Answer:
Hello,
|FD|=15
Step-by-step explanation:
Since the triangles are similar, the bissects are also.
k*35=21 ==> k=21/35
k*25=|FD|
|FD|=(21/35)*25=15
Hãy tìm hàm gốc f(t) có hàm ảnh Laplace như dưới đây:
F(p)=6/p(2p^2+4p +10)
It looks like we're given the Laplace transform of f(t),
[tex]F(p) = L_p\left\{f(t)\right\} = \dfrac6{p(2p^2+4p+10)} = \dfrac3{p(p^2+2p+5)}[/tex]
Start by splitting up F(p) into partial fractions:
[tex]\dfrac3{p(p^2+2p+5)} = \dfrac ap + \dfrac{bp+c}{p^2+2p+5} \\\\ 3 = a(p^2+2p+5) + (bp+c)p \\\\ 3 = (a+b)p^2 + (2a+c)p + 5a \\\\ \implies \begin{cases}a+b=0 \\ 2a+c=0 \\ 5a=3\end{cases} \implies a=\dfrac35,b=-\dfrac35, c=-\dfrac65[/tex]
[tex]F(p) = \dfrac3{5p} - \dfrac{3p+6}{5(p^2+2p+5)}[/tex]
Complete the square in the denominator,
[tex]p^2+2p+5 = p^2+2p+1+4 = (p+1)^2+4[/tex]
and rewrite the numerator in terms of p + 1,
[tex]3p+6 = 3(p+1) + 3[/tex]
Then splitting up the second term gives
[tex]F(p) = \dfrac3{5p} - \dfrac{3(p+1)}{5((p+1)^2+4)} - \dfrac3{5((p+1)^2+4)}[/tex]
Now take the inverse transform:
[tex]L^{-1}_t\left\{F(p)\right\} = \dfrac35 L^{-1}_t\left\{\dfrac1p\right\} - \dfrac35 L^{-1}_t\left\{\dfrac{p+1}{(p+1)^2+2^2}\right\} - \dfrac3{5\times2} L^{-1}_t\left\{\dfrac2{(p+1)^2+2^2}\right\} \\\\ L^{-1}_t\left\{F(p)\right\} = \dfrac35 - \dfrac35 e^{-t} L^{-1}_t\left\{\dfrac p{p^2+2^2}\right\} - \dfrac3{10} e^{-t} L^{-1}_t\left\{\dfrac2{p^2+2^2}\right\} \\\\ \implies \boxed{f(t) = \dfrac35 - \dfrac35 e^{-t} \cos(2t) - \dfrac3{10} e^{-t} \sin(2t)}[/tex]
What is the measure of m?
Answer:
√245
Step-by-step explanation:
altitude on hypotenuse theorem:
m^2=7*35
m^2=245
m=√245
Given FE=23.5, find BD.
Answer:
11.75
Step-by-step explanation:
The required triangle is attached below :
The triangle AFE has it's by the mid segment as BD ;as B is the mid-point of line EA ; and D is the mid-point of line FA ;
HENCE, The Length of the midsegment BD = 1/2FE
Hence, BD =. 1/2 * 23.5
BD = 23.5 / 2 = 11.75
4. Lynn can walk two miles intenta
24 minutes. At this rate, how long will
it take her to walk 6 miles?
Please answer this and show the work/explain
2/7m - 1/7 = 3/14
(2/7)m - (1/7) = 3/14
2m/7 =(3/14) + (1/7)
2m/7 = (3/14) + 2(1/7)
here we are multiplying 2 with 1/7 to make the denominator same for addition.
2m/7 = (3/14) +(2/14)
2m/7 = (3 + 2)/14
2m/7 = 5/14
2m = (5 *7)/14
2m = 35/14
2m = 5/2
m = 5/4
m = 1.25
So the value of "m" is 1.25
What is the image of -8 ,8 after a dilation by a scale factor of one fourth centered at the origin?
Answer:
(-2, 2)
Step-by-step explanation:
If you have a point (x, y) and you do a dilation by a scale factor K centered at the origin, the new point will just be (k*x, k*y)
So, if the original point is (-8, 8)
And we do a dilation by a scale factor k = 1/4
Then the image of the point will be:
(-8*(1/4), 8*(1/4))
(-8/4, 8/4)
(-2, 2)
find the value of the trigonometric ratio. make sure to simplify the fraction if needed
Answer:
Sin A = o/h
= 9/41
Step-by-step explanation:
since Sin is equal to opposite over hypotenuse, from the question, the opposite angle of A is 9 and hypotenuse angle of A is 41. Thus the answer for Sin A= 9/41
Help please!??!!?!?
9514 1404 393
Answer:
a) CP = SP/1.1
b) CP = $59.50
c) GST = $5.95
Step-by-step explanation:
a) Divide by the coefficient of CP.
SP = 1.1×CP
CP = SP/1.1
__
b) Use the formula with the given value.
CP = $65.45/1.1 = $59.50
__
c) You can do this two ways: subtract CP from SP, or multiply CP by 0.1.
GST = SP -CP = $65.45 -59.50 = $5.95
GST = CP×0.10 = $59.50 × 0.10 = $5.95
What are the x-intercepts for the function ƒ(x) = -x(x − 4)?
A 0
B -1, 4
C 4
D 0, 4
What are the solutions to the quadratic equation 4x2 − x − 3 = 0?
Answer:
D
Step-by-step explanation:
f(x)=-x(x-4)
f(x)=-x²+4x
-x²+4x=0
x(-x+4)=0
x=0, x=4
(2)
4x²-x-3=0
(4x²+3x)-(4x-3)=0
x(4x+3)-1(4x+3)=0
x=1, x=-3/4
A 10-ft ladder, whose base is sitting on level ground, is leaning at an angle against a vertical wall when its base starts to slide away from the vertical wall. When the base of the ladder is 6 ft away from the bottom of the vertical wall, the base is sliding away at a rate of 4 ft/sec. At what rate is the vertical distance from the top of the ladder to the ground changing at this moment?
Answer:
2.5/ft per sec
Step-by-step explanation:
its vertica.
The height of the ladder is decreasing at a rate of 24 ft/sec.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
Let's denote the distance between the base of the ladder and the wall by x.
The length of the ladder = L.
Now,
L = 10 ft
dx/dt = 4 ft/sec
x = 6 ft.
The rate of change of the height of the ladder with respect to time.
Using the Pythagorean theorem, we have:
L² = x² + y²
Differentiating both sides with respect to time t, we get:
2L (dL/dt) = 2x(dx/dt) + 2y(dy/dt)
Substituting L = 10 ft, x = 6 ft, and dx/dt = 4 ft/sec.
20(dL/dt) = 12(4) + 2y(dy/dt)
Simplifying and solving for dy/dt.
dy/dt = (20/2y)(dL/dt) - 24
Now,
The height of the ladder.
Using the Pythagorean theorem again, we have:
y² = L² - x²
= 100 - 36
= 64
y = 8
Now,
Substituting y = 8 ft, dL/dt = 0
(since the length of the ladder is constant), and dx/dt = 4 ft/sec.
dy/dt
= (20/2(8))(0) - 24
= -24 ft/sec
Therefore,
The height of the ladder is decreasing at a rate of 24 ft/sec.
Learn more about the Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ2
Which of the following graphs represents a one-to-one function? On a coordinate plane, a function has two curves connected to a straight line. The first curve has a maximum of (negative 6, 4) and a minimum of (negative 4.5, negative 1). The second curve has a maximum of (negative 3.5, 2) and a minimum of (negative 2.5, 0.5). The straight line has a positive slope and starts at (negative 2, 1) and goes through (1, 2). On a coordinate plane, a circle intersects the x=axis at (negative 2, 0) and (2, 0) and intercepts the y-axis at (0, 4) and (0, negative 4). On a coordinate plane, a v-shaped graph is facing up. The vertex is at (0,0) and the function goes through (negative 4, 4) and (4, 4). A coordinate plane has 7 points. The points are (negative 4, 1), (negative 3, 4), (negative 1, 3), (1, negative 3), (3, negative 4), (4, negative 2), (5, 3). Mark this and return
Answer:
d. this graph
Step-by-step explanation:
Value of [(3/2)^(-2)] is *
Answer:
[tex] { (\frac{3}{2} )}^{ - 2} \\ = { (\frac{2}{3}) }^{2} \\ = \frac{4}{9} \\ thank \: you[/tex]
the mode of 3,5,1,2,4,6,0,2,2,3 is
giving out brainliest
A kite is a ........... quadrilateral
Answer:
yes
Step-by-step explanation:
The complete sentence is,
A kite is a convex quadrilateral.
We have to given that,
To find a kite is which type of a quadrilateral.
We know that,
A quadrilateral known as a kite has four sides that may be divided into two pairs of neighboring, equal-length sides.
The two sets of equal-length sides of a parallelogram, however, are opposite one another as opposed to being contiguous.
Hence, The complete sentence is,
A kite is a convex quadrilateral.
Learn more about quadrilateral visit:
https://brainly.com/question/23935806
#SPJ7
HELPPP!!!
find the area of a triangle with a height of 9cm and a base of 5 cm
Answer:
A = 22.5 cm^2
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh where b is the base and h is the height
A = 1/2(5)(9)
A = 45/2
A = 22.5 cm^2
[tex]\begin{gathered} {\underline{\boxed{ \rm {\red{Area \: \: of \: \: triangle \: = \: \frac{1}{2} \: \times \: base \: \times \: height}}}}}\end{gathered}[/tex]
Base of triangle = 5 cm.Height of triangle is 9 cm.Solution[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \frac{1}{2} \: \times \: 5 \: cm \: \times \: 9 \: cm[/tex]
[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \frac{1}{2} \: \times \: 45 \: cm[/tex]
[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \frac{45 \: {cm}^{2} }{2} \: \\ [/tex]
[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \cancel\frac{45}{2} \: \: ^{22.5 \: {cm}^{2} } \: \\ [/tex]
[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: 22.5 \: {cm}^{2} [/tex]
Hence , the area of triangle is 22.5 cm²
The least-squares regression equation
y = 8.5 + 69.5x can be used to predict the monthly cost for cell phone service with x phone lines. The list below shows the number of phone lines and the actual cost.
(1, $90)
(2, $150)
(3, $200)
(4, $295)
(5, $350)
Calculate the residuals for 2 and 5 phone lines, to the nearest cent.
The residual for 2 phone lines is $___
The residual for 5 phone lines is $___
Answer:
First one: 2.5
Second: -6
8.5+69.5(5) = 147.5
150 - 147.5 = 2.5
8.5 + 69.5(5) = 356
350 - 356 = -6
ED2021
The residual for 2 phone lines is $2.5.
The residual for 5 phone lines is -$6.
What is the residual in a least-square regression equation?
The residual is the vertical distance separating the observed point from your expected y-value, or more simply put, it is the difference between the actual y and the predicted y.
How to solve the question?In the question, we are asked to find the residual for 2 and 5 lines using the least-squares regression equation y = 8.5 + 69.5x and the actual costs given to us.
We know that the residual is the vertical distance separating the observed point from your expected y-value, or more simply put, it is the difference between the actual y and the predicted y.
Thus for 2 phone lines:-
Actual Cost = $150.
Predicted Cost, y = 8.5 + 69.5*2 = 147.5.
Residual = Actual Cost - Predicted Cost = 150 - 147.5 = $2.5.
Thus, the residual for 2 phone lines is $2.5.
Thus for 5 phone lines:-
Actual Cost = $350.
Predicted Cost, y = 8.5 + 69.5*2 = 356.
Residual = Actual Cost - Predicted Cost = 350 - 356 = -$6.
Thus, the residual for 2 phone lines is -$6.
Learn more about the residual in a least-square regression equation at
https://brainly.com/question/20165292
#SPJ2
Use the graph to complete the statement. O is the origin. r(180°,O) ο Ry−axis : (2,5)
A. ( 2, 5)
B. (2, -5)
C. (-2, -5)
D. (-2, 5)
9514 1404 393
Answer:
B. (2, -5)
Step-by-step explanation:
Reflection across the y-axis is the transformation ...
(x, y) ⇒ (-x, y)
Rotation 180° about the origin is the transformation ...
(x, y) ⇒ (-x, -y)
Applying the rotation after the reflection, we get ...
(x, y) ⇒ (x, -y)
(2, 5) ⇒ (2, -5)
_____
Additional comment
For these transformations, the order of application does not matter. Either way, the net result is a reflection across the x-axis.
Answer:
(2,-5)
Step-by-step explanation:
What is the remainder when () = 3 − 11 − 10 is divided by x+3
Answer:
-18/x+3
Step-by-step explanation:
find the measure of x
Answer:
[tex]B)\ x=43[/tex]
Step-by-step explanation:
One is given a circle with many secants within the circle. Please note that a secant refers to any line in a circle that intersects the circle at two points. A diameter is the largest secant in the circle, it passes through the circle's midpoint. One property of a diameter is, if a triangle inscribed in a circle has a side that is a diameter of a circle, then the triangle is a right triangle. One can apply this to the given triangle by stating the following:
[tex]x+47+90=180[/tex]
Simplify,
[tex]x+47+90=180[/tex]
[tex]x+137=180[/tex]
Inverse operations,
[tex]x+137=180[/tex]
[tex]x=43[/tex]
Helppppp plzzzzzzz!!!!!!!!!!! 15+ PTS and brainliest!!!!!!!!
Write the equation of the line with slope of 0, and y-intercept of 9.
Answer:
y=0x+9. Hope this helped.
Step-by-step explanation:
slope intercept form: y=mx+b
m represents slope
b represents the y intercept. Please give me the brainliest:)
Type an equation for the
following pattern.
x
1 -2
2
4
3
-6
y=[? ]x+[ ]
4
-8
S
- 10
Answer:
y=-2x
Step-by-step explanation:
first find the slope: (-2-(-4))/(1-2)=2/-1=-2 so m=-2
now we have y=-2x+b, to find b we plug in any of the points
-2=-2(1)+b-2=-2+b b=0so the equation is y=-2x
Calculate a high estimate for each. Show your work?81×37
Step-by-step explanation:
2997
81
×
37
=2997
it just a simple calculation just multiply the numbers
Given the following matrices, what 3 elements make up the first column of the product matrix DA?
We have to figure out what the product of DA is,
[tex]\begin{bmatrix}-1&2&3\\8&-4&0\\6&7&1\\ \end{bmatrix}\begin{bmatrix}1\\3\\5\\ \end{bmatrix}=\begin{bmatrix}a\\b\\c\\ \end{bmatrix}[/tex]
We know that,
[tex]\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\\\end{bmatrix}\begin{bmatrix}x\\y\\z\\\end{bmatrix}=\begin{bmatrix}ax+by+cz\\dx+ey+fz\\gx+hy+iz\\\end{bmatrix}[/tex]
So,
[tex]a=-1\cdot1+2\cdot3+3\cdot5=-1+6+15=20[/tex]
[tex]b=8\cdot1+(-4)\cdot3+0\cdot5=8-12=-4[/tex]
[tex]c=6\cdot1+7\cdot3+1\cdot5=6+21+5=32[/tex]
So the solution is,
[tex]a,b,c=\boxed{20,-4,32}[/tex]
Hope this helps :)
write your answer in simplest radical form
Answer:
[tex]s=6\sqrt{3}[/tex]
Step-by-step explanation:
In any 30-60-90 triangles, the sides are in ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the hypotenuse of the triangle.
In the given diagram, the hypotenuse is marked as 12 miles. Therefore, the side opposite to the 30 degree angle must be [tex]12 \div 2=6[/tex] miles. The final leg, [tex]s[/tex], must then represent the [tex]x\sqrt{3}[/tex] part of our ratio, hence [tex]\implies \boxed{6\sqrt{3}}[/tex]
Please help explanation if possible
Answer:
N=18
Step-by-step explanation:
Hope it will help you
If it does pls give me Brainlest
Have a nice day
Answer:
18
Step-by-step explanation:
use the concept of similarity and enlargement.
[tex] \frac{15}{n} = \frac{5}{6 } [/tex]
[tex]n = \frac{15 \times 6}{5} [/tex]
[tex]n = 18[/tex]
The question is in the screenshot
Answer:
AC is about 4.29
Step-by-step explanation:
we need to use simple trigonometry for this problem
the tangent of an angle is the ratio between the opposite side and the adjacent side
so the tangent of the angle 35º is BC / AC
tan(35) is about 0.7
this means that BC / AC = 0.7
we know BC is 3
so 3 / AC = 0.7
3 = 0.7(AC)
AC is about 4.29
what value of x is in the solution set of 8x-6>12+2x
Answer:
x>3
Step-by-step explanation:
8x - 2x > 12+ 6
-> 6x > 18
-> x > 3
[tex] \: \: \: \huge \rm{answer: \blue{ \boxed{ \rm{ \pink{x > 3}}}}}[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
[tex] \huge \blue{ \boxed{ \pink{\boxed{ \rm{ \blue{armed }\: account}}}}}[/tex]
➙[tex] \huge \rm8x-6>12+2x \\ \rm \huge8x-2x>12+6 \\ \huge\rm6x>18 \\ \huge \boxed{\rm{x>3}}[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖
I hope you understood!✏
➖➖➖➖➖➖➖➖➖➖➖➖➖➖
Step-by-step explanation:
[tex] \huge \boxed{ \boxed{\rm{Hope \: this \: helps}}}[/tex]
PLEASE HELP!!!
Evaluate each expression.
(252) =
Answer:
1/5
Step-by-step explanation:
Luisa and Rachelle are competing for employee of the month. It is the last week, and the employee who processes the most client accounts will win. Luisa processed 15 accounts Monday, 22 accounts Tuesday, and 17 accounts Wednesday. Rachelle processed 24 accounts Monday, 18 accounts Tuesday, and 11 accounts Wednesday. Who has processed the most accounts this week, and by how many
Answer:
Luisa processed the most accounts this week, by 1.
Step-by-step explanation:
Luisa:
15 on Monday, 22 on Tuesday and 17 on Wednesday.
So a total of 15 + 22 + 17 = 54.
Rachelle:
24 on Monday, 18 on Tuesday, 11 on Wednesday.
So a total of 24 + 18 + 11 = 53.
Who has processed the most accounts this week, and by how many?
54 - 53 = 1, so Luisa processed the most accounts this week, by 1.
How many degrees must the flyswatter pass through before it is horizontal?
Answer:
90°
Step-by-step explanation:
assuming it's upright and you swat it down it will go down by 90°
