Coordinates are the group of a number used to indicate the position of a point in a graph or at a scale.the coordinate of Cristian's house are (11,0)
Given-
Jayda's house is located at (1, 5).
A fast-food restaurant is located at (9, 1).
Fast-food restaurant partitions the way from Jayda's house to Cristian's house by a ratio of 4:1
What is the coordinate point?Coordinates are the group of a number used to indicate the position of a point in a graph or at a scale.
Let the coordinate of jadya's be A (1,5))
Let the coordinate of Cristian's be B ([tex]x_2,y_2[/tex])
Let the coordinate of fast food restaurant be R (9,1)
The ratio is 4:1. Thus m is 4 and n is 1.
The coordinate of the point B is,
[tex]x_R=\dfrac{nx_1+mx_2}{m+n}[/tex]
[tex]9=\dfrac{1\times1+4\times x_2}{1+4}[/tex]
[tex]9=\dfrac{1+4 x_2}{5}[/tex]
[tex]4 x_2=9\times 5-1[/tex]
[tex]x_2=\dfrac{44}{4} =11[/tex]
Find the other point of Critian's house,
[tex]y_R=\dfrac{ny_1+my_2}{m+n}[/tex]
[tex]1=\dfrac{1\times5+4\times y_2}{1+4}[/tex]
[tex]1=\dfrac{5+4 y_1}{5}[/tex]
[tex]4y_1=5-5[/tex]
[tex]y_1=0[/tex]
Thus the coordinate of Cristian's house are (11,0).
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30 PTS HELP ME ASAP! PLEASE! IM TIRED AND NEED HELP!
y=7x+10 is the equation of a regression line in a scatter plot where x is the number of hours after a store opened and y is the total number of customers that have entered the store.
1. What does the slope of 6.9 mean in the correct context?
2. According to the regression equation, how many customers have entered the store after 5 hours? (Show all of your work)
Answer:
Step-by-step explanation:
Slope is an average. In this particular context, the slope of 6.9 (or 7) means that an average of 7 people entered the store every hour.
If x is the number of hours the store is open and we are told to find the number of customers that have entered the store after 5 hours, we fill in the equation as follows:
y = 7(5) + 10 and
y = 35 + 10 so
y = 45.
If you use 6.9 instead of 7:
y = 6.9(5) + 10 and
y = 34.5 + 10 so
y = 45.5
Since you can't count a half of a person, using 7 instead of 6.9 makes more sense.
17. The sides of a central angle in a circle are
A. two radii.
B. a tangent and a radius.
C. two chords.
D. a diameter and a tangent.
A radiator contains 10 quarts of fluid, 30% of which is antifreeze. How much fluid should be drained and replaced with pure antifreeze so that the new mixture is 40% antifreeze?
Answer:
1 3/7 quarts should be drained off and replaced with pure antifreeze.
1 3/7 ≈ 1.4286
Current amount of antifreeze in quarts is -
30/ 100 × 10 = 3
40% ---> 4 quarts
Let the amount drained of and replaced with antifreeze be x-
The amount left after draining off is 10 − x.
The amount of antifreeze is 30/ 100 (10−x).
30/100(10-x)+x=4
3-3/10x+x=4
3+x(1-3/10)=4
x=1*10/7=1 3/7 quarts
check;
10- 1 3/7 = 8 4/7
=(30/100*8 4/7)+1 3/7
=(3/10 * 60/7) + 10/7
=3*6/7 + 10/7
=28/7
=4
4 liters of pure antifreeze is mixed into 10 quarts.
Answer: A
Step-by-step explanation:
Edge
Two bags contain blue and red marbles. The first bag contains 3 blue and 5 red marbles. The second bag contains
2 blue and 4 red marbles. A marble is drawn from each bag. What is the probability that both marbles are blue?
Answer: 1/8
Step-by-step explanation:
First Bag and Second Bag
[tex]\dfrac{3\ blue}{8\ total}[/tex] x [tex]\dfrac{2\ blue}{6\ total}[/tex] = [tex]\dfrac{6}{48}[/tex]
which reduces to [tex]\boxed{\dfrac{1}{8}}[/tex]
The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?
A.V=[tex]\frac{2}{3}\\[/tex](pi)(r²)
B.V=[tex]\frac{4}{3}\\[/tex](pi)(r³)
C.V=[tex]\frac{1}{3}\\[/tex](pi)(r³)
D.V=[tex]\frac{1}{3}\\[/tex](pi)(r²)
Answer:
B
Step-by-step explanation:
Assume the radius is r so the diameter is 2r
Height=2*d=2(2r)=4r since the diameter is twice the radius
Volume of cone=1/3 * pi*r^2*h
= 1/3 * pi*r^2*(4r)
=4/3 *pi *r^3
So B
Answer: B
h=2d
r=d/2
so h in terms of r is;
h=4r
V=pi*r^2*h/3
V=pi*r^2*4r/3=pi*4r^3/3=4/3(pi)(r^3)
what is the value of x
Answer:
Correct me if I am wrong, but I believe it is B.
Step-by-step explanation:
Answer:
C. 28
Step-by-step explanation:
From the diagram diagram; [tex]\angle BAC=(x+6)\degree[/tex] and [tex]\angle ABD=2x\degree[/tex].
The opposite sides of a rhombus are parallel.The diagonals act as transversals. Therefore the co-interior angles will add up to 180 degrees.The pair of co-interior angles are [tex]\angle BAD[/tex] and [tex]\angle ABC[/tex].
Also the diagonals of a rhombus bisect corner angles.
This implies that:
[tex]\angle BAD=2(\angle BAC)\implies \angle BAD=2(x+6)\degree[/tex].
[tex]\angle ABC=2(\angle ABD)\implies \angle ABC=2(2x)\degree[/tex].
The co-interior angles are supplementary so we form the equation:
[tex]\angle BAD+\angle ABC=180\degree[/tex]
[tex]\implies 2(x+6)\degree+2(2x)\degree=180\degree[/tex]
Expand the parenthesis to get:
[tex]\implies 2x+12+4x=180\degree[/tex]
Group the similar terms:
[tex]\implies 2x+4x=180-12[/tex]
Simplify
[tex]\implies 6x=168[/tex]
Divide both sides by 6.
[tex]\implies \frac{6x}{6}=\frac{168}{6}[/tex]
[tex]\therefore x=28[/tex]
The correct answer is C.
Given: △ABC is equilateral. The radius of each circle is r. Find: AB
Answer:
2r (1 + √3)
Step-by-step explanation:
Circle O₁ is tangent to AB. Let's call the point of intersection point D. If we draw a radius from the center O₁ to D, we know this forms a right angle.
△ABC is an equilateral triangle, so we know m∠A = 60°. If we draw a line from A to O₁, we know that bisects the angle, so m∠DAO₁ = 30°.
So △DAO₁ is a 30-60-90 triangle. We can find the length AD:
AD = r √3
Now on the other side, circle O₃ is tangent to AB. Let's call the point of intersection point E. We know it's the same triangle we found earlier, so:
EB = r √3
And finally, we can draw a rectangle connecting O₁, O₃, E, and D. The distance between O₁ and O₃ is 2r, so:
DE = 2r.
Therefore:
AB = r√3 + 2r + r√3
AB = 2r√3 + 2r
AB = 2r (1 + √3)
Here's a graph showing the steps. Hopefully this helps, let me know if you have questions!
desmos.com/calculator/hgaonfzxsm
Daniel is packing his bags for his vacation. He has 5 unique socks, but only 4 fit in his bag How many different groups of 4 socks can he take
Answer:
5
Step-by-step explanation:
How does the graph of y= sec(x-2)+2 comparé to the graph of y= sec(x) ?
Answer:
The function y= sec(x-2)+2 is shifted two units to the right and 2 units upwards., compared to y=sex(x).
Step-by-step explanation:
To solve this problem we need to know the rules for translation of graphs:
Given the function y = f(x):
y=f(x-a) is the same graph shifted 'a' units to the right. If 'a' is negative, then, the graph is shifted to the left. y = f(x) - a is the same graph, but shifted 'a' units downwards. If 'a' is negative, then the graph will be shifted upwards.In this case, our main function is y=sec(x). And the function y= sec(x-2)+2 is shifted two units to the right and 2 units upwards.
Answer:
D. it is shifted two units up and two units right
Step-by-step explanation:
this is the correct answer on ed-genuity, hope this helps! :)
15. Find the area of a triangle with a base of 10 in. and an altitude of 14 in. (The formula for the area of a triangle is A = bh ÷ 2.)
A. 280 sq in.
B. 24 sq in.
C. 70 sq in.
D. 140 sq in.
Hello There!
We know that the formula of a triangle is "Base Multiplied By Height And Then Divide It By 2"
First, let's plug in our numbers. Our base is going to be 10 inches so we have 10 multiplied by our height which is 14 inches and we get a product of 140.
Next, we divide 140 by 2 to get a quotient of 70.
Finally, our answer is 70in squared
Half of the product of two consecutive numbers is 105. To solve for n, the smaller of the two numbers, which equation can be used?
A.) n^2 + n – 210 = 0
B.) n^2 + n – 105 = 0
C.) 2n^2 + 2n + 210 = 0
D.) 2n^2 + 2n + 105 = 0
Answer:
A
Step-by-step explanation:
Consecutive nnumbers are spaced 1 units apart.
Such as 4,5,6,...
or 12,13,14,...
Thus,
if smaller number is n, then the next number (consecutive) is n+1
Since, half of the product of them is 105, we can write the equation as:
[tex]\frac{1}{2}((n)(n+1))=105[/tex]
We can do some algebra and make it in quadratic form as shown below:
[tex]\frac{1}{2}((n)(n+1))=105\\\frac{1}{2}(n^2 + n)=105\\n^2+n=2*105\\n^2+n=210\\n^2+n-210=0[/tex]
Answer choice A is right.
Answer:
A.) n^2 + n – 210 = 0
Step-by-step explanation:
just took edg 2022. hope this helps!
The bill for five glasses of apple juice and four salads is $9.50, but the total for four glasses of apple juice and five salads is $10.30. What would the be the bill for a glass of juice and a salad?
Answer:2.20
Step-by-step explanation:
Please help, I'm taking the semester test.
Drag and drop an answer to each box to correctly explain the derivation of the formula for the volume of a pyramid.
Consider a prism and a pyramid with the same base and height.
The volume of the prism is blank, the volume of the pyramid.
The formula for the volume of a prism is V=Bh ,
where B is the area of the base and h is the height, so the formula for the volume of a pyramid is blank
Picture shown below
The volume of a pyramid is one-third of the volume of a prism with the same base area and height, yielding the formula V = (1/3)Bh for the volume of a pyramid.
Explanation:When comparing the volume of a prism and a pyramid with the same base and height, the volume of a pyramid is one-third of the volume of the prism. Therefore, the formula for the volume of a prism is V = Bh, where B is the base area and h is the height. Applying this to the pyramid, the pyramid's volume becomes V = (1/3)Bh. This formula tells us that the volume of a pyramid is equal to one-third of the product of the area of its base and its height.
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The quoient of two rational numbers is positive. What can you conclude about signs of the dividend and the divisor?
Answer:
the two signs are the same
Step-by-step explanation:
Whenever the quotient or product of two operands is positive, the signs of the operands are both the same, both negative or both positive.
__
Comment on the general case
Whenever the product of any number of operands is positive, the number of negative signs among the factors is even.
A quotient is the product of one operand and the reciprocal of another (the denominator). A number and its reciprocal have the same sign.
What is the area of the sector bound by the center of the circle and arc CD in the circle below? Circle A is shown with a radius labeled 15 feet and a central angle marked 45 degrees. 9.42 ft2 19.54 ft2 34.89 ft2 88.31 ft2
Answer:
D.Area of sector=88.31 square feet.
Step-by-step explanation:
We are given that a circle A and its radius is 15 feet.
The central angle is equal to 45 degrees.
Radius of circlle=15 feet
Angle at center=[tex]\theta=45^{\circ}[/tex]
We know that the area of sector
Area of sector=[tex]\frac{\theta}{360}\times \pi r^2[/tex].
We take value of [tex]\pi=3.14[/tex]
Substituting all given values in the given formula
Area of sector=[tex]\frac{45}{360}\times 3.14\times 15\times 15[/tex]
Area of sector=[tex]\frac{31792.5}{360}[/tex]
Area of sector= 88.3125 square feet
Hence, area of sector=88.31 square feet.Therefore, option D is correct answer.
What is the length of the missing side? What is the area of the figure?
Show ALL work.
Answer:
Missing side=25 units.
Area of the figure= 470 sq units.
Step-by-step explanation:
The figure is made up of a rectangle and a triangle.
To get the base of the triangle, we find the difference between the two parallel sides, that is, 16ft and 31 ft.
31ft-16ft=15ft
The height of the triangle is 20 since it is parallel and equal to the length of the rectangle.
We therefore use pythagoras theorem to find ?
a²+b²=c²
15²+20²=c²
625=c²
c=25
ii. The figure is a trapezium therefore we use the following formula to find the area.
A= 1/2(a+b)h, where a and b are the two parallel sides. and h the distance between them.
=(1/2)(31+16)×20
=470 sq units
if y is the midpoint of xz, y is located at (3,-1), and z is located at (11,-5), find the coordinates of x
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ X(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad Z(\stackrel{x_2}{11}~,~\stackrel{y_2}{-5}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{11+x}{2}~~,~~\cfrac{-5+y}{2} \right)=\stackrel{\stackrel{midpoint}{y}}{(3,-1)}\implies \begin{cases} \cfrac{11+x}{2}=3\\[1em] 11+x=6\\ \boxed{x=-5}\\ \cline{1-1} \cfrac{-5+y}{2}=-1\\[1em] -5+y=-2\\ \boxed{y=3} \end{cases}[/tex]
We define midpoint formula as
[tex]Y(x_m, y_m)=Y(\dfrac{x_2+x_1}{2}, \dfrac{y_2+y_1}{2})[/tex]
Also here are the coordinates of every point in variables so you won't get confused.
[tex]
Y(x_m, y_m) \\
X(x_1, y_1) \\
Z(x_2, y_2)
[/tex]
Which means there are two equations. One to find x of point X and one to find y of point X.
[tex]
x_m=\dfrac{x_2+x_1}{2}\Longrightarrow 3=\dfrac{11+x_1}{2} \\
6=11+x_1\Longrightarrow\underline{x_1=-5} \\ \\
y_m=\dfrac{y_2+y_1}{2}\Longrightarrow-1=\dfrac{-5+y_1}{2} \\
-2=-5+y_1\Longrightarrow\underline{y_1=3}
[/tex]
So point X has coordinates: [tex]\boxed{X(-5, 3)}[/tex]
Hope this helps.
r3t40
Help with this question, please!
Answer:
The last choice is the one you want.
Step-by-step explanation:
Simply take the x coordinate and subtract 4, then do the same with the y coordinate since the vector movement is <-4, -4>. The first coordinate F is <4,0>. Subtract 4 from both of those coordinates and end up at <0, -4>. The second coordinate G is <1, 3>. Subtract 4 from both of those and end up at <-3, -1>. The third coordinate H is <2, 6>. Subtract 4 from both of those and end up at <-2, 2>. The last coordinate I is <4, 2>. Subtract 4 from both of those and end up at <0, -2>.
NEED HELP WITH A MATH QUESTION
For this case we have that the total of objects is given by:
Large blue objects, small blue objects, large red objects and small red objects.
In total we have: [tex]17 + 3 + 8 + 12 = 4[/tex]0 objects.
If we want to find the probality of obtaining small and blue objects we have to:
[tex]p = \frac {3} {40}[/tex]
ANswer:
[tex]p = \frac {3} {40}[/tex]
Suppose the population of a town is 127,000 in 2014. The population increases at a rate of 5.2 percent every year. What will the population of the town be in 2020? Round your answer to the nearest whole number.
Answer:
172,146
Step-by-step explanation:
you can use the exponential growth formula and get y=127000(1.052)^6. after that, you can just solve (make sure you use PEMDAS) and get 172,146.
The population in 2020 will be 177800.
What is population growth rate definition?The annual average rate of change of population size, for a given country, territory, or geographic area, during a specified period.
Population growth rate formula[tex]P = P^{'} (1+i)^{n}[/tex]
where,
P is the future population size
[tex]P^{'}[/tex] is the initial population size
[tex]i[/tex] is the growth rate
n is number of periods, such as years
According to the given question
we have
Initial population = 127000
[tex]i[/tex] = 5.2% = [tex]\frac{5.2}{100} = 0.052[/tex]
n = 6 years (2020-2014 = 6years)
therefore,
population of the town in 2020 = 127000[tex](1+0.052)^{6}[/tex]
Population of town in 2020 = 127000×[tex](1.052)^{6}[/tex]
Population of town in 2020 = 127000 ×1.4
Population of town in 2020 = 177,800
Hence, the population of town in 2020 will be 177800.
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PLEASE HELP ASAP! SUPER URGENT!! Find each lettered angle measure without using a protractor. State the reason why you gave the measure you did using the correct vocabulary from the unit.
m∠a Reason:
m∠b Reason:
m∠c Reason:
Answer:
Step-by-step explanation:
a: 70°
Reason: a is supplementary to the angle that measures 110°, so 180° - 110° = 70°
b: 55°
Reason: b is vertical to the angle between 100° and 25° (which add up to 125°) and since all of those angles added together have to equal 180°, then the unidentified angle between 100° and 25° = 55°. b is vertical to that angle so b = 55°
c: 25°
Reason: c is vertical the angle measuring 25° so c = 25° also.
A rancher wants to fence in an area of 1,000,000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. Find a function that models the amount of fencing in terms of the width of the field, w, where w is the measurement of the fence down the middle of the field.
Answer:
f(w) = 3w + 2,000,000/w
Step-by-step explanation:
We know that the area of a rectangle is the product of its length and width:
A = LW
Filling in the given values lets us write an expression for the length of the field.
1,000,000 = Lw
L = 1,000,000/w
Since there are 3 fences of length w and two of length L, the total perimeter fence length is the sum ...
f(w) = 3w + 2(1,000,000)/w
Combining the constants, we have a function for the perimeter fence length in terms of the width of the field:
f(w) = 3w +2,000,000/w
Final answer:
The function that models the amount of fencing required for a 1,000,000 square foot rectangular field divided in half by a fence is F(w) = 3w + 2,000,000 / w. This represents the total length of fencing as a function of the width w.
Explanation:
The student is asking for a function that models the amount of fencing required for a rectangular field with an area of 1,000,000 square feet, which is then divided in half by a fence parallel to the width, w. To begin, let's denote the length of the field as L and the width as w. Since the area of the rectangle is given by L multiplied by w, and we know that the area is 1,000,000 square feet, we can express the length L in terms of w as L = 1,000,000 / w.
Now, total fencing required would be the perimeter of the rectangle plus the additional fence dividing it in half. The perimeter is calculated as 2w + 2L. Therefore, the total fencing F in feet would be F(w) = 2w + 2L + w.
Substituting L with 1,000,000 / w, the function becomes F(w) = 2w + 2(1,000,000 / w) + w = 3w + 2,000,000 / w. This function represents the total length of fencing needed in terms of the width w of the field.
Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 254°
Answer: 614° and -106°
Step-by-step explanation:
You have this angle in degrees:
254°
Then, in order to find the measure of a positive angle conterminal with the given angle in degrees (254°), you need to add 360 degrees. Therefore, the measure of the positive angle is:
[tex]254\°+360\°=614\°[/tex]
Now, to find the measure of a negative angle coterminal with the given angle in degrees (254°), you need to subtract 360 degrees. Therefore, this is:
[tex]254\°-360\°=-106\°[/tex]
{8x + 9y = −3 6x + 7y = 1 What values of x and y satisfy the system of equations
Answer:
A) 8x + 9y = −3
B) 6x + 7y = 1
We multiply A) by -(6/8)
A) -6x -6.75y = 2.25 then we add this to equation B
B) 6x + 7y = 1
.25y = 3.25
y = 13
and x = -15
Step-by-step explanation:
The value of x= -15 and the value of y= 13 for the given system of equations: 8x+9y=−3 and 6x+7y=1.
Let’s solve the system of equations:
8x+9y=−3
6x+7y=1
We can solve the system of equations using elimination.
Steps to solve:
1. Solve the second equation for y:
y= 1/7
2. Substitute this value of y into the first equation:
8x+9(1/7)=−3
8x+9/7 =−3
8x=−120
x=−15
3. Substitute x=-15 back into the second equation to solve for y:
6(−15)+7y=1
−90+7y=1
7y=91
y=13
Therefore, the value of x= -15 and the value of y= 13 for the given system of equations: 8x+9y=−3 and 6x+7y=1.
Lisa has $150 at most to spend on clothes. She wants to buy a pair of jeans for $58 and will spend the rest on t-shirts that cost $14 each. (5 points each) 2. Create an inequality to represent the number of t-shirts that Lisa can purchase. You can create a visual model in a paint program if that helps. Make sure you explain what the variable represents in your inequality
The inequality used in this situation will be 14x + 58 < 150.
What is inequality?The word inequality means a mathematical expression in which the sides are not equal to each other.
Let the no. of T-shirts Lisa can buy be = X
Cost of each T-shirt = $14
No. of jeans she bought = 1
Cost of jeans = $58
Total money she has = $150
Hence, the inequality will be 14X + 58 < 150.
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Lisa can spend a maximum of $92 on T-shirts after buying jeans, and with each T-shirt costing $14, she can buy up to 6 T-shirts as represented by the inequality 14t <= $92, where t is the number of T-shirts.
Explanation:To create an inequality representing the number of T-shirts Lisa can purchase, let's define the variable t to represent the number of T-shirts. Lisa has $150 to spend, and she wants to buy a pair of jeans for $58, leaving $150 - $58 = $92 for T-shirts. Each T-shirt costs $14, so if Lisa buys t T-shirts, the cost for the T-shirts is 14t. The inequality to represent the maximum number of T-shirts Lisa can buy is 14t ≤ $92.
Now, to solve for t, we divide both sides of the inequality by 14: t ≤ $92 / $14, which simplifies to t ≤ 6.57. Since Lisa cannot buy a fraction of a T-shirt, the maximum number of T-shirts she can buy is 6.
Photo question; find the length
[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} \theta =135\\ r=11.4 \end{cases}\implies s=\cfrac{\pi (135)(11.4)}{180}\implies s=8.55\pi \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill s\approx 26.86~\hfill[/tex]
Answer:
[tex]\boxed{\textbf{26.9 m}}[/tex]
Step-by-step explanation:
The formula for the arc (s) of a circle is
[tex]s = r\theta \times \dfrac{\pi }{180^{^{\circ}}}[/tex]
where θ is measured in degrees.
Data:
r = 11.4 m
θ = 135°
Calculation:
[tex]s = \text{11.4 m} \times 135^{^{\circ}}\times\dfrac{\pi}{180^{^{\circ}}} = \textbf{26.9 m}\\\\\text{The length of the arc is }\boxed{\textbf{26.9 m}}[/tex]
What solid is generated when the semicircle is rotated about the line?
A. sphere
B. cone
C. solid cylinder
D. hollow cylinder
Answer:
If the semicircle rotated around the line, it would become a sphere. So, A. sphere.
Step-by-step explanation:
A sphere is generated when a semicircle is rotated about the line.
What is solid revolution?A solid of revolution is a solid figure obtained by rotating a plane curve around some straight line.
What is sphere?Sphere is the set of all points in three-dimensional space lying the same distance from a given point or the result of rotating a semicircle about one of its diameters.
According to the given question.
A semicircle is rotated about the line.
Now,
From the definition of sphere we can say that, when a semicircle is rotated about a line a sphere will generate.
Therefore, a sphere is generated when a semicircle is rotated about the line.
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What is the equation of the ellipse with vertices at (-25, 0), (25, 0) and co-vertices (0, -15), (0, 15)?
Check the picture below.
[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ a=25\\ b=15 \end{cases}\implies \cfrac{(x-0)^2}{25^2}+\cfrac{(y-0)^2}{15^2}=1\implies \cfrac{x^2}{625}+\cfrac{y^2}{225}=1[/tex]
In the diagram shown, /Il m, m
1 = 3x + 25 and m_8 = 4x - 17.
Find the measure of 2.
29
49°
131°
151
Answer:
29°
Step-by-step explanation:
Angles 1 and 8 are alternate exterior angles where a transversal crosses parallel lines, so are congruent.
m∠1 = m∠8
3x+25 = 4x-17
42 = m . . . . . . . . add 17-3x
Then the measure of ∠1 is 3·42 +25 = 151 (degrees), and the measure of its supplement, ∠2 is ...
m∠2 = 180° -151° = 29°
prove algebraically that the straight line with equation x=2y+5 is a tangent to the circle with equation x^2+y^2=5
I have gotten 4/5 marks but I need to get 5/5
Thank you!
A tangent line will have a couple of characteristics:
there is exactly one point of intersection with the circlea perpendicular line through the point of tangency intersects the center of the circleSubstituting for x in the equation of the circle, we have ...
(2y+5)^2 +y^2 = 5
5y^2 +20y +20 = 0 . . . . simplify, subtract 5
5(y +2)^2 = 0 . . . . . . . . . factor
This equation has exactly one solution, at y = -2. The corresponding value of x is ...
x = 2(-2) +5 = 1
So, the line intersects the circle in exactly one point: (1, -2).
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The center of the circle is (0, 0), so the line through the center and point of intersection is ...
y = -2x . . . . . . . . . slope is -2
The tangent line is ...
y = 1/2x -5/2 . . . . . . slope is 1/2
The product of slopes of these lines is (-2)(1/2) = -1, indicating the lines are perpendicular.
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We have shown ...
the tangent line intersects the circle in one point: (1, -2)the tangent line is perpendicular to the radius at the point of tangency.