AB is tangent to \odot ⊙ O at A (not drawn to scale). Find the length of the radius r, to the nearest tenth.
Answers
Answer:
r = 15.2
Step-by-step explanation:
Where AB meets the circle creates a right angle. This is a right triangle problem involving missing sides. This means that we will use Pythagorean's theorem to find the length of the radius. Pythagorean's theorem applies this way:
[tex]10^2+r^2=(r+3)^2[/tex]
Foiling the right side gives us the equation:
[tex]100 + r^2=r^2+6r+9[/tex]
When we combine like terms, we find the squared terms cancel each other out, leaving us with
100 = 6r + 9 and
91 = 6r so
r = 15.2
Related Questions
A right rectangular prism has these dimensions: Length ? Fraction 1 and 1 over 2 units Width ? Fraction 1 over 2 unit Height ? Fraction 3 over 4 unit How many cubes of side length Fraction 1 over 4 unit are required to completely pack the prism without any gap or overlap? 36 45 51 60
Answers
The volume of the rectangular prism is length x width x height:
Volume = 1 1/2 x 1/2 x 3/4 = 9/16 cubic units.
The volume of cube is length^3 = 1/4^3 = 1/64
Divide the volume of the rectangular prism by the volume of the cube:
Number of cubes = 9/16 / 1/64 = 36
The answer is 36
True or false? Based only on the given information, it is guaranteed that AD= CD
Answers
Answer:
True
Step-by-step explanation:
Based on Angle-Angle-Side, you would have two congruent triangles and those two sides are equal/congruent.
It is true, from the given information only we can say that AD = CD.
What is Congruency?In geometry, two figures or objects are congruent if their shape and size are same.
What is AAS criterion of Congruency?If two angles and a side which does not come between these two angles is congruent with two angles and a side which does not come between these two of another triangle, then the triangles are said to be congruent by AAS criterion.
In the given question
∠ABD = ∠CBD ( Given)
∠BAD = ∠BCD (Right angles)
BD = DB (Common side of both triangles)
Δ ABD ≅ Δ CBD (AAS criterion)
The two triangles are congruent hence AD = CD.
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Ten cars were in a race.Two cars did not finish.How would you find the number of cars that did finish
Answers
Answer:
Step-by-step explanation:
10-2= the number of cars that finished
The blueprints for a new barn have a scale of 1/2 inch = 1 foot. A farmer wants to make sure she will have enough room for 12 new horse stalls to fit along one of the barn walls. Each stall has a width of five feet. If the blueprint of the barn is 20 inches by 30 inches, will there be enough room for the stalls?
Answers
Answer: yes
Step-by-step explanation: Wall would be 60 feet wide. 60 / 5 = 12.
Answer:
Yes
Step-by-step explanation:
Given :
1/2 in = 1 foot
re-written as : 1 in = 2 feet
THe blueprint is drawn to be 30 inches long
this is equivalent to 30 in x 2 feet/in = 60 feet long
With a minimum width of 5 feet per stall,
the number of stalls in 60 feet = 60 feet / 5 feet = 12 stalls
Hence there will be enough room for 12 stalls.
Which of the following parabolas opens up?
Answers
ANSWER
A. Directrix y=-5, focus; (-2,6)
EXPLANATION
In other to figure out the parabola that opens up we need to know the relation between the directrix and focus.The focus is always inside the parabola and the directrix is always outside.If the directrix is above the focus,the parabola opens downwards.If the directrix is below the focus, the parabola opens upwards.How do you determine whether the directrix is above or below.You just have to compare the y-value of the focus to the directrix because the orientation is parallel to the y-axisFor the first option, the directrix y=-5 is below the focus (-2,6).Since the focus must lie inside the parabola, this parabola must open up.For the second option, the directrix, y=-5 is above the focus (2,-6). This parabola opens downwards.For the third option, the directrix, y=5 is above the focus (-6,-2). This parabola opens downwards.For the second option, the directrix, y=5 is above the focus (6,2). This parabola opens downwards.What is the domain of y=sqrt x+5?
Answers
Answer:
interval notation: [-5,infinity)
or answer X=> -5
Step-by-step explanation:
For this case we must find the domain of the following function:
[tex]f (x) = \sqrt {x + 5}[/tex]
By definition, the domain of a function is given by all the values for which the function is defined.
The given function stops being defined when the argument of the root is negative. Thus, the domain is given by all values of "x" greater than or equal to -5.
Answer:
Domain: [tex]x\geq-5[/tex]
PLS HELP BRAINLIEST
Answers
Answer:
a) AB = 17 m
b) AC = 20.8 m
Step-by-step explanation:
Pythagorean theorem
a^2 + b^2 = c^2
a)
AB^2 = (26-11)^2 + 8^2
AB^2 = 15^2 + 8^2
AB^2 = 225 + 64
AB^2 = 289
AB = 17 m
b)
AC^2 = AB^2 + BC^2
AC^2 = 17^2 + 12^2
AC^2 =289 + 144
AC^2 = 433
AC = 20.8 m
. Evaluate –x + 3.9 for x = –7.2.
Answers
Given.
-x + 3.9
Plug in.
-7.2 + 3.9 = -3.3
Answer.
-3.3
Answer:
11.1
Step-by-step explanation:
−(−7.2)+3.9
=7.2+3.9
=11.1
The graph of which equation includes the points (0, 10) and (10, 11)?
y = 10x + 11
y = x + 10
y= 1/10x + 10
y = 1/10x + 11
Answers
Answer:
y=1/10x +10
Step-by-step explanation:
when we replace the x in this equation with numbers representing x in the points given, we are going to end up with the points that represents y in the question.
Answer:
C. [tex]y=\frac{x}{10} +10[/tex]
Step-by-step explanation:
Here we are given two points from which the line passes through . hence we use the two point form to evaluate the equation of line.
The two points are
(0,10) and (10,11)
the two point formula is
[tex]\frac{y-y1}{x-x1} = \frac{y2-y1}{x2-x1}[/tex]
Here x1=0, x2=10, y1=10, y2=11
Now we keep these values in the two point form formula given above
[tex]\frac{y-10}{x-0} = \frac{11-10}{10-0}\\\frac{y-10}{x} = \frac{1}{10}\\y-10=\frac{x}{10}\\y=\frac{x}{10}+10[/tex]
Hence our third option is correct.
Easy Points!
Solve for x:
2x + 5 = 9
Happy Summer
Answers
Answer:
x = 2
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS = Parenthesis, Exponents (& roots), Multiplication, Division, Addition, Subtraction,
and is the order in which you follow for order of operation questions.
First, subtract 5 from both sides.
2x + 5 (-5) = 9 (-5)
2x = 9 - 5
2x = 4
Isolate the x, Divide 2 from both sides:
(2x)/2 = (4)/2
x = 4/2
x = 2
x = 2 is your answer.
~
x=2
First thing you would do:
Subtract 5:
2x=4
Then, you would:
Divide by 4 by 2:
x=2
Triangle $ABC$ has side lengths $AB = 9$, $AC = 10$, and $BC = 17$. Let $X$ be the intersection of the angle bisector of $\angle A$ with side $\overline{BC}$, and let $Y$ be the foot of the perpendicular from $X$ to side $\overline{AC}$. Compute the length of $\overline{XY}$.
Answers
Answer:
[tex]\dfrac{72}{19}[/tex]
Step-by-step explanation:
Consider triangle ABC. Segment AX is angle A bisector. Its length can be calculated using formula
[tex]AX^2=\dfrac{AB\cdot AC}{(AB+AC)^2}\cdot ((AB+AC)^2-BC^2)[/tex]
Hence,
[tex]AX^2=\dfrac{9\cdot 10}{(9+10)^2}\cdot ((9+10)^2-17^2)=\dfrac{90}{361}\cdot (361-289)=\dfrac{90}{361}\cdot 72=\dfrac{6480}{361}[/tex]
By the angle bisector theorem,
[tex]\dfrac{AB}{AC}=\dfrac{BX}{XC}[/tex]
So,
[tex]\dfrac{9}{10}=\dfrac{BX}{17-BX}\Rightarrow 153-9BX=10BX\\ \\19BX=153\\ \\BX=\dfrac{153}{19}[/tex]
and
[tex]XC=17-\dfrac{153}{19}=\dfrac{170}{19}[/tex]
By the Pythagorean theorem for the right triangles AXY and CXY:
[tex]AX^2=AY^2+XY^2\\ \\XC^2=XY^2+CY^2[/tex]
Thus,
[tex]\dfrac{6480}{361}=XY^2+AY^2\\ \\\left(\dfrac{170}{19}\right)^2=XY^2+(10-AY)^2[/tex]
Subtract from the second equation the first one:
[tex]\dfrac{28900}{361}-\dfrac{6480}{361}=(10-AY)^2-AY^2\\ \\\dfrac{22420}{361}=100-20AY+AY^2-AY^2\\ \\\dfrac{1180}{19}=100-20AY\\ \\20AY=100-\dfrac{1180}{19}=\dfrac{1900-1180}{19}=\dfrac{720}{19}\\ \\AY=\dfrac{36}{19}[/tex]
Hence,
[tex]XY^2=\dfrac{6480}{361}-\left(\dfrac{36}{19}\right)^2=\dfrac{6480-1296}{361}=\dfrac{5184}{361}\\ \\XY=\dfrac{72}{19}[/tex]
The measure of angle θ is 7π/4. The measure of its reference angle is __°, and tan θ is __.
Answers
Answer:
Step-by-step explanation:
Even though I have been teaching calculus and precalc for several years now, my mind automatically wants to think in degrees as opposed to radians. So I converted the angle from radians to degrees to get 315. This angle lies in QIV. The reference angle is a 45 degree angle, since 360 - 315 = 45. This is a 45 degree angle, but if you consider direction, measuring clockwise gives you a negative angle. So it could be that the reference angle needs to be identified as -45 degrees. It depends upon what lesson you are dealing with. Regardless, because this is a 45-45-90 right triangle, both the legs measure the same length (because of the Isosceles Triangle Theorem), which is 1. Therefore, if the angle is 45 degrees, then the tangent of it is 1/1 = 1.
I don't understand how to do question c, d and f. Can someone please help me?
Answers
Answer:
Step-by-step explanation:
As with any equation involving fractions, you can multiply the equation by the least common denominator to eliminate fractions. Then solve in the usual way.
c) 1/a +b = c
1 +ab = ac . . . . multiply by a
1 = ac -ab . . . . subtract ab
1 = a(c -b) . . . . . factor out a
1/(c -b) = a . . . . divide by the coefficient of a
__
d) (a-b)/(b-a) = 1
a -b = b -a . . . . . multiply by b-a
2a = 2b . . . . . . . . add a+b
a = b . . . . . . . . . . divide by the coefficient of a
Please be aware that this makes the original equation become 0/0 = 1. This is why a=b is not an allowed condition for this equation. As written, it reduces to -1 = 1, which is false. One could say there is no solution.
__
f) bc +ac = ab . . . . . multiply by abc
bc = ab -ac . . . . . . subtract ac
bc = a(b -c) . . . . . . factor out a
bc/(b -c) = a . . . . . . divide by the coefficient of a
Twenty different statistics students are randomly selected. For each of them, their body temperature (degreesC) is measured and their head circumference (cm) is measured. If it is found that requals0, does that indicate that there is no association between these two variables? Choose the correct answer below. A. No, because if requals0, the variables are in a perfect linear relationship. B. No, because while there is no linear correlation, there may be a relationship that is not linear. C. No, because r does not measure the strength of the relationship, only its direction. D. Yes, because if requals0, the variables are completely unrelated.
Answers
The correlation coefficient 'r' equals 0 indicates that there is no linear relationship between two variables. However, there could be a non-linear relationship present that is not captured by 'r'. Therefore, one should also consider other statistical tests or data visualization methods to fully understand the relationship between variables.
Explanation:When a correlation coefficient, or 'r', equals 0, it conveys that there is no linear correlation between the two observed variables. However, this does not necessarily mean that the two variables are entirely unassociated. The correct answer to the student's question is B: No, because while there is no linear correlation, there may be a relationship that is not linear.
This means that in the context of the problem, just because 'r' equals 0 between student's body temperature and head circumference, it doesn't conclude there is no relationship between these two variables. There could be a non-linear or curve relationship present, which cannot be determined by the correlation coefficient.
Remember, the correlation coefficient 'r' only measures the strength and direction of a linear relationship between two variables. It doesn't help in determining non-linear relationships. Therefore, it's important to also consider other statistical tests or visual data assessment methods when analyzing associations between variables.
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Need help with math question
Answers
Answer:
B.
Step-by-step explanation:
The parabola opens to the right since the focus is to the right of the vertex. So the square part will definitely contain a y. By elimination the answers can't be A or C. The vertex is (2,3) so the answer is B.
Longer answer:
formula to use is (y-k)^2=4p(x-h) where the vertex is (h,k)
So (2,3) is our vertex so enter it in giving
(y-3)^2=4p(x-2)
p is 5 since 2 and 7 are 5 units apart
p is positive because again focus is right of vertex
the answer is
(y-3)^2=20(x-2)
Answer:
B
Step-by-step explanation:
Substitute a point in the equation:
(2,3)
(3 - 3)^2 = 20(2 - 2)
(3-3)^2 = 0
Which is True
You could also use y-y1=m(x-x1)
Ethan goes to a store an buys an item that costs x dollars. He has a coupon for 5% off, and then a 9% tax is added to the discounted price. Write an expression in terms of x that represents the total amount that Ethan paid at the register.
Answers
Final answer:
Ethan pays a total of 1.0355x dollars at the register for an item with an original price of x dollars, after applying a 5% discount and adding a 9% sales tax to the discounted price.
Explanation:
To calculate the total amount Ethan paid at the register, we need to take into account both the discount and the tax applied to the item's original price. First, we calculate the discounted price by subtracting the 5% off. Then, we add a 9% sales tax to that discounted price.
The original price is x dollars. The discount of 5% is 0.05x, so the discounted price is x - 0.05x, which simplifies to 0.95x. Next, we need to calculate the sales tax on the discounted price. The 9% tax on the discounted price is 0.09 * 0.95x, which is 0.0855x. Finally, to find the total amount paid, we add the sales tax to the discounted price:
Total Amount Paid = (0.95x) + (0.09 * 0.95x) = 0.95x + 0.0855x = 1.0355x
The measure of arc QR is _____
Answers
Answer:
132 degrees.
Step-by-step explanation:
SR and PQ are both 48 degrees. A circle is 360 degrees.
360-96 because 48+48 is 96, is 264. PS and QR are also the same so 264/2 is 132.
in a certain pentagon, the interior angles are a,b,c,d,e where a,b,c,d,e are integers strictly less than 180. ("Strictly less than 180" means they are "less than and not equal to" 180.) If the median of the interior angles is 61 and there is only one mode, then what are the degree measures of all five angles?
Answers
Answer:
least to greatest: {61, 61, 61, 178, 179}
Step-by-step explanation:
If the third-largest angle is 61°, the smallest three angles cannot be larger than 183°. Since the total of all angles must be 540°, and the total of the largest two cannot be greater than 179°×2 = 358°, the sum of the smallest three must be at least 540° -358° = 182°.
So, the possible sets of angles with the smallest 3 totaling 182° or 183° are (in degrees) ...
{60, 61, 61, 179, 179} . . . . two modes
(61, 61, 61, 178, 179} . . . . . one mode -- the set you're looking for
Answer:
61,61,61,178,179
Step-by-step explanation:
your welcome. :)
The point A (3, 4) is reflected over the line x = 2, and then is reflected over the line x = -4. What are the coordinates of A'?
(1, 2)
(9, 4)
(-9, 4)
(1, 4)
Answers
Answer:
(- 9, 4)
Step-by-step explanation:
A(3, 4) is 1 unit to the right of x = 2
Thus it's reflection will be 1 unit to the left of x = 2, that is
A(3, 4 ) → A'(1, 4) ← y- coordinate remains unchanged
--------------------------------------------------------------------
A'(1, 4 ) is 5 units to the right of x = - 4
Thus it's reflection will be 5 units to the left of x = - 4
A'(1, 4) → A''(- 9, 4 )
Under the 2 parallel reflections
A(3, 4) → A''(- 9, 4 )
Translate and simplify: the difference of -5 and -30
Answers
Answer:
they are the same . If u add (-5) + (-30) that will be equal to (-35)
Answer:
25
Step-by-step explanation:
1) -5-(-30)
2) -5+30
3) 25
Need help with this math question
Answers
Answer:
[tex]x =7\sqrt{3}[/tex]
Step-by-step explanation:
By definition, the tangent of a z-angle is defined as
[tex]tan(z) =\frac{opposite}{adjacent}[/tex]
For this case
[tex]opposite = 7[/tex]
[tex]adjacent = x[/tex]
[tex]z=30\°[/tex]
So
[tex]tan(30) =\frac{7}{x}[/tex]
[tex]x =\frac{7}{tan(30)}[/tex]
[tex]x =7\sqrt{3}[/tex]
Answer:
7√3 = x
Step-by-step explanation:
Arbitrarily choose to focus on the 30 degree angle. Then the side opposite this angle is 7 and the side adjacent to it is x.
tan 30 degrees = (opp side) / (adj side), or (1√3) = 7 / x.
Inverting this equation, we get √3 = x/7.
Multiplying both sides by 7 results in 7√3 = x
Which quadratic equation models the situation
correctly?
y = 27(x – 7)2 + 105
y = 27(x - 105)2 +7
y = 0.0018(x – 7)2 + 105
y = 0.0018(x - 105)2 + 7
Answers
Answer:
y = 0.0018(x -105)² +7
Step-by-step explanation:
The vertex of the function is at (x, y) = (105, 7), so the equation will be of the form ...
y = a(x -105)² +7
We can use x=0 to find the value of "a". At x=0, y=27, so ...
27 = a(0 -105)² +7
20 = 11025a
20/11025 = a ≈ 0.0018
So, the model is ...
y = 0.0018(x -105)² +7
Answer:
d
Step-by-step explanation:
find the exact value of sin 165° by using a sum or difference formula
Answers
Answer: (√2 - √6)/4
Step-by-step explanation:
I am going to use the sum formula: sin(A + B) = sin A cos B + cos A sin B
Let's say A = 135° and B = 30°
sin(135° + 30°) = sin(135°) * cos(30°) + cos (135°) * sin(30°)
= (√2)/2 * 1/2 + (-√2)/2 * (√3)/2
= (√2)/4 + (-√6)/4
= (√2 - √6)/4
Suppose you invest $100 a month in an annuity that
earns 4% APR compounded monthly. How much money
will you have in this account after 2 years?
A. $2400.18
B. $2518.59
C. $1004.48
D. $3908.26
Answers
Answer:
$2502.60
Step-by-step explanation:
The formula for the amount of an annuity due is ...
A = P(1 +r/n)((1 +r/n)^(nt) -1)/(r/n)
where P is the monthly payment (100), r is the annual interest rate (.04), n is the number of compoundings per year (12), and t is the number of years (2). Given these numbers, the formula evaluates to ...
A = $100(1.00333333)(1.00333333^24 -1)/0.00333333
= $100(301)(0.08314296)
= $2502.60
_____
This value is confirmed by a financial calculator. The given answer choices all appear to be incorrect. The closest one corresponds to an annual interest rate (APR) of 4.286%, not 4%.
. Which of the following is a rational expression?
1/x
3x-4
x^2+x
x/2
Answers
Answer:
1/x
Step-by-step explanation:
1/x is rational because the x is in the denominator of the fraction. x/2 could be rewritten as (1/2)x, which is linear.
Convert 50 kilogram to pounds. (The conversion factor from kilogram to pound is 2.2046.) A. 52.2 lb. B. 110.2 lb. C. 22.6 lb. D. 47.8 lb.
Answers
Answer: (B) = 110.2
50*2.2046 = 110.23
9. If the diagonal of a square is 12 centimeters, the area of the square is
A. 102 cm2.
B. 36 cm2.
C. 144 cm2.
D. 72 cm2.
Answers
Answer:
D. 72 cm²
Step-by-step explanation:
The area of a square is given by ;
Area= l² where l = length
Given that the diagonal is 12 cm, let assume length of the square to be l
Apply the Pythagorean relationship where a=b=l
l² + l² = 12²
2 l² = 144
l²= 144/2
l²= 72
l =√72 =8.485 cm
⇒length of the square= l= 8.485 cm
⇒Area of the square= l² = 8.485² = 72 cm²
Answer:
36 cm2.
Step-by-step explanation:
The area of square A is 324 cm2. Since the dimensions of square A are three times larger than the dimensions of square B, the scale factor is 3.
To find the area of square B, first square the scale factor, 3.
3 squired =9
Next, divide the area of square A by 9.
324÷ cm2 ÷ 9 =36 cm2
Please help me. I need help asap!
Answers
Answer:
Step-by-step explanation:
They want you to translate N^3 into another form that would still be correct.
log N^3 = 3 * log N is the answer that I think you want. Try it it.
Suppose N = 6
Then N^3 = 6*6*6 = 216
log 216 = 2.3345
Now try it the other way.
3*log(6) = 3*0.7782
3*log(6) = 2.3345
Same answer as before.
The parabola y = x² - 4 opens:
A.) up
B.) down
C.) right
D.) left
Answers
Answer:
Up
Step-by-step explanation:
Here the easy rules to remember the orientation of the parabolas are
a) If x is squared it opens up or down. And its coefficient of {[tex]x^{2}[tex] is negative it opens down.
b) If y is squared it opens side ways right or left. It its coefficient of [tex]y^{2}[/tex]
Hence in our equation of parabola
[tex]y = x^ 2-4[/tex]
x is squared and its coefficient is positive , hence it opens up towards positive y axis.
Hamadi and Aisha solve this problem in two different ways. Carlos paid a total of $64 to rent a car. The rental company charges a one-time fee of $20, with an additional charge of $0.50 per mile driven. How many miles did Carlos drive the rental car? Use the drop-down menus to complete the sentences below.
Answers
Final answer:
To determine how many miles Carlos drove, we subtract the one-time rental fee from the total cost and then divide by the per-mile charge, resulting in Carlos having driven 88 miles.
Explanation:
To find out how many miles Carlos drove the rental car, we need to use the information about the total cost and the cost structure provided by the rental company. The total cost includes a one-time fee and a charge per mile driven. We can set up an equation to represent this situation. Let m represent the number of miles driven.
The equation based on the given costs would be:
20 + 0.50m = 64
Now, solve for m:
m = 88
Carlos drove 88 miles with the rental car.