Answer:
g(-1) = 1
Step-by-step explanation:
We can substitute x = -1 into g(x) to find g(-1).
g(-1) = (-1)³ + 6(-1)² + 12(-1) + 8 = -1 + 6 - 12 + 8 = 1
Answer:
g(-1) = 1
Step-by-step explanation:
Given polynomial:
g(x) = x³+6x²+12x+8Evaluating x = -1 on the given polynomial,we obtain
g(-1) = -1³ + 6(-1)² +12(-1) + 8Simplifying using PEMDAS,
g(-1) = -1*-1*-1 + 6(-1*-1) + 12(-1) + 8g(-1) = -1 + 6*1 + (-12) + 8g(-1) = -1 + 6 -12 + 8g(-1) = 5 - 4g(-1) = 1Hence,the function's value is 1.
Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−6, −6), B(6, 6), C(0, 6). Determine the scale factor used.
2
one half
3
one third
Answer:
the scale factor is 2
Step-by-step explanation:
Take each x and y value and multiply it by 2 and you get the coordinates for the image.
Helping in the name of Jesus.
The scale factor is 2. Point B goes from (3,3) to (6,6). 6/3 is 2. Similar triangles have the same shape and the three angles' measurements are likewise the same.
Their sides are the only thing that differs. The scale factor, which is what is referred to here as this, is the ratio of one triangle's sides to those of another triangle. To calculate the scale factor for the smaller triangle to the bigger triangle, divide one of the sides in the bigger triangle by its corresponding side in the smaller triangle. In the example, the scale factor would be 2 if you divided 40 by 20.
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If f(x) = 5x +40, what is (fx) when x =-5?
a -9
a -8
c 7
d 15
Answer:
D.
Step-by-step explanation:
f(x) = 5x+40
f(-5) = 5(-5)+40
f(-5) = -25+40
f(-5) = 15
The quadrilateral below is a rhombus. Find the missing measures. Any decimal answers should be rounded to the nearest tenth.
NK =
m
NL =
m
ML =
m
JM =
m
m
A rhombus with MK = 24 m, JL = 20, ∠MJL = 50°. So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.
We need the information about the measurements or a description of the missing measures in the rhombus. We can make it MK = 24 m, JL = 20, ∠MJL = 50° for example. Since it's a rhombus, all sides are equal in length. Therefore, NK = MK = 24 m, JM = JL = 20 m, and ML = NL.
To find ML (or NL), we can use the Law of Cosines on the triangle MJL. In this case,
ML² = JM² + JL² - 2(JM)(JL)cos(∠MJL):
ML² = 20² + 20² - 2(20)(20)cos(50°)
ML² = 400 + 400 - 800cos(50°)
ML² ≈ 617.4
Taking the square root of both sides, we get ML ≈ √617.4 ≈ 24.8 m.
So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.
The complete question is The quadrilateral below is a rhombus. Given MK = 24 m, JL = 20, ∠MJL = 50°. Find NK, NL, ML, and JM. Any decimal answers should be rounded to the nearest tenth.
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what property is being used in 2a+5a=(2+5)a
Answer:
distributive property
A line is perpendicular to y = -x-2
and intersects the point (-5, 10).
What is the equation of this
perpendicular line?
y = x + [?]
The equation of the perpendicular line is y = x + 15.
How to determine the equation of the perpendicular line
In this problem we need to determine the equation of the line perpendicular to another line, that intersects at the point (x, y) = (- 5, 10). The explicit form of the equation of the line is defined by the following first order polynomial:
y = m · x + b
Where:
m - Slopeb - y-Interceptx - Independent variabley - Dependent variableThe first line has a slope - 1 and the slope of the second line is:
m' = - 1 / m
m' = 1
Then, the intercept of the second line is:
b = y - m · x
b = 10 - (- 5)
b = 15
The equation of the perpendicular line is y = x + 15.
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what is the average rate of change for f(x)+2^x+2 over interval −1 ≤ x ≤ 1
Answer:
adsefrthgfdsfgd
Step-by-step explanation:
Armando kicks a football into the air. The function f(x) = -6x to the power of 2 + 36x +.23 models the height of the football from the ground, in feet, with respect to the time x in seconds. Use a graph or table to estimate the time for the ball to return to the ground after being kicked.
Thus, the total time to reach the ball at ground after being kicked is 6 seconds.
Define about the quadratic function:The maximum value or minimum value of a quadratic function are located at its vertex, which is shaped like a U. The quadratic function's axis of symmetry crosses the function (a parabola) at its vertex.
This graph's opening side plus vertex determine the quadratic function's range. To ascertain the quadratic function's range, locate the lowest and highest f(x) values on the function graph.
Standard form for quadratic function:
f(x) = ax² + bx + c,
In which, a, b, and c - real numbers and a ≠ 0.
Given function for the which explain the height of ball with time:
f(x) = -6x² + 36x + 0.23
f(x) is the height of ball taken from ground.
x is the time in seconds.
Draw the graph of the function using the graphing tool.
The diagram is attached.
The vertex of the graph lies at (3, 54.23).
x - 3 seconds
f(x) = 54.23 ft
So, time taken by ball to reach at height of 54.23 ft is 3 seconds.
Total time to reach the ball at ground = 2*3 = 6 seconds
Thus, the total time to reach the ball at ground after being kicked is 6 seconds.
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Find the integer that exceeds –5 by the same amount that 13 exceeds –1. \
Answer:
7
Step-by-step explanation:
13 exceeds - 1 by - 1 + 13 = 12, then
- 5 + 12 = 7
Answer:
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
13 exceeds - 1 by - 1 + 13 = 12, then
- 5 + 12 = 7
grams per cubic centimeter to kilograms per cubic meter
Grams per cubic centimeter to kilograms per cubic meter is 1000.
1 g/cm³ = 1000 1 kg/m³
How to convert from g/cm³ to kg/m³?The conversion value:
1 gram = 1/1000 kg1 cm³ = 1/1000000 m³Find the conversion from grams per cubic centimeter to kilograms per cubic meter!
Grams per cubic centimeter = g/cm³Kilograms per cubic meter = kg/m³Multiply the number with the each conversion value!
See that the cubic centimeter is as a denominator. So, we reverse the fractional value.
1 g/cm³
= 1 × 1/1000 × 1000000/1 kg/m³
= 1000 kg/m³
Hence, the conversion value from grams per cubic centimeter to kilograms per cubic meter is 1000.
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pedro has determined that the probability his shot will score in a lacrosse game is 0.30. what is the probability that he will score on two consecutive shots? a) 0.09. b) 0.15. c) 0.30. d) 0.60.
The probability that Pedro will score on two consecutive shots is option a) 0.09.
The probability of two independent events occurring together is the product of their individual probabilities. In this case, the probability of scoring on two consecutive shots is the product of the probability of scoring on the first shot and the probability of scoring on the second shot.
To determine the probability that Pedro will score on two consecutive shots in a lacrosse game, you can use the following formula:
Probability of two consecutive scores = Probability of first score × Probability of second score
Pedro's probability of scoring on a single shot is 0.30. Therefore:
Probability of two consecutive scores = 0.30 × 0.30 = 0.09
So, the correct answer is a) 0.09.
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Find the measure of the given angles. Show work!!
Given:
The figure of a right angle triangle.
To find:
The value of x and measures of all angles of the triangle.
Solution:
According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees.
Using angle sum property, we get
\((x+60)^\circ+(x+50)^\circ+90^\circ=180^\circ\)
\((2x+200)^\circ=180^\circ\)
\((2x)^\circ=180^\circ-200^\circ\)
\((2x)^\circ=-20^\circ\)
It can be written as
\((2x)=-20\)
Divide both sides by 2.
\(x=-10\)
The value of x is -10.
Now,
\(m\angle A=x+50\)
\(m\angle A=-10+50\)
\(m\angle A=40\)
And,
\(m\angle B=x+60\)
\(m\angle B=-10+60\)
\(m\angle B=50\)
Therefore, the value of x is -10, measure of angle A is 40 degrees and measure of angle B is 50 degrees.
3.) Make up a word problem for this expression. 3(8a + 5c + 6e)
Answer: A math teacher writes 3(8a + 5c + 6e) on the board and asks her students to simplify the expression. If a student has values of a = 2, c = 3, and e = 4, what is the result of simplifying the expression?
Step-by-step explanation:
the weights (in pounds) of three adult males are 160, 215, and 195. what is the standard error of the mean for these data?
The standard error of the mean for these data is 13.14 pounds..
The standard error of the mean (SEM) is a measure of the variability of the sample mean. It is calculated as the standard deviation of the sample divided by the square root of the sample size.
To find the SEM for the given data, we first need to calculate the sample mean:
(160 + 215 + 195) / 3 = 190
Then we need to calculate the deviation of each value from the mean:
160 - 190 = -30
215 - 190 = 25
195 - 190= 5
Next, we need to square these deviations:
(-30)² = 900
25² = 625
5² = 25
Next, we need to calculate the variance:
(900 + 625 + 25) / 3 = 516 2/3
Then we need to calculate the standard deviation:
√(516 2/3) = 22.73
Finally, we can calculate the standard error of the mean:
22.73 / √(3) = 13.14
So, the standard error of the mean for these data is 13.14 pounds.
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3.30. let x, y ∈ z. prove that x − y is even if and only if x and y are of the same parity
x - y is even if and only if x and y have the same parity.
To prove that x - y is even if and only if x and y have the same parity, we will show that:
1. If x and y have the same parity, then x - y is even.
2. If x - y is even, then x and y have the same parity.
1. If x and y have the same parity, then they are either both even or both odd. Let's consider these two cases:
a. If x and y are both even, then x = 2m and y = 2n (for integers m and n). In this case, x - y = 2m - 2n = 2(m - n), which is also even (since m - n is an integer).
b. If x and y are both odd, then x = 2m + 1 and y = 2n + 1 (for integers m and n). In this case, x - y = (2m + 1) - (2n + 1) = 2m - 2n = 2(m - n), which is even (since m - n is an integer).
2. If x - y is even, then x - y = 2k (for some integer k). Now we will show that x and y must have the same parity:
a. If x is even (x = 2m), then y = x - 2k = 2m - 2k = 2(m - k), which is also even. So x and y are both even.
b. If x is odd (x = 2m + 1), then y = x - 2k = (2m + 1) - 2k = 2(m - k) + 1, which is odd. So x and y are both odd.
- y is even if and only if x and y have the same parity.
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??????????????????????????
Answer:
D
Step-by-step explanation:
A)
3(2) + 4(-2) = -2 2(2)-4(-2) = -8
6 - 8 = -2 4 + 8 = -8
Correct Incorrect
B)
3(6) + 4(-5) = -2 2(6) - 4(-5) = -8
18 - 20 = -2 12 + 20 = -8
Correct incorrect
C)
3(4) + 4(4) = -2
12 + 8 = -2
incorrect
D)
3(-2) + 4(1) =-2 2(-2) - 4(1) = -8
-6 + 4 = -2 -4 - 4 = -8
Correct Correct
Best way is process of elimination
A security car is parked 25 ft from a movie theater. Find at what speed the reflection of the security strobe lights is moving along the wall of the movie theater when the reflection is 30 ft from the car. The strobe lights are rotating with the speed 2 revolutions per second.
Answer:
v=20π ft/s
Step-by-step explanation:
Given:
Distance from the security car to the movie theater, D=25 ft
Distance of the reflection from the car, d=30 ft
Speed of rotation of the strobe lights, 2 rev/s
To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.
We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.
ω=2πf
=> ω=2π(2)
=> ω=4π rad/s
The distance between the security car and the reflection on the wall of the theater is...
r=30-25= 5 ft
The speed of reflection is given as (this is the linear velocity)...
v=ωr
Plug our know values into the equation.
v=ωr
=> v=(4π)(5)
∴ v=20π ft/s
Thus, the problem is solved.
The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.
To solve this problem, we can use the concept of related rates. Let's consider the following variables:
x: Distance between the security car and the movie theater wall
y: Distance between the reflection of the security strobe lights and the security car
θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights
We are given:
x = 25 ft (constant)
y = 30 ft (changing)
θ = 2 revolutions per second (constant)
We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.
Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:
x^2 + y^2 = z^2
Differentiating both sides of the equation with respect to time (t), we get:
2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)
Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.
Plugging in the known values, we have:
2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)
Simplifying the equation, we find:
60(dy/dt) = 120π
Dividing both sides by 60, we get:
dy/dt = 2π ft/s
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Please please help please please ASAP
The floor of a room with dimensions 16 by 12 is covered with square tiles, each of length 0.32. How many of such tiles will be needed to cover one third of the room?
Answer:
625 tiles
Step-by-step explanation:
According to the scenario, computation of the given data are as follows,
Total room floor area = 16 × 12 = 192
So, area of one third room = 192 × (1 ÷ 3)
Area of one third room = 64
Length of each tiles = 0.32
As it is a square tile, width = length, = 0.32
o, total area of each tile = 0.32 × 0.32 = 0.1024
So, number of tiles to cover 64 area of room = 64 ÷ 0.1024 = 625 tiles.
Hence, 625 tiles needed to cover one third of room.
Determine+the+percentile+indicating+the+bottom+ranking+20%.+in+other+words,+what+is+the+dollar+number+that+defines+where+the+lowest+values+fall.
The dollar number that defines where the lowest values falls is
20% percentile value =$20
This is further explained below.
What is the dollar number that defines where the lowest value falls?Generally, Now we need to determine the 20th percentile ($20). It indicates that we need to locate a dollar amount that marks the point at which the 20 % data has a value lower than that number.
i=(p/100)*n
Where i is the position of p^th
percentile when the data is presented in ascending order.
i=20/100*50
i=1000/100
i=10
Therefore
n=50
p=20
In conclusion, the 10th position for given data is 20,
Therefore, 20% percentile value =$20
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Use the function f(x) = 2x3 -3x2 + 7 to complete the exercises
f(-1) =
f(1) =
f(2) =
Answer:
f(-1) = 8f(1) = 6f(2) = 11Step-by-step explanation:
Given the function
f(x) = 2x³ -3x²+ 7
putting x=-1 to find f(-1)
f(-1) = 2(-1)³ -3(-1)²+ 7
= -2 + 3 + 7
= 8
putting x=1 to find f(1)
f(1) = 2(1)³ -3(1)²+ 7
= 2 - 3 + 7
= 6
putting x=2 to find f(2)
f(2) = 2(2)³ -3(2)²+ 7
= 16 - 12 + 7
= 11
Therefore,
f(-1) = 8f(1) = 6f(2) = 11confirm that the expected counts are large enough to use a chi-square distribution to calculate the p-value. what degrees of freedom should you use?
The expected counts are large enough to use a chi-square distribution to calculate the p-value because the predicted-counts are at least 5, the degree-of-freedom that should be used is 2.
The "degree-of-freedom" is defined as the number of independent parameters or variables that must be specified to completely describe a system or equation.
We see that the projected counts(expected-counts) are large enough to use a chi-square distribution if all predicted counts are at least 5,
So, This condition is satisfied and it satisfies that the expected counts are large enough to use a chi-square distribution to calculate the p-value.
In the table we see that the number of categories are three : {Red, Black, Green},
So, degree of freedom is = (number of categories) - 1 = 3 - 1 = 2.
Therefore, the degree of freedom is 2.
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The given question is incomplete, the complete question is
Confirm that the expected counts are large enough to use a chi-square distribution to calculate the p-value. The information table is given below.
What degrees of freedom should you use?
Consider the case in which the proportionality constant C is equal to 1/2. Plot the graph of y=1/2x. How would you graph?
To graph the equation y = (1/2)x, we can plot points on a coordinate plane and connect them to create a straight line. Here's how to do it:
1. Choose some x-values to evaluate the equation. Let's select a range of x-values, such as -10, -5, 0, 5, and 10.
2. Substitute each x-value into the equation to find the corresponding y-values. For example:
- For x = -10, y = (1/2)(-10) = -5
- For x = -5, y = (1/2)(-5) = -2.5
- For x = 0, y = (1/2)(0) = 0
- For x = 5, y = (1/2)(5) = 2.5
- For x = 10, y = (1/2)(10) = 5
3. Plot the points (x, y) on a graph. In this case, the points would be:
(-10, -5), (-5, -2.5), (0, 0), (5, 2.5), (10, 5)
4. Connect the plotted points with a straight line. The line should pass through all the points.
The resulting graph is a straight line with a slope of 1/2, passing through the origin (0, 0), and extending infinitely in both directions.
Here is a rough sketch of the graph:
```
|
6 | .
| .
5 | .
| .
4 | .
|
3 | .
|
2 | .
|
1 | .
|
0 -----------------------
-10 -5 0 5 10
```
Note: The above graph is a visual representation and may not be to scale. The line should pass through the plotted points accurately.
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What is the approximate area of a circle show below?
Answer:
b) 2827
Step-by-step explanation:
Pi*30(squared)=2827m
how do i solve this problem
The solution to the problem is the simplified expression: 5x³ - x² - 3x + 13.
To solve the given problem, you need to simplify and combine like terms. Start by adding the coefficients of the same degree terms.
(3x³ - x² + 4) + (2x³ - 3x + 9)
Combine the like terms:
(3x³ + 2x³) + (-x²) + (-3x) + (4 + 9)
Simplify further:
5x³ - x² - 3x + 13
In this expression, the highest power of x is ³, and the corresponding coefficient is 5. The term -x² represents the square term, -3x represents the linear term, and 13 is the constant term. The simplified expression does not have any like terms left to combine, so this is the final solution.
Remember to check for any specific instructions or constraints given in the problem, such as factoring or finding the roots, to ensure you address all requirements.
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Write
17
−
1
12
in surd form.
Answer:exact form: decimal form=
70082
Explanation=Write in radical form: exact form: decimal form: ...
Answer: exact form: decimal form: ...
Answer:
(Theres not much of a way for me to type the answer, so i added it into a png. hope it helps!)
Which number line represents the solutions to |x – 2| = 6? A number line from negative 10 to 10 in increments of 1. Two points, one at negative 8 and one at 4. A number line from negative 10 to 10 in increments of 1. Two points, one at 4 and one at 8. A number line from negative 10 to 10 in increments of 1. Two points, one at negative 2 and one at 6. A number line from negative 10 to 10 in increments of 1. Two points, one at negative 4 and one at 8.
Answer:
x = 8 or x = -4, i.e., the last number line
Step-by-step explanation:
|x – 2| = 6 translates to
x-2 = 6 or x-2 = -6 if you eliminate the absolute operation. So there are two solutions that you can solve independently:
x-2 = 6 => x = 8
x-2 = -6 => x = -4
Answer:
d
Step-by-step explanation:
just got it right :)
Express the solution using interval notation
The solution to the inequality 5/w > 4/45, using interval notation, is given as follows:
(-∞, 56.25).
How to obtain the interval notation?The inequality for this problem is defined as follows:
5/w > 4/45.
Applying cross multiplication, we have that the solution can be obtained as follows:
4w < 45 x 5
w < 45 x 5/4
w < 56.25.
The solution is found similarly to an equality, isolating the desired variable, and finding the desired range of values.
The solution w < 56.25 is composed by values to the left of x = 56.25 on the number line, that is, values between negative infinity and 56.25, hence the interval is given as follows:
(-∞, 56.25).
Missing InformationThe problem is incomplete, hence it was adapted to show the solution to an inequality, and then written in interval notation.
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A shoemaker sold a pair of for $245.99 if the buyer a $300.00 bill, how much will the buyer receive in change?
*two decimal places don't forget your $ sign. Example: $50.00 NOT 50*
Answer:
$54.01
Step-by-step explanation:
All you have to do is $300.00-$245.99 .
all I need is the percentages for 7 and 9 please help my brain isn't doing what it's supposed to
Answer:
Number 7 the answer when rounded to the nearest hundredth is 5.88%
Number 9 the answer is 43.333 repeating.
Step-by-step explanation:
To find the percent of boys that preferred the Beatles, we need to find the total amount of boys who voted. We can see it is 34. To find the percent, we do 2/34 which is equal to 0.05882352941. This as a percent is 5.88% rounded.
To find the amount of girls surveyed from the total, we find the total surveyed and do 26/60. This is equal to 0.4333333 repeating. This is equal to 43.33333% repeating.
#YourWelcome.
Noah's score is represented by x. Mai scores three times as many points as Noah. Which expression represents Mai score
Ox+3
Ox-3
Ox+3
Answer:
it's 3x
the statement says Mai scores three times as many points as Noah...which means Mai scored Noah's points multiplied by 3
3×x
=3x