianna ate breakfast
The outside temperature t when Arianna ate breakfast was 55°F.
An equation is a mathematical statement showing that two expressions are equal. It is written with an equal sign (=) between two expressions, with one expression on the left side of the equal sign, and the other expression on the right side.
According to the given statements-
Let the outside temperature at the time of breakfast be t°F.
The temperature dropped by 20°F by the time of dinner.
So the temperature at the time of breakfast = t - 20
Also, when she ate dinner the temperature was 35°F
So the equation for outside temperature t when Arianna ate breakfast will be -
t - 20 = 35
Simplifying we get,
t = 35 + 20
t = 55°F
Hence, the outside temperature t when Arianna ate breakfast was 55°F.
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Tell whether the lines are "parallel", "perpendicular", or "neither. " 3x – 2y = –15 2x + 3y = –15
Equation of the two lines 3x – 2y = –15 , 2x + 3y = –15 are perpendicular to each other.
Equation of the two different lines are :
3x – 2y = –15
2x + 3y = –15
Convert both the equation into slope intercept form :
y = mx + c
Where 'm' represents the slope of the line and 'c' represents the y- intercept.
Equation of first line
3x – 2y = –15
⇒ 2y = 3x + 15
⇒ y = 3/2x + 15/2
Here slope 'm₁ ' is equal to 3/2.
2x + 3y = –15
⇒ 3y = -2x -15
⇒ y = -2/3x - 5
here slope 'm₂ ' is equal to -2/3
For parallel lines slope should be equal.
here m₁ ≠ m₂
Not parallel lines.
For perpendicular lines :
m₁ × m₂ = -1
Here , (3/2 ) × ( -2/3 ) = -1
Lines are perpendicular to each other.
Therefore, the product of the slope is equal to -1 lines are perpendicular to each other.
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If y varies directly as x and x = 33 when y = 22, find x when y = 32.
The value of x when y is 32 is 21.3
How to determine the value of x?From the question, we have the following parameters that can be used in our computation:
y varies directly as x
This means that
Y/X = y/x
From the question, we have the following values
x = 33 when y = 22
So, we have
33/22 = y/x
When x = 32, we have
33/22 = 32/x
Solve for x
x = 22 * 32/33
Evaluate
x = 21.3
Hence, the value of x is 21.3
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Find the component form of the um of u and v with direction angle u and v.
Magnitude
u = 14
Angle
u = 45°
Magnitude
v = 70
Angle
v = 180°
(14cos45° + 70cos180°, 14sin45° + 70sin180°) = (17.9, -55.1) is the component form of the sum of u and v with direction angles u and v.
What's an angle?The amount of rotation that occurs between two planes or straight lines is what is meant to be meant by the geometrical term "angle." A full circle is 360 degrees, and an angle is measured in degrees. Right angles (90 degrees), acute angles (less than 90 degrees), and obtuse angles (more than 90 degrees) are the most prevalent types of angles. Depending on how they relate to one another, angles can also be broken down into complementary or supplementary categories. The sum of complementary and supplementary angles is 90 degrees, while the sum of the two is 180 degrees.
Component form :The vector addition formula can be used to determine the component form of the sum of u and v. According to this formula, the direction angle of the vector sum is equal to the arctangent of the ratio of the sum of the y-components of the two vectors to the sum of the x-components of the two vectors, while the magnitude of the vector sum of two vectors is equal to the square root of the sum of the squares of each vector's magnitude.
The component form of the sum of the given vectors u and v is as follows:
Magnitude = √(14²) + (70²)) = 70.45
The direction angle is arctan((14 × sin(45) + 70×sin(180)) / (14×cos(45) + 70×cos(180)))
= 153.43°
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g the speed limit on certain interstate highways is 75 miles per hour. (a) what is this in feet per second? ft/s (b) how many kilometers per hour is this? km/h
(a) The speed in feet per second is 110 feet per second.
(b) The speed in kilometers per hour is 120.75 kilometers per hour
The speed limit on certain interstate highways, s = 75 miles per hour
a) We have to find the speed in feet per second.
1 mile = 5280 feet
75 miles = 75 x 5280
75 miles = 396,000 feet
s = 396,000 feet/hour
s = 39600/3600 feet/second
s = 110 feet per second
b) We have to find the speed in kilometers per hour.
1 mile = 1.61 km
75 miles = 75 x 1.61
75 miles = 120.75 km
s = 120.75 kilometers per hour
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suppose you own a swimming pool with dimensions 4.93 m x 9.69 m x 1.75 m. what is the volume of your pool in gallons?
22084.78 gallons is the volume of your pool.
Any rectangular solid's volume, V, is equal to the sum of its dimensions, height, width, and depth. In terms of the area of the base, we might alternatively express the formula for a rectangular solid's volume. The base's surface area, B, is equal to its length x width.
Dimensions of the pool = 4.93 m x 9.69 m x 1.75 m
Volume = 4.93 x 9.69 x 1.75
= 83.6 cubic meter
1 cubic meter = 264.172 gallons
83.6 cubic meter = 83.6 x 264.172
= 22084.78 gallons
Hence, 22084.78 gallons is the volume of your pool.
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Sam has some water in a jug. He pours all of this water into a second jug. Use the ruler tool to draw the correct level of water on the second jug
By using the ruler tool to draw the correct level of water on the second jug, the measurement of water is observed to be 500 ml or half litre.
The capacity and shapes of both the given jugs are different.
The first jug is measured in terms of millilitres and second jug is measured in terms of lites.
It is given that water is poured from one jug into the other. The measurement of the water level on both the jugs will be the same.
From the conversion of measurements, we know, 1 litre = 1000 millilitres
On the second jug into which water is poured, the first measurement line is 0.25 L. The second bigger line is 0.5 L.
The water level is observed to be till the second line in the second jug. Thus, the water on second jug is 0.5 L or 500 ml.
The question is incomplete. The complete question has the picture of two jugs. It is attached in the attachment below.
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S. Maya is spending money at the average rate of $3 per day. After 14 days she has $68 left. The amount left depends on the number of days that have passed. Hint: Is spending money a positive or negative.
1. Write an equation for the situation.
B. Use your equation to find out when she will have $35 left.
C. How much money does Maya have after 9 days?
C. How much money does Maya have after 9 days?
E. Explain what the slope and y-intercept represent for this problem
a) The slope equation representing Maya's spending situation is x - 3n = 68, where x is the initial amount Maya has and n is the number of days she has spent her money.
b) Using the above equation, after 25 days, Maya will have $35 left.
c) Using the above equation, after 9 days, Maya will have $83 left.
d) The slope is the average rate Maya spends per day, which is $3 while the y-intercept represents the initial amount she has.
What is a slope equation?A slope equation is written in the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Maya's average spending rate per day = $3
The number of days Maya has spent money = 14 days
The amount left after 14 days = $68
Let the initial amount Maya has = x and the number of days she has spent her money = n
Equation:a) x - 3n = 68
x = 68 + 3n
x = 68 + 3(14)
x = 68 + 42
x = 110
= $110
b) 110 - 3n = 35
-3n = -75
n = 25
c) 110 - 3(9)
= 110 - 27
= 83
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if two distinct members of the set $\{ 2, 4, 12, 14, 21, 28, 98 \}$ are randomly selected and multiplied, what is the probability that the product is a multiple of 196? express your answer as a common fraction.
The probability that the numbers are selected and multiplied to be a multiple of 196 is 1/3.
196 is the multiple we require.We list the components of 196, which are 14*14=2*7*2*7.
Therefore, the required numbers that will be present in any product must have at least these as its factors.So, we choose 98 now, and it's possible that all it takes to achieve 196 is to multiply that by 2. Therefore, if we take 98 as one of our numbers, the other numbers that must be multiplied are 2,4,12,14,28. That makes 5 pairs necessary.
So, we choose 98 now, and it's possible that all it takes to achieve 196 is to multiply that by 2. Therefore, if we take 98 as one of our numbers, the other numbers that must be multiplied are 2,4,12,14,28. That makes 5 pairs necessary. We can now take pairings like (21,28) and (14,28) based on the prime factorization (14,28).
The total number of possible pairs is ⁷C₂ = 21
Therefore, the required probability =7/21=1/3
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Please help me solve this. I don’t understand it at all. Please explain and give me the answers please and thank you
The Pythagorean Theorem states that the square of the lengths of the two sides of a right triangle adds to the square of the length of the hypotenuse.
How do you prove Pythagorean triples?The Pythagorean Theorem states that a ² +b ² =c ² for a right-angled triangle ABC, right-angled at B. The whole integers a, b, and c form a Pythagorean triple if a and b are the lengths of the two sides of a right-angled triangle with hypotenuse c.
Draw a BD that is perpendicular to AC and meets at D. So, the Pythagorean theorem is established. Recall that the Pythagorean Theorem only applies to right-angled triangles. Two even numbers and one odd number, or all odd numbers, cannot form a Pythagorean triple. The square of an odd number is an odd number, and the square of an even number is an even number, hence this is true. A, B, and C are the three positive integers, and the Pythagorean triples are written as a ² +b ² =c ².
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Mike drew a four sided figure with four right angles. It is 4 cm long and 3 cm wide. What type of figure did Mike draw?
The figure drawn by Mike is rectangle according to the angles and dimensions.
As the statement mentioned, the sides are at 90° degree or perpendicular to each other. It is seen in only two figures, which are square and rectangle. The square has all the sides equal whole rectangle has opposite sides equal.
As the length and width is different in the figure, the opposite sides signifying length and width will be equal. Therefore, opposite sides will be equal in the figure and hence it will be rectangle.
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