For this tangent line approximation question, my answer is D. 4. Is my work correct?
f(x) = f(a) + (x - a)f'(a)
a = -0.5
x = 0
f(0) = 2 + 0.5(4) = 4
Answers
If you wanted, you can simplify the linear approximation L(x)
L(x) = f(a) + (x-a)*f'(a)
L(x) = f(-0.5) + (x-(-0.5))*f'(-0.5)
L(x) = 2 + (x+0.5)*4
L(x) = 2+4x+2
L(x) = 4x+4
Then plug in x = 0
L(x) = 4x+4
L(0) = 4(0)+4
L(0) = 4
But your method is a shorter route.
Related Questions
When the polynomial is written in standard form, what are the values of the leading coefficient and the constant? 5x + 2 - 3x^2
Answers
Constant = 2
When you order them in standard form, you need to put them in ascending order of the exponents. Therefore the -3x^2 would come first, which makes the number attached (-3) the lead coefficient.
Also, since the number (2) without an x attached would be last (due to the power of x technically being 0), than that is the constant.
The equation of a circle is x2+y2-6y+1=0 what are the coordintes of the center and the length of the radius
Answers
The coordinates of the centre will be ( 0,3) and the length of the radius is equal to 2√2.
What is a circle?The circle is defined as the locus of the point traces around a fixed point called the centre and is equidistant from the out trace.
The general form of the equation of the circle is given as:-
( x - h )² + ( y - k )² = r²
We have an equation:-
x² + y² - 6y + 1 = 0
x² + y² - 6y + 9 - 9 + 1 = 0
( x - 0 )² + ( y - 3 )² = 8
By comparing the equation from the standard form we will get the centre ( 0,3) and the radius r = 2√2.
Therefore the coordinates of the centre will be ( 0,3) and the length of the radius is equal to 2√2.
To know more about circle follow
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An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 4 cm long. A second side of the triangle is 7.4 cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter. A. 44.4 cm, 11.1 cm B. 44.4 cm, 3.2 cm C. 11.1 cm, 4.9 cm D. 24 cm, 4.9 cm
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Simplify: 8x - 4(2x - 5) - 2
Answers
[tex]8x - 8x + 20 - 2 \\ = 18[/tex]
Hope this helps. - M
Need this geometry answer quick!
(I think its answer c but not sure)
Answers
angle B =50
angle C = 130
Sarah is hiking on a trail near her home. She traveled 5 miles before stopping for a break. After the break, Sarah plans on increasing her speed to 3 miles per hour. Which equation models the total distance, D, Sarah travels after hiking for an additional h hours?
A. D = 3h + 5
B. D = 3(h - 5)
C. D = 3h - 5
D. D = 5h + 3
Answers
Answer: A. [tex]D=3h+5[/tex]
Step-by-step explanation:
Given: The rate of increasing speed = 3 miles per hour
The distance she traveled before stopping = 5 miles
Let h represents the number of additional hours for hiking.
Then the equation that models the total distance 'D' Sarah travels after hiking for an additional h hours is given by :-
[tex]D=3h+5[/tex]
Can somone help me with this 1 problem? In the figure shown, △RST is an isosceles triangle with RS≅RT. Which is the measure of ∠T?
A.21°
B.40°
C.70°
D.110°
Answers
Based on your information, T and S are congruent. So we know that the measure of angle T is 3x+7. But we need to solve for x. Let's add all the angle values together and set it to 180 because the angles of a triangle sum to 180.
1) 2(3x+7) + 2x - 2 = 180
2) 6x + 14 + 2x - 2 = 180
3) 8x + 12 = 180
4) 8x = 168
5) x = 21
6) m<T = 3x + 7 = 3(21) + 7 = 63 + 7 = 70
I got C, but it is always helpful to double check work. Hope this helps!
In an isosceles triangle, base angles are congruent, meaning ∠R would equal ∠T. However, no angle measures are provided, making it impossible to determine the measure of ∠T with the given information.
Explanation:The given figure is an isosceles triangle, triangle RST, where RS is congruent to RT. In an isosceles triangle, the base angles are congruent, meaning that they have the same measure. Therefore, if we know the measure of one of the base angles, we know the measure of the other. The problem, however, does not provide the measures for any of the angles. This makes determining the measure of ∠T impossible with the given information. We would need to know either the measure of angle R or S or the measure of the angle at the vertex, angle T, to find the measure of ∠T. Without additional information, we cannot definitively choose between options A, B, C, or D.
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The trapezoids are similar. the area of the smaller trapezoid is 131 m2. find the area of the larger trapezoid to the nearest whole number. (1 point)
Answers
A ball is rolling in a circular path that has a radius of 10 inches as shown in
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we know that
[circumference]=2*pi*r
for r=10 in
[circumference]=2*pi*10-----> 62.8 in
if 360° (full circle) has a length of --------> 62.8 in
54°------------------------------> X
x=54*62.8/360-----> x=9.42 in
the answer is 9.42 in
12q^2-17q-7
A. (3q+1)(4q-7)
B. (3q-1)(4q+7)
C. (3q+7)(4q-1)
D. (3q-7)(4q+1)
Answers
A bakery has 49 donuts and 28 muffins for sale. What is the ratio of muffins to donuts? Please answer ASAP 99 Points :V
Answers
In a ratio, the first thing or item mentioned is first in the ratio. Let the muffins stand for x, and the donuts stand for y. It asks for the ratio of muffins to donuts.
x:y
Plug in the numbers.
28:49
Both numbers are divisible by 7.
28/7= 4 49/7=7
4:7 <=== simplified ratio
I hope this helps!
~kaikers
Donuts: 49
Muffins to donuts: 28/49
Answer = 28/49 = 4/8 = 1/2
~Hope this helped~
Solve the system of equations using the substitution method.
{2x+8y=4 x=−3y+5
Enter your answers in the boxes.
Answers
I believe the answer is (14,-3)
have a great day & good luck!
Which is the first step in drawing a line graph?
A. Plot a point for each piece of data.
B. Draw x- and y-axes on graph paper.
C. Create a scale that covers the data range.
D. Draw a line of best fit to show a trend.
Answers
Answer:
B) Draw x- & y-axes on graph paper.
Step-by-step explanation:
You need a graph before you can create your line.
The area of a rectangle is represented by the expression 6x^3y^5. Which of the following could be the dimensions of the rectangle?
2xy^2 and 3x^2y^3
2xy^2 and 4x^2y^3
2x^3y and 3y^4
2x^3y and 3xy^4
Answers
Answer:a&c
Step-by-step explanation:
The Freshman class has 27 more boys than girls. If there are 283 freshman, how many are girls?
Answers
283 = x + (x + 27)
Here, we are adding the number of girls with 27 more people than this amount of girls. This will allow us to add the number of girls, x, with the number of boys, x + 27, to get a total of 283.
This equation can be simplified if we add the like terms together: the x's.
So,
283 = 2x + 27.
Since this is a multi-step equation, we must use the reversed order of operations; undo addition first.
283 - 27 = 2x + 27 - 27
256 = 2x + 0
256 = 2x
Now, we must undo multiplication by dividing.
256/2 = 2x/2
128 = 1x
So, x, the number of girls, is equal to 128.
Hope this helps you! :)
If it costs $7.50 to park, how much will the stadium make from parking 10,600 vehicles?
Answers
Simple interest is calculated on the principal in an account using the formula I=prt. How much simple interest does $3,500.00 earn in 6 months at an annual interest rate of 2.5%?
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HELP ASAP WILL GIVE BRAINLIEST
Answers
I mean it could also be viewed as if they intersect at every point so I'm sorry if its wrong (the M is slightly above the N so it should be parallel)
Its perpendicular if it only intersected at one point- 1 solution
If it intersects at every point- infinitely many solutions
The lines are parallel because they are side by side and have the same distance continuously between them. Please give me brainliest because I need one more to turn Virtuoso
Given the system of inequalities below: -3x - y < 12 and 2x + 3y ≥ 9
Answers
y(less than or equal to)-2/3x+9
You bought 12 one-gallon bottles of apple and orange juice for a school dance. the apple juice was on sale for $1.00 per one-gallon bottle. the orange juice was $1.75 per one-gallon bottle. you spend $15.00. how many bottles of each type of juice did you buy?
Answers
x: bottles of apple juice
y: bottles of orange juice
We write the system of equations:
x + y = 12
1x + 1.75y = 15
Solving the system of equations we have:
x = 8
y = 4
Answer:
you did buy:
8 bottles of apple juice
4 bottles of orange juice
Consider this system of linear equations:
22x − y = -23 (equation 1)
11x + 12y = 1 (equation 2)
Answers
1. You have the folllowing system of equations given in the problem above:
22x − y = -23 (equation 1)
11x + 12y = 1 (equation 2)
2. If you multiply the equation 2 by -2, and then sum the equation 1+equation 2, you obtain:
-25y=-25
y=1
3. Then, you must substitute y=1 into the equation 1, then you have:
x=-1
4. As you can see, when you solve it, the solutions are:
x=-1
y=1
22x − y = -23
-
(11x + 12y = 1) *2
22x − y = -23
-
22x + 24y = 2
0 -25y = -25
y = 1
22x - 1 = -23
x = 1
x2+y2-4+2y-11=0 what are the center and radius of the circle?
Answers
You need to complete the square for both x and y.
[tex] x^2 - 4x + y^2 + 2y = 11 [/tex]
[tex] x^2 - 4x + 4 + y^2 + 2y + 1 = 11 + 4 + 1 [/tex]
[tex] (x - 2)^2 + (y + 1)^2 = 16 [/tex]
[tex] (x - 2)^2 + (y + 1)^2 = 4^2 [/tex]
The center is (2, -1).
The radius is 4.
A house on a floor plan is 10.5 inches long and 6.5 inches wide. If the scale used is 0.5 inch = 2 ft, how long is the actual house?
Answers
1. You have the following information given in the problem above:
- The house on the plan is 10.5 inches long and 6.5 inches wide.
- The scale used is 0.5 inch=2 ft
2. Therefore, you have:
0.5 inch-------2 feet
10.5 inches--x
x=10.5x2/0.5
x=42 feet
Therefore, the answer is: 42 feet long.
Help! Thanks in advance!
Screenshotted question!
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
T.A. =
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Please, see the attached file.
Thanks.
Answer:
Step-by-step explanation:
This is probably easy but I'm not smart and don't know what else to do I know this is the correct formula it's just confusing to me because there're three numbers and I'm just really dumb.
Answers
Right side rectangle = 4 × 1 = 4
Left side rectangle = 4 × 1 = 4
Both triangles = 4 × 3 = 12
Both triangles = 6
3 + 4 + 4 + 12 = 23
I think the answer is 23 cm
Hope this helped☺☺
Area of a right triangular prism = 1/2(2B) + Ph
The 1/2 and 2 cancel each other out: B + Ph.
Base of the triangular prism: 3 × 4 = 12 cm²
Perimeter of the base (use the Pythagorean Theorem →a² + b² = c²← to figure out the missing side; hypotenuse): 3² + 4² = c²
9 + 16 = c²
√25 = 5
3 + 4 + 5 = 12 cm
Height of triangular prism: 1 cm
Plug these numbers into the formula (B + Ph):
(12 + 12×1) = 24 cm²
The area of the right triangular prism is 24 cm².
Andy currently runs a total of 12 miles each week. He plans to increase the number of miles he runs each week by 1.5 miles untill he is running a total of 26 miles each week. How many weeks will it take Andy to reach his goal?
Answers
26 = 1.5n + 12
14 = 1.5n
It will take 9.333 weeks for andy to reach 26 miles, so at 10 weeks he will be running more than 26.
Four girls and eight boys are running for president or vice president of the student council. find each probability: find the prbability that two girls are elected
Answers
The probability that a girl is elected for one office is 4/12, since there are 4 girls out of 12 students.
The probability that a girl is elected for the second office is 3/11. This is because after one girl is elected, there are 3 girls left out of 11 students left.
Together, this gives us
4/12(3/11) = 12/132 = 1/11
The probability that two girls are elected president and vice president from a group of 4 girls and 8 boys is calculated using a hypergeometric distribution, resulting in a probability of 1/11.
The question is asking for the probability that two girls are elected president and vice president of the student council when there are four girls and eight boys running for these positions. This is an example of a hypergeometric distribution problem, as we are selecting without replacement from a finite population divided into two groups.
To find the probability, we need to determine the number of successful outcomes divided by the total number of possible outcomes. The successful outcome is that the two elected individuals are both girls. Since there are 4 girls, there are 4 choose 2 ways to select 2 girls, which equates to 6 possible successful outcomes. The total number of ways to choose 2 individuals from 12 candidates (4 girls + 8 boys) is 12 choose 2, resulting in 66 possible outcomes.
The probability can be calculated by dividing the number of successful outcomes by the total number of possible outcomes.
Probability = Successful outcomes / Total outcomes = 6 / 66 = 1 / 11
TIMED, need the answer ASAP, will give brainiest
Answers
A silo is constructed using a cylinder with a hemisphere on top. The circumference of the hemisphere and the circumference of the cylinder are equal. The diameter of the circular base of the cylinder is 10 feet. The cylinder is 40 feet tall. One of the circular bases on the cylinder is in contact with the ground. What is the area of the surface of the silo that will be exposed to rain, wind, and sun?
Answers
The area of the surface of the silo that will be exposed to rain, wind, and sun is 450π square feet.
Explanation:Solution:
To find the area of the surface of the silo that will be exposed to rain, wind, and sun, we need to find the combined surface area of the hemisphere and the cylinder.
The radius of the circular base of the cylinder is half of its diameter, which is 10/2 = 5 feet.The height of the cylinder is 40 feet.The circumference of both the hemisphere and the cylinder is equal, so the circumference of the circular base of the cylinder is 2πr, where r is the radius of the base.The surface area of the hemisphere is equal to half of the surface area of a sphere with the same radius, which is 2πr²/2 = πr².The surface area of the circular base of the cylinder is πr².The surface area of the curved surface of the cylinder is the circumference of the base multiplied by the height of the cylinder, which is 2πr * 40.Now, let's calculate:
Surface area of the hemisphere = π(5)^2 = 25π square feetSurface area of the circular base of the cylinder = π(5)^2 = 25π square feetSurface area of the curved surface of the cylinder = 2π(5) * 40 = 400π square feetTo find the total surface area, we add up the surface areas of the hemisphere, the circular base, and the curved surface:
Total surface area = Surface area of hemisphere + Surface area of circular base + Surface area of curved surface = 25π + 25π + 400π = 450π square feet.
Therefore, the area of the surface of the silo that will be exposed to rain, wind, and sun is 450π square feet.