The intersection point is only one. Then the equation of the line is tangent to the circle at point (1, -2).
What is a circle?It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
Prove algebraically that the straight line with equation x = 2y + 5 is a tangent to the circle with equation x² + y² = 5.
x = 2y + 5 ...1
x² + y² = 5 ...2
If the intersection of the point of the circle and line is one. Then the line is tangent to the circle.
Then from equations 1 and 2, we have
(2y + 5)² + y² = 5
4y² + 25 + 20y + y² - 5 = 0
5y² + 20y + 20 = 0
5y² + 10y + 10y + 20 = 0
5y (y + 2) + 10(y + 2) = 0
(5y + 10)(y + 2) = 0
y = -2, -2
Then the value of y is unique then the value of x will be unique.
The value of x will be
x = 2(-2) + 5
x = -4 + 5
x = 1
The intersection point is only one. Then the equation of the line is tangent to the circle at point (1, -2).
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What number is 32% of 100?
Answer:
32
P = 100 × 32%(0.32) = 32
Answer:
32
Step-by-step explanation: You multiply 100 by 0.32 which is 32% as a decimal
Caroline, Colin & Sarah share some money.
Caroline gets
1
9
of the money.
Colin and Sarah share the rest in the ratio 1:3.
What proportion does Colin get?
Caroline, Colin & Sarah share some money.Caroline will get [tex]\dfrac{2}{3}[/tex] when Caroline, Colin & Sarah share some money.
What is the ratio?The ratio defined as the sharing of the two or three things or it represent that one thing or number is how many times to the other.
One part is excluded in the problem. That part is:
"Caroline gets [tex]\dfrac{1}{9}[/tex] of the money."
If Caroline gets 1/9th, then remaining is:
[tex]1-\dfrac{1}{9}=\dfrac{8}{9}[/tex]
Colin and Sarah share in ratio 3 is to 1, that means 3 + 1 = 4 parts...
8/9th in 4 parts means, each part is:
[tex]\dfrac{\dfrac{8}{9}}{4}=\dfrac{2}{9}[/tex]
We know Colin gets "3" parts of the total, each part is (2/9)th, so 3 parts would be:
[tex]3\times \dfrac{2}{9}=\dfrac{6}{9}=\dfrac{2}{3}[/tex]
Colin gets [tex]\dfrac{2}{3}[/tex] money when three of them share money.
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Harry invests $1000 in an investment account that earns 6% interest, compounded annually. How much money will he have in the account after 30 years?
the answer to that question is 1800
Maddi has a bin shaped like a right prism. She knows that the area of the base of the bin is 14 in² and the volume of the bin is 392 in³.
What is the height of Maddi's bin?
28 in.
33 in.
38 in.
43 in.
Answer:
The answer is 28 in
Step-by-step explanation:
I divided 392/14=28
hopefully it helps.
please mark brainliest.
Answer:
it is 28
Step-by-step explanation:
i took the exam
The area of a parallelogram is the product of the base b and the height h. Identify the formula.
Answer:
b x h
Step-by-step explanation:
product of the base (b) and the height (h) just means b x h.
solve this question please
Answer:
Step-by-step explanation:
a) 1.8 kg in grams is 1800 g
b) If 6 toys weigh 1800g; then 1 toy weighs 300 g(6:1)
c) If 1 toy weighs 300 g, 4 toys weigh 1200 g and you convert in kg which is 1.2 kg
What is 1,391 rounded to the nearest hundred
Answer:
1400
Step-by-step explanation:
i hope this helps u
Answer:
1,400
Step-by-step explanation:
It's closer to 400 than 300
An angle that measures 125° is composed of three smaller angles. Two of the smaller angles measure 25° and 40 degrees Tom thinks he can use the equation 25 degrees + (40 degrees - 25 degrees) = s to find the measure of the unknown smaller angle, s. Explain why Tom is incorrect and tell how to find the measure of the third smaller angles
The measure of the other angle is 60°.
What is an Angle ?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
As given in the question
An angle that measures 125° is composed of three smaller angles.
Two of the smaller angles measure 25° and 40 degrees
Tom thinks he can use the equation 25 degrees + (40 degrees - 25 degrees) = s to find the measure of the unknown smaller angle, s
Tom is incorrect because the sum of the smaller angles will be equal to the bigger angle and the equation he has written is wrong.
The right equation and method will be
25 +40+x = 125
x = 125-40-25
x = 60°
Therefore the measure of the other angle is 60°.
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Drag and drop to complete the proof below:
Given: DE is tangent to circle C, at point F
Prove:
E
D
F
חד
C
The sum of angle ∠FEC and angle ∠ECF is 90°. Then they are complementary angles.
What is a circle?It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.
DE is tangent to circle C, at point F.
Then prove that angle ∠FEC and angle ∠ECF are complementary angles.
We know that the radius of the circle and the tangent on the circle make a right angle at the circumference.
Then angle ∠EFC will be 90°.
The sum of all interior angles of the triangle is 180°. Then we have
∠FEC + ∠ECF + ∠EFC = 180°
∠FEC + ∠ECF + 90° = 180°
∠FEC + ∠ECF = 90°
The sum of angle ∠FEC and angle ∠ECF is 90°. Then they are complementary angles.
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The tracking number for a package is 693840002. You mistakenly type 698340002 and get tracking information on a different package. Why was the tracking number you entered not recognized as being incorrect?
Answer:
See below ~
Step-by-step explanation:
The tracking number for the package is : 693840002
The number you have typed in is : 698340002
The place values of 8 and 3 in the tracking number have been switched. Therefore, as it is not the same tracking number, you get tracking information of a different package which corresponds to the number.
Determine the distance between the points plotted on the graph. Round to the nearest tenth, if necessary.
Answer:
d= 4[tex]\sqrt{2}[/tex] or 5.66
Step-by-step explanation:
(-2,7) and (2,3)
d = [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]
d= [tex]\sqrt{(2-(-2))^{2} + (3-7)^{2} }[/tex]
d = [tex]\sqrt{16 + 16}[/tex]
d= 4[tex]\sqrt{2}[/tex] or 5.66
Ella conducted a survey to find out the amount of time high schoolers spend surfing the Internet. From the data collected, the range of time spent was 1 hour. What does this range say about the data?
All the students surveyed spend exactly 1 hour surfing the Internet.
All the students surveyed spend an average of 1 hour surfing the Internet.
The difference between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour.
The quotient between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour.
The statement third “the difference between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour” is correct.
What is range?It is defined as the difference between the maximum value in the data set to the minimum value in the data set.
As we know, the difference between the greatest and lowest values, called the range.
According to this response, the range is 1 hour, which is the difference between the most and least amount of time spent surfing the Internet. This is based on the term “Range.”
Thus, the statement third “the difference between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour” is correct.
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Answer:
The difference between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour!
Step-by-step explanation:
PLEASE HELP!!!!!!!!
WILL GIVE BRAINLY IF RIGHT!!!!!!!!
Simplify.
[tex]\sqrt{(2\pi-4\sqrt{5})^2}[/tex]
Answer:
2π - 4√5
(= -2.66 to nearest hundredth).
Step-by-step explanation:
√(2π - 4√5)^2
= 2π - 4√5 (by the definition of a square root)
If you want an approximate value it is
-2.66 to the nearest hundredth
4x4 y3 + v y + 7
Leading term:
Leading coefficient:
Constant term:
Answer:
Leading term: 4x⁴y³
Leading coefficient: 4
Constant term: 7
The leading term contains the highest degree and power of variable.The leading coefficient is the number written in front of the variable with the largest exponent.The constant term is the simplified number written where there are no variables.Answer:
Leading terms : 4x⁴y³
Leading co-efficient: 4
Constant: 7
Step-by-step explanation:
Leading term: Leading term is the term that holds the highest degree of the polynomial.
Leading co-efficient is the coefficient of the leading term.
Constant term is the term without any variable
Vera needs repairs on her car. The mechanic’s estimate says that he will provide 7.3 hours of labor. His rate is $55 per hour. The total cost of the labor will be
What is the solution?
Answer:
1200c^3
Step-by-step explanation:
cut the shape it to half with a square and a prism and calculate them separately then add the volume!
Hope this helps! ;-)
Is the triangle proved similar?
Sequence of 2,-6,-14,-22 determine the n term
Answer:
[tex]a_{n}[/tex] = - 8n + 10
Step-by-step explanation:
the sequence has a common difference between consecutive terms , that is
- 6 - 2 = - 14 - (- 6) = - 22 - (- 14) = - 8
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 2 and d = - 8 , then
[tex]a_{n}[/tex] = 2 - 8(n - 1) = 2 - 8n + 8 = - 8n + 10
Hello please help me………….thank you
Answer:
1. False —> that’s how you find the perimeter.
2. False —> area is measured in square units.
3. False —> you can only use a multiplication.
4. True —> (2x6) + (2x8) = 28 inches.
5. False —> 5x5 = 25 square meters.
—-
Have a nice day!!
Answer:
Step-by-step explanation:
1 False. The suggestion given is for Perimeter, not area.
2 False. The perimeter is given in units not square units. For example, the Perimeter of square with one side of 7 in is 4 * 7 inches is 28 inches
3 False. You can only use multiplication equations to find a rectangle's area (or at least it is the easiest way to do it.) Higher math courses find areas by using multiplication and addition, but I'm pretty sure you are not in a higher math course.
4.True
5 False. The area of a square is 5 * 5 = 25. Not 4*5 = 20
solve for x !
[tex]x {}^{2} - 5x + 6 = 0[/tex]
ty! :)
Step-by-step explanation:
[tex] {x}^{2} - 5x + 6 = 0\\ {x}^{2} - 3x - 2x + 6 = 0\\ x(x - 3) - 2(x - 3) = 0\\ (x - 3)(x - 2) = 0 \\ either \\ x - 3 = 0 \\ x = 3 \\ or \\ x - 2 = 0 \\ x = 2[/tex]
please answer this question
The integration of the provided integration expression which is evaluated without using the beta function is equal to 1/1011.
What is integration?It is the reverse of differentiation. The differentiation is the rate of change of the function with respect to variables.
The integration is given below.
[tex]\rightarrow \rm \int _0^{\infty} \dfrac{x^{1010}}{(1 +x)^{2022}} \ dx[/tex]
Then the integration can be written as
[tex]\rightarrow \rm \int _0^{\infty} \dfrac{x^{1010}}{[(1 +x)^{1011}]^2} \ dx[/tex]
Let (1 + x)¹⁰¹¹ = t. Then 1011x¹⁰¹⁰ dx = dt.
Then we have
[tex]\rightarrow \int_{1}^{\infty } \dfrac{dt}{1011 \ t^2}[/tex]
Then integrate
[tex]\rightarrow \dfrac{1}{1011} \left [ \dfrac{-1}{t} \right ]_{1}^{\infty }\\\\\\\rightarrow \dfrac{1}{1011} \left [ \dfrac{1}{t} \right ]^{1}_{\infty }\\\\\\\rightarrow \dfrac{1}{1011} \left [ 1- 0 \right ]\\\\\\\rightarrow \dfrac{1}{1011}[/tex]
The integration of the provided integration expression which is evaluated without using the beta function is equal to 1/1011.
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please type the write answer
Step-by-step explanation:
the only thing that I can tell you about it
4) The lower cable meets the tree at a height of 12 feet and extends out 32 feet from the base of the tree. If the tria
similar, how tall is the tree?
56 ft
The tree is ft tall.
Question 4
Question 16
The triangular prism below represents the shape of Sylvia's tent.
Sylvia's Tent
6 feet
6 feet
10 feet
8.5 feet
What is the volume of the tent in cubic feet?
C 255
D 360
A 180
B 241
1 point
Answer:
180^3'
Step-by-step explanation:
6x6=36.
36x10=360.
360 divided by 2= 180.
:}
Determine the x coordinate of the center of a circle if its diameter's endpoints are located at (7,-2) and (9,5).
Answer:
(2,8)
Step-by-step explanation:
Find the area of the figure. Round to the nearest hundredth where necessary.
15 cm
14 cm
23 cm
19 cm
34 cm
The area of the given figure is 787.5 square centimeter
What is Area of Rectangle?The area of Rectangle is length times of width.
The given figure has a rectangle whose length is 23 cm
width is 14 cm
Area of rectangle = 23×14
=322 square centimeter
Area = 15+34/2 ×19
=931/2
Total area = 322+931/2
=787.5 square centimeter
Hence, the area of the given figure is 787.5 square centimeter
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20 Points Help Please! Calculate the area of triangle ABC with CD, given A(6,0) B(1,5) C(2,0) D(4,2) with thorough explanation.
The area of the triangle ABC with the coordinates A(6,0) B(1,5) C(2,0) is 10 square units
How to determine the area of the triangle ?The coordinates are given as:
A(6,0) B(1,5) C(2,0) D(4,2)
The area of the triangle is calculated using:
Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|
Using the above formula, we have:
Area = 0.5 * |6 * (5 - 0) + 1 * (0 - 0) + 2 * (0 - 5)|
Evaluate the sum of products
Area = 0.5 * |20|
Remove the absolute bracket
Area = 0.5 * 20
Evaluate the product
Area = 10
Hence, the area of the triangle ABC is 10 square units
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Is substitutions the best method to use when one variable is already known
What is the number sentence for "1 less than N is the sum of Z and
2"?
[tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]
What is the number sentence for "1 less than n is the sum of z and 2?"
[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]
❖ First, Notice it says "1 less than n". This expression indicates that
we subtract 1 from n, which looks as follows:-
[tex]\Large\textit{n-1}[/tex]
❖ Now, It also says "the sum of z and 2". This indicates that we add z and
2:-
[tex]\Large\textit{z+2}[/tex]
❖ Now, Combine these two little expressions into one equation:-
[tex]\implies\sf{n-1=z+2}[/tex]
Good luck with your studies.#TogetherWeGoFar
[tex]\rule{300}{1}[/tex]
Look at the image below. Whats the area of the triangle (PLEASE HELP)
Answer:
28
Step-by-step explanation:
the formula for finding the area of a triangle is 1/2×base×height. the height is the spot where you can create a right angle with the base, which here is 14 meaning the equation is 1/2(4)(14)