Answer:
(x - 4)² + (y - 5)² = 4
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (4, 5) and r = 2, thus
(x - 4)² + (y - 5)² = 2², that is
(x - 4)² + (y - 5)² = 4 ← second option on list
The required equation represents a circle with the same center as the circle shown but with a radius of 2 units is (x-4)^2 + (y-5)^2 = 4
Equation of a circleThe standard equation of a circle is expressed as:
(x-a)^2 + (y-b)^2 = r^2
where:
(a, b) is the centre = (4, 5)
r is the radius = 3 units
Substitute to have;
(x-4)^2 + (y-5)^2 = 2^2
(x-4)^2 + (y-5)^2 = 4
Hence the required equation represents a circle with the same center as the circle shown but with a radius of 2 units is (x-4)^2 + (y-5)^2 = 4
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Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing!
Answer:
the right answer is : A
Step-by-step explanation:
Answer:
the answer is B
Step-by-step explanation:
im smort
Find two numbers, if their sum is 49 and their difference is 1/2 .
This question is for my little sister who needs help with her Math.
I'm too busy to help.
Answer: 49.5 and -0.5
Step-by-step explanation:
a + b =49
a - b = 0.5
a= 49.5
b= -0.5
The two numbers are approximately 24.25 and 24.75.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
Let's call the two numbers x and y.
According to the problem, we have two equations:
x + y = 49 (since their sum is 49)
x - y = 1/2 (since their difference is 1/2)
We can solve this system of equations using the method of substitution.
First, we can rearrange the second equation to solve for one of the variables in terms of the other:
x - y = 1/2
x = y + 1/2
Now we can substitute this expression for x into the first equation:
(y + 1/2) + y = 49
2y + 1/2 = 49
2y = 48.5
y = 24.25
Now we can use this value of y to solve for x:
x = y + 1/2 = 24.25 + 1/2 = 24.75
Therefore, the two numbers are approximately 24.25 and 24.75.
Learn more about algebra here:
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Eric created a rectangular patio 1 ft.² paving stones which are sold in batches by a dozen the patio measures 7‘ x 8‘ how many batches of Pavingstone did Eric need
Answer:
The number of batches of paving stones Eric needs is 5 batches
Step-by-step explanation:
Here we have the size of of one paving stone = 1 ft²
The dimensions, size, of one patio = 7 ft × 8 ft = 56 ft²
Therefore, the number of paving stones Eric needs per patio is given by the relation;
[tex]Number\, of\ paving\ stones \ required =\frac{size\, of \, one\, patio}{size \, of \, one\, paving\, stone} = \frac{56 \, ft^2}{1 ft^2/(paving \, stone)} = 56 \, paving \, stones[/tex]
Since the paving stones are sold in batches of one dozen, we have ;
4 batches = 48 paving stones and 5 batches = 60 paving stones
Therefore, the number of batches of paving stones Eric needs = 5 batches.
Please help I will give Brainliest please. Just tell what I need to do or solve I need help ASAP *image*
Answer:
Step-by-step explanation:
Hard to figure out huh
hi!! <3 i attached a picture of a easy trigonometry question can you please help if you don’t mind <33
Answer:
Side AB has a length of 4, and side BC has a length of 11.7
A ski run is 1000 yards long with a vertical drop of 208 yards. Find the angle of depression from the top of the ski run to the bottom.
Answer:
angle of depression = -12 degrees
Step-by-step explanation:
Sin = opposite/hypotenuse
sin = -208/1000
inv sin 0.208 = -12
To solve this problem, we just need to use trigonometric ratio and use the ratio that best fits this problem. The angle of depression is equal to 76.23 degrees.
Trigonometric RatioUsing SOHCAHTOA, we can easily solve this problem, but we need to first know which ratio to use
Data;
opposite (ski run) = 1000 yardsadjacent (vertical drop) = 208 yardssince we have the value of opposite and adjacent, we can solve this using the tangent of the angle
[tex]tan\theta = \frac{opposite}{adjacent} \\tan \theta = \frac{1000}{208} \\tan\theta = 4.807\\\theta = sin^-^1 (4.0807)\\\theta = 76.23^0[/tex]
From the calculation above, the angle of depression is equal to 76.23 degrees.
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NEED HELP! ASAP PLEASE!
Answer:
(0,-41)
Step-by-step explanation:
You can see that for each 9 units that x goes up, y goes up by 19. If we continue this pattern, it will take 2 more jumps of 9 units for the x value to be 0 or to reach the y intercept. Adding 19 twice to -79 gives -41. Hope this helps!
Write the equation of a line that passes through the point (4, 2) and is parallel to the line graphed below.
Answer:
Step-by-step explanation:
(-2, 2) (2, -3)
(-3 - 2)/(2 + 2)
-5/4 the slope
y - 2 = -5/4(x + 2)
y - 2 = -5/4x - 5/2
y- 4/2 = -5/4x - 5/2
y = -5/4x - 1/2
In parallelogram WXYZ, what is CY?
Answer:
The correct answer is 11 ft.
Step-by-step explanation:
The diagonals of a parallelogram bisect each other. This means that the portion marked x+4 is the same length as the portion marked 2x-7; this gives us the equation x+4=2x-7.
Subtract x from each side:
x+4-x=2x-7-x
4=x-7.
Add 7 to both sides:
4+7=x-7+7
11=x
Answer:
11
Step-by-step explanation:
On edge
what is m equal to.
4(m − 13) − 8 = 8
Answer:
m = 17
Step-by-step explanation:
[tex]4(m - 13) - 8 = 8 \\ 4(m - 13) = 8 + 8 \\ 4(m - 13) = 16 \\ (m - 13) = \frac{16}{4} \\ m - 13 = 4 \\ m = 4 + 13 \\ \huge \red { \boxed{m = 17}}[/tex]
Select the expressions that are equivalent to 6(x + 7).
(7 + x) 6
6x + 42
(x + 7)6
42x + 6
Answer:
[tex]6x + 42[/tex]
Step-by-step explanation:
Apply the distributive property:
[tex]6x + 6 \times 7[/tex]
Multiply 6 by 7
[tex]6x + 42[/tex]
Molly wants to put a fence around an area. The fence will follow the diagram of the triangle shown below. (Look at picture) About how much fencing does Molly need?
Answer:
Step-by-step explanation:
43feet
Find the surface area.
Any help will be appreciated thank you
Answer:
Find the area of the shape
First the two triangles
3 x 4 = 12 so the area of both triangles is twelve
Now it is only 1 big rectangle left
The side lengths can be added 3 + 4 + 5 = 12
12 x 11 = 132
132+12=144
144 is the surface area/area
If you have any questions please ask
Step-by-step explanation:
What is the range of the function y= e^4x
Answer:
The answer would be {y|y>0}
Step-by-step explanation:
hope this helps
Solve the equation for x, and enter your answer below.
10x - 15x + 5= -45 + 40
Answer: x = 2
Step-by-step explanation:
[tex]10x - 15x + 5= -45 + 40[/tex]
subtract 5
[tex]10x - 15x= -45 + 40-5[/tex]
Combine like terms;
[tex]-5x=-10[/tex]
Divide by -5
[tex]x=\frac{-10}{-5}\\ x=2[/tex]
Answer:
[tex]x = 2[/tex]
Step-by-step explanation:
[tex]10x - 15x + 5 = - 45 + 40 \\ 10x - 15x = - 5 - 45 + 40 \\ - 5x = - 10 \\ \frac{ - 5x}{ - 5} = \frac{ - 10}{ - 5} \\ x = 2[/tex]
There is a unique positive real number x such that the three numbers
log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.
The number x can be written as m/n, where m and n are relatively prime positive integers.
Find m+n.
Step-by-step explanation:
If the log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.
Let a = log82x, b = log4x and c = log2x
If a = log8 2x; 8^a = 2x... (1)
If b = log4 x; 4^b = x ... (2)
If c = log2 x; 2^c = x...(3)
Since a, b c are in GP, then b/a = c/b
Cross multiplying:
b² = ac ...(4)
From eqn 1, x = 8^a/2
x = 2^3a/2
x = 2^(3a-1)
From eqn 2; x = 4^b
x = 2^2b
From eqn 3: x = 2^c
Equating all the values of x, we have;
2^(3a-1) = 2^2b = 2^c
3a-1 = 2b = c
3a-1 = c and 2b = c
a = c+1/3 and b = c/2
Substituting the value of a = c+1/3 and b = c/2 into equation 4 we have;
(c/2)² = c+1/3×c
c²/4 = c(c+1)/3
c/4 = c+1/3
Cross multiplying;
3c = 4(c+1)
3c = 4c+4
3c-4c = 4
-c = 4
c = -4
Substituting c = -4 into equation 3 to get the value of x we have;
2^c = x
2^-4 = x
x = 1/2^4
x = 1/16
Since the number x can be written as m/n, then x = 1/16 = m/n
This shows that m = 1, n = 16
m+n = 1+16
m+n = 17
The required answer is 17.
The value of m+n in which m and n are relatively prime positive integers is 17.
What is geometric sequence?Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.
There is a unique positive real number x such that the three numbers log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio. The progression is,
[tex]\log_82 x,\log_4x, \log_2x[/tex]
The above numbers are in geometric progression. Thus, the ratio of first two terms will be equal to the ratio of next two terms as,
[tex]\dfrac{\log_4x}{\log_82x}=\dfrac{\log_2x}{\log_4x}\\(\log_4x)^2={\log_2x}\times{\log_82x}\\[/tex]
Using the base rule of logarithmic function,
[tex]\left(\dfrac{\log x}{\log 4}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log8}\\\left(\dfrac{\log x}{\log 2^2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log2^3}[/tex]
Using the Power rule of logarithmic function,
[tex]\left(\dfrac{\log x}{2\log 2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{3\log2}\\\dfrac{\log x}{4}=\dfrac{\log 2+\log x}{3}\\3\log x=4(\log2x)\\\log x^3=\log(2x)^4\\x^3=16x^4\\x=\dfrac{1}{16}[/tex]
The number x can be written as
[tex]\dfrac{m}{n}[/tex]
Here, m and n are relatively prime positive integers. Thus, the value of m+n is,
[tex]m+n=1+16=17[/tex]
Hence, the value of m+n in which m and n are relatively prime positive integers is 17.
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What is the equation of the following line? Be sure to scroll down first to see all answer options.
A. y = 3x
B. y = x
C. y = 2x
D. y = -1/3x
E. y = -3x
F. y = 1/3x
pls help it will mean alot!!
due rn!!
Answer:
f(x) = 4^x
f(4) = 4^4 = 256
Hope this helps!
:)
the answer is 256 but i am not sure
hope this helps and be safe :)
I don’t understand this question. Can anyone help? I need answers ASAP. Thanks for all the help
There's some unknown (but derivable) system of equations being modeled by the two lines in the given graph. (But we don't care what equations make up these lines.)
There's no solution to this particular system because the two lines are parallel.
How do we know they're parallel? Parallel lines have the same slope, and we can easily calculate the slope of these lines.
The line on the left passes through the points (-1, 0) and (0, -2), so it has slope
(-2 - 0)/(0 - (-1)) = -2/1 = -2
The line on the right passes through (0, 2) and (1, 0), so its slope is
(0 - 2)/(1 - 0) = -2/1 = -2
The slopes are equal, so the lines are parallel.
Why does this mean there is no solution? Graphically, a solution to the system is represented by an intersection of the lines. Parallel lines never intersect, so there is no solution.
Caleb’s puppy weighs 2,250 grams. If the puppy weighed 600 grams at his last visit to the veterinarian’s office, what is the percent increase in the puppy’s weight rounded to the nearest whole number? Enter your answer in the box.
Answer:
[tex]73\%[/tex]
Step-by-step explanation:
Given: Present weight of Caleb’s puppy = 2,250 grams
Puppy weighed 600 grams at his last visit to the veterinarian’s office.
To find: percent increase in the puppy’s weight rounded to the nearest whole number
Solution:
Increase in puppy's weight = 2250 - 600 = 1650 grams
Percent increase in the puppy’s weight =( Increase in puppy's weight/Present weight of Caleb’s puppy) × 100 = [tex]\frac{1650}{2250}(100)=73.33 \%[/tex]
[tex]73.33\%[/tex] is rounded to [tex]73\%[/tex]
What happens to the parabola when a<1 compared to the parent function?
Answer: The parabola is wider than the parent function
Step-by-step explanation:
If "a" is a fraction less than one, then the parabola becomes wider.
See graph (attached)
i think of a number multiply it by 3 and subract 2 . The result is 14
Answer:
5.3
Step-by-step explanation:
Answer:
The answer is 5.3
Step-by-step explanation:
5.3x3-2= 13.9 but when you round its 14
A trapezoid was broken into a triangle and rectangle. The base of the triangle b is ______cm.
Find the area of the shaded regions:
The pink is the shaded region.
40π
You dont need paper hw since we're in quarantine
Answer:40
Step-by-step explanation:
If you have 24 square tiles, how many different rectangles can you make? Each rectangle must use all of the tiles and have no holes or gaps. Sketch each rectangle and label its length and width.
Answer:
4
Step-by-step explanation:
A rectangle has a shorter side and a longer side.
The longer side is called the length and the shorter side is called width.
with the 24 tiles you can make the following rectangles (consider the first number the length and the second number the width, and that each unit represents a tile):
24 x 1
12 x 2
8 x 3
6 x 4
A total of 4 different rectangles.
I am not counting the rectangles than have the same sides shifted, for example 2 x 12 because it is the same as 12 x 2 and we are asked for the rectangles to be different.
I attache an image of the sketch of each rectangle with the labels of length and width (not to scale).
Evaluate the expression 3 x
{10 +1} +5.
Answer:
38
Step-by-step explanation:
3 x {10 +1} +5.
PEMDAS
Parentheses first
3 x {11} +5.
Then multiply and divide
33+5
38
Answer:
38
Step-by-step explanation:
3 x {10 +1} +5 Following PEMDAS, solve in the parentheses
3 x 11 + 5 Multiply 3 x 11
33 + 5 Add
38
7. What is the value of the expression 3(2 - 7)
Answer:
-15
Step-by-step explanation:
3(2 - 7)
PEMDAS says parentheses first
Subtract
3 (-5)
Multiply
-15
how many times does 6 go into 29
Answer:
4 times
Step-by-step explanation:
Answer:
4.8333333 or 4 5/6 times
Step-by-step explanation:
29/6 = 4.83333333
I need this answer please tell me the answer
Answer:
less than
[tex]1 \frac{1}{2} [/tex]
I believe
a rectangle has an area of 24m². its length is 5m longer than the width.
write an expression for the rectangle's length
Answer:
2x+2(x+5)) = 24
Step-by-step explanation:
2x+ 2(x+5) = 24
x is represented by the shorter side. Multiply by 2 because of the 2 sides. For the longer side, since it is 5m longer than the shorter side, you have to write (x+5). Multiply by 2 because of the 2 sides. Finally, add them both together since it is the area and set it equal to 24.
