Prove algebraically that the straight line with equation x = 2y + 5 is
a tangent to the circle with equation x2 + y2 = 5
Answer:
[tex]{ \tt{line : x = 2y + 5}} \\ { \tt{circle : {x}^{2} + {y}^{2} = 5}} \\ substitute \: line \: in \: circle \\ { \tt{ {(2y + 5)}^{2} + {y}^{2} = 5 }} \\ { \tt{4 {y}^{2} + 20y + 25 + {y}^{2} = 5}} \\ { \tt{5 {y}^{2} + 20y + 20 = 0 }} \\ { \tt{ {y}^{2} + 4y + 4 = 0 }} \\ y = - 2 \\ x = 2( - 2) + 5 = 1 \\ { \tt{centre = ( - 1, \: 2)}} \\ { \tt{radius = 5 \: units}} \\ hence \: proved[/tex]
Answer:
radius 5
centre -1,2
Step-by-step explanation:
If sin theta = 8/17 and cot theta < 0, what is sec theta?
Answer:
[tex]-\frac{17}{15}[/tex]
Step-by-step explanation:
By definition, [tex]\cot \theta=\frac{1}{\tan \theta}[/tex] and [tex]\sec \theta=\frac{1}{\cos \theta}[/tex]. Since since [tex]\cot \theta[/tex] is negative, [tex]\tan \theta[/tex] must also be negative, and since [tex]\sin \theta[/tex] is positive, we must be in Quadrant II.
In a right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse. The cosine of an angle in a right triangle is equal to its adjacent side divided by the hypotenuse. Therefore, we can draw a right triangle in Quadrant II, where the opposite side to angle theta is 8 and the hypotenuse of the triangle is 17.
To find the remaining leg, use to the Pythagorean Theorem, where [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or longest side, of the right triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the right triangle.
Solving, we get:
[tex]8^2+b^2=17^2,\\b^2=17^2-8^2,\\b^2=\sqrt{17^2-8^2}=\sqrt{225}=15[/tex]
Since all values of cosine theta are negative in Quadrant II, all values of secant theta must also be negative in Quadrant II.
Thus, we have:
[tex]\sec\theta=\frac{1}{\cos \theta}=-\frac{1}{\frac{15}{17}}=\boxed{-\frac{17}{15}}[/tex]
Please help ASAP !!!
Answer:
C
Step-by-step explanation:
the domain is for which values of x is that function defined (is that a valid function).
the range is what values that function can produce based on all the different x-values as input.
so, checking option A
that means all x values are negative.
that means all values inside the square root are negative.
the resulting function values are a discussion class of numbers and not part of the interval of (0, infinity).
so, it cannot be A.
checking option B
the domain range includes the value 6 for x.
but that would make this function for x=6 an invalid expression of 1/0
so, it cannot be B.
checking option C
the value range for x (domain) is x>6 (and excluding x=6).
and the result range is all positive numbers including 0.
there is no violation of any function principle.
the answer is C.
checking option D
similar to C, but the result range is defined as all numbers, negative and positive.
but for the domain the function can never produce negative numbers.
so, it is not D.
1. What percentage of the students like football? a. 25% b. 30% c. 35% d. 40% 2. How many students prefer swimming? lime a. 100 b. 120 C. 130 d. 140 3. How many students do not like volleyball the most? a. 140 b. 240 C. 340 d. 440 4. How many students were asked about their favorite sport? a. 400 b. 300 c. 200 d. 100 pakisagot po please asap po
Step-by-step explanation:
the answer is in the above image
The table shown below represents a function. Which of the following values could not be used to complete the table?
Answer:
-5
Step-by-step explanation:
For a given x value a function can have only one y value.
-5 cannot have both 15 and 20 as the y value
prt.3 identify the slope
Answer:
m = - 2
Step-by-step explanation:
First coordinate : ( -2 , 9 )
Second coordinate : ( 1 , 3 )
Formulae : m=(y2-y1)/(x2-x1)
Substituting,
m = ( 3 - 9 ) / ( 1 + 2 )
m = - 6 / 3
m = - 2
If this helps you, please mark brainliest!
Y=(x+2)(x-4)
Expanded form:
Y-intercept
One-half (x + 6) = 18
Answer:
x = 30
Step-by-step explanation:
I'm going to assume the equation you needed help with was:
[tex]\frac{1}{2}(x+6) = 18[/tex]
If not, let me know and I'll redo it.
[tex]\frac{1}{2} x+3 = 18\\\frac{1}{2} x = 15\\x = 30[/tex]
PLEASE HELP!!!!! very urgent asap!!! need help please
Answer:
easy
Step-by-step explanation:
Emily kicked the ball in 1 straight direction , it went 10 ft reversed direction and come back to her , how is this possible ?
she accidentally kicked a boomerang
she kick it up
it isn't
she kick it left to the wall
Answer:
She kicked it up
Step-by-step explanation:
How is this math?
I believe your answer is B.) She kicked it up. Think about it, if she kicks it straight up, it goes up ten feet, and then it comes back down (Revered direction) to her.
In the diagram below, the area of $\triangle BCD$ is 60. What is the length of side $\overline{BC}$?
Area of triangle = 1/2 bh
60 = 1/2 (15) h
8 = h
Quadrilateral area = h x (b1 + b2)/2 = 8 x (15+9)/2 = 96 sq units
96 -60 = triangle BAD area = 36 sq units
The length of side BC in the triangle BCD is 8.
What is an area?An area is the amount of space occupied by a two dimensional shape or figure.
From the diagram:
Area of triangle BCD = (1/2) * base * height = (1/2) * CD * BC
60 = (1/2) * 15 * BC
BC = 8
The length of side BC in the triangle BCD is 8.
Find out more on area at: https://brainly.com/question/25292087
Larry runs a dog-walking service. He charges $5/h plus a flat fee of $6. One day, he earned $16. Determine which
equation represents this.
Answer:
5h+6=16
Step-by-step explanation:
He gets 6 dollars and for every hour he walks he gets 5 dollars so he must of walked dogs for 2 hours and plug it in you get your equation.
Answer:
5(2)+6=16
Step-by-step explanation:
That should be it! Contact me if you need to know why.
- y = 7 is a line which is-(A) Parallel to y-axis (B) Parallel to x-axis (C) Passing through (7, 7) (D) Passing through origin
Answer:
B
Step-by-step explanation:
- y = 7 , that is y = - 7
Is a horizontal line parallel to the x- axis and passing through all points with a y- coordinate of - 7
Find all solutions to the equation in the interval [0, 2pie]. Enter the solutions in increasing order. cos 2x = sin x
Answer:
cos2x=sinx
<=> 1-2sin^{2}x =sinx
solve and we have x=3pie/2, x=pie/6,x= 5pie/6
Step-by-step explanation:
Please help, find the area of the polygon.
Answer:
126cm²
Step-by-step explanation:
first divide the figure into two( rectangle and a triangle)
area of a rectangle=length x width
16cmx7xcm
112xcm²
area of a triangle=1/2base x height
1/2x7cmx(20-16)cm
1/2x7cmx(4)cm
14cm²
total area of the figure=area of rectangle+area of triangle
=112cm²+14cm²
=126cm²
hope this is helpful
someone please help me!!!!!!!
Step-by-step explanation:
In the second step while opening the bracket, instead of 'a', there should be - 4a.
Answer:
From Step 2 every step is wrong
Step-by-step explanation:
Ste p 1 : 3a - 5b = 12 - 4(b + a)
Step 2 : 3a - 5b = 12 - 4b - 4a [ Last term instead - 4a she\he wrote + a ]
Step 3 : 7a - 5b = 12 - 4b
Step 4 : 7a = 12 + b
[tex]Step 5 : a = \frac{12 + b}{7}[/tex]
help
PLEASE HEPP ME PLEASE
Answer:
Step-by-step explanation:
VOLUME...
1) π*r^2*h
π*(2.5)^2 *h
(π)*(2.5)^2* 6
= 117.8
2) π*r^2*h + 1/2 *[(4/3) · π · r3]
(π)*(3)^2* 3 + 1/2 *[(4/3) · π · 3^3]
84.8+ 56.5 = 141.41
3) (1/3) π*r^2*h
(1/3) π*3^2*h
3^2 + h^2 = 36
h = sqrt(27) = 5.1
(1/3) π*3^2*5.1
= 48.06
~~~~~~~~~~~~~~~~~~~~~~~~~~~
Height of 1/2 of glass #2
84.8+ 56.5 = 141.41
thus 1/2 of #2 = 70.5
70.5 - 56.6 = 14 (all of 1/2 sphere filled plus 14 into cylinder)
14/[(π)*(3)^2* 3]= .16 of the cylinder... 3*(0.16) = .48
total height = 3.48
What is the measure of A
Given:
A figure of a triangle.
To find:
The measure of angle A.
Solution:
Label the points in the figure as shown below.
In the below figure,
[tex]\angle ACB\cong \angle DCE[/tex] (Vertically opposite angles)
[tex]m\angle ACB=m\angle DCE[/tex] (Congregant angles)
[tex]m\angle ACB=8x+4[/tex]
Using exterior angle theorem in triangle ABC, we get
[tex]m\angle A+m\angle C=\text{Exterior }m\angle B[/tex]
[tex]m\angle BAC+m\angle ACB=130^\circ[/tex]
[tex](3x-6)+(8x+4)=130^\circ[/tex]
[tex]11x-2=130^\circ[/tex]
Isolate the variable term x.
[tex]11x=130^\circ+2[/tex]
[tex]11x=132^\circ[/tex]
[tex]x=\dfrac{132^\circ}{11}[/tex]
[tex]x=12^\circ[/tex]
Now, the measure of angle A is:
[tex]m\angle A=3x-6[/tex]
[tex]m\angle A=3(12^\circ)-6[/tex]
[tex]m\angle A=36^\circ-6[/tex]
[tex]m\angle A=30^\circ[/tex]
Therefore, the correct option is B.
Solve for p in the literal equation 2p + 38 = 9.
p =
Answer:
p = -29/2
Step-by-step explanation:
2p + 38 = 9
Subtract 38 from each side
2p + 38-38 = 9-38
2p = -29
divide by 2
2p/2 = -29/2
p = -29/2
Answer:
p=-14.5
Step-by-step explanation:
2p + 38 = 9
-38 -38
2p = -29
[tex]\sqrt{2}[/tex] [tex]\sqrt{2}[/tex]
p = -14.5
PLSSS HELPPP no linkss plsss im begging
Answer:
Step-by-step explanation:
Please help I’ll give brainliest
Answer:
2 is the base
Step-by-step explanation:
2^3
2 is the base and 3 is the exponent
Can someone help giving branliest to first correct answer
Find the expression for f(x) that makes the following equation true for all values of x 9^x⋅3^x+2=3^f(x).
Answer:
3x+2
Step-by-step explanation:
khan told me that my explanation
SUPER IMPORTANT AND I NEED HELP 30 points if you answer
Polygon Y is a scaled copy of Polygon X using a scale factor of 1/3
Polygon Y's area is what fraction of Polygon X's area?
Answer:
1/9th
Step-by-Step Explanation:
The area is measured in units squared, then you have to square 1/3 which is 19th.
Answer:
1/9
Step-by-step explanation: i think so
Write 51000201078 in words
Answer:
Fifty - one billion two hundred one thousand seventy eight
- Let me know if you have any questions regarding my answer :)
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
[tex]\boxed{51,000,201,078}[/tex]
⟹ Fifty one billion two hundred and one thousand seventy eight.
⁺˚*･༓☾✧.* ☽༓･*˚⁺‧
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Indicate the equation of the given line in standard form, writing the answer in the equation box below.
The line containing the longer diagonal of a quadrilateral whose vertices are A(2, 2), B(-2,-2), C(1, -1), and D16, 4).
9514 1404 393
Answer:
x -3y = 4
Step-by-step explanation:
A plot of the points reveals the longer diagonal to be BD. (Also, point C is on that line.)
We can write the standard form equation of the line through (x1, y1) and (x2, y2) as ...
(y2 -y1)x -(x2 -x1)y = (y2 -y1)x1 -(x2 -x1)y1
For points (-2, -2) and (16, 4), this equation is ...
(4 -(-2))x -(16 -(-2))y = (4 -(-2))(-2) -(16 -(-2))(-2)
6x -18y = -12 +36
Dividing by the greatest common factor (6), we have the standard-form equation ...
x -3y = 4
The two lines represent the amount of water, over time in two tanks that are the same size. Which container is filling more slowly
3/2x-4=20
Solve for x
Answer:
x= 12
Step-by-step explana
2x = 20 + 4
2x= 24
x= 2 4/2
x= 12
Which ordered pair would form a proportional relation ship with the point graphed below (-10, -40)
Answer:
(5,20)
Step-by-step explanation:
Looking at the pair, we can see that the value of y is simply the value of x multiplied by 4
so we have to multiply the value of x by 4 to get the value for y
So any of the options we can see this proportional relationship is correct
Looking at the options, we can see the third option. (5,20)
20/5 is 4 which makes the option correct
What is the explicit formula for this arithmetic sequence?
-10,-17, -24, -31, ...
Answer:
D
Step-by-step explanation:
The starting term is a1.
That's the very first term.
a1 = - 10
The second term = -17 which means that you added - 7 to - 10.
So d must be - 7
The formula must be
an = a1 + (n - 1)*d
an = -10 + (n - 1)(-7)
You might wonder why it is n - 1. The reason is because the first term is already added on the right side. The -1 means that we have already included the first term.
We should try the formula out to see what it does. Let's find a4
a4 = -10 + (4 -1)*-7
a4 = -10 + 3(-7)
a4 = -10 - 21
a4 = - 31 which is what the question suggests.