Answer:
The point of intersection is:
[tex]\displaystyle \left(\frac{6\sqrt{5}}{5}, \frac{3\sqrt{5}}{5}+5\right)\approx \left(2.68, 6.34)[/tex]
Step-by-step explanation:
We want to find the point in QI at which the line with the equation:
[tex]y=0.5x+5[/tex]
Intersect a circle with a radius of 3 and a center of (0, 5).
First, write the equation of a circle. The equation for a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h, k) is the center and r is the radius.
Since our center is (0, 5), h = 0 and k = 5. The radius is 3. So, r = 3. Substitute:
[tex](x-0)^2+(y-5)^2=(3)^2[/tex]
Simplify:
[tex]x^2+(y-5)^2=9[/tex]
At the point where the two equations intersect, its x-coordinate and y-coordinate will be the same. Therefore, we can substitute the equation of the line into the equation of the circle and solve for x. So:
[tex]x^2+((0.5x+5)-5)^2=9[/tex]
Simplify:
[tex]x^2+(0.5x)^2=9[/tex]
Square:
[tex]x^2+0.25x^2=9[/tex]
Combine like terms:
[tex]\displaystyle 1.25x^2=\frac{5}{4}x^2=9[/tex]
Solve for x:
[tex]\displaystyle \begin{aligned} x^2&=\frac{36}{5} \\ x&=\pm\sqrt{\frac{36}{5}} \\ x&\Rightarrow \frac{6}{\sqrt{5}}=\frac{6\sqrt{5}}{5}\approx2.68\end{aligned}[/tex]
Note that since we are looking for the point of intersection in QI, x should be positive. So, we can ignore the negative answer.
To find the y-coordinate, substitute the x-value back into either equation. Using the linear equation:
[tex]\displaystyle y=0.5\left(\frac{6\sqrt{5}}{5}\right)+5=\frac{3\sqrt{5}}{5}+5\approx 6.34[/tex]
So, the point of intersection in QI is:
[tex]\displaystyle \left(\frac{6\sqrt{5}}{5}, \frac{3\sqrt{5}}{5}+5\right)\approx \left(2.68, 6.34)[/tex]
Need help with it math
Answer:
oh itsA
Step-by-step explanation:
i did 1 plus 24
1. supplementary
2. complementary
3. 45
4. 8
5. 67
6. 135
7. 98
8. 157
9. x= 10
10. x= 6
11. x= 30
12. x=14
6 +7 ( □ +7 5) = 1
help me pls
Answer:
Can't be possible.
Step-by-step explanation:
Given:
6+7(x+75)=1
So according to given equation it can't be possible because when we add some value in 6 their result will be always greater than 1.
Which value is equal to 1/2 ?Select all that apply.
Please help fast fast !! Will give brainliest
Answer:
The Answer to your problem is A i'm pretty sure mark me brainliest plss and a thanks heart !!
PLEASE HELP. Last 3 times I asked people put spam, please do not this is urgent.
WILL MARK BRAINLIEST
Answer:
A) 2^12
Step-by-step explanation:
3x - y = 12
3(5) - 3 = 12
15 - 3 = 12
12 = 12
[tex]\frac{8^x}{2^y}[/tex]
[tex]\frac{8^5}{2^3}[/tex]
[tex]\frac{32768}{8}[/tex]
4096
2^12
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
Answer:
132.3328 or 132.33 if you round do the nearest hundredth
Step-by-step explanation:
To find area, just multiply length by width. 14.26x9.28=132.3328
If x = 0 and y > 0, where is the point (x, y) located?
Answer:
upper half y axis
Step-by-step explanation:
If x = 0 we are on the y axis. If y >0 we are on the upper half of the y axis
Which equation best matches the graph shown below?
Answer:
y=0.5(x+6)(x+5)
Step-by-step explanation:
Since the parabola goes upwards as it expands from the vertex, the "a" value is definitely positive so the answer must be either the top-left or bottom-right. Next, use the roots to find the final answer. The roots are on the left side of the y-axis which indicates that they are negative. Now you know that the answer is the bottom-right answer because if both roots are negative, then the expressions must include addition to create 0 which is the y-value at the bases.
2. 5 9. 14. ?. 27
18
20
21
16
Which is the missing number people :)))
Answer:
20
Step-by-step explanation:
The pattern goes
+3, +4, +5, +6, +7...
14+6=20
The missing number is 20
You start driving for 3 miles, turn right, and drive north for another 13 miles. At the end of driving, what is your straight line distance from your starting point? Round to the nearest tenth of a mile.
Answer:
13.34
Step-by-step explanation
Pythagorean Theorem: c= sqrt(a^2+b^2) or a^2=+b^2=sqrt(c)
3^2+13^2= sqrt(178) = 13.34166= 13.34
What is the surface area of the rectangular prism shown below?
A: 159
B: 294
C: 318
D: 378
(All squared)
Which inequality about the number line shown below is true
i got it wrong dont lisen to this
Answer:
option D
Step-by-step explanation:
D is equal to 0 that is greater than B which is -2 by theory
PLease help me with this math qestion
Answer:
n+3 = 15 ; n = 12
3n -6 = 12; n=6
Step-by-step explanation:
more than means it comes after
a number
n
3 more than
n+3
is 15
n+3 = 15
Subtract 3 from each side
n+3-3 = 15-3
n = 12
Subtract from comes after
three times a number
3n
six subtracted from
3n -6
is 12 means equal to
3n -6 = 12
To solve add 6 to each side
3n -6+6 =12+6
3n = 18
Divide by 3
3n/3 =18/3
n =6
Answer:
A = 3 - x = 15 B = 6 - 3 times x = 12
Step-by-step explanation:
77 out of 100 people Prefer sunny days what percentage of people prefer sunny days
Answer:
77% prefer sunny days because 77/100 is equivalent to 77%
what's the formula of finding an area of a room?
Answer:
For a square or rectangular room you will need the length and width
Then you multiply I.e length x width gives Area
bye :-)
What is the scale factor from ∆ABC to ∆DEF?
Answer:
D
Step-by-step explanation:
6*8 = 48
4*8 = 32
The circumference of a circle is 47 in. Find its diameter, in inches.
[tex]{ \bf{ \underbrace{Given :}}}[/tex]
Circumference of the circle = 47 inch.
[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]
The diameter of the circle.
[tex]{ \bf{ \underbrace{Solution :}}}[/tex]
[tex]\sf\orange{The\:diameter\:of\:the\:circle\:is\:15\:inch.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\blue{Step-by-step\:explanation}}{\blue{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }[/tex]
[tex]\longrightarrow{\blue{}}[/tex] 47 in = 2 π [tex]r[/tex]
[tex]\longrightarrow{\blue{}}[/tex] [tex]r[/tex] = [tex]\frac{47 \times 7}{2 \times 22}[/tex] in
[tex]\longrightarrow{\blue{}}[/tex] [tex]r[/tex] = [tex]\frac{329}{44}[/tex] in
[tex]\longrightarrow{\blue{}}[/tex] [tex]r[/tex] = 7.477 in
Now,
[tex]\sf\pink{Diameter\: of \:the \:circle\: =\: 2 \:r }[/tex]
= 2 x 7.477 in
= 14.954 in
= 15 in ( round to nearest whole number )
Therefore, the diameter of the circle is 15 inch.
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]
The diameter of the circle is approximately 14.97 inches.
We have,
To find the diameter of a circle given its circumference, we can use the formula:
Circumference = π * Diameter
Given the circumference of the circle is 47 inches, we can rearrange the formula to solve for the diameter:
Diameter = Circumference / π
Substituting the given circumference into the formula:
Diameter = 47 / π
Calculating the value:
Diameter ≈ 14.97 inches
Therefore,
The diameter of the circle is approximately 14.97 inches.
Learn more about Circle here:
https://brainly.com/question/11833983
#SPJ6
Which of the following expressions are equivalent to 63? Check all that are true.
Answer:
A & E
Step-by-step explanation:
Main equation: [tex]6^{3} = 216[/tex]
A. [tex]\frac{6^{7} }{6^{4}} = 6^{3} = 216[/tex]
B. 18
C. [tex](6^{1})^{2} = 36[/tex]
D. 81
E. 6 * 6 * 6 = 216
F. [tex]6^{2} + 6^{1} = 36 + 6 = 42[/tex]
Hope this helps!
Please mark as the Brainliest!
Two search-and-rescue teams leave base camp at the same time, looking for a lost child. The first team, on horseback, heads north at 9 mph, and the other team, on foot, heads south at 2.5 mph.
How long will it take them to search a distance of 46 miles between them?
Answer:
yes because no matter how far you run i will find you
Step-by-step explanation:
How do you know the absolute value of a number?
Step-by-step explanation:
It is very simple
Any number's absolute value should be positive
Let's say absolute value of 3 - >answer is 3
But absolute value of - 3 - > is also 3
Hope you understood it.
Answer:
Step-by-step explanation: In order to find the absolute value all you do is see what number you have and turn into an positive, say "what is the absolute value" of -5" it would just be 5,
Hope this helps :)
Let U be the set of all books, N the set of all novels, and H be the set of all hardcover books. Describe, in words, the following sets:
Given:
U be the set of all books, N the set of all novels, and H be the set of all hardcover books.
To find:
The description for the sets [tex]N\cap H[/tex] and [tex]H'[/tex] in words.
Solution:
We have,
U = The set of all books
N = The set of all novels
H = The set of all hardcover books.
We know that [tex]N\cap H[/tex] means common elements of set N and set H.
Therefore, [tex]N\cap H[/tex] is set of all books that are both novels and hardcover books.
We know that [tex]H'[/tex] is the set of elements of universal set except the elements of set H.
Therefore, [tex]H'[/tex] is the set of all books that are not hardcover books.
How many ounces in 31/2 pounds
Answer:
248 ounces
Step-by-step explanation:
I hope this helps :D
Answer:
248 ounces is the correct answer hope you will like it and Mark me as BRAINLIEST!!!!
The size of a large milkshake is 1.4 times the size of a medium milkshake. Write 1.4 as a percent. F u
Answer:
1.4%
Step-by-step explanation:
1.4 = [tex]\frac{14}{1000}[/tex]
=[tex]\frac{14/10}{1000/10}[/tex]
=[tex]\frac{1.4}{100}[/tex]
=1.4%
In the diagram below of RST. L is a point on RS, and M is a point on RT, such that LM parallel to ST
If RL = 3 LS= 12 LM=7. and ST=x+ 2, what is the length of ST?
Answer:
ST is 28
Step-by-step explanation:
Using the similarity formla
RL/LS = LM/ST
3/12 = 7/x+2
3(x+2)=84
x +2= 84/3
x+2 = 28
x= 28-2
x = 26
ST = x+2
ST = 26+2
ST = 28
Hence the length of ST is 28
a driver travelled a distance of 864 km in 12 hours what is the speed of car
answer:
speed= 72 km - per • hour
Answer:
Speed of car = 72 km per hour
when a number is decreased by 20% of itself, the result is 104. what is the number?
Answer:
the number is 520
Step-by-step explanation:
hope this helps!
The scores and their final grade for a statistics student are given. What is the student’s weighted mean score?
Homework
Quiz
Quiz
Project
Final Exam
Score
86
81
96
99
89
Percent of final grade
20
15
15
25
25
Answer:
a) final exam: 90.2 B b) percent of final grade: 20 F
Step-by-step explanation:
calculator: a)86+81+96+99+89=451/5=90.2
b) 20+15+15+25+25=100/5=20
The weighted mean of a distribution is the sum of the product of the data elements of the distribution by the proportion of each element.
The weighted mean score of the students is 90.75
To calculate the weighted mean score, we simply multiply the score of each student by the percentage grade.
So, we have:
[tex]Mean = 86 \times 20\% + 81 \times 15\% + 96 \times 15\% + 99 \times 25\% + 89 \times 25\%[/tex]
This gives:
[tex]Mean = 17.20 + 12.15 + 14.40 + 24.75 + 22.25[/tex]
[tex]Mean = 90.75[/tex]
Hence, the weighted mean score of the students is 90.75
Read more about weighted mean at:
https://brainly.com/question/15904675
The coordinates of the endpoints of BC are B(5,1) and (-3,-2). Under the
transformation R90, the image of BC is B'C". State the coordinates of points B
and C.
Given:
The coordinates of the endpoints of segment BC are B(5,1) and (-3,-2).
Under the transformation [tex]R_{90^\circ}[/tex] the image of [tex]\overline{BC}[/tex] is [tex]\overline{B'C'}[/tex].
To find:
The coordinates of points B' and C'.
Solution:
We know that transformation [tex]R_{90^\circ}[/tex] means 90 degrees counterclockwise rotation about the origin.
If a figure is rotated 90 degrees counterclockwise rotation about the origin, then
[tex](x,y)\to (-y,x)[/tex]
Using this rule, we get
[tex]B(5,1)\to B'(-1,5)[/tex]
Similarly,
[tex]C(-3,-2)\to C'(-(-2),-3)[/tex]
[tex]C(-3,-2)\to C'(2,-3)[/tex]
Therefore, the coordinates of required points are B'(-1,5) and C'(2,-3).
The cost of a piece of furniture is calculated as follows:
Wood: Rs.300, Paint: Rs.200 and wages Rs.200
If the cost of the wood and paint are increased by 12% and 7% respectively, find the new cost of the furniture.
Answer:
Examining whole-body center of mass (COM) motion is one of method being used to quantify dynamic balance and energy during gait. One common method for estimating the COM position is to apply an anthropometric model to a marker set and calculate the weighted sum from known segmental COM positions. Several anthropometric models are available to perform such a calculation. However, to date there has been no study of how the anthropometric model affects whole-body COM calculations during gait. This information is pertinent to researchers because the choice of anthropometric model may influence gait research findings and currently the trend is to consistently use a single model. In this study we analyzed a single stride of gait data from 103 young adult participants. We compared the whole-body COM motion calculated from 4 different anthropometric models (Plagenhoef et al., 1983; Winter, 1990; de Leva, 1996; Pavol et al., 2002). We found that anterior-posterior motion calculations are relatively unaffected by the anthropometric model. However, medial-lateral and vertical motions are significantly affected by the use of different anthropometric models. Our findings suggest that the researcher carefully choose an anthropometric model to fit their study populations when interested in medial-lateral or vertical motions of the COM. Our data can provide researchers a priori information on the model determination depending on the particular variable and how conservative they may want to be with COM comparisons between groups. Copyright © 2017 Elsevier Ltd. All rights reserved.
Step-by-step explanation:
if two lines are parallel and one has a slope of 1/6, what is the slope of the other line?
Explain how u got the answer!
Answer: 525
Step-by-step explanation:
1000 dogs in 2013 and 4500 dogs in 2016
15 percent in animal shelters
(4500-1000)x0.15 = 525
