Answer:
B. DE = 58
Step-by-step explanation:
The base angles (<F and <E) of the ∆DEF are congruent/equal. This means that ∆DEF is an isosceles triangle.
This implies that, the two sides (DF and DE) that are opposite to the base angles are congruent/equal.
DE = 40 (given) => option B is INCORRECT
Therefore:
8x - 24 = 40
Solve for x
8x - 24 + 24 = 40 + 24
8x = 64
8x/8 = 64/8
x = 8 (option C is CORRECT)
Let's find DF and FE:
DF = 8x - 24
Plug in the value of x
DF = 8(8) - 24
DF = 64 - 24
DF = 40 (Option D is CORRECT)
FE = 6x + 10
FE = 6(8) + 10
FE = 48 + 10
FE = 58 (Option A is CORRECT)
The only incorrect statement is:
B. DE = 58
Which phrase describes the expression 505n ?
Answer:
I believe it would be "505 times n"
Step-by-step explanation:
If tis is not what you are looking for I am sorry, but the question was vague.
There are 50 pennies in a roll. If you have 150 rolls of pennies, how many pennies do you have?
Answer: 7500
Step-by-step explanation:
multiply 150 by 50
Can someone help me please?
Slope : -2
y - intercept : 3
Equation : y = -2x+3
Answer:
Step-by-step explanation:
Slope: -0.5
Y-Intercept: 3
y = -0.5x+3
help how to do this due in a few hours
Answer:
x=52 y=116
Step-by-step explanation:
because they give you the angle 116.
those two are actually equal.
y=116
since that is true, you can do 180-116=64.
now, you subtract 64-12
which is 52.
Find the exact value of sin A in simplest radical form.
Using the sine rule,
[tex] \frac{a}{sin(a)} = \frac{b}{sin(b)} = \frac{c}{sin(c)} [/tex]
Here we are going to use the values of A and C,
[tex] \frac{12}{sin(a)} = \frac{14}{sin(90)} \\ \frac{12}{sin(a)} = \frac{14}{1} \\ sin(a) = 12 \div 14 \\ sin(a) = 0.8571[/tex]
So sin(A) = 12/14 = 6/7 = 0.8571, but since the question says in its simplest radical form, I think the closest answer to it should be
[tex] \frac{ \sqrt{3} }{2} [/tex]
Voce 2x-u - 1x2-3x+3 = 2
Answer:
u=−x2−x+1
Step-by-step explanation:
Let's solve for u.
2x−u−1x^2−3x+3=2
Step 1: Add x^2 to both sides.
−x2−u−x+3+x2=2+x2
−u−x+3=x2+2
Step 2: Add x to both sides.
−u−x+3+x=x2+2+x
−u+3=x2+x+2
Step 3: Add -3 to both sides.
−u+3+−3=x2+x+2+−3
−u=x2+x−1
Step 4: Divide both sides by -1.
−u/−1=x2+x−1
−1/u=−x2−x+1
Answer:
u=−x2−x+1
Find the component form of the resultant vector.
u=-12i + 35j
Find: -8u
A) 10V 47 - 1 + 10j
B) -40i + 35j
C) 961 – 280j
D) 151 – 5V3.j
Answer:
C) 96i – 280j
Step-by-step explanation:
Multiplying vector by constant:
When a vector is multiplied by a constant, each component of the vector is multiplied by this constant.
In this question:
u = -12i + 35j
-8u = -8(-12i + 35j) = (8*12i - 8*35j) = 96i - 280j.
The answer is C) 96i – 280j
Simran has a bag containing white and yellow marbles. Simran randomly selects one marble from the bag,
records the result, and returns the marble to the bag. The results of the first 65 selections are shown below.
A white marble was selected 41 times.
A yellow marble was selected 24 times.
Based on these results, what is the probability that the next marble Simran selects, rounded to the nearest
Answer:
d. 63%
Step-by-step explanation:
percent, will be white?
A41% b50% c59% d63%
The probability of white = P (w) = 41/65= 0.63
The probability of yellow = P (y)= 24/65= 0.369=0.37
The probability of choosing white is 0.63 . When rounded to nearest percent gives
0.63*100/100
=0.63*100 percent
= 63 percent
= 63%
the probability of getting the next marble white is the same as the probability of getting a white.
The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart? a. The residuals are normally distributed. b. The model over predicts the value of the dependent variable for small values and large values of the independent variable. c. The model fails to capture the relationship between the variables accurately, and there may exist nonlinear relationship. d. The residuals have a constant variance.
Answer: Hello the scatter plot related to your question is missing attached below is the scatter plot
answer : The model fails to capture the relationship between the variables accurately, and there may exist nonlinear relationship ( C )
Step-by-step explanation:
The conclusion that can be drawn based upon the scatter chart is that The model fails to capture the relationship between the variables accurately, and there may exist nonlinear relationship
A scatter plot helps in observing the relationship within different numeric variables but the scatter plot attached fails in the showing the actual relationship
Find the volume of the prism. round to the nearest tenth
Answer:
V = 310.5 cm³
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Volume of a Prism Formula: V = lwh
l is lengthw is widthh is heightStep-by-step explanation:
Step 1: Define
Identify variables
l = 13.8 cm
w = 4.5 cm
h = 5 cm
Step 2: Solve for V
Substitute in variables [Volume of a Prism Formula]: V = (13.8 cm)(4.5 cm)(5 cm)Multiply: V = (62.1 cm²)(5 cm)Multiply: V = 310.5 cm³Find the area of the triangle
Answer:
About 292.72
Step-by-step explanation:
We can imagine a circle circumscribed around the triangle, then solve it as we normally do using the apothem. By dividing 360 by the number of sides (3) we know that the central angle constructed by the apothem and radiuses would be 120. Divided by 2 (because we are using a right triangle to solve it) is 60. Now with this you can either use trig ratios (sin, cos, or tan) or use special right triangles (30-60-90 or 45-45-90). I used special rights. With this I know my apothem is [tex]\frac{13\sqrt{3} }{3}[/tex]. Perimeter is 26 times 3 which is 78. The formula for area of regular polygons is 1/2(perimeter times apothem). When we plug our values in the answer is about 292.72. You are lucky that I just had my test on this, I hope it helps.
Here is my work since this is very visual for me:
Hi, i need to calculate roots x1 and x2 using the vieta theorem, can anyone help me? I have found the answer for x1 and x2, its 1,5 and 2, all i need is a solution on how to get this answer, the equation is in the picture, will give you brainliest if you type down the correct solution for me, thanks.
I have left a similar equation that i did. The only thing why i cant do the equation, because in front of x2 there’s an number, so i don’t understand.
Answer:
Solution given:
x²-12x+11=0
Comparing above equation with ax²+bx+c
we get
a=1
b=-12
c=11
By using Vieta's theorem
X1+X2=[tex] \frac{-b}{a} [/tex]=[tex] \frac{- -12}{1} [/tex]=12
again
X1X2=[tex] \frac{c}{a} [/tex]=[tex] \frac{11}{1} [/tex]=11
x1.x2=11
x1+x2=12
Find the 12th term of the sequence: 48, 44, 40, 36...
A.4 B.8 C.12 D.16
Answer:
the answer that I found is A. 4
Answer:
So the answer is 4
48,44,40,36,32,28,24,20,16,12,8,4
You can just do 4×12=48
Step-by-step explanation:
4 is being subtracted
An isosceles right triangle has legs of equal length. If the
hypotenuse is 10 centimeters long, find the length of each leg.
Answer:
[tex] \displaystyle 5\sqrt{2}[/tex]
Step-by-step explanation:
we have a right angle isosceles triangle
in order to figure out the length of each leg we can consider Pythagoras theorem given by
[tex] \displaystyle {a}^{2} + {b}^{2} = {c}^{2} [/tex]
remember that,
isosceles triangle has two equal legs so a=b and given that the the hypotenuse is 10
substitute:
[tex] \displaystyle {a}^{2} + {a}^{2} = {10}^{2} [/tex]
simplify addition:
[tex] \displaystyle {2a}^{2}= 100[/tex]
simplify square:
divide both sides by 2:
[tex] \displaystyle {a}^{2}= 50[/tex]
square root both sides:
[tex] \displaystyle {a}^{}= \sqrt{50}[/tex]
[tex] \displaystyle {a}^{}= 5\sqrt{2}[/tex]
hence,
the length of each leg is 5√2
The diagram shows two right angled triangles, joined together along a common side.
Calculate the area of the triangle ACD.
you must show all your working.
(Pleaseee it’s really urgent!)
Answer:
AC² = 10.8²+14.4² = 324
AC = √324= 18
area = AC.DC÷2
area=18×24÷2
area=216
Answer:
216 centimeters squared
Step-by-step explanation:
working is above
SOLVE THR SIMULTANEOUS EQUATIONS
3X+Y=8
X-3Y=11
ANSWER PLEASE
Answer:
if you just wanted the equations fixed: y= -3x + 8 & y= 1/3x - 11/3
but if you wanted x then x = 7/2
Step-by-step explanation:
3x + y = 8 *subtract 3x from both sides*
y = -3x + 8
x - 3y = 11 *add 3y to both sides*
x = 3y + 11 subtract 11 from both sides*
x - 11 = 3y * divide both sides by 3*
1/3x - 11/3 = y --> y = 1/3x - 11/3
and to solve for x i just used ma thway but if you did want to solve it you'd need to put the equations equal to each other --> -3x + 8 = 1/3x - 11/3
Can someone help me really please
Answer:
b
Step-by-step explanation:
3/3 = 1
Answer:
C
Step-by-step explanation:
e If M P = Rs 420,SP. 405 then
find discount
Answer:
discount=MP-SP
=Rs420-Rs405
=Rs15
Step-by-step explanation:
Convert the rectangular coordinates (-9, 3V3) into polar form. Express the angle
using radians in terms of te over the interval 0
Answer:
[tex](6\sqrt{3},\,\frac{5\pi}{6})[/tex]
Step-by-step explanation:
The radius r can be found from the relationship
[tex]r^2=x^2+y^2\\r^2=(-9)^2+(3\sqrt{3})^2\\r^2=81+27=108\\r=\sqrt{108}\\r=6\sqrt{3}[/tex]
The point is in Quadrant II (-, +), so use the inverse cosine function to find the angle.
[tex]\cos{\theta}=\frac{x}{r}=\frac{-9}{6\sqrt{3}}\\\cos{\theta}=-\frac{9}{6\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}\\\cos{\theta}=-\frac{9\sqrt{3}}{6\cdot3}\\\cos{\theta}=-\frac{\sqrt{3}}{2}\\\\\cos^{-1}\frac{-\sqrt{3}}{2}}=\frac{5\pi}{6}[/tex]
See the attached image.
I NEEED SOMEBODY TO HELP ME OUT WITH THIS QUESTION THXS
Answer:
The answer is less than that is the answer
I need some help please
9514 1404 393
Answer:
(d) {-7, -2, 11, 20}
Step-by-step explanation:
You can put the domain values into the function and evaluate to find the corresponding range values. Here, we'll do them "all at once."
y = 3{-4, -1, 2, 5} +5
= {-12, -3, 6, 15} +5
= {-7, 2, 11, 20} . . . . . matches choice d
_____
To save yourself some arithmetic, you can observe that the answer choices differ in the 2nd and 4th values, so you only need to evaluate the function for x=-1 or x=5 to determine the correct answer choice.
Can somebody help me
Answer:
Angles in a triangle sum to 180.
So
x= 180 - 75 - 43
x=62°
Answer:
x=62°
Step-by-step explanation:
x= 180 - 75 - 43
What is the value of x?
5% equals what fraction, in lowest terms?
Answer:
1/20
Step-by-step explanation:
According to G0ogle 5 percent equals 1/20 in lowest terms.
Answer:
5% equals 5/100 which is 1/20 in lowest terms.
Step-by-step explanation:
5% is basically equivalent to 5/100. 5/100 in lowest terms is 1/20 since you divide the numerator and denominator by 5.
I hope this helps, have a nice day.
The scale on a map is 55 cm : 88 km.
If the distance between two cities is 5656 km, how far apart in cm are the two cities on the map?
Answer:
look at the picture i have sent
Answer:
The cities are 35 cm apart in map.
The scale on a map is 5 cm : 8 km.
Step-by-step explanation:
mrk me brainliest please
PLEASE HELP FAST WILL MARK BRAINLIEST PLEASEEE
Answer:
[tex]\frac{8x^{18} }{y^{2} }[/tex]
Step-by-step explanation:
How much is three times two
Answer:
the answer is 6.
Step-by-step explanation:
Answer:
6.
Step-by-step explanation:
3+3=6 = 2×3=6
you can do draw 3 circles 2 times and add it all together.
I need help please.
Joelle bought some fruit at the store. They bought 5 apples and a bunch of bananas. The bananas cost $1.50, and the total cost was $5.24. How much did each apple cost?
Define your variable: a represents…
Write an equation using your variable that matches the situation.
Solve your equation. Show all your steps.
Write your answer in a complete sentence.
Answer:
$3.74
Step-by-step explanation:
we already know the cost of the banana's and it gives us the total price including apples. So $5.24 - $1.50 = $3.74, and the 3.74 is the cost of apples
Consider the initial value problem my''+cy'+ky=F(t), y(0)=0, y'(0)=0, modeling the motion of a spring mass dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m=2 kilograms, c=8 kilograms per second, k=80 Newtons per meter, and F(t)=20 sin(6t) Newtons.
1. Solve the initial value problem. y(t)=?
2. Determine the long term behavior of the system. Is lim as t goes to infinity of y(t)=0? If it is, enter zero. If not, enter a function that approximates y(t) for very large positive values of t. For very large positive values of t, y(t) is approximately.. ?
Answer:
Hence, the [tex]y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t))\end{array}[/tex] and approximately value of [tex]y(t)[/tex] is [tex]-0.844[/tex].
Given :
[tex]my''+cy'+ky=F(t), y(0)=0, y'(0)=0,[/tex]
Where [tex]m=2[/tex] kilograms
[tex]c=8[/tex] kilograms per second
[tex]k=80[/tex] Newtons per meter
[tex]F(t)=20\sin (6t)[/tex] Newtons
Explanation :
(1)
Solve the initial value problem. [tex]y(t)[/tex]
[tex]my''+cy'+ky=F(t), y(0)=0, y'(0)=0,[/tex]
[tex]\Rightarrow 2y''+8y'+80y=20\sin (6t)[/tex]
[tex]\Rightarrow y''+4y'+40y=10\sin (6t)[/tex]
Auxilary equations :[tex]F(t)=0[/tex]
[tex]\Rightarrow r^2+4r+40=0[/tex]
[tex]\Rightarrow r=\frac{-4\pm\sqrt{4^2-4\times 1\times 40}}{2\times 1}[/tex]
[tex]\Rightarrow r=\frac{-4\pm\sqrt{16-160}}{2}[/tex]
[tex]\Rightarrow r=\frac{-4\pm\sqrt{-144}}{2}[/tex]
[tex]\Rightarrow r=\frac{-4\pm12i}{2}[/tex]
[tex]\Rightarrow r=-2\pm6i[/tex]
The complementary solution is [tex]y_c=e^{-2t}\left(c_1\cos 6t+c_2\sin 6t\right)[/tex]
The particular Integral, [tex]y_p=\frac{1}{f(D)}F(t)[/tex]
[tex]y_{y} &=\frac{1}{D^{2}+4 D+40} 25 \sin (6 t) \\\\ y_{y} &=\frac{25}{-6^{2}+4 D+40} \sin (6 t) \quad\left(D^{2} \text { is replaced with }-6^{2}=-36\right) \\\\y_{y} &=\frac{25}{4 D+4} \sin (6 t) \\\\y_{y} &=\frac{25}{4(D+1)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4(D+1)(D-1)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4\left(D^{2}-1\right)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4(-36-1)} \sin (6 t) \\\\y_{y} &=-\frac{25}{148}(D-1) \sin (6 t) \\y_{y} &=-\frac{25}{148}\left(\frac{d}{d t} \sin (6 t)-\sin (6[/tex]
Hence the general solution is :[tex]y=y_c+y_p=e^{-2t}(c_1\cos 6t+c_2\sin 6t)-\frac{25}{148}(6\cos 6t-\sin 6t)[/tex]
Now we use given initial condition.
[tex]y(t) &=e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\\y(0) &=e^{-\alpha 0)}\left(c_{1} \cos (0)+c_{2} \sin (0)\right)-\frac{25}{148}(6 \cos (0)-\sin (0)) \\\\0 &=\left(c_{1}\right)-\frac{25}{148}(6) \\\\c_{1} &=\frac{75}{74} \\\\y(t) &=e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\[/tex]
[tex]y^{\prime}(t)=-2 e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)+e^{-2 t}\left(-6 c_{1} \sin 6 t+6 c_{2} \cos 6 t\right)-\frac{25}{148}(-36 \sin (6 t)-6 \cos (6 t)) \\\\y^{\prime}(0)=-2 e^{0}\left(c_{1} \cos 0+c_{2} \sin 0\right)+e^{0}\left(-6 c_{1} \sin 0+6 c_{2} \cos 0\right)-\frac{25}{148}(-36 \sin 0-6 \cos 0) \\\\0=-2\left(c_{1}\right)+\left(6 c_{2}\right)-\frac{25}{148}(-6) \\\\0=-2 c_{1}+6 c_{2}+\frac{75}{74} \\\\0=-2\left(\frac{75}{74}\right)+6 c_{2}+\frac{75}{74} \\\\[/tex][tex]\begin{array}{l}0=-\frac{150}{74}+6 c_{2}+\frac{75}{74} \\\\\frac{150}{74}-\frac{75}{74}=6 c_{2}\end{array}[/tex]
[tex]\begin{array}{l}c_{2}=\frac{25}{148}\\\\\text { Substitute } c_{1} \text { and } c_{2} \text { in } y(t) \text { . Then }\\\\y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t))\end{array}[/tex]
(2)
[tex]y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\y(t)=\left(\frac{75}{74} e^{-2 t} \cos 6 t+\frac{75}{148} e^{-2 t} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\y(t)=\frac{75}{74}\left(e^{-2 t}-1\right) \cos 6 t+\frac{25}{148}\left(3 e^{-2 t}+1\right) \sin 6 t \\\\|y(t)| \leq \frac{75}{74} e^{-2 t}-1|\cos 6 t|+\frac{25}{148}\left|3 e^{-2 t}+1\right||\sin 6 t| \\\\[/tex]
[tex]|y(t)| \leq \frac{75}{74}\left|e^{-2 t}-1\right|+\frac{25}{148}\left|3 e^{-2 t}+1\right| \\\\\lim _{t \rightarrow \infty} y(t) \leq \lim _{t \rightarrow \infty}\left\{\frac{75}{74}\left|e^{-2 t}-1\right|+\frac{25}{148}\left|3 e^{-2 t}+1\right|\right\} \\\\\lim _{t \rightarrow \infty} y(t)=\left\{\frac{75}{74}\left|\lim _{t \rightarrow \infty}\left(e^{-2 t}-1\right)\right|+\frac{25}{148}\left|\lim _{t \rightarrow \infty}\left(3 e^{-2 t}+1\right)\right|\right\} \\[/tex]
[tex]\lim _{t \rightarrow \infty} y(t)=\left\{\frac{75}{74}(-1)+\frac{25}{148}(1)\right\}=-\frac{75}{74}+\frac{25}{148}=-\frac{-150+25}{148}=-\frac{125}{148} \approx-0.844[/tex]