Answer:
[tex]\displaystyle \Big(\frac{3\sqrt{5}}{5},\frac{6\sqrt5}{5}+4\Big)[/tex]
Step-by-step explanation:
Recall that 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.
Then for a center of (0, 4) and a radius of 3, our equation is:
[tex]x^2+(y-4)^2=9[/tex]
We want to know at what point does the circle intersect with the line:
[tex]y=2x+4[/tex]
Therefore, we can solve for x. To do so, substitute the linear equation into the circle equation:
[tex]x^2+((2x+4)-4)^2=9[/tex]
Simplify:
[tex]x^2+(2x)^2=9[/tex]
Square:
[tex]x^2+4x^2=5x^2=9[/tex]
Divide both sides by 5:
[tex]\displaystyle x^2=\frac{9}{5}[/tex]
Therefore:
[tex]\displaystyle x=\pm\frac{3}{\sqrt{5}}=\pm\frac{3\sqrt{5}}{5}[/tex]
In QI, x is always positive, so we only need to consider the positive case:
[tex]\displaystyle x=\frac{3\sqrt{5}}{5}[/tex]
Using the linear equation again, we can see that:
[tex]\displaystyle y=2\Big(\frac{3\sqrt{5}}{5}\Big)+4=\frac{6\sqrt{5}}{5}+4[/tex]
Therefore, the point in which a circle with center (0, 4) and a radius of 3 intersects the line with equation y = 2x + 4 in the first quadrant is the point:
[tex]\displaystyle \Big(\frac{3\sqrt{5}}{5},\frac{6\sqrt5}{5}+4\Big)[/tex]
Or approximately:
[tex]\approx (1.342, 6.683)[/tex]
And we are finished!
Ethan says that if the diameter of a bicycle wheel is 3.5 feet then its
radius must be 1.75 feet. Is Ethan correct?
Answer: Yes he is correct
Explanation:
The radius is half the diameter
radius = diameter/2 = 3.5/2 = 1.75
Answer:
yes hes right.
Step-by-step explanation:
d = 2 x 1.75
d = 3.5
c = 2 x pi x 1.75
c = 3.5
ur answer is 3.5 ethans right
13 POINTS MATH
Look at the image to see the problem!!
Multiply and Simplify:
(5a+7b)(3a−8b)
Question 2 options:
15a2−19ab−56b2
15a2+21ab−56b2
15a2−56b2
15a2−40ab−56b2
Help plz I’ll mark brainliest
Answer:
you're answer is definitely d
Line l passes through point (0, -1) and is parallel to the line whose equation is y = -2x + 7. Which equation best describes the graph of line l? a) y = -2x + 6, b) y = 2x + 6, c) y = 1/2x - 1, d) y = -2x - 1
Answer:
[tex]y = -2x -1[/tex]
Step-by-step explanation:
Given
Passes through: (0, -1)
Parallel to: y = -2x + 7
Required
Determine the line equation
If the line is parallel to y = -2x + 7, then it has the same slope as y = -2x + 7.
For an equation of form: [tex]y = mx + b[/tex]
The slope is m
By comparison:
[tex]m = -2[/tex]
So, the slope of the extorted is -2.
The equation is then calculated using:
[tex]y = m(x - x_1)+ y_1[/tex]
[tex]y = -2(x - 0)-1[/tex]
[tex]y = -2(x )-1[/tex]
[tex]y = -2x -1[/tex]
factorize by splitting the middle term 6x-11x+4
Answer: (2x - 1)(3x - 4)
(split -11x as -8x and -3x)
Step-by-step explanation:
I am assuming that it is actually 6x^2 - 11x + 4
To find out how to split the middle term: The two numbers should multiply to a*c (6*4 = 24) and add to b (-11)
-8, -3 works
(6x^2 - 8x) + (-3x + 4)
2x(3x - 4) + -1(3x - 4)
(2x - 1)(3x - 4)
Please help
Look at picture
Supplementary angles
Answer:
Step-by-step explanation:
[tex]3)\frac{5x}{2}+125 = 180\\\\\frac{5x}{2}=180-125\\\\\frac{5x}{2}=55\\\\ 5x = 55*2\\\\ x =\frac{55*2}{5}\\\\ x = 11*2 = 22[/tex]
4) 3x+ 42 + 90= 180
3x + 132 = 180
3x = 180 -132
3x = 48
x = 48/3
x = 16
Water is leaking out of an inverted conical tank at a rate of 12,500 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate (in cm3/min) at which water is being pumped into the tank. (Round your answer to the nearest integer.)
Answer:
12500cm x3= 37500
6x3=18
37500+18=37518
Tiy deposit $500 in a savings account that earns 7% interest compounded annually.
The box plot describes the height of flowers selected randomly from two gardens. Use the box plot to find the median of Garden Y and Garden Z? (HELP PLEASE THIS IS FOR AN IMPORTANT TEST)
Answer:
Garden y median =6, garden z median =3
Answer: Look at the explanation please
Step-by-step explanation:
Garden Y has the median of 6 inches
Garden Z has the median of 4 inches
A comparative inference about thre two gardens would look like something like this
The flowers in Garnden Y generally grow taller than the flowers that are in Garden Z
Hopes this helps :)
Pls help me i have a min to finish pls I’ll make brainliest
answer:
it is not proportional.
step-by-step explanation:
14-10.50=3.5
17.50-14=3.5
24.50-17.50=7
in order for it to be proportional, they would all have to equal the same number and since in this case, they don't it is non-proportional
hopefully, this helps :)
have a nice day !!
i'm extremely sorry i couldn't help sooner :(
need help ASAP Will mark u brainlyest
Which set of angle measures could be measures of the interior angle of a triangle?
Answer:
b
Step-by-step explanation:
23-105-45
Answer: 60°, 60°, and 60° is the set of interior angles of triangle.
What base of this triangle
A. 10
B. 8
C. 80
D. 18
I gave Brainlist
Answer:
a is the base
Step-by-step explanation:
its right there
1/4( -1 + 4)+3/5 please help ME missing work!
Answer:
1.35
Step-by-step explanation:
I believe this is right but it could be wrong. Hope this helps! <3
2(x + 4) + 5( 6 - x)
Answer:
3x+32
Step-by-step explanation:
2(x+4) +5(6-x)
Use the distributive property
2x+8+24-5xSimplify
3x+32How can you find the domain and range on this??
Answer:
1) Function
2) Set Notation
3) Domains: {-4, -2, -1, 1, 3, 4}
4) Ranges: {-3, -2, 0, 2, 3}
Step-by-step explanation:
1) This is a function because the x-values are NOT repeated, and it passes the vertical line test.
2) This is a set notation because it has the symbol --> { } and it is "help define the elements of a set." You can search up "set notation" and you would get the idea. However, this is not an inequality because in inequality you would have, ex: x < 4 ≤ x
3) Domains mean the x-intercept. Remember to list domains from least to greatest!
4) Range means y-intercept. Remember to list the ranges from least to greatest! If a range is repeated then you do NOT need to re-write that number again.
If you drive 5 miles east and then 4 miles south, how far are you, to the nearest tenth
of a mile from your starting point?
Answer:
6.4 miles
Step-by-step explanation:
5^2 + 4^2 = d^2
25 + 16 = d^2 = 41
d = 6.40 miles
The nearest tenth of a mile from your starting point is 6.4.
What is Pythagoras theorem?The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.
How to write nearest tenth?To round a number to the nearest tenth, we need to look to the right of the tenths place, which is the hundredths place. If the digit in the hundredths place is 5 or greater than 5, we need to add one to the digit in the tenths place. If it is 4 or less than 4, the tenths place digit remains the same. All the digits to the right of the tenths place should be changed to 0. That means, while rounding off a number to the nearest tenth, we will stop the rounding at the tenths place.
According to the question
If you drive 5 miles east and then 4 miles south
We have to find the nearest tenth of a mile from your starting point
From the diagram, we have to use Pythagoras theorem
D = [tex]\sqrt{4^{2} +5^{2} }[/tex]
D = [tex]\sqrt{16+25}[/tex]
D = [tex]\sqrt{41}[/tex]
D = 6.40312
Round 6.40312 to the required nearest tenth
D = 6.4
Hence, The nearest tenth of a mile from your starting point is 6.4.
Find out more information about Pythagoras theorem here
https://brainly.com/question/343682
#SPJ2
The Earth is approximately 8.0 × 103 miles in diameter, from pole to pole. What number is the distance equivalent to?
Answer:
The diameter of earth from pole to pole is equal to [tex]8000[/tex] miles.
Step-by-step explanation:
The number to which the distance is equivalent is
[tex]8 * 10^3\\8 * 1000\\= 8000[/tex]
Thus, the diameter of earth from pole to pole is equal to [tex]8000[/tex] miles.
1. Frank is making a candle with the mold below. 4 in. 2 in. 2 in, He plans to fill half of the mold with wax. What volume of the mold will he fill? A 8 in. B 9 in.3 C 24 in. D 192 in.3
Answer:
A
Step-by-step explanation:
4x2x2=16
16/2=8
C The triangles in this picture are similar. Find the height of the tree.
Answer:
Please find attached pdf
Step-by-step explanation:
What is the measure of the missing angle?
Answer: 42
explanation is not needed
Evaluate c - 2 when c = 7.
Stuck? Watch a video or use a hint.
What is my final answer
Answer:
5
Step-by-step explanation:
Subtract 7-2=5.
200 percent of d is 18 what is d please help this is a question i have been needing help on for a long time
Step-by-step explanation:
what do u mean ??
200 per cent of 8???
If that's so, 200/ 8 * 100 = 2,500
Answer:
9
Step-by-step explanation:
When we calculate percentages, we multiply the numbers divided by 100. Therefore, 200% is the same as ×2.
Someone pls hurry!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:6 songs
Step-by-step explanation:
I DONT KNOW WHAT IM DOING, PLEASE HELP
Answer:
you should check out Microsoft Math! It's a free app :)
Complete the following statement.
Mac mixes 14 ounces of red paint with 6 ounces of blue paint. The ratio of blue paint to total paint is because for every 6 ounces of , there is 20 ounces of .
Answer:
The Ratio you are looking for is 5:8
Step-by-step explanation:
Answer:
6: azul
20: lila o morado
please give me the square root of 2
1. Mother gave donations worth Php 23 900.50 to the Children Foundation and
Php 32 097.50 to the Home for the Aged from her savings. If she had
Php 60 555.75 in her bag, how much money will be left to her?
What is asked?
What are given?
What operation should be used to solve the problem?
What is the number sentence?
What is the complete answer?
Answer:
What is asked? Total amount left to her.
what are the given? Php 32,097.50 , Php 23,900.50 and Php 60,555.75
what operation should be used to solve the problem? Addition and subtraction
what is the number sentence? Php 23, 900.50+Php32, 097.50=n , Php 60, 555.75 - N = M
what is the complete answer? Php 14,557.75 is the total amount left to her.
36 hours to 2 days
The ratio is
(Type an integer or a simplified fraction)
