Answer: To find the equation of the tangent line to a function at a specific point, we can use the following steps:
Find the derivative of the function f(x) = 3x3 − x2 + 2
f'(x) = 9x^2 - 2x
Substitute the point a = 0 into the derivative to find the slope of the tangent line at that point
f'(0) = 9(0)^2 - 2(0) = 0
Use the point-slope form of a linear equation, y - y1 = m(x - x1) to find the equation of the tangent line, where m is the slope and (x1, y1) is the point at which the tangent line touches the function.
y - f(a) = m(x - a)
y - (3*0^3 - 0^2 + 2) = 0(x - 0)
y - 2 = 0
So the equation of the tangent line to the function f(x) = 3x3 − x2 + 2 at a = 0 is:
y = 2
Therefore, the correct answer is A. y = 2
Step-by-step explanation:
Determine whether the following graph represents y as a function of x. If it does, explain why and estimate the domain and range. If it does not, explain why, describe a portion of the graph that could be removed to turn it into a function, and estimate the domain and range of the result.
The graph does not represent y as a function of x, as each value of x is mapped to two outputs.
The portion that could be removed to make it a function is given as follows:
y < 0.
Hence the domain and the range are given as follows:
-3 ≤ x ≤ 3.0 ≤ y ≤ 3.When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
On the circle, a vertical line through the circle would cross the line twice, meaning that each input is mapped to two outputs, hence the relation is not a function.
We have to remove one of the outputs for the relation to be a function, hence, removing y < 0, the domain and the range are given as follows:
-3 ≤ x ≤ 3. -> values of x.0 ≤ y ≤ 3. -> values of y.More can be learned about relations and functions at brainly.com/question/10283950
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A triangle was dilated by a scale factor of 6. if sin a° = four fifths and segment de measures 30 units, how long is segment ef? triangle def in which angle f is a right angle, angle d measures a degrees, and angle e measures b degrees segment ef = 15.5 units segment ef = 24 units segment ef = 30 units segment ef = 37.5 units
The triangle DEF's section EF measures 24 units in length.
As per the data given in the above question are as bellow,
The provided details are as follow,
Procedure: Calculating the length that results from distorting a triangle by a scale factor
The triangle mentioned in the previous sentence is summarised in the diagram below. Using a trigonometric relationship, we discover that the following formula best describes the length of the section EF:
[tex]$\sin a^{\circ}=\frac{E F}{D E}$[/tex]
If we know that DE=30 and [tex]$\sin a^{\circ}=\frac{4}{5}$[/tex], then the length of the segment EF is:
[tex]E F=D E \cdot \sin a^{\circ} \\& E F=30 \cdot\left(\frac{4}{5}\right) \\[/tex]
EF=24
Sine (sin), cosine (cos), and tangent (tan), which are defined in terms of the ratios of the sides of a right triangle, are the fundamental trigonometric functions.
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Note: The correct question would be as bellow,
A triangle was dilated by a scale factor of 6. If sin a° = four fifths and segment DE measures 30 units, how long is segment EF?triangle DEF in which angle F is a right angle, angle D measures a degrees, and angle E measures b degrees
15.5 units
24 units
30 units
37.5 units
What is the length of the line segment joining the points (-1, 4) and (2 , -5)?
a. 3√2
b. 3√10
c. √2
d. √10
Answer:
b
Step-by-step explanation:
calculate the length using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 1, 4 ) and (x₂, y₂ ) = (2, - 5 )
d = [tex]\sqrt{(2-(-1))^2+(-5-4)^2}[/tex]
= [tex]\sqrt{(2+1)^2+(-9)^2}[/tex]
= [tex]\sqrt{3^2+81}[/tex]
= [tex]\sqrt{9+81}[/tex]
= [tex]\sqrt{90}[/tex]
= [tex]\sqrt{9(10)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{10}[/tex]
= 3[tex]\sqrt{10}[/tex]
Pls help I’m so stuck
By evaluating the given equation, we will see that they made 1,524 dollars by selling tickets.
What was the total ticket sales?We know that each adult ticket costs $12 and each student ticket costs $9, then the expression for the total cost is:
c(a, b) = 12a + 9s
Where a is the number of adults and s is the number of students.
Here we know that there where 64 adults and 84 students, so the total cost will be:
c(64, 84) = 12*64 + 9*84 = 1,524
They made $1,524 by selling tickets.
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Which shows how to find 35% of 25 using mental maths?
Only possible answers:
2.5 + 2.5 + 2.5 + 1.25 = 8.75
.25 + .25 + .25 + .25 = 1
3.5 + 3.5 + 3.5 + .35 = 10.85
3.5 + 3.5 + 3.5 + 3.5 = 14
The option that shows how to find 35% of 25 using mental maths is A. 2.5 + 2.5 + 2.5 + 1.25 = 8.75
How to calculate the value?In Mathematics, a percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
In this case, it should be noted that 35% of 25 will be:
= 35% × 25
= 0.35 × 25
= 8.75
Using mental mathematics, the correct option that shows this is A.
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Maggie brought $10 to the candy store. She will buy a certain amount of fudge. One pound of fudge costs $2.30. If p represents the amount of fudge, in pounds, Maggie buys, which expression
Answer: $10=2.30p
Step-by-step explanation:
Solve the system of equations using elimination.The graph shows the solution to a system of inequalities:
Solid line joining ordered pairs 0, 3 and 7, 0. Shade the portion of the graph below the line in the first and fourth quadrants.
Which of the following inequalities is modeled by the graph?
2x + 5y ≥ 14; x ≥ 0
2x + 5y ≤ 14; x ≥ 0
2x − 5y ≤ 14; x ≥ 0
−2x − 5y ≤ 14; x ≥ 0
The inequality that is modeled by the graph is 2x + 5y ≥ 14; x ≥ 0
This inequality corresponds to the solid line that passes through the ordered pairs (0,3) and (7,0). The line has a slope of -2/5, and it can be written in the form y = (-2/5)x + b, where b is the y-intercept, and it can be calculated as b = (5/2)x + 14. The shading is below the line and in the first and fourth quadrants, which corresponds to the inequality 2x + 5y ≥ 14; x ≥ 0.
The other inequalities provided in the options do not correspond to the graph:
2x + 5y ≤ 14; x ≥ 0, the shading is above the line
2x − 5y ≤ 14; x ≥ 0, the slope is positive and the shading is above the line
−2x − 5y ≤ 14; x ≥ 0, the slope is positive and the shading is above the line
So, the inequality that is modeled by the graph is 2x + 5y ≥ 14; x ≥ 0
In a right triangle, sin (8x - 9)° = cos (x+6)°. Solve for x. Round your answer to the nearest hundredth if necessary.
To solve the triangle, or identify unknown portions in terms of known portions, we can apply the Pythagorean theorem and the properties of sines, cosines, and tangents. The x is 8 .
Find value of x ?To solve the triangle, or identify unknown portions in terms of known portions, we can apply the Pythagorean theorem and the properties of sines, cosines, and tangents.
Pythagorean theorem: a2 + b2 = c2.
Sine: sin A=a/c, sin B=b/c.
Cosines: cos A = b/c, cos B = a/c.
Identity based on trigonometry
cos x sin (90-x)
therefore, if we have
(4x plus 10) o = Cos (6x)
(4x plus 10) o = Sin (90- 6x)
4x + 10 = 90 - 6x
4x+6x = 90 - 10
10x = 80
x = 80/10
x = 8
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Antonio's toy boat is bobbing in the water under a dock. The vertical distance
�
HH (in
cm
cmstart text, c, m, end text) between the dock and the top of the boat's mast
�
tt seconds after its first peak is modeled by the following function. Here,
�
tt is entered in radians.
�
(
�
)
=
5
cos
(
2
�
3
�
)
−
35.5
H(t)=5cos(
3
2π
t)−35.5H, left parenthesis, t, right parenthesis, equals, 5, cosine, left parenthesis, start fraction, 2, pi, divided by, 3, end fraction, t, right parenthesis, minus, 35, point, 5
How long does it take the toy boat to bob down from its peak to a height of
−
35
cm
−35 cmminus, 35, start text, space, c, m, end text?
Answer: To find the time it takes for the toy boat to bob down from its peak to a height of -35 cm, we need to find the value of t when H(t) = -35.
So, we can substitute -35 for H(t) in the given equation:
5 cos (2π/3t) - 35.5 = -35
Now we can solve for t by isolating it on one side of the equation:
5 cos (2π/3t) = 0.5
cos (2π/3t) = 0.1
2π/3t = cos^-1(0.1)
3t = 2π * cos^-1(0.1)/π
t = 2 * cos^-1(0.1)
The time it takes for the toy boat to bob down from its peak to a height of -35 cm is approximately 2 * cos^-1(0.1) seconds.
Step-by-step explanation:
Use the line on the graph to write an equation that represents the function.
Question 3 (2 points)
Lauren deposited $300 to start her savings account. After one year, she had $312 in
her account. If she did not deposit or withdraw any money that year, how much
interest did she earn?
A
She earned $12 at 4% interest rate. The solution has been obtained by using simple interest.
What is simple interest?
Simple interest is the cost of borrowing that is computed using the original principal amount alone and a constant interest rate.
We are given that Lauren deposited $300 to start her savings account and after one year, she had $312 in her account.
This means that the difference between both the amounts is the interest because it is mentioned that she did not deposit or withdraw any money that year.
So, the interest is $12.
The rate of interest is found using simple interest
⇒S = p*r*t
⇒12 = 300*r*1
⇒0.04 = r
This means that interest rate is 4%.
Hence, she earned $12 at 4% interest rate.
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Find the area of the circle. Round to the nearest tenth. Use 3.14 or 22/7 for π.
The area of a circle is 158.3 sq. m.
Consider we need to find the area of the given circle.
The radius of a circle is 7.1 m.
The area of a circle is the place occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the circumference of a circle is called the area of the circle.
The area of the circle is:
[tex]A = \pi r^{2}[/tex] , where r is the circle's radius.
Putting r = 7.1 , π = 3.14, we get
[tex]A = 3.14 *(7.1)^{2}[/tex]
A = 158.2874
A ≈ 158.3
So, the area of a circle is 158.3 sq. m.
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What is the value of x in this triangle?
Enter your answer in the box.
Answer: 39*
Step-by-step explanation:
102+39= 141
180-141=39
Answer:
x = 39°
Step-by-step explanation:
We know that,
→ Sum of sides of triangle = 180°
Forming the equation,
→ 39° + 102° + x = 180°
Now the value of x will be,
→ 39° + 102° + x = 180°
→ 141° + x = 180°
→ x = 180° - 141°
→ [ x = 39° ]
Hence, the value of x is 39°.
can some1 help me with this pls
Answer:
b
Step-by-step explanation:
Open up the second bracket by changing all signs to the opposite
2a²-3ab+5b² -a²+2ab-3b²
=a²-ab+2b²
1. List five different vocabulary words that could be used to describe each given expression.
a-d+c
The five different vocabulary words that could be used to describe the expression are
SummationAlgebraBinaryLinearCombinationHow to determine the vocabulary wordsFrom the question, we have the following parameters that can be used in our computation:
a-d+c
Using the above as a guide, the vocabulary words and the meanings are as follows
Sum: The expression "a-d+c" involves adding the values of a, c and subtracting the value of d, which is a mathematical operation called "sum".Algebraic and Combination: The expression "a-d+c" is a combination of variables and mathematical operations, which falls under the category of Algebraic.Binary: The expression "a-d+c" contains two mathematical operations, subtraction, and addition, and it is called a binary expression.Linear: The expression "a-d+c" is linear since it only contains variables and constants, and it doesn't have any exponents or roots.Read more about expression at
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what is 7x-21=11x-73
Answer:
[tex]7x - 21 = 11x - 73 \\ \dashrightarrow \: 11x - 7x = 73 - 21 \\ \dashrightarrow \: 4x = 52 \\ \ \: \: \: \: dividing \: both \: sides \: by \: 4 \\ \dashrightarrow \: \cancel \frac{4x}{4} = \cancel \frac{52}{4} \\ \\ \dashrightarrow \: \: \boxed{ x = 13}[/tex]
hope helpful :)
Two friends, Jacob and Ariana, took summer jobs. The equation y = 16. 5 x y=16. 5x represents Jacob's earnings in dollars and cents, y y, for working x x hours. Ariana earned $708 in 24 hours. How much more does Ariana earn per hour than Jacob?
Ariana earned $708 in 24 hours, so $312 more Ariana earn per hour than Jacob.
We have to find how much more Ariana earn per hour than Jacob.
The equation y = 16.5x represents Jacob's earnings in dollars and cents, y, for working x hours.
Ariana earned $708 in 24 hours.
So the value of x = 24
Now putting the value of x in equation y = 16.5x
y = 16.5 × 24
y = 396
Jacob's earnings = $396
Difference between the Ariana earning and Jacob earning = $708 - $396
Difference between the Ariana earning and Jacob earning = $312
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help thank you :)
You are beautiful. Don't let anyone tell you different<3
Answer:
11/20
Step-by-step explanation:
Add 1/5 and 1/4. You get 9/20.
Subtract that from 1 and you get 11/20 :)
Answer:
11/20
Step-by-step explanation:
1/5+1/4
4/20+5/20= 9/20
20/20-9/20=11/20
Triangle ABC has vertices A(-1, 10), B(2, 1),
and C(-4, 1). What are the coordinates of
the centroid of the triangle?
The coordinates of the centroid of triangle ABC are given as follows:
(-1, 4).
How to obtain the coordinates of the centroid of the triangle?The coordinates of the centroid of a triangle are obtained finding the mean of the coordinates of the three vertices of the triangle.
This means that the x-coordinate of the centroid of triangle ABC is given as follows:
(-1 + 2 - 4)/3 = -1.
(mean of the x-coordinates of each of the three vertices).
The y-coordinate of the centroid of triangle ABC is given as follows:
(10 + 1 + 1)/2 = 4.
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the numberline shows the temperatures at 2:00 AM. and 2:00 P.M. in the Gobi Desert. Find and interpret the distance between the points?
2:00am -13F 2:00pm 38F
Answer:
There is a difference of 51 degrees
Step-by-step explanation:
-13 to zero is 13 degrees
zero to 38 degrees is 38 degrees
13 + 38 is an increase of 51 degrees
What is 2 to the 43000000th power
Step-by-step explanation:
so much sorry about that
Answer: 2^43000000 (the answer is impossibly large)
x+2x-15 somebody solve this right now and quickly please
Answer:
3(x-5)
Step-by-step explanation:
Answer:
3(x - 5)
Step-by-step explanation:
Make terms..
x + 2x - 15 =
3x - 15
Now lets find a common factor of them..
3x - 15
3(x - 5)
Thus,
3(x - 5), Is your answer
Diana say that the qadrillatral in the right is a rhombus Melissa says the qadrillatral left is a rhombus
Diana and Melissa are correct based on the description of the rhombus's appearance. Option C. is correct.
Moving from the details to the fact to make judgements is known as inductive reasoning. Inferential reasoning, which involves moving from known facts to precise conclusions, is typically used to determine it.
A parallelogram's special case is the rhombus.
In a rhombus, the opposing sides and angles are parallel and equal.
The sides of a rhombus are all the same length, while the diagonals are split at right angles. The rhombus is frequently referred to as a diamond or rhombus.
It can be inferred that Melissa and Diana are correct to claim that the image is a rhombus from the description of rhombus attributes.
The given question is incomplete. The complete question is 'Who is correct?
An image shows two quadrilaterals. They are facing different directions, but each of them has two pairs of opposite sides that are parallel and equal in length.
A. Diana is correct. Only the quadrilateral on the right has two pairs of parallel sides and all sides the same length.
B. Melissa is correct. Only the quadrilateral on the left has two pairs of parallel sides and all sides the same length.
C. Both are correct. Both quadrilaterals have two pairs of parallel sides and all sides the same length.
D. Neither is correct. Neither figure has all sides the same length.'
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How many solutions does the equation 6x + 12 = 2(3x + 6) have? Explain.
Answer: No solution
Step-by-step explanation:
6x + 12 = 2(3x + 6)
Expand the right side:
6x + 12 = 6x + 6
Subtract 6x from both sides:
12 = 6
This is obviously not true, so there are no solutions to this equation :>
Please I need help!!!!!!! As Lily files her taxes, she learns that her federal total tax due ends up being $206. According to her Federal income tax withheld, how much of a tax refund can she expect back?
A. $206. 00
B. $874. 50
C. $1,080. 50
D. $13,369. 50
If the federal income tax withheld is $1080.50 and the federal total tax is $206 , then the tax refund that she expect back is (b) $874.50 .
The Lilly's federal total tax is = $206 ;
the federal income tax withheld is = $1080.50 ;
The amount of the refund is the difference between the federal income tax withheld and federal total tax .
So , the refund is = (federal income tax withheld) - (federal total tax) ;
Substituting the values ,
we get ;
Refund = 1080.50 - 206
= $874.50
Therefore , tax refund that she expect back is $874.50 .
The given question is incomplete , the complete question is
As Lily files her taxes, she learns that her federal total tax due ends up being $206. According to her Federal income tax withheld is $1080.50 , how much of a tax refund can she expect back ?
(a) $206.00
(b) $874.50
(c) $1,080.50
(d) $13,369.50
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Mr. Chi wants to sell his house. The state he lives in charges a 3.5% sales tax on the sale of a house. The county charges a 3.4% sales tax, and the city charges a 1.1% sales tax. If Mr. Chi sells his home for $313,800, what is his total tax bill?
Answer: 32082.2
Step-by-step explanation:
Based on the given conditions, formulate:: 341300 * (2.3% + 4.4% + 2.7%)
Calculate the sum or difference: 341300 * 0.094
Calculate the product or quotient: 32082.2
Step-by-step explanation:
Simplify the square root of 3/8
Provide numerical measures of individuals. The values of a quantitative variable can be added or subtracted and provide meaningful results?
Quantitative variables provide numerical measures that can be added/subtracted with meaningful results.
Discrete variables are quantitative and have a finite or countable number of positive values.
Continuous variables are quantitative and have an infinite number of possible values that are not countable and also measure with some sort of scale that uses numbers.
Qualitative variables allow for the classification of individuals based on some attribute or characteristic and also provide numerical measures of individuals.
Arithmetic operations such as addition and subtraction can be performed on the values of a quantitative variable and will provide meaningful results.
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(a) select one of the pairs of systems and write down its number. (b) for the pair selected, identify each system and state one function of that system. (c) explain how the two systems work together to help maintain homeostasis in an individual.
a. Pair 2 is selected.
b. Respiratory system, its function is to breathe. Digestive system, its function is to break down food into nutrients.
c. The two systems work together by sharing the region of the mouth and upper throat.
First picture in Pair 2 is Respiratory system, which its function is to breathe. Second picture in Pair 2 is Digestive system, which its function is to break down food into nutrients such as carbohydrates, fats and proteins. The respiratory system takes in oxygen from the air, and also gets rid of carbon dioxide. The digestive system absorbs water and nutrients from the food we consume.
How does the respiratory system and the digestive system work together?The respiratory system is mainly used to transport air, whilst the digestive system is used to transport fluids and solids, from water and food we eat. The respiratory and the digestive systems share the area of the mouth and upper throat, in which air, fluids, and solids can be mixed.
The digestive system does homeostasis by ensuring that the stomach area has the right pH balance. The body uses both positive and negative mechanisms to perform homeostasis. If the body detects an imbalance, the other systems work together to counterbalance and restore the right equilibrium.
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Mark charged a battery . Each minute , the percentage of battery’s capacity that was charged increased by 2.5 percent after 17 minutes of charging the battery was 61.5 percent full
how full was the battery when the charging began ??
percent
how long from the time that mark started charging did it take the battery to be fully charged ?
minutes
The initial battery charge was of:
19%.
The time it takes for the battery to be full is of:
32.4 minutes.
What is a linear function?The linear function in slope-intercept format is given as follows:
y = mx + b
In which:
m is the slope, representing the rate of change of the battery change.b is the intercept, representing the initial battery charge.Each minute , the percentage of battery’s capacity that was charged increased by 2.5 percent, hence the slope m is given as follows:
m = 2.5.
Hence:
y = 2.5x + b.
After 17 minutes of charging the battery was 61.5 percent full, hence when x = 17, y = 61.5, and the intercept b is obtained as follows:
61.5 = 2.5(17) + b
b = 61.5 - 2.5 x 17
b = 19.
The battery is fully charged when y = 100, hence the time is obtained as follows:
2.5x + 19 = 100
2.5x = 81
x = 81/2.5
x = 32.4 minutes.
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