To solve this question, we have to find the equation of the circle with given center and where it passes. Doing this, we get that the equation of the circle is:
[tex](x - 16)^2 + (y - 30)^2 = 1156[/tex]
Equation of a circle:
The equation of a circle with center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
Center at (16, 30)
This means that [tex]x_0 = 16, y_0 = 30[/tex]
Thus
[tex](x - 16)^2 + (y - 30)^2 = r^2[/tex]
Passes through the origin:
We use this to find the radius squared, as this means that [tex]x = 0, y = 0[/tex] is part of the circle. Thus
[tex](x - 16)^2 + (y - 30)^2 = r^2[/tex]
[tex](0 - 16)^2 + (0 - 30)^2 = r^2[/tex]
[tex]r^2 = 16^2 + 30^2 = 1156[/tex]
Thus, the equation of the circle is:
[tex](x - 16)^2 + (y - 30)^2 = 1156[/tex]
For another example to find the equation of a circle, you can look at https://brainly.com/question/23719612
find the missing side lengths
Answer:
Step-by-step explanation:
Because it is a 45-45-90 triangle
b=5
a= 5[tex]\sqrt{2}[/tex]
Amira is twice as old as her cousin Pam. Nine years ago, their combined age was 18. What are their present ages?
Answer:
Amira is currently 24 years old and Pam is currently 12 years old
Step-by-step explanation:
Let Amira's age be [tex]a[/tex] and Pam's age be [tex]p[/tex]. Currently, Amira is twice as old as Pam. Therefore, we can write the equation [tex]a=2p[/tex].
We can write a second equation using the other information given in the question. Nine years ago, Amira and Pam's combined ages was 18. If Amira and Pam are currently [tex]a[/tex] and [tex]p[/tex] years old, respectively, then their respective ages 9 years ago would ben [tex]a-9[/tex] and [tex]p-9[/tex]. Since these add up to 18, we have the equation [tex](a-9)+(p-9)=18[/tex].
Therefore, we have a system of equations:
[tex]\begin{cases}a=2p,\\a-9+p-9=18\end{cases}[/tex]
Substitute the first equation into the second one:
[tex]2p-9+p-9=18[/tex]
Combine like terms:
[tex]3p-18=18[/tex]
Add 18 to both sides:
[tex]3p=36[/tex]
Divide both sides by 3:
[tex]p=\frac{36}{3}=\boxed{12}[/tex]
Now substitute this into any of the equations (I'll choose the first):
[tex]a=2p,\\a=2(12),\\a=\boxed{24}[/tex]
Therefore, Amira is currently 24 years old and Pam is currently 12 years old.
If log2 X + log4 X = 5, find X for the 3 decimal places.
Answer:
[tex]x=32768.000[/tex]
Step-by-step explanation:
One is given the following expression:
[tex]log_2(x)+log_4(x)=5[/tex]
Use the logarithm base change rule, which states the following:
[tex]log_b(y)=\frac{log(y)}{log(b)}[/tex]
Remember, a logarithm with not base indicated is another way of writing a logarithm to the base of (10). One can apply the base change rule to this situation:
[tex]log_2(x)+log_4(x)=5[/tex]
[tex]\frac{log(x)}{log(2)}+\frac{log(x)}{log(4)}=5[/tex]
Factor out (log(x)),
[tex](log(x))(\frac{1}{log(2)}+\frac{1}{log(4)})=5[/tex]
Inverse operations:
[tex]log(x)=\frac{5}{\frac{1}{(log(2)+log(4)}}[/tex]
Simplify,
[tex]log(x)=5(log(2)+log(4))[/tex]
[tex]log(x)=4.51545[/tex]
Now rewrite the logarithm, remember, a logarithm is another way of writing an exponent, in the following format:
[tex]b^x=y\ \ -> log_b(y)=x[/tex]
[tex]log(x)=4.51545[/tex]
[tex]10^4^.^5^1^5^4^5=x[/tex]
[tex]32768.000=x[/tex]
If there were 23 cats, 15 snakes, and 8 dogs, how many legs would there be in all?
124
step by step explanation4×23 =92(for cats)
4×8=32(for dogs)
then 92+32=124
Factor the greatest common factor. 5xy4-20x2y3
Answer:
Step-by-step explanation:
The greatest common factor of 5 and -20 is 5
x: the greatest common factor is x
y: the greatest common factor is y^3
Answer: 5xy^3(y - 4x)
Answer these 3 questions and show how por favor! 39-says what is his age
Answer:
I dont know. sorry sorry
Help plzzzz!!!!!!! thank you .
Answer:
120°
Step-by-step explanation:
<U + <T = 180
or, 6x-6+9x+21=180
or, 15x=165
or, x=11
so, <T = 9×11+21 = 120
what’s the answer for the first question? pls help i don’t have much time…
Answer and Step-by-step explanation:
1.
Since we known how much money Jane and Mark have in total, we can subtract the amount Jane has to find the amount Mark has.
750 - 175 = $575
Mark has $575.
2.
We know how many cards Jamal sold, so if we add it to the amount he still has left, we can find the original amount of cards Jamal had.
17 + 83 = 100
Jamal had 100 cards.
#teamtrees #PAW (Plant And Water)
Answer:
Mark will have $575.
Step-by-step explanation:
Take the total amount ($750) and subtract Jane's contribution ($175) to get Mark's contribution($575).
$750-$175=$575
A group of three undergraduate and five graduate students are available to fill certain student government posts. If four students are to be randomly selected from this group, find the probability that exactly two undergraduates will be among the four chosen.
Answer:
[tex]Pr = 0.4286[/tex]
Step-by-step explanation:
Given
Let
[tex]U \to\\[/tex] Undergraduates
[tex]G \to[/tex] Graduates
So, we have:
[tex]U = 3; G =5[/tex] -- Total students
[tex]r = 4[/tex] --- students to select
Required
[tex]P(U =2)[/tex]
From the question, we understand that 2 undergraduates are to be selected; This means that 2 graduates are to be selected.
First, we calculate the total possible selection (using combination)
[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]
So, we have:
[tex]Total = ^{U + G}C_r[/tex]
[tex]Total = ^{3 + 5}C_4[/tex]
[tex]Total = ^8C_4[/tex]
[tex]Total = \frac{8!}{(8-4)!4!}[/tex]
[tex]Total = \frac{8!}{4!4!}[/tex]
Using a calculator, we have:
[tex]Total = 70[/tex]
The number of ways of selecting 2 from 3 undergraduates is:
[tex]U = ^3C_2[/tex]
[tex]U = \frac{3!}{(3-2)!2!}[/tex]
[tex]U = \frac{3!}{1!2!}[/tex]
[tex]U = 3[/tex]
The number of ways of selecting 2 from 5 graduates is:
[tex]G = ^5C_2[/tex]
[tex]G = \frac{5!}{(5-2)!2!}[/tex]
[tex]G = \frac{5!}{3!2!}[/tex]
[tex]G =10[/tex]
So, the probability is:
[tex]Pr = \frac{G * U}{Total}[/tex]
[tex]Pr = \frac{10*3}{70}[/tex]
[tex]Pr = \frac{30}{70}[/tex]
[tex]Pr = 0.4286[/tex]
Help anyone can help me do this question,I will mark brainlest.
Answer:
18. 28 cm*2
19. 24 m
Step-by-step explanation:
18. length × l = 16
l*2= 16
l = 4
RQ = 4 cm
PR =7cm
Area of parallelogram = b×h
= 7×4
=28cm*2
19. 8 +8 + (6-2) +( 6- 2)
=24 m
Center (-1,5); passes through (-4,-6)
Answer:
what is the question
Step-by-step explanation:
y= -(x+3)^2 -5
What is the leading coefficient?
How do you find the vertex?
Answer:
To find the leading coefficient, first expand the function:
[tex]y= -(x+3)^{2} -5\\\\y=-(x^{2} +6x+9)-5\\\\y=-x^{2} -6x-9-5\\\\y=-x^{2} -6x-14[/tex]
The leading coefficient is the coefficient of the highest-order term, which, in this case, would be the -1 from -x².
To find the vertex: see image below
Vertex = (-3, -5)
As James bought his textbooks for classes one semester, he estimated the cost to the nearest ten dollars. He knew he could cover the cost up to $315. His math book cost $68.41, biology text was $105.35, literature text cost $72.49, and the AutoCAD text was $59.91. What rounded sum did James determine
Answer:
$310
Step-by-step explanation:
The first step is to add the costs of the textbook together :
$68.41 + $105.35 + $72.49 + $59.91 = $306.16
In order to round off to the nearest ten dollars, look at the units figure, if the number is greater or equal to 5, add 1 to the ten figure. If this is not the case, add zero. Replace the unit digit with zero
The unit digit is greater than 6, so 1 is added to the tens digit. The amount becomes $310
(2x-7)²-6(2x-7)(x-3)=0
Answer:
-8x² - 106x + 175 = 0
Step-by-step explanation:
Given:
(2x - 7)²- 6(2x - 7)(x-3) = 0
Find:
Solution of the following explanation
Computation:
(2x - 7)²- 6(2x - 7)(x-3) = 0
[(2x)² + (7)² - (2)(2x)(7)] - (12x - 42)(x-3) = 0
[4x² + 49 - 28x] - [12x² - 36x - 42x + 126] = 0
[4x² + 49 - 28x] - [12x² - 78x + 126] = 0
-8x² - 106x + 175 = 0
A man drove his car a distance of 260 miles in 4 hours. If continuing at this rate how many miles will he travel in 8 miles
Answer:
520
Step-by-step explanation:
260/4=520/8
Method 1: Cross Multiply
Method 2: Find GCF
In how many years will the interest of a sum Rs 3600 at the rate of 5.5% per year be Rs 594.8?
Answer:
in 3.04 years the will give required intrest
A portion of the Quadratic Formula proof is shown. Fill in the missing statement. Statements Reasons x² + x + b 4ac 4a? b? 4a² Find a common denominator on the right side of the equation a 2a X? + b 2a b? =4ac 4a? Add the fractions together on the right side of the equation a b2 - 4ac x+ Rewrite the perfect square trinomial on the left side of the equation as a binomial squared 2a 4a 2 Take the square root of both sides of the equation Vb -4ac x+ b 2a + 4a b - 4ас X + 2a + 4a 4ac + 2a 4a 1o ano 4a
Answer:
The fourth option.
x + b/2a = +- sqrt((b^2 - 4ac)/(4a^2))
Step-by-step explanation:
Instructions: Find the missing side. Round your answer to the nearest
tenth.
19
х
66°
X =
Step-by-step explanation:
the missing side is the adjacent side of the angle 66..which also has an opposite side of 19, therefore you use tan
tan66=19/x
tan66x/tan66=19/tan66
x=8.5
I hope this helps
Measure of base of the triangle, value of x is 8.46 unit.
What is trigonometric ratio?Trigonometric ratios can be calculated by taking the ratio of any two sides of a right triangle. Given the scale of the other two sides, we can evaluate the third side using the Pythagorean theorem. We can compare the length of any two sides and the angle of the base using trigonometric ratio. The angle θ is an acute angle (θ < 90°) and is usually measured counterclockwise with respect to the positive x-axis. The basic formula for trigonometric ratios is:
sin θ = Perpendicular/Hypotenuse
cos θ = Base/Hypotenuse
tan θ = Perpendicular/Base
sec θ = Hypotenuse/Base
cosec θ = Hypotenuse/Perpendicular
cot θ = Base/Perpendicular
Given,
In right triangle,
Base of the triangle is x
Measure of angle = 66°
Perpendicular = 19 unit
tanθ = Perpendicular/base
tan66° = 19/x
2.246 = 19/x
x = 19/2.246
x = 8.46 unit
Hence, 8.46 unit is measure of base of the triangle, that is value of x.
Learn more about trigonometric ratio here:
https://brainly.com/question/25122825
#SPJ7
simplify 3/4×(4)1/3÷(3)1/4
Answer:
The answer is 1
Step-by-step explanation:
3/4×13/3÷13/43/4×13/4×4/13=1A student graphed function f(x) =( x+2)² - 5. How would the new function be written if it is translated 3 units to the right, shifted 2 units down and vertically stretched by a factor of 2?
Answer:
f(x)=2(x-3)-2
Step-by-step explanation:
when you hear if it translate to the right, it mean subtract " - "
so translate 3 unit right, it mean minus 3.
and same if translate left, it mean add, "+"
But if it mean shift down, it mean minus -
and if it mean shift up, it mean add +
so shift down 2 unit, mean -2
stretch factor of 2, mean multiply by 2
I hope this help! Im gonna explain further more if you have any question☺
The transformation of a function involves changing the features of the original function to another.
The new function is: [tex]f"(x) = 2(x- 1)^2 - 14[/tex]
The function is given as:
[tex]f(x) = (x + 2)^2 - 5[/tex]
When translated right, the rule is:
[tex](x,y) \to (x - h, y)[/tex]
In this case;
[tex]h= 3[/tex] --- i.e. 3 units right
So, the function becomes
[tex]f'(x) = (x + 2 - 3)^2 - 5[/tex]
[tex]f'(x) = (x - 1)^2 - 5[/tex]
When shifted down, the rule is:
[tex](x,y) \to (x, y - b)[/tex]
In this case;
[tex]b =2[/tex] --- i.e. 2 units down
So, the function becomes
[tex]f'(x) = (x- 1)^2 - 5-2[/tex]
[tex]f'(x) = (x- 1)^2 - 7[/tex]
When vertically stretched, the rule is:
[tex](x,y) \to (x, ay)[/tex]
In this case;
[tex]a =2[/tex] --- i.e. factor of 2
So, the function becomes
[tex]f"(x) = 2*[(x- 1)^2 - 7][/tex]
[tex]f"(x) = 2(x- 1)^2 - 14[/tex]
Hence, the new function is: [tex]f"(x) = 2(x- 1)^2 - 14[/tex]
Read more about function transformations at:
brainly.com/question/24326503
16. Select the equation that has only one solution.
A. 8 x + 3 = 3 X + 8
B. 12 x = 12 x + 7
C.4 x + 11 = 11 + 4 x
D. 6 x + 20 = 6 x
Answer:
A is the answer...........
Explanation
8x+3=3x+8
8x-3x=8-3
5x=5
x=5/5
x=1
The given figure shows a small garden. The shaded area is
reserved for planting flowers and the rest of the area is for
grass. Find the ratio of the area of the garden reserved for
planting flowers to the area reserved for grass.
Answer:
2 : 3
Step-by-step explanation:
We'll begin by calculating the area of the entire garden. This can be obtained as follow:
Length of garden (L) = 12 m
Width of garden (W) = 5 m
Area of entire garden (A) =?
A = L × W
A = 12 × 5
Area of entire garden is 60 m²
Next, we shall determine the area of the garden reserved for flower. This can be obtained as follow:
Length of flower garden (L₁) = 12 – 4
= 8 m
Width of flower garden (W₁) = 3 m
Area of flower garden (A₁) =?
A₁ = L₁ × W₁
A₁ = 8 × 3
A₁ = 24 m²
Next, we shall determine the area of the garden reserved for grass. This can be obtained as follow:
Area of entire garden (A) = 60 m²
Area of flower garden (A₁) = 24 m²
Area of grass garden (A₂) =?
A = A₁ + A₂
60 = 24 + A₂
Collect like terms
A₂ = 60 – 24
A₂ = 36 m²
Finally, we shall determine the ratio of the area of the garden reserved for flowers to the area reserved for grass. This can be obtained as follow:
Area of flower garden (A₁) = 24 m²
Area of grass garden (A₂) = 36 m²
Ratio of flower garden to grass garden = A₁ : A₂
= 24 : 36
= 24 / 36
= 2 : 3
Therefore, the ratio of the area of the garden reserved for flowers to the area reserved for grass is 2 : 3
-URGENT- please helppp-
Answer:
Last option. She didn't use the reciprocal.
Answer:
The second, third, and fourth
Step-by-step explanation:
When you multiply two fractions, you multiply the numerator and denominator, not add them. Also, when you divide by a fraction and want to turn it into multiplication, you multiply by the reciprocal, which she didn't do. Hope this helps!
Write an inequality to describe the region represented on the number line.
H
-4 -3 -2 - 1 0 1 2 3 4
O x>-3
O x>-3.5
O x<-3
O x<-3.5
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the required number line is not included in the question.
A general explanation is as follows:
An open circle means > or <
A closed circle means >= or <=
Take, for instance, the attached number line:
The open dot on -3 means >-3 or <-3
The arrow points to the right direction, means >-3 i.e. greater than -3
Hence, the inequality is:
[tex]x > -3[/tex]
HELPPPPPPPPPPPPPPPPP PLZ
Answer:
GH = 8.4
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan J = opp side / adj side
tan J = HG / HJ
tan 40 = GH / 10
10 tan 40 = GH
8.39099=GH
Rounding to the nearest tenth
GH = 8.4
Independent Practice
Find the first, fourth, and eighth terms of the sequence.
an=0.5 · 3n−1a subscript n baseline equals 0.5 times 3 superscript n minus 1 baseline
A.
0.667; 4.5; 364.5
B.
3; 0.375; 0.0234375
C.
0.5; 13.5; 1093.5
D.
0.5; 121.5; 280.5
Answer:
C.
0.5; 13.5; 1093.5
Step-by-step explanation:
Solve:-
2x+8= 22
..........
2x+8 = 22
2x+8-8 = 22-8
2x = 14
2x/2 = 14/2
x=7
Hope this helps :)
Answer:
[tex]2x+8=22[/tex]
[tex](2x+8)+(-8)=22+(-8)[/tex]
[tex]2x+8-8=22-8[/tex]
[tex]x=7[/tex]
OAmalOHopeO
(I will give brainliest!)
Solve for x using the distributive property
7(x-2)-3(x+3)=5(x-3)+x
Answer:
Step-by-step explanation:
7(x-2) -3(x+3) = 5(x-3) +x , distribute in parenthesis
7x -14 -3x -9 = 5x -15 +x , isolate like terms
7x -3x -5x -x = 14 +9 -15, combine like terms
-2x = 8, divide both sides by -2
x= -4
find the inequality represented by the graph
Answer:
First, find the function of the line:
slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{0-3}{0-4} =\frac{-3}{-4}=\frac{3}{4}[/tex]y-intercept = 0Therefore, the function is [tex]y=\frac{3}{4} x[/tex].
Since it's the area under the graph that's shaded(not ≥ or >) and the graphed line is dotted(not ≤ or ≥), then the inequality would be [tex]y<\frac{3}{4} x[/tex].
Which graph represents a function?
Answer:
The second one
Step-by-step explanation:
This is because when you do the vertical line test none of the lines should intersect more then one point. Remember in a function every x-value (input) has only one y-value (output).
