Answer:
Step-by-step explanation:
Equation of circle: (x - h)² + (y - k)² = r² where (h,k) is the center.
Center( -4 , 4) and r = 5
(x -[-4])² + (y - 4)²= 5²
(x + 4)² + (y-4)² = 25
x² + 2*4*x +4² + y² - 2*y*4 + 4² = 25
x² +8x + 16 + y² - 8y + 16 = 25
x² + 8x + y² - 8y + 16 + 16 -25 = 0
x² + 8x + y² - 8y +7 = 0
We have that the an equation of a circle given the center (-4,4) and radius r=5 is mathematically given as
(x-4)^2+(y-4)^2=5^2
Equation of a circle
Question Parameters:
Given the center (-4,4) and radius r=5
Generally the equation for the Equation of a circle is mathematically given as
(x-x')^2+(y-y')^2=r^2
Therefore, The resultant equation will be
(x-x')^2+(y-y')^2=r^2
(x-4)^2+(y-4)^2=5^2
Hence,an equation of a circle given the center (-4,4) and radius r=5 is
(x-4)^2+(y-4)^2=5^2
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https://brainly.com/question/2263981
What are the solutions to the system of equations?
{y=2x²−6x+3
{y=x−2
Answer:
x = 1, y = −1
x = 5/2, y = 1/2
Step-by-step explanation:
From the question given above, the following data were obtained:
y = 2x² − 6x + 3 ........ (1)
y = x − 2 ...... (2)
We can obtain the solutions to the equation as follow:
y = 2x² − 6x + 3 ........ (1)
y = x − 2 ...... (2)
Substitute the value of y in equation 2 into equation 1
y = 2x² − 6x + 3
y = x − 2
2x² − 6x + 3 = x − 2
Rearrange
2x² − 6x − x + 3 + 2 = 0
2x² − 7x + 5 = 0
Solve by factorization
Obtain the product of 2x² and 5. The result is 10x².
Find two factors of 10x² such that their sum will result to −7x.
The factors are −2x and −5x.
Replace −7x in the equation above with −2x and −5x as shown below:
2x² − 2x − 5x + 5 = 0
2x(x − 1) − 5(x − 1) = 0
(x − 1)(2x − 5) = 0
x − 1 = 0 or 2x − 5 = 0
x = 1 or 2x = 5
x = 1 or x = 5/2
Substitute the value of x into equation 2 to obtain y
y = x − 2
x = 1
y = 1 − 2
y = −1
x = 5/2
y = x − 2
y = 5/2 − 2
y = (5 − 4)/2
y = 1/2
SUMMARY:
x = 1, y = −1
x = 5/2, y = 1/2
Guys please help me solve this I’m struggling
Answer:
[tex]Max\ z = 1[/tex]
[tex]Min\ z = -9[/tex]
Step-by-step explanation:
Given
[tex]z = 4x + 5y[/tex]
[tex]x \ge -1[/tex]
[tex]y \le 2x +3[/tex]
[tex]y \le -1[/tex]
Required
The maximum and minimum of z
To do this, we make use of the graphical method
See attachment for graphs of
[tex]x \ge -1[/tex]
[tex]y \le 2x +3[/tex]
[tex]y \le -1[/tex]
The corner points of the function are:
[tex](x,y) = (-1,1)[/tex]
[tex](x,y) = (-1,0)[/tex]
[tex](x,y) = (-1,-1)[/tex]
We have:
[tex]z = 4x + 5y[/tex]
Calculate z with the above values
[tex]z = 4(-1) + 5(1) = 1[/tex]
[tex]z = 4(-1) + 5(0) = -4[/tex]
[tex]z = 4(-1) + 5(-1) = -9[/tex]
So, we have:
[tex]Max\ z = 1[/tex]
[tex]Min\ z = -9[/tex]
Good Afternoon I am really stuck on this question whoever solves it I will give them brainliest with no unacceptable question thank you so much!
Answer:
Card picked=2
P(factors of 28)={1,2,4,7,14,28}
total cards=4
in percentage=4 x 20 + 20
80+20=100
Therefore 2 in percentage will be
2 x 20 + 20
=40+20=60%
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:
6. Alex and Brian park their bikes side-by-side. Alex leaves to visit friends, and Brian leaves 30 minutes later,
headed for the same destination. Alex pedals 5 miles per hour slower than Brian. After 1 hour, Brian passes Alex. At
what speed are they each pedaling?
Answer:
See below.
Step-by-step explanation:
When Brian passes Alex they both have travelled the same distance.
Call this distance d.
Let the speed that Brian passes = x miles/hour.
Distance = speed * time so:
For Alex:
d = (x - 5) * 1.5 ( Alex cycles for 1 + 30 minutes = 1.5 hours)
For Brian:
d = x * 1
So substituting d = x in Alex's equation:
x = 1.5(x - 5)
x = 1.5x - 7.5
7.5 = 0.5x
7/5 / 0.5 = x
15 = x.
ANSWER:
Brian's speed is 15 miles/hour.
Alex's speed is 15 - 5 = 10 miles/hour.
Please help me fast
Answer:
864
Step-by-step explanation:
A=6a^2=6·12^2=864
Answer:
864 in^2
Step-by-step explanation:
2(144+144+144) = 2(432) = 864 in^2.
Hope this helped!
How can you use what you know about 5(2) to find 5(-2)?
Please help
Answer:
-10
Step-by-step explanation:
5(2) or fives times two is positive ten. The rule about multiplying with negatives is a negative times a positive is a negative. We take the multiplication answer from 5(2)=10 and apple the nagative from 5(-2). Hope this helps:)
Value of the boat after 3 years?
after each year it's 83% of it's value from last year (100%-17%=83%)
the function in 19000 * (0.83) ^x
3 will be filled in for x
19000 * (0.83) ^3= 10863.953
$10863.95
Answer:
$10,863.95
Step-by-step explanation:
y = 19,000[tex](.83)^{t}[/tex]
y = 19,000[tex](.83)^{3}[/tex]
y =$10,863.95
need help asap pls !
Answer:
L={∅}
Step-by-step explanation:
20) solve:
[tex] {8}^{2} + 2 = [/tex]
21) solve:
[tex]4(2x + 5y = [/tex]
22) simplify the expression
[tex]4( {2}^{2} + 30) - 4 = [/tex]
Mr. Ellington has a total of 32 students in his class , The ratio of girls to boys is 3:5, how many girls are in Mr . Ellington's class ?
Add the ratio: 3 + 5 = 8
Divide total students by that:
32/8 = 4
The ratio for girls is 3, multiply the 4 by 3:
4 x 3 = 12
There are 12 girls
Answer:
12
Step-by-step explanation:
If the ratio of girls to boys is 3:5, that means that for every 8 total students, 3 would be girls and 5 would be boys. Therefore 3/8 of the students are girls and 5/8 are boys. If 3/8 are girls, then:
[tex]\frac{3}{8}[/tex] of 32
= [tex]\frac{3}{8} * 32[/tex]
[tex]=\frac{3 * 32}{8} \\= \frac{96}{8} \\= 12[/tex]
There are 12 girls.
There is 10% salt solution and a 30% salt solution. How much of each is needed to make 10L mixture that is 25% salt solution?
Answer:
2.5L of 10% salt solution and 7.5L of the 30% salt solution
Step-by-step explanation:
let the amount of L in the 10% solution be 'x'
let the amount of L in the 30% solution be '10-x'
* because they add up to a total of 10L
10%(x) + 30%(10-x) = 25%(10)
0.1x + 3 - 0.3x = 2.5
-0.2x = -0.5
x = 2.5
x =2.5
10-x = 7.5
2.5 of 10% solution and 7.5% of 30% solution
A plank 6m long leans against a vertical wall so that the foot of the plank is 4m away from the wall. A lizard climbs 2m up the plank. Calculate the horizontal distance between the lizard and the wall.
Answer: [tex]\dfrac{8}{3}\ m[/tex]
Step-by-step explanation:
Given
Length of the plank is [tex]6\ m[/tex]
Foot of the flank is [tex]4\ m[/tex] away from the wall
Lizard climbs 2 m up the wall
from the figure, the two triangles are similar
[tex]\therefore \dfrac{2}{6}=\dfrac{x}{4}\\\\\Rightarrow x=4\times \dfrac{2}{6}\\\\\Rightarrow x=\dfrac{4}{3}\ m[/tex]
So, the distance from the wall is
[tex]\Rightarrow 4-x\\\\\Rightarrow 4-\dfrac{4}{3}\\\\\Rightarrow \dfrac{8}{3}\ m[/tex]
What is the volume?
9 ft
4 ft
2 ft
HELPPPP
Answer:
72?
Step-by-step explanation:
V=whl=4 x 2 x9=72
find the missing side
Answer:
x ≈ 13.7
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos70° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{40}[/tex] ( multiply both sides by 40 )
40 × cos70° = x , then
x ≈ 13.7 ( to the nearest tenth )
A game involves correctly choosing the 5 correct numbers from 1 through 18 that are randomly drawn. What is the probability that a person wins the game, if they enter a) once? b) 7 times with a different choice each time?
Answer:
[tex]=\frac{1}{8568}\ = .00011\\\ =\frac{7}{8568} = .00081[/tex]
Step-by-step explanation:
[tex]5/18\cdot \:4/17\cdot \:3/16\cdot \:2/15\cdot \:1/14=\frac{1}{8568}[/tex]
A person walks away from a pulley pulling a rope slung over it. The rope is being held at a height 10 feet below the pulley. Suppose that the weight at the opposite end of the rope is rising at 4 feet per second. At what rate is the person walking when s/he is 20 feet from being directly under the pulley
The image of this question is missing and so i have attached it.
Answer:
dd/dt = 4.47 ft/s
Step-by-step explanation:
From the image attached, let's denote the following;
d = horizontal distance beneath pulley
h = height of pulley
l = diagonal from the pulley to the head of the person
v = velocity of rope rising
Using pythagoras theorem;
l² = d² + h²
Differentiating with respect to time and considering h = c^(te) gives;
2l(dl/dt) = 2d(dd/dt)
We are given;
d = 20 ft
h = 10 ft
v = 4 ft/s
We know that velocity in this case is change in diagonal distance with time. Thus;
v = dl/dt = 4 ft/s
From earlier, we saw that;
2l(dl/dt) = 2d(dd/dt)
Thus, reducing it gives
(dl/dt)(l/d) = dd/dt
Now, l² = d² + h²
l = √(d² + h²)
Also, v = dl/dt = 4
Thus;
4(√(d² + h²))/d = dd/dt
4(√(20² + 10²))/20 = dd/dt
dd/dt = 4.47 ft/s
The perimeter of a rectangle is 56 feet and
its area is 192 square feet. What are the
dimensions of the rectangle?
Answer:
Step-by-step explanation:
P = 2(L + W)
Area = L*W
Area = 192
(L + W)*2 = 56
L+W = 28
L = 28 - W
W*(28 - W) = 192
28W - w^2 = 92
-w^2 + 28w - 192 = 0
w^2 - 28w + 192 = 0
This factors into
(w - 12)(w - 16) = 0
w - 12 = 0
w = 12
L = 28 - 12 = 16
Help anyone can help me do the question,I will mark brainlest.
Answer:
a) 30
b)600pi
Step-by-step explanation:
For the first questions, since the arc is 240°, the area of the sector and circumference will be 240/360 or 2/3 of the total of the circles'. Therefore 125.6 x 3/2 is the circumference, which is 188.4. When we divide this by 6.28, we get 30
Now, since the area is pi r^2 where we know that r=30, we get 900pi as the area of the whole thing, however since the sector is 2/3 of the whole circle, 2/3 x 900pi = 600pi
Triangle ABC is a right triangle.
Triangle A B C. Angle A is x degrees, B is 90 degrees, C is (x minus 10) degrees. The exterior angle to angle C is (2 x + 40) degrees.
Which equations can be used to find the value of x? Check all that apply.
x + 90 + (x minus 10) = 180
x + 90 + (2 x + 40) = 180
2 x + 80 = 180
x + 90 = 2 x + 40
(x minus 10) + 90 = 2 x + 40
Answer:
x + 90 + (x minus 10)= 180° can be used to find the value of x.
Answer:
A) X+90+ (x-10) - 180
C) 2x+80 = 180
D) x+90 = 2x+40
Step-by-step explanation:
DJVJNNSMKAJABJSHSNSB
Which composite function can be used to find the
force of the object based on its volume?
The density of titanium is 4.5 g/cm3. A titanium object
is accelerating at a rate of 800 cm/s2. The mass of
the object can be modeled by the function m(v) =
4.5v, where v is the volume in cubic centimeters.
Additionally, the force of the object can be found
using the function F(m) = 800m.
A. F(m(v)) = 177.8V
B. F(m(v)) = 795.5v
C. F(m(v)) = 804.5v
D. F(m(V)) = 3,600V
Given:
The mass function is:
[tex]m(v)=4.5v[/tex]
where v is the volume in cubic centimeters.
The force function is:
[tex]F(m)=800m[/tex]
To find:
The composite function can be used to find the force of the object based on its volume.
Solution:
The composite function can be used to find the force of the object based on its volume is:
[tex]F(m(v))=F(4.5v)[/tex] [tex][\because m(v)=4.5v][/tex]
[tex]F(m(v))=800(4.5v)[/tex] [tex][\because F(m)=800m][/tex]
[tex]F(m(v))=3600v[/tex]
Therefore, the correct option is D.
Answer: F(m(v)) = 3,600v
Step-by-step explanation:DDDD
Match the answers……………..
9 in 8956 = 900
9 in 95675 = 90000
9 = 9 in 124569
9 in 68795 = 90
90000 = 9 in 2549652.........
hope it helps...
#What is the value of the discriminant for the quadratic equation –3 = –x2 + 2x?
Discriminant = b2 – 4ac
–8
4
8
16
Answer:
16
Step-by-step explanation:
the quadratic equation –3 = –x2 + 2x can be changed into :
x²-2x-3= 0
a=1, b= -2 , and c = -3
so, the discriminant = (-2)²-4(1)(-3)
= 4 + 12 = 16
A sample of 50 observations is taken from an infinite population. The sampling distribution of : a.is approximately normal because of the central limit theorem. b.cannot be determined. c.is approximately normal because is always approximately normally distributed. d.is approximately normal because the sample size is small in comparison to the population size.
Answer:
a.is approximately normal because of the central limit theorem.
Step-by-step explanation:
The central limit theorem states that if we have a population with mean μ and standard deviation σ and we take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
For any distribution if the number of samples n ≥ 30, the sample distribution will be approximately normal.
Since in our question, the sample of observations is 50, n = 50.
Since 50 > 30, then our sample distribution will be approximately normal because of the central limit theorem.
So, a is the answer.
Pls help me ! L need help here
Answer:
H. 40 inches
Step-by-step explanation:
On Wednesday, he is 40 inches taller. ... That would make 5 days of growth, for 100 inches. But this is only 3 days therefore he would grow 40 inches taller
What is (0,6] n (6,8]?
Answer:
(6) the letter n : intersection which means the number you will find at the first bracket and has the same number at the other bracket
7. In which step does a mistake first occur?
8 + 2 + (3 X 3 -2)
Step 1: 8 +2 + (3 x 1)
Step 2: 8 +2 + 3
Step 3: 4 + 3
Step 4: 7
Answer:
17
Step-by-step explanation:
8+2+(3×3-2)=8+2+(9-2)=8+2+7=17
mistake in the first step
firstly we do × and ÷
then + and -
The tens digits of a certain two-digit number is 1/3 of the units digit. When the digits are reversed, the new number exceed twice the original number by 2 more than the sum of the digits. Find the original number.
Answer:
The orginal number is 26.
Step-by-step explanation:
So the units digit can be 3 6 or 9
The tens digit can be 1 2 or 3
So the original number can be 13
31 = 2*13+ (1+3) + 2
31 =? 26 + 4 + 2
This doesn't work. The right side is 32
26
62 = 2*26 + 8 + 2
62 = 52 + 8 + 2
This is your answer.
3 and 9 won't work because 39 is odd and so is 93. The result has to be even.
Rhombus LMNO is shown with its diagonals.
Rhombus L M N O is shown. Diagonals are drawn from point L to point N and from point M to point O and intersect at point P. All sides are congruent.
Angle MNO measures 112°. What is the measure of angle LMN?
Answer:
hope this help
Step-by-step explanation:
Answer:
90
51
10
Step-by-step explanation:
