Answer:
Step-by-step explanation:
perimeter of rectangle = 1100
let breadth be x
length = 300 + x
perimeter of rectangle = 2(l + b)
1100 = 2(300 + x + x)
1100 = 2(300 + 2x)
1100 = 600 + 4x
1100 - 600 = 4x
500 = 4x
500/4 = x
125 = x
therefore breadth is 125 feet
length = 300 + 125
=425 feet
Answer:
The rectangular field is 425 feet by 125 feet.
Step-by-step explanation:
Let w represent the width of the rectangular field.
Since the length is 300 feet more than the width, the length can be modeled by the expression (w + 300).
The perimeter of a rectangle is given by the formula:
[tex]P=2(w+\ell)[/tex]
Where P is the perimeter and w and l are the width and length, respectively.
We are given that the perimeter is 1,100 feet. Substitute:
[tex]1100=2(w+\ell)[/tex]
Divide both sides by two:
[tex]550=w+\ell[/tex]
We know that l = (w + 300). So:
[tex]550=w+(w+300)[/tex]
Simplify:
[tex]2w=250[/tex]
Divide both sides by two. So, the width is:
[tex]w=125\text{ feet}[/tex]
Since the length is 300 feet more than the width, that means the length is 425 feet.
The rectangular field is 425 feet by 125 feet.
1:prove that the tangent at the point (1,-2) to the circle x²+y²=5 also touches the circle x²+y²-8x+6y+20=0 .Also find the point of contact.
2:find the length of tangent to the circle
3x²+3y²-7x-6y=12 drawn from (6,-7)
Circle 1 has center at (0, 0)
The tangent passes through the center and point (1, -2).
Equation of tangent at (1, -2):
x*1 + y*(-2) = 5x - 2y = 5x = 2y + 5If the same line is tangent to circle 2 then they have one common point.
Solve the system:
x = 2y + 5x² + y² - 8x + 6y + 20 = 0Substitute x:
(2y + 5)² + y² - 8(2y + 5) + 6y + 20 = 04y² + 20y + 25 - 16y - 40 + 6y + 20 = 05y² + 10y + 5 = 0y² + 2y + 1 = 0(y + 1)² = 0y + 1 = 0y = -1 ⇒ x = 2(-1) + 5 = -2 + 5 = 3We see only one point of contact, (3, -1), this proves the line is tangent to circle 2 as well.
#2Given circle:
3x² + 3y² - 7x - 6y = 12 and external point (6, -7).Rewrite the equation of the circle as:
3x² + 3y² - 7x - 6y = 12x² + y² - 7/3x - 2y = 4x² - 2*7/6x + 49/36 + y² - 2y + 1 = 4 + 49/36 + 1(x - 7/6)² + (y - 1)² = 229/36The center is (7/6, 1) the radius is √229/36
The length of the tangent t is the leg of the right triangle with another leg r being the radius and the hypotenuse d being the distance between the center and the external point:
t² = d² - r²t² = (6 - 7/6)² + (-7 - 1)² - 229/36t² = 36 - 14 + 49/36 + 64 - 229/36t² = 86 - 180/36t² = 81t = 9What is the slope of the line that passes through (a,b) and (1/a,b)?
Answer:
slope = 0
Step-by-step explanation:
Since the y- coordinates of both points are equal, both b
This indicates the line is horizontal and parallel to the x- axis
The slope of the x- axis is zero then the slope of the line is zero
Answer:
slope of the line is 0
Step-by-step explanation:
(a , b)=(x1 , y1)
(1/a , b)=(x2 , y2)
slope=y2 -y1/x2 -x1
=b-b/ 1/a -a
=0/1-[tex]a^{2}[/tex]/a
=0*a/1-[tex]a^{2}[/tex]
=0/1-[tex]a^{2}[/tex]
=0
Which of the following statements is true?
A: The product of two rational numbers is irrational.
B: The sum of two rational numbers is rational.
C: The product of a non-zero rational number and an irrational number is rational.
D: The sum of a rational number and an irrational number is rational.
Now suppose that bigger cups are ordered and the machine’s mean amount dispensed is set at μ=12. Assuming we can precisely adjust σ, what should we set σtobe so that the actual amount dispensed is between 11 and 13 ounces, 95% of the time?
Answer:
σ should be adjusted at 0.5.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean 12.
Assuming we can precisely adjust σ, what should we set σtobe so that the actual amount dispensed is between 11 and 13 ounces, 95% of the time?
13 should be 2 standard deviations above the mean of 12, and 11 should be two standard deviations below the mean.
So 1 should be worth two standard deviations. Then
[tex]2\sigma = 1[/tex]
[tex]\sigma = \frac{1}{2}[/tex]
[tex]\sigma = 0.5[/tex]
σ should be adjusted at 0.5.
One of the solutions to x2 − 2x − 15 = 0 is x = −3. What is the other solution?
x = −5
x = −1
x = 1
x = 5
Answer: x = 5
Step-by-step explanation:
x² - 2x - 15 = 0
x² + 3x - 5x - 15 = 0
x(x + 3) - 5(x + 3) = 0
Therefore, x + 3 = 0
x = 0 - 3 = -3
Also, x - 5 = 0
x = 0 + 5 = 5
Therefore, the solutions to x² - 2x - 15 = 0 is x = -3 and x = 5. Therefore, the correct option is D.
Determine where the function is increasing, decreasing, and constant.
Answer:
X y better because it has X and Y is no no
The man brought three buses for 9694820. One bus cost Rs352750
another us cost Rs 3029870. Find the cost of third bus.
Answer:
Cost of 3 buses = 9694820
cost of 1 bus=352750
cost of another bus=3029870
cost of the third bus= 9694820-(352750+3029870)=6312200
Which line is perpendicular to a line that has a slope of 1 half
Answer:
-2
Step-by-step explanation:
1/2 slope
flip fraction 2/1
change sign -2/1 or -2
What is the total surface area of a cylinder with a radius of 9ft and a height of 13ft?
Answer:
753.6 ft^2
Step-by-step explanation:
given:
radius=9 ft
height=13 ft
total surface area of cylinder=2πrh+2πr2
=2*3.14*9*13 + 2*3.14*(9)^2
=244.92 + 2*3.14*81
=244.92 + 508.68
=753.6 ft^2
Answer:
753.6 ft|2
Step-by-step explanation:
thanks correct me if you want.
The following tables each show the amount of money, in dollars, in four different bank accounts over time.
Which table best represents an exponential relationship?
A.
Years 1 2 3 4 5
Account Balance 1100.00 1350.00 1600.00 1850.00 2100.00
B.
Years 1 2 3 4 5
Account Balance 1100.00 1210.25 1320.50 1430.75 1541.00
C.
Years 1 2 3 4 5
Account Balance 1100.00 1190.00 1340.00 1550.00 1820.00
D.
Years 1 2 3 4 5
Account Balance 1100.00 1210.00 1331.00 1464.10 1610.51
Answer:
C
Step-by-step explanation:
it is not my percentage, it is not constant, it is increasing over time
The height of a triangle is 2 m more than twice the length of the base. The area of the triangle is 30 m2. Find the height of the
triangle.
Answer:
Step-by-step explanation:
Let x be the height ..... then the base = 2x + 2
So we have
Area = (1/2) (base) (height)
20 = (1/2)(2x + 2)(x) simplify
20 = x (x + 1)
20 = x^2 + x subtract 20 from both sides
x^2 + x - 20 = 0 factor
(x + 5) ( x - 4) = 0
Only the second factor makes sense
x - 4 = 0 add 4 to both sides
x = 4 ft and this is the height
And the base = 2(4) + 2 = 10 ft
How do i do this math equasion?
Answer:
f(t) = -16t² + 36
Step-by-step explanation:
f(t) = a(t - h)² + k
This is vertex form where (h, k) is the (x, y) coordinate of the vertex
The vertex is give as (0, 36)
f(t) = a(t - 0)^2 + 36
f(t) =at² + 36
use point (1, 20) to find "a"
20 = a(1²) + 36
20 = a + 36
-16 = a
f(t) = -16t² + 36
What is the base of the expression (Eleven to the power of 12)? 3 11 12 21
Answer: 11
Step-by-step explanation:
when the question asks you what is the BASE of the EXPRESSION it means that the base is always the BIGGER number which is 11 and the power which is ALWAYS ON THE TOP RIGHT which is 12
hope that helps
If f(x) = 2x² - 4x and g(x) = 5 - 2x, evaluate fx) - g(x) for x = 5.
A 15
B 5
C 35
D. 20
ET
Answer:
35
Step-by-step explanation:
2x² - 4x- (5 - 2x)
2x² - 4x - 5 + 2x
2x²-2x - 5 = f(x) - g(x)
Now use 5
[tex]2 ({5}^{2} ) - 2(5) - 5 \\ = 35[/tex]
2
Draw all the lines of symmetry on a diagram of a regular:
a
hexagon
b
heptagon
с
Octagon
Answer:
hi ahmm.i want to say that it is to draw I thought it is a question but it is actually to draw so u should draw this all shapes
Four times the sum of 5 and some number is 4. What is the number
Answer:
n = -4
Step-by-step explanation:
1. the sum of 5 and some number translates to 5 + x.
2. 5 + x is getting multiplied by 4, so the equation will then become 4(5 + n).
3. This entire equation is equal to 4, which we can see where the problem says "is four". In other words, four times the sum of 5 + n is equal to 4. 4(5 + n) = 4
4. Now you can solve the equation. When solved, the answer is n = -4
What is an equation of the line that passes through the points (-2, 3) and (6, -1)?
Answer:
y = (-1/2)×X + 2
Step-by-step explanation:
the steps are in the pic above.
The average height of BYU freshman from a random sample of 450 freshman at BYU is 68 inches with a standard deviation of 1.5 inches. What is the 98% confidence interval for the average height of BYU freshman?
a. (59.86, 60.14)
b. (67.83, 68.17)
c. (66.5. 69.5)
d. (67.86, 68.14)
Answer:
b. (67.83, 68.17)
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.327\frac{1.5}{\sqrt{450}} = 0.17[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 68 - 0.17 = 67.83.
The upper end of the interval is the sample mean added to M. So it is 68 + 0.17 = 68.17.
This means that the correct answer is given by option B.
Please help me I am stressed out
Answer:
a) 0.3 liters
b) 3 ÷ 10 = 0.3 liters
Step-by-step explanation:
3 ÷ 10
3 × 1/10
0.3
35_56×34
help pls
I need it
Answer:
_1869
Step-by-step explanation:
step by step
35-56 × 34
Multiply 56 and 34 to get 1904.
Subtract 1904 from 35 to get -1869.
= -1869
I
Answer:
1904 IS THE ANSWER YOU CAN CHECK THIS EQUATION IN YOUR MOBILE'S CALCATOR
What is 5x + 7 > 37 I am really stuck
Answer:
x > 6
Step-by-step explanation:
Problem: 5x + 7 > 37
Subtract 7 from both sides: 5x > 30
Divide both sides by 5: x > 6
Answer: x > 6
Which of the question below could be the equation of this parabola ?
A) x=-4x^2
B) y=4x^2
C) x=4y^2
D) y=-4x^2
Evaluate given function. Pleas helpp
Answer:
[tex]f(9) =-80[/tex]
Step-by-step explanation:
Given
The attached functions
Required
Find f(9)
We have:
[tex]f(x) =-x^2 - 2x + 19[/tex]
So:
[tex]f(9) =-9^2 - 2*9 + 19[/tex]
[tex]f(9) =-81 - 18 + 19[/tex]
[tex]f(9) =-80[/tex]
NEED HELP FAST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
A.) y = 0.4x^(2) + 3.4x + 4
Step-by-step explanation:
x = -5
y = -3
Complete the solution of the equation. Find the
value of y when x equals 17.
-x + y = -27
Answer:
y= -10
Step-by-step explanation:
Answer:
-10
Step-by-step explanation:
-17+y=-27
y=-27+17
y=-10
10
El tiempo aproximado en caminar de tu casa (C) a la de tu amigo (A) pasando por la tienda (T)
es de 14 minutos; Si caminas a la misma velocidad, ¿Cuántos minutos te tomará caminar
directamente a la casa (C) de tu amigo (A)? Redondea al entero más cercano.
500yd
A
700yd
Respuesta:
10.0 minutos
Explicación paso a paso:
Distancia total recorrida caminando de C a A pasando por T:
500 yardas + 700 yardas = 1200 yardas
Tiempo necesario para recorrer 200 yardas = 14 minutos
Caminando directamente de C a A:
La distancia se puede obtener usando una relación trigonométrica:
Hipotenusa = √ (opuesto² + adyacente²)
Hipotenusa = √500² + 700²
Hipoteno = 860.23252 yardas
Por eso ; Si
1200 yardas = 14 minutos
860.23252 yardas = x
Multiplicar en cruz:
1200x = 12043,255
x = 12043,255 / 1200
x = 10.036 minutos
El tiempo necesario para caminar directamente será: 10.0 minutos
Explain the rule that governs the pronunciation of the word stick
Answer:
Es una triste noticia que se involucre a las lenguas en peleas políticas coyunturales, sobre todo cuando el debate deriva hacia una estrategia de crispación que exige el falseamiento de la realidad, las ofensas y las manipulaciones. Las lenguas maternas forman parte de la identidad, de la raíz más profunda de sus hablantes, y ofenderlas o someterlas a coyunturas crea heridas íntimas. Confieso que siento una inmediata antipatía ante cualquier persona, política o no, que desprecia la manera que tenemos los andaluces de pronunciar el español. Es la manera en la que yo aprendí a relacionarme con la vida.
Step-by-step explanation:
You decide to work out your weekly pay by using the following formula:
p = 5hr
p is weekly pay
h is hours worked
r is rate of pay per hour
This week you worked 8 hours a day, for 5 days, at an hourly rate $6.88.
How much did you earn? $
Answer:
p = 5(8)(6.88)
p = $275.20
pls tell ineed now fast plss
Answer:
g = 12
Step-by-step explanation:
g + 7 - 4 = 15
g = 15 - 3 = 12
Given that P(x) = 2W/W+1 + W-4/2W-3 , evaluate p(0)
Answer:
5
Step-by-step explanation:
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