Answer:
To show that T<0,2> (0,1), we need to evaluate the transformation T at the point (0,1) and check if the result is in the range of T.
T<0,2> (0,1) means that the transformation T takes the point (0,1) in the input space to a point in the output space that has coordinates (0,2).
Let's evaluate T at (0,1):
T<0,2> (0,1) = D3(0,1) + (0,1)
= (0+0, 3+1)
= (0, 4)
The output point (0,4) is not equal to (0,2), which means that T<0,2> (0,1) is false. Therefore, T<0,2> does not map the point (0,1) to (0,2).
To determine if T<0,2> (x,y) = D3 (x,y) is a true statement for any point (x,y), we need to check if the transformation T always equals the function D3.
T<0,2> (x,y) = (x, 3+y)
D3(x,y) = (x,y,3)
Since T and D3 have different ranges (T has a range of R^2 and D3 has a range of R^3), the statement T<0,2> (x,y) = D3(x,y) is not true for any point (x,y).
Therefore, we cannot equate T<0,2> and D3, and the statement T<0,2> (x,y) = D3 (x,y) is false for any point (x,y).
Greatest Common Factor and Factor the following polynomial by grouping ab+8a+2b+16
The greatest common factor (GCF) of the polynomial ab+8a+2b+16 is 2.
To factor the given polynomial ab + 8a + 2b + 16 by grouping, follow these steps:
1. Group the terms in pairs: (ab + 8a) + (2b + 16).
2. Factor out the Greatest Common Factor (GCF) from each group. - For the first group (ab + 8a), the GCF is "a". So, factor out "a" from the group: a(b + 8).
-For the second group (2b + 16), the GCF is "2". So, factor out "2" from the group: 2(b + 8).
3. Notice that both groups have a common factor of (b + 8). So, factor out (b + 8) from the entire expression: (b + 8)(a + 2).
Thus, the factored form of the polynomial ab + 8a + 2b + 16 by grouping is (b + 8)(a + 2).
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Write an equation of the parabola in intercept form that passes through (-18,72) with x-intercepts of -16 and -2
The equation of the parabola in intercept form is y = -6(x+ 16 )(x + 2).
What is Parabola?A parabola is a type of curve that is formed when a point called the focus moves along a straight line called the directrix.
In other words a parabola is defined as the set of all points in a plane that are equidistant to the focus and the directrix.
The shape of a parabola is similar to a U or a V shape, and it can either be open upwards or downwards, depending on the orientation of the curve.
The Intercept form of a parabola is given by
y = a(x - p)(x - q)
Where p and q are the x - coordinates at which the parabola crosses the x-axis (i.e, the x-intercepts).
Here we have
The parabola in intercept form that passes through (-18,72) with x-intercepts of -16 and -2
Let y = a(x-p)(x-q) is the equation of parabola
From the data, x-intercepts p = - 16 and p = -2
=> y = a(x+ 16 )(x + 2) ---- (1)
Given that the parabola passes through (-18, 72)
=> 72 = a(- 18 + 16 )(-8 + 2)
=> 72 = a(-2)(-6)
=> 72 = - 12a
=> a = - 6
Substitute a = -6 in equation (1)
=> y = -6(x+ 16 )(x + 2)
Therefore,
The equation of the parabola in intercept form is y = -6(x+ 16 )(x + 2).
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for a teachers program, 6 items are proposed due to time constraint only 4 items will be approved. how many permutations of 4 items programs are there
There are 360 permutations of 4 item programs for a teacher's program.
A permutation is an arrangement of items in a specific order. To find the number of permutations of 4 items from a set of 6 items, we can use the formula:
nPr = n! / (n-r)!
Where n is the total number of items, r is the number of items we want to choose, and n! is the factorial of n (n * (n-1) * (n-2) * ... * 1).
Plugging in the given values, we get:
6P4 = 6! / (6-4)!
= 6! / 2!
= (6 * 5 * 4 * 3 * 2 * 1) / (2 * 1)
= 720 / 2
= 360
Therefore, there are 360 permutations of 4 item programs for a teacher's program.
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The brain weight of a newborn baby is about 13% of the body weight of the newborn. If a newborn weighs 2,900 grams, about how much does the brain weigh?
Answer:
The brain of the newborn baby has a mass of about 377 grams.
Step-by-step explanation:
Fractions are written as a ratio of two integers. For instance, a/b is a fraction.
Given the following parameters
Body mass = 2900 grams.
If the Brain mass of a newborn baby is about 13% of the mass of the newborn, then the mass of the brain is given as;
mass of brain = 13% of 2900
Mass of brain = 0.13 * 2900
Mass of brain = 377grams
Which of the following ordered pairs satisfies the equation
3x-2y=5?
Please help I will give you 5 stars 20 points and a heart its urgent
b. Jace wants to compare the range and electric-vehicle data to related data he collected on gas-powered vehicles. Choose and make appropriate data displays.
A box and whisker plot is the appropriate display for the data, as it shows the minimum and the maximum value of the data-set, while the range is the difference of the maximum value by the minimum value.
What is shown by the box and whisker plot?From left to right, the five features of the box and whisker plot are listed as follows
Minimum value.Lower quartile.Median.Upper quartile.Maximum value.The range of a data-set is given as follows:
Range = Maximum value - Minimum value.
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Enter the x– coordinate of the solution to this system of equations. 6y = – 4x + 20 2x + 4y = 12 The x– coordinate is
Step-by-step explanation:
4y = - 4x +20 (2x) + 4y = 12
4y = -4x + 40x + 4y = 12
36x = 4y - 4y _12
36 x = 12
÷12
36x ÷ 12 = 12 ÷ 12
3x = 1
÷3
3x ÷ 3 =1
x = 1 over 3
Use P=PV(i1−(1+i)−n)
to determine the monthly payment for a $60,000 loan compounded monthly for 5 years at a 4.0%.
Answer:
$1,111.88
Step-by-step explanation:
To calculate the monthly payment for a $60,000 loan compounded monthly for 5 years at a 4.0% interest rate, we can use the formula:
P = PV(i / (1 - (1 + i)^(-n)))
where:
P = monthly payment
PV = present value or loan amount
i = interest rate per period
n = total number of periods
In this case, the loan amount is $60,000, the interest rate per period is 4.0% / 12 = 0.00333, and the total number of periods is 5 years x 12 months/year = 60 months.
Substituting these values into the formula, we get:
P = 60000(0.00333 / (1 - (1 + 0.00333)^(-60)))
P = $1,111.88 (rounded to the nearest cent)
Therefore, the monthly payment for a $60,000 loan compounded monthly for 5 years at a 4.0% interest rate is $1,111.88.
a trapezoid has a perimeter of 117 cm. the two shortest rides have the sane length. The third side is 12 cm longer than on short ride. The final side is 9cm less than three times one short side. How long is each side of the trapezoid.
write an equation to represent this problem. Solve your equation and write your answer in a complete sentence
Answer: The equation is 117 = 2x + (x + 12) + (3x - 9) The two short sides are 19 cm long, the third side is 31 cm long, and the fourth side is 48 cm long.
Step-by-step explanation:
Let x represent the length of the shortest sides
The equation for the problem is:
117 = 2x + (x + 12) + (3x - 9)
Simplify:
117 = 6x + 3
114 = 6x
19 = x
Plug x in for all the sides:
Short sides = 19 cm
Third side = (19) + 12 = 31 cm
Fourth side = 3(19) - 9 = 57 - 9 = 48 cm
Sentence:
The two short sides are 19 cm long, the third side is 31 cm long, and the fourth side is 48 cm long.
Hope this helps!
Convert the rectangular coordinates to polar coordinates with r > 0 and 0 < θ (-5,0) (r, θ) = (________)
The answer is (r, θ) = (5, π).
To convert the rectangular coordinates (-5,0) to polar coordinates (r, θ) with r > 0 and 0 < θ < 2π, we can use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)
First, we need to find the value of r.
r = √((-5)² + (0)²)
r = √(25 + 0)
r = 5
Next, we need to find the value of θ.
θ = tan⁻¹(0/(-5))
θ = tan⁻¹(0)
θ = 0
However, since we need 0 < θ < 2π and the point (-5,0) is in the second quadrant, we need to add π to our θ value.
θ = 0 + π
θ = π
So, the polar coordinates of the point (-5,0) are (r, θ) = (5, π).
Therefore, the answer is (r, θ) = (5, π).
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For every 8 green marbles, Jen has 9 purple marbles. If she has 72 green marbles, how many purple marbles does she have?
If Jen has 72 green marbles, then she has 81 purple marbles.
If Jen has 8 green marbles for every 9 purple marbles, then the ratio of green marbles to purple marbles is 8:9.
If Jen has 72 green marbles, we can use this ratio to determine how many purple marbles she has.
Let's set up a proportion
8/9 = 72/x
where x is the number of purple marbles Jen has.
To solve for x, we can cross-multiply:
8x = 9 × 72
Multiply the terms
8x = 648
Move 8 to right hand side
x = 648 / 8
Divide the numbers
x = 81
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Help me pleaseeeeeee
The following are the values for the missing measures of x in the set of similar polygons:
1). x = 14
2). x = 9
3). x = 3
4). x = 2.
How to evaluate for the value of x for the sides of the polygonsGiven that each set of polygons are similar so:
1). 4/10 = 5.6/x
x = (5.6 × 10)/4 {cross multiplication}
x = 56/4
x = 14
2). x/18 = 6/12
x = (6 × 18)/12 {cross multiplication}
x = 9
3). x/4 = 4.5/6
x = (4.5 × 4)/6 {cross multiplication}
x = 18/6
x = 3
4). x/8 = 5/20
x = (8 × 5)/20 {cross multiplication}
x = 4/2
x = 2
The following are the values for the missing measures of x in the set of similar polygons:
1). x = 14
2). x = 9
3). x = 3
4). x = 2.
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Please help! I'm being timed!
Answer:1 4/10
Step-by-step explanation:
We can reduce this to lowest terms by dividing the numerator and denominator or 4/10 by 2 to get the equivalent fraction 1 and 2/5
Find the measure of the central angle defined by the arc in radians if the radius is 23 units and the arc length is 23π units.
a. ???? radians
b. 7????/4 radians
c. 5????/4 radians
d. 3????/2 radians
e. None of these are correct.
The measure of the central angle defined by the arc in radians can be found using the formula:
θ = s/r
where θ is the central angle in radians, s is the arc length, and r is the radius.
Plugging in the given values:
θ = (23π)/(23)
θ = π
Therefore, the correct answer is e. None of these are correct, as the measure of the central angle in radians is π.
To get from Boone to Charlotte, you would have to drive about 156.6 km on the shortest route. To get from Boone to Anchorage, AK, you would have to drive 4,212.7 miles. How many orders of magnitude larger is the distance from Boone to Anchorage than Boone to Charlotte? (1 mi = 1.61 km).
Answer: 1.64. To find the difference in orders of magnitude between the two distances, we first need to convert both distances to the same unit of measurement. We'll convert both distances to kilometers.
The distance from Boone to Charlotte is already in kilometers, so we don't need to do any conversion for that distance.
The distance from Boone to Anchorage is in miles, so we'll need to convert that distance to kilometers. To do this, we'll multiply the number of miles by the conversion factor 1.61 km/mi:
4,212.7 mi × 1.61 km/mi = 6,782.45 km
Now that both distances are in kilometers, we can compare them to find the difference in orders of magnitude. An order of magnitude is a factor of 10, so we'll divide the larger distance by the smaller distance and then take the base 10 logarithm of the result:
log10(6,782.45 km / 156.6 km) = log10(43.3) ≈ 1.64
So the distance from Boone to Anchorage is about 1.64 orders of magnitude larger than the distance from Boone to Charlotte.
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Can someone please tell me what x=
Answer: It is and answer that is not known yet
Step-by-step explanation: so 5x5=x x would be 25
Diego’s family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less. Starting from a full tank, can Diego’s family drive the car for 25 days without the warning light coming on? Explain or show your reasoning.
Answer: no
Step-by-step explanation:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
13.4 12.8 12.2 11.6 11 10.4 9.8 9.2 8.6 8 7.4 6.8 6.2 5.6 5 4.4 3.8
18 19 20 21
3.2 2.6 2 1.4
With this table, you can see that Diego and his family would only make it to 21 days before the warning light comes on.
Work out q when r is 45
Answer: 171
Step-by-step explanation:
If r=20 and q=76 and they're directly proportional, multiply r×3.8
20×3.8=76
The multiplication factor is 3.8, so apply it to when r=45
45×3.8=171
Chris makes $16 per hour at his job. He works twice as many hours on the weekend as he does on during the week. He wants to earn at least $500 this week. Weill he meet his goal if he works 11 hours during the week?
Answer:
Step-by-step explanatio
List all the zeros of the polynomial function F(x) = x^4 - 2x^3 - 6x^2 +22x - 15
The zeros of the function are: x = 1, x = -3, and the other two zeros may be irrational or complex.
What are Functions?A function is a mathematical rule that assigns a unique output value for each input value. It is a set of ordered pairs where the first element is the input and the second element is the output.
Using the Rational Root Theorem, the possible rational roots of the polynomial function F(x) = x⁴ - 2x³ - 6x² + 22x - 15 are:
±1, ±3, ±5, ±15
Using synthetic division, we can find that x = 1 and x = -3 are zeros of the function. Therefore, the zeros of the function are:
x = 1, x = -3, and the other two zeros may be irrational or complex.
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what is the answer of square root of 27 to the power of 3
Step-by-step explanation:
For solving this problem, we will use √ab=√a√b. Therefore, the value of 3√27 is 9√3. Note: In the above solution, we factored 27 which is inside the root.
What the pOH of a solution containing [OH-] = 4.91 x
10-11 mol L-1 ?
Report your answer to at least 1 decimal place
The pOH of a solution containing [OH-] = 4.91 x 10-11 mol L-1 is 10.3. We can round the pOH to 10.3.
The pOH of a solution is the negative logarithm of the concentration of hydroxide ions (OH-) in the solution. It can be calculated using the formula:
pOH = -log[OH-]
In this case, the concentration of hydroxide ions is [OH-] = 4.91 x 10-11 mol L-1. Plugging this value into the formula, we get:
pOH = -log(4.91 x 10-11)
Using a calculator, we can find the pOH to be 10.309.
To report the answer to at least 1 decimal place, we can round the pOH to 10.3.
Therefore, the pOH of a solution containing [OH-] = 4.91 x 10-11 mol L-1 is 10.3.
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Carter makes $15.25 per hour at his part time job. He saves (3)/(5) of his earnings. About how many hours will Carter have to work in order to save $300?
Carter will have to work about 33 hours in order to save $300.
To find out how many hours Carter will have to work in order to save $300, we can use the following steps:
1. First, we need to determine how much Carter saves per hour. Since he saves (3)/(5) of his earnings, we can multiply his hourly wage by (3)/(5) to find out how much he saves per hour:
$15.25 * (3)/(5) = $9.15
2. Next, we need to determine how many hours Carter will have to work in order to save $300. To do this, we can divide $300 by the amount he saves per hour:
$300 / $9.15 = 32.79 hours
3. Since Carter can't work a fraction of an hour, we'll round up to the nearest whole hour:
33 hours
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What is the answer to this problem
The required equation of the line in slope-intercept form is y = 2x + 24.
What is the slope-intercept form of a line?To find the slope-intercept form of a line, we need to use the formula: y = mx + b
Where "m" is the slope and "b" is the y-intercept.
Here,
To find the slope of the line passing through the two given points (-2,20) and (-1,22), we can use the slope formula:
m = (y₂ - y₁) / (x₁ - x₁)
where (x₁, y₂) = (-2,20) and (x₁, y₂) = (-1,22).
m = (22 - 20) / (-1 - (-2))
m = 2 / 1
m = 2
Now that we have the slope, we can use one of the given points and the slope to find the y-intercept. Let's use the point (-2,20):
y = mx + b
20 = 2(-2) + b
20 = -4 + b
b = 24
Therefore, the equation of the line in slope-intercept form is y = 2x + 24.
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For the figure at right, determine if the two triangles are congruent. If so, create a proof (flowchart or two-column) to explain why. Then, solve for x. If the triangles are not congruent, explain why not. Homework Help ✎
Answer:
x = 32
Step-by-step explanation:
(41)² - (40)² = 1681 - 1600
= 81
[tex] \sqrt{81} = 9[/tex]
|EC| = 9
x = 41 - 9
x = 32
The 2 triangles share 2 sides of common lengths and a common angle between these sides, therefore they are congruent.
The diagram below shows the graph of h(t), which models the height, in feet, of a rocket t seconds after it was shot into the air 
The domain is the set of all t-value (inputs) used by the function/graph.
The least t-value is 0. The greatest is 4.
The domain is [0,4].
The domain of graph for function h(t) is [0,4].
What is Domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values of a function like f(x) are part of this collection. A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
We have,
a diagram below shows the graph of h(t), which models the height in t seconds.
we know that the domain are the input values.
Here the domain is the set of all t-value used in the graph.
So, from the graph we can see that the least t-value is 0 and the greatest is 4.
Thus, the domain of graph is [0,4].
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Yolanda wants to rent a boat and spend at most $39. The boat costs $7 per hour, and Yolanda has a discount coupon for $3 off. What are the possible numbers of hours Yolanda could rent the boat? Can someone please help me!! ALKES IS A LOT! PLEASE HELP ME!!
Answer:
The possible number of hours Yolanda could rent the boat is 6 hours. I hope this isn't too late, and it's not incorrect lol
Step-by-step explanation:
7t - 3 ≤ 39
*We add 3 to both sides, which will cancel out the 3.*
7t ≤ 42
*We divide 42 by 7 to isolate the variable*
t ≤ 6
The payoff table may be huge, and it would be helpful if we could simplify it. One way is to reject dominated or inadmissible actions. These are choices that should not be made because there are other choices that are always better. More accurately, q, is dominated by 2. if, for all j 1, ...,S, Cij is less than or equal to Caj, and there is at least one value of j such that Cij <0. [...]
You are correct that one way to simplify a payoff table is to reject dominated or inadmissible actions.
This means identifying choices that should not be made because there are other choices that are always better.
To determine if an action q is dominated by another action r, we can compare the payoffs for each state of the world j (from 1 to S) for both actions. If the payoff Cij for action q is less than or equal to the payoff Caj for action r for all j, and there is at least one value of j for which Cij is less than Caj, then action q is dominated by action r.
In other words, if there is another action that always has a higher payoff than action q, regardless of the state of the world, then action q is dominated and should not be chosen.
By rejecting dominated actions, we can simplify the payoff table and focus on the remaining actions that have the potential to provide the highest payoffs. This can help us make more informed decisions and choose the best course of action.
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Solve the quadratic equation x2+8x+30=0 by completing the square.
Answer:
(x + 4)2 = -26 x = -4 ± √26
Step-by-step explanation: x2 + 8x + 30 = 0
x2 + 8x = -30
x2 + 8x + (8/2)2 = -30 + (8/2)2
(x + 4)2 = -22
x + 4 = ±√22
x = -4 ± √22
math sucks lol