ANSWER
A. Right
EXPLANATION
A tangent to a circle touches the circle at only one point.
The point where a tangent and a radius meet at is called the point of tangency.
The tangent to a circle meets the radius of a circle at a right angle.
This is because the angle between the tangent and the radius of the circle is 90°
The correct answer is A.
Final answer:
When a radius and a tangent intersect at the point of tangency, they form a right angle. This fact is part of basic geometric principles covered in high school mathematics.
Explanation:
The type of angle formed when the radius of a circle and a tangent intersect at the point of tangency is a right angle. This geometric principle is a result of the fact that a tangent to a circle is perpendicular to the radius at the point of tangency. This concept falls within the branch of mathematics known as geometry, which is a crucial topic in high school math education.
Need help
Choices
4
3
2
1
Answer:
1
Step-by-step explanation:
The amplitude is the maximum distance away from the middle of the wave. Here we can see that the middle of the wave is the x axis and the farthest point (largest difference between the y coordinate of the x-axis, or the line y = 0, and the wave) is 1 unit away.
Answer:
1
Step-by-step explanation:
Max's T-shirt business uses the demand function P = -Q + 28 and the supply function P = Q - 12. According to these functions, what will the equilibrium point be for Max's T-shirt business?
A. (20,8)
B. (12,28)
C. (8,20)
D. (28,12)
A and c —————- Bc 20 +8 is 28
Answer:
The answer is (8,20) on APEX. just did the test. good luck!
Consider f and c below. f(x, y) = (7 + 8xy2)i + 8x2yj, c is the arc of the hyperbola y = 1/x from (1, 1) to 3, 1 3 (a) find a function f such that f = ∇f. f(x, y) = (b) use part (a) to evaluate c f · dr along the given curve
c.
[tex]\dfrac{\partial f}{\partial x}=7+8xy^2[/tex]
[tex]\dfrac{\partial f}{\partial y}=8x^2y[/tex]
The first equation gives
[tex]f(x,y)=7x+4x^2y^2+g(y)[/tex]
Differentiating with respect to [tex]y[/tex] gives
[tex]8x^2=8x^2y+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=K[/tex]
for some constant [tex]K[/tex]. So
[tex]f(x,y)=7x+4x^2y^2+K[/tex]
and by the fundamental theorem of calculus,
[tex]\displaystyle\int_C\nabla f\cdot\mathrm d\vec r=f\left(3,\frac13\right)-f(1,1)=25-11=\boxed{14}[/tex]
To find a function f such that f = ∇f, we need to find a function whose gradient is equal to itself. The function f(x, y) = 0 is such that ∇f = f. To evaluate c·f · dr along the curve c, we need to find the dot product of the tangent vector to c and the function f.
Explanation:To find a function f such that f = ∇f, we need to find a function whose gradient is equal to itself. Let's start by finding the partial derivative of f with respect to x and y. ∂f/∂x = (7 + 8y2)i + 16xyj and ∂f/∂y = 16xyi + 8x2j. Equating both partial derivatives to f gives us the following equations:
7 + 8y2 = (7 + 8y2)i + 16xyj
8x2 = 16xyi + 8x2j
Simplifying these equations, we find:
i = 0
j = 0
Therefore, the function f(x, y) = 0 is such that ∇f = f.
In order to evaluate c·f · dr along the curve c, we need to find the dot product of the tangent vector to c and the function f. The tangent vector to c is given by dr/dt = (-1/t2, 1/t3). Evaluating f at (x, y) = (1, 1/t) gives us f(1, 1/t) = (7 + 8/t2)i + 8/t2j. Taking the dot product of this with (-1/t2, 1/t3) yields:
c·f · dr = ((7 + 8/t2)(-1/t2) + 8/t2/t3)dt = (-7/t4 + 8/t2/t3)dt = (-7/t4 + 8/t5)dt.
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Which is the factored form of x2(x-2)-3(x-2)?
From the equation, you can see that each value in the equation is multiplied (x - 2)
To get it into factored form, you can just factor out (x - 2) from the equation, and you would be left with:
x²(x - 2) - 3(x - 2)
(x - 2)(x² - 3) Your answer is A
Write an algebraic expression to represent the following verbal expression. the cube of the difference of a number and 43
Answer:
(n - 43)³
Step-by-step explanation:
Let the number be n.
Then the desired expression is (n - 43)³
Answer:
Algebraic expression = (x-43)^3
Step-by-step explanation:
Given , the verbal expression is the cube of the difference of a number and 43.
Let x be the number
Now, according to question
Difference means subtraction in which a number is subtracted from the other number
Difference of a number and 43
It means 43 is subtracted from x
Now , the algebraic expression =x-43
Cube of the difference of a number x and 43 =(x-43)(x-43)(x-43)
Cube of a number means multiply a number three times with self .
Therefore, Cube of the difference of a number x and 43=[tex](x-43)\times (x-43)\times(x-43)[/tex]
Cube of the difference of a number x and 43=(x-43)^3
Because in multiply when base same then power of the number added.
Hence,the algebraic expression =(x-43)^3.I
Please help me with this pleaseee
Answer:
x = 88.2
Step-by-step explanation:
The angle at the top of the triangle = 90° - 10° = 80°
and the left side of the triangle is x ( opposite sides of a rectangle )
Using the tangent ratio in the right triangle
tan80° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{500}{x}[/tex]
Multiply both sides by x
x × tan80° = 500 ( divide both sides by tan80° )
x = [tex]\frac{500}{tan80}[/tex] ≈ 88.2
Mary went to the circus. During the dog show, she counted 54 legs between the dogs and the trainers who were having
the dogs perform their amazing tricks. If there were a total of 15 dogs and trainers in the performance, how many of
each were there?
Select the correct response.
#1. 6 Trainers and 9 Dogs
#2. 13 Dogs and 2 Trainers
#3. 1 Trainer and 14 Dogs
#4. 3 Trainers and 12 Dogs
Answer:
d
Step-by-step explanation:
d is most likely
There are 3 trainers and 12 dogs. The correct answer would be an option (D).
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
Let's assume the number of trainers would be x and dogs would be y
As per the given information, we can write the system of equations as
x+y=15 .....(i)
2x+4y=54 .....(ii)
From equation (i),
x = 15 - y
From equation (ii), and solve for y
2(15-y)+4y=54
30-2y+4y=54
2y=24
y = 12
Substitute the value of y = 12 in equation (iii), and we get the value of x = 3
Hence, there are 3 trainers and 12 dogs.
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Helpppppppppppppppppp?????
The 3rd one. The number of 8 ounce glasses of milk in 1 gallon. If you read all the options carefully you can see that there’s no way that the other options could be “normally” distributed. The only on that could be “normal” is the 3rd one. Hope I helped!
What is the slope of the line?
1
-1
-1/3
1/3
Answer
m = 1
Explanation
Simple Method: Rise (go up) over Run (go left or right)
Start from a perfect point then rise and run.
Rise: 3, Run: 3 = 3/3 = 1
Alternatively, you could pick two points and use the formula y2 - y1/x2 - x1
Just as an example, I will choose (-2, -3) and (2, 1)
plug in:
1 + 3/2 + 2 = 4/4 = 1
ANSWER
1
EXPLANATION
The slope of the given line is obtained using the formula:
[tex]m = \frac{rise}{run} [/tex]
From the diagram the rise is 2 units and the run is 2 units.
This implies that,
[tex]m = \frac{2}{2} = 1[/tex]
Hence the slope of the given line is 1.
The average January surface water temperatures (°C) of Lake Michigan from 2000 to 2009 were 5.07, 3.57, 5.32, 3.19, 3.49, 4.25, 4.76, 5.19, 3.94, and 4.34. The data set has the following statistics:
x = 4.312
2 = 0.577
What is the standard deviation? Round to the nearest thousandth.
0.333
0.760
2.077
18.593
Answer: Second Option
[tex]\sigma=0.760[/tex]
Step-by-step explanation:
We have the average January surface water temperatures (°C) of Lake Michigan from 2000 to 2009.
5.07, 3.57, 5.32, 3.19, 3.49, 4.25, 4.76, 5.19, 3.94, 4.34
We know that the average [tex]{\displaystyle {\overline {x}}}[/tex] of the data is:
[tex]{\displaystyle {\overline {x}}}=\frac{\sum_{i=1}^{10}x_i}{10}=4.312[/tex]
We also know that the variance [tex]\sigma^2[/tex] is equal to 0.577.
So by definition the standard deviation [tex]\sigma[/tex] is:
[tex]\sigma=\sqrt{\sigma^2}\\\\\sigma=\sqrt{0.577}\\\\\sigma=0.760[/tex]
Answer:0.760
just right by chance
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Use the probability distribution graph to answer the question.
P(X ≤ a) = 0.6
What is the value of a?
Answer:
a = 5.
Step-by-step explanation:
The graph here is a probability density graph. What will represent [tex]P(X\le a)[/tex] on the graph?
[tex]P(X\le a)[/tex] is the area
between the graph and the x-axis, to the left of [tex]a[/tex].The area under the graph between 0 and 9 is a trapezoid. Consider the trapezoid in three slices from left to right:
A right triangle of area [tex]\displaystyle \frac{1}{2}\times 0.2\times 4 = 0.4[/tex],A rectangle of area [tex]0.2 \times (5 - 4) = 0.2[/tex], andAnother right triangle of area [tex]\displaystyle \frac{1}{2} \times 0.2 \times (9 - 5) = 0.4[/tex].The area of the leftmost triangle plus that of the rectangle is exactly 0.6. In other words, the area to the left of [tex]a = 5[/tex] between the graph and the x-axis is [tex]0.6[/tex]. [tex]P(X \le 5) = 0.6[/tex]. [tex]a = 5[/tex].
As a side note [tex]a = 5[/tex] shall be the only answer to this question since the area under the graph to the left of [tex]a[/tex] can only increase or stay constant but not decrease as the value of [tex]a[/tex] increases.
To angle are supplementary. Measure of one angle is 56 degrees, what is the measure of the second angle
Answer:
124°
Step-by-step explanation:
Supplementary angles add to 180°.
56° + second angle = 180°
Subtract 56° from both sides of the equation:
second angle = 180° - 56° = 124°
The coordinates of Trapezoid EFGH are E(8, 8), F(8,10), G(1, 6), and H(4, 1). The image of EFGH under dilation is E’F’G’H’. If the coordinates of vertex E’ are (4, 4), what are the coordinates of vertex F’? A)(2, 6) B)(4, 6) C)(2, 5) D)(4, 5)
Answer:
D) (4,5)
Step-by-step explanation:
Vertex E was dilated by 1/2 because 8/2 = 4. Thus, you will divide all the other coordinates by the same scale factor.
Please help will mark brainliest (answer must be right)
True or false
The points on a line can be paired one to one with real numbers ?
Answer: TRUE
Step-by-step explanation: This is true, because there is an infinite amount of real numbers in both, and they are both countably infinite (so these infinities are equal). Hope this helps!
Which of the following ordered pairs represents an output of 5 and an input of -8?
(-8,-8)
(-8,5)
(5, 5)
(5, -8)
Answer:
(-8,5)
Step-by-step explanation:
The output corresponds to the y-value of an ordered pair while the input corresponds to the x-value of an order pair.
An ordered pair is written like this (x,y)
A rectangular prism is 4 inches long, 6 inches wide, and has a height of 5 inches. What is its volume?
60 in 3
120 in 3
148 in 3
240 in 3
Answer:
Step-by-step explanation:
The volume of a rect. prism is V = (length)(width)(height).
Here the volume is V = (4 in)(6 in)(5 in) = 120 in³ or 120 in^3
Note: Please use " ^ " to indicate exponentiation: 120 in^3
Answer:
120 in 3
Step-by-step explanation:
(5Q) Which is the graph of the given function?
Answer:
The graph of the given equation is letter A.
Step-by-step explanation:
I used the geogebra application to plot the graph of the equation.
You input the formula and the app will show you its graph.
Fins the zeros, multiplicity, and effect on the graph of the function in
f(x) = -x (3x-2)^2(x+9)^5
and
f(x) = x^3+10x^2+25x
Answer:
See explanation
Step-by-step explanation:
Zeroe of the function is such velue of x at which f(x)=0.
1. Consider the function [tex]f(x)=-x(3x-2)^2 (x+9)^5.[/tex]
Zeros are:
[tex]-x(3x-2)^2(x+9)^5=0\\ \\x=0\text{ or }x=\dfrac{2}{3}\text{ or }x=-9.[/tex]
Zero [tex]x=0[/tex] has multiplicity of 1, zero [tex]x=\dfrac{2}{3}[/tex] has multiplicity of 2, zero [tex]x=-9[/tex] has multiplicity of 5.
At [tex]x=0[/tex] or [tex]x=-9[/tex] the graph of the function crosses the x-axis, at [tex]x=\dfrac{2}{3}[/tex] the graph of the function touches the x-axis.
2. Consider the function [tex]f(x)=x^3+10x^2+25x=x(x^2+10x+25)=x(x+5)^2.[/tex]
Zeros are:
[tex]x(x+5)^2=0\\ \\x=0\text{ or }x=-5.[/tex]
Zero [tex]x=0[/tex] has multiplicity of 1, zero [tex]x=-5[/tex] has multiplicity of 2.
At [tex]x=0[/tex] the graph of the function crosses the x-axis, at [tex]x=-5[/tex] the graph of the function touches the x-axis.
Mike spent $7920 on his vacation, which was 11% of his monthly salary. What was his monthly salary
Answer: $72000
7290 divided by 11 = 720 720 times 100 = 72000At a game show, there are 6 people (including you and your friend) in the front
row
The host randomly chooses 3 people from the front row to be contestants.
The order in which they are chosen does not matter
There are 6C3 20 total ways to choose the 3 contestants
What is the probability that you a your friend are both chosen?
a. 3/20
b.4/20
c.2/20
d.2/3
Answer: 4/20
Step-by-step explanation:
Option b is correct. The probability that you and your friend are both chose is 4/20.
What is probability?The probability provides a means of getting an idea of likelihood of occurrence of different events resulting from a random experiment in terms of quantitative measures ranging between zero and one.
Formula for probabilityP(E) = number of favorable outcomes/Total number of outcomes
Where,
P(E) is the probability of an event.
What is combination?An arrangement of objects where the order in which the objects are selected does not matter is called combination.
Combination Formula[tex]C_{n,k} = \frac{n!}{(n-k)!k!}[/tex]
Where,
n is total number of objects in set
[tex]C_{n, k}[/tex] is number of combinations
k is number of choosing objects from the set
According to the given question
We have
Total six people.
And,
There are total [tex]6C_{3}[/tex] ways to choose the 3 contestants.
⇒ [tex]6C_{3} = \frac{6!}{(6-3)!3!}[/tex] = [tex]\frac{(6)(5)(4)(3!)}{(3!)(3!)}[/tex] = 20
⇒ total number of outcomes = 60
⇒ There are 20 ways to select 3 contestant among 20 people.
Now, the number of ways that, you and your friend are chosen, along with 1 person from a set of 4 is given by
[tex]C_{4,1} = \frac{4!}{1!3!}= 4[/tex]
⇒ total number of favorable outcomes = 4
Therefore,
The probability that you and your friend are both chose = [tex]\frac{4}{20}[/tex]
Hence, option b is correct.
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Determine the angle at the centre of a circle with radius 6.0 cm for an arc length of 8.0 cm.
3/4 radians
2/3 radians
4/3 radians
4π/3 radians
Answer:
Third option.
Step-by-step explanation:
You need to remember that the formula used to calculate the arc lenght is:
[tex]arc\ length=r C[/tex]
Where "r" is the radius and "C" is the central angle in radians.
You need to solve for "C":
[tex]C=\frac{arc\ length}{r}[/tex]
You know the radius and the arc lenght, therefore, you can substitute values to calculate the central angle in radians. Therefore, this is:
[tex]C=\frac{8.0cm}{6.0cm}[/tex]
[tex]C=\frac{4}{3}radians[/tex]
1. x/5 = 10 *
2. x + 2 = 15 *
3. 5x = 40 *
4. 2y = 44 *
5. r - 15 = 30 *
Answer:
Step-by-step explanation:
1) x/5 = 10
multiply by 5 : x = 50
2) x + 2 = 15
add -2 : x = 13
3) 5x = 40
divid by 5 : x =8
4) 2y = 44
divid by 2 : y = 22
5. r - 15 = 30
add 15 ; 5r =45
divid by 5 : r = 9
A triangle has side lengths 32, 45 and 18. What type of triangle is it?
A) right
B) acute
C) obtuse
D) none of the above
A triangle has side lengths 44, 36 and 30. What type of triangle is it?
A) right
B) acute
C) obtuse
D) none of the above
Answer:
Part A) Option C. obtuse
Part B) Option B. acute
Step-by-step explanation:
we know that
Applying the Pythagoras Theorem
if [tex]c^{2}=a^{2}+b^{2}[/tex] ----> is a right triangle
if [tex]c^{2}>a^{2}+b^{2}[/tex] ----> is an obtuse triangle
if [tex]c^{2}<a^{2}+b^{2}[/tex] ----> is an acute triangle
where
c is the greater side
Part A) A triangle has side lengths 32, 45 and 18. What type of triangle is it?
we have
[tex]c^{2}=45^{2}=2,025[/tex]
[tex]a^{2}+b^{2}=32^{2}+18^{2}=1,348[/tex]
therefore
[tex]c^{2}>a^{2}+b^{2}[/tex]
Is an obtuse triangle
Part B) A triangle has side lengths 44, 36 and 30. What type of triangle is it?
we have
[tex]c^{2}=44^{2}=1,936[/tex]
[tex]a^{2}+b^{2}=36^{2}+30^{2}=2,196[/tex]
therefore
[tex]c^{2}< a^{2}+b^{2}[/tex]
Is an acute triangle
The period of this function is
2π
π/8
π/4
π/2
I’m not quite sure what the function is but if it’s sine the period is pi/8
ANSWER
The period is
[tex] \frac{\pi}{8} [/tex]
EXPLANATION
The given function completes four cycles on the interval
[tex]
[ - \frac{\pi}{4} , \frac{\pi}{4} ][/tex]
Therefore the period is
[tex] = \frac{ \frac{\pi}{4} - \frac{\pi}{4} }{4} [/tex]
Simplify the numerator:
[tex] = \frac{ \frac{\pi}{2}}{4} [/tex]
Simplify further to get:
[tex]= \frac{\pi}{8} [/tex]
The scatter plot shows the results of a survey in which 10 students were asked how many hours they spent studying for a test and the score they earned. How many students scored a 90 or above? Enter your answer in the box.
✔the answer was 5
Answer:the answer is 5
Answer:
answer is 5
Step-by-step explanation:
Given that the scatter plot shows the results of a survey in which 10 students were asked the number of hours they spent studying for a test and the score they earned.
The scatter plot shows
2 students got 100, 1 student between 90 and 100 and 2 students got 90.
Others got below 90
Hence no of students who scores 90 or above = 5
At the start of an experiment, the temperature of a solution was -12°C. During the expirament
Answer:
The final temperature of the solution was 5°C
Step-by-step explanation:
we know that
1) At the start of an experiment, the temperature of a solution was -12°C
In this moment the temperature is -12°C
2) During the experiment, the temperature of the solution rose 5°C each hour during 4 hours
so
5°C*4=20°C
In this moment the temperature is -12°C+20°C=8°C
3) The temperature changed by -3°C
In this moment the temperature is 8°C-3°C=5°C
Answer:
The final temperature of the solution was 5°C
Step-by-step explanation:
2.04 miles
2.5 miles
2.22 miles
2.94 miles
Answer:
[tex]h=2.04\ miles[/tex]
Step-by-step explanation:
Let
h-----> the high of the balloon
we know that
In the right triangle of the figure
[tex]tan(63\°)=\frac{4}{h}[/tex]
[tex]h=\frac{4}{tan(63\°)}[/tex]
[tex]h=2.04\ miles[/tex]
The center is a(?,?)
The radius is _____ units.
Answer:
The center is at [tex](2,4)[/tex]
3 units
Step-by-step explanation:
You can observe in the graph a circle.
The x-coordinate and the y-coordinate of the center of the circle shown in the figure are:
[tex]x=2[/tex] and [tex]y=4[/tex]
Therefore, the point of the center of the circle is:
[tex](2,4)[/tex]
You can observe that the diameter goes from -1 to 5, then the diameter is:
[tex]diameter=1units+5units\\\\diameter=6units[/tex]
The radius is half the diameter. Therefore, you can say that the radius of this circle is:
[tex]radius=\frac{diameter}{2}\\\\radius=\frac{6units}{2}\\\\radius=3units[/tex]
ANSWER
The center is (2,4)
The radius is 2√2 units
EXPLANATION
Each of the ticks is 1 unit
Counting two ticks from the origin to the right and 4 units up will land us at the center of the circle.
Hence the center is (2,4)
The circle passes through (0,2).
The radius is
[tex]r = \sqrt{ {(2 - 0)}^{2} + {(4 - 2)}^{2} } [/tex]
[tex]r = \sqrt{8} = 2 \sqrt{2} [/tex]
Please help 20 points
Answer:
LOLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL
Step-by-step explanation:
6 / 2 (1 + 2) = 9
PLEASE EXPLAIN HOW IT IS 9!!! I followed PEMDAS, and I keep getting 1
Answer:
9
Step-by-step explanation:
6 / 2 (1 + 2) = 9
PEMDAS
Parentheses first
1+2 =3
Substitute this in
6 / 2 (3) = 9
Multiplication and Division from left to right
Division first
6/2 =3
Substitute this in for 6/2
3 (3) =9
3*3 =9