1. Assume that segments that appear to be tangent are tangent.
Find ML to the nearest tenth.
2. Assume that segments that appear to be tangent are tangent.
Find WY.
Answers
1. Applying the pythagroean theorem, ML = 6.4.
2. Applying the two tangents theorem, WY = 37.
What is the Two Tangents Theorem?The two tangents theorem states that two tangents drawn from a circle to meet at a point outside the circle are congruent.
Thus:
1. ΔJKL is a right triangle, find JL using the Pythagorean theorem:
JL = √(16² - 9.6²)
JL = 12.8
Therefore:
ML = 1/2(JL)
ML = 1/2(12.8) (radius of circle)
ML = 6.4.
2. Based on the two tangents theorem, we have:
43 - 2x = 12x + 1
-2x - 12x = -43 + 1
-14x = -42
x = 3
WY = 43 - 2x
Plug in the value of x
WY = 43 - 2(3)
WY = 37
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Related Questions
For a certain company, the cost for producing x items is 60x+300 and the revenue for selling x items is 100x−0.5x2.
The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!
Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)
Part b: Find two values of x that will create a profit of $50 .
Answers
The profit function of the company is the difference between the cost and the revenue functions of the company
The expression of the profit function is [tex]- 0.5x^2 + 40x - 300[/tex]The two values of x that creates a profit of $50 are x = 10 and x = 70How to set up the profit functionThe given parameters are:
C(x) = 60x + 300 --- the cost function
R(x) = 100x - 0.5x^2 ---- the revenue function
The profit function is calculated as:
P(x) = R(x) - C(x)
So, we have:
[tex]P(x) = 100x - 0.5x^2 - 60x - 300[/tex]
Rewrite as:
[tex]P(x) = - 0.5x^2 + 100x - 60x - 300[/tex]
[tex]P(x) = - 0.5x^2 + 40x - 300[/tex]
This means that the expression of the profit function is [tex]- 0.5x^2 + 40x - 300[/tex]
The two values of x that creates a profit of $50This means that:
P(x) = 50
So, we have:
[tex]- 0.5x^2 + 40x - 300 = 50[/tex]
Subtract 50 from both sides
[tex]- 0.5x^2 + 40x - 350 = 0[/tex]
Multiply through by -2
[tex]x^2 - 80x + 700 = 0[/tex]
Expand
[tex]x^2 - 70x - 10x + 700 = 0[/tex]
Factorize
[tex]x(x - 70) - 10(x - 70) = 0[/tex]
Factor out x - 70
[tex](x - 10)(x - 70) = 0[/tex]
Solve for x
x = 10 or x = 70
Hence, the two values of x that creates a profit of $50 are x = 10 and x = 70
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If O is an angle in standard position and its terminal side passes through the point
(8,-7), find the exact value of csc 0 in simplest radical form.
Answers
Step-by-step explanation:
Let first find the x and y xomponets.
X componets is 8 and the y componets is -7 so
[tex]r = \sqrt{ {x}^{2} + {y}^{2} } [/tex]
[tex]r = \sqrt{ 64 + 49} [/tex]
[tex]r = \sqrt{113} [/tex]
[tex] \csc(x) = \frac{r}{y} [/tex]
So
[tex] \csc(x) = - \frac{ \sqrt{113} }{ 7} [/tex]
4:20::8:x
What is x equal to?
Answers
May be May be
Hope it is correct
which one is the correct answer
Answers
Answer:
55
Step-by-step explanation:
In this figure, 52.9% of the area is painted yellow. How much of the area is painted yellow? 22.218 in² 25.921 in² 44.436 in² 48.139 in² A square with sides measuring 7 inches. A right triangle attached to one side of the square has a long leg of 12 inches.
Answers
Answer:
the answer is 48.139 in²
Step-by-step explanation:
I took the test.
48.139 in² of the figure area is painted yellow in color.
What is an area?An area is amount of space occupied by a two dimensional shape or object.
The area of the figure = Area of the square + Area of the triangle
Area of the figure = (7 in * 7 in) + (1/2) * (12 * 7) = 91 in²
Since 52.9% of the area is painted yellow, hence:
Area painted yellow = 52.9% of 91 = 48.139 in²
48.139 in² of the figure area is painted yellow in color.
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some number minus -15 is equal to the product of the number and 9
Answers
Answer:
x = 15/8
Step-by-step explanation:
Let x = unknown number
Given:
some number minus -15 is equal to the product of the number and 9
⇒ x - -15 = x · 9
⇒ x + 15 = 9x
⇒ 15 = 9x - x
⇒ 15 = 8x
⇒ x = 15/8
Answer:
15/8
Step-by-step explanation:
Let's assume that the number is 'n'. Provided that number 'n' minus -15 is equal to the product of the number 'n' and 9. Simply jot down the above statement in mathematical form:
[tex] \implies\:\sf{\red{n \: - \: ( - 15) \: = \: n \: \times \: 9}}[/tex]
Now, simply solve the above equation.
[tex]\implies\:\sf{n \: + \: 15 \: = \: 9n}[/tex]
Take the like terms on one sides.
[tex]\implies\:\sf{9n \: - \: n \: = \: 15}[/tex]
Do the rest calculations.
[tex]\implies\:\sf{8n \: = \: 15}[/tex]
[tex]\implies\:\sf{\red{n \: = \: \dfrac{15}{8}}}[/tex]
Hence, the required value of n is 15/8.
what digit number is in the hundred thousand place in 621,938
Answers
Answer:
6
Step-by-step explanation:
6 in hundred thousands place
Answer:
Six is the correct answer.
1a. Solve the differential equations
y" + 5y' + 6y = 0, y(0) = 1 and y'(0) = 2
Note that each equation has right hand side zero. So, you don’t have to use the Laplace transform. You just use the characteristic equaiton.
Answers
y'' + 5y' + 6y = 0
has characteristic equation
r² + 5r + 6 = (r + 2) (r + 3) = 0
with roots at r = -2 and r = -3, hence the differential equation's characteristic solution is
[tex]y(t) = C_1 e^{-2t} + C_2 e^{-3t}[/tex]
Given that y(0) = 1 and y'(0) = 2, we have
[tex]y(t) = C_1 e^{-2t} + C_2 e^{-3t} \implies 1 = C_1 + C_2[/tex]
[tex]y'(t) = -2C_1 e^{-2t} - 3C_2 e^{-3t} \implies 2 = -2C_1 - 3C_2[/tex]
and solving the resulting system of equations yields C₁ = 5 and C₂ = -4.
So the particular solution to the ODE is
[tex]\boxed{y(t) = 5 e^{-2t} - 4 e^{-3t}}[/tex]
Anna, Betty and Candy shared a box of sweets. Anna took 8 more than 1/3 of the number of sweets in the box. Betty took 18 more than half of the remaining number of sweets . If Candy took the last 6 sweets, how many sweets were there in the box at first?
Answers
Answer: 108
Step-by-step explanation: Let the total number of sweets be x
Therefore, Anna - (x/3)+8
After Anna, remaining amount is x - ((x/3)+8) = 2x/3 + 8
Betty took (2x/3 + 8)/2 + 18 = x/3 + 22
Remaining = x - ((x/3)+8) - (x/3 + 22) = x/3 -30
Candy took the rest which is 6 i.e.
x/3 - 30 = 6
x/3 = 36
x = 108
ellie has 4 liter of punch for the party.she needs to measure out servings in milliliters.how many of punch does ellie have?
Answers
Answer:
Ellie has 4000 milliliters of punch.
4liters=4000 milliliters
What is the expression for f(x) when we rewrite 36^x•6^x-2 as 6^f(x)
Answers
Answer:
X
Step-by-step explanation:
[tex]36 {}^{x} (6 {}^{x - 2} )[/tex]
[tex]36 {}^{x} ( \frac{6 {}^{x} }{6 {}^{2} } )[/tex]
[tex]36 {}^{x} ( {6}^{x} ) \frac{1}{6 {}^{2} } [/tex]
[tex]6 {}^{2} (6 {}^{x} )6 {}^{ - 2} [/tex]
[tex]6 {}^{x} [/tex]
F(x)=x.
Answer: f (x) = 3x-2
Step-by-step explanation:
Which is larger, 0.8 or 71/100?
Answers
Answer:
0.8
Step-by-step explanation:
Convert 71/100 into a decimal
.71
0.8 > .71
bre
RE
What is the value of arctan (-13);
MA
OA. 60°
OB. 90°
OC -60°
OD. 0°
O E. 45°
Answers
Answer:
The answer to this question is 60degree
A factor tree is shown for 1,255 what is the simplest form of sqaure root 1,225
Answers
Answer:
Simplest form is 35.
35*35=1225
maths please help u thingy
Answers
[tex]\begin{array}{cll} term&\stackrel{u_n+u_{n-1}+1}{value}\\ \cline{1-2} u_1&1\\ u_2&3\\ u_3&\stackrel{u_n}{3}+\stackrel{u_{n-1}}{1}+1\\ &5\\ u_4&\stackrel{u_n}{5}+\stackrel{u_{n-1}}{3}+1\\ &9\\ u_5&\stackrel{u_n}{9}+\stackrel{u_{n-1}}{5}+1\\ &15 \end{array}[/tex]
in recursive sequence notation, is another way of saying
"the next term will be the current one plus the one before it, plus one"
If an item cost 30 and it was on sale at 60 percent off
Answers
Answer:
12
Step-by-step explanation:
30*(100-60)/100
30*4/10
3*4
12
sale price =12 (answer) this means the cost of the item to you is 12$. you will pay 12$ for a item with original price of 30$ when discounted 60% off 30%
When f(x) is a differentiable function
satisfying [tex]\lim_{x \to \\\pi } \frac{f(x)}{x-\pi}[/tex]
Find [tex]\lim_{x \to \\\pi } \frac{sin(2f(x))}{x-\pi}[/tex]
Answers
Presumably, the first limit is some finite number
[tex]\displaystyle \lim_{x\to\pi} \frac{f(x)}{x-\pi} = c[/tex]
Since x - π clearly approaches 0 as x approaches π, we must also have f(x) approaching 0,
[tex]\displaystyle \lim_{x\to\pi} f(x) = 0[/tex]
Recall the double angle identity,
sin(2t) = 2 sin(t) cos(t)
and rewrite the limit as
[tex]\displaystyle \lim_{x\to\pi} \frac{\sin(2 f(x))}{x - \pi} = \lim_{x\to\pi} \frac{2 \sin(f(x)) \cos(f(x))}{x - \pi} = 2 \lim_{x\to\pi} \frac{\sin(f(x))}{f(x)} \times \frac{f(x) \cos(f(x))}{x - \pi}[/tex]
Recall that
[tex]\displaystyle \lim_{x\to0}\frac{\sin(x)}x=1[/tex]
which means
[tex]\displaystyle \lim_{x\to\pi}\frac{\sin(f(x))}{f(x)} = \lim_{f(x)\to0}\frac{\sin(f(x))}{f(x)} = 1[/tex]
and by continuity,
[tex]\displaystyle \lim_{x\to\pi} \cos(f(x)) = \cos\left(\lim_{x\to\pi} f(x)\right) = \cos(0) = 1[/tex]
Then
[tex]\displaystyle 2 \lim_{x\to\pi} \frac{\sin(f(x))}{f(x)} \times \frac{f(x) \cos(f(x))}{x - \pi} \\\\ = 2 \left(\lim_{x\to\pi}\frac{\sin(f(x))}{f(x)}\right) \left(\lim_{x\to\pi} \frac{f(x)}{x-\pi}\right) \left(\lim_{x\to\pi}\cos(f(x))\right) \\\\ = 2 \times 1 \times c \times 1 = \boxed{2c}[/tex]
Please help I will give brainliest and points, I cannot figure this out I also need the work please please please
Answers
Answer:
~Male Y/n here~ I think that your A will be 77 feet in distance and your B would be 25 feet above ground.
(Hope this helps!)
3 x − 7 y = − 17 determine slope
Answers
Help me pls!!!
3x-2(6-x)=7x+2(5+x)-6
Answers
[tex]3x-2(6-x)=7x+2(5+x)-6\\3x-12+2x=7x+10+2x-6\\5x-12=9x+4\\-4x = 16\\x = -4[/tex]
Hope that helps!
Answer:
x=-4
Step-by-step explanation:
when you are done, you can search this problem and figure out the 13 steps there are.
Calculate the product: 2 9 × 63 . A. 7 B. 14 C. 18 D. 45
Answers
Answer:
The answer isn't listed in your options, are you sure you didn't make any typos?
Step-by-step explanation:
29*63=1,827
Consider the polynomial equation x(x − 3)(x + 6) (x – 7) = 0. Which of the following are zeros of the
equation? Select all that apply.
-7
-6
-3
0
3
6
7
Answers
Answer:
0, 3, -6, 7
Step-by-step explanation:
x(x − 3)(x + 6) (x – 7) = 0
so x = 0
or x - 3 = 0, x = 3
or x + 6 = 0, x = -6
or x - 7 = 0, x = 7
Answer: 0, 3, -6, 7
what is 353% as a decimal??
Answers
Answer: Your answer is 3.53 as a Decimal.
Hope this helps!
Answer:
3.53
Step-by-step explanation:
If you have been wondering what is 353% in decimal form, or if you have been looking for how to change 353% to decimal, then you are definitively right here.
353%, 353 pct and 353 percent all mean 353 by the hundred. 353 percent as a decimal equals:
353% as a decimal = 3.53
353 percent as a decimal = 3.53
Lilly uses 9 flowers in each bouquet. She needs flowers for at most 18 bouquets. Determine how many flowers Lilly needs for the bouquets QUICKK HELLPPP
Answers
Answer:
hi Abdulaziz how are you how is school do you work hard
Lily needs at least 162 flowers for her 18 bouquets.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Lilly uses 9 flowers in each bouquet and she needs flowers for at most 18 bouquets.
Therefore, The number of flowers she needs can be obtained by multiplying the number of bouquets and the number of flowers in each bouquet which is,
= 9×18.
= 162 flowers.
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Lisa works in a store that sells t-ey . shirts to tourists. The t-shirts sell for $24 each, including tax. Last week Lisa sold 32 t-shirts. How much mondid Lisa collect by selling these t-shirts?
Answers
Answer:
768$
Step-by-step explanation:
I multiplied 24$ times 32.
these numbers form an addition and subtraction fact family for 6,7,13 here the choices 7+13=20 13+7=20 13-13=0 13-0=13 and 7+0=7 6+0=6 13-0=13 13-13=0 and 7+6=13 6+7=13 13-6=7 13-7=6 7+6=13 13=7+6 13-6=7 7=13-6
Answers
Answer:
7+6=13 6+7=13 13-6=7 13-7=6 7+6=13 13=7+6 13-6=7 7=13-6bStep-by-step explanation:
this involves any number that when subtracted or added it gives each other the values of the family
Example:-7 + 6 equals 13, 13 - 6 equals 7,
so you see how they relate,please mark me brainiest
^_^
Answer:
7+6=13 6+7=13 13-6=7 13-7=6 7+6=13 13=7+6 13-6=7 7=13-6b
Step-by-step explanation:
I studied. :)
Find the value of the major arc ABC when the angle measures 40 degrees
Answers
Answer:
Step-by-step explanation:
if we draw diameter through A and let it meet the circumference at D .
Let O be the center.
∠DAC=90-40=50°
∠DOC=2×50=100°
arc ABD=180°
arc ABC=180+100=280°
Pleaseplaeas help I will give hearts and 5 stars!
Answers
Answer: y=25x
Step-by-step explanation:
Solve for x in the equation x2-12x+36 = 90-
X = 6+3 V10
O x=6+27
12+3V22
O
X = 12+3 V10
X=
Answers
Answer:
5.4
Step-by-step explanation:
x2-12x+36 = 90
=> 2x - 12x + 36 = *90
=> 2x - 12x = 90 - 36
=> -10x = 54
=> (-10x)/-10 = (54)/-10
=> x = 5.4
Brandon was 6.5 pounds when he was born. In the next month his weight increased by 40%. How much did he weigh at the end of the month?
Answers
Answer:
i believe the answer is 9.1
Step-by-step explanation:
6.5 x 40% or in other words .4 is 2.6.
then you add 2.6 to 6.5 and that gives you 9.1