The equation represents a circle whose center is (-4, 1) and has a radius r = √2
How to find the center and radius of the circle?We have the equation:
[tex]x^2 + y^2 + 8x - 2y + 15 = 0[/tex]
We can rewrite this as:
[tex](x^2 + 8x ) + (y^2 - 2y ) + 15 = 0\\\\\\\\(x^2 + 8x + 16) - 16 + (y^2 - 2y + 1) - 1 + 15 = 0\\\\(x + 4)^2 + (y - 1)^2 - 16 - 1 + 15 = 0\\\\(x + 4)^2 + (y - 1)^2 = 2[/tex]
Where we just completed squares.
Comparing this with the general circle equation, we can see that the center is the point (-4, 1) and the radius is √2.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
Answer:
Step-by-step explanation:
The angle of elevation to a nearby tree from a point on the ground is measured to be 54^{\circ} ∘ . How tall is the tree if the point on the ground is 89 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary.
The height of the tree to the nearest hundredth is 122.49 feet
Application of SOH CAH TOAThese are used to determine the sides and angle of a right triangle
Given
Angle of elevation= 54 degrees
Base distance = 89 feet
Required
Height of tree
Using the SOH CAH TOA
tan 54 = H/89
H = 89tan54
H = 122.49
Hence the height of the tree to the nearest hundredth is 122.49 feet
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The table below shows the value of Henry's car at the end for each of the first 3 years after it is purchased. The values form a geometric
sequence.
Year
Value
dollars)
18000
116200
14580
(in
What will be the approximate value of the car at the end of the 10th year?
O
A. $6,974
B. $8,610
C. $11,810
D. $7,748
Using a geometric sequence, it is found that the approximate value of the car at the end of the 10th year will be given by:
A. $6,974.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
In this problem, the first term and the common ratio are given, respectively, by:
[tex]a_1 = 18000, q = \frac{16200}{18000} = 0.9[/tex]
Hence the equation is:
[tex]a_n = 18000(0.9)^{n-1}[/tex]
At the end of the 10th year, the value will be of:
[tex]a_{10} = 18000(0.9)^{10-1} = 6974[/tex]
Hence option A is correct.
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To remain healthy, a person needs at least 8 hours of sleep. A company wants to know if their employees get enough sleep. A random sample of 24 employees revealed that the average number of hours of sleep an employee gets is 6.7 with standard deviation of 2.3. What should be the test statistic?
Answer:
how many hours a week the employees are working?
Step-by-step explanation:
I could be wrong but that's my fault if it's wrong sorry
what is the value of the digit 5in the number 734.95?
Answer:
0.05
explanation
value means total value
so it's 5*0.01
=0.05
Please help Fast! Need answer by 1:00 pm
A tub of water is emptied at a rate of 3 gallons per minute. The equation y –12 = –3(x – 1) models the amount of water remaining, where x is time (in minutes) and y is the amount of water left (in gallons). Analyze the work shown below to determine the initial amount of water.
1. Solve for the y-variable.
y – 12 = –3(x – 1)
y – 12 = –3x + 3
y = –3x +15
2. Write the equation using function notation.
f(x) = –3x +15
The tub started with
gallons of water.
The initial amount of the water is 15 gallons
Linear functionsThese are functions that has a leading degree of 1. Given the equation that represents the amount of water remaining after x minutes;
y - 12 = -3(x- 1)
y -12 = -3x + 3
y = -3x +3 + 12
y = -3x + 15
In order to determine the initial amount of water, we will substitute x =0 into the function
y = -3(0) + 15
y = 15
Hence the initial amount of the water is 15 gallons
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Answer:
15
Step-by-step explanation:
Lindsay sketches a right triangle with lengths f, g, and h as shown. She uses the Pythagorean Theorem to write the equation f2 + g2 = h2 to represent the triangle. How can Lindsay correct her error? Explain your reasoning.
Answer:
hope you can understand
3^x+3^x =54 what's the value of x ?
Answer:
x = 3
Step-by-step explanation:
if you need an explanation let me know
Answer:
x = 3
Step-by-step explanation:
Given:
[tex] \implies \rm 3 {}^{x} + {3}^{x} = 54[/tex]
To Find:
Value of xSolution:
We could re-write 3^x+3^x as:
[We factored here][tex] \implies \: 2(3 {}^{x} ) = 54[/tex]
Divide both sides by 2
[tex] \implies \cfrac{2(3 {}^{x}) }{2} = \cfrac{54}{2} [/tex]
[tex] \implies \: 3 {}^{x} = 27[/tex]
Take logarithm on both sides
[tex] \implies \: \log(3 {}^{x} ) = \log(27)[/tex]
[tex] \implies \: x \times \log(3) = \rm \: log \: (27)[/tex]
[tex] \implies \: x = \cfrac{ \log(27)}{ \log \:(3)} [/tex]
[tex] \implies \boxed{x = 3}[/tex]
Hence, x = 3 .
can i have help with this
Answer:
x^32
Step-by-step explanation:
A fraction bar is a division symbol. When you are dividing, you can subtract the exponents.
x^56 / x^24
= x ^ (56-24)
= x^32
Answer:
x^32
Step-by-step explanation:
a^m/a^n = a^(m-n)
so, x^56/x^24 = x^(56-24) = x^32
2-53. a message is released at 1930 hours greenwich mean time on 2 january 1991. what is the correctly stated date-time group (dtg) assigned to the me
Step-by-step explanation:
. In Figure 5.144, of ΔABC, where
m(∠C) = 30, m(∠ABD) = 5x,
m(∠A) = 4x. Find m(∠ABC) in
degrees.
Combine the like terms to create an equivalent expression:−3z−z
Answer:
-4z
Step-by-step explanation:
Hi student! Let me help you out.
_____________________
Note that, -3z and -z are like terms. This means we can combine them right off the bat, which gives us [tex]\mathrm{-4z}[/tex].
[tex]\mathrm{-3z-z=-4z}[/tex]. -4z is our final answer.
Hope that this helped you! have a good day ahead.
Best Wishes!
[tex]\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. AIm high. Dream big.}}}}}\bigstar\star[/tex]
◈◈-Greetings!-◆◆
___________________
Answer:
-4z
Step-by-step explanation:
-3z-z
On combining like terms,
= -4z
Here,the terms are -3z and -z, where - and - combines and + is the result,so we need to add the expression.Explain why cos(−3π4)=cos(5π4).
Answer:
See below
Step-by-step explanation:
Think about what happens when you rotate around a circle [tex]-\frac{3\pi}{4}[/tex] radians. This means that you are going clockwise [tex]-\frac{3\pi}{4}[/tex] radians.
Likewise, if you went [tex]\frac{5\pi}{4}[/tex] radians counterclockwise, you'd end up in the same place, so the cosine values must be the same.
Peter takes 7 minutes and 30 seconds to run 1 mile. How many miles can he run in 15 minutes?
miles
Answer:
2 miles
Step-by-step explanation:
Peter takes 7 minutes and 30 seconds per mile.
7 times 2 is 14 minutes.
30 seconds times 2 is 1 minute.
If you add these 2 values together you get 15 minutes.
So we need to times the miles by 2 to get 2 miles.
I hope this helps, have a lovely day.
some one please help me slove this I can't figure it out I will give Brainliest answer to who ever answer frist...
keeping in mind that twin sides stemming from a common vertex make twin angles at the "base", Check the picture below.
Solve for x.
x/12 = -4
Answer:
[tex] \frac{x}{12} = - 4[/tex]
[tex] \frac{x}{12} = \frac { - 4}{1} [/tex]
[tex]x \times 1 = 12 \times - 4[/tex]
[tex]x = - 48[/tex]
value of x is -48
Answer:
x=-48.
Step-by-step explanation:
To find x we should multiply both sides, by 12:
[tex]\sf \cfrac{x}{12}\times12=\-4\times12[/tex]
↪
The 12s cancel on the left:
[tex]x=-4\times12[/tex]
After multiplying we obtain [tex]\sf x=-48[/tex]. Which is our answer.
Hope that this helped you! Have a good day ahead.
Best Wishes!
[tex]\star\bigstar\underline{\underline{\overline{\overline{\text{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]
◆◆-Greetings!-◈◈
--
What is the force, in N, when a pressure of 22 N/m² is exerted on an area of 750 cm²?
Answer:
1.65 N
Step-by-step explanation:
Step 1: convert cm^2 to m^2
1 cm^2 = 0.0001 m^2
750 cm^2 = 0.075 m^2
Step 2: multiply pressure by area
F = P*A = 22 N/m^2 * 0.075 m^2 = 1.65 N
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A rectangular prism with a length of 3.8 meters and a width of 1.5 meters has a volume of 16.53 cubic meters.
What is the height of the prism?
2.9 m
6.525 m
11.23 m
21.83 m
Answer:
2.9 meters.
Step-by-step explanation:
First we multiply the length, 3.8, by the width, 1.5, to get the base, 5.7 (this step is not entirely necessary, but makes it much easier). Then we divide the volume, 16.53, by the base, 5.7, to get the height, 2.9 meters.
Answer:
i think its 21.83 i may be wrong but im pretty sure its 21.83
Step-by-step explanation:
Book on Language made From Pi or π
Answer:
Step-by-step explanation:
help me, please i need your help
The answer to each question in the image is given below:
y - 0.32y = 0.68yy + 0.32y = 1.32yy + [tex]\frac{2}{5}[/tex]y = [tex]\frac{7}{5}y[/tex]y - [tex]\frac{2}{5}y[/tex] = [tex]\frac{3}{5}y[/tex] Meaning of equivalent equations.An equivalent equation can be defined as an equation that has the same meaning and also has the same answer with another equation or with an equation it is said to be equivalent with.
The above equation are equivalent to each other meaning they can be used to derive each other.
In conclusion, the list above is the right pairs of equivalent equations.
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If a rectangle’s perimeter is 86 units and the width is 15 units, what is the length in units?
Answer:
I think the answer would be 28
A restaurant bill is £132
A 10% service charge is included in the bill.
How much is the service charge?
Answer:
1.1x= 132
Step-by-step explanation:
Find the period and amplitude of the function.
y=5cos2O
Answer:
period pi and amplitude 5
how do i solve 8(2-6v) + 19 = -61
Answer:
v=2
Step-by-step explanation:
simplify 4^(3)*4^(5)
A. 16^8
B. 4^8
C. 4^15
D. 16 * 15
Answer:
B. 4^8
Step-by-step explanation:
The indices of the base 4 can be added while multiplying i.e. 3+5=8 but the base remains the same.
Answer:
B
Step-by-step explanation:
Because in powers we just add so it will be 4^3+5
=4^8
help pls im being timed i cant do mathhh
The first term of a geometric sequence is 2, and the 4th term is 250. Find the 2 terms between the first and the 4th term.
Answer:
second term: 10
third term: 50
Step-by-step explanation:
The equation for any geometric sequence is [tex]a_{n} = a_{1} *r^{n-1}[/tex] where n is the term number you want to find, [tex]a_{1}[/tex] is the first term in the sequence, and [tex]r[/tex] is the common ratio. The equation for this sequence specifically uses 5 as its common ratio, so the equation is [tex]a_{n} =2*5^{n-1}[/tex]
[tex]a_{1} = 2*5^{1-1}=2*5^{0} =2*1=2[/tex]
[tex]a_{2} = 2*5^{2-1}=2*5^{1} =2*5=10[/tex]
[tex]a_{3} = 2*5^{3-1}=2*5^{2} =2*25=50[/tex]
[tex]a_{4} = 2*5^{4-1}=2*5^{3} =2*125=250[/tex]
Andre took 6 kicks and made 4 goals: 4/6
Tom wants to take more than 20 kicks and make an equivalent fraction to Andre.
what are two possible fractions of goals Tom can make
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
A correct answer is option A which is x² + (y – 3)² = 36 is the equation of the circle that has a diameter of 12 units and a center that lies on the y-axis.
What is a circle?A circle is a two-dimensional geometry on the plane having a center point and the circular line is drawn equidistant from the center point.
The general form of the equation of a circle is given as:-
( x - h )² + ( y - k )² = r²
By comparing the given equation we can see the following results:-
x² + (y – 3)² = 36
( x - ( 0 ))² + ( y - 3 )² = 6²
We can see that the coordinate of the center are ( 0, 3 ) and the radius is 6 so the diameter is 12.
Therefore the correct answer is option A which is x² + (y – 3)² = 36 is the equation of the circle that has a diameter of 12 units and a center that lies on the y-axis.
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Answer:
A and E (first and last, ending in "=36")
x2 + (y – 3)2 = 36
x2 + (y + 8)2 = 36
Step-by-step explanation:
just took the quiz
Which organisms reproduce through a...se...xu...al reproduction? (Select all that apply.)
starfish
yeast
fungi
bacteria
PICK MORE THAN ONE and no links please 1+1
Answer:
bacteria and fungi
Step-by-step explanation:
Single organism makes an exact copy of itself
Bacteria, some plants and fungi, few animals (sponges)
Offspring are identical to parent