The equation of the tangent line to the given curve (which is parallel to line (2x−y+9=0) is y−2x−3=0.
What is the equation of tangent?There are two important elements to finding an equation that defines a tangent line: its slope and its point of contact with a curve.
The equation of the given curve is;
[tex]\rm y=x^2-2x+7[/tex]
On differentiating with respect to x, we get:
dx/dy=2x−2
The equation of the line is;
2x−y+9=0
y=2x+9
The slope of the line =2
If a tangent is parallel to line 2x−y+9=0, then the slope of the tangent is equal to the slope of the line.
Therefore, we have:
2=2x−2
2x=4
x=2
Now, at x=2
y=22−2×2+7=7
Thus, the equation of the tangent passing through (2,7) is given by,
y−7=2(x−2)
y−2x−3=0
Hence, the equation of the tangent line to the given curve (which is parallel to line (2x−y+9=0) is y−2x−3=0.
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Suppose two lines are parallel.
Which of the following statements must be true? Select all that apply.
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Explanation:
Let's go through each answer choice one by one to see if it's true or false.
A) This is true. Parallel lines have equal slopes, but different y intercepts.B) This is true because of the corresponding angles theorem.C) This is false. The statement applies to perpendicular lines, rather than parallel ones.D) This is false in general. The only time it's true is when the consecutive interior angles are 90 degrees each. Otherwise, the statement is false.E) This is true. Let's say we drew any diagonal line we wanted. Now imagine picking a point on that line and shifting it up 5 units. Do this for another point and draw a line through the two separated points. This forms a parallel line. The upper line has been shifted up 5 units compared to the lower line.F) This is false in general. It's only true when both alternate interior angles are 90 degrees each; otherwise, it is false.Write 0.423 as a fraction.
Answer:
= [tex]\frac{0.423}{1}[/tex]
=[tex]\frac{423}{1000}[/tex]
so the answer is 423/1000
Step-by-step explanation:
hope it helps
A store manager wants to estimate the proportion of customers who spend money in this store. How many customers are required for a random sample to obtain a margin of error of at most 0.075 with 80% confidence
The 73 customers who spend money in this store if margin of error of at most 0.075 with 80% confidence.
What is the margin of error(MOE)?It is defined as an error that provides an estimate of the percentage of errors in real statistical data.
The formula for finding the MOE:
[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]
Where Z is the z-score at the confidence interval
s is the standard deviation
n is the number of samples.
We have p = 0.50 MOE = 0.075
Z = 1.282 at 80% confidence from the Z table.
[tex]\rm 0.075 = (1.282)\sqrt{\dfrac{0.50(1-0.50)}{n}}[/tex]
After solving, we get:
n = (0.5)(0.5)/(0.0585)²
n = 73
Thus, the 73 customers who spend money in this store if margin of error of at most 0.075 with 80% confidence.
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The diameter of a basketball is approximately 9 inches. What is its volume? Round your answer to the nearest whole number.
A. 382 in to the 3 power.
B. 38 in to the 3 power.
C. 339 in to the 3 power
D. 3052 in to the 3 power
Step-by-step explanation:
Cost prevents one of the biggest barriers to restaurants offering healthier menu options. Fast-food chains like McDonald's have made their fortune by offering food with a long shelf life, which tends to be less healthy. As pointed out in The New Yorker, even if every restaurant in America decided to drop the fries and embrace kale and watermelon radish salads, the U.S. lacks the agricultural infrastructure to support that kind of dietary shift. Big farm crops like soybeans (for frying oil), corn (for high fructose corn syrup), and grain (livestock feed) receive millions of tax breaks and other government subsidies, making it hard for smaller farms to compete.
PLEASE I NEED FAST
X
Y
Z
find the value of missing variables
Answer:
.................... .
Math question 10 points help….
Answer:
A) [tex]\frac{x}{11} < -21[/tex]
Step-by-step explanation:
Let "a number" be denoted by the variable, x. Set the equation:
"A number divided by 11": x/11
"is less than": <
"-21": -21
Put all the parts together:
"A number divided by 11 is less than -21": x/11 < -21
A) [tex]\frac{x}{11} < -21[/tex] is your answer.
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what is the square root f 12
Answer:
Step-by-step explanation:
3.46410161514
Answer: The answer is 3.46410161514
If the measure of angle B=35 degrees, a=43, and c=19 then find the measure of angle A
Answer: 123.3364311 degrees approximately
Round that value however your teacher instructs.
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Explanation:
Use the law of cosines to find side b
[tex]b^2 = a^2 + c^2 - 2*a*c*\cos(B)\\\\b^2 = 43^2 + 19^2 - 2*43*19*\cos(35)\\\\b^2 \approx 871.5055596\\\\b \approx \sqrt{871.5055596}\\\\b \approx 29.521273\\\\[/tex]
Now use the law of sines to find angle A.
[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\\\\frac{\sin(A)}{43} \approx \frac{\sin(35)}{29.521273}\\\\\sin(A)\approx 43*\frac{\sin(35)}{29.521273}\\\\\sin(A) \approx 0.8354581\\\\A \approx \sin^{-1}(0.8354581) \text{ or } A \approx 180-\sin^{-1}(0.8354581)\\\\A \approx 56.6635689^{\circ} \text{ or } A \approx 123.3364311^{\circ}\\\\[/tex]
Due to the side angle side (SAS) congruence theorem, we know that only one triangle is possible (notice angle B is between sides 'a' and c). This means only one of those values for angle A is possible.
The question is: Which one?
Well if you were to use the converse of the pythagorean theorem, then you'll find that the triangle is obtuse.
For any obtuse triangle, the longest side is always opposite the obtuse angle (aka the angle over 90 degrees). The side a = 43 is the longest side of this particular triangle.
This means angle A must be obtuse and the only possibility is that angle A = 123.3364311 degrees approximately.
Find the inverse of y = 3x - 1.
please help, i need to find the equation please
Answer: [tex]y=\frac{7}{2} x+10[/tex]
Step-by-step explanation:
y=mx+b
b=the y intercept
m=slope
In this graph, the y intercept is 10 so we can substitute b for that.
You find the slope with 2 points on the line.
(2,17) (6,31)
[tex]\frac{31-17}{6-2}[/tex]=[tex]\frac{14}{4}[/tex] which is simplified to [tex]\frac{7}{2}[/tex]
You can substitute m for [tex]\frac{7}{2}[/tex] now and your equation is [tex]y=\frac{7}{2} x+10[/tex]
consider the function: f(x)= 2x(x+3) what would be the best description of f(x)? A:linear function B:quadratic function C:exponential function D:None of the above
Answer:
B) Quadratic Function
Step-by-step explanation:
[tex]f(x)=2x(x+3)=2x^2+6x[/tex], which is a second-degree polynomial, so it is a quadratic function.
Please help me with this it's algebra WILL GIVE BRAINLIEST and 5 points
Answer: Graph C
Step-by-step explanation:
y-2 < -2x+2
y<-2x+4
slope is negative so it goes down. y int is 4.
insert (0, 0) into equation and 0 < 4 is true so shade where the origin is.
Which graph summarizes a set of data using the minimum value, first quartile, median, third quartile, and maximum value? histogram dot plot box plot
Answer:
box plot
Step-by-step explanation:
please help for problems
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PLEASE HELP!
Before you answer:
-No spam (Will be reported)
-No incorrect answers (Will be reported)
-Correct answers and explanations will be mark as BRAINLIEST
Answer:
See below
Step-by-step explanation:
Use the formulae directly
For a cone, with base radius = r and height = h, here are the related formula
[tex]\textrm{Slant height l} = \sqrt{r^2 + h^2}[/tex] (1)
[tex]\textrm{Lateral surface area} = \pi r l[/tex]
[tex]\textrm {Base area} = \pi r^2[/tex]
[tex]\textrm { Total Surface Area SA} = \textrm{Base Area + Lateral Area} = \pi r^2 + \pi rl = \pi r(r + l)[/tex] (2)
[tex]\textrm{Volume V = } (1/3) \pi r^2h[/tex] (3)
Therefore directly plugging in the numbers in the above equations:
Note:
l = slant height in cm
SA = total surface area in sqcm
V = Volume in cubic cm
Figure(a)
r = 4, h = 8
[tex]\textrm{l} = \sqrt{4^2 + 8^2} =\sqrt{80} = 8.944 \\\textrm{SA} = 4\pi(4 + 8.944) = 4\pi(12.944) = 162.66\\\textrm{V} = (1/3)\pi(4^2)(8) = 134.04[/tex]
Figure(b)
r = 7, h =15
[tex]\textrm{l} = \sqrt{7^2 + 15^2} =\sqrt{274} = 16.55[/tex]
[tex]\textrm{SA} = 7\pi(7 + 16.55) = 517.89[/tex]
Figure (c)
r = 5, l = 8
[tex]h = \sqrt{l^2 - r^2} = \sqrt{8^2 - 5^2} = \sqrt{39} = 6.245\\SA = \textrm{SA} = 5\pi(5 + 8) = 204.2\\V = (1/3)\pi(5^2)(6.245) = 163.5[/tex]
Solve the problem and define the variable (50 points)
Answer:
i dont now but i thin it is 5
Step-by-step explanation:
The scale of this map is 1 inch = 50 miles. How many miles is it between Milwaukee and Mackinac Bridge? Assume the distance between the two (Milwaukee and Mackinac Bridge) on the map is 4 inches.
Answer:
200 miles
Explanation:
Here map to actual to scale: 1 inch = 50 miles
On map distance: 4 inchesTo find actual distance, simply multiply map distance by scale factor
Actual Distance : 4 × 50 = 200 miles
helpppp!!!!!!!!!!! i’m so confused
John is traveling at 48 miles per hour and his distance can be written as d = 48t.
How far will John travel if he travels for 5 hours?
The diameter of a circle is 8 inches. What is the circle's circumference? d=8 in Use 3.14 for . inches
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[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
The diameter of a circle is 8 in. What is its circumference?
[tex]\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]
Formula for Circumference:-
[tex]\bigstar\boxed{C=\pi d}}[/tex]
Where
C = Circumferenceπ = pi (we're asked to use 3.14 for pi, so we'll do that)d = diameter (we're given that it's equal to 8 in)Substitute the values:-
[tex]\sf{C=(3.14)(8)}[/tex]
Multiply:-
[tex]\boxed{\sf{C=25.12\:inches}}[/tex]
Good luck.
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Answer:
25.12 inches
Step-by-step explanation:
Given that,
→ Diameter = 8 in
→ Radius (r) = 8/2 = 4 in
→ π = 3.14
Formula we use,
→ 2πr
Then the circle's circumference is,
→ 2πr
→ 2 × 3.14 × 4
→ 2 × 12.56
→ [ 25.12 in ]
Thus, circle's circumference is 25.12 in.
Identify the type of display that would be most appropriate for the description of the given data set. The number of pets in each student's household.
send a screen shot of the whole question so i can help becuase there is no data here to even help you with
Step-by-step explanation:
Answer:
A Bar graph is most appropriate for this example
I NEED HELP FAST!!!
What is the distance between 14,-15 and 10,-7
Answer:
8.94 units
Step-by-step explanation:
Distance formula The distance between two points with coordinates
(14,-15) and (10,-7) round to nearest 100th
¿se puede hacer un triangulo con las siguientes medidas:2cm ,3cm ,10cm? ayudenme es para mañana
Não, não podemos fazer um triângulo com os comprimentos dos lados de 2 cm, 3 cm e 10 cm. Isso ocorre porque a soma de 2+3 < 10. (in english: No, we cannot make a triangle with the side lengths of measurement 2 cm, 3 cm, and 10 cm. This is because sum of 2+3 < 10).
What is triangle inequality theorem?Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
[tex](a+b) > c\\(b+c) > a\\(c+a) > b[/tex]
Now, for this case, the sides given are:
a =2 cm,b = 3 cm,and c = 10 cmBut we see that:
a+ b = 5 cm which is < c which is of 10 cm.
Thus, these lengths don't satisfy the triangle inequality theorem, and therefore, cannot be sides of any triangle.
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Which points are on a graph where y varies directly with x and y = 3 when x = -3
a. (1, 1); (0, 1); (3, 3)
b. (0, 0); (4, 8); (5, 10)
c. (1, 0); (3, 2); (5, 4)
d. (-1, 1); (0, 0); (-5, 5)
A coordinate system is a method of determining the position of points or other geometric components on a manifold. The points which vary are on a graph where y varies directly with x are (-1, 1), (0, 0), and (-5, 5).
What are coordinates?A coordinate system is a method of determining the position of points or other geometric components on a manifold, such as Euclidean space, by using one or more integers, or coordinates.
Given that y varies directly with x, therefore, we can write,
y∝x
y = kx
Also, y=3 and x=-3, therefore, the value of k can be written as,
3=k(-3)
k=-1
Now, the points which vary are on a graph where y varies directly with x are (-1, 1), (0, 0), and (-5, 5).
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Mike is shopping for new clothes.
Answer:
Step-by-step explanation:
this may be a bad question but is negative 7 still a prime number?
Answer:
nope
Step-by-step explanation:
A circle has a radius of 12 ft. What is the area of the sector formed by a central angle measuring (3pi)/4 radians?
Use 3.14 for pi
Can you also show me how to solve it
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{1}{2}\theta r^2~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=12\\ \theta =\frac{3\pi }{4} \end{cases}\implies \begin{array}{llll} A=\cfrac{1}{2}\left( \cfrac{3\pi }{4} \right)(12)^2\implies A=\cfrac{432\pi }{8} \\\\\\ A=54\pi \implies \stackrel{using~\pi =3.14}{A=169.56} \end{array}[/tex]
NEED HELP PLS I WILL GIVE BRAINLIEST
A^2 -b^2 / a +b
Apply the difference of two squares formula to the top :
A^2 - b^2 = (a+b)(a-b)
now you have :
(A+b)(a-b) / a+b = 12
the two (a+ b)’s cancel each other out so you are left with a-b = 12
answer: a-b = 12
what is the oppsite number from -64
Answer:
+64
Step-by-step explanation:
the opposite of a positive number is it's negative version while the opposite of a negative number is it's positive version.
so from the question above, the opposite of -64 is+64
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[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
What is the opposite number from -64?
[tex]\blue{\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]
If a number's negative, its opposite is a positive; if a number's positive, its opposite is a negative.
Since -64 is negative, its opposite is
[tex]\bigstar\sf{64}[/tex]
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8(r+9) What is the answer?
Answer:
8r+72
Step-by-step explanation:
Answer:
8r + 72
Step-by-step explanation:
you multiply 8 by each number(or letter) in the parentheses, so 8 * r is basically 8r, and 8*9 is 72