Answer:
4) 2(x - 3)^2 + 2(y + 5)^2 = 96.
Step-by-step explanation:
2x^2 – 12x + 2y^2 + 20y – 28 = 0
2(x^2 – 6) + 2(y^2 + 10y) = 28
2 ( (x - 3)^2 - 9)) + 2((y + 5)^2 - 25) = 28
2(x - 3)^2 - 18 + 2(y + 5)^2 - 50 = 28
2(x - 3)^2 + 2(y + 5)^2 = 28 + 18 + 50
2(x - 3)^2 + 2(y + 5)^2 = 96
Answer:
[tex]4) 2(x-3)^2+2(y+5)^2=96[/tex]
Step-by-step explanation:
[tex]2x^2 -12x +2y^2 + 20y - 28 = 0[/tex]
It basically represents a circle.
Equation of circle
[tex]\left(x-a\right)^2+\left(y-b\right)^2=r^2\:[/tex]
[tex]2x^2-12x+2y^2+20y=28[/tex]
[tex]$\frac{1}{2} (2x^2-12x+2y^2+20y)=28 \cdot \frac{1}{2} $[/tex]
[tex]x^2-6x+y^2+10y=14[/tex]
Organize the variables
[tex]\left(x^2-6x\right)+\left(y^2+10y\right)=14[/tex]
Now we have to complete the square for both groups:
[tex]\left(x^2-6x+9\right)+\left(y^2+10y+25\right)=14+9+25[/tex]
[tex]\left(x-3\right)^2+\left(y+5\right)^2=14+9+25[/tex]
[tex]\left(x-3\right)^2+\left(y+5\right)^2=48[/tex]
Now, I would proceed with:
[tex]\sqrt{48} =\sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 3} =4\sqrt{3}[/tex]
[tex]\left(x-3\right)^2+\left(y+5\right)^2=(4\sqrt{3} )^2[/tex]
We got the center and the circle radius
[tex]\left(3,\:-5\right)\\r=4\sqrt{3}[/tex]
But this is not what you want:
So, just multiply both sides by 2 and you'll get:
[tex]2\left(x-3\right)^2+2\left(y+5\right)^2=96[/tex]
In a circle, area and circumference can be found using the formulas A=(pi)r^2 and C=2(pi)r, respectively, Write a formula for A in terms of C.(your answer should not contain r)
Answer:
[tex]A = \dfrac{C^2}{4\pi}[/tex]
Step-by-step explanation:
Given that
Area of a circle [tex]A=\pi r^2[/tex]
Circumference of the circle [tex]C = 2 \pi r[/tex]
Let us re-write the equation of area of circle:
[tex]A=\pi r^2[/tex]
[tex]A = \pi \times r \times r[/tex]
Multiplying and dividing with 2:
[tex]A = \dfrac{2\pi r}{2} \times r\\\text{Putting }2\pi r = C:\\\Rightarrow A = \dfrac{C}{2} \times r\\\text{Multiplying and dividing by } 2\pi:\\\Rightarrow A = \dfrac{C}{2} \times \dfrac{2\pi r}{2\pi}\\\text{Putting }2\pi r = C:\\\Rightarrow A = \dfrac{C \times C}{4 \pi}\\\Rightarrow A = \dfrac{C^2}{4 \pi}[/tex]
Hence, A in terms of C can be represented as:
[tex]A = \dfrac{C^2}{4\pi}[/tex]
Which line segment could be mid segment of abc? 21 points!!!!
Answer:
DF
Step-by-step explanation:
the mid segment is a line that connects the midpoints.
Answer:
DF or option 3
Step-by-step explanation:
DF, since it connects midpoints of sides AB and CB and is parallel to one side: AC
Thus the answer is DF or option 3
I WILL GIVE YOU BRAINLIEST!! what is the solution to the following equation? x^2+5x+7=0
Answer:
The answer is C
Step-by-step explanation:
By using the quadratic formula, you get
a=1
b=5
c=7
so, when you substitute, you get:
-5±√5²-4(2)(7)
____________
2(1)
The next step is solving the square root and multiplying
In 2005 a house was purchased for $280,000 and
in 2013 it was sold at $334,000. Assuming that
the value of the house increased at a constant
annual rate what will be the price of the house in
the year 2018?
Given that in 2005 a house was purchases for 280,000 and was later sold in 2013 for 334,000, determine the increase value of the house and what the price of the house will be in 2018.
First, we subtract the two values of the house on both dates.
334,000 - 280,000 = 54,000
Then, divide the difference by the amount of years from 2005 to 2013.
54,000/8 = 6,750
Since, it says the value increases at a constant rate, this indicates that it is a linear function.
So, the linear function would start at 280,000 as the y-intercept and the slope is 6,750.
Linear Function: y = 6750x + 280,000
Lastly, to find the price of the house in 2018, we just need to plug in 13 for x since x represents the years.
y = 6750x + 280,000
Plug in 13 for x.
y = 6750(13) + 280,000
y = 87750 + 280,000
y = 367,750
Thus, the value of the house in 2018 is $367,750.
The sum of three consecutive integers is 915. What are the integers?
A. 304, 306, 308
B. 305, 306, 307
C. 300, 300, 315
D. 304, 305, 306
Answer:
304,305,306
Step-by-step explanation:
x +x+1+x+2=915
3x+3=915
3x=915-3
3x=912
x=304
The three consecutive integers are 304, 305 and 306, option D is correct.
What is Number system?A number system is defined as a system of writing to express numbers.
Let the three consecutive numbers be x, x+1 and x+2
Sum of three consecutive integers is 915.
x+x+1+x+2=915
3x+3=915
Subtract 3 on both sides
3x=912
Divide both sides by 3
x=304
Hence, the three consecutive integers are 304, 305 and 306, option D is correct.
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If the volume of a sphere inscribed in a cubic box is 36pi, find the surface area of the box
Answer:
Surface area of the cube = 216 square units
Step-by-step explanation:
Let the length of a side of a cube = x unit
Diameter of the sphere inscribed in this cube = length of a side of the cube
Volume of the sphere = [tex]\frac{4}{3}\pi r^{3}[/tex]
Where r = radius of the sphere = [tex]\frac{x}{2}[/tex] units
36π = [tex]\frac{4}{3}\pi (\frac{x}{2})^{3}[/tex]
36π = [tex]\frac{4x^{3}\pi }{24}[/tex]
36×24 = 4x³
x = [tex]\sqrt[3]{\frac{36\times 24}{4} }[/tex]
x = 6 units
Length of a side of the cube = 6 units
Surface area of the cube = 6×(Side)²
= 6×(6)²
= 216
= 216 square units
Which value of b would make x^2 + bx- 2 factorable? -2 -1 0 3
Answer:
3
Step-by-step explanation:
Work backwards in this problem:
(x+1)(x+2)
x^2+x+2x+2
x^2+3x+2
b=3
Radon-219 has a half-life of about 4 s.
After 20 s, how many milligrams of a 500 mg sample will remain?
435.3 mg
211.6 mg
31.3 mg
15.6 mg
Help please I’ll make you the brainliest if right
Answer:
15.6 mg
Step-by-step explanation:
First 4 s- 500/2= 250 mg
After 8 s- 250/2= 125 mg
After 12 s- 125/2= 62.5 mg
After 16 s- 62.5/2= 31.25 mg
At 20 s- 31.25/2= 15.625 mg
The milligrams of a 500 mg sample will remain at 15.625 mg.
We have given that,
5.6 mg
Radon-219 has a half-life of about 4 s.
What is the sample?A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population.
After 20 s,
First 4 s- 500/2= 250 mg
After 8 s- 250/2= 125 mg
After 12 s- 125/2= 62.5 mg
After 16 s- 62.5/2= 31.25 mg
At 20 s- 31.25/2= 15.625 mg
Therefore, the milligrams of a 500 mg sample will remain 15.625 mg.
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Please help me with this question. Will give 10 points.
Answer:
x = 2.99
Step-by-step explanation:
We can use ratios to solve
5.4 2.6
--------- = ---------
6.21 x
Using cross products
5.4x = 2.6* 6.21
5.4x =16.146
Divide each side by 5.4
5.4x = 16.146/5.4
x = 2.99
A linear equation written in the form y = mx + c is known as,
a) y-intercept
b) point-slope form
c) standard form
d) slope-intercept form
Answer:
it is a slope intercept form
At the beginning of the month, a rain barrel contained 12 ounces of water. At the end of the month there are 8 1/4 cups of water in the rain barrel.
How many cups of rain water were added to the barrel during the month?
Answer:
The cups of rain water that were added to the barrel during the month is:
6.75 cups.Step-by-step explanation:
First, you must know the conversion units between ounces and cups:
1 cup = 8 ounces.Then, at the beginning of the month, the rain barrel contained 12 ounces, what is in cups:
1 cup = 8 ounces. X = 12 onces.We operate:
X = (12 * 1) / 8 X = 1.5 cupsNow, how at the end of the month there are 8 1/4 cups of water in the rain barrel, in a decimal number it is equal to:
8 1/4 cups = 8.25 cupsTo know what is the cups of rainwater were added to the barrel during the month, you must subtract the number of cups at the beginning of the month to the number of cups at the end of the month:
Cups of rainwater that were added = 8.25 cups - 1.5 cups Cups of rainwater that were added = 6.75 cups.Answer:
6.75
Step-by-step explanation:
i just took the test
PLEASE can someone help with this??IT IS important
Answer:
1) x=5 so angles are 25°, 80° and 75°
Step-by-step explanation:
The angles of a triangle should add up to 180. So e.g., for the first one, you know that
5x + 16x + 15x = 180
so
36x = 180
x = 5
Answer:
4
Step-by-step explanation:
I, m
The volume of a solid cylinder is 1584 cubic cm and its height is 14 cm. The radius is
Answer: 6 cm
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula:
Volume of a cylinder (V): π x radius ² x height
Replacing with the values given and solving for v (Volume)
1584 = π x r ² x 14
Solving for r:
1584 / (π x 14) = r²
36.01 = r²
√36.01 = r
6 cm = r
In conclusion, the radius of the cylinder is 6 centimeters.
Feel free to ask for more if needed or if you did not understand something.
Answer:
The radius is 6 cm
Step-by-step explanation:
To solve this, we will follow the steps below:
write down the formula for finding the volume of a cylinder
volume of a cylinder =πr²h
from the question volume of the cylinder = 1584 cm²
height = 14 cm
substitute the formula and solve for r
π is a constant and is ≈ 3.14
1584 = 3.14×r²×14
1584= 43.96 r²
divide both-side of the equation by 43.96
36≈ r²
take the square root of both-side
√36 = √r²
6 = r
r = 6cm
The radius is 6 cm
What is the greatest common factor of 4x5y2+16x3y4−8x6y3?
Answer:
4x^3y^2
Step-by-step explanation:
Then the remaining would be
x^2+4y^2-2x^3y
Answer:
4x^3y^2
Step-by-step explanation:
Please refer to the picture attached.
The GCF of 24 and 32 is
Start by setting up a factor tree for each number.
Factor in anyway that you'd like.
At the end, circle all prime numbers.
Remember, prime numbers are numbers
with only 2 factors, 1 and the number itself.
Now write these factors in least to greatest
multiplying them separate rows.
Circle factors they have in common.
Since 3 pairs of two's match up, multiply by 2 three times to get 8.
So the GCF is 8.
Answer:
8
Step-by-step explanation:
3 multiplied by 8 = 24
and 4 multiplied by 8 = 32
A taxi charges a flat rate of $3.00 plus $1.50 per mile. If Xander has $45.00, what inequality represents m, the distances in miles he can travel in the taxi?
Answer:
1 1/5
Step-by-step explanation:
48/40 = 1 8/40
1 8/40 Simplify to 1 1/5
Hope this helps!
Answer:
D. m≤28
Step-by-step explanation:
Just trust me my friendings
is six hundred seventy-two thousand__0.8 is it greater than less than or equal to 5th grade mathhh
Answer:
Equal to grade 5 math.
Find x in this proportion.
5/2x =25/4
x =
2/5
5/2
4/5
8/5
Answer:
2/5
Step-by-step explanation:
make it reciprocal
2x/5 = 4/25
cross multiply the numbers
2x × 25 = 4×5
2x= 20/25
2x= 4/5
x = 2/5
Solve for x in the diagram below.
100°
20
2=
Answer:
x = 40
Step-by-step explanation:
The answer is x = 40. This is because the two angles that are x are 1. congruent and 2. supplementary with 100° (They all add up to 180°). I can show this with a simple equation.
1. 2x + 100 = 180
2. 2x = 80
3. x = 40
Hope this helps! (Please consider giving brainliest)
Linda is building steps for her porch. What is the volume of the steps?
144,000 cm3
288,000 cm3
324,000 cm3
540,000 cm3
Answer:
The volume of the steps is:
324,000 cm3Step-by-step explanation:
Remember that the volume regularly is:
Volume = height * width * depth.There are many forms to solve this exercise, but I'll show you two:
1. Imagine that aren't steps but a big solid, then its volume would be:
Volume of big solid = 60 cm * 60 cm * 120 cm Volume of big solid = 432000 cm3Now you can subtract the volume of a small solid with measures 30 cm * 30 cm * 120 cm (where is the blank for the step):
Volume of a small solid = 30 cm * 30 cm * 120 cm Volume of a small solid = 108000 cm3Now you subtract:
Volume of the building steps = 432000 cm3 - 108000 cm3 Volume of the building steps = 324000 cm32. The building steps are formed by three solid with volume 30 cm * 30 cm * 120 cm, so:
Volume of the building steps = 3 (30 cm * 30 cm * 120 cm) Volume of the building steps = 324000 cm3Which line plot displays a data set with an outlier?
Thank you
WILL MARK BRAINLIEST
｡☆✼★ ━━━━━━━━━━━━━━ ☾
It would be the last graph (bottom right)
An outlier is a point that is much further away from the rest of the data
As you can see, that graph has one piece of data that is much further away from the rest of the data
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
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Solve for y: 4y = 32 A. y = 4 B. y = 6 C. y = 8 D. y = 9
Answer:
C
Step-by-step explanation:
4y=32
Taking 4 to the other side
y=32/4
y=8
Answer:
c
Step-by-step explanation:
c
how how many students hade more than 6 candy bars (use the picture above)
Answer:
About 5 if your are including 6, or just 3.
Step-by-step explanation:
To find it you can just count the numbers greater than 6.
Hope this helps.
brainliest if correct
Answer:
3 Students
Step-by-step explanation:
There is only two more slots for how many candy bars each student has, in the "7" slot there is only one student that has seven candy bars and in the "8" slot there is two students that had eight candy bars.
1+2=3
I hope that helped.
Ivan has a $500 bond with a 5.8% coupon. Ivan purchased this bond for $515.
What is the yield of this new bond?
Answer:
The yield is 5.974%
Step-by-step explanation:
We proceed as follows ;
coupon rate = Annual coupon payment/bond face value.
The face value is the original amount which the bond was bought and that is $515 according to the question. While the coupon rate is 5.8%
mathematically, annual coupon payment = coupon rate * bond face value = 0.058 * 515 = $29.87
mathematically;
current yield = Annual coupon payment/bond price
current yield = 29.87/500
= 0.05974 or simply 5.974%
so the answer is c. 5.6%
Step-by-step explanation:
Answer:
A 6.0%
Step-by-step explanation:
coupon rate = Annual coupon payment/bond face value.
The face value is the original amount which the bond was bought and that is $515 according to the question. While the coupon rate is 5.8%
mathematically, annual coupon payment = coupon rate * bond face value = 0.058 * 515 = $29.87
mathematically;
current yield = Annual coupon payment/bond price
current yield = 29.87/500
= 0.05974 or simply 5.974%
5.974 rounded to 6.0 %
Which equation describes the line that passes through points (2,5) and (0,9)?
What is the image of (6,-4) after a reflection over the y-axis?
Answer:
(-6,-4)
Step-by-step explanation:
Hope this helps! (:
What is the slope of the line given by the equation y= -3x
Answer:
-3
Step-by-step explanation:
The given equation is in slope intercept form.
The form is y=mx+b
This is where "m" is the slope, and "b" is the y intercept.
So in this equation, m=-3.
Therefore, the slope is -3.
factorise 9 X square + Y square + Z square - 6 X Y + 2 Y Z - 6 x z hence find its value when X is equals to 1 by equal to 2 and Z = 2 - 1
a) Factor 9x² + y² + z² - 6xy + 2yz - 6xz
This looks a lot like
(x+y+z)² = x² + y² + z²+ 2xy + 2yz + 2xz
except instead of x there's (-3x). So this must be
(-3x+y+z)² = (-3x)² + y² + z² + 2((-3x)y + (-3x)z + yz)
= 9x² + y² + z² - 6xy + 2yz - 6xz
Looks good.
Answer: (-3x+y+z)²
Since it's a square we could also negate the inside and write this (3x-y-z)²
b) I'll guess that says we want to evaluate this when x=1, y=2, z= -1
(-3(1) + 2 -1)² = (-2)² = 4
Answer: 4
please help!!!! I need the answers.
Answer:
Angle A: 40°
Angle B: 50°
Angle C: 90°
Side A: 14
Side B: 12
Side C: 11.2 or 11 if you round to the nearest whole number.
Step-by-step explanation:
Angle A;
Since we know angles B and C we can use those to help us find angle since all three angles should add up to 180°.
90-50=40
Angle A= 40°
Side C;
Since we know all the angles now and the other two side lengths, we will use those to help us find Side C.
cos 40°= C/14
C/14= cos 40°
C/14= .8
C= .8 x 14
C= 11.2
Hope this helps! Have a great day! :)
39 calls in 6.5 days is ______ calls per day? *
Answer:
39/6.5=6 calls per day
Answer:
6
Step-by-step explanation:
6 ( 6.5)= 39
