Answer:
see explanation
Step-by-step explanation:
Under a clockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ) , then
(3, 3 ) → (- 3, 3 )
(3, 4 ) → (- 4, 3 )
(5, 3 ) → (- 3, 5 )
What is the standard form of the ellipse equation
25x2 - 150x + 9y2 = 0?
O
(x - 3)2
32
y
1
+
52
0 (x - 5)
1
y2
22
(y - 3)2
22
0x2
+
14
1
O
x2
32
(y - 3)2
22
= 1
Answer: The correct answer is in the first option.
Step-by-step explanation:
Equation of an Ellipse
[tex]\dfrac{x^{2} }{a^{2} } +\dfrac{y^{2} }{b^{2} } =1\\\\25x^{2} - 150x + 9y^{2} = 0\\\\\text {Let's \: perform \: the \: transformations:}\\\\\dfrac{25x^{2} }{25 \cdot 9} -\dfrac{150x}{25 \cdot 9} +\dfrac{9y^{2} }{25 \cdot 9} =0\\\\\dfrac{x^{2} }{3^{2} } -\dfrac{6x}{3^{2} } +\dfrac{y^{2} }{5^{2} } =0\\\\\dfrac{x^{2} -6x}{3^{2} } +\dfrac{y^{2} }{5^{2} } +\dfrac{3^{2} }{3^{2} } -\dfrac{3^{2} }{3^{2} } =0\\\\\dfrac{x^{2} -6x+3^{2} }{3^{2} } +\dfrac{y^{2} }{5^{2} } =\dfrac{3^{2} }{3^{2} }[/tex]
[tex]\dfrac{(x-3)^{2} }{3^{2} } +\dfrac{y^{2} }{5^{2} } =1[/tex]
1. Resuelve las ecuaciones:
a. x2 + 12x + 32 = 0
b. 9x2 +6x + 1 = 0
2. Resuelve las ecuaciones:
a. 2x2 +5x = 0
b. 2x2 -32 = 0
3. Calcula el valor de m para que la ecuación x2 + mx + 9 = 0 tenga solución doble.
4. Resuelve las ecuaciones:
a. x4 - 25x2 + 144 = 0
b. x4 + 9x2 - 162 = 0
AYUDA ;v
Answer:
1. a) x1 = -8 y x2 = -4
b) x1 = -1/3
2. a) x1 = 0 y x2 = -5
b) x1 = 4 y x2 = -4
3. m debe ser 6. Asi tendriamos (x+3)²=0
4. a) x1 = 4, x2 = -4, x3 = 3 y x3 = -3
b) x1 = 3, x2 = -3 las otras dos raices son complejas.
Step-by-step explanation:
1. a) [tex]x^{2}+12x+32=0[/tex]
Factorizando:
[tex](x+8)(x+4)=0[/tex]
Entonces: x1 = -8 y x2 = -4
4. a) x1 = 4, x2 = -4, x3 = 3 y x3 = -3
b) [tex]9x^{2}+6x+1=0[/tex]
Factorizando:
[tex](3x+1)(3x+1)=0[/tex]
[tex](3x+1)^{2}=0[/tex]
Entonces: x1 = -1/3
2. a) [tex]2x^{2}+5x=0[/tex]
Aplicando factor comun:
[tex]x(x+5)=0[/tex]
Entonces: x1 = 0 y x2 = -5
b) [tex]2x^{2}-32=0[/tex]
Despejamos x.
[tex]2x^{2}=32[/tex]
[tex]x^{2}=16[/tex]
Entonces: x1 = 4 y x2 = -4
3. m debe ser 6. Asi tendriamos (x+3)²=0
4. a) [tex]x^{4}-25x^{2}+144=0[/tex]
Hacemos cambio de variable: [tex]w=x^{2}[/tex]
[tex]w^{2}-25w+144=0[/tex]
Ahara podemos factorizar:
[tex](w-16)(w-9)=0[/tex]
Usando el cambio de variable nuevamente.
[tex](x^{2}-16)(x^{2}-9)=0[/tex]
Entonces los valores de x son: x1 = 4, x2 = -4, x3 = 3 y x3 = -3
b) [tex]x^{4}+9x^{2}-162=0[/tex]
Hacemos cambio de variable: [tex]z=x^{2}[/tex]
[tex]z^{2}+9z-162=0[/tex]
Ahara podemos factorizar:
[tex](z-9)(z+18)=0[/tex]
Usando el cambio de variable nuevamente.
[tex](x^{2}-9)(x^{2}+18)=0[/tex]
Entonces los valores de x son: x1 = 3, x2 = -3 las otras dos raices son complejas.
Espero ye haya servido!
c. Suppose you are given the functa. If f(x) = 10x − 1, the value of f(−2) is __________. b. If g(x) = −5x + 13, the value of g(1) is __________. c. If h(x) = x2 − x − 12, the value of h(3) is __________.ion h(x) = −2x + 3 and asked for h(4). This is the same as asking for the value of the function at x = __________.
Answer:
c. f(-2)= -21
b. g(x)=8
c. h(3)= -19
h(4)= -5
Step-by-step explanation:
What is [tex]\pi r^2[/tex] ?
Answer:
The formula to determine the area of the circle.
Step-by-step explanation:
↔
what would be the u to usub and what would be the steps to solving this integral?
Presumably, ln⁵(x) is the same as (ln(x))⁵ (as opposed to a quintuply-nested logarithm, log(log(log(log(log(x)))))).
Then substituting u = ln(x) and du = dx/x gives
[tex]\displaystyle\int\frac{\mathrm dx}{x\ln^5(x)} = \int\frac{\mathrm du}{u^5} = -\frac1{4u^4}+C = \boxed{-\frac1{4\ln^4(x)}+C}[/tex]
A group of 40 workers can do a construction in 16 days. When has elapsed 4 days, 10 workers retired. How many days of delay the construction will be delivered?
Answer:
4 days
Step-by-step explanation:
The time it would take the group of 40 workers to deliver the work, [tex]t_{estimated}[/tex] = 16 days
The number of workers that retired after 4 days = 10 workers
Therefore, the number of workers remaining = 40 - 10 = 30 workers
The time it would take 1 worker to do the work = The number of work days in the construction = 40 × 16 = 640 work days
The amount of work done in 4 days = 40 × 4 = 160 work days
The amount of work remaining after the elapsed 4 days = (640 - 160) work days = 480 work days
The number of days, n, it would take the remaining 30 workers to do the remaining work, is given as follows;
n = 480 work days/(30 workers) = 16 days
The actual total number of work days it took for the work to be delivered, [tex]t_{actual}[/tex] = 4 days + 16 days = 20 days
The number of days delay the construction will be delivered, [tex]t_{delay}[/tex], is given as follows = [tex]t_{actual}[/tex]
[tex]t_{delay}[/tex] = [tex]t_{actual}[/tex] - [tex]t_{estimated}[/tex]
∴ [tex]t_{delay}[/tex] = 20 days - 16 days = 4 days
The number of days delay the construction will be delivered, [tex]t_{delay}[/tex] = 4 days
Ah(t)
1800-
A ball is dropped from a height of 1296 ft. Its height h,
in feet, after t seconds is given by h(t) = 1296 - 1612.
After how long will the ball reach the ground?
0 0
1296
0-
0
12
The ball will reach the ground in seconds.
(Type an integer or a simplified fraction.)
HELP ME WITH THIS PROBLEM PLEASE!!
Answer:
w ≈ 33.9 in
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
w² + w² = 48²
2w² = 2304 ( divide both sides by 2 )
w² = 1152 ( take the square root of both sides )
w = [tex]\sqrt{1152}[/tex] ≈ 33.9 in ( to the nearest tenth )
Given a circle with centre O and radius 2.4cm. P is a point such that the lenght of the tengent from Q to the circle is 4.5cm. Find the lenght of OP
Answer:
5.1 cm
Step-by-step explanation:
(Probable) Question;
Given a circle with center O and radius 2.4 cm. P is a point on the tangent that touches the circle at point Q, such that the length of the tangent from P to Q is 4.5 cm. Find the length of OP
The given parameters are;
The radius of the circle with enter at O, [tex]\overline{OQ}[/tex] = 2.4 cm
The length of the tangent from P to the circle at point Q, [tex]\overline{PQ}[/tex] = 4.5 cm
The length of OP = Required
By Pythagoras's theorem, we have;
[tex]\overline{OP}[/tex]² = [tex]\overline{OQ}[/tex]² + [tex]\overline{PQ}[/tex]²
∴ [tex]\overline{OP}[/tex]² = 2.4² + 4.5² = 26.01
[tex]\overline{OP}[/tex] = √26.01 = 5.1
The length of OP = 5.1 cm
pls help me solve this multiplication fractions. (show work)
Answer:
32:3/4
33:4/3
34:40
35:48
Javier jogs & of a -
mile in 8 minutes
how many minutes will
it take him to jog
1 mile?
Answer:
It will take him 10 minutes to jog 1 mile.
Step-by-step explanation:
can i have brianliest please
If the woman in the picture below measured the angle of elevation from herself to the top of castle and found it to be 64 degrees, and she also measured the distance from herself to the base of the castle as being 124 meters, what would the height of the castle be? (round to the nearest whole meter.)
Answer:
254m
Step-by-step explanation:
The setup will be in form of a right triangle. Hence;
The angle of elevation = 64degrees
distance from herself to the base of the castle = 124 meters (Adjacent)
Required
Height of the castle (Opposite)
Using the SOH CAH TOA identity
Tan theta = opp/adj
Tan 64 = H/124
H = 124tan64
H = 124(2.05030)
H = 254.23
H ≈ 254m
Hence the height of the castle to the nearest whole meters is 254metres
geometry help translations
Answer:
A' (9,4)
B' (8,-1)
C' (5,1)
Answered by GAUTHMATH
Answer:
A' = 9,4
B' = 8,-1
C' = 5,1
Step-by-step explanation:
Does this graph show a function? Explain how you know.
Answer:
A is the correct one
cause according to function rule the vertical line should cut only on a one point to be function
as here we can see that vertical line cuts here at two point
Which of the following is an arithmetic sequence with common difference –5?
A: 8, 3, -2, -7
B: 5, -25, 125, -625
C: 5, 25, 125, 625
D: 0, 5, 10, 15
Answer:
A
Step-by-step explanation:
because 3-8= -5
and -2-3=-5
The slope of a line is 5/9 and the slope of another line is -975. The two lines
are
Answer:
the third option - they are perpendicular to each other.
Step-by-step explanation:
for a perpendicular slope we need to exchange the x and y values (remember, a slope is the ratio of y/x) and flip the sign.
and that is exactly what happened here.
if the sum of an angle measures of a polygon with sides s is 2340, what is s
Answer:
polygon is 15 side
Step-by-step explanation:
Here sum of interior angels is 2340 degrees. Therefore, the polygon is 15 side
Rewrite the expression in the form a^n.
1/a^-5/6
Step-by-step explanation:
here's the answer to your question
Answer:
[tex]\frac{1}{a^{\frac{-5}{6} } }[/tex]
[tex]\frac{1}{a^{-n} }[/tex][tex]\frac{1}{a^{-5/6} } =a^{5/6}[/tex][tex]ans: a^{5/6}[/tex]OAmalOHopeO
Describe the following picture:
a relation but not a function
a function but not a relation
a function and a relation
neither a function or a relation
Answer:
A relation but not a function
Step-by-step explanation:
A relation is a relationship between two sets of information ( x and y in this case )
This graph shows a relation as the x and y values share some sort of relationship
A function is a relation in which each input has it's own output.
We can determine if a relation is a function on a graph by using the vertical line test.
If you draw a vertical line and more than 1 point is on that line then the relation is not a function
If we were to draw a vertical line on the y axis there would be three points on that line therefore the relation is not a function
So we can conclude that the picture represents a relation but not a function
Need answer for this
Answer:
A) R=1850-25t
B) 1700
C) 74
If the point A at (5, 3) is rotated clockwise about the origin through 90°, what
will be the coordinates of the new point?
Answer:
(5,-3) in the 4th quadrant
Step-by-step explanation:
The arithmetic mean of 10 consecutive even integers is 3. What is the least of these 10 even integers?
PLS HELP WILL GIVE BRAINLIEST
Answer:
-6
Step-by-step explanation:
2n can be the smallest integer, and 2n + 18 will be the largest integer.
The sum of this, divided by two, will result in the average/mean.
(2n + 2n + 18)/2 = 3
Multiply each side by 2:
(2n + 2n + 18)/2 ⋅ 2 = 3 ⋅ 2
2n + 2n + 18 = 6
Combine the like terms:
4n + 18 = 6
Subtract 18 from both sides:
4n + 18 - 18 = 6 - 18
4n = -12
Divide each side by 4:
4n/4 = -12/4
n = -3
Since we decided to go by 2n:
2n = 2(-3) = -6
The perimeter of a rectangle is 24 cm. If the length is 7 cm, find it width
Answer:
The width is 5 cm
Step-by-step explanation:
The perimeter of a rectangle is
P = 2(l+w)
Substitute what we know
24 = 2(7+w)
Divide each side by 2
24/2 = 2/2(7+w)
12 = 7+w
Subtract 7 from each side
12-7 = 7+w-7
5 =w
The width is 5 cm
The formula for perimeter = 2 x length + 2 x width
Fill in the known dimensions:
24 = 2 x 7 + 2 x width
Simplify:
24 = 14 + 2 x width
Subtract 14 from both sides:
10 = 2 x width
Divide both sides by 2:
Width = 5 cm
Answer: Width = 5 cm.
how can the graph of g(x) =x2+4 be obtained from the graph of f(x) =x2
Answer:
see explanation
Step-by-step explanation:
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
The graph of g(x) is the graph of f(x) shifted up by 4 units
Let f be the function defined as follows:1. If a = 2 and b = 3, is f continuous at x = 1? Justify your answer.2. Find a relationship between a and b for which f is continuous at x = 1.Hint: A relationship between a and b just means an equation in a and b.3. Find a relationship between a and b so that f is continuous at x = 2.4. Use your equations from parts (ii) and (iii) to find the values of a and b so that f is continuous at both x = 1 and also at x = 2?5. Graph the piece function using the values of a and b that you have found. You may graph by hand or use your calculator to graph and copy and paste into thedocument
Answer:
1. not continuous, as the function definitions deliver different function values at x=1 when approaching this x from the left and from the right side.
2.
2 = a + b
3.
0 = 2a + b
4.
a = -2
b = 4
Step-by-step explanation:
the function is continuous at a specific point or value of x, if the f(x) = y functional value is the same coming from the left and the right side at that point.
1. that means that for x=1
3 - x = ax² + bx
so,
3 - 1 = a×1² + b×1 = a + b
2 = a + b
we have to use a=2 and b=3
2 = 2 + 3 = 5
2 is not equal 5, so the assumed equality is false, so the function is not continuous there.
2. point 1 gave us already the working relationship between a and b.
2 = a + b
only if that is true, is the function continuous at x=1.
3. now for x=2
5x - 10 = ax² + bx
5×2 - 10 = a×2² + b×2 = 4a + 2b
10 - 10 = 4a + 2b
0 = 4a + 2b
0 = 2a + b
4. to find a and b to be continuous at both locations x=1 and x=2 both expressions in a and b must apply.
so, they establish a system of 2 equations with 2 variables.
2 = a + b
0 = 2a + b
a = 2 - b
0 = 2×(2-b) + b = 4 - 2b + b = 4 - b
b = 4
therefore
a = 2 - 4 = -2
5. I cannot draw a graph here.
just use now the function
3 - x, x < 1
‐2x² +4x, 1 <= x < 2
5x - 10, x >= 2
Find the length of side x in simplest radical form with a rational denominator
Help please!
Answer:
x = 6
Step-by-step explanation:
x = 3 sin(90) / sin (30)
x = 3(1)/(1/2)
x = 3 ÷ [tex]\frac{1}{2}[/tex]
x = 6
Find the value of the polynomial 5x – 4x^2 + 3 at x = 2 and x = –1
Answer:
Let the polynomial be f(x) = 5x – 4x^2 + 3
Now, for x = 2,
f(2) = 5(2) – 4(2)^2 + 3
=> f(2) = 10 – 16 + 3 = –3
Or, the value of the polynomial 5x – 4x^2 + 3 at x = 2 is -3.
Similarly, for x = –1,
f(–1) = 5(–1) – 4(–1^)2 + 3
=> f(–1) = –5 –4 + 3 = -6
The value of the polynomial 5x – 4x2 + 3 at x = -1 is -6.
Answered by GAUTHMATH
Answer:
x=2 => 5×2 - 4×2² + 3 = 10-16+3 = -3
x=-1 => 5×-1 - 4×(-1)² + 3 = -5 - 4 + 3 = -6
Step-by-step explanation:
is in the answer.
remember that squaring a negative number creates a positive result.
A club has 30 members. How many ways are there to select a President. Vice-
President and Secretary from this club? Assume no one can occupy more than one
position.
Answer:
Answer is 90 ways
Step-by-step explanation:
You multiply the members (30) by the number of positions (3) to get your answer
Find the pre-image of 10 under the function f:x ->3x+1
Answer:
see above
Step-by-step explanation:
Answer right xa hola
A 42 inch wire is bent into the shape of a rectangle whose width is twice its
length. Set up an equation to find the length of the rectangle.
Answer: Choice A
2(2L + L) = 42
=================================================
Explanation:
The length is L, which is some placeholder for a positive number.
The width is twice as much as this, so it's 2L
The perimeter is found by adding up the four sides (two of which are L, the other two are 2L)
So we have L+L+2L+2L = 2(2L+L) representing the perimeter.
Or we could use this formula
P = 2(L+W)
where L and W are the length and width respectively.
Either way, we end up with 2(2L + L) = 42
Answer:
42 = 2( l+2l)
Step-by-step explanation:
width = 2 length
Perimeter = 2 (l+w)
42 = 2( l+2l)
Divide each side by 2
42/2 = 2 (3l) /2
21 = 3l
Divide by 3
21/3 = 3l/3
7 = l
The length is 7
width is 2*l = 2*7 = 14
