The general equation of a circle is written like [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the centre and r is the radius.
Solving the QuestionFirstly, we're given that the centre is (8,6).
Plug this into the general equation:
[tex](x-h)^2+(y-k)^2=r^2\\(x-8)^2+(y-6)^2=r^2[/tex]
We're given this other point on the circumference of the circle, (8,0), which is 6 units away from the center.
Therefore, the radius is 6 units. Plug this into the general equation too:
[tex](x-8)^2+(y-6)^2=r^2\\(x-8)^2+(y-6)^2=6^2\\(x-8)^2+(y-6)^2=36[/tex]
Answer[tex](x-8)^2+(y-6)^2=36[/tex]
Which expression is equivalent to (r^5/4
Answer:
2
Step-by-step explanation:
• Multiplying two numbers with same bases is the same as adding their powers:
∴ [tex](\frac{4^{\frac{5}{4} } \cdot 4^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]
⇒ [tex](\frac{4^{\frac{5}{4} } ^ + ^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]
⇒ [tex](\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]
• Dividing two numbers with same bases is the same as subtracting their powers:
∴ [tex](\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]
⇒ [tex](4^{{\frac{6}{4} - \frac{1}{2} }})^{\frac{1}{2} }[/tex]
⇒ [tex](4^{1})^{\frac{1}{2} }[/tex]
⇒ [tex]4^{\frac{1}{2}[/tex]
• Raising anything to the power of [tex]\frac{1}{2}[/tex] is the same as square-rooting it:
∴ [tex]4^{\frac{1}{2}[/tex]
⇒ [tex]\sqrt{4}[/tex]
⇒ 2
Please answer hurry!
By trigonometric functions we find that the measure of angle A is approximately 0.12π radians.
How to determine the missing angle in a right triangleIn this question we have a right triangle, of which the length of two sides are known (AB, BC). We can know the measure of angle A by trigonometric functions:
[tex]\tan A = \frac{BC}{AC}[/tex]
[tex]\tan A = \frac{2}{5}[/tex]
A ≈ 0.12π radians
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What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
x<3
Step-by-step explanation:
–2(5 – 4x) < 6x – 4
(–10 + 8x) < 6x – 4
8x –6x < –4 + 10
2x < 6
x < 3
In a certain card game, the probability that a player is dealt a particular hand is. Explain what this probability means. If you play this card game 100 times, will you be dealt this hand exactly times? why or why not?.
No, you will not be dealt this hand exactly 48 times. This can be obtained by understanding the concept of probability.
What does the probability mean?The probability means that out of 100 times nearly 48 times the player is dealt the particular hand.
No, you will not be dealt this hand exactly 48 times since 48 times is an approximate value out of 100 times.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: In a certain card game, the probability that a player is dealt a particular hand is 0.48. Explain what this probability means. If you play this card game 100 times, will you be dealt this hand exactly 48 times? Why or why not?
Wey wey wonders how much water it would take to fill her cup. she drops her pencil in her cup and notices that it only fits diagonally. the pencil is 17 centimeters long and the cup is 15 centimeters tall. how much water can the cup hold? use paper to help you with your thinking.
Answer:
240π cm³ (exact)
754 cm³ (approximate)
Step-by-step explanation:
I assume the shape of the cup is a cylinder. The height of the cylinder is 15 cm.
Think of a vertical rectangle that contains the vertical axes of the cylinder.
Two sides of the rectangle are diameters of the bases of the cylinder. The other two side are heights of the cylinder. The pencil is 17 cm long and is a diagonal of this rectangle. We can find the diameter of the base of the cylinder using the Pythagorean theorem.
In a rectangle that is 15 cm long, the diagonal measures 17 cm.
a² + b² = c²
15² + b² = 17²
b = 8
The diameter of the cup is 8 cm.
radius = 8 cm/2 = 4 cm
V = πr²h
V = π(4 cm)²(15 cm) = 240π cm³ (exact)
V = 754 cm³ (approximate)
A badminton net is tethered to the ground with a strand of rope that forms a 50 angle with the ground. What is the length of the rope, x? Write an equation and show work below. Round to the nearest tenth.
Answer:
5.4 ft to nearest tenth.
Step-by-step explanation:
We know the adjacent side of the right triangle and we need the hypotenuse so we use the cosine:
cos 50 = 3.5/x
x = 3.5 / cos 50
= 5.445 ft.
Find the equation of the line that
is perpendicular to y = 6x-2 and
contains the point (6, -2).
y =
= [2²] x + [ ]
Answer:
y = - [tex]\frac{1}{6}[/tex] x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 6x - 2 ← is in slope- intercept form
with slope m = 6
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{6}[/tex] , then
y = - [tex]\frac{1}{6}[/tex] x + c ← is the partial equation
to find c substitute (6, - 2 ) into the partial equation
- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1
y = - [tex]\frac{1}{6}[/tex] x - 1 ← equation of perpendicular line
A cruise line ship left Port A and traveled 90 miles due west and then 400 miles due north. At this point, the ship docked at Port B What is the shortest distance between Port A and Port B?
Answer:
410 Miles
Step-by-step explanation:
Please refer to the photo attached. (Apologies for the legitimately terrible drawing)
The Shortest Distance between any 2 points is the distance thats connects the 2 points directly.
In this case, we can use Pythgoras's Theorem to find AB which is the shortest distance between A and B.
By Pythagoras's Theorem,
[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ {ab}^{2} = {ac}^{2} + {cb}^{2} \\ {ab}^{2} = {90}^{2} + {400}^{2} \\ab = \sqrt{ {90}^{2} + {400}^{2} } \\ = 410 \: miles[/tex]
Which of the following shows 2x^3Y - 3x^2 + 7y^2x - 12y written in standard form? Answers in photo thank you
Answer:
[tex] \large{ \boxed{\tt{2 {x}^{3}y + 7 {y}^{2} x - 3 {x}^{2} - 12y}}}[/tex]
- All you gotta do is writing the polynomial in the descending order of the power of the variable.
---- HappY LearninG <3 -------
Someone please help meeeeeee
Answer:
a ≈ 16.5 cm , b ≈ 23.8 cm
Step-by-step explanation:
using the Law of Sines in Δ ABC
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]
we require to calculate ∠ C
∠ C = 180° - (42 + 75)° = 180° - 117° = 63°
Then to find a
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex] ( substitute values )
[tex]\frac{a}{sin42}[/tex] = [tex]\frac{22}{sin63}[/tex] ( cross- multiply )
a × sin63° = 22 × sin42° ( divide both sides by sin63° )
a = [tex]\frac{22sin42}{sin63}[/tex] ≈ 16.5 cm ( to the nearest tenth )
similarly to find b
[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex] ( substitute values )
[tex]\frac{b}{sin75}[/tex] = [tex]\frac{22}{sin63}[/tex] ( cross- multiply )
b × sin63° = 22 × sin75° ( divide both sides by sin63° )
b = [tex]\frac{22sin75}{sin63}[/tex] ≈ 23.8 cm ( to the nearest tenth )
Answer:
Step-by-step explanation:
Sine rule of Law of sine:[tex]\sf \boxed{\bf\dfrac{a}{Sin \ A}=\dfrac{b}{Sin \ B}=\dfrac{c}{Sin \ C}}[/tex]
Side 'a' faces ∠A.
Side 'b' faces ∠B.
Side 'c' faces ∠C.
We have to find ∠C using angle sum property of triangle.
∠C + 75 + 42 = 180
∠C +117 = 180
∠C = 180 - 117
∠C = 63°
[tex]\sf \dfrac{a}{Sin \ 42}= \dfrac{22}{Sin \ 63}\\\\ \dfrac{a}{0.67}=\dfrac{22}{0.89}\\\\[/tex]
[tex]\sf a = \dfrac{22}{0.89}*0.67\\\\ \boxed{a = 16.56 \ cm }[/tex]
[tex]\sf \dfrac{b}{Sin \ B} = \dfrac{c}{Sin \ C}\\\\ \dfrac{b}{Sin \ 75}=\dfrac{22}{Sin 63}\\\\ \dfrac{b}{0.97} =\dfrac{22}{0.89}\\\\[/tex]
[tex]\sf b = \dfrac{22}{0.89}*0.97\\\\ \boxed{b =23.98 \ cm }[/tex]
A triangle is given by A ( 3,2 ) B (-1,5) and C (0,-1) . What is the equation of the line through B parallel to AC ( give ans and how it works pls )
Answer:
Step-by-step explanation:
Solution :
hello :
note :
Use the point-slope formula.
y - y_1 = m(x - x_1) when : x_1= -1 y_1= 5
m= the slope is : (YC - YA)/(XC -XA)
(-1-2)/(0-3) = -3/-3 =1
( parallel to AC means same slope)
an equation in the point-slope form is : y -5 = 1(x+1)
y=x+6
A school cafeteria uses 10
8 bowls of chocolate pudding.
How many cups of milk are in each bowl of chocolate pudding?
cups
Using proportions, it is found that there are 5 cups of milk in each bowl of chocolate pudding.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The cafeteria used 10 quarts for 8 bowls, hence the number of quarts per bowl is:
10/8 = 1.25
Each quart has 4 cups, hence the number of cups is:
4 x 1.25 = 5 cups.
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Explain how to find the 41st term of the arithmetic sequence where a1 = 5 and a7 = 34.
The 41th term of the arithmetic sequence is 66.
What is arithmetic sequence in math's ?Arithmetic sequences are those that contain these patterns. The difference between successive terms in an arithmetic series is constant. Because the difference between consecutive words is always two, the sequence 3, 5, 7, and 9 is an example of arithmetic.
[tex]a_{n}=a_{1}+(n-1)d[/tex]
[tex]a_n[/tex] = the nᵗʰ term in the sequence.
[tex]a_1[/tex] = the first term in the sequence.
d = the common difference between terms.
According to the given information:Finding arithmetic sequence for the nth term:
aₙ = a₁ + (n-1)d
d = the common difference
a₇ = a₁ + (7-1)d
34 = 5 + 6d
29 = 6d
d = 29/6
Now ,
Finding the 41st term of the arithmetic sequence.
a₄₁ = a₁ + (n-1)d
= 5 + (41-1)d
= 5 + 40d
= 5 + 40(29/6)
= (198)* 1/3
= 66
The 41th term of the arithmetic sequence is 66.
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Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
2x - y = 7
2y = 4x - 14
Since there are same number of either side, hence the solution has infinite number of solution
System of equationsSystem of equations are equation that consist of two or more equations with unknown variables.
Given the equations
2x - y = 7
2y = 4x - 14
This can also be written as
2x - y = 7
y = 2x - 7
Substitute equation 2 into 1
2x - (2x - 7) = 7
2x-2x+7= 7
7 = 7
Since there are same number of either side, hence the solution has infinite number of solution
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A _____ is an interval estimate of an individual y value, given values of the independent variables. Group of answer choices prediction interval confidence interval interval estimation regression
A confidence interval is an interval estimate of an individual y value, given values of the independent variables.
According to statement
we have to find a interval which give an estimate of an individual y value, given values of the independent variables.
Confidence interval tells that more than just the possible range around the estimate. It also tells about how stable the estimate is. A stable estimate is one that would be close to the same value if the survey were repeated.
So, A confidence interval is an interval estimate of an individual y value, given values of the independent variables.
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The box-and-whisker plots show the points scored in each Super Bowl by the AFC and NFC. About how many points higher is the upper quartile for the NFC than the AFC?
The upper quartile for NFC is 3 points higher than that of AFC.
What is the difference in the upper quartiles?A box plot is used to study the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%
On the box, the third line on the box represents the upper quartile. 75% of the scores represents the upper quartile.
Upper quartile for AFC : 26
Upper quartile for NFC : 23
Difference = 26 - 23 = 3
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A group of scientists is conducting an experiment on the effects of media on children. they randomly select 100 children and randomly assign each child to one of four treatment groups. each treatment group has a specific amount of screen time during a one-week time frame. the first group has no screen time, the second group has two hours of screen time, the third group has four hours of screen time, and the fourth group has six hours of screen time. after the first week, the scientists conduct the same experiment, with the same subject groups, for three more weeks so that each group experiences each of the four treatments. which statements about this study are true?
The statements that are true about this study are
This study uses random samplingThis study uses a control groupThis study uses a repeated measures designThis is further explained below.
What is an experiment?Generally, a scientific technique is used to create a discovery, test a theory or show an established truth.
In conclusion, The following are accurate claims concerning this study:
Random sampling is used in this investigation. In this investigation, a control group is used. Repeated measurements are employed in this investigation.
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A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles.
Find the probability of tossing a head and drawing a red marble. Explain your reasoning.
Using it's concept, there is a 0.1667 = 16.67% probability of tossing a head and drawing a red marble.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
For the coin, one out of two outcomes are heads.For the marble, two out of six marbles are red.Hence the probability of tossing a head and drawing a red marble is:
[tex]\frac{1}{2} \times \frac{2}{6} = \frac{1}{6} = 0.1667[/tex]
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15. Juan has a fair six-sided die, if Juan rolls the die
twice in a row, what is the probability that the die
will show a 3 both times?
Answer:
1/36
Step-by-step explanation:
The probability for showing a three the first time is 1/6, and then again is another 1/6, multiply and you get 1/36
What’s 2 + 2 + 5 + 69 + 89. This will definitely help me out.
Answer:
167
Hope this helps you out
Answer:
167
Step-by-step explanation:
Break it into steps.
2+2+5 = 9
69 + 9 = 78
78 + 89 = 167
Hope this helps.
Which ordered pair is a solution to the system of linear equations? 2x 3y= 6 –3x 5y = 10
The given system of equations has the solution, x = 0, and y = 2, giving the ordered pair (0, 2). Hence, the first option is the right choice.
In the question, we are asked for the ordered pair, which is the solution to the system of equations:
2x + 3y= 6 ... (i)
–3x + 5y = 10 ... (ii).
To solve for the solution to the system of equations, we use the elimination method.
We multiply (i) by 3, and (ii) by 2, and then add the resultant equations to eliminate x as follows:
6x + 9y = 18 {(i) * 3}
-6x + 10y = 20 {(ii) * 2}
_____________
19y = 38,
or, y = 38/19 = 2.
Substituting, y = 2, in (i), we get:
2x + 3y = 6,
or, 2x + 3(2) = 6,
or, 2x + 6 = 6,
or, 2x = 6 - 6 = 0,
or, x = 0/2 = 0.
Thus, the given system of equations has the solution, x = 0, and y = 2, giving the ordered pair (0, 2). Hence, the first option is the right choice.
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The complete question is:
"Which ordered pair is a solution to the system of linear equations?
2x + 3y= 6
–3x + 5y = 10
(0,2)
(2,0)
(3,2)
(2,3)"
Determine the slope of the line
Answer:1+1
Step-by-step explanation:
suppose cos(A) = 4/5. use the trig identity sin^2(A)+cos^2(A)=1 to find sin(A) in quadrant IV. round to the ten-thousandth.
a. -0.3954
b. -0.6000
c. 0.6485
d. 0.4500
In quadrant IV, [tex]\sin(A)[/tex] is negative. So
[tex]\sin^2(A) + \cos^2(A) = 1 \implies \sin(A) = -\sqrt{1-\cos^2(A)} = -\dfrac35 = \boxed{-0.6000}[/tex]
The table represents a function.
X f(x)
-4 -2
-1 5
3 4
5 -8
What is f(5)?
-8
-1
1
8
Answer: -8
Step-by-step explanation:
When x = 5, f(x) = -8.
The value of the function f(5) = -8.
We have,
The concept used to find the value of f(5) is function evaluation.
In this case, we are given a function represented by a table with x and f(x) values.
To evaluate the function at a specific value, such as f(5), we look for the corresponding x-value in the table and determine the corresponding f(x) value.
In this example, we found that when x = 5, f(x) is -8 by looking at the table provided.
To find the value of f(5), we need to look at the table and find the corresponding value of the function when x = 5.
From the given table, when x = 5, f(x) is -8.
Therefore,
The value of the function f(5) = -8.
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PLEASE HELP IM SO STUCK
Answer:
-4
Step-by-step explanation:
Slope = y/x
1. y=12 x=-3
12/-3=-4
2. y=8, x=-2
8/-2 = -4
3. y=4, x=-1
4/-1 = -4
4. 0/0 = 0
5. y=-4, x=1
-4/1 = -4
Hope it helps I had this question last year on Acellus.
Consider rolling a fair die thrice and tossing a fair coin sixteen times. Assume that all the tosses and rolls are independent. The chance that the total number of heads in all the coin tosses equals 12 is (
The probability that the total number of heads in all the coin tosses equals 12 is 0.0273.
Given a fair dice and tossing a fair coin sixteen times.
We have to find the probability that the total number of heads in all the coin tosses equals 12.
The probability lies between 0 and 1.
Probabiltiy of coming head when the coin is tossed 1 time is 0.5 and probability of coming tails is also 0.5.
Let X shows the sum of heads while tossing.
P(X=12)=?
We can find the probability using binomial theorem.
=[tex]16C_{12} (0.5)^{12} (0.5)^{2}[/tex]
We have to toss sixteen times and out of 16 times we need head 12 times.
=16!/12!4!*0.00024*0.0625
=1820*0.000015
=0.0273
Hence the probability that the total number of heads in all the coin tosses equals 12 is 0.0273.
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For what value of mc009-1 is the function one-to-one?
(1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c)
2
5
11
13
Using the concept of an one-to-one function, it will be one-to-one for c = 13.
What is an one-to-one function?A function is said to be one-to-one if each output is mapped to only one input.
In this problem, outputs 2, 5 and 11 have already been matched to inputs 1, 3 and 5, respectively, hence the output for input 6 has to be c = 13 for a one-to-one function.
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Work out the area of the triangle.
?m2
The area of the triangle is 557. 7cm²
Area of a triangle
In order to determine the area of a triangle, we have to know the size of the base and the size of the height
The formula for finding the area of a triangle is given as = half the base multiplied by the height
In mathematical form, it is written as;
Area = 1/ 2 × base × height
From the figure given, we have their lengths to be'
base = 57. 2 m
height = 19. 5 m
Let's substitute the values
Area = 1/ 2 × 57. 2 × 19. 5
Area = 1/ 2 × 1115. 4
Find the ratio
Area = 557. 7 m²
The area of the triangle is 557. 7cm²
Hence, the area of the triangle is 557. 7cm²
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how many positive odd factors of 48 are greater than 2 and less than 10
Answer:
Just 1 positive, odd factor
Step-by-step explanation:
48 has many factors. But not many odd factors. Only 3 is odd and bigger than 2 and less than 10.
So, just one odd, positive factor.
The image is listed below. Any help would be appreciated!
Check the picture below.
part A
since the base of the triangular base is 16, and the altitude "h" splits the base in two equal halves, half that is just 8, so we're looking at a right triangle with a hypotenuse of 17 and a side of 8, thus
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{17}\\ a=\stackrel{adjacent}{8}\\ b=\stackrel{opposite}{h}\\ \end{cases} \\\\\\ \sqrt{17^2-8^2}=h\implies \sqrt{225}=h\implies \boxed{15=h}[/tex]
part B
well, the prism is simply two triangles and 3 rectangles, le's simply add their areas.
[tex]\stackrel{two~triangles}{2\left[ \cfrac{1}{2}(\stackrel{base}{16})(\stackrel{height}{15}) \right]}~~ + ~~\stackrel{two~rectangles}{2(20)(17)}~~ + ~~\stackrel{one~rectangle}{(20)(16)} \\\\\\ 240~~ + ~~680~~ + ~~320\implies \text{\LARGE 1240}[/tex]