Answers
Answer:
The point of intersection would be (3,-2)
Step-by-step explanation:
To determine the intersection of the conics we can use a system of equations since they intersect when they are both equal.
Then, we have these equations:
[tex]\begin{gathered} (x+1)^2+(y+2)^2=16\text{ (1)} \\ (y+2)^2=16-(x+1)^2\text{ (1)} \\ (y+2)^2=4(x-3)\text{ (2)} \end{gathered}[/tex]Equalize equations (1) and (2).
[tex]\begin{gathered} 4(x-3)=16-(x+1)^2 \\ \end{gathered}[/tex]Solve for the x-coordinate.
[tex]\begin{gathered} 4x-12=16-(x^2+2x+1) \\ 4x-12=16-x^2-2x-1 \\ x^2+6x-27=0 \\ (x-3)(x+9)=0 \\ \text{Possible x-intersections:} \\ x=3 \\ x=-9 \end{gathered}[/tex]Since the circle has a radius of 4, we know that the intersection cannot be x=-9. Then, the x-coordinate to use is x=3.
Substitute x=3 into one of the equations to determine the y-coordinate:
[tex]\begin{gathered} (y+2)^2=4(3-3) \\ (y+2)^2=0 \\ y^2+4y+4=0 \\ (y+2)(y+2)=0 \\ y-\text{coordinate:} \\ y=-2 \end{gathered}[/tex]Hence, the point of intersection would be (3,-2)
Related Questions
Give the range of the relation. 2), (18, 4) (11, -3), (2, -2), (2, 0), (6, a. range: 11, 6, 2, 18 b. range: -3, -2, 2, 4 c. range: 11, 6, 0, 2, 18 d. range: -3, -2, 0, 2, 4
Answers
Give the range of the relation. (18, 4) (11, -3), (2, -2), (2, 0), (6, 2)
a. range: 11, 6, 2, 18
b. range: -3, -2, 2, 4
c. range: 11, 6, 0, 2, 18
d. range: -3, -2, 0, 2, 4
we know that
the range are the possible values of y in the data set
so
In this problem
range 4,-3,-2,0,2
therefore
the answer is the option dExampleIf you have(3,1), (2,8), (7,3), (5,0)the range are the values of ysothe value of y is the second coordinate in each ordered pair(3,1) ------> y-coordinate is 1(2,8)-----> 8(7,3) ----> 3(5,0) ----> 0thereforethe range is 1,8,3,0orderRange (0,1,3,8)use synthetic division to find the awnser write the quotient and write any remainders in fraction form (3x^3-x^2-9x+5)÷(x-2)
Answers
The given expressions are
[tex]\begin{gathered} 3x^3-x^2-9x+5 \\ x-2 \end{gathered}[/tex]We have to use the coefficients only to divide. Remember that the number 2 must multiply all the numbers in the quotient. The synthetic division would be:
x3 x2 x
| 3 -1 -9 5
2 | 6 10 2
3 5 1 7
Notice that the remainder is 7, the quotient would be the coefficients under the line.
The quotient is[tex]3x^2+5x^{}+1[/tex]Notice that the quotient doesn't include the number 7 because that's the remainder.
The remainder is 7.We can express the quotient, the remainder, and the divisor as follows:[tex]\frac{3x^3-x^2-9x+5}{x-2}=3x^2+5x+1+\frac{7}{x-2}[/tex]Question 8 of 10, Step 1 of 15/10CorrectIn a park, the ratio of adults to children is 12 to 11. If there are 368 people in the park, how many children are there?AnswerекеKeyboard ShochildrenSubmit Answer
Answers
STEP - BY - STEP EXPLANATION
What to find?
Number of children in the park.
Given:
• Ratio of adult to children =12: 11
,• Total ratio =23
,• Number of people in the park =368
To solve the given problem, we will follow the steps below:
Step 1
Use the formula below to solve the given problem:
[tex]Number\text{ }of\text{ }children=\frac{ratio\text{ of children}}{total\text{ ratio}}\times number\text{ of people}[/tex]Step 2
Substitute the values into the formula.
[tex]Number\text{ }of\text{ }children=\frac{11}{23}\times368[/tex][tex]=\frac{4048}{23}[/tex][tex]=176[/tex]Therefore, there are 176 children in the park.
Find the number of complex roots and the number of possible real roots for the equation: 2x^4-3x^3+x^2-7x+3=0
Answers
You have the following polynomial:
2x⁴ - 3x³ + x² + 7x + 3 = 0
Based on the grade of the previous polynomial, you can conclude that there are 4 roots.
The complex roots are always present in pairs. Then, it's possible the given polynomial has 4 complex roots. In case there are 2 real roots, then, there are two comlpex roots.
Otherwise, there are 4 real roots.
Then, you can conclude for the possible roots of the polynomial:
- 4 real roots
- 4 complex roots
- 2 real roots and 2 complex roots
On the grid below triangle MNP is plotted with vertices at M(-10,-2), N(-6,-9) and P(1,-5). The line y=-2/3x is also drawn.(a) Draw the image of triangle MNP after a reflection in y=-2/3x. Give the coordinates of the transformed vertices below.(b) Explain why triangle M'N'P' must have the same area as triangle MNP.
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We have the following:
The reflection is:
[tex]\begin{gathered} M(-10,-2)\rightarrow M^{\prime}(2,10) \\ N(-6,-9)\rightarrow N^{\prime}(9,6) \\ P(1,-5)\rightarrow P^{\prime}(5,-1) \end{gathered}[/tex]a) The graph is:
b)
Since the sides are still the same length, for this reason keep the same area
If three times the sum of a number and 1 is 15, find the number.
Answers
The number is 4.6
Let the number be x
The equation will be 3x+1=15
on solving the equation we get
3x = 15-1
X = 14/3
X = 4.6
To learn more about Numbers click here: https://brainly.com/question/29624796
please help me figure out how to determine the range of the following graph (the line y=5 is a horizontal asymptote)
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we are given the graph of the function and we are interested in finding the range of the function. Recall that the range of a graph is simply the set of values on the y axis, for which there is a point on the graph that has that y coordinate.
One easy way to spot this set, is by taking any point on the graph and then drawing a horizontal line. Wherever the line crosses the y axis, that point is included in the range.
From the graph, we can see that no part of the graph has values with y coordinate less than 5. That is, any number less than 5 in the y coordinate would indicate that there is no point on the graph at that "height". So every number less than 5 is excluded from the range.
We are also told that line y=5 is a horizontal asymptote. This means that despite the graph is really close to the line y=5 (and it keeps getting closer and closer as x increases), it never touches the line. This means that the point 5 is excluded from the range.
Finally, we can see that above the horizontal line y=5, if we draw a horizontal line on the graph, it will touch the y axis. This means that every number greater than 5 is part of the range. Then, the set of numbers that represent the range is
[tex](5,\text{infinity)}[/tex]Use the Pythagorean theorem to find each missing length to the nearest tenth I want you tell how to do please
Answers
Let the unknown side be h
Pythagoras theorem states that the square of the hypotenuse is equal to the square of the opposite plus the square of the adjacent in any right angled triangle
[tex]\begin{gathered} \text{From the figure, } \\ \text{hypotenus = h} \\ \text{Let opposite = 3, adjacent = 10} \\ \text{Therefore, applying pythagoras theorem,} \\ h^2=3^2+10^2 \\ h^2=9+100 \\ h^2=109 \\ h=\sqrt[]{109} \\ h=10.44 \\ h\approx10.4\text{ (nearest tenth)} \end{gathered}[/tex]The missing length is 10.4
You are asked to create a graphic that would make it easy to quickly tell which locations require that ear protection be worn after 12 hours of exposure with the understanding that the sound level limit is 87. Would the proposed new graphic accomplish this purpose?
Answers
Answer:
Step-by-step explanation:
The answer would be "Yes, because ordering from lowest sound level to highest sound level makes it easy to use the exposure graph to see what time is permitted."
Hopes this helps.
3. Create a fraction with a denominator of 100 that is equivalent to to Your answer DELL
Answers
80/100
Explanation:We are to find an equivalent fraction to 8/10. But in this case the denominator needs to be 100
[tex]\begin{gathered} \text{Given denominator = 10} \\ \text{new denominator = 100} \\ \frac{\text{new denominator }}{\text{given denominator }}=\frac{100}{10}=\text{ 10} \end{gathered}[/tex]This means the multiplying number to the given denominator is 10.
For equivalent fraction, we multiply the numerator and the denominator by the same number
So we would multiply the given numerator too by the multiplying number 10
[tex]\begin{gathered} \text{Given numerator = 8} \\ \text{New numerator = 8}\times10\text{ = 80} \end{gathered}[/tex]The equivalent fraction to 8/10 becomes:
[tex]\begin{gathered} Thefraction=\frac{\text{new numerator}}{\text{new denominator}} \\ Thefraction=\frac{80}{100} \end{gathered}[/tex]Z1 and Z2 are a linear pair and the mZ1 is 9 times the measure of Z2. Find mZ1.mZ1 =degrees
Answers
Question 3 The graph of the equation x + 3y=6 intersects the y- axis at which coordinate point? (0, 2) (0, 6) (0, 18) (6, 0)
Answers
The intersection with the y-axis ocurrs at x=0. That is, by substituting x=0 in our given expression, we get
[tex]0+3y=6[/tex]which gives
[tex]\begin{gathered} 3y=6 \\ y=\frac{6}{3} \\ y=2 \end{gathered}[/tex]Then, the intersection point is (0,2). Which corresponds to the first option.
the following data set shows the number of books checked out from the library during the first two weeks of the month .36, 39, 40, 42, 45, 2, 38, 41, 37, 38, 35, 37, 35, 38
Answers
According to the given data set, we can observe that there's one day where people only checked out 2 books which is way too low compared to the other days, which represents an outlier.
Hence, the answer is 1) there is one outlier, indicating very few books were checked out on that day.Rodney thinks that sqaure to the third power of 64 is greater than 17/4. Sam thinks that 17/4 is greater. Who is right and why?
Answers
The result of a square to the third power is a number that mutiplied 3 times by itself results in the number inside the square.
For example
[tex]\sqrt[3]{8}=2[/tex]because 2*2*2=8.
In this case:
[tex]\sqrt[3]{64}=4[/tex]That is because 4*4*4=64.
Now, we compare this with 17/4:
[tex]\frac{17}{4}=4.25[/tex]Thus, since 4 is less than 17/4. The one who is right is Sam, because 17/4 is greater than 4
In an all boys school, the heights of the student body are normally distributed with a mean of 71 inches and a standard deviation of 3.5 inches. Out of the 1707 boys who go to that school, how many would be expected to be taller than 75 inches tall, to the nearest whole number?
Answers
The formula for the z score of a number is given by:
[tex]z=\frac{x-\overline{x}}{\sigma}[/tex]Where:
[tex]\begin{gathered} x=\text{ the observed value} \\ \overline{x}=\text{ the mean} \\ \sigma=\text{ the standard deviation} \end{gathered}[/tex]In this case,
[tex]\begin{gathered} x=75 \\ \overline{x}=71 \\ \sigma=\text{ 3.5} \end{gathered}[/tex]Therefore, the z score of x=75 is given by:
[tex]z=\frac{75-71}{3.5}=\frac{4}{3.5}\approx1.143[/tex]Therefore, the probability that a boy is taller than 75 inches is given by the area under the normal probability distribution curve between z=1.143 and z=∞, P(z > 1.143):
The area is approximately 0.1265.
Therefore, the required probability is 0.1265.
Convert the probability to percent by multiplying with 100:
[tex]0.1265\times100=12.65[/tex]Hence, about 12.65 % of all the boys are taller than 75 inches.
Therefore, the total number of boys that are taller than 75 inches is given by:
[tex]\frac{12.65}{100}\times1707\approx216[/tex]Therefore, the number of boys expected to be taller than 75 inches is approximately:
216
You bought a notebook and four erasers at Target. The notebook cost 5$.You spent a total of 25$ at target. How much did each eraser cost
Answers
You bought:
1 notebook
4 eraser
Total Cost = 25.
Now, given Notebook = $5, so
25 - 5 = 20 dollars are left for [4 erasers]
So, each eraser would cost:
20/4 = 6 dollars
Thus,
Each Eraser Cost = $6
Suppose you were given $600 from your uncle. You deposited that money in a bank and added $50 per month.
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The 1-variable equation that we need to solve to find how many months it would take to save $10,000 is given when we equal s(x)=10,000.
Hence, the answer is:
[tex]50m+600=10,000[/tex]Now, to find how many months it would take to save 10,000, we need to solve for m the previous equation. Therefore:
[tex]50m+600=10,000[/tex]Subtract both sides 600
[tex]50m+600-600=10,000-600[/tex][tex]50m=9400[/tex]Then, divide both sides by 50:
[tex]\frac{50m}{50}=\frac{9400}{50}[/tex][tex]m=188[/tex]Hence, it would take 188 months to save $10,000
Sallys recipe for chocolate chip cookies yields 48, 1 oz cookies. If she want to make 48,2 oz cookies what is her conversation factor??(Hint : how many total oz cookies is in the original recipe yield and the new recipe yields)
Answers
Pick a situation related to your major that would be modeled by one of the models discussed in class. Describe why this model would be helpful. Models are any application/word problem used for exponential/logarithmic functions. For example, exponential growth or decay are models of exponential functions. Now, choose one that would fit with your career path and describe why it would be helpful.
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To measure sound, we use the measure decibel which in fact is a logartimic funcion of the amplitude of a soud
To measure eartquakes, we use the Richter scale whci is a logaritmic function of the amplitude of the force of an earthquake
To calculate how long a body has been dead, the coroner must know how long the body temperature has not been at 98.6 degrees. Because the rate of the body cooling is proportionate to temperature differences between the body and its surroundings, the answer is found by calculating exponential decay using logarithms.
Tano went to a professional basketball game He spent $54.85 for a ticket S4 99 for a hot dog and $2 15 for a soda What is the total amount that he spent? Use mental math to find the sum. A S60.99 O B 961.00 O C 561.99 OD 96200
Answers
The total amount is calculated as the sum of the cost of the ticket, the cost of the hot dog, and the cost of the soda.
So, the total amount is:
[tex]54.85+4.99+2.15=61.99[/tex]Answer: $ 61.99
To answer it using mental math, we can add 0.85 and 0.15 and get 1, add 54 and 2 and get 56 and approximate 4.99 to 5.
Then, the sum 1 + 56 + 5 is equal to 62.00 but we need to subtract 0.01 because of the approximation. Therefore the final result is:
62.00 - 0.01 = 61.99
2x+3y=5 at (-2,3) find the equation of the tangent line
Answers
The slope of the tangent line to the line 2x+3y=5 can be found by differentiating 2x+3y=5.
Differentiating 2x+3y=5 with respect to x, we get
[tex]\begin{gathered} 2+3\frac{dy}{dx}=0 \\ 3\frac{dy}{dx}=-2 \\ \frac{dy}{dx}=\frac{-2}{3} \end{gathered}[/tex]m=dy/dx is the slope of tangent line.
Hence, slope, m=-2/3.
Now, the equation of the tangent line passing through point (x1, y1)=(-2, 3) with slope m=-2/3 can be found as,
[tex]\begin{gathered} m=\frac{y_1-y}{x_1-x} \\ \frac{-2}{3}=\frac{3-y}{-2-x} \\ -2(-2-x)=3(3-y) \\ 4+2x=9-3y \\ 3y+2x=5 \end{gathered}[/tex]Therefore, the equation of the tangent line is 3y+2x=5.
if i can't do the practice test how am I gonna pass the actual test lol
Answers
According to the given diagram, angles COD and DOE are complementary angles because they are on a right triangle, which means they sum 90°.
[tex]\begin{gathered} m\angle COD+m\angle DOE=90 \\ 54+m\angle DOE=90 \\ m\angle DOE=90-54 \\ m\angle DOE=36 \end{gathered}[/tex]Therefore, angle DOE is 36°.I need help with this I need to know what I’m doing wrong.. do I need to put a negative for (y+8^2) or a positive 8 so confused… help #4write in standard equation for a circle and identify center and radius
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4) You have the following equation:
[tex]x^2+10x+y^2-16=0[/tex]In order to determine the radius and center of the circle, complete squares for x. You don't complete squares for y because there is no term with y in the given expression. It is only a y^2 term.
By adding 25 and subtracting 25 left side of the equation you obtain:
[tex]x^2+10x+25+y^2-16-25=0[/tex]The first three terms are a perfect square (x + 5)^2, then, by using this factor and by simplifying in the previous equation you can write:
[tex](x+5)^2+y^2-41=0[/tex]Finally, add 41 both sides:
[tex](x+5)^2+y^2=41[/tex]The previous equation is in standard form for a circle equation:
[tex](x-h)^2+(y-k)^2=r^2[/tex](h,k) is the center of the circle and r the radius. By comparin the previous equation with the expression you obtain you obtain:
center of the circle = (-5,0)
radius r = √41
The ratio of men to women in a certain factory is 3 to 4. There are 228 men. find the number of women
Answers
Given
The ratio of men to women in a certain factory is 3 to 4. There are 228 men. find the number of women
Solution
Let the number of women be x
[tex]\begin{gathered} Men\text{ : Women} \\ 3\text{ : 4} \\ 228:\text{ x} \end{gathered}[/tex][tex]\frac{3}{4}=\frac{228}{x}[/tex]cross multiply
[tex]\begin{gathered} 3\times x=4\times228 \\ 3x=912 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{3x}{3}=\frac{912}{3} \\ \\ x=304 \end{gathered}[/tex]The number of women is 304
Find the product of the complex numbers. Leave your answer in polar form
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Given: Two complex numbers below
[tex]\begin{gathered} z_1=2+2i \\ z_2=-3+3i \end{gathered}[/tex]To Determine: The product of the given complex numbers
[tex]z_1z_2=(2+2i)(-3+3i)[/tex][tex]\begin{gathered} z_1z_2=2(-3+3i)+2i(-3+3i) \\ z_1z_2=-6+6i-6i+6i^2 \\ z_1z_2=-6+6i^2 \end{gathered}[/tex]Please note that
[tex]\begin{gathered} i=\sqrt[]{-1} \\ i^2=(\sqrt[]{-1})^2_{} \\ i^2=-1 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} z_1z_2=-6+6i \\ z_1z_2=-6+6(-1) \\ z_1z_2=-6-6 \\ z_1z_2=-12+0i \end{gathered}[/tex]Let us convert the product to polar form
Please note that
[tex]\begin{gathered} if,z=x+iy,the\text{ polar form is} \\ z=r(\cos \theta+i\sin \theta) \\ \text{where} \\ r=\sqrt[]{x^2+y^2} \\ \tan \theta=\frac{y}{x} \\ \theta=tan^{-1}(\frac{y}{x}) \end{gathered}[/tex]Apply the conversion into the product we got
[tex]\begin{gathered} z_1z_2=-12+0i,x=-12,y=0 \\ r=\sqrt[]{x^2+y^2}=\sqrt[]{(-12)^2+0^2} \\ r=\sqrt[]{144+0} \\ r=\sqrt[]{144} \\ r=12 \\ \theta=\tan ^{-1}(\frac{0}{-12}) \\ \theta=\tan ^{-1}(0) \\ \theta=\pi \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} z_1z_2=r(\cos \theta+i\sin \theta) \\ r=12,\theta=\pi \\ z_1z_2=12(\cos \pi+i\sin \pi) \end{gathered}[/tex]Hence, the product of the complex numbers in polar form is
12(cosπ+isinπ)
Focus (1,4)Directrix=x-7,What is the vertex (h,k)?what is p?what is the equation?
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Let's begin by listing out the information given to us:
[tex]undefined[/tex]Graph: x < -2 I need help graphing this problem
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Kindly check below.
1) Usually, whenever we need to graph an inequality, we need to treat it as if it was an equation.
2) So if we consider that x=-2 is a vertical line that passes through point -2, we can start with that.
3) Since the sign is < then we need to plot a dashed line delimiting the region to be shaded, given that -2 is not included. And finally, as it is lesser than -2 we can paint the region to the left of -2, where the numbers lesser than -2 are located.
4) So, our graph is:
A zebra and a giraffe are having a race, 300 yards from a row of trees (the starting line) to the edge of a stream (the finish line). When they start evenly, the zebra wins the race by 50 yards.They decide to race again, but in the second race the zebra has to start 50 yards behind the row of trees (350 yards from the finish line), while the giraffe starts at the usual starting line. The zebra and the giraffe always run at the same speeds from race to race. Who wins the second race? Explain your reasoning.
Answers
A zebra and a giraffe are having a race, 300 yards from a row of trees (the starting line) to the edge of a stream (the finish line). When they start evenly, the zebra wins the race by 50 yards.
They decide to race again, but in the second race the zebra has to start 50 yards behind the row of trees (350 yards from the finish line), while the giraffe starts at the usual starting line. The zebra and the giraffe always run at the same speeds from race to race. Who wins the second race? Explain your reasoning.
we have that
The speed is equal to divide tthe distance by the time
speed=d/t
t=d/speed
The zebra and the giraffe always run at the same speeds from race to race.
so
Race 1
Zebra ------> t=300/speed1
giraffe ----> t=(300-50)/speed2 -----> t=250/speed2
where t is the finishing time of the zebra
equate both equations
300/speed1=250/speed2
300/250=speed1/speed2
1.2=speed1/speed2
speed1=1.2speed2
that means ----> the spped of the zebra is 1.2 times the speed of the giraffe
Race 2
Zebra ----> t1=350/(1.2speed2) ------> t1=292/speed2
Giraffe ----> t2=300/speed2 ------> t2=300/speed2
compare the times
t1 < t2
that means
the zebra wins the race 2What is the length of the longer post's shadow? Write your answer in a COMPLETE SENTENCE.
Answers
Given
The length of two vertical post is 2meters and 0.45 meter respectively.
And, the length of shadow of the shorter post is 0.85meter.
To find:
The length of the shadow of the longer post.
Explanation:
It is given that,
The length of two vertical post is 2meters and 0.45 meter respectively.
And, the length of shadow of the shorter post is 0.85meter.
That implies,
Then,
[tex]\begin{gathered} \frac{2}{0.45}=\frac{x}{0.85} \\ x=\frac{2\times0.85}{0.45} \\ x=\frac{1.7}{0.45} \\ x=3.78m \end{gathered}[/tex]Hence, the length of the shadow of the longer post is 3.78m.
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Carter and Anna are making presentations for a class project. Carter's slideshow starts with a verbal introduction that is 13 seconds long, and then each slide is left up for 10 seconds. Anna leaves each slide onscreen for 6 seconds, and her introduction lasts 17 seconds. Carter and Anna notice that their presentations have both the same number of slides and the same duration. How long is each presentation? How many slides are in each presentation?
Answers
Given
Carter and Anna are making presentations for a class project.
Carter's slideshow starts with a verbal introduction that is 13 seconds long, and then each slide is left up for 10 seconds.
Anna leaves each slide onscreen for 6 seconds, and her introduction lasts 17 seconds.
Carter and Anna notice that their presentations have both the same number of slides and the same duration.
To find how long is each presentation and how many slides are in each presentation.
Now,
Let x be the time taken for each presentation and y be the number of slides.
Then, the equations are,
[tex]\begin{gathered} 13+10y=x\text{ \_\_\_\_(1)} \\ 17+6y=x\text{ \_\_\_\_\_(2)} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} 13+10y=17+6y \\ 10y-6y=17-13 \\ 4y=4 \\ y=1 \end{gathered}[/tex]Substitute y=1 in (1).
Then,
[tex]\begin{gathered} 13+10y=x \\ 13+10\times1=x \\ x=13+10 \\ x=23 \end{gathered}[/tex]Hence, the time taken for each presentation is 23 seconds and the number of slides is 1.